Hummer, Merritt-senior thesis final April 2010.pdf - CASTLE Lab ...
Hummer, Merritt-senior thesis final April 2010.pdf - CASTLE Lab ...
Hummer, Merritt-senior thesis final April 2010.pdf - CASTLE Lab ...
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Greening the Grid:<br />
Optimal Tax Policy for<br />
Wind and Solar Technology<br />
<strong>Merritt</strong> S. <strong>Hummer</strong><br />
<strong>April</strong> 2010<br />
Advisor: Professor Warren Powell<br />
Submitted in partial fulfillment<br />
of the requirements for the degree of<br />
Bachelor of Science in Engineering<br />
Department of Operations Research and Financial Engineering<br />
Princeton University
I hereby declare that I am the sole author of this <strong>thesis</strong>.<br />
I authorize Princeton University to lend this <strong>thesis</strong> to other institutions or<br />
individuals for the purpose of scholarly research.<br />
________________________________________<br />
<strong>Merritt</strong> <strong>Hummer</strong><br />
I further authorize Princeton University to reproduce this <strong>thesis</strong> by photocopying or<br />
by other means, in total or in part, at the request of other institutions or individuals<br />
for the purpose of scholarly research.<br />
________________________________________<br />
<strong>Merritt</strong> <strong>Hummer</strong><br />
ii
Abstract<br />
Wind and solar energy provided less than 1% of the United States total<br />
energy supply in 2008. Yet the nascent renewable energy industry is gaining<br />
momentum, and fast: the U.S. leapfrogged Japan to become the third largest<br />
photovoltaic market in the world after the country’s installed solar photovoltaic<br />
capacity soared 36% in 2009 alone [79]. The U.S. retained its top spot as the world’s<br />
largest wind energy producer, increasing its installed wind power capacity by 39%<br />
in 2009 [78].<br />
Renewable energy capacity is poised to grow dramatically in the coming<br />
decades with the advent of technological improvements, government incentives,<br />
and the broader environmentalist movement. The Department of Energy set a goal<br />
to supply 25% of the nation’s electricity from wind energy by 2030. While it has not<br />
yet published a formal goal for solar power, the DOE has signaled its intentions by<br />
earmarking substantial funding for further research and development of solar<br />
technology.<br />
This <strong>thesis</strong> examines how the federal tax policy can be designed in a way that<br />
fosters the growth of wind and solar contributions to the electricity supply.<br />
Specifically, the <strong>thesis</strong> seeks to quantify and optimize the economic impact of two<br />
variables: a carbon tax and a tax credit for renewable energy installations in the<br />
residential sector. The model will project the cumulative cost or benefit to society of<br />
policy proposals—both real and hypothetical—in a single period and over time.<br />
iii
Acknowledgements<br />
I would like to thank my advisor, Professor Warren Powell, for giving me the<br />
freedom to explore this subject. While traveling through a labyrinth of potential<br />
<strong>thesis</strong> topics in the fall semester, Professor Powell never ceased to spark my interest<br />
by suggesting a new turn. Indeed, this <strong>thesis</strong> would not have been possible without<br />
his guiding hand and endless stream of new ideas. I am also indebted to Professor<br />
Hugo Simao, who helped to launch me into the land of <strong>senior</strong> theses.<br />
Thank you also to my friends and family for their support in this and all<br />
endeavors. To my parents, thank you for all the feedback you gave me along the<br />
way. Special thanks to my ORFE classmates, many of whom I have gotten to know<br />
well over the last four years. You comprise a dynamic, talented, and eclectic group<br />
of which I am proud to be a member! In particular, thank you, Daphne, Phoebe,<br />
Jaimeson, and Austin, for supplying a generous dose of levity when needed.<br />
Finally, thank you to Princeton University, and to the many people I do not<br />
have room to name here, for providing me with much more than a person could<br />
reasonably expect.<br />
iv
The habit of expression leads to the search for something to express.<br />
-‐ Henry Adams<br />
v
Table of Contents<br />
Abstract ..................................................................................................................... iii<br />
Acknowledgements.....................................................................................................iv<br />
1. Introduction to the Energy Problem...................................................................... 1<br />
1.1 The Current Renewable Energy Profile of the United States......................................................6<br />
1.2 Tax Subsidies for Renewable Energy ....................................................................................................8<br />
1.2.1 Residential Renewable Energy Tax Credit.......................................................................................9<br />
1.2.2 Residential Energy Efficiency Tax Credit .........................................................................................9<br />
1.2.3 State-wide Renewable Tax Credits................................................................................................... 10<br />
1.3 The Cost of Carbon ..................................................................................................................................... 10<br />
1.3.1 The Social Cost of Carbon..................................................................................................................... 10<br />
1.3.2 The Carbon Tax ........................................................................................................................................ 11<br />
1.4 Overview of the Thesis ............................................................................................................................. 13<br />
2. Methodology of Cost Comparison....................................................................... 14<br />
2.1 Foundations for this Approach ............................................................................................................. 15<br />
2.2 Factors Affecting Retail Electricity Prices in the United States............................................... 18<br />
2.3 Solar Photovoltaics..................................................................................................................................... 19<br />
2.3.1 Assumptions in Solar Calculations................................................................................................... 19<br />
2.3.2 Solar Energy Potential in the United States................................................................................. 21<br />
2.3.3 Peak Sun Hours and PV Modules ...................................................................................................... 23<br />
2.3.4 Installation and Maintenance Costs................................................................................................ 25<br />
2.3.5 Electricity Production of the PV Module........................................................................................ 28<br />
2.3.6 Overall Price of Solar Electricity in this Model ........................................................................... 29<br />
2.3.7 Government Incentives.......................................................................................................................... 30<br />
2.4 Wind Energy.................................................................................................................................................. 31<br />
2.4.1 Assumptions in Wind Calculations................................................................................................... 31<br />
2.4.2 Wind Energy Potential in the United States ................................................................................ 32<br />
2.4.3 Modeling Wind Energy using the Weibull Distribution.......................................................... 34<br />
2.4.4 Electricity Production of the Wind Turbine................................................................................. 36<br />
2.4.5 Installation and Maintenance Costs................................................................................................ 41<br />
2.4.6 Overall Price of Wind Electricity in this Model........................................................................... 43<br />
2.4.7 Government Incentives.......................................................................................................................... 44<br />
2.5 Retail Electricity .......................................................................................................................................... 45<br />
2.5.1 Regional Cost Discrepancies ............................................................................................................... 45<br />
2.6 Price Comparison of Electricity Sources........................................................................................... 47<br />
3. Applying Government Forces to the Electricity Market ....................................... 49<br />
3.1 The Quantitative Model............................................................................................................................ 51<br />
3.1.1 Decision Variables................................................................................................................................... 51<br />
3.1.2 Market Response...................................................................................................................................... 52<br />
3.1.3 The Cost Function and Constraints.................................................................................................. 53<br />
3.1.4 Incorporating Variability in Solar Costs........................................................................................ 54<br />
3.2 The Impact of Government Incentives on Electricity Allocation............................................ 62<br />
3.2.1 Impact of the Carbon Tax on Allocation........................................................................................ 62<br />
vi
3.2.2 Impact of the Renewable Tax Credit on Allocation .................................................................. 64<br />
3.3 The Impact of Government Incentives on Electricity Prices.................................................... 67<br />
3.3.1 Background on the Electricity Price-Carbon Tax Relationship........................................... 67<br />
3.3.2 Improvement upon Linearity in the Electricity-Carbon Tax Relationship ..................... 68<br />
3.4 Laying the Groundwork for Policy Optimization .......................................................................... 72<br />
4. Optimizing Environmental Tax Policy.................................................................. 74<br />
4.1 Structure of the Cost-‐Benefit Analysis in One Time Period...................................................... 75<br />
4.1.1 Government Net Revenue..................................................................................................................... 76<br />
4.1.2 Consumer Net Revenue.......................................................................................................................... 78<br />
4.1.3 Net Social Benefit..................................................................................................................................... 82<br />
4.1.4 Summary Table......................................................................................................................................... 82<br />
4.2 Calculating the Social Cost of Carbon ................................................................................................. 83<br />
4.3 Modeling Consumer Behavior ............................................................................................................... 85<br />
4.3.1 Inducement to Change Threshold..................................................................................................... 85<br />
4.3.2 Renewable Adoption Rate, or Switchover Rate.......................................................................... 88<br />
4.4 Declining Costs of Renewable Technology Over Time................................................................ 93<br />
4.4.1 Solar Photovoltaic Cost Trends.......................................................................................................... 93<br />
4.4.2 Wind Turbine Cost Trends................................................................................................................... 95<br />
5. Results of the Mathematical Model.................................................................... 97<br />
5.1 Net Savings to Society for One Time Period.................................................................................... 98<br />
5.1.1 Net Savings with Lockstep Technology Improvement............................................................. 98<br />
5.1.2 Optimal Policies in the One Period Model...................................................................................104<br />
5.1.3 Delinking Wind and Solar Technology Improvement Variables.......................................107<br />
5.2 Net Savings to Society Over Time ......................................................................................................111<br />
5.2.1 Net Cost to Society with Variable Rates of Technology Improvement ...........................111<br />
5.2.2 Optimal Policies in the Time Lapse Model..................................................................................115<br />
6. Summary and Conclusion ..................................................................................117<br />
6.1 Summary of the Thesis ...........................................................................................................................117<br />
6.2 Limitations of this Model.......................................................................................................................119<br />
6.3 Areas for Further Investigation ..........................................................................................................121<br />
6.4 Final Thoughts............................................................................................................................................122<br />
Appendix..................................................................................................................123<br />
References ...............................................................................................................134<br />
vii
For my parents
1. Introduction to the Energy Problem<br />
Ever since the Industrial Revolution took hold around the turn of the<br />
nineteenth century, progress has implied pollution: societal<br />
advancement and urban development have gone hand in hand with environmental<br />
damage, arguably the greatest externality of modernization. In the decades<br />
following industrialization, the atmospheric concentration of carbon dioxide, the<br />
most important greenhouse gas, rose 36% [28]. Almost the entire increase is due to<br />
human activities, primarily deforestation and the burning of fossil fuels [29].<br />
The global community is at a crossroads in human history. With the long-‐<br />
term well-‐being of the environment teetering on a precipice, the next phase of<br />
progress must correct the errors of the past. Forthcoming innovation must steer<br />
civilization away from the recklessness of former generations and toward<br />
sustainability and energy efficiency. The most important challenge of the twenty-‐
Introduction to the Energy Problem<br />
first century will be solving the energy problem: how can the global community<br />
sustain its rate of growth without causing a gradual death of the natural world?<br />
Moreover, as demand for the earth’s natural resources increases in response<br />
to growing populations and economies worldwide, the rate at which resources are<br />
replaced cannot keep up with the rate at which they are depleted. In other words, if<br />
developed and developing countries do not choose to alter their course out of<br />
concern for the environment, they will eventually be forced to change due to the<br />
scarcity of nonrenewable resources like petroleum, natural gas, and coal.<br />
Besides adverse environmental effects and scarce supply of fuels, there are<br />
also geopolitical forces at play to motivate the U.S. to reevaluate its current energy<br />
portfolio. Energy importers around the world, the U.S. included, are subjected to<br />
energy price volatility as a result of precarious political situations in oil exporting<br />
countries. Political instability even in countries considered “marginal oil suppliers”<br />
can cause major price spikes [37]. In October 2007, Turkey threatened to invade<br />
northern Iraq, and within two weeks the price of oil jumped $7 to $94.53 per barrel,<br />
despite the fact that Iraq<br />
produces less than 4% of the<br />
world’s oil supply per day [37].<br />
The political circumstances in<br />
Saudi Arabia, Russia, and the<br />
United Arab Emirates—three of<br />
the top oil exporters globally—<br />
are hardly more predictable.<br />
Table 1. Major Oil Exporting Nations [39]<br />
Top World Oil Net Exporters, 2008<br />
(thousand barrels per day)<br />
Rank Country Exports<br />
1 Saudi Arabia 8,406<br />
2 Russia 6,874<br />
3 United Arab Emirates 2,521<br />
4 Iran 2,433<br />
5 Kuwait 2,390<br />
6 Norway 2,246<br />
7 Angola 1,948<br />
8 Venezuela 1,893<br />
9 Algeria 1,888<br />
10 Nigeria 1,883<br />
2
Introduction to the Energy Problem<br />
Clearly, the fragile political equilibria in oil supplying nations are inextricably tied to<br />
economic interests of importing nations.<br />
Fluctuating oil prices, an uneasy dependence on other nations, and<br />
environmental concerns have prompted the U.S. Department of Energy (DOE) to<br />
explore alternatives to its current energy mix. Part of the DOE’s multi-‐pronged<br />
strategy is to encourage citizens to transition to energy sources broadly defined as<br />
“renewable,” which applies to hydropower, geothermal, biomass, wind, and solar<br />
power. To that end, the Office of Energy Efficiency and Renewable Energy (EERE) is<br />
charged with leading federal research and development in energy efficiency and<br />
pursuing high-‐risk, high-‐value renewable energy projects that would not be carried<br />
out as aggressively by the private sector on its own [38].<br />
Still, there is much progress to be made before the U.S. can reconcile its<br />
“addiction” to fossil fuels with a changing global landscape. Currently, fossil fuels<br />
provide the vast majority of energy consumed in the United States [23]. In 2009, the<br />
United States, second only to China, emitted 5.7 billion tons of carbon dioxide—a<br />
figure that is projected to grow by 0.3% each year through 2030 [30] [31]. All forms<br />
of renewable energy only supplied 7% of U.S. energy in 2008 despite attracting<br />
widespread attention from politicians, scholars, and the press. Solar and wind<br />
energy represented a mere 1% and 7% of that category, respectively, or less than<br />
1% of total U.S. energy supply together [4].<br />
Despite the lackluster numbers in the renewable sector, the DOE has set<br />
ambitious goals: the “20-‐in-‐10” plan, announced by President George W. Bush in the<br />
2007 State of the Union address, seeks a 20% reduction in U.S. gasoline<br />
3
Introduction to the Energy Problem<br />
consumption by 2017. “20-‐in-‐10” is complemented by the “20% Wind Energy by<br />
2030” goal, which aims for a major increase in wind’s contribution to the U.S.<br />
electricity supply [40] [4]. Wind-‐generated electricity has gained traction since the<br />
formal 20% goal was published in an exhaustive July 2008 report.<br />
Renewable energy skeptics often point to the cost of solar and wind power as<br />
the biggest hindrance to the adoption of renewable technology. Indeed, experts<br />
generally agree that it is highly unlikely that the nation will be able to meet the<br />
DOE’s goals without some form of government intervention. One of the conclusions<br />
of Aghion, Hemous, and Veugelers’s [41] policy analysis is that even though the<br />
private market for green technology is ready to take off, “in the absence of the right<br />
push from government this will be difficult, if not impossible” [41]. Put another<br />
way, “governments must initially redirect market forces towards cleaner energy<br />
before market forces can take over” [41]. Ultimately, public intervention will be as<br />
critical as private initiative to the success of renewable energy.<br />
To accelerate the shift from fossil fuels to renewable energy, renewable<br />
technology must become cost-‐competitive with traditional fuels. There are three<br />
main ways in which the government can play a role in accomplishing this:<br />
• Providing subsidies or tax credits for renewable energy installations, making<br />
such investments more attractive to consumers.<br />
• Imposing a carbon tax on emissions of CO2, thereby increasing the cost of<br />
coal, petroleum, and natural gas. Alternatively, the government could set a<br />
cost on carbon via a cap-‐and-‐trade system whereby firms are allowed to buy<br />
and sell emissions credits in the marketplace; this “tax-‐free” model of<br />
4
Introduction to the Energy Problem<br />
distributing tradable pollution rights has become politically popular,<br />
especially after its documented success in reducing other pollutants, namely<br />
sulfur dioxide and nitrous oxide, in the United States [42].<br />
• Contributing financial and human capital toward the research, development,<br />
and deployment of renewable energy technologies. The technology will<br />
become cheaper and more accessible as it improves.<br />
By utilizing these and other policies to induce a change in consumer behavior,<br />
governments in the United States and abroad will have a chance to meet clean<br />
energy targets of their choosing.<br />
As sustainable energy becomes more and more relevant in today’s world, the<br />
importance of developed nations recalibrating their energy portfolios cannot be<br />
understated. The world is in their hands. Notwithstanding the obvious moral<br />
reasons why developed countries should lead the green energy movement, doing so<br />
is also to their benefit; as President Obama put it in his State of the Union address on<br />
January 27, 2010, “The nation that leads the clean energy economy will be the<br />
nation that leads the global economy” [21]. As if to quell an unsettling fear to many<br />
Americans, he added, “And America must be that nation.” Already, the race has<br />
begun.<br />
5
1.1 The Current Renewable Energy Profile of the United States<br />
Introduction to the Energy Problem<br />
Not to anyone’s surprise, the U.S. is still heavily dependent upon fossil fuels<br />
to run its daily operations. The most recent data available shows that 84% of U.S.<br />
energy is supplied by fossil fuels. That number has remained steady in recent<br />
decades, but the Energy Information Administration projected that the share of<br />
fossil fuels in total energy consumption will drop to 78% by 2035 [45]. According to<br />
Rep. Henry A. Waxman (D), co-‐author of the American Clean Energy and Security<br />
Act of 2009 1 , “Our goal is to strengthen our economy by making America the world<br />
leader in new clean-‐energy and energy-‐efficiency technologies” [15].<br />
As illustrated in Figure 1, renewable energy only represents a sliver of the<br />
energy supply at this point. Biomass power, or “power obtained from energy in<br />
plants and plant-‐derived materials,” supplied the majority of energy from the<br />
renewable sector in<br />
2008 [43]. Biomass<br />
materials include<br />
food crops, grassy<br />
plants, wood,<br />
residues from<br />
agriculture or<br />
forestry, alcohol<br />
Figure 1. The Role of Renewable Energy in the<br />
Nation's Energy Supply, 2008 [26]<br />
fuels, and municipal and industrial wastes [43]. One of the chief advantages of<br />
biomass power is its versatility: biomass can be used for direct heating, generating<br />
1 This bill has not yet been passed the Senate. It passed the house on June 26, 2009 [94].<br />
6
Introduction to the Energy Problem<br />
electricity, or meeting transportation needs, in which case it is converted into liquid<br />
fuel [43]. It also provides an important service in waste management [43].<br />
Hydropower, the other major component of the renewable sector in 2008,<br />
harnesses the energy in moving water. While there are many forms of hydropower,<br />
hydroelectric dams are the most common, largely because hydroelectricity can be<br />
Figure 2. Top Hydropower Producing States, 2007 [53]<br />
far less expensive than fossil<br />
fuel-‐generated electricity in<br />
areas well suited to building<br />
dams. Six percent of U.S.<br />
electricity was supplied by<br />
hydroelectricity in 2008; that<br />
number will likely rise in the<br />
future as the country builds<br />
out its hydroelectric capacity. Major hydroelectric dams in the United States are<br />
located in the Northwest, the Tennessee Valley, and on the Colorado River [43].<br />
Approximately 31% of total U.S. hydropower is generated in Washington, which is<br />
home to the nation’s largest hydroelectric facility [44].<br />
Wind, solar, and geothermal energy round out the renewable energy<br />
component. These renewable sources, while quite intuitive in nature, have proven<br />
difficult to master technologically, with each one presenting unique challenges.<br />
Wind is an inherently volatile resource that can supply an overabundance or a lack<br />
of energy at any time without warning, which prompts the need for stored energy to<br />
provide consistent power. Like wind power, solar power also varies by hour,<br />
7
Introduction to the Energy Problem<br />
season, and location, sometimes unpredictably, making a secondary energy source<br />
all but necessary. Finally, geothermal energy, which is simply heat from the earth, is<br />
captured beneath the earth’s surface. The drilling and exploration associated with<br />
geothermal energy makes for a very expensive, and sometimes unfruitful,<br />
enterprise.<br />
Together, wind, solar, and geothermal energy supplied 13% of renewable<br />
energy in 2008, or, equivalently, roughly 1% of the total U.S. energy supply. Yet<br />
there is reason to believe that contributions from these three sources, backed by<br />
technological advances and support from the federal government, will grow rapidly<br />
in the coming years. In theory, wind, solar, and geothermal sources offer enormous<br />
potential for meeting future energy demands; the obstacle will be to harness and<br />
distribute the energy in a cost-‐effective manner.<br />
1.2 Tax Subsidies for Renewable Energy<br />
If the government is so inclined, it may offer attractive subsidies to<br />
encourage consumer behavior that it deems favorable. Subsidies are a powerful<br />
means to ease financial burdens on consumers or to encourage spending in a certain<br />
area. Tax subsidies and incentives take a great many forms, the most attractive of<br />
which is the tax credit. Unlike tax deductibles, which only reduce taxable income,<br />
tax credits reduce the amount of taxes owed dollar for dollar. Currently, the federal<br />
government offers child and dependent care credits, education credits, and first-‐<br />
time homebuyer credits, to name just a few [49]. In 2005, Congress enacted a<br />
personal tax credit for investment in renewable energy.<br />
8
1.2.1 Residential Renewable Energy Tax Credit<br />
Introduction to the Energy Problem<br />
The tax incentive of greatest interest here is the Residential Renewable<br />
Energy Tax Credit. It applies directly to American consumers, unlike the many tax<br />
breaks granted to corporations and industry. Originally created under the Energy<br />
Policy Act of 2005, it offers a 30% personal tax credit to Americans who install<br />
renewable technology in their homes; qualifying technologies include solar heating<br />
and solar electric technology, wind turbines, fuel cells 2 , and geothermal heat pumps<br />
[32]. The American Recovery and Reinvestment Act of 2009 further enhanced the<br />
Residential Renewable Energy Tax Credit by removing the original $2,000<br />
maximum credit amount for eligible technologies, bringing the credit to its most<br />
generous design since its inception [32]. 3 It is not due to expire until December<br />
2016.<br />
1.2.2 Residential Energy Efficiency Tax Credit<br />
The other federal tax credit offered to American consumers in the clean<br />
energy sector is the Residential Energy Efficiency Tax Credit. It provides a 30%<br />
personal tax credit for the cost of “upgrading the efficiency of a building’s envelope”<br />
[51]. Such home improvements include insulation materials or pigmented metal<br />
roofs designed to reduce a home’s heat loss and gain, advanced main air circulating<br />
fans, biomass stoves, and much more [51]. The Residential Energy Efficiency Tax<br />
Credit has a cap of $1,500, and it is set to expire in December 2010 [51].<br />
2 Fuel cells are “electrochemical cells in which the energy of a reaction between a fuel, such as liquid<br />
hydrogen, as an oxidant, such as liquid oxygen, is converted directly and continuously into electrical<br />
energy” [50]. The exhaust of fuel cells consists only of water.<br />
3 This enhancement to the tax credit excludes fuel cell technology.<br />
9
1.2.3 State-‐wide Renewable Tax Credits<br />
Introduction to the Energy Problem<br />
In addition to federal tax incentives, many state governments offer their own<br />
tax breaks for renewable energy or energy efficiency. In total, twenty-‐two states<br />
offer personal tax credits for renewable energy [52]. 4 Of those, five states—Arizona,<br />
Maryland, Montana, New Mexico, and New York—offer more than one personal tax<br />
credit for renewable energy. In comparison, just thirteen states offer personal tax<br />
credits for energy efficiency [52].<br />
1.3 The Cost of Carbon<br />
Despite its widespread usage in everyday publications, the “cost of carbon” is<br />
ambiguous and may refer to two distinct concepts: the social cost of carbon, and the<br />
carbon tax. For clarity’s sake, neither of these concepts will hereafter be called the<br />
“cost of carbon”; they will be referred to only by their more descriptive names.<br />
1.3.1 The Social Cost of Carbon<br />
The social cost of carbon (SCC) is formally defined as the marginal cost of<br />
emitting an additional unit of carbon (in the form of carbon dioxide) [5]. It is usually<br />
expressed in dollars per metric ton of carbon. It is calculated by quantifying the<br />
long-‐term environmental damage done by the additional unit of carbon, and<br />
discounting the damage to its present value in dollars. The SCC, therefore, can be<br />
interpreted as “a measure of the seriousness of climate change”: the more grim the<br />
4 Alabama, Arizona, Georgia, Hawaii, Idaho, Indiana, Iowa, Kentucky, Louisiana, Maryland,<br />
Massachusetts, Montana, New Mexico, New York, North Carolina, North Dakota, Oregon, Rhode<br />
Island, South Carolina, Utah, Vermont, and West Virginia [52].<br />
10
Introduction to the Energy Problem<br />
assumptions about the environmental impact of carbon, the higher the SCC estimate<br />
will be.<br />
To complicate matters for policymakers, there is no single widely accepted<br />
SCC value. In fact, estimates of the SCC vary considerably. The not-‐for-‐profit<br />
Investor Responsibility Research Center projects that the SCC will be $28.24 per ton<br />
in 2012 [6]. Richard Tol, a leading authority on SCC research, estimates that the<br />
mean SCC is $23 per ton with a 1% chance that it exceeds $78 per ton [5]. Other<br />
estimates put the cost of carbon at a much higher price than that; the United Nations<br />
Intergovernmental Panel on Climate Change (IPCC) pointed out that there was a $98<br />
difference between the highest and lowest peer-‐reviewed estimates in 2005 [8].<br />
According to the IPCC, peer-‐reviewed estimates of the SCC put its mean value at $43<br />
per ton with a standard deviation of $83 per ton in 2005 dollars [35].<br />
The SCC value is critically important to shaping energy legislation, which will<br />
have a varying degree of impact based on SCC assumptions. The gap in estimates,<br />
however, is not likely to narrow anytime soon. The variance in SCC estimates is<br />
mostly attributable to different choices of discount rate, uncertainty about the<br />
science of climate change, and varying assumptions about future population growth,<br />
economic growth, and greenhouse gas emissions [5].<br />
1.3.2 The Carbon Tax<br />
As is evident from its name, the carbon tax is not an economic measure but<br />
rather a government-‐imposed levy on carbon dioxide emissions. Importantly, the<br />
carbon tax is not strictly a tax per ton of carbon emitted; it is understood to be a tax<br />
per ton of carbon dioxide, which is only partially composed of carbon. As of this<br />
11
Introduction to the Energy Problem<br />
writing, there is no federal carbon tax in the United States. 5 Over a year ago,<br />
President Obama proposed climate legislation with an implicit tax of $13.70 per ton<br />
of carbon dioxide within a cap-‐and-‐trade framework, but Congress has yet to vote<br />
on a bill [46]. In comparison, many European nations successfully enacted carbon<br />
taxes as early as 1990. Sweden’s tax is the most expensive at $150 per ton 6 , but it<br />
appears not to have had a dragging effect on the local economy [47].<br />
In a perfect market, the penalty for emitting one ton of carbon into the air<br />
should be set equal to the marginal damage done by the additional ton, i.e. the social<br />
cost of carbon. It would then become a Pigouvian tax, or a tax levied on market<br />
activity that generates negative externalities not internalized by the private market.<br />
However, because markets are imperfect and the value of the SCC is uncertain, many<br />
governments around the world question whether a carbon tax is warranted at all.<br />
In later chapters, the hypothetical range for a carbon tax in the U.S. is $0 to<br />
$100 per ton carbon dioxide. This is based upon estimates of the SCC in past<br />
literature. According to the IPCC Climate Change Syn<strong>thesis</strong> Report in 2007, most<br />
models show that “global carbon prices rising to $20 to $80 per ton by 2030 are<br />
consistent with stabilization” of CO2 in the atmosphere in 2100 [8]. Admittedly, it is<br />
unlikely that the U.S. Congress would impose a steep carbon tax in the near future,<br />
but the range is extended to $100 per ton to allow for the possibility.<br />
5 However, certain districts in California and Colorado have adopted carbon taxes [47].<br />
6 Fuels used for electricity generation are exempt from the carbon tax, and the industrial sector is<br />
mandated to pay only 50% of the tax [47].<br />
12
1.4 Overview of the Thesis<br />
Introduction to the Energy Problem<br />
In analyzing government intervention in the solar and wind energy markets,<br />
this <strong>thesis</strong> will examine the interplay of government-‐sponsored tax credits and a<br />
potential carbon tax. Chapter 2 explains the methodology used for arriving at costs<br />
for wind and solar energy installations in each of the fifty states. Chapter 3 offers a<br />
cost function to minimize electricity costs incurred by residential consumers across<br />
the country, and it illustrates the effects of government intervention on the national<br />
electricity mix and price. Chapter 4 builds off of Chapter 3 by developing a cost-‐<br />
benefit model to assess the impact of different tax policies. The results and<br />
subsequent analysis in Chapter 5 demonstrate the overall social benefit of varying<br />
degrees of government intervention in the solar and wind energy markets. Finally,<br />
Chapter 6 summarizes the results and suggests areas for further research.<br />
13
2. Methodology of Cost Comparison<br />
Prior to exploring the effects of hypothetical government policies on<br />
energy usage, it is necessary to gather relevant information about the<br />
state of energy usage today. The first objective in this methodology is to compute<br />
and compare the costs, state by state, of electricity from three different sources:<br />
solar photovoltaic (PV) panels, wind turbines, and conventional retail electricity, a<br />
proxy for fossil fuels. From there, the data will lead to conclusions about where<br />
renewable energy can have the greatest impact, and what degree of government<br />
intervention (if any) is required in order to achieve the desired change.<br />
This task is heavily reliant upon data at both regional and national levels.<br />
Fortunately, the Department of Energy website houses a massive aggregation of<br />
data that enables any dedicated researcher to answer myriad questions concerning<br />
energy costs in the United States. One of those questions—how to sensibly
Methodology of Cost Comparison<br />
regionalize energy sources by exploiting cost disparities for solar, wind, and retail<br />
electricity across the United States—is explored here.<br />
2.1 Foundations for this Approach<br />
Rather than analyze the costs of all five of the renewable resources, this<br />
chapter will conduct an in-‐depth study of wind and solar energy only. Wind and<br />
solar have a great deal in common: both are considered to have significant long-‐<br />
term potential, and both are vastly untapped sources of energy, as noted in the<br />
introduction. Because electricity generation is the biggest market that wind and<br />
solar energy have in common, this analysis will focus solely on electricity in the<br />
United States, as opposed to other forms of energy like direct heating and powering<br />
vehicles. 7 This allows for the direct<br />
comparison of wind and solar to fossil<br />
fuel-‐generated electricity, which will<br />
hereafter be called “retail electricity.”<br />
Retail electricity implies “the<br />
<strong>final</strong> sale of power from an electricity<br />
provider to an end-‐use consumer” [48].<br />
Quite simply, the average retail<br />
electricity price in New York reflects<br />
the price that everyday New Yorkers<br />
7 Solar energy is used both for direct heating and electricity generation, whereas wind energy is<br />
limited to electricity generation.<br />
Figure 3. U.S. Electric Power Industry<br />
Net Generation, 2008 [27]<br />
15
Methodology of Cost Comparison<br />
are paying per kilowatt-‐hour on electrical bills. Typically, a varying mix of energy<br />
sources provides retail electricity to any region and state; from an analytical point of<br />
view, it is therefore impractical, if not nearly impossible, to separate coal-‐generated<br />
electricity from natural gas-‐ and petroleum-‐generated electricity for any area.<br />
Instead, it makes more sense to treat the three as a package and then utilize retail<br />
electricity price data, which is readily available for every state and sector. Local<br />
retail electricity prices serve as a benchmark against which electricity prices from<br />
solar and wind energy are compared; in other words, solar and wind power are<br />
considered economically competitive when and if their price points decline to those<br />
of retail electricity.<br />
Of course, retail electricity in the United States is not a perfect proxy for fossil<br />
fuel-‐generated electricity. As Figure 3 shows, fossil fuels—coal, natural gas, and<br />
petroleum—represent 70% of electricity generated in the United States. The<br />
remaining 30% comes from nuclear power (20%), renewables (9%), and “other”<br />
(1%). However, given the vast complexity of the different electricity mixes servicing<br />
consumers across the United States and the lack of available data decomposing the<br />
prices within each mix, a consumer’s local retail electricity price is generally a fair<br />
substitute for the price the consumer would pay if 100% of the electricity in the U.S.<br />
were generated by fossil fuels. Also, nuclear and hydroelectric power are roughly<br />
cost-‐competitive with fossil fuels in the regions where they are currently used, so<br />
16
Methodology of Cost Comparison<br />
the combined 26% of electricity consumption from those sources does not skew the<br />
retail price data. 8<br />
Within the retail electricity market, this analysis will utilize data from the<br />
residential sector exclusively. Accordingly, the analysis will look only at electricity<br />
generated by solar and wind power for<br />
residential use. From now on, “solar<br />
energy” is defined as rooftop solar<br />
photovoltaic panels that are installed to<br />
provide electricity to individual homes. In a<br />
similar vein, “wind energy” is defined as<br />
small-‐scale, individual wind turbines for<br />
residential electricity production rather<br />
than large-‐scale wind farms.<br />
Figure 4. Residential Energy Use in<br />
Different Types of Homes [12]<br />
Additionally, only residences falling under the category of “single-‐family<br />
detached home” are considered so as to exclude apartments and other shared<br />
residential buildings where cost calculations per household are somewhat<br />
ambiguous. Given that the energy consumption of single-‐family detached homes<br />
accounts for 80% of total residential energy use, as shown in Figure 4, the analytical<br />
results will be representative of the residential sector at large [12].<br />
8 The U.S. average levelized cost for plants entering service in 2016 is: $104.2/MWh for fossil fuel<br />
plants, $107.3/MWh for nuclear plants, and $114.1/MWh for hydropower facilities [91]. The<br />
definition of levelized cost is “the present value of the total cost of building and operating a<br />
generating plant over its economic life, converted to equal annual payments” [90].<br />
17
2.2 Factors Affecting Retail Electricity Prices in the United States<br />
Methodology of Cost Comparison<br />
The three major components of the electricity price are the generation,<br />
transmission, and distribution of electricity. Yet the average breakdown shown in<br />
Figure 5 is just that: an average. For a number of reasons, states do not pay<br />
equivalent retail electricity prices per kilowatt-‐hour of electricity. In fact, the range<br />
is quite large. There are many sources of variability driving regional electricity<br />
prices [11]:<br />
• Fuel type – Electricity prices will vary based on the availability and type of<br />
fuels in the region.<br />
• Power plants – Construction and maintenance is more costly for certain<br />
kinds of plants.<br />
• Weather conditions impact demand for electricity and, in turn, electricity<br />
prices.<br />
• State regulations (or lack<br />
thereof) regarding pricing:<br />
“Some states are fully regulated<br />
by the Public Service<br />
Commissions, while in others<br />
there is a combination of<br />
unregulated prices (for<br />
generators) and regulated prices<br />
(for transmission and<br />
distribution)” [11].<br />
Figure 5. Major Components of U.S.<br />
Average Electricity Price, 2008 [11]<br />
(Cents per kWh and Share of Total)<br />
18
Methodology of Cost Comparison<br />
In addition to regional variation, electricity prices also vary by sector and over<br />
time. Residential consumers tend to pay the steepest rates because distribution<br />
costs are higher for them than for industrial and commercial consumers.<br />
Seasonality also plays a role in electricity prices; during the summer or winter,<br />
when demand for cooling or air conditioning is highest, prices tend to be the most<br />
expensive.<br />
2.3 Solar Photovoltaics<br />
The government records retail electricity prices across the country at regular<br />
intervals, but this practice has not been extended to the renewable electricity sector<br />
just yet. As a relatively new product targeted at mainstream consumers, solar<br />
photovoltaic panels do not have well-‐documented per-‐kilowatt-‐hour prices on a<br />
state-‐by-‐state basis. The growing interest in the renewable energy industry,<br />
however, prompts the need for knowledge of regional solar technology prices; the<br />
paucity of available price data is resolved here by building an entire data set from<br />
the ground up.<br />
2.3.1 Assumptions in Solar Calculations<br />
This analysis does not consider solar thermal technology. Solar thermal<br />
collectors—including flat plate, evacuated tube, and parabolic dish collectors—are<br />
typically used to heat water in homes. Instead, the focus is on solar electric<br />
technology: photovoltaic (PV) panels that provide electricity to homes by converting<br />
solar radiation into direct current. Photovoltaic literally means “capable of<br />
producing a voltage when exposed to radiant energy, especially light” [25]. Whereas<br />
19
Methodology of Cost Comparison<br />
solar thermal collectors can only transfer heat from the sun, PV panels enable<br />
individuals to use computers, refrigerators, and other appliances integral to<br />
American modern life. Figure 6 illustrates the distinction between solar thermal<br />
collectors and photovoltaic panels.<br />
Figure 6. Comparison of solar photovoltaic cells<br />
and solar thermal collectors [20]<br />
The first assumption is that all homes have the roof surface area necessary to<br />
support a rooftop solar installation that could theoretically power 100% of its<br />
electricity needs, notwithstanding one obvious problem. In reality, most households<br />
would not want to be completely reliant on solar power, which, like wind power, can<br />
be unreliable depending on weather conditions. Solar power is naturally a<br />
complement to, but not a replacement of, other sources of energy.<br />
To that end, the second assumption is that PV panels are grid-‐connected,<br />
meaning that the PV panels provide electricity to the home while the sun is shining,<br />
but when the solar resource is unavailable or limited, electricity from the grid<br />
supplies the household’s electricity needs. Likewise, any excess electricity produced<br />
20
Methodology of Cost Comparison<br />
by the solar PVs is fed back into the grid. Connecting a solar electric system to the<br />
grid eliminates the need to purchase electricity storage devices like batteries.<br />
The third major assumption is that the lifespan of a solar PV panel is twenty<br />
years, which is the standard length of time that PV module manufacturers provide a<br />
warranty [54].<br />
2.3.2 Solar Energy Potential in the United States<br />
Of course, the intensity of the sun varies greatly across the United States,<br />
which in turn affects the potential for solar energy use in different regions. The<br />
relative measure of sunshine that represents an area’s potential for solar energy is<br />
daily peak sun hours; a peak sun hour is one kilowatt-‐hour per square meter of<br />
sunlight. It is a better comparative measure than hours of sunlight per day because<br />
it accounts for both intensity and duration of sunlight. Figure 7 is a solar insolation 9<br />
map of the United States. Reddish tones essentially represent “dense” sunlight—<br />
that is, the sun provides more kilowatt-‐hours of energy per square meter per day in<br />
the red and orange states.<br />
Table 2. Average Peak Sun Hours Per Day [19]<br />
States with most peak sun States with least peak sun<br />
hours per day<br />
hours per day<br />
New Mexico, 6.77 Vermont, 2.95<br />
Arizona, 6.50 Illinois, 3.14<br />
Nevada, 6.20 New Hampshire, 3.40<br />
Wyoming, 6.06 New York, 3.58<br />
Hawaii, 6.02 Pennsylvania, 3.60<br />
California, 5.74 Connecticut, 3.63<br />
9 Insolation: Solar radiation received at the earth’s surface [55].<br />
21
Methodology of Cost Comparison<br />
Peak sun hour data for all fifty states was compiled from the National Solar<br />
Radiation Data Base [19]. There are measurement stations in or near major cities<br />
throughout the United States. For states that have more than one primary station,<br />
the stations’ measurements are averaged. The states with the highest and lowest<br />
peak sun hours per day are represented in Table 2. Combined with data on annual<br />
residential electricity consumption in each of the fifty states [56], it is possible to<br />
calculate the PV panel wattage required to theoretically meet 100% of the electricity<br />
demand of a typical single-‐family home in each state. 10 The wattage of the PV panel<br />
is the major determinant of the cost of the solar electric installation.<br />
Figure 7. Solar PV Resource Map of the United States [7]<br />
10 When the sun is shining, the PV panels of the calculated wattage will be capable of meeting 100%<br />
of household demand. When the sunlight is limited or unavailable, the PV panels may not fully meet<br />
demand.<br />
22
€<br />
€<br />
Methodology of Cost Comparison<br />
Based on the insolation map alone, one could conjecture that solar energy is<br />
most economical in the Southwest, especially Arizona, New Mexico, southern<br />
California, and surrounding states. But the attractiveness of solar energy in any<br />
region will depend on the relative prices of other electricity sources, which is why<br />
building a regional price data set for renewable energy sources is so crucial.<br />
2.3.3 Peak Sun Hours and PV Modules<br />
where<br />
The formula that represents the PV module wattage required in each state is:<br />
W i<br />
elec<br />
solar d i<br />
= 1.15 ⋅ solar<br />
k i<br />
solar<br />
W i = PV wattage required to provide 100% of the average single-‐family<br />
€<br />
home’s electricity consumption in state i (kW)<br />
elec<br />
d i = average daily electricity consumption of a single-‐family home in<br />
state i (kWh)<br />
solar<br />
k i = average peak sun hours per day in state i (hours)<br />
i = states 1, 2, …, 51 (including District of Columbia)<br />
€ A factor of 1.15 is included in the calculation to account for energy loss resulting<br />
from the conversion of direct current into alternating current, which is necessary in<br />
order to power most household appliances.<br />
Table 3. Average Electricity Consumption in Single-‐Family Homes [19]<br />
States with highest electricity States with lowest electricity<br />
consumption (kWh/month) consumption (kWh/month)<br />
Tennessee, 1,344 Maine, 530<br />
Alabama, 1,305 California, 580<br />
Louisiana, 1,276 Vermont, 592<br />
Kentucky, 1,217 New York, 604<br />
Virginia, 1,207 Rhode Island, 608<br />
23
Methodology of Cost Comparison<br />
For reference, electricity consumption data for average single-‐family homes<br />
in a selection of states is listed in Table 3. Homes in southern states tend to<br />
consume the most electricity per month, whereas homes in the Northeast and<br />
California consume the least amount of electricity. The discrepancy is large, with<br />
some southern states consuming more than twice as much electricity as California<br />
and Northeastern states.<br />
Climate is one of the major factors affecting regional electricity consumption.<br />
Hot summers require the use of more air conditioning and other space cooling, so<br />
homes in southern states tend to use more electricity in the summer. Cold winters<br />
also increase energy use for space heating, but most U.S. households rely on natural<br />
gas rather than electricity for heating. However, “in the South the reverse is true,<br />
meaning that households in southern states will tend to have a peak of electricity<br />
use in winter as well as in summer” [92]. Another factor influencing regional<br />
electricity consumption is the average age of the housing stock: “New homes, which<br />
are more prevalent in the South, tend to use more electricity” [92].<br />
Conversely, the lower electricity consumption in Northeastern states is<br />
explained by cooler summers, which decrease electricity demand for air<br />
conditioning, and by a greater reliance on fuel oil for heating during the winters<br />
[93]. Additionally, New Englanders are “more likely to live in older buildings and in<br />
apartments than householders nationwide,” which usually means they live in<br />
smaller residences that require less electricity [93].<br />
24
€<br />
€<br />
€<br />
2.3.4 Installation and Maintenance Costs<br />
Methodology of Cost Comparison<br />
Solar electric installations are priced according to wattage capacity, so the<br />
formula for the average installation cost of a PV module capable of providing 100%<br />
household electricity consumption in state i is as follows:<br />
where<br />
solar solar solar<br />
C install,i = W i ⋅ c install<br />
solar<br />
= average<br />
€<br />
cost of installing a residential PV module in state i ($)<br />
C install,i<br />
solar<br />
c install = average installation cost of the residential PV module ($/kW)<br />
solar<br />
W i = PV wattage required to provide 100% of the average single-‐family<br />
home’s electricity consumption in state i (kW)<br />
Due to the technological advancement of PV panels, the average cost per<br />
kilowatt installed has fallen dramatically over the past several years. Today, the<br />
total installation cost 11 is around $7,000 per kilowatt for residential solar modules,<br />
or as low as $5,000 per kilowatt for utility-‐scale installations [57] [33]. The $7,000<br />
per kilowatt estimate is used here, although the installation cost might be lower for<br />
those who have the expertise to install the PV modules themselves. The economies<br />
of scale in PV installations are assumed to be negligible for residential modules,<br />
which tend to be quite small.<br />
Moreover, maintenance costs 12 also need to be incorporated into the total<br />
cost of the solar energy system. Even though the annual maintenance cost for solar<br />
PV panels is very low, it is the only other component of the total cost of a solar<br />
11 Includes solar module itself, plus inverter, mounts, racks, wiring, and labor for installation.<br />
12 Includes electrical inspections and replacement of inverters.<br />
25
€<br />
€<br />
Methodology of Cost Comparison<br />
electric system. A rule of thumb used in the PV industry is to expect annual<br />
maintenance costs of 2% of the initial capital cost [58]. Therefore, the present value<br />
of all future maintenance costs is represented by:<br />
where<br />
solar<br />
solar (0.02 ⋅ C install,i)<br />
1<br />
C mntc,i = 1 −<br />
r (1+ r) −n<br />
⎡⎡ ⎤⎤<br />
⎢⎢ ⎥⎥<br />
⎣⎣ ⎦⎦<br />
solar €<br />
= present value of all maintenance costs over lifetime of the PV module<br />
C mntc,i<br />
in state i ($)<br />
r = interest rate (assume real interest rate of 2%)<br />
n = lifetime of the PV module (assume 20 years)<br />
solar<br />
C install,i defined as above<br />
€<br />
Based on historical trends, a nominal long-‐term interest rate of 5% and an inflation<br />
€<br />
rate of 3% are projected in the future, resulting in a real long-‐term interest rate r of<br />
€<br />
€<br />
2% [62].<br />
Combining the installation and maintenance costs, the average total cost of<br />
the solar PV installation in state i over its lifetime is represented by:<br />
where<br />
€<br />
solar solar € solar<br />
, C install,i,<br />
C mntc,i ≥ 0<br />
C total,i<br />
solar solar solar solar<br />
C total,i = C install,i(1−<br />
β ) + C mntc,i<br />
β solar = federal investment tax credit for residential solar installations,<br />
0 ≤ β solar ≤1<br />
26
Methodology of Cost Comparison<br />
Because tax credits imply a dollar-‐for-‐dollar reduction in the income taxes a person<br />
must pay, the effective cost of the wind installation is simply the percentage (1-‐tax<br />
credit) of the original installation cost.<br />
Appendix A-‐1 provides a list of the installation costs, maintenance costs, and<br />
total costs 13 using this methodology for all 51 states. 14 The calculations show that<br />
solar PV systems capable of meeting 100% of household need are cheapest in New<br />
Mexico, due to the combination of intense sunlight and lower-‐than-‐average<br />
electricity consumption in that state. Still, with a price tag of $32,000, a PV module<br />
in New Mexico is not cheap. In other states, however, PV installations of this kind<br />
appear so expensive as to be infeasible: in Alabama, Tennessee, and West Virginia,<br />
PV modules meeting the specifications described would cost over $100,000, which<br />
is far more than the average consumer would spend on retail electricity bills in an<br />
entire lifetime. 15<br />
The range in costs demonstrates that the economic practicality of solar<br />
power varies greatly across the United States. It is important to note, however, that<br />
households could install modules far smaller than those discussed in this analysis<br />
and in some cases achieve a reduction in their electrical bills. Here, the assumption<br />
that households will build modules to meet 100% of their electric need is solely for<br />
13<br />
For now, assuming the absence of any subsidy from the federal or state government.<br />
14<br />
Including the District of Columbia.<br />
15<br />
At this point, two things to bear in mind are that this number reflects neither investment tax<br />
credits nor expected price declines of PV modules. The latter is discussed in Section 4.2.1.<br />
27
€<br />
€<br />
€<br />
Methodology of Cost Comparison<br />
purposes of comparison, so that data of a solar-‐powered home can be juxtaposed to<br />
that of wind-‐powered and fossil fuel-‐powered homes.<br />
2.3.5 Electricity Production of the PV Module<br />
The next step is to find the total electricity produced by a solar PV system<br />
over its useful life. Using previously defined variables, this is simply:<br />
where<br />
solar solar solar<br />
E total,i = 0.87W i ⋅ k i ⋅ 365n<br />
solar<br />
= the<br />
€<br />
total output of electricity over the lifespan of the solar PV module<br />
E total,i<br />
for the average residential single-‐family home in state i (kWh)<br />
solar<br />
W i = PV wattage required to provide 100% of the average single-‐family<br />
home’s electricity consumption in state i (kW)<br />
solar<br />
k i = average peak sun hours per day in state i (hours)<br />
n = lifetime of the PV module (assume 20 years)<br />
The total output is reduced by approximately 13% due to energy loss in the<br />
€<br />
conversion of direct current into alternating current. Also, the peak sun hour data<br />
k solar is daily, hence n, measured in years, must be adjusted by a factor of 365 (days<br />
per year). Finally, plugging W into the equation, the total output value E for the<br />
average module in each state matches the home’s expected electricity consumption<br />
in state i over that time period, or<br />
elec<br />
365n ⋅ d i<br />
just as intended. After all, consumers will want to spend just enough money to<br />
install a PV module sized to€ meet their electricity consumption—no more and no<br />
less.<br />
28
€<br />
2.3.6 Overall Price of Solar Electricity in this Model<br />
Methodology of Cost Comparison<br />
Having calculated the total cost of the PV module over its lifetime as well as<br />
the total output of electricity over its lifetime, the price per kilowatt-‐hour of<br />
electricity generated by the solar PV system in state i follows as such:<br />
where<br />
p i<br />
solar<br />
solar C total,i<br />
=<br />
solar<br />
E total,i<br />
solar<br />
p i = overall price per kilowatt-‐hour of electricity that consumers will pay<br />
€<br />
over lifespan of the PV module in state i ($/kWh),<br />
solar<br />
p i ≥ 0<br />
Calculations for output of electricity and overall price per kilowatt-‐hour by<br />
state are included in Appendix A-‐1. Not surprisingly, the€ solar-‐generated electricity<br />
prices are cheapest in states with the greatest number of peak sun hours per day,<br />
and are most expensive in states with the fewest number of peak sun hours per day.<br />
Table 4 provides the “tails” of the overall price calculations. The calculations<br />
confirm the expectation that states with abundant sunshine have a natural price<br />
advantage because more solar radiation is captured per square foot of photovoltaic<br />
panel per day. Consumers in less sunny states (i.e., states with fewer peak sun<br />
hours) are forced to purchase larger, and therefore more expensive PV systems in<br />
Table 4. Solar-‐Generated Electricity Prices<br />
States with highest solar States with lowest solar<br />
electric prices ($/kWh) electric prices ($/kWh)<br />
Vermont, 0.37 New Mexico, 0.16<br />
Illinois, 0.35 Arizona, 0.17<br />
New Hampshire, 0.32 Wyoming, 0.18<br />
New York, 0.31 Nevada, 0.18<br />
Pennsylvania, 0.31 Hawaii, 0.18<br />
29
Methodology of Cost Comparison<br />
order to capture a comparable amount of energy from the sunlight to meet their<br />
electricity needs.<br />
On the whole, the weighted average price of solar-‐generated electricity 16<br />
from residential PV modules is $0.25/kWh without any government tax incentive,<br />
which remains much higher than the “baseline” price of retail electricity of<br />
$0.11/kWh. Chapter 4 will explore how improvements in PV technology, combined<br />
with different levels of a tax credit, can significantly reduce the price of solar<br />
electricity.<br />
2.3.7 Government Incentives<br />
As discussed in the introduction, a substantial federal tax credit of 30% is<br />
available to those who install PV modules in their homes. Taking advantage of the<br />
federal tax credit in addition to any state-‐specific tax incentives can lower the cost of<br />
installation to the point that, in some areas, the price of solar electricity competes<br />
with retail electricity. For example, in Arizona, solar electricity costs $0.17/kWh in<br />
the absence of any tax credit; with a 30% tax credit, the price paid by the consumer<br />
drops to $0.13/kWh, and with an aggressive 50% tax credit, the price drops even<br />
further to $0.10/kWh, which is the average price for retail electricity in the state.<br />
One can easily see how effective the tax credit is as an instrument to<br />
influence consumers. Chapter 3 will explore in greater depth how the level of the<br />
renewable energy tax credit in addition to a carbon tax influences the relative prices<br />
of solar, wind, and retail electricity.<br />
16 The price is weighted over the 51 states.<br />
30
2.4 Wind Energy<br />
Methodology of Cost Comparison<br />
Within the last couple of decades, wind energy has developed a following<br />
within the United States. But like solar PVs, wind turbines have yet to penetrate the<br />
mainstream market (though many believe they are on the verge of doing so). As a<br />
result, no state-‐by-‐state price data for wind energy yet exists. To address this need,<br />
the approach used to build the solar price data set is adapted for wind energy.<br />
2.4.1 Assumptions in Wind Calculations<br />
To remain consistent with the approach taken to solar calculations, the wind<br />
energy in this study is limited to “small wind,” or the use of wind turbines for<br />
individual homes. As is true across the renewable energy sector, installation costs<br />
are dependent upon scale: generally, the larger the wind or solar installation, the<br />
cheaper the resulting electricity will be per kilowatt-‐hour. Thus, to eliminate<br />
variance in costs due to scale, only small-‐scale wind turbines intended for<br />
residential use are considered.<br />
Three main assumptions regarding small wind turbines are made to parallel<br />
the solar calculation approach. The first is that the single-‐family homeowners in<br />
this study are willing to devote some space on their property to a wind turbine. It<br />
may be in the backyard, the front yard, or anywhere they like so long as the wind<br />
turbine is built to provide enough electricity to meet 100% of the home’s electricity<br />
demand. Secondly, as with the PV modules, all residential wind turbines are<br />
assumed to be on-‐grid. When the wind is blowing, the homeowner will use the<br />
turbine-‐generated electricity, but when winds are low or no wind is blowing at all,<br />
the owner can rely upon electricity from the grid. If excess electricity is generated<br />
31
Methodology of Cost Comparison<br />
by the turbine, it is sent to the utility to be transferred to a neighbor [22]. The third<br />
assumption is that the wind turbines have a lifespan of twenty years, which is<br />
consistent with objective assessments of the useful life of turbines on the market<br />
today [59]. However, the American Wind Energy Association has suggested that the<br />
actual operating life of a typical wind turbine may be much longer than that [60].<br />
2.4.2 Wind Energy Potential in the United States<br />
Wind energy is akin to solar energy in that its “potential” in a given state or<br />
region is determined by one thing: the area’s average wind speed. (For solar power,<br />
the analogous metric was the area’s peak sun hours.) Of course, a number of factors<br />
determine a region’s wind speed, like height above sea level, proximity to a<br />
coastline, and local terrain, to name just a few—but ultimately, only the wind speed<br />
matters.<br />
The National Renewable Energy <strong>Lab</strong>oratory (NREL) created a wind resource<br />
map (Figure 8), wherein the states with orange and pink coloring have “fair” to<br />
“good” wind energy potential. “Excellent,” “outstanding,” and “superb” wind<br />
potential ratings are primarily reserved for coastlines, with some “excellent” ratings<br />
peppered throughout the country, particularly in the Midwest region. Data from the<br />
American Wind Energy Association (AWEA) in Table 5 corroborates the visual<br />
display of the wind resource. The AWEA estimates that the United States could<br />
potentially generate 10.8 billion megawatts from its onshore wind resources on an<br />
annual basis, which is more than twice as much electricity as the U.S. consumes<br />
annually [17]. However, today, the “installed wind power fleet” generates just 48<br />
32
Figure 8. Wind Energy Resource Map [3]<br />
Table 5. Top States for Wind Energy Potential [17]<br />
States with greatest<br />
wind energy<br />
potential<br />
Annual wind<br />
energy potential<br />
(billions of kWh)<br />
North Dakota 1,210<br />
Texas 1,190<br />
Kansas 1,070<br />
South Dakota 1,030<br />
Montana 1,020<br />
Nebraska 868<br />
Wyoming 747<br />
Oklahoma 725<br />
Methodology of Cost Comparison<br />
33
Methodology of Cost Comparison<br />
billion kilowatt-‐hours of electricity—that’s only a tiny fraction (less than one-‐half of<br />
one percent) of the generation potential in any of the windiest states in Table 5 [17].<br />
By contrast, the wind resource map clearly shows that a large portion of the<br />
country remains white, representing little or no wind potential in those areas.<br />
(White areas have been assigned a wind power class of 1 or 2 by the NREL, and only<br />
classes 3 through 7 are represented by color on the map.) As the wind energy cost<br />
calculations will soon show, the white states are at a huge cost disadvantage when it<br />
comes to installing wind turbines.<br />
2.4.3 Modeling Wind Energy using the Weibull Distribution<br />
Given the volatile nature of wind as a natural resource, it is helpful to think of<br />
wind speed in a state as a distribution rather than as a discrete average value. Past<br />
literature has demonstrated that wind speeds can be modeled by the Weibull<br />
distribution, the shape of which reflects the behavior of wind: light and moderate<br />
winds are fairly common, but strong gales are relatively infrequent. The Weibull<br />
probability density function is given by<br />
where [18]<br />
P(V ) = k<br />
c<br />
⎛⎛ V<br />
⎜⎜<br />
⎝⎝ c<br />
⎞⎞<br />
⎠⎠<br />
k −1<br />
⎟⎟<br />
exp − V ⎛⎛<br />
⎜⎜<br />
⎝⎝ c<br />
⎞⎞ ⎛⎛ k⎞⎞<br />
⎜⎜ ⎟⎟ ⎟⎟<br />
⎝⎝ ⎠⎠ ⎠⎠<br />
P(V) = the probability<br />
€<br />
of occurrence of speed V<br />
k = the dimensionless Weibull shape parameter<br />
c = the Weibull scale parameter<br />
34
Methodology of Cost Comparison<br />
The scale parameter c indicates how ‘windy’ the location is overall. 17 The<br />
shape parameter indicates how dense the wind distribution is around the mean<br />
speed. A shape parameter of 1 represents a “heavy tails” region with lots of low<br />
speed winds combined with high speed winds, whereas a shape parameter of 3<br />
represents a region with wind speeds consistently around the median. Typical wind<br />
behavior, however, is best represented by a shape parameter of 2, under which<br />
condition the Weibull distribution is referred to as the Rayleigh distribution [18].<br />
More formally, the parameters can be evaluated using the equations [9]<br />
−1 −1.086<br />
ki = (σi V i )<br />
−1<br />
V i = ci Γ(1+ ki )<br />
where V i is the annual mean wind speed in state i and σi is the variance of the<br />
monthly means. However,<br />
€<br />
because wind speed variance data broken down by state,<br />
€<br />
as opposed to region, is unavailable, two reasonable assumptions are made in order<br />
to apply the Weibull function:<br />
• The U.S., as a whole, has a Weibull shape parameter of 2. Due to the<br />
lack of wind volatility data available at the state (as opposed to<br />
regional) level, this constant parameter is used for all states.<br />
• The gamma function in V i when k = 2 is approximately equal to 1, so<br />
V i ≈ c i . 18 This simplifying assumption allows for NREL mean wind<br />
€<br />
data by state to be the direct input into the Weibull model.<br />
17 €<br />
To come up with c values for every state, each state was first assigned a wind class per the wind<br />
resource map from the NREL. This is, of course, a somewhat subjective method because wind<br />
potential is not defined along state lines, and it is often the case that a mix of wind classes make up a<br />
single state. In such cases, the wind classes are averaged to come up with a reasonable state-‐wide<br />
wind classification. Appendix A-‐3 lists the wind class assignments by state as well as their<br />
corresponding c (i.e., average wind speed) values.<br />
18<br />
Γ(n) = (n-‐1)!, so Γ(1+(1/k)) = Γ(1+(1/2)) = (1/2)! = .89.<br />
35
Methodology of Cost Comparison<br />
Figures 9 and 10 show the Weibull PDFs for two very different states from a<br />
wind energy perspective: Alabama, which has virtually no wind energy potential<br />
according to the NREL map, and Montana, one of the top states for wind energy. The<br />
MATLAB code in Appendix A-‐4 was used to generate these graphs. Having assumed<br />
a constant shape parameter across the country, similar graphs can be generated for<br />
other states merely by adjusting the scale parameter. The Weibull PDFs shown<br />
below are useful representations of wind speed, for wind is so inconsistent as to<br />
render a simple average uninformative.<br />
Figure 9. Alabama Wind Distribution<br />
2.4.4 Electricity Production of the Wind Turbine<br />
Figure 10. Montana Wind Distribution<br />
Once armed with wind distributions for each of the 51 states, the next task is<br />
to compute the electricity generation of a wind turbine over its lifetime, which will<br />
depend primarily on two variables: the distribution of wind speeds in the state, and<br />
the size of the wind turbine in the state, measured by rotor diameter. Rotor<br />
diameters of small, residential-‐use wind turbines are generally ten meters or less<br />
[16]. Just like with the solar calculations, the assumption here is that consumers<br />
36
€<br />
€<br />
€<br />
€<br />
€<br />
Methodology of Cost Comparison<br />
will install wind turbines powerful enough to meet 100% of their residential<br />
electricity needs per year.<br />
As defined in Hasan [9], the electrical energy generated over the course of<br />
one year by the wine turbine is obtained from the equation<br />
where<br />
wind<br />
E annual,i<br />
wind<br />
E annual,i<br />
∫<br />
V 2<br />
wind wind<br />
= Wi (V )Ti (V )dV<br />
V 1<br />
€<br />
= annual electricity generated by the wind turbine in state i (kWh)<br />
wind<br />
Wi (V ) = power output of the wind turbine as a function of wind speed V in<br />
state i (kW)<br />
wind<br />
Ti (V ) = number of hours in a year during which the wind blows with<br />
speed V in state i (hours)<br />
V 1 = cut-‐in speed (the minimum speed at which the wind turbine will<br />
generate useable power, usually around 3 meters per second)<br />
V 2 = cut-‐out speed (the speed at which the wind turbine ceases to function<br />
and shuts down, usually around 20 meters per second for small wind<br />
turbines [14])<br />
Consequently, the total electricity generated by the wind turbine in state i over the<br />
course of its useful life is<br />
turbine.<br />
wind wind<br />
E total,i = n ⋅Eannual,i<br />
, where n is the lifetime of the wind<br />
The annual<br />
€<br />
number of hours during which V ≥ Vx is given by the equation [9]<br />
€<br />
wind −1 k<br />
Ti (V ≥Vx ) = 8760 exp {− (Vx ci ) }<br />
37
€<br />
€<br />
€<br />
€<br />
€<br />
€<br />
Methodology of Cost Comparison<br />
where the factor 8760 represents the number of hours in a year. The effective<br />
power output 19 in kilowatts from a wind turbine, W(V), is given by the AWEA<br />
formula [61]<br />
where<br />
ρ air<br />
A i<br />
0.5⋅ρ wind air ⋅A i ⋅ Cperf ⋅V<br />
Wi (V ) = 3 ⋅ Ngen ⋅ Ngear 1000<br />
= air density (1.225 kg/m<br />
€<br />
3 )<br />
= average rotor swept area required to meet a typical household’s<br />
electricity needs in state i: π*(rotor radius) 2 (unit: square meter)<br />
C perf = coefficient of performance of the wind turbine, also known as capacity<br />
factor (35% for a good design, but 59% is the theoretical maximum,<br />
known as the Betz limit)<br />
N gen = generator efficiency (80% for a grid-‐connected induction generator)<br />
N gear = gearbox/bearings efficiency (95% for a good design)<br />
The only variable in the W(V) calculation that changes from state to state is<br />
A i , the rotor swept area of the wind turbine. The ideal rotor swept area for state i—<br />
that is, the<br />
A i required in order for the wind turbine to yield precisely 100% of the<br />
average household’s electricity consumption—is determined by setting the integral<br />
€<br />
E equal to the average annual electricity consumption per household in state i, and<br />
then solving for<br />
€<br />
A i , as follows:<br />
€<br />
19 After efficiency losses.<br />
365d i<br />
∫<br />
elec<br />
V2 = Wi<br />
V1 wind wind<br />
(V )Ti (V )dV<br />
38
Methodology of Cost Comparison<br />
However, in practice, consumers in the market cannot specify their rotor<br />
swept area to a precise decimal unless they order a customized wind turbine, which<br />
is unlikely. To address this, the MATLAB code in Appendix A-‐4 returns the matrix<br />
EnergyProduced, which lists, by state, annual electricity output from a range of<br />
commercially available wind turbine sizes. Because wind turbines are usually<br />
manufactured and sold with no smaller than one-‐half meter increments in rotor<br />
diameter, the matrix simulates the real-‐life process of a consumer selecting the wind<br />
turbine that most closely meets, but probably does not exactly meet, his or her<br />
household’s electricity need.<br />
In North Dakota, for example, a 7-‐meter diameter wind turbine (with a 38.48<br />
m 2 swept area) is the size that most closely meets the average North Dakota home’s<br />
electricity needs. Inputting 38.48 m 2 for<br />
A NorthDakota , the W(V)T(V) function for North<br />
Dakota is shown in Figure 11. 20 The <strong>final</strong> step is to compute the integral<br />
wind<br />
E annual,ND<br />
€<br />
from the cut-‐in speed (3 m/s) to the cut-‐out speed (20 m/s). For North Dakota, the<br />
EnergyPerYearND integration returns 13,070 kWh produced€ per year, which is<br />
approximately equal to the 12,936 kWh consumed per year by the average single-‐<br />
family home in North Dakota, as intended. This method is repeated for all fifty-‐one<br />
states.<br />
In the wind turbine industry, turbines are typically advertised by their power<br />
rating, as distinct from their effective power output. The effective power output<br />
formula used above yields a realistic measure of the power a consumer can expect<br />
20 The accompanying MATLAB code to produce this plot is included in Appendix A-‐4.<br />
39
Figure 11. W(V)T(V) Function for North Dakota<br />
Methodology of Cost Comparison<br />
from a wind turbine of a certain size. The advertised power rating, on the other<br />
hand, is essentially an overstatement of the turbine’s realistic production;<br />
troublingly, there are no standards to which turbine manufacturers must comply<br />
regarding the wind speeds they use in their power rating calculations. Nor do<br />
turbine manufacturers account for generator and gearbox efficiency, both of which<br />
lower the expected power output of a wind turbine. Instead, turbine manufacturers<br />
use a more “ideal” version of the W(V) formula:<br />
wind<br />
0.5⋅ρ wind air ⋅A i ⋅ Cperf ⋅V<br />
Power Rating = W rating,i = 3<br />
1000<br />
where all variables are defined as before, except that V is set equal to 10 meters per<br />
second (m/s),<br />
€<br />
a wind speed in the upper quartile for most regional wind<br />
distributions. Turbine manufacturers use a high wind speed—sometimes even<br />
higher than 10 m/s—to advertise the power their turbines are capable of producing,<br />
40
€<br />
€<br />
Methodology of Cost Comparison<br />
but not necessarily the power the turbines achieve frequently throughout the day.<br />
Power ratings become relevant in the next section because turbine prices are<br />
usually set according to the manufacturer’s power rating despite the lack of explicit<br />
industry-‐wide standards.<br />
Appendix A-‐3 provides a listing of wind classes, corresponding annual mean<br />
wind speeds, turbine rotor diameters, turbine power ratings required to meet<br />
electricity need, and integrations of<br />
wind<br />
E annual,i<br />
2.4.5 Installation and Maintenance Costs<br />
for all of the states.<br />
€<br />
Similar to solar energy, the greatest expense associated with wind energy is<br />
the up-‐front capital cost of the technology. Also like solar energy, the cost of a wind<br />
turbine installation is directly proportional to the wattage of the installed system.<br />
The one-‐time installation cost for a wind turbine is represented by the equation<br />
where<br />
wind wind wind<br />
C install,i = W rating,i⋅<br />
c install<br />
wind<br />
C install,i = average cost of installing a residential wind turbine in state i ($)<br />
€<br />
wind<br />
c install<br />
= average installation cost of the turbine per kilowatt-‐hour ($/kW)<br />
wind<br />
W rating,i = the kilowatt rating of the wind turbine by its manufacturer (kW)<br />
While<br />
wind<br />
c install can vary significantly depending on the scale of the project, the<br />
€<br />
average cost in 2009 for residential-‐sized wind installations was $4,000 per kilowatt<br />
[63]. € 21 (This compares favorably to residential PV panels, which are installed for<br />
$7,000 per kilowatt.) Most homeowners will need wind turbines of at least five<br />
kilowatts in order to provide a sufficient amount of electricity to their homes; this<br />
21 Prices range from $1,000 per kilowatt for utility-‐scale installations to $5,000 per kilowatt for very<br />
small wind installations.<br />
41
€<br />
Methodology of Cost Comparison<br />
puts the approximate lower bound of a wind turbine installation at $20,000, which,<br />
for the average homeowner, is a hefty upfront payment no matter its benefits.<br />
The present value of all maintenance costs for the residential turbine is<br />
modeled in the same way as maintenance costs for a PV module. That is,<br />
where, as before,<br />
wind<br />
wind (0.02 ⋅ C install,i)<br />
1<br />
C mntc,i = 1−<br />
r (1+ r) −n<br />
⎡⎡ ⎤⎤<br />
⎢⎢ ⎥⎥<br />
⎣⎣ ⎦⎦<br />
wind €<br />
= present value of all maintenance costs over lifetime of the wind<br />
C mntc,i<br />
turbine in state i ($)<br />
r = interest rate (assume real interest rate of 2%)<br />
n = lifetime of the wind turbine (assume 20 years)<br />
€<br />
Combining the installation and maintenance costs, the average total lifetime cost in<br />
€<br />
dollars of the wind turbine in state i is represented by:<br />
€<br />
where<br />
wind wind € wind<br />
, C install,i,<br />
C mntc,i ≥ 0<br />
C total,i<br />
wind wind wind wind<br />
C total,i = C install,i(1−<br />
β ) + C mntc,i<br />
β wind = federal investment tax credit for residential wind turbines, 0 ≤ β wind ≤1<br />
A notable difference between the total costs by state of the solar electric<br />
€<br />
€<br />
versus the wind electric systems is, interestingly enough, symbolic of the difference<br />
between the sun and wind as natural resources: the sun, which shines in all states<br />
indiscriminately (albeit with varying levels of irradiation), gives rise to total solar<br />
electric costs which are relatively consistent around a nationwide mean. The wind,<br />
on the other hand, is distributed much less evenly across the states, resulting in<br />
42
€<br />
Methodology of Cost Comparison<br />
wide disparities in wind electricity costs. As an example, a wind turbine can be<br />
installed for as little as $14,852 in California, a Class 3 wind state—yet a wind<br />
turbine producing the same amount of electrical output per year would cost $27,617<br />
in Connecticut, a Class 2 wind state. 22<br />
Perhaps coincidentally, in addition to having very little wind as a resource,<br />
Class 1 states tend to consume more electricity per year than the average state. The<br />
combination of these two factors drives wind energy costs up considerably. Clearly,<br />
there are certain states—like Alabama, Georgia, and Kentucky—that are unlikely<br />
candidates for wind energy, absent heavy government subsidies or a dramatic<br />
reduction in technology costs.<br />
2.4.6 Overall Price of Wind Electricity in this Model<br />
Having computed the cost and energy generation data for each state, the<br />
pieces are now put together to arrive at the end result. The overall price per<br />
kilowatt-‐hour of electricity generated by the wind turbine in state i is:<br />
where<br />
p i<br />
p i<br />
wind<br />
wind C total,i<br />
= wind<br />
E total,i<br />
= C wind wind wind<br />
install,i(1<br />
− β ) + C mntc,i<br />
V2 wind wind<br />
n Wi (V )Ti (V )dV<br />
∫<br />
V 1<br />
wind<br />
= € overall price per kilowatt-‐hour of electricity that consumers will<br />
pay over lifespan of the wind turbine in state i ($/kWh),<br />
€<br />
wind<br />
p i ≥ 0<br />
22 The cost disparity is solely due to the difference in the wind resource in California and<br />
Connecticut. California, which has a lot of wind, will generate more electricity per wind turbine than<br />
other states. To compensate for the lesser wind resource, consumers in Connecticut must install<br />
larger wind turbines to produce the same amount of energy as consumers in California.<br />
43
Methodology of Cost Comparison<br />
One can see that the wind calculations follow a similar form to the solar<br />
calculations in Section 2.3. Likewise, the wind calculations yield the same intuitive<br />
results as the solar calculations. States with the greatest wind energy potential (per<br />
Table 5) have the lowest overall wind-‐generated electricity prices (per Table 6), and<br />
vice versa. The figures in Table 6 demonstrate that wind energy tends to be quite<br />
polarized: wind-‐generated electricity is so effective in some states that it is cost-‐<br />
competitive with fossil fuels already, whereas in other states wind-‐generated<br />
electricity is more than twenty times the price of retail electricity. In the latter<br />
states, consumers must build enormous wind turbines in order to catch the limited<br />
energy available in the wind. The expense is far from recouped, even over a twenty-‐<br />
year-‐plus useful life of a wind turbine.<br />
State-‐by-‐state calculations for installation costs, maintenance costs, total<br />
costs, and overall per-‐kilowatt-‐hour prices are listed in Appendix A-‐3.<br />
2.4.7 Government Incentives<br />
Table 6. Overall Cost of Wind-‐Generated Electricity<br />
States with highest wind<br />
electricity prices<br />
($/kWh)<br />
States with lowest wind<br />
electricity prices<br />
($/kWh)<br />
Alabama, 2.12 Montana, 0.10<br />
Kentucky, 2.12 Idaho, 0.11<br />
Louisiana, 2.12 North Dakota, 0.12<br />
Mississippi, 2.12 Nevada, 0.12<br />
Florida, 2.12 Wyoming, 0.12<br />
Unlike solar energy, wind energy has achieved “grid parity,” or cost<br />
competitiveness with fossil fuels, in some states without the help of a tax incentive.<br />
44
Methodology of Cost Comparison<br />
However, for the large number of states where wind energy is on the cusp of<br />
reaching grid parity, a tax credit can move the needle. Indeed, wind energy installed<br />
capacity has been growing at a faster and faster rate as wind turbines become more<br />
economical. For example, in a state like Maine, which has a higher-‐than-‐average<br />
retail electricity price of 16.5¢ per kilowatt-‐hour, a 30% tax credit brings down the<br />
price of wind-‐generated electricity from 17.7¢ to 13.7¢ per kilowatt-‐hour, allowing<br />
the renewable source to beat the retail price.<br />
2.5 Retail Electricity<br />
Because retail electricity data is readily available on the Energy Information<br />
Administration website, there is no need to build estimates from the ground up à la<br />
solar and wind calculations. For reference, the average retail prices of electricity in<br />
2008 for all fifty-‐one states has been reproduced in Appendix A-‐2. What will<br />
henceforth be called the “baseline” price of electricity is $0.11 per kilowatt-‐hour, the<br />
weighted average cost of retail electricity for residential consumers in the U.S. in<br />
2008. The median retail electricity price in 2008 was $0.09 per kilowatt-‐hour,<br />
suggesting that some states with larger weights have higher electricity prices.<br />
California and New York, which have two of the highest retail electricity prices<br />
nationwide, are prime examples.<br />
2.5.1 Regional Cost Discrepancies<br />
Just as solar and wind energy have regional cost disparities, so too does the<br />
price of retail electricity vary with region. Areas of the country with coal deposits,<br />
like Wyoming, Kentucky, and West Virginia, tend to have cheaper retail electricity<br />
45
Methodology of Cost Comparison<br />
on average. Coal is, after all, the cheapest fossil fuel, and it makes up almost half of<br />
retail electricity generation in the U.S. Table 7 shows that all but three of the top ten<br />
coal-‐producing states have retail electricity prices below the national median.<br />
As a region, the Northwest—primarily Idaho, Washington, Oregon—claims<br />
the cheapest electric rates in the nation. Unlike the rest of the country, a significant<br />
portion of electricity in the Northwest comes from hydropower thanks to the<br />
region’s numerous dams. In contrast, states in the Northeast typically pay the<br />
highest electrical bills. Of the ten most expensive electrical rates in the country, all<br />
but three (Hawaii, Alaska, and California) belong to Northeastern states, as Table 8<br />
shows.<br />
State<br />
Table 7. Electricity Prices and Coal Production [67] [56]<br />
Percent of<br />
Total U.S. Coal<br />
Production<br />
Retail<br />
Electricity Price<br />
(cents/kWh)<br />
Rank in Price of<br />
Retail Electricity<br />
(1 = cheapest)<br />
Montana 25.4 8.77 18<br />
Illinois 16.5 10.12 31<br />
Wyoming 14.4 7.75 8<br />
West Virginia 8 6.73 2<br />
Kentucky 6.3 7.34 5<br />
Pennsylvania 6.1 10.95 34<br />
Ohio 4 9.57 29<br />
Colorado 3.6 9.25 23<br />
Texas 2.7 12.34 39<br />
Indiana 2.1 8.26 14<br />
Though there is some debate as to why the Northeast experiences higher<br />
retail prices, some argue that it stems from “a deliberate policy of favoring cleaner<br />
(and more expensive) sources of electricity” [68]. Others blame the population<br />
46
Methodology of Cost Comparison<br />
density of the region, suggesting that the rates are excessive due to transmission<br />
congestion [68]. Regardless, there is no question that there are marked price<br />
discrepancies from state to state.<br />
Table 8. Most Expensive Retail<br />
Electricity Prices, By State (2008) [56]<br />
State<br />
2.6 Price Comparison of Electricity Sources<br />
Retail<br />
Electricity Price<br />
(cents/kWh)<br />
Hawaii 24.12<br />
Connecticut 19.11<br />
New York 17.10<br />
Maine 16.52<br />
Massachusetts 16.23<br />
Alaska 15.18<br />
New Hampshire 14.88<br />
California 14.42<br />
Vermont 14.15<br />
New Jersey 14.14<br />
The cost methodology introduced in this chapter provides a framework for<br />
building a data set not otherwise available for analysis and manipulation. As<br />
frontier technologies, wind turbines and solar PVs simply do not have nearly as<br />
much compiled data available to the public as do traditional sources of energy. But<br />
by boiling down solar electricity, wind electricity, and retail electricity to a<br />
comparable measure—the “overall” price of electricity per kilowatt-‐hour—this<br />
methodology serves as a springboard for further analysis. A recurring theme<br />
throughout the forthcoming chapters is that of exploiting cost disparities between<br />
47
Methodology of Cost Comparison<br />
regions for the good of both society and the environment. The comparable price<br />
metric is crucial in that it is the single most important determinant of market forces,<br />
which will ultimately accept or reject solar and wind technologies.<br />
48
3. Applying Government Forces to the Electricity Market<br />
In Chapter 2, electricity prices from different sources were calculated in<br />
the absence of government intervention. But in the real world,<br />
governments can enact legislation to manipulate consumer decision making for the<br />
good of society, and they do so often. The commonly cited justification for wielding<br />
government power in such a way is “market failure,” or the inability of a market to<br />
allocate resources efficiently. Markets left to their own devices may ignore<br />
externalities imposed on society at large—like pollution—by free and private<br />
economic activity. Following that line of thought, the argument can be made that<br />
energy in its various forms is currently mispriced because social costs are not built<br />
into market prices. In the context of this energy problem, the two main tactics used
Applying Government Forces to the Electricity Market<br />
to address the mispricing of energy are the carbon tax (explicit or implicit 23 ) and the<br />
tax credit (one of many forms of a subsidy). Both are powerful levers with which<br />
the government can alter market prices.<br />
Such influence in the electricity market is particularly meaningful due to the<br />
price inelasticity of electricity; that is to say, as the price of the electricity increases<br />
or decreases, the quantity consumed remains relatively constant. Consumers’<br />
inability to live without electricity and producers’ price monopoly in some states<br />
(which leaves consumers with no cheaper substitutes) are both causes of the<br />
inelasticity of demand for electricity. In the case of the California Electricity Crisis in<br />
2001, upticks in the per-‐kilowatt-‐hour price of electricity prompted a call for<br />
government intervention from an otherwise helpless public [64]. In brief,<br />
Americans are keenly aware of the price of electricity due to its necessity.<br />
The price-‐altering effects of government incentives, therefore, are crucial to<br />
the future of renewable energy. As a pair, the carbon tax and the renewable tax<br />
credit motivate the same directional shift: transitioning from fossil fuels to “clean”<br />
energy. Yet they do so in opposite ways (by penalizing or rewarding consumers)<br />
and with arguably different rates of success. Notwithstanding the philosophical or<br />
political underpinnings of legislators’ preferences for one method to the other, this<br />
chapter will examine the impact of the carbon tax and renewable tax credit in<br />
conjunction as well as the isolated impact of each on its own.<br />
23 An explicit carbon tax is a levy on an emitted ton of carbon dioxide regardless of its source. An<br />
implicit carbon tax could exist in a cap-‐and-‐trade framework, whereby the government distributes a<br />
certain number of carbon credits to power plants and allows the plants to trade the credits amongst<br />
themselves, resulting in a market-‐driven price for one ton of carbon dioxide emissions.<br />
50
€<br />
€<br />
3.1 The Quantitative Model<br />
Applying Government Forces to the Electricity Market<br />
This model assumes that three different sources of electricity are available to<br />
every household in the United States: the local utility, a residential PV module, and a<br />
residential wind turbine. It is assumed that the three different sources are perfect<br />
substitutes, meaning that there is no differentiation in quality among them.<br />
Consequently, consumers will always prefer the least expensive option. Chapter 4<br />
will account for consumer behavior that departs from this assumption.<br />
3.1.1 Decision Variables<br />
In this model, the government is the decision-‐making agent. The degree to<br />
which it manipulates prices in the electricity market will influence consumers’<br />
choices, also known as the “market response.” The three major decisions made by<br />
the government in this model are represented by<br />
c carbon = the “cost of carbon,” a government-‐enforced tax on emissions of<br />
carbon dioxide ($/ton CO2)<br />
β wind = federal tax credit for wind installations<br />
β solar = federal tax credit for solar installations<br />
The carbon tax might more appropriately be called the “cost of carbon<br />
€<br />
dioxide,” because the amount of tax owed is based on tons of carbon dioxide<br />
emitted, not carbon alone. Yet the media and politicians have colloquialized the<br />
phrase “cost of carbon,” so it will be used as it is intended.<br />
Even though the Residential Renewable Energy Tax Credit is currently<br />
designed to provide equivalent incentives for wind and solar energy, the solar and<br />
51
€<br />
€<br />
Applying Government Forces to the Electricity Market<br />
wind tax credits are treated as separate decisions here should the government<br />
decide to disjoin them.<br />
3.1.2 Market Response<br />
Consumers are also decision-‐making agents in the sense that they must<br />
choose a preferred source of electricity. But because their decisions are greatly<br />
influenced by the actions of the government, consumer decisions are relegated to<br />
market response variables rather than decision variables.<br />
Prices are calculated at a state-‐wide level, so the model predicts that all<br />
households within a state will respond in the same way to the relative pricing of<br />
retail, wind, and solar electricity. In aggregate, the market response variables are<br />
represented by<br />
retail carbon<br />
µ i (c ) = the proportion of the electricity portfolio allocated to retail<br />
electricity in state i<br />
wind wind<br />
µ i (β ) = the proportion of the electricity portfolio allocated to wind<br />
electricity in state i<br />
solar solar<br />
µ i (β ) = the proportion of the electricity portfolio allocated to solar<br />
electricity in state i<br />
€<br />
Treating retail, wind, and solar electricity as perfect substitutes would lead to 100%<br />
of households within a given state selecting the cheapest source of electricity.<br />
However, Section 3.1.4 complicates this result by incorporating variability of solar<br />
electricity prices into the model.<br />
Ultimately,<br />
€<br />
retail wind<br />
µ i , µi , and<br />
€<br />
solar<br />
µ i are determined by the relationship of the<br />
prices of retail, wind, and solar electricity. Indirectly, then, each of the market<br />
52
€<br />
€<br />
€<br />
€<br />
Applying Government Forces to the Electricity Market<br />
response variables is dependent on all three decisions: the carbon tax, the wind<br />
turbine subsidy, and the solar PV subsidy. For clean notation purposes, the market<br />
response variables are written as functions of the government decisions that most<br />
contribute to each of the variables. For retail electricity, that is the carbon tax; for<br />
wind electricity, the wind turbine subsidy; and for solar electricity, the solar PV<br />
subsidy. The method to calculate each of the market response variables is<br />
developed in Section 3.1.4.<br />
3.1.3 The Cost Function and Constraints<br />
The cost function for the residential electricity price in state i is given by<br />
€<br />
F( c carbon , β wind , β solar ) =<br />
wind wind wind wind solar solar<br />
µ i (β ) ⋅ p i (β ) + µi (β ) ⋅ ˆ<br />
such that<br />
€<br />
and where<br />
€<br />
c carbon ≥ 0<br />
1 ≥ β wind ≥ 0<br />
1 ≥ β solar ≥ 0<br />
wind wind wind<br />
wind wind C install,i(1−<br />
β ) + C mntc,i<br />
p i (β ) = wind<br />
E total,i<br />
retail cabon<br />
p i (c ) = p pretax,i<br />
solar solar<br />
p i (β ) + µi<br />
retail carbon retail cabon<br />
(c ) ⋅ p i (c )<br />
= the average wind electricity price in state i ($/kWh)<br />
retail + c carbon<br />
CO2 mi = the average retail electricity price in state i after the<br />
implementation of the carbon tax ($/kWh)<br />
53
€<br />
€<br />
where<br />
Applying Government Forces to the Electricity Market<br />
CO2 mi = the ratio of electricity produced in state i to the<br />
output of CO2 from burning of fossil fuels to<br />
generate electricity in state i (kWh/ton CO2) [65]<br />
solar solar<br />
p ˆ i (β ) = the “achievable” solar electricity price in state i based on a<br />
Note that<br />
solar<br />
p i<br />
normal distribution ($/kWh)<br />
solar<br />
p ˆ i is used instead of<br />
solar<br />
p i , the average price of solar electricity in<br />
state i. If were used, the optimal solution would lead to the complete exclusion<br />
€<br />
€<br />
of solar power; households would choose between the other two options because,<br />
€<br />
when comparing deterministic average prices, either wind or retail electricity is<br />
cheaper than solar electricity in every state. However, it is not necessarily the case<br />
that wind or retail electricity is always cheaper than solar electricity. There are<br />
myriad factors affecting renewable electricity inputs that influence the ultimate<br />
price a household pays. These sources of variability naturally lend themselves to a<br />
distribution for the price of renewable electricity rather than a deterministic<br />
average value. The lower tail on a solar price distribution in state i may match or<br />
beat the average price of wind electricity in the state; hence, to exclude solar<br />
electricity from the optimal solution would be misleading. Section 3.1.4 discusses<br />
the method for overcoming this problem.<br />
3.1.4 Incorporating Variability in Solar Costs<br />
Wind and solar electricity pricing is something of a curiosity in the United<br />
States. Note that in Figure 12, the weighted average price of wind electricity in the<br />
U.S. far exceeds the weighted average price of solar electricity. Harkening back to<br />
54
Applying Government Forces to the Electricity Market<br />
the data in Chapter 2, it is apparent that the small group of states with very<br />
expensive wind electricity skew the data. To a smaller degree, the same effect<br />
influences solar electricity data. Figure 13 24 provides a more realistic price<br />
comparison: once the states with impractically high prices for wind and solar<br />
electricity are excluded, the weighted average prices drop significantly—and the<br />
positions of wind and solar energy flip, with average wind electricity prices beating<br />
average solar electricity prices in all but one scenario. 25 Evidently, it would require<br />
an aggressive tax credit for the average price of solar electricity to match that of<br />
wind electricity with no tax credit.<br />
Figure 12. Price Comparison of Electricity Sources<br />
24 The * on Figure 13 indicates that the graph does not represent a true weighted average national<br />
price, but rather a weighted average price that has been “cleaned” of impractical states.<br />
25 As seen in Figure 13, the scenario is a 0% tax credit for wind installations combined with a 50%<br />
tax credit for solar installations. This is highly unlikely.<br />
55
Applying Government Forces to the Electricity Market<br />
Incorporating solar PVs into the optimal electricity portfolio is neither<br />
impossible nor impractical, however; modeling solar electricity prices as a<br />
distribution will illustrate as much. There are many dimensions of variability that<br />
might interact to make solar PVs a cheaper option than wind turbines for some<br />
consumers. For instance, an experienced, practical consumer is more likely to<br />
obtain cheaper credit, negotiate a better deal with a PV installation contractor, and<br />
know where to go to purchase inexpensive parts for repair and maintenance. Aside<br />
from market savvy, some consumers will happen to live in towns that have more<br />
peak sun hours per day than their state’s average, making a solar PV panel a<br />
relatively wiser investment. Others might require smaller PV panels than their<br />
state’s average by virtue of using electricity more conservatively or living in more<br />
energy efficient homes by design.<br />
Figure 13. Price Comparison of Electricity Sources<br />
(excluding upper quartile prices)<br />
56
Applying Government Forces to the Electricity Market<br />
These factors illustrate that there is not a single estimated price for solar<br />
electricity, but rather a range of costs that reflects individual practicality in addition<br />
to attributes of the physical environment. To reflect the noise in these factors,<br />
several variables in the<br />
p i<br />
solar<br />
solar C total,i<br />
=<br />
solar<br />
E total,i<br />
calculation are treated as normal<br />
distributions. 26 They are the daily electricity consumption of a single-‐family home,<br />
€<br />
the peak sun hours per day, the installation cost of a solar module per kilowatt, the<br />
useful lifetime of a solar module, and the present value of all future maintenance<br />
costs, as follows:<br />
€<br />
€<br />
€<br />
d ˆ elec elec 2<br />
i ~ N(d i , 4 )<br />
k ˆ solar solar 2<br />
i ~ N(k i , 0.75 )<br />
solar solar 2<br />
c ˆ install ~ N(c install,<br />
1000 )<br />
ˆ<br />
n solar ~ N(n solar , 5 2 )<br />
C ˆ solar solar 2<br />
mntc,i ~ N(C mntc,i,<br />
2000 )<br />
The variables included<br />
€<br />
in the model are deemed to be the most significant<br />
contributors to variability € in solar electricity prices within a state. Yet there are<br />
numerous other variables that could affect the price per kilowatt-‐hour of the PV<br />
module over the course of its life. The following factors also play a role in the<br />
efficiency of the PV module and consequential pricing of solar electricity [20]:<br />
€<br />
• The orientation of the PV module toward the sun – the optimal<br />
orientation in locations above the equator is southward<br />
• The inclination of the roof – the average optimal angle is 35 degrees<br />
26 (1− β<br />
As a reminder, solar<br />
p i =<br />
solar solar<br />
solar solar 0.02c install,i 1<br />
)(W i c install)<br />
+ 1−<br />
r (1+ r) −n<br />
⎡⎡ ⎤⎤<br />
⎢⎢ ⎥⎥<br />
⎣⎣ ⎦⎦ is the expanded form of<br />
solar solar<br />
0.87W i k i ⋅ 365n<br />
€<br />
p i<br />
solar<br />
solar C total,i<br />
=<br />
solar<br />
E total,i<br />
57
€<br />
Applying Government Forces to the Electricity Market<br />
• The PV technology itself – how advanced and modern it is<br />
However, the encumbrance of incorporating every possible source of price<br />
variability prohibits the inclusion of less impactful factors. The five aforementioned<br />
variables will suffice to meet the needs of this analysis.<br />
Now, finding a threshold value at which solar costs compete with wind costs<br />
is a matter of comparing the normal distribution of the solar price<br />
deterministic wind price<br />
€<br />
wind<br />
p i . More formally, one solves for<br />
solar wind 1<br />
fi ( p i ) = solar<br />
σi Φ p ⎛⎛<br />
i<br />
⎜⎜<br />
⎝⎝<br />
€<br />
€<br />
⎞⎞<br />
⎟⎟<br />
⎠⎠<br />
wind solar<br />
− µi<br />
solar<br />
σi solar<br />
fi in<br />
solar<br />
p ˆ i to the<br />
which is the z-‐score 27 of the average wind cost in state i on the solar price<br />
€<br />
distribution for state i. The z-‐score is then converted into a percentile that<br />
represents the percentage of state i’s electricity portfolio that can be transferred<br />
from wind electricity to solar electricity at no additional cost. The consumers who<br />
are able to achieve lower-‐tail solar prices probably have a number of the normally<br />
distributed variables working to their advantage.<br />
New Mexico will serve as an example case of this method. The means of the<br />
normally distributed solar price inputs in New Mexico are<br />
solar<br />
k NM = 6.77 hours,<br />
solar<br />
c install = $7,000,<br />
n solar = 20 years, and<br />
elec<br />
d NM = 21 kWh,<br />
solar<br />
C mntc,i = $11,514.<br />
€<br />
The MATLAB code in Appendix A-‐5 plots the solar electricity price distribution for<br />
€<br />
€<br />
New Mexico based on the means and variances€ of the input variables. The<br />
distribution is shown in Figure 14. The vertical red line and blue line mark the<br />
average price of wind and retail electricity in New Mexico, respectively. This visual<br />
27 A measure of the distance in standard deviations of a sample from the mean.<br />
58
Applying Government Forces to the Electricity Market<br />
demonstrates that solar electricity can and should be included in the state’s<br />
electricity portfolio from an economic point of view so long as the households<br />
utilizing solar electricity are beneath a threshold percentile on the price<br />
distribution.<br />
Figure 14. Distribution of Solar Electricity Price<br />
Generalizing this method across all of the states, the<br />
SolarAllocationByState m-‐file (included in Appendix A-‐6) returns two<br />
vectors that give the percentiles of deterministic wind and retail electricity prices on<br />
the solar price distribution for each state. A percentile of “1” in either vector<br />
suggests that the entire solar electricity price distribution falls below the average<br />
price of wind or retail electricity, depending on the vector.<br />
The states returning percentiles of 1 in the wind vector are those with decent<br />
solar energy potential but little wind energy potential, like Alabama, Georgia, and<br />
South Carolina. (Hence, wind electricity prices fall on the upper-‐tail of the solar<br />
59
Applying Government Forces to the Electricity Market<br />
price distribution.) The states returning high percentiles in the retail vector are<br />
those with decent solar energy potential or inordinately expensive retail electricity,<br />
or some combination of both. (The higher the deterministic retail price, the higher<br />
its percentile on the solar distribution.) Such states are California, Hawaii, Arizona,<br />
North Carolina, Tennessee, New York, and Louisiana. Appendix A-‐6 includes a<br />
comprehensive listing of all states and the corresponding wind and retail<br />
percentiles on their respective solar price distributions.<br />
Incorporating solar variability into the cost function, the optimal solution is<br />
no longer a binary allocation of “0” or “1” to a single source in each state, but rather<br />
a division of allocation between two energy sources (solar and retail or solar and<br />
wind). One limitation of this model is that because wind and retail prices<br />
are treated as deterministic values rather than as distributions, the model precludes<br />
the possibility of states choosing a blend of wind and retail electricity as their<br />
electricity sources. Table 9 provides a snapshot of optimal allocations in each state.<br />
60
State<br />
%<br />
Retail<br />
Applying Government Forces to the Electricity Market<br />
Table 9. Optimal Electricity Allocations by State<br />
(No Carbon Tax and No Tax Credit)<br />
%<br />
Wind<br />
%<br />
Solar<br />
State<br />
%<br />
Retail<br />
%<br />
Wind<br />
%<br />
Solar<br />
.AL 97.8 0 2.2 .MT 0 90.6 9.4<br />
.AK 0 91.1 8.9 .NE 98.1 0 1.9<br />
.AZ 91.3 0 8.7 .NV 0 83 17.1<br />
.AR 96.9 0 3.1 .NH 0 89 11<br />
.CA 0 83.3 16.7 .NJ 0 57.9 42.1<br />
.CO 93.7 0 6.3 .NM 88.5 0 11.5<br />
.CT 0 80.3 19.7 .NY 0 86.2 13.8<br />
.DE 96.6 0 3.4 .NC 93.2 0 6.8<br />
.DC 97.5 0 2.5 .ND 98.3 0 1.7<br />
.FL 95.3 0 4.7 .OH 90.1 0 9.9<br />
.GA 97.7 0 2.3 .OK 96.7 0 3.3<br />
.HI 0 0 100 .OR 97.8 0 2.2<br />
.ID 97.9 0 2.1 .PA 97.2 0 2.8<br />
.IL 97.9 0 2.2 .RI 0 90.3 9.7<br />
.IN 98.1 0 1.9 .SC 95.8 0 4.2<br />
.IA 97.1 0 2.9 .SD 96.9 0 3.1<br />
.KS 97.4 0 2.7 .TN 97.3 0 2.7<br />
.KY 98.4 0 1.6 .TX 92.2 0 7.8<br />
.LA 96.0 0 4.0 .UT 97.6 0 2.4<br />
.ME 0 77.3 22.7 .VT 0 90.1 9.9<br />
.MD 96.1 0 3.9 .VA 96.4 0 3.6<br />
.MA 0 83.7 16.3 .WA 97.0 0 3.0<br />
.MI 96.2 0 3.8 .WV 98.3 0 1.7<br />
.MN 96.2 0 3.8 .WI 94.6 0 5.4<br />
.MS 98.1 0 1.9 .WY 92.3 0 7.7<br />
.MO 97.9 0 2.1<br />
61
Applying Government Forces to the Electricity Market<br />
3.2 The Impact of Government Incentives on Electricity Allocation<br />
To minimize the cost function in Section 3.1, households will prefer<br />
whichever source of electricity is cheapest for them. The government, then, is<br />
charged with the task of understanding how potential policies will affect the price of<br />
electricity from different sources. Using the methodology developed thus far, one<br />
can project how the electricity portfolio allocations as well as the electricity prices<br />
will respond to varying levels of government intervention.<br />
3.2.1 Impact of the Carbon Tax on Allocation<br />
First, it is important to note that while the maximum carbon tax in this study<br />
is $100 per ton CO2, no serious proposal to Congress has yet exceeded $13.70 per<br />
ton CO2. It is interesting as an academic exercise to explore hypothetical scenarios<br />
with a carbon tax above $13.70, but the likelihood of a bill with a high carbon tax<br />
making its way through Congress in the near term is slim.<br />
That said, a number of conclusions can be drawn from Figures 15-‐17 on the<br />
following page. These illustrations show how the optimal nationwide electricity mix<br />
changes according to a varying carbon tax. Additionally, the three graphs represent<br />
three different levels of the renewable tax credit: a zero tax credit, a moderate tax<br />
credit (30%), and an aggressive tax credit (50%). Figures 15-‐17 support the<br />
expectation that as the carbon tax and renewable tax credit increase, more<br />
consumers will opt for renewable energy sources.<br />
Yet there is a more nuanced interpretation of these figures that may have<br />
implications for policy decisions. As the illustrations plainly show, an increasing<br />
carbon tax causes a steady decline in the national allocation to retail electricity.<br />
62
Applying Government Forces to the Electricity Market<br />
Figure 15<br />
Figure 16<br />
Figure 17<br />
63
Applying Government Forces to the Electricity Market<br />
Households will begin switching to clean sources as the price of carbon-‐based retail<br />
electricity rises above that of renewable electricity. But the implementation of a tax<br />
begs a question about trade-‐offs: what incremental social benefit to the country (in<br />
the form of less pollution and greater national security) justifies a palpable increase<br />
in retail prices? Moreover, what target electricity mix should the government hope<br />
to achieve by implementing a carbon tax of $X per ton? Figures 15-‐17 hint at the<br />
answers to these questions, which will be more fully developed in Chapter 4.<br />
In the first scenario (no tax credit), the fact that less than half of the country<br />
will use renewable electricity even with a $90 carbon tax (see Figure 15) suggests<br />
that the carbon tax, at some level, may backfire: imposing a tremendous tax burden<br />
of $90 per ton on consumers is only sufficient to induce a large minority of<br />
households to switch electricity sources. It is very likely that, in this scenario, a high<br />
carbon tax does more economic harm than societal good. Finding the point at which<br />
the economic burden justifies the social benefit is crucial to designing a policy<br />
solution. For now, it is sufficient to note that the tax, while effective in inducing<br />
consumer behavior, must be moderated lest the burden outweigh the benefit.<br />
3.2.2 Impact of the Renewable Tax Credit on Allocation<br />
Figures 15-‐17 indicate that the renewable tax credit is perhaps even more<br />
influential than the carbon tax as a policy tool. To investigate this further, Figures<br />
18 and 19 hold the carbon tax constant, isolating the change induced by the tax<br />
credit. Assuming the government continues on its current path of providing the<br />
same tax credit for all renewable technology (<br />
€<br />
β solar = β wind ), Figures 18 and 19<br />
present the projected national electricity mix under the circumstances of a<br />
64
Applying Government Forces to the Electricity Market<br />
Figure 18<br />
Figure 19<br />
65
Applying Government Forces to the Electricity Market<br />
moderate and aggressive tax credit and no tax credit at all. To add an additional<br />
layer of change, the first graph represents a scenario with no carbon tax, and the<br />
second a scenario with a $13.70 carbon tax. 28<br />
As a whole, there is a steady decline in the retail allocation as the renewable<br />
tax credit is increased. Again, the point of interest is where the economic burden,<br />
this time on the government, justifies the social benefit of more renewable energy.<br />
As opposed to the carbon tax, which encumbers consumers with higher prices, the<br />
tax credit diminishes the government’s spending power because each claimed tax<br />
credit represents a loss of tax revenue that the government would otherwise collect.<br />
A high tax credit for renewable energy could deplete tax revenue to the point that<br />
cutbacks are made to other programs. Hence, there is a need to reconcile the<br />
conflicting aims of conserving finances and encouraging investment in renewable<br />
energy technology. Chapter 4 will quantify this problem from the perspective of<br />
society as a whole.<br />
As a side note, Figure 18 shows a 22% allocation to wind electricity under a<br />
30% tax credit, which suggests that the U.S. government should be able to meet its<br />
goal of “25% Wind Energy by 2030” by continuing current practices. Given enough<br />
time to respond to the historically low prices in the wind industry right now,<br />
consumers in the market should reach the optimal electricity mix in the long term.<br />
Over the next decade, wind electricity prices are projected to decline another 11%,<br />
catalyzing an increase in the wind allocation and bringing it near the target 25%.<br />
28 $13.70 comes from President Obama’s proposed cap-‐and-‐trade scheme, which has yet to be<br />
approved. Analysts have predicted that the carbon allowances (i.e., the right to emit one ton of<br />
carbon dioxide) would be traded at a price of $13.70 by 2012 under the scheme [66].<br />
66
Applying Government Forces to the Electricity Market<br />
3.3 The Impact of Government Incentives on Electricity Prices<br />
While it is important to understand how government intervention will<br />
impact the national electricity mix, it is equally important to determine how<br />
electricity prices change as a result of government intervention. Both the electricity<br />
mix and electricity prices must be considered in order to arrive at a prudent<br />
renewable energy policy.<br />
3.3.1 Background on the Electricity Price-‐Carbon Tax Relationship<br />
Unfortunately, existing scholarly work does not typically account for the<br />
subtleties in average electricity prices’ response to a carbon tax. For example, in a<br />
presentation given as part of the Science, Technology, and Environmental Policy<br />
(STEP) Seminar Series at Princeton University, the relationship between the U.S.<br />
average electricity generation price and the CO2 emissions price (i.e., the “cost of<br />
carbon”) was assumed to be linear. Figure 20 duplicates the illustration used in the<br />
presentation, “Alternative Approaches to CO2 Capture and Storage at Existing Coal<br />
Power Plant Sites” [1]. 2930<br />
29 The legend in Figure 20 contains two other lines that are not relevant to the discussion at hand,<br />
but for the reader’s reference, “Written-‐off PC-‐V plant” refers to a vented plant that produces<br />
pulverized coal, and “PC-‐CCS retrofit” refers to a coal plant retrofitted with CO2 capture and storage<br />
technology.<br />
30 Note that Figure 20 plots the average electricity generation price, which only accounts for 68% of<br />
the U.S. average retail electricity price according to the Energy Information Administration [11]. The<br />
other components of the electricity price are distribution (24%) and transmission (7%) of electricity<br />
[11]. Following those calculations, the U.S. average retail electricity price would be $0.09 per<br />
kilowatt-‐hour based on the $60/MWh generation cost in Figure 20. This average price, while lower<br />
than the $0.11/kWh average price used thus far, is entirely reasonable depending on the year of the<br />
data used to create the graph.<br />
67
Applying Government Forces to the Electricity Market<br />
The assumption of linearity is a faulty one because it neglects the presence of<br />
renewable technology. A linear electricity price-‐carbon tax relationship implies that<br />
the electricity mix in the U.S. is static and that no consumers switch to carbon-‐free<br />
renewables as the price of retail electricity rises. Of course, that assumption is<br />
erroneous, especially in an age when renewable energy is gaining traction in the<br />
marketplace.<br />
Figure 20. Graph used in STEP Seminar [1]<br />
3.3.2 Improvement upon Linearity in the Electricity-‐Carbon Tax Relationship<br />
The plot in Figure 20 is in need of a model predicting how electricity<br />
portfolio allocations change in response to a carbon tax. A dynamic electricity<br />
portfolio is crucial in order to show how the average electricity price changes under<br />
different circumstances. Conveniently, one need only apply the data compiled thus<br />
far in order to improve the average electricity price curve in Figure 20. Rather than<br />
increasing linearly, a more realistic electricity price curve will show that prices level<br />
68
Applying Government Forces to the Electricity Market<br />
Figure 21<br />
Figure 22<br />
69
Applying Government Forces to the Electricity Market<br />
off as the carbon tax increases and as consumers rely more heavily on renewables<br />
instead of conventional retail electricity.<br />
Figures 21-‐23 display more refined electricity price curves than the one used<br />
in the STEP presentation. All three plot the U.S. average electricity price in relation<br />
to a carbon tax, or, equivalently, a “greenhouse gas emissions price,” as it was<br />
expressed in Figure 20. Figure 21 treats the renewable tax credit as a single value<br />
(so β solar = β wind ), whereas Figure 22 and 23 shows how varying the solar and wind<br />
tax credits, respectively, while keeping the other credit constant can influence the<br />
price curve. Figures 21 and 22 reveal a few interesting characteristics of the<br />
electricity price curve, namely<br />
Figure 23<br />
70
Applying Government Forces to the Electricity Market<br />
• The carbon tax exerts a diminishing marginal impact on electricity prices.<br />
The price curves extending outward from the initial value of c carbon = 0<br />
appear to be linear, but their slopes gradually taper off as the carbon tax<br />
€<br />
increases. This result illustrates that as the carbon tax rises, more and more<br />
people rely on renewable energy. An increased allocation to non-‐carbon<br />
renewables leads to an average electricity price that is more “immune” to a<br />
carbon tax. Theoretically, if the carbon tax were high enough, the slope of<br />
the electricity price curve would eventually become zero.<br />
• The nonlinearity of the price curve becomes more pronounced as the tax<br />
credit increases. Figures 21-‐23 illustrate that a higher tax credit for one or<br />
both renewables accelerates the tapering off of the price curve, which is a<br />
natural consequence of more consumers choosing to rely on either wind or<br />
solar or both.<br />
• The electricity price curves representing different tax credits splay outward<br />
as the carbon tax increases, demonstrating that a tax credit and a carbon tax<br />
acting in concert can have a marked effect on the price of electricity.<br />
• The carbon tax may be considered a futile burden at a certain level. This<br />
effect is most clearly seen in the turquoise and purple lines in Figure 22, but<br />
it applies to all scenarios in principle. Once the price curve flattens to a<br />
near-‐zero slope, increasing the carbon tax no longer produces a significant<br />
change in allocation, but it penalizes consumers who continue to use retail<br />
electricity.<br />
71
Applying Government Forces to the Electricity Market<br />
• The price curves in Figure 23 diverge slightly more than the prices curves in<br />
Figure 22, suggesting that the wind credit exerts greater influence over the<br />
price curve than the solar credit. This is consistent with the finding that for<br />
most consumers, it more economical to invest in wind power before solar<br />
power.<br />
3.4 Laying the Groundwork for Policy Optimization<br />
This chapter sought to visually demonstrate the effects of government<br />
intervention on the electricity mix and average electricity price in the United States.<br />
What the graphs reveal in totality is the very wide spectrum of outcomes that could<br />
result from government intervention: depending on the nature of the implemented<br />
policy, the U.S. electricity market could undergo drastic change, maintain the status<br />
quo, or even fall backward if the current Residential Renewable Energy Tax Credit is<br />
rescinded or reduced. Even relatively minor changes—like instituting a carbon tax<br />
of $5, or increasing the tax credit to 35%—could lead hundreds of thousands, if not<br />
millions, of consumers to acquaint themselves with renewable technology.<br />
Having developed a model to predict the optimal electricity mix under<br />
different scenarios, the next step is to complete a more rigorous analysis of the costs<br />
and benefits associated with any given set of carbon tax and tax credit policies. The<br />
improved electricity price curves presented in this chapter will fine-‐tune the cost<br />
estimation to American consumers of higher electricity prices. Likewise, the<br />
projected electricity mixes will facilitate the quantification of social benefits of a<br />
change in the electricity mix, namely reduction in long-‐term damage caused by CO2<br />
72
Applying Government Forces to the Electricity Market<br />
in the atmosphere. The interplay of the positive and negative consequences of<br />
change in the electricity mix will drive the optimal policy solution.<br />
73
4. Optimizing Environmental Tax Policy<br />
Chapter 3 explored the degree to which the U.S. residential electricity<br />
market would respond to carbon taxes and investment tax credits for<br />
renewable technology based on economic considerations alone. This chapter aims<br />
to place that analysis in a broader context, showing how a carbon tax and tax credits<br />
will affect the proverbial “bottom line,” which is, in this case, the benefit or cost—<br />
the profit or loss, so to speak—to the whole of society. The goal is to determine the<br />
carbon tax and tax credit policies that maximize the overall benefit to society, which,<br />
if formulated suitably, will strike a balance between encouragement of clean energy<br />
and spending restraint.
Optimizing Environmental Tax Policy<br />
The method to maximize the benefit to society draws upon foundations in<br />
environmental economics. As environmental economist Dan Phaneuf writes, “Cost-‐<br />
benefit analysis provides an organizational framework for identifying, quantifying,<br />
and comparing the costs and benefits of a proposed policy action” [69]. While the<br />
costs of the proposed policy are usually easily quantifiable in dollar value, the<br />
benefits are less so: there is significant debate as to how, and whether, to place a<br />
dollar value on improved air and water quality and other such “priceless” benefits<br />
arising from environmental policies. Yet the environmental economist is “tasked<br />
with recommending policies that reflect scarcity” of available funds in society,<br />
eradicating the possibility of pursuing “zero pollution objectives” [69]. Instead,<br />
utilizing a cost-‐benefit framework, as environmental economists often do, will<br />
provide practical solutions in the policy arena.<br />
4.1 Structure of the Cost-‐Benefit Analysis in One Time Period<br />
In order to translate the benefit of reduced pollution into dollar form, the<br />
benefit to society is defined as the net savings accrued over time from the energy<br />
policy in place. (Even though the absolute price of electricity will rise in response to<br />
a carbon tax, consumers will also save a certain amount, depending on the social<br />
cost of carbon, for having averted environmental damage by emitting less carbon<br />
dioxide.) Accordingly, if the energy policy were to do more harm than good, the cost<br />
to society would be defined as the net losses accrued over time.<br />
There are three major components of the cost-‐benefit analysis: Government<br />
Net Revenue, Consumer Net Revenue, and Social Benefit from CO2 Reduction. The<br />
75
€<br />
€<br />
Optimizing Environmental Tax Policy<br />
sum of these three components is the net benefit to society of a proposed<br />
environmental tax policy consisting of a carbon tax, renewable tax credits, or both.<br />
Because the burden of the social cost of carbon is not borne by either the<br />
government or the consumers exclusively, but rather by the whole of society, it is<br />
separated from the first two terms.<br />
The cost-‐benefit analysis is presented here in one time period for the sake of<br />
clarity in explanation. In later sections a time component will be added, projecting<br />
policies out forty years to get a sense for their long-‐term impact on society.<br />
4.1.1 Government Net Revenue<br />
A policy consisting of a carbon tax and investment tax credit produces two<br />
effects on the government cash flow: a carbon tax serves as a stream of incoming<br />
revenue over a period of time, and the tax credit represents a one-‐time outflow of<br />
cash from the government to a consumer who installs solar or wind technology.<br />
In time period t, government spending on tax credits for residential wind<br />
energy installations is represented by the one-time subsidy cost<br />
where<br />
wind<br />
βt and<br />
β t<br />
51<br />
wind wind<br />
C t,install,i<br />
∑ h i (µ t,i<br />
i=1<br />
wind wind<br />
− µ0,i )<br />
€<br />
cost of wind turbines, respectively, in state i at time t. The remnant of the term,<br />
€<br />
wind<br />
hi(µ t,i − µ0,i<br />
wind<br />
C t,install,i<br />
are the tax credit for wind installations and the installation<br />
wind ), is the number of new households installing wind turbines in state i<br />
at time t; it excludes households who have installed wind turbines previously. 31<br />
31 Appendix A-‐7 contains a breakdown electricity generation resource mixes for all states. This data<br />
from the Environmental Protection Agency provides the<br />
benefit calculations.<br />
€<br />
wind solar retail<br />
µ 0,i , µ0,i , µ0,i constants used in the cost-‐<br />
76
Optimizing Environmental Tax Policy<br />
Likewise, government spending on tax credits for residential solar energy<br />
installations is represented by<br />
€<br />
the government of tax credits in time period t is<br />
β t<br />
51<br />
solar solar<br />
C t,install,i<br />
∑ h i(µ t,i<br />
i=1<br />
solar solar<br />
− µ0,i )<br />
where all variables are defined for solar PV installations. Together, the total cost to<br />
gov<br />
Ct,tax credit<br />
= β t<br />
51<br />
wind wind<br />
C t,install,i<br />
∑ h i(µ t,i<br />
i=1<br />
51<br />
wind wind solar solar<br />
− µ0,i ) + βt C t,install,i<br />
∑ h i(µ t,i<br />
€<br />
electricity source to power their homes for the duration of the technology’s lifetime.<br />
€<br />
€<br />
€<br />
i=1<br />
solar solar<br />
− µ0,i )<br />
Consumers who take advantage of the tax credit will have a renewable<br />
Therefore, the government’s one-‐time payments to consumers who install<br />
renewable technology in time t are effectively spread out over twenty years. A<br />
comparable measure of revenue, then, must also be viewed over the lifetime of the<br />
renewable installations. For twenty years following time t, the government will<br />
collect a carbon tax from the consumers who fail to install renewable technology in<br />
time period t. The present value of this stream of income over time is represented by<br />
where<br />
gov<br />
Rt,carbon tax<br />
€<br />
c carbon = carbon tax ($/ton CO2)<br />
= c carbon retail CO2 µ t<br />
mt 1<br />
1−<br />
r (1+ r) −n<br />
⎡⎡ ⎤⎤<br />
⎢⎢ ⎥⎥<br />
⎣⎣ ⎦⎦<br />
retail<br />
µ t = national allocation to retail electricity in time t<br />
CO2 mt = carbon dioxide emissions from the residential sector from electricity<br />
use in time t (metric tons CO2)<br />
r = the discount rate (2%)<br />
77
n = the number of time periods the tax is collected (20 years)<br />
Optimizing Environmental Tax Policy<br />
The complete expression for government net revenue is dictated by the<br />
decision variables<br />
wind<br />
βt ,<br />
wind<br />
βt , and<br />
c carbon embedded in the revenue and cost<br />
functions. Government net revenue in time period t is simply the future stream of<br />
€ €<br />
carbon tax income from retail<br />
€<br />
electricity users less one-‐time tax credits to adopters<br />
of renewable technology:<br />
overall cost-‐benefit analysis.<br />
€<br />
gov gov<br />
gov<br />
Rnet = Rt,carbon<br />
tax − Ct,tax credit<br />
The government net revenue function is one of three main components of the<br />
4.1.2 Consumer Net Revenue<br />
The structure of cash flow in time t from the consumer’s perspective is a little<br />
more elaborate than that of government cash flow. Consumers incur one-‐time<br />
installation costs for wind and solar technology, which are subsidized by the tax<br />
credit from the government. The installation costs provide a source of electricity for<br />
twenty years. However, three more line items must be factored into the consumer<br />
net revenue calculation: the present value of the change in spending on retail<br />
electricity, the present value of the change in spending on wind turbine<br />
maintenance, and the present value of the change in spending on solar module<br />
maintenance. These last three lines account for the future costs that are incurred or<br />
eliminated based on the decision—to install or not to install renewable<br />
technology—made in time t. Like carbon tax revenue, future revenue or costs<br />
incurred by consumers are discounted to the present.<br />
78
Optimizing Environmental Tax Policy<br />
In time period t, the one-time wind installation cost incurred by consumers in<br />
aggregate is represented by<br />
€<br />
51<br />
wind<br />
C t,install,i<br />
∑ h i(µ t,i<br />
i=1<br />
wind wind<br />
− µ0,i )<br />
Likewise, the one-time solar installation cost incurred by consumers in aggregate is<br />
represented by<br />
€ 51<br />
wind<br />
= C t,install,i<br />
51<br />
solar<br />
C t,install,i<br />
∑ h i(µ t,i<br />
i=1<br />
solar solar<br />
− µ0,i )<br />
The sum of the one-‐time installation costs incurred in time period t is then<br />
con<br />
Ct,install ∑ h i (µ t,i<br />
i=1<br />
wind − µ0,i<br />
wind solar<br />
) + C t,install,i<br />
€<br />
other hand, the tax credits are inflows of cash from the consumer perspective. That<br />
51<br />
∑ h i (µ t,i<br />
i=1<br />
solar solar<br />
− µ0,i )<br />
The installations costs are outflows of cash from the consumer perspective. On the<br />
is, the government’s loss is the consumer’s gain:<br />
gov<br />
Ct,tax credit<br />
con<br />
= Rt,tax credit<br />
In other words, from the perspective of society, the inflow of the tax credit cash to<br />
consumers neutralizes the<br />
€<br />
outflow of tax credit cash from government; the tax<br />
credit is simply a redistribution of income.<br />
A carbon tax and tax credit policy implemented at the beginning of time<br />
period t will influence cash flows not only during time t, but also after time t. For<br />
example, consider what would happen if the government began to enforce a carbon<br />
tax of $10 per ton. The tax might induce some percentage of consumers to invest in<br />
renewable energy, leaving everyone else with higher retail electricity bills.<br />
Consumers who do choose to invest in renewable technology will incur<br />
79
€<br />
€<br />
€<br />
Optimizing Environmental Tax Policy<br />
maintenance expenses over time. Hence, the incremental increases or decreases in<br />
spending originating from the tax policy in time t must be included in the consumer<br />
net revenue calculation.<br />
is given by<br />
where<br />
The present value of the incremental spending on retail electricity over time<br />
con<br />
Ct,elec =<br />
51<br />
retail elec retail<br />
∑365 p 0,i d i<br />
hi µ 0,i − 365 p t,i<br />
i=1<br />
r<br />
51<br />
retail elec retail<br />
∑ d i<br />
hi µ t,i<br />
i=1<br />
retail<br />
p t,i = the price of retail electricity at time t ($/kWh)<br />
1<br />
1−<br />
(1+ r) −n<br />
⎡⎡ ⎤⎤<br />
⎢⎢ ⎥⎥<br />
⎣⎣ ⎦⎦<br />
elec<br />
d i = the average daily electricity consumption of a single-‐family home in<br />
state i (kWh)<br />
h i = the number of single-‐family detached homes in state i<br />
As before, the discount rate is 2% and the incremental change in spending is<br />
€<br />
discounted over twenty years. The payment<br />
51<br />
retail elec retail<br />
∑365 p 0,i d i<br />
hi µ 0,i − 365 p t,i<br />
i=1<br />
51<br />
retail elec retail<br />
∑ d i<br />
hi µ t,i<br />
i=1<br />
is calculated as such in order to isolate the incremental spending on retail electricity<br />
€<br />
that arises from the tax policy. Hence, the spending on retail electricity at time t is<br />
subtracted from the spending on retail electricity at time 0 (i.e., before the policy is<br />
implemented).<br />
given by<br />
The present value of the incremental change in wind maintenance costs is<br />
80
€<br />
€<br />
Because<br />
wind<br />
C 0,mntc,i<br />
con<br />
Ct,windmntc 51<br />
wind wind<br />
= ∑µ 0,i<br />
hi C 0,mntc,i − ∑µ<br />
t,i<br />
i=1<br />
Optimizing Environmental Tax Policy<br />
wind wind<br />
hi C t,mntc,i<br />
is already defined as a present value, the present value of the<br />
€<br />
incremental change can be simply expressed as a difference between<br />
€<br />
and t = t. In the same way, the present value of the incremental change in solar<br />
maintenance costs is given by<br />
con<br />
Ct,solarmntc €<br />
is summarized by the equation<br />
51<br />
51<br />
i=1<br />
solar solar<br />
= ∑µ 0,i<br />
hi C 0,mntc,i − ∑µ<br />
t,i<br />
i=1<br />
51<br />
i=1<br />
€<br />
solar solar<br />
hi C t,mntc,i<br />
wind<br />
C 0,mntc,i at t = 0<br />
Finally, the impact of the carbon tax and tax credit on consumer net revenue<br />
con con<br />
con con con<br />
con<br />
Rnet = Rt,tax<br />
credit − Ct,install + Ct,elec + Ct,wind<br />
mntc + Ct,solar mntc<br />
The last three cost terms are added, rather than subtracted, because of the<br />
way the<br />
€<br />
terms are defined, but there is no inconsistency among the cost variables. 32<br />
For the consumer, the only source of revenue arising out of the tax policy is the tax<br />
credit from the government. Absent a decline in the cost of renewable technology,<br />
individual consumers will not benefit financially from a tax policy designed to<br />
reduce pollution; they will, however, benefit as a society from scaled back CO2<br />
emissions.<br />
32<br />
con<br />
Ct,install Ct,elec term.<br />
is defined as the difference between installation costs at t=0 and t=t, where t=t is the first<br />
con con<br />
, Ct,wind<br />
mntc<br />
where t=0 is the first term.<br />
con<br />
, Ct,solar mntc<br />
are defined as incremental changes in cost between t=0 and t=t,<br />
81
4.1.3 Net Social Benefit<br />
Optimizing Environmental Tax Policy<br />
With no direct recipient besides the entirety of society, the social benefit of<br />
environmental tax policy is an important, and too often neglected, component of<br />
cost-‐benefit analysis. The benefit to society from the tax policy is quantified as<br />
B society = c SCC CO2 CO2 (m0 − mt )<br />
where c SCC is the social cost of carbon ($/ton CO2) and<br />
CO2 mt is carbon dioxide<br />
€<br />
emissions from the residential sector from electricity use in time t (metric tons<br />
€<br />
CO2). €<br />
33 If the policy achieves its desired effect (i.e., to reduce consumption of fossil<br />
fuels), then<br />
€<br />
CO2 CO2 m0 ≥ mt and<br />
4.1.4 Summary Table<br />
B society will be positive.<br />
€<br />
In its most condensed form, the benefit to society calculation is given by<br />
gov con society<br />
Rnet + Rnet + B<br />
This result, along with the foundational calculations and methods presented in<br />
Chapters 2, 3, and 4, are€ encapsulated in Table 10. This summary table contains the<br />
major decisions, assumptions, and cost-‐benefit line items that ultimately lead to a<br />
quantification of the net benefit (or cost) to society as a result of the tax policy. Of<br />
course, the <strong>final</strong> net benefit figure is the product of numerous underlying<br />
assumptions, including the social cost of carbon, consumer behavior patterns, and<br />
the current cost of installing renewable technology, to name only a few. A more<br />
thorough discussion of these assumptions follows.<br />
33 Using data from the Department of Energy: the U.S. residential sector emitted 1,261,000,000<br />
metric tons of carbon dioxide in 2008. 80% of those emissions, or 1,008,800,000 were emitted by<br />
single-‐family detached homes. Roughly 60% of emissions were generated for electricity<br />
consumption, so the <strong>final</strong> figure comes to 605,280,000 metric tons of carbon dioxide for electricity<br />
generation in single-‐family detached homes.<br />
82
4.2 Calculating the Social Cost of Carbon<br />
Optimizing Environmental Tax Policy<br />
Climate change legislation in the United States and abroad often leads to<br />
contentious political debate due to the fact that long-‐term environmental damage is<br />
very difficult to quantify. While almost everyone agrees that releasing carbon<br />
dioxide into the atmosphere causes harm to the planet, there is little consensus in<br />
the academic community as to the precise value of the social cost of carbon, which is<br />
formally defined as the marginal cost of emitting an additional ton of carbon. That<br />
one input can wield such influence over the direction of legislation underscores the<br />
importance of using a credible estimate.<br />
Table 10<br />
An interagency working group within the U.S. government issued a report,<br />
Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866, to<br />
83
Optimizing Environmental Tax Policy<br />
standardize the estimates of the SCC used in all federal offices. For 2010, the EPA<br />
selected four SCC estimates for its use in regulatory analyses: $5, $21, $35, and $65<br />
per ton, as shown in Table 11 [36]. The first three values are based on SCC models<br />
using 5%, 3%, and 2.5% discount rates, respectively. The fourth value, $65,<br />
represents an upper-‐tail estimate at the 95 th percentile using a 3% discount rate;<br />
such an estimate acknowledges the risk discussed in SCC literature that the<br />
expected welfare loss might be unbounded due to uncertainty about climate change<br />
[36] [5].<br />
Table 11. Estimated Social Cost of CO2,<br />
2010-‐2050 (in 2007 dollars) [36]<br />
While the carbon tax is a decision variable in this model, the social cost of<br />
carbon is not. Following the U.S. government’s lead, the adopted value for the social<br />
cost of carbon is $35 per ton—the interagency working group’s SCC estimate that is<br />
most in line with other SCC estimates from literature in the field.<br />
84
4.3 Modeling Consumer Behavior<br />
Optimizing Environmental Tax Policy<br />
One of the biggest challenges of modeling the impact of a carbon tax and tax<br />
credit over time is predicting how market agents will respond to new policies. If the<br />
government suddenly instituted a $30 carbon tax, not all consumers would invest in<br />
renewable technology at the same time: some would switch to an alternative energy<br />
source right away, others would switch after a few years’ time, and still others<br />
would probably prefer to stick with retail electricity despite the higher prices.<br />
Consumer behavior depends on many factors, two of which will be given special<br />
consideration here: the economic incentive to switch, and time.<br />
4.3.1 Inducement to Change Threshold<br />
Chapter 3 assumed that consumers would adopt whichever electricity source<br />
is cheapest in their state, whether that is a renewable or non-‐renewable source. The<br />
optimal portfolio allocations presented in Chapter 3 presuppose that, over time,<br />
rational market participants will always select the electricity source that is the least<br />
expensive, even if only marginally so.<br />
Yet the real world operates a bit differently, especially in the short term.<br />
There are inconveniences associated with installing a wind or solar system that may<br />
prevent consumers from switching electricity sources, even if their retail electricity<br />
rates are rising. Therefore, consumers will only switch away from retail electricity if<br />
the benefit of doing so is “worth it” to them; there must be sufficient expected<br />
financial gain from switching in order to pursue a residential renewable installation<br />
project. (Alternatively, consumers with an environmentalist bent might view<br />
protecting the environment as sufficient compensation for switching.) To get an<br />
85
Optimizing Environmental Tax Policy<br />
idea of how much compensation consumers require for the inconvenience of<br />
switching to a new and somewhat less reliable source of energy, it is helpful to look<br />
at consumer behavior in the United States today.<br />
Hawaiians currently pay the highest retail electricity rates in the nation. At<br />
$0.24 per kilowatt-‐hour, retail electricity in Hawaii is about four times as expensive<br />
as in Idaho, where residential consumers pay only $0.06 per kilowatt-‐hour. This is<br />
due in large part to Hawaii’s reliance on petroleum oil, which is more expensive<br />
than coal or natural gas. 34 Figure 24 shows the rise in the price of petroleum liquids<br />
just in the past year.<br />
Figure 24. Electric Power Industry Fuel Costs,<br />
January 2009 through December 2009 [71]<br />
Yet despite Hawaii’s lofty retail prices, only 6.5% of Hawaii’s electricity<br />
comes from renewable energy sources. This would be far less remarkable if it were<br />
not for Hawaii’s exceptional potential for solar energy. In Chapter 2, Hawaii ranked<br />
34 Hawaii gets 77.3% of its electricity from petroleum, 13.7% from coal, 6.5% from renewables<br />
excluding hydroelectric power, 1% from hydroelectric power, and 0.8% from other gases [72].<br />
86
Optimizing Environmental Tax Policy<br />
as the fifth cheapest state for residential solar electricity, with a price of $0.18 per<br />
kilowatt-‐hour. Even without government incentives, solar electricity is cheaper<br />
than retail electricity in Hawaii! Purely on the basis of cost comparison, Hawaiians<br />
should be allocating much more than 6.5% of their electricity to renewable sources.<br />
Clearly, there exists some resistance to increasing the renewable energy<br />
allocation that is unaccounted for in retail and solar electricity prices. Based on the<br />
calculations in Chapter 2, the solar electricity price in Hawaii represents a 26.6%<br />
potential savings from the retail electricity price in 2008. Ostensibly, there is a<br />
certain threshold for the savings percentage over which Hawaiians would begin to<br />
switch to renewable sources in greater numbers.<br />
While the discrepancy between retail and solar electricity prices in Hawaii is<br />
the greatest wonder of all, the same behavioral phenomenon is observed in other<br />
states, most notably in California, where wind electricity is 14.2% cheaper than<br />
retail electricity, and in Rhode Island, where wind electricity is 11.9% cheaper than<br />
retail electricity. To a lesser degree, wind electricity is also more economical in<br />
Alaska, Nevada, and New Hampshire before government incentives. Even so, all of<br />
these states continue to allocate only a small fraction of their electricity to the wind<br />
resource.<br />
However, determining the precise value of the savings threshold required to<br />
motivate consumers to consider renewable energy is outside the scope of this <strong>thesis</strong>.<br />
Rather, this model attempts to incorporate the consumer behavior observed in<br />
Hawaii and other states, but not to fixate on the level of the threshold, which will<br />
henceforth be called the “inducement to change” threshold.<br />
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Optimizing Environmental Tax Policy<br />
Applying the consumer behavior observed in these states to the framework<br />
presented here, an inducement to change threshold of 27% is built into the model.<br />
The assumption is that consumers will not be willing to embark on researching,<br />
purchasing, and installing residential renewable systems unless they are<br />
compensated by a 27% savings rate compared to retail electricity prices. The 27%<br />
figure comes from the current 26.6% price discrepancy in Hawaii; despite the fact<br />
that 27% appears to be too low an inducement threshold for Hawaii, the model<br />
assumes that consumers in other states would find 27% savings sufficiently enticing<br />
to shift into the renewable electricity market. The anomalous resistance to solar<br />
energy in Hawaii is likely to diminish over time as solar PVs enter the mainstream<br />
market.<br />
4.3.2 Renewable Adoption Rate, or Switchover Rate<br />
The second component of modeling consumer behavior is tracking consumer<br />
response to renewable technology over time. Even if the potential savings from<br />
renewable electricity exceed the inducement to change threshold, it is unlikely that<br />
all consumers will immediately flood the renewable energy markets. Realistically,<br />
adoption of renewable energy technology will be staggered. When, and under what<br />
circumstances, a consumer adopts the technology will depend on the consumption<br />
style of the individual.<br />
Sociologist Everett Rogers first introduced the theory of diffusions of<br />
innovations in 1962. Rogers proposed that consumers in the marketplace fall into<br />
five distinct categories: innovators, early adopters, early majority, late majority, and<br />
laggards. Each consumer’s classification drives the timing of his or her adoption of a<br />
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Optimizing Environmental Tax Policy<br />
new technology, as represented in the bell curve of Figure 25. Innovators and early<br />
adopters, who are typically regarded as the technology enthusiasts in a society,<br />
comprise only a small portion of the market. They are often characterized by self-‐<br />
sufficiency, a willingness to take risks, an interest in technology, and a visionary<br />
quality [73]. In contrast, the early majority tends to be more pragmatic, risk averse,<br />
and unwilling to invest in unproven applications [73]. Consumers in the late<br />
majority tend to be even more cautious when evaluating innovations, “taking more<br />
time than average to adopt them, and often at the pressure of peers” [74]. Finally,<br />
laggards are consumers that tend to be “anchored in the past, are suspicious of the<br />
new,” and often belong to older generations [74].<br />
Figure 25. Technology Adoption Bell Curve [70]<br />
In his book Crossing the Chasm, Silicon Valley consultant Geoffrey Moore<br />
posits that a chasm exists between early adopters and the early majority, making it<br />
difficult for new and unfamiliar high tech products to enter mainstream markets.<br />
(This is certainly true of solar PVs and wind turbines, both of which have already<br />
established a foothold among technology enthusiasts.) Moore asserts that most high<br />
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Optimizing Environmental Tax Policy<br />
tech ventures struggle to cross this chasm successfully [75]. To do so requires a<br />
shrewd marketing technique, strategic control over prices and distribution, or some<br />
other means of attracting the interest of more orthodox consumers. In the context<br />
of solar and wind energy, the carbon tax and renewable tax credit are two of the<br />
most powerful means of crossing the chasm aside from an overall drop in renewable<br />
technology prices.<br />
The technology adoption curve—essentially a probability density<br />
distribution 35 —is considered the gold standard in the high tech venture industry<br />
today. Its cumulative density forms an S-‐curve like that in Figure 26. The S-‐curve is<br />
an appropriate model for consumer behavior because it captures the three standard<br />
phases of a technology’s market share expansion: stalled adoption, rapid adoption,<br />
and mass adoption. It could be argued that wind and solar technology are currently<br />
situated at the inflection point between Phase I and Phase 2 on the S-‐curve, on the<br />
brink of rapid adoption. According to Aghion, Hemous, and Veugelers, “There are<br />
Figure 26. Phases of Technology Adoption [76]<br />
35 Rogers provided the following breakdown of the consumer population: 2.5% innovators, 13.5%<br />
early adopters, 34% early majority, 34% late majority, and 16% laggards, for a total of 100%.<br />
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Optimizing Environmental Tax Policy<br />
some signs, particularly from the venture capital market, that private green<br />
innovation machine might be ready to take off” and ascend the steep slope of Phase<br />
II [41].<br />
The background on Moore and Rogers’ work serves to prove the point that<br />
consumers cannot be treated as uniformly rational automatons, but rather as<br />
individuals with differing preferences and tolerances for risk. Besides having<br />
dissimilar consumption habits, consumers will adopt technology at different rates<br />
due to inertia; the general inconvenience associated with installing a new electric<br />
system will slow down the rate of adoption. Most homeowners are so preoccupied<br />
with their jobs, children, and other responsibilities that installing renewable<br />
technology may be an afterthought even if it would reduce electrical bills.<br />
To incorporate these ideas into the policy optimization model, Rogers’<br />
adoption bell curve was translated into the cumulative density function in Figure 27.<br />
The consumer behavior schedule in Table 12 sets benchmarks for the proportion of<br />
consumers that are expected to adopt renewable technology over time according to<br />
Rogers’ model. The cost savings of renewable electricity compared to retail<br />
electricity are projected alongside the market adoption rate. Obviously, the<br />
cumulative market penetration will increase as the savings from adopting<br />
renewable technology grow over time. The consumer behavior schedule of Table 12<br />
(with slight modifications 36 ) was built into the model to garner a more realistic<br />
prediction of consumer response to tax policy over time.<br />
36 Due to inertia and the fact that renewable technology may not be effective in all states, Rogers’<br />
model was adapted such that renewable energy technology reaches a maximum adoption of 80%,<br />
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Market<br />
Adoption<br />
Rate<br />
Table 12. Consumer Behavior Schedule<br />
Absolute<br />
Savings %<br />
(Projected)<br />
Inducement<br />
Threshold<br />
Optimizing Environmental Tax Policy<br />
Savings in<br />
Excess of<br />
Inducement<br />
0.0% 0% 27% 0%<br />
0.4% 5% 27% 0%<br />
1.0% 10% 27% 0%<br />
1.8% 15% 27% 0%<br />
2.5% 20% 27% 0%<br />
4.0% 25% 27% 0%<br />
6.0% 30% 27% 3%<br />
10.0% 35% 27% 8%<br />
16.0% 40% 27% 13%<br />
22.0% 45% 27% 18%<br />
30.0% 50% 27% 23%<br />
37.0% 55% 27% 28%<br />
50.0% 60% 27% 33%<br />
63.0% 65% 27% 38%<br />
72.0% 70% 27% 43%<br />
78.0% 75% 27% 48%<br />
84.0% 80% 27% 53%<br />
90.0% 85% 27% 58%<br />
94.0% 90% 27% 63%<br />
98.0% 95% 27% 68%<br />
100.0% 100% 27% 73%<br />
Figure 27<br />
even after laggards have adopted. This presupposes that some consumers will never adopt<br />
renewable energy technology.<br />
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4.4 Declining Costs of Renewable Technology Over Time<br />
Optimizing Environmental Tax Policy<br />
Technological progress is another crucial dimension of assessing the impact<br />
of a tax policy over time. Fortunately for the green energy movement, most industry<br />
analysts project that the price of renewable electricity will fall significantly in the<br />
coming years as renewable technology is brought to scale. Still, there is appreciable<br />
uncertainty regarding the future prices of solar and wind electricity, so a well-‐<br />
designed, robust policy should allow for a range of prices.<br />
4.4.1 Solar Photovoltaic Cost Trends<br />
Between 1995 and 2005, the average installation cost of solar PVs declined<br />
by 4.8% per year in real dollars [77]. But for a two-‐year period until 2007,<br />
installation costs remained flat due to the fact that, starting in 2005, “U.S. and global<br />
PV markets expanded significantly, creating shortages in the supply of silicon for PV<br />
module production and putting upward pressure on PV module prices” [77]. Since<br />
then, PV module designers and producers have reacted to the silicon shortage, and<br />
PV technology has recommenced its movement down the price curve, falling 4% in<br />
2008 and a further 27% in 2009 alone [81] [33]. Two recent developments made<br />
this possible: producers ramped up polysilicon production following the 2005<br />
shortage, and PV innovations (like polycrystalline thin film technology) required<br />
less silicon than earlier generations of PV technology [80].<br />
A further decline in PV costs is all but imminent. Clean Edge, a research firm<br />
devoted to the clean-‐tech sector, predicted that the installed cost for solar PV will<br />
drop another 60% within the next decade to well under $3,000 per kilowatt [33].<br />
Such a decline would put solar power at grid parity with fossil fuels, ushering in a<br />
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Optimizing Environmental Tax Policy<br />
new age of cost competitive renewable electricity. Figure 28 extrapolates future<br />
price declines of PV technology according to cumulative production, not years: by<br />
the time worldwide PV cumulative production grows by two orders of magnitude,<br />
the price per kilowatt-‐hour of solar electricity will fall below that of wholesale coal<br />
electricity.<br />
Figure 28. Projected costs of solar PV technology as<br />
cumulative production increases [34]<br />
A number of catalysts are accelerating the movement toward grid parity. In<br />
green tech hotbeds like Silicon Valley, venture capitalists are investing huge sums in<br />
the research and development of photovoltaic technology. As a percent of U.S.-‐<br />
based venture capital investments, green energy rose from 11.4% in 2008 to 12.5%<br />
in 2009, the highest historical share in the history of green-‐tech as an asset class<br />
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Optimizing Environmental Tax Policy<br />
[33]. The true impact of this funding will not manifest itself for years, but promising<br />
sprouts are already emerging: Argonne National <strong>Lab</strong>, for example, is developing a<br />
“solar paint” that forms interconnected solar cells like those on PV panels when it<br />
dries [83]. It can be applied to almost any surface, including walls, roof, and<br />
windows. Meanwhile, engineers at Princeton University have developed a<br />
technique for producing electricity-‐conducting plastics that could “slash the cost of<br />
solar panels” if commercialized [82]. These and other research projects are likely to<br />
transform the solar power landscape before the decade is over.<br />
4.4.2 Wind Turbine Cost Trends<br />
Due to its historical cost advantage, wind energy has been scaled up much<br />
more quickly than solar energy. The difference is certainly huge: global wind power<br />
capacity reached 157.9 gigawatts at the end of 2009, compared to global solar<br />
power capacity of<br />
6.43 gigawatts [78]<br />
[85]. As Figure 29<br />
illustrates, installed<br />
wind capacity is<br />
expected to swell in<br />
coming years, which<br />
will likely have the<br />
effect of further<br />
depressing installed<br />
Figure 29<br />
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wind costs.<br />
Optimizing Environmental Tax Policy<br />
Having reached grid parity with fossil fuels in some states, wind turbine<br />
prices are already stabilizing. Today, residential wind turbines can be installed for<br />
approximately $4,000 per kilowatt before incentives, and the installation cost for<br />
large-‐scale wind farms can dip as low as $1,690 per kilowatt [33]. Twenty-‐five<br />
years ago, the installation cost was six times what it is today [84].<br />
Yet even though wind turbine prices have dropped precipitously since the<br />
1980s, Clean Edge research projects that they will drop another 11% in the coming<br />
decade [33]. Roughly speaking, the cost of wind energy “has dropped by<br />
approximately 15% with each doubling of installed capacity worldwide” [84]. If that<br />
trend continues, billowing winds could soon eclipse coal as the most economical<br />
source of electricity.<br />
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5. Results of the Mathematical Model<br />
The cost-‐benefit framework presented in Chapter 4 serves as a<br />
springboard for tax policy analysis and optimization. In this chapter,<br />
the framework will be applied to numerous hypothetical tax policies in an endeavor<br />
to pinpoint the combination of carbon tax and investment tax credit that best serves<br />
the interests of society. Because the model in Chapter 4 encapsulates both private<br />
and social costs, the optimal tax policy will minimize the holistic “cost to society.”<br />
Resting on a model fine-‐tuned for consumer behavior, the social cost of<br />
carbon, and declining technology prices over time, the forthcoming analysis aims to<br />
present a meaningful and accurate portrayal of the economic consequences of<br />
various tax policies, both in the short term and in the long term.
5.1 Net Savings to Society for One Time Period<br />
Results of the Mathematical Model<br />
For now, the cost-‐benefit analysis is limited to one time period in order to<br />
gain an understanding of the short-‐term costs and benefits of various tax policies.<br />
Because the model is designed to calculate cost to society annually, the time period<br />
examined is the first year following the implementation of the tax policy. Recall that<br />
the one-‐period cost or benefit to society is measured as the change in the present<br />
value of the future costs or benefits to society that directly result from consumer<br />
decisions in the first year of the new tax policy. Because those decisions carry<br />
financial implications through the entire lifetime of the renewable energy system,<br />
the future costs and benefits related to the consumer decision must be discounted<br />
back to the first year in order to fully reflect the one-‐period cost or benefit to society<br />
of the tax policy.<br />
5.1.1 Net Savings with Lockstep Technology Improvement<br />
On the following pages, Figures 30-‐35 plot the net savings or net cost to<br />
society in year one as a function of the carbon tax and federal tax credit. Each point<br />
on the surface represents a different combination of the carbon tax and federal<br />
investment tax credit (ITC). On these graphs, the color red reflects the most positive<br />
part of the surface (i.e., the greatest net savings to society), and the rest of the color<br />
spectrum reflects a descending surface, where blue marks the tax policies with the<br />
highest net cost to society (or least net savings, as the case may be).<br />
Each of the six graphs plots the cost-‐benefit function with a different<br />
underlying assumption about the state of technological improvement. For instance,<br />
Figure 30, which assumes a 0% decline in renewable technology costs, portrays the<br />
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Figure 30<br />
Figure 31<br />
Results of the Mathematical Model<br />
99
Figure 32<br />
Figure 33<br />
Results of the Mathematical Model<br />
100
Figure 34<br />
Figure 35<br />
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Results of the Mathematical Model<br />
cost-‐benefit analysis of tax policies implemented today. Figures 31-‐35, however,<br />
plot the cost-‐benefit function assuming 10%, 30%, 50%, 70%, and 90% declines in<br />
renewable technology costs, respectively, at the starting point of the time period.<br />
For these graphs, the time period represented is not today, but rather some point in<br />
the future—specifically, the first year in which technology costs decline to the level<br />
indicated on the graph.<br />
Figures 30-‐35 assume that costs of wind and solar technology decline in<br />
lockstep, whereby wind turbines and PV panels are clumped together as “renewable<br />
technology.” Such a simplification allows one to interpret how technological<br />
progress will affect the overall cost-‐benefit analysis without getting bogged down in<br />
forecasted rates of technology improvement. In the next section, cost declines of<br />
solar and wind technology are considered separately.<br />
As a whole, this set of graphs lends itself to an interesting analysis. 37 The<br />
interplay between the carbon tax, the federal tax credit, and the net cost to society<br />
evolves considerably as renewable energy becomes cheaper. In a scenario with no<br />
or little decline in the cost of renewable technology (Figures 30 and 31), the net cost<br />
to society soars after the federal tax credit crosses 50%. While a higher tax credit<br />
would benefit consumers, the onus of paying for the installations would shift to<br />
government. Yet consumers retain the power to decide whether to install<br />
renewable technology, and because the installation costs are so artificially<br />
depressed, consumers will choose to switch to renewable technology before it is<br />
37 It is important to bear in mind that the scale of the z-‐axis on each graph is different. Adjusting the<br />
z-‐axis scale was necessary in order to show the curvature of each surface. As a warning, comparing<br />
the graphs side by side is misleading unless scale is taken into account.<br />
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Results of the Mathematical Model<br />
economical to do so. This leads to an unsustainable burden on the government to<br />
heavily subsidize installations at the whim of the consumer.<br />
As renewable technology declines 30% from its initial cost (Figures 32), the<br />
net cost to society of tax policies becomes less negative across the board; in fact,<br />
with some moderate tax policies, society actually incurs net savings. Although the<br />
curvature of the surfaces in Figures 30-‐32 is consistent, the lower bound of the z-‐<br />
axis changes such that tax credits in Figure 32 are significantly less costly to society<br />
than tax credits in Figure 30, the base case today.<br />
In Figure 33, which depicts the cost-‐benefit of policies with a 50% decline in<br />
renewable technology costs, implementing environmental tax incentives becomes<br />
categorically beneficial to society: at no point on the surface does a tax policy return<br />
a net cost to society. Indeed, the scenario in Figure 33 marks a turning point in the<br />
cost-‐benefit calculations. The sudden attractiveness of the tax policies can be<br />
explained by the fact that, with 50% cost declines, renewable technology <strong>final</strong>ly<br />
becomes a genuinely economical investment across the country. By shifting to<br />
renewable energy, savings from carbon taxes and the social cost outweigh the net<br />
cost to government of subsidizing renewable installations. Overall, society benefits<br />
from every tax policy on the surface, though some policies generate more savings<br />
than others, as evidenced by the prominent peak at the 50% tax credit, $0 carbon<br />
tax point.<br />
Figures 34 and 35 present even more optimistic outcomes of the cost-‐benefit<br />
analysis. In these scenarios, the slope of the surface has essentially rotated ninety<br />
degrees from its starting slope in Figures 30-‐32. Not only does the carbon tax cease<br />
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Results of the Mathematical Model<br />
to burden society in these scenarios, the most extreme tax policy on the surface<br />
(100% tax credit, $100 carbon tax) generates the maximum net savings to society in<br />
both Figures 34 and 35.<br />
While that tax policy might seem an unlikely candidate for an optimum, there<br />
are a few explanations for this result. The consumer behavior model in Chapter 4<br />
predicts that there are some laggards in society who resist adopting renewable<br />
energy technology even when the savings from doing so exceed the inducement<br />
threshold by a large margin. Skepticism, discomfort with new technology, and<br />
firmly ingrained habit may all contribute to this behavior. In theory, some laggards<br />
may continue to use retail electricity even after the government imposes a carbon<br />
tax as high as $100. The government, then, collects large premiums from laggards<br />
who prefer not to switch to wind or solar energy. Meanwhile, the rest of society will<br />
have adopted solar and wind technology, reducing the social cost of carbon to all of<br />
society. With 70% and 90% cost declines, renewable technology is so cheap that the<br />
optimal action is for the government to encourage as many people to switch as<br />
possible (hence, implementing the 100% tax credit).<br />
5.1.2 Optimal Policies in the One Period Model<br />
In Figures 30-‐32, the scale of the z-‐axes prohibits the viewer from<br />
determining the optimal policy by sight. Figure 36 remedies this problem, providing<br />
a zoomed in view of Figure 30. In this scenario, which represents a one-‐year time<br />
period starting today, the optimal policy is a 50% tax credit combined with a $0<br />
carbon tax. The fact that a policy with no carbon tax is optimal suggests that now is<br />
an inopportune time to implement a carbon tax, despite many politicians’ insistence<br />
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Figure 36. Close-‐up of Figure 30<br />
Results of the Mathematical Model<br />
on doing so. It is apparent that a carbon tax would result in a total cost to<br />
consumers that is greater in magnitude than the benefit of reducing pollution, as<br />
quantified by the social cost of carbon. To put it plainly, the cost-‐benefit analysis in<br />
one time period indicates that society simply would not benefit from a carbon tax,<br />
be it explicit or implicit in a cap-‐and-‐trade system.<br />
Of course, the suitability of a given tax policy changes for every scenario.<br />
Even though the carbon tax inflicts more harm than good today, it may be an<br />
important component of the environmental tax policy in a future scenario with<br />
improved technological capabilities. Table 13 provides a summary of the optimal<br />
tax policies and corresponding net savings to society associated with each<br />
scenario. 38 There is no timeless policy, as the table shows; the policy that delivers<br />
38 While it may seem ironic that a tax policy would generate savings, recall that the cost-‐benefit<br />
calculation is designed for neither the consumers nor the government. Rather, “net benefit” or “net<br />
savings” refers to the benefit accruing to society as a whole. Because the externality of carbon<br />
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Results of the Mathematical Model<br />
the greatest benefit to society depends entirely on the technological development of<br />
renewable technology at each stage.<br />
According to the cost-‐benefit analysis of independent scenarios depicted in<br />
Figures 30-‐35, the optimal tax policy hovers around a 50% tax credit and $0 carbon<br />
tax for all scenarios until renewable technology costs decline by more than 50%.<br />
For scenarios in which renewable technology installation expense is 60% to 90%<br />
reduced from its level today, the optimal single-‐time period tax policy suddenly<br />
leaps to a 100% tax credit and a $100 carbon tax.<br />
Of course, it is worthwhile to keep in mind that the latter scenarios<br />
sensationalize the benefit of environmental tax policy to a degree. It is dubious<br />
whether the costs of both solar and wind technology will ever jointly decline so far<br />
Renewable<br />
Tech Cost<br />
Decline<br />
Table 13<br />
Optimal Tax Policy by Scenario<br />
Carbon Tax<br />
($/ton)<br />
Federal<br />
Tax Credit<br />
Net Savings<br />
to Society<br />
(billions)<br />
0% 0 50% 4.7<br />
10% 0 60% 14.4<br />
20% 0 50% 26.0<br />
30% 0 50% 41.9<br />
40% 0 50% 61.5<br />
50% 0 50% 110.7<br />
60% 100 100% 305.6<br />
70% 100 100% 545.6<br />
80% 100 100% 795.7<br />
90% 100 100% 1,055.8<br />
dioxide emissions is quantified and incorporated into the cost-‐benefit analysis, any tax policy under<br />
consideration for implementation should return positive net savings. Otherwise, it is not worth<br />
pursuing.<br />
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Results of the Mathematical Model<br />
as 80%, for example. The discussion in Chapter 4 testified that such declines are<br />
entirely plausible for solar PVs, but the costs of wind turbines have already begun to<br />
plateau. The difference in maturity of the wind and solar PV markets necessitates<br />
the separation of the “decline in renewable technology” into two distinct variables:<br />
the decline in cost of wind turbines, and the decline in cost of solar PVs.<br />
5.1.3 Delinking Wind and Solar Technology Improvement Variables<br />
The symmetry of solar and wind technological improvements is the biggest<br />
drawback in the one time period cost-‐benefit analysis. In recognition of this<br />
shortcoming, Figures 37-‐41 on pages 109-‐110 were created to give greater context<br />
to the cost-‐benefit outcomes. Each graph represents a different underlying policy<br />
with a tax credit growing in increments of 20%. The most important insights<br />
gleaned from these surfaces are:<br />
• A substantial decline in the cost of either wind or solar technology will lead<br />
to greater net savings to society than a moderate decline in the costs of both<br />
wind and solar technology.<br />
• As solar technology costs decline, the net benefit to society is preceded by a<br />
small dip into net cost territory. This occurs because the government,<br />
through tax credits, artificially lowers the cost of solar PVs to the point that<br />
more consumers choose to install solar technology than is economical. The<br />
cost of installations outweighs the benefit from reduced pollution at the dip.<br />
This is easiest to see in Figure 40.<br />
• As wind technology costs decline, the net benefit to society increases<br />
everywhere on the curve. Even large tax credits do not lead consumers to<br />
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Results of the Mathematical Model<br />
switch before it is advantageous to do so. This result is consistent with the<br />
relatively mature wind turbine market; because wind electricity prices have<br />
already fallen to grid parity levels in many states, a further decline in wind<br />
turbine costs will only benefit consumers.<br />
• Interestingly, society benefits more from large declines in solar technology<br />
costs than from large declines in wind technology costs. Again, this finding is<br />
consistent with the relative maturities of these markets: the solar PV market<br />
is much less mature than the wind turbine market, so advances in the former<br />
technology will have a greater impact on society than advances in the latter<br />
market. In other words, the “Solar Tech Cost Decline” axis reflects<br />
reductions from a larger base cost; therefore, the same percentage decrease<br />
in costs is more notable for solar than for wind technology.<br />
• The concavity of the surface shows that the marginal change in net benefit to<br />
society rises as technology improves. That is, when solar PVs are reduced<br />
from 60% to 70% off their original price, the incremental rise in the net<br />
benefit to society will be greater than when solar PVs decline from 10% to<br />
20%. This finding alludes to the consumer behavior model in Chapter 4:<br />
steep reductions in cost will open up the renewable technology market to<br />
the early majority, then the late majority, and eventually the laggards. Prior<br />
to the steep reductions in cost (for solar PV especially), only innovators and<br />
early adopters will utilize the renewable energy technology, limiting the<br />
marginal impact on the net benefit to society.<br />
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Results of the Mathematical Model<br />
• Intuitively, society incurs the greatest net savings when cost declines for<br />
wind and solar technology both approach 100%.<br />
The main takeaway from the graphs is that technological improvement is<br />
unequivocally a good thing for society. In the case of solar power, the tax credit<br />
should be implemented with discretion due to potential for distortion of incentives.<br />
Figure 37<br />
Figure 38<br />
109
Figure 39<br />
Figure 40<br />
Figure 41<br />
Results of the Mathematical Model<br />
110
5.2 Net Savings to Society Over Time<br />
Results of the Mathematical Model<br />
Section 5.1 graphically illustrated the cost-‐benefit analysis of numerous tax<br />
policies in one time period. The ideas derived from the single period analysis are<br />
integral to evaluating tax policy, and they naturally lead to a more expansive<br />
discussion of the longer term trade-‐offs inherent in carbon taxes and investment tax<br />
credits. An essential dimension of that discussion, of course, is time. Time<br />
considerations were excluded until this point in order to establish a firm grounding<br />
in the cost-‐benefit framework. But now, the cost-‐benefit analysis is conducted over<br />
forty years to get a sense for the long-‐term reverberations of environmental tax<br />
policies for wind and solar technology.<br />
5.2.1 Net Cost to Society with Variable Rates of Technology Improvement<br />
By virtue of representing one time period each, Figures 30-‐35 were forced to<br />
assume a flat decline in the cost of technology. In a multi-‐period model, building in a<br />
gradual rate of technology improvement over time adds realism to the cost-‐benefit<br />
analysis. Using industry experts’ projections, the following assumptions are built<br />
into the time progression model:<br />
• Solar PVs will decline in cost 60% in the next ten years and 80% in the next<br />
twenty years. After twenty years, the cost stabilizes, having reached (or<br />
come close to) its steady state price.<br />
• Wind turbines will decline in cost 11% in the next ten years and 22% in the<br />
next twenty years. After twenty years, the cost stabilizes, having reached (or<br />
come close to) its steady state price.<br />
111
Results of the Mathematical Model<br />
Hence, the multi-‐period model sidesteps the solar-‐wind linkage problem<br />
encountered in the single-‐period model.<br />
A second major difference between the single-‐ and multi-‐period models is<br />
the object of the calculation. The single-‐period cost-‐benefit analysis calculated the<br />
present value of the change in electricity-‐related costs to society as a result of the<br />
first year of the tax policy. In contrast, the multi-‐period model calculates the<br />
present value of the total cost to society of all electricity-‐related expenses for the<br />
next forty years. Figures 42 and 43 39 —the same graph from two different<br />
viewpoints—show how different tax policies affect the present value of the cost to<br />
society over forty years.<br />
In the single-‐period graphs, higher surfaces indicated greater net savings.<br />
But here, the lower the surface, the lower the present value of the cost to society.<br />
Therefore, the optimal tax policy over time corresponds to the lowest point on the<br />
graph, which is an 80% tax credit combined with a $0 carbon tax. The tax policy<br />
that results in the highest net cost to society is, essentially, no tax policy at all—a 0%<br />
tax credit combined with a $0 carbon tax.<br />
Obviously, this optimal policy result is slightly different from that in the<br />
single-‐period analysis. The disagreement is explained by the different assumptions<br />
in each model: the single-‐period model assumes an instant decline in technology<br />
costs, whereas the multi-‐period model assumes a gradual rate of decline in<br />
technology costs over time. Hence, the optimal policy outcomes from the two<br />
models are not<br />
39 Appendix A-‐10 contains the code used to generate these graphs.<br />
112
Results of the Mathematical Model<br />
Figure 42. Front View: Present Value of Cost to Society Over 40 Years<br />
Figure 43. Back View: Present Value of Cost to Society Over 40 Years<br />
113
Results of the Mathematical Model<br />
comparable. The single-‐period model returns the optimal policy for one year<br />
depending on current technology costs, but because technology costs are always<br />
changing, society is better served by a policy optimized over time, as in the multi-‐<br />
period model. 40<br />
Figures 42 and 43 beg the question, why is such a high investment tax credit<br />
optimal? Along the tax credit axis, the present value of the cost to society<br />
continuously decreases until the tax credit reaches 80%. The answer relates to the<br />
current state of wind and solar technology. Despite the fact that wind technology<br />
has come down to a cost competitive level in some states, in most states it has not;<br />
the same is true for solar power everywhere. Until renewable energy technology<br />
becomes truly cost competitive, society is made better off by federal tax credits that<br />
will encourage renewable energy installations.<br />
Because experts project that the cost of solar technology will decline rapidly<br />
this decade, the annual cost of the tax credit to government will become increasingly<br />
cheaper. On the other hand, society will accumulate more and more savings from<br />
averted social costs of carbon. The present value of the benefits of installing<br />
renewable technology in the short term greatly outweigh the installation costs.<br />
In fact, it is probable that the model actually understates the negative<br />
economic consequences of the carbon tax. Instituting a carbon tax will lead to job<br />
loss and unemployment as companies are forced to find ways to cut costs. And<br />
because carbon is an input in the manufacturing process of virtually any product on<br />
40 Assuming that the government is unwilling to adapt the policy annually.<br />
114
Results of the Mathematical Model<br />
the marketplace, a carbon tax will raise prices of goods across the board. In<br />
quantifying the negative impact on society of rising electricity costs, the model does<br />
not fully capture the indirect ramifications of a carbon tax.<br />
5.2.2 Optimal Policies in the Time Lapse Model<br />
Optimal or not, most American politicians today would balk at the idea of an<br />
80% investment tax credit. Faced with pressure to balance the budget, policy<br />
makers usually seek to find streams of revenue in bills they propose that require<br />
spending. As such, it is unlikely that Congress would approve an investment tax<br />
credit higher than 30% without some level of a carbon tax. Acknowledging this<br />
reality, Table 14 provides a summary of the optimal tax credits according to carbon<br />
tax level.<br />
Optimal Tax Credit by Carbon Tax<br />
Carbon Tax<br />
($/ton)<br />
Table 14<br />
Federal<br />
Tax Credit<br />
Cost to<br />
Society<br />
(billions)<br />
0 80% 1,477.8<br />
10 80% 1,486.8<br />
20 70% 1,496.6<br />
30 70% 1,494.0<br />
40 70% 1,498.6<br />
50 60% 1,503.4<br />
60 60% 1,506.9<br />
70 60% 1,510.5<br />
80 60% 1,513.6<br />
90 90% 1,515.3<br />
100 90% 1,516.7<br />
115
Results of the Mathematical Model<br />
If the federal government were to impose no carbon tax at all, the cost-‐<br />
benefit model indicates that it could minimize the cost to society by implementing<br />
an 80% tax credit for renewable energy installations. Such a policy would reduce<br />
the cost to society by $330 billion compared to a scenario without any government<br />
intervention, which has a $1.808 trillion cost to society over the next forty years.<br />
In essence, the government faces the same decision as the individual<br />
homeowner considering an investment in wind or solar technology. That is, the<br />
government must weigh sacrificing money in the short term with reaping benefits in<br />
the long term. Like consumers, the government must also decide how to adjust its<br />
budget according to its investment decisions. In practice, the government is likely to<br />
impose a sub-‐optimal carbon tax in order to balance its own budget, shifting the<br />
higher cost to the taxpayer.<br />
The tax policies in Table 14 may be as implausible as they are idealistic. Yet<br />
if there is one thing the cost-‐benefit analysis makes clear, it is that the government<br />
can do no worse than to do nothing. Even if political tensions prohibit it from<br />
ratifying an optimal tax policy, implementing incentives at any level is a move in the<br />
right direction.<br />
116
6. Summary and Conclusion<br />
The twenty-‐first century will see dramatic changes in the way that societies<br />
harness and distribute power. Right now, the developed world is at the brink of a<br />
clean tech revolution: the rapid advancement of solar technology and the<br />
exponential growth in wind power capacity worldwide are testaments to the<br />
promise of fossil fuel alternatives. The fervor surrounding the renewable energy<br />
industry is fueled, at least in part, by the threat of scarce resources. If renewable<br />
energy technology is widely adopted all over the world, the perils imposed by fossil<br />
fuels—economic, environmental, and political—will diminish. The question at<br />
present is if, and when, that will happen.<br />
6.1 Summary of the Thesis<br />
This <strong>thesis</strong> sought to explore how public policy can be designed to encourage<br />
residential investment in solar and wind technology. Confronted with a dearth of
Summary and Conclusion<br />
solar and wind electricity price data, the first task was to build a data set “from the<br />
ground up.” This required compiling state-‐level data on wind and solar resources,<br />
electricity consumption, population distribution, retail electricity prices, running<br />
rates for solar PV and wind turbine installation, and other contributors to local<br />
electricity prices. After coming up with a comparative price per kilowatt-‐hour of<br />
electricity for each of the three sources in all fifty states plus D.C., the data was<br />
applied to a cost function with government decision variables as inputs. Minimizing<br />
the cost function dictated the optimal electricity mix and prices in each state based<br />
on varying levels of government intervention. Subsequently, single-‐period and<br />
multi-‐period cost-‐benefit analyses were developed to predict the economic<br />
consequences of the different tax policies.<br />
The upshot of the cost-‐benefit analysis is that society benefits most from a<br />
substantial investment tax credit for renewable energy. Even though a carbon tax<br />
also encourages consumers to switch to renewable energy, it does so at a greater<br />
cost to society than the investment tax credit. The optimal tax policy was an 80%<br />
tax credit and no carbon tax. If this policy were implemented today, the projected<br />
electricity mix in the United States in twenty years shows solar as the leading source<br />
of electricity, followed by retail and wind electricity. Obviously, this result, which<br />
rests on optimistic assumptions about the rate of decline in PV costs, paints a<br />
drastically different picture from the reality today.<br />
118
6.2 Limitations of this Model<br />
Summary and Conclusion<br />
Any economic model must stand on assumptions that, at least to some extent,<br />
depart from reality. The following idealizations in this model limit the credibility of<br />
the results:<br />
• Households must choose between retail, solar, and wind electricity. To<br />
simplify the analysis, this model ignored the options of nuclear power,<br />
often cited as a clean and relatively cheap alternative to fossil fuels.<br />
• Retail, solar, and wind electricity are treated as perfect substitutes. In<br />
actuality, wind and solar energy suffer from more than just cost<br />
disadvantages; engineers and innovators are still trying to develop ways to<br />
ensure that solar and wind resources provide consistent power like fossil<br />
fuels. The unreliability of solar and wind power is a major roadblock to its<br />
commercialization.<br />
• The technology adoption paradigm used to model consumer behavior is<br />
based on past technologies’ patterns of market penetration. Whether<br />
renewable energy technology follows or deviates from this paradigm<br />
remains to be seen.<br />
• Rates of technological improvement are highly uncertain. There is no<br />
guaranteed timeline for how long it will take for a breakthrough to occur.<br />
Furthermore, the progress of solar PV technology and, to a lesser extent,<br />
wind turbines is subject to private and public funding, which are largely<br />
contingent on the economy.<br />
119
Summary and Conclusion<br />
• The cost-‐benefit analysis in this model does not fully account for the<br />
economic repercussions of a carbon tax. The cost to society is captured by<br />
the marginal change in retail electricity prices caused by the carbon tax, but<br />
the model does not consider other side effects, like job loss, reduced<br />
competitiveness of American companies, and inflation that is caused by<br />
companies’ passing higher cost of goods sold onto consumers.<br />
• Another limitation of the model used to predict the price of retail electricity<br />
under different carbon tax regimes is the omission of any forecasting of the<br />
change in retail prices due to shrinkage of the rate base. As consumers<br />
switch to wind and solar, the power plants will be selling fewer kWh of<br />
electricity, but the fixed costs of running the plant will remain virtually the<br />
same. Those costs will need to be spread over fewer customers, putting<br />
even more upward pressure on retail electricity prices beyond the carbon<br />
tax pass-‐through. A step-‐variable cost structure will exist where a plant<br />
cannot be closed down until enough customers switch to justify closing the<br />
whole plant. During the transition period, prices will be higher until<br />
the electricity demand shrinks enough to enable closure of a power plant.<br />
This factor has not been accounted for in the model.<br />
In spite of these limitations, the methodology and results presented in this<br />
<strong>thesis</strong> are intended to serve as a springboard for related analyses pertaining to tax<br />
policies in the renewable energy space.<br />
120
6.3 Areas for Further Investigation<br />
Summary and Conclusion<br />
Environmental tax policy and, more generally, renewable energy incentives<br />
present many directions for further research. It may be advantageous to learn more<br />
about the consumer response, both real and perceived, to renewable energy<br />
technology. It would be particularly helpful to identify what steps might be taken to<br />
lower the “inducement to change” threshold in states like Hawaii. Additionally, it<br />
would be worth researching whether consumers will respond to renewable energy<br />
in the same way that they responded to personal computers, cell phones, and iPods,<br />
or whether renewable energy will depart from standard patterns of technology<br />
adoption.<br />
This analysis might be refined by breaking down the United States by county<br />
rather than by state. Some liberties are taken when one is forced to classify an<br />
entire state’s wind resource. A more robust analysis would divide the United States<br />
into smaller territories, though the paucity of data at such levels makes this<br />
challenging.<br />
The renewable portfolio standard (RPS) implemented in some states is<br />
another form of government regulation that deserves attention. The RPS is “a policy<br />
that seeks to increase the proportion of renewable electricity used by retail<br />
customers” by requiring electric utilities to provide a certain percentage of<br />
electricity from renewable sources, including wind, solar, biomass, and geothermal.<br />
[87]. Thus far, twenty-‐seven states have approved such a standard. If successful,<br />
the RPS policy will dramatically increase the proportion of retail electricity derived<br />
from renewable sources, effectively nullifying the treatment of retail electricity as a<br />
121
Summary and Conclusion<br />
proxy for fossil fuels in this <strong>thesis</strong>. A full list of the thirty-‐seven states and their<br />
respective renewable portfolio standards is included in Appendix A-‐11.<br />
6.4 Final Thoughts<br />
The energy problem facing the world today is one of trade-‐offs. From a<br />
consumer’s perspective, the less environmentally friendly choice is often the less<br />
expensive choice. From the government’s perspective, the opportunity cost of a<br />
dollar spent on green energy is a dollar that could have gone to public schools,<br />
Medicare, Social Security, or a host of other federally funded programs. With so<br />
many interconnected, conflicting objectives at play, the “optimal” policy solution is<br />
as dependent on judgment and preferences as it is on quantifiable parameters.<br />
Going forward, educating the public about the country’s troublesome<br />
dependence on fossil fuels will be as important as designing policies to remedy it.<br />
The energy problem is at risk of going unaddressed if there is not strong public<br />
support behind finding alternatives to fossil fuels. In a recent Gallup poll, a slight<br />
majority of Americans said that U.S. should prioritize development of energy<br />
supplies (defined in the question as oil, gas, and coal) over protection of the<br />
environment [89]. This year marked the first time in the question’s ten-‐year history<br />
that Americans indicated a preference for energy over environment.<br />
It is the nature of the American political system to give voters the loudest<br />
voice of all. Unless Americans begin to prioritize environmental concerns ahead of<br />
economic worries, the government will act as a barrier, rather than a facilitator, of<br />
the inevitable movement toward renewable energy.<br />
122
Appendix<br />
A-1. Solar Appendix: Excel worksheet for Solar Calculations<br />
State<br />
Average<br />
peak<br />
sun<br />
hours<br />
per day<br />
Avg<br />
daily<br />
elec<br />
consmpt<br />
(kWh)<br />
Solar<br />
panel<br />
required<br />
(kW)<br />
Avg<br />
install.<br />
cost<br />
($)<br />
Pres<br />
value of<br />
maint.<br />
cost ($)<br />
Total cost<br />
(inst +<br />
main) of<br />
module<br />
($)<br />
Total output<br />
of<br />
electricity<br />
of module<br />
(kWh)<br />
Cost per<br />
kWh over<br />
lifespan<br />
($/kWh)<br />
.Alabama 4.23 43 11.63 81,427 24,100 105,527 404,095 0.26<br />
.Alaska 3.77 22 6.64 46,486 13,759 60,245 205,609 0.29<br />
.Arizona 6.50 37 6.62 46,371 13,725 60,096 353,622 0.17<br />
.Arkansas 4.25 37 9.92 69,430 20,549 89,980 346,191 0.26<br />
.California 5.74 19 3.81 26,669 7,893 34,563 179,598 0.19<br />
.Colorado 5.37 23 4.99 34,896 10,328 45,225 219,853 0.21<br />
.Connecticut 3.73 25 7.72 54,061 16,000 70,061 236,574 0.30<br />
.Delaware 3.63 31 9.97 69,801 20,659 90,460 297,266 0.30<br />
DC 4.23 25 6.89 48,232 14,275 62,507 239,361 0.26<br />
.Florida 5.41 38 8.11 56,739 16,793 73,532 360,125 0.20<br />
.Georgia 4.87 38 9.07 63,463 18,783 82,247 362,602 0.23<br />
.Hawaii 6.02 21 4.10 28,717 8,499 37,217 202,822 0.18<br />
.Idaho 4.81 35 8.45 59,152 17,507 76,659 333,804 0.23<br />
.Illinois 3.14 26 9.49 66,404 19,654 86,058 244,625 0.35<br />
.Indiana 4.21 35 9.48 66,328 19,631 85,960 327,611 0.26<br />
.Iowa 4.40 29 7.59 53,147 15,730 68,877 274,351 0.25<br />
.Kansas 5.18 30 6.70 46,876 13,874 60,751 284,880 0.21<br />
.Kentucky 4.94 40 9.29 65,022 19,245 84,267 376,846 0.22<br />
.Louisiana 4.83 42 9.96 69,727 20,637 90,364 395,115 0.23<br />
.Maine 4.35 17 4.59 32,158 9,518 41,675 164,115 0.25<br />
.Maryland 4.47 36 9.16 64,124 18,979 83,103 336,282 0.25<br />
.Massachusetts 3.95 21 6.06 42,430 12,558 54,988 196,629 0.28<br />
.Michigan 4.10 22 6.31 44,161 13,070 57,231 212,421 0.27<br />
.Minnesota 4.53 27 6.93 48,475 14,347 62,823 257,630 0.24<br />
.Mississippi 4.43 41 10.73 75,129 22,236 97,365 390,471 0.25<br />
.Missouri 4.56 37 9.27 64,884 19,204 84,088 347,119 0.24<br />
.Montana 4.69 27 6.62 46,371 13,725 60,096 255,153 0.24<br />
.Nebraska 5.01 34 7.74 54,157 16,029 70,185 318,322 0.22<br />
.Nevada 6.20 32 6.00 41,974 12,423 54,397 305,317 0.18<br />
.New Hamp 3.40 21 7.01 49,061 14,521 63,581 195,700 0.32<br />
.New Jersey 4.21 24 6.54 45,765 13,545 59,311 226,046 0.26<br />
.New Mexico 6.77 21 3.56 24,951 7,385 32,336 198,177 0.16<br />
.New York 3.58 20 6.36 44,530 13,180 57,709 187,030 0.31<br />
.North Carolina 5.01 37 8.60 60,215 17,822 78,037 353,932 0.22<br />
.North Dakota 5.01 35 8.11 56,791 16,808 73,599 333,804 0.22<br />
.Ohio 4.05 30 8.62 60,346 17,861 78,207 286,737 0.27<br />
.Oklahoma 5.29 36 7.84 54,882 16,244 71,126 340,617 0.21<br />
.Oregon 4.09 33 9.30 65,112 19,272 84,384 312,439 0.27<br />
.Pennsylvania 3.60 29 9.15 64,077 18,965 83,043 270,636 0.31<br />
.Rhode Island 4.23 20 5.42 37,937 11,228 49,165 188,268 0.26<br />
.South Carolina 5.06 40 9.02 63,115 18,680 81,795 374,678 0.22<br />
.South Dakota 5.23 32 7.14 50,011 14,802 64,813 306,865 0.21<br />
.Tennessee 4.41 44 11.49 80,437 23,807 104,244 416,172 0.25<br />
.Texas 5.64 37 7.59 53,161 15,734 68,896 351,764 0.20<br />
.Utah 5.55 26 5.45 38,140 11,288 49,428 248,341 0.20<br />
.Vermont 2.95 19 7.57 52,966 15,676 68,642 183,314 0.37<br />
.Virginia 4.13 40 11.02 77,135 22,830 99,965 373,750 0.27<br />
.Washington 4.45 35 9.09 63,641 18,836 82,477 332,256 0.25<br />
.West Virginia 3.65 37 11.76 82,290 24,356 106,645 352,384 0.30<br />
.Wisconsin 4.29 24 6.37 44,604 13,202 57,806 224,497 0.26<br />
.Wyoming 6.06 29 5.42 37,935 11,228 49,163 269,707 0.18
A-2. Retail Electricity Prices in the United States, 2008 [56]<br />
Appendix<br />
State<br />
Proportion of<br />
U.S. Pop'n<br />
Avg retail elec<br />
price ($/kWh)<br />
State<br />
Proportion of<br />
U.S. Pop'n<br />
Avg retail elec<br />
price ($/kWh)<br />
.Alabama 1.5% 0.0932 .Montana 0.3% 0.0877<br />
.Alaska 0.2% 0.1518 .Nebraska 0.6% 0.0759<br />
.Arizona 2.1% 0.0966 .Nevada 0.9% 0.1182<br />
.Arkansas 0.9% 0.0873 .New Hampsh 0.4% 0.1488<br />
.California 12.0% 0.1442 .New Jersey 2.8% 0.1414<br />
.Colorado 1.6% 0.0925 .New Mexico 0.7% 0.0912<br />
.Connecticut 1.1% 0.1911 .New York 6.4% 0.1710<br />
.Delaware 0.3% 0.1316 .N Carolina 3.1% 0.0940<br />
.DC 0.2% 0.1118 .North Dakota 0.2% 0.0730<br />
.Florida 6.0% 0.1122 .Ohio 3.8% 0.0957<br />
.Georgia 3.2% 0.0910 .Oklahoma 1.2% 0.0858<br />
.Hawaii 0.4% 0.2412 .Oregon 1.2% 0.0819<br />
.Idaho 0.5% 0.0636 .Pennsylvania 4.1% 0.1095<br />
.Illinois 4.2% 0.1012 .Rhode Island 0.3% 0.1405<br />
.Indiana 2.1% 0.0826 .S Carolina 1.5% 0.0919<br />
.Iowa 1.0% 0.0945 .S Dakota 0.3% 0.0807<br />
.Kansas 0.9% 0.0819 .Tennessee 2.1% 0.0784<br />
.Kentucky 1.4% 0.0734 .Texas 8.1% 0.1234<br />
.Louisiana 1.5% 0.0937 .Utah 0.9% 0.0815<br />
.Maine 0.4% 0.1652 .Vermont 0.2% 0.1415<br />
.Maryland 1.9% 0.1189 .Virginia 2.6% 0.0874<br />
.Massachusetts 2.1% 0.1623 .Washington 2.2% 0.0726<br />
.Michigan 3.2% 0.1021 .West Virginia 0.6% 0.0673<br />
.Minnesota 1.7% 0.0918 .Wisconsin 1.8% 0.1087<br />
.Mississippi 1.0% 0.0936 .Wyoming 0.2% 0.0775<br />
.Missouri 2.0% 0.0769<br />
124
A-3. Wind Appendix: Excel worksheet for Wind Calculations<br />
State<br />
Avg<br />
Elec<br />
Cons<br />
per Year<br />
(kWh)<br />
Wind<br />
Class<br />
(1-7)<br />
Annual<br />
avg<br />
wind<br />
speed<br />
(m/s)<br />
Rotor<br />
diam.<br />
req<br />
(m)<br />
Pwr<br />
rating<br />
req<br />
(kW)<br />
Avg<br />
install.<br />
cost ($)<br />
Pres<br />
value of<br />
maint.<br />
cost ($)<br />
Total<br />
cost of<br />
turbine<br />
($)<br />
Annual<br />
output<br />
of<br />
turbine<br />
(kWh)<br />
Appendix<br />
Cost per<br />
kWh<br />
over<br />
turbine<br />
life<br />
($/kWh)<br />
.Alabama 15,660 1 2.20 32.0 126 502,749 164,413 667,162 15,740 2.12<br />
.Alaska 7,968 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15<br />
.Arizona 13,704 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.12<br />
.Arkansas 13,416 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20<br />
.California 6,960 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.12<br />
.Colorado 8,520 5 6.20 5.5 4 14,852 4,857 19,709 9,310 0.12<br />
.Connecticut 9,168 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20<br />
.Delaware 11,520 2 4.75 8.0 8 31,422 10,276 41,698 10,820 0.20<br />
.DC 9,276 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20<br />
.Florida 13,956 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.12<br />
.Georgia 14,052 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.05<br />
.Hawaii 7,860 1 2.20 22.5 62 248,551 81,283 329,835 7,780 2.03<br />
.Idaho 12,936 5 6.20 6.5 5 20,743 6,784 27,527 13,000 0.11<br />
.Illinois 9,480 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20<br />
.Indiana 12,696 2 4.75 8.5 9 35,472 11,600 47,073 12,210 0.18<br />
.Iowa 10,632 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14<br />
.Kansas 11,040 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14<br />
.Kentucky 14,604 1 2.20 31.0 118 471,818 154,298 626,116 14,780 2.12<br />
.Louisiana 15,312 1 2.20 31.5 122 487,161 159,316 646,476 15,260 2.12<br />
.Maine 6,360 2 4.75 6.0 4 17,675 5,780 23,455 6,080 0.18<br />
.Maryland 13,032 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20<br />
.Massach 7,620 2 4.75 6.5 5 20,743 6,784 27,527 7,140 0.18<br />
.Michigan 8,232 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.21<br />
.Minnesota 9,984 3 5.35 6.5 5 20,743 6,784 27,527 9,570 0.15<br />
.Mississippi 15,132 1 2.20 31.5 122 487,161 159,316 646,476 15,260 2.12<br />
.Missouri 13,452 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20<br />
.Montana 9,888 5 6.20 5.5 4 14,852 4,857 19,709 9,310 0.10<br />
.Nebraska 12,336 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.14<br />
.Nevada 11,832 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12<br />
.New Hamp 7,584 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15<br />
.New Jersey 8,760 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.18<br />
.New Mex 7,680 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15<br />
.New York 7,248 2 4.75 6.5 5 20,743 6,784 27,527 7,140 0.18<br />
.N Carolina 13,716 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20<br />
.N Dakota 12,936 4 5.80 7.0 6 24,057 7,867 31,925 13,070 0.12<br />
.Ohio 11,112 2 4.75 8.0 8 31,422 10,276 41,698 10,820 0.18<br />
.Oklahoma 13,200 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.14<br />
.Oregon 12,108 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12<br />
.Pennsyl 10,488 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14<br />
.Rhode Isl 7,296 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.12<br />
.S Carolina 14,520 1 2.20 30.5 114 456,721 149,361 606,082 14,300 2.05<br />
.S Dakota 11,892 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12<br />
.Tennessee 16,128 2 4.75 9.5 11 44,310 14,491 58,800 15,250 0.18<br />
.Texas 13,632 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20<br />
.Utah 9,624 3 5.35 6.5 5 20,743 6,784 27,527 9,570 0.15<br />
.Vermont 7,104 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.15<br />
.Virginia 14,484 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.18<br />
.Washington 12,876 4 5.80 7.0 6 24,057 7,867 31,925 13,070 0.12<br />
.W Virginia 13,656 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.12<br />
.Wisconsin 8,700 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.18<br />
.Wyoming 10,452 5 6.20 6.0 4 17,675 5,780 23,455 11,070 0.12<br />
125
A-4. Weibull modeling for wind calculations – MATLAB file<br />
%Weibull wind2.m file<br />
Appendix<br />
Scale = [2.2 5.4 2.2 4.8 5.4 6.2 4.8 4.8 4.8 2.2 2.2 2.2 6.2 4.8 4.8 5.4<br />
5.4 2.2 2.2 4.8 4.8 4.8 4.8 5.4 2.2 4.8 6.2 5.4 5.8 5.4 4.8 5.4 4.8 4.8 5.8<br />
4.8 5.4 5.8 5.4 5.4 2.2 5.8 4.8 4.8 5.4 5.4 4.8 5.8 5.4 4.8 6.2];<br />
Shape = 2;<br />
SCALE = zeros(1000,51);<br />
for i = 1:1000<br />
for j = 1:51<br />
SCALE(i,j)=Scale(j);<br />
end<br />
end<br />
windspeed = wblrnd(SCALE,Shape,1000,51);<br />
%PDF of wind speeds in Alabama<br />
WblPDFAL = wblpdf(windspeed(1:1000,1),Scale(1),Shape);<br />
%PDF of wind speeds in Montana<br />
WblPDFMT = wblpdf(windspeed(1:1000,27),Scale(27),Shape);<br />
%PDF of wind speeds in N. Dakota<br />
WblPDFND = wblpdf(windspeed(1:1000,35),Scale(35),Shape);<br />
%figure 1 - Alabama<br />
plot(windspeed(1:1000,1),WblPDFAL,'d')<br />
xlabel('Wind speed V (m/s)')<br />
ylabel('Probability Density')<br />
title('Weibull PDF Modeling Wind Speeds in Alabama')<br />
%figure 2 - Montana<br />
plot(windspeed(1:1000,27),WblPDFMT,'d')<br />
xlabel('Wind speed V (m/s)')<br />
ylabel('Probability Density')<br />
title('Weibull PDF Modeling Wind Speeds in Montana')<br />
%figure 3 - North Dakota<br />
plot(windspeed(1:1000,35),WblPDFMT,'d')<br />
xlabel('Wind speed V (m/s)')<br />
ylabel('Probability Density')<br />
title('Weibull PDF Modeling Wind Speeds in North Dakota')<br />
syms V;<br />
%Power produced by the wind turbine (Montana example)<br />
rho = 1.225; %air density (kg/m^3)<br />
Cp = .35; %coefficient of performance (.35 is Cp for a good<br />
design)<br />
Ng = .80; %generator efficiency (.80 is standard for a gridconnected<br />
induction generator or a permanent magnet generator)<br />
Nb = .95; %gearbox/bearings efficiency<br />
AforMT = 23.76; %rotor swept area (23.76 m^2 for 5.5-m diameter in MT)<br />
AforND = 38.48; %rotor swept area (38.48 m^2 for 7-m diameter in ND)<br />
WMT = 0.5.*rho.*AforMT.*Cp.*windspeed(1:1000,27).^3.*Ng.*Nb/1000;<br />
%returns wind turbine power in kW based on wind speed WblPDF<br />
WND = 0.5.*rho.*AforND.*Cp.*windspeed(1:1000,35).^3.*Ng.*Nb/1000;<br />
%returns wind turbine power in kW based on wind speed WblPDF<br />
%Use this T value to plot figure 3 - Montana and ND only<br />
TMT = WblPDFMT.*8760; %# of hours/yr during which wind blows with speed V<br />
TND = WblPDFND.*8760; %# of hours/yr during which wind blows with speed V<br />
126
%figure 4 - Montana - illustration of integral<br />
plot(windspeed(1:1000,27),WMT.*TMT,'d')<br />
xlabel('Wind speed V (m/s)')<br />
ylabel('Annual Energy Produced as a Function of Wind Speed V (kWh)')<br />
title('W(V)*T(V): Annual Energy Produced in Montana as a Function of V<br />
(kWh)')<br />
Appendix<br />
%figure 5 - N. Dakota - illustration of integral<br />
plot(windspeed(1:1000,35),WND.*TND,'d')<br />
xlabel('Wind speed V (m/s)')<br />
ylabel('Annual Energy Produced as a Function of Wind Speed V (kWh)')<br />
title('W(V)*T(V): Annual Energy Produced in North Dakota as a Function of V<br />
(kWh)')<br />
%Definining P(V), T(V), W(V) in Hasan paper<br />
PofVmt = (Shape/Scale(27))*(V/Scale(27))*(exp(-V/Scale(27))^Shape); %pdf<br />
of Weibull distribution<br />
TofVmt = PofVmt*8760; %# of hours/yr when wind blows with speed V (hours)<br />
WofVmt = 0.5*rho*AforMT*Cp*V^3*Ng*Nb/1000; %power output in MONTANA of<br />
wind turbine as a function of wind speed V (kW)<br />
PofVnd = (Shape/Scale(35))*(V/Scale(35))*(exp(-V/Scale(35))^Shape); %pdf<br />
of Weibull distribution<br />
TofVnd = PofVnd*8760; %# of hours/yr when wind blows with speed V (hours)<br />
WofVnd = 0.5*rho*AforND*Cp*V^3*Ng*Nb/1000; %power output in MONTANA of<br />
wind turbine as a function of wind speed V (kW)<br />
%V1 and V2 speeds<br />
cutin = 3; %cut-in speed is 3 m/s<br />
cutout = 20; %cut-out speed is 20 m/s<br />
%Calculates integral of total energy production PER YEAR<br />
EnergyPerYearMT = int(WofVmt*TofVmt,cutin,cutout) %%Montana<br />
EnergyPerYearND = int(WofVnd*TofVnd,cutin,cutout) %%North Dakota<br />
%Code below is to calculate what rotor diameter should be for every state<br />
in order to produce enough electricity to meet household need. Must adjust<br />
PofV values for every state because states have different scale parameters.<br />
Rotor = 1:0.5:33; %rotor diameter in m<br />
SweptArea = pi.*(Rotor./2).^2; %meters squared<br />
EnergyProduced = zeros(65,51);<br />
for i = 1:51<br />
for j = 1:65<br />
EnergyProduced(j,i) = int((Shape/Scale(i))*(V/Scale(i))*(exp(-<br />
V/Scale(i))^Shape)*8760*0.5*rho*SweptArea(j)*Cp*V^3*Ng*Nb/1000,cutin,cutout<br />
);<br />
end<br />
end<br />
%This matrix is used to match state's electricity need to appropriate size<br />
%wind turbine for that state (based on wind speeds)<br />
EnergyProduced<br />
%Ratings of Wind Turbines Required to Meet Elec Demand for Avg Home in<br />
%State. The rated wind speed generally corresponds to the point at which<br />
%the conversion efficiency is near its maximum.<br />
ratedspeed = 10; %units m/s - speed at which turbines are rated by<br />
manufacturers<br />
127
A-5. MATLAB code for calculating solar cost variability in New Mexico:<br />
%%NewMexico.m<br />
Appendix<br />
dbarNM = 21; %average daily electricity consumption (kWh)<br />
sbarNM = 6.77; %average peak sun hours per day in New Mexico (hours/day)<br />
cbarNM = 8950; %average cost of solar electric installation in NM ($/kW)<br />
mbarNM = 11514; %present value of future maintenance costs in NM ($)<br />
lbarNM = 20; %expected lifetime of installation in NM (years)<br />
dsdvNM = 3.00; %stdev of daily electricity consumption<br />
ssdvNM = 0.50; %stdev of peak sun hours per day<br />
csdvNM = 1500; %stdev of cost of solar electric installation per kW<br />
msdvNM = 1500; %stdev of present value of future maintenance costs<br />
lsdvNM = 5; %stdev of lifetime of PV panel<br />
betaNM = 0.30; %investment tax credit for solar installation (assume 30%)<br />
dhatNM = normrnd(dbarNM,dsdvNM,[1 1000]);<br />
shatNM = normrnd(sbarNM,ssdvNM,[1 1000]);<br />
chatNM = normrnd(cbarNM,csdvNM,[1 1000]);<br />
mhatNM = normrnd(mbarNM,msdvNM,[1 1000]);<br />
lhatNM = normrnd(lbarNM,lsdvNM,[1 1000]);<br />
CsolarNM = zeros(1,1000);<br />
CsolarNM = ((dhatNM./shatNM).*chatNM.*(1betaNM)*(1.15)+mhatNM)./((365)*(0.9)*(1.15)*(dhatNM).*(lhatNM));<br />
muNM = mean(CsolarNM)<br />
sigmaNM = std(CsolarNM)<br />
pdfNM = normpdf(-0.2:0.01:0.70,muNM,sigmaNM);<br />
plot(-0.2:0.01:0.70,pdfNM);<br />
axis([0 0.60 0 5.5]);<br />
%figure1<br />
xlabel('Cost per kWh ($)');<br />
ylabel('Density');<br />
title('PDF of Solar PV Cost per kWh in New Mexico (30% tax credit)')<br />
p = 100*(0:0.25:1);<br />
y = prctile(CsolarNM,p);<br />
zNM = [p;y];<br />
zNM<br />
NMwindc = 0.11;<br />
z = ((NMwindc-muNM)/sigmaNM)<br />
prob = normcdf([-1000,z]);<br />
prob(2)-prob(1)<br />
128
A-6. MATLAB code for calculating solar cost variability in all states<br />
%%SolarCostAllocation.m<br />
Appendix<br />
windcosts0 = [2.594723938 0.176704752 2.599649102 0.222667636 0.177191647<br />
0.132437511 0.226777615 0.223207007 0.223602611 2.595417434 2.596107115<br />
0.15241116 0.13077839 0.222771653 0.22484129 0.173225314 0.17484687<br />
2.594688469 2.601675583 0.174133292 0.225803518 0.174768048 0.226539946<br />
0.172377988 2.603822722 0.223265134 0.131779291 0.175086733 0.152536013<br />
0.152766422 0.222414576 0.176144175 0.17200815 0.222883262 0.152377618<br />
0.225548631 0.173213186 0.151401751 0.17586933 0.173147277 2.596384978<br />
0.153309522 0.222947191 0.226252625 0.176389147 0.154777828 0.22575902<br />
0.151670857 0.17469029 0.226823923 0.134277327];<br />
dhat = zeros(1000,51); %initialize dhat matrix<br />
shat = zeros(1000,51); %initialize shat matrix<br />
chat = zeros(1000,51); %initialize chat matrix<br />
mhat = zeros(1000,51); %initialize mhat matrix<br />
lhat = zeros(1000,51); %initialize lhat matrix<br />
dhat = dmatrix; %calls dmatrix in Dmatrix.m file<br />
shat = smatrix; %calls smatrix in Smatrix.m file<br />
chat(1:1000,1:51) = 8950; %assume all states have uniform install./kW cost<br />
mhat = mmatrix; %calls mmatrix in Mmatrix.m file<br />
lhat(1:1000,1:51) = 20; %assume solar PVs have uniform expected<br />
lifetimes across US<br />
dsdv = 3.00; %stdev of daily electricity consumption<br />
ssdv = 0.50; %stdev of peak sun hours per day<br />
csdv = 1500; %stdev of cost of solar electric installation per kW<br />
msdv = 1500; %stdev of present value of future maintenance costs<br />
lsdv = 5; %stdev of lifetime of PV panel<br />
beta = 0.00; %investment tax credit for solar installation<br />
%generate noise<br />
dnoise = dsdv*randn(1000,51);<br />
snoise = ssdv*randn(1000,51);<br />
cnoise = csdv*randn(1000,51);<br />
mnoise = msdv*randn(1000,51);<br />
lnoise = lsdv*randn(1000,51);<br />
%generate n=1000 sample for variables<br />
d = dhat + dnoise;<br />
s = shat + snoise;<br />
c = chat + cnoise;<br />
m = mhat + mnoise;<br />
l = lhat + lnoise;<br />
%generate sample costs for solar PVs by state<br />
Csolar = zeros(1000,51);<br />
Csolar = ((d./s).*c.*(1-beta)*(1.15)+m)./((365)*(0.9)*(1.15)*(d).*(l));<br />
%initialize vectors<br />
mu = [1:51];<br />
sigma = [1:51];<br />
zscores = [1:51];<br />
zscores2 = [1:51];<br />
%loop to find mu and sigma of *solar costs* and z scores of *wind costs*<br />
(in the solar cost distribution) for each state<br />
129
for i=1:51,<br />
mu(i) = mean(Csolar(1:1000,i));<br />
sigma(i) = std(Csolar(1:1000,i));<br />
zscores(i) = ((windcosts(i)-mu(i))/sigma(i));<br />
zscores2(i) = ((retailcosts0(i)-mu(i))/sigma(i));<br />
end<br />
mu;<br />
sigma;<br />
zscores;<br />
zscores2;<br />
%initialize vector<br />
prob = zeros(51,2);<br />
%loop to return appropriate allocation of solar PVs for each state's<br />
%electricity portfolio<br />
for j=1:51,<br />
prob(j,1:2) = normcdf([-1000,zscores(j)]);<br />
prob2(j,1:2) = normcdf([-1000,zscores2(j)]);<br />
end<br />
prob<br />
prob2<br />
SolarAllocationByState = prob(1:51,2) - prob(1:51,1)<br />
SolarTransferFromRetail = prob2(1:51,2) - prob2(1:51,1)<br />
State<br />
Wind<br />
Percentile<br />
Retail<br />
Percentile<br />
State<br />
Wind<br />
Percentile<br />
Appendix<br />
Retail<br />
Percentile<br />
.Alabama 100.00 2.19 .Missouri 11.22 1.68<br />
.Alaska 7.51 4.59 .Montana 2.90 8.71<br />
.Arizona 100.00 45.85 .Nebraska 6.02 4.50<br />
.Arkansas 22.03 2.99 .Nevada 7.00 7.94<br />
.California 7.23 13.75 .New Hampshire 12.61 5.59<br />
.Colorado 5.11 2.79 .New Jersey 7.93 10.23<br />
.Connecticut 8.26 10.90 .New Mexico 23.79 6.13<br />
.Delaware 45.49 6.55 .New York 11.75 27.01<br />
.DC 13.26 6.39 .North Carolina 17.11 28.18<br />
.Florida 100.00 8.45 .North Dakota 5.32 2.76<br />
.Georgia 100.00 2.14 .Ohio 13.03 2.96<br />
.Hawaii 100.00 42.01 .Oklahoma 9.69 2.13<br />
.Idaho 7.47 2.49 .Oregon 24.56 2.33<br />
.Illinois 10.90 2.00 .Pennsylvania 29.95 3.39<br />
.Indiana 12.16 2.82 .Rhode Island 5.49 3.55<br />
.Iowa 5.09 2.93 .South Carolina 100.00 5.33<br />
.Kansas 8.42 1.72 .South Dakota 4.11 2.62<br />
.Kentucky 100.00 1.40 .Tennessee 10.08 21.50<br />
.Louisiana 100.00 30.51 .Texas 22.29 5.19<br />
.Maine 10.55 6.41 .Utah 7.27 3.03<br />
.Maryland 12.93 3.07 .Vermont 9.80 5.12<br />
.Massachusetts 6.64 6.46 .Virginia 9.16 2.51<br />
.Michigan 10.01 2.00 .Washington 24.82 4.84<br />
.Minnesota 34.04 2.54 .West Virginia 2.64 1.62<br />
.Mississippi 100.00 9.95 .Wisconsin 9.66 2.90<br />
.Wyoming 10.37 2.15<br />
130
Appendix<br />
A-7. Data from the Environmental Protection Agency used in Chapter 4 [86]<br />
GENERATION RESOURCE MIX (%)<br />
Other BioGeo-<br />
State Coal Oil Gas fossil mass Hydro Nuclear Wind Solar thermal Other<br />
AK 9.5 11.6 56.6 0.0 0.1 22.3 0.0 0.0 0.0 0.0 0.0<br />
AL 56.9 0.1 10.1 0.1 2.3 7.4 23.1 0.0 0.0 0.0 0.0<br />
AR 48.2 0.4 12.6 0.0 3.6 6.5 28.6 0.0 0.0 0.0 0.0<br />
AZ 39.6 0.0 28.5 0.0 0.1 6.4 25.4 0.0 0.0 0.0 0.0<br />
CA 1.0 1.3 46.7 1.1 2.9 19.9 18.1 2.1 0.3 6.5 0.1<br />
CO 71.7 0.0 24.1 0.0 0.1 2.6 0.0 1.6 0.0 0.0 0.0<br />
CT 11.9 9.4 26.4 2.3 2.1 1.4 46.4 0.0 0.0 0.0 0.0<br />
DC 0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0<br />
DE 59.4 15.0 19.6 6.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0<br />
FL 28.4 16.9 38.1 0.6 2.0 0.1 13.1 0.0 0.0 0.0 0.8<br />
GA 63.9 0.7 7.2 0.0 2.3 2.8 23.1 0.0 0.0 0.0 0.0<br />
HI 14.2 78.8 0.0 1.6 2.6 0.8 0.0 0.1 0.0 1.9 0.0<br />
IA 77.5 0.3 5.6 0.0 0.3 2.2 10.3 3.7 0.0 0.0 0.0<br />
ID 0.9 0.0 14.3 0.0 5.3 78.9 0.0 0.0 0.0 0.0 0.6<br />
IL 47.5 0.2 3.7 0.1 0.4 0.1 48.0 0.1 0.0 0.0 0.0<br />
IN 94.2 0.2 2.8 2.1 0.1 0.3 0.0 0.0 0.0 0.0 0.3<br />
KS 75.2 2.2 2.5 0.0 0.0 0.0 19.2 0.9 0.0 0.0 0.0<br />
KY 91.1 3.8 1.7 0.0 0.4 3.0 0.0 0.0 0.0 0.0 0.0<br />
LA 24.9 3.8 47.3 3.0 2.9 0.9 16.9 0.0 0.0 0.0 0.3<br />
MA 25.3 15.0 42.7 1.7 2.5 1.2 11.5 0.0 0.0 0.0 0.0<br />
MD 55.7 7.3 3.6 1.3 1.0 3.2 27.9 0.0 0.0 0.0 0.0<br />
ME 1.8 8.6 42.6 1.7 21.9 23.3 0.0 0.0 0.0 0.0 0.0<br />
MI 57.8 0.7 11.2 0.8 2.1 0.3 27.0 0.0 0.0 0.0 0.0<br />
MN 62.1 1.5 5.1 0.6 1.9 1.5 24.3 3.0 0.0 0.0 0.1<br />
MO 85.2 0.2 4.3 0.1 0.0 1.4 8.8 0.0 0.0 0.0 0.0<br />
MS 36.9 3.2 34.0 0.0 3.5 0.0 22.4 0.0 0.0 0.0 0.0<br />
MT 63.8 1.5 0.1 0.0 0.2 34.3 0.0 0.0 0.0 0.0 0.0<br />
NC 60.5 0.4 2.4 0.1 1.4 4.3 30.8 0.0 0.0 0.0 0.2<br />
ND 94.8 0.1 0.0 0.2 0.0 4.2 0.0 0.7 0.0 0.0 0.0<br />
NE 66.2 0.1 2.6 0.0 0.1 2.8 28.0 0.3 0.0 0.0 0.0<br />
NH 16.7 5.6 27.8 0.3 3.8 7.1 38.7 0.0 0.0 0.0 0.0<br />
NJ 19.1 1.8 25.1 1.0 1.4 0.0 51.6 0.0 0.0 0.0 0.1<br />
NM 85.2 0.1 11.9 0.0 0.0 0.5 0.0 2.3 0.0 0.0 0.0<br />
NV 44.9 0.1 47.4 0.3 0.0 4.2 0.0 0.0 0.0 3.1 0.0<br />
NY 13.8 16.2 22.5 0.7 1.2 16.9 28.7 0.1 0.0 0.0 0.0<br />
OH 87.2 0.9 1.7 0.2 0.2 0.3 9.4 0.0 0.0 0.0 0.0<br />
OK 51.7 0.1 43.0 0.0 0.4 3.5 0.0 1.2 0.0 0.0 0.0<br />
OR 7.0 0.1 27.0 0.1 1.8 62.5 0.0 1.5 0.0 0.0 0.0<br />
PA 55.4 2.3 5.0 0.6 0.9 0.7 35.0 0.1 0.0 0.0 0.0<br />
RI 0.0 0.9 99.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0<br />
SC 38.7 0.7 5.3 0.1 1.7 1.7 51.8 0.0 0.0 0.0 0.0<br />
SD 46.0 0.3 4.2 0.0 0.0 47.2 0.0 2.4 0.0 0.0 0.0<br />
TN 61.0 0.2 0.5 0.0 0.6 9.0 28.7 0.0 0.0 0.0 0.0<br />
TX 37.3 0.6 49.3 1.3 0.3 0.3 9.6 1.1 0.0 0.0 0.2<br />
UT 94.3 0.1 3.1 0.0 0.0 2.1 0.0 0.0 0.0 0.5 0.0<br />
VA 44.9 5.4 10.4 0.7 3.1 0.1 35.4 0.0 0.0 0.0 0.0<br />
VT 0.0 0.2 0.0 0.0 7.2 21.2 71.2 0.2 0.0 0.0 0.0<br />
WA 10.3 0.1 8.4 0.4 1.6 70.7 8.1 0.5 0.0 0.0 0.0<br />
WI 67.3 1.1 10.5 0.1 1.9 2.8 16.0 0.1 0.0 0.0 0.1<br />
WV 97.7 0.2 0.3 0.1 0.0 1.5 0.0 0.2 0.0 0.0 0.0<br />
WY 95.1 0.1 0.7 0.6 0.0 1.8 0.0 1.6 0.0 0.0 0.1<br />
US 49.6 3.0 18.8 0.6 1.3 6.5 19.3 0.4 0.0 0.4 0.1<br />
131
Appendix<br />
A-8. Sample MATLAB code for graphing carbon tax, tax credit, and net<br />
savings to taxpayers in three dimensions (Chapter 5, single-period):<br />
CarbonTax = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100];<br />
GovtITC = [0 10 20 30 40 50 60 70 80 90 100];<br />
figure(1)<br />
surf(GovtITC,CarbonTax,CosttoTP10);<br />
xlabel('Federal Tax Credit (%)','fontsize',11,'fontweight','b');<br />
ylabel('Carbon Tax ($/ton CO2)','fontsize',11,'fontweight','b');<br />
zlabel('Savings (Cost) to Society ($)','fontsize',10,'fontweight','b');<br />
title({'Net Savings (Cost) to Society with varying Carbon Tax and ITC';'10%<br />
Decline in Cost of Renewable Technology'},'fontsize',11,'fontweight','b');<br />
This code was adapted for all six graphs. Matrices CosttoTP10, CosttoTP30,<br />
et cetera were produced by a macro in Excel.<br />
A-9. Sample MATLAB code for graphing solar price decline, wind price<br />
decline, and net savings to taxpayers in three dimensions (Chapter 5):<br />
SolarDecline = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100];<br />
WindDecline = [0 10 20 30 40 50 60 70 80 90 100];<br />
figure(1)<br />
surf(WindDecline,SolarDecline,Subsidy10);<br />
xlabel('Wind Tech Cost Decline (%)','fontsize',11,'fontweight','b');<br />
ylabel('Solar Tech Cost Decline (%)','fontsize',11,'fontweight','b');<br />
zlabel('Savings (Cost) to Society ($)','fontsize',10,'fontweight','b');<br />
title({'Net Savings (Cost) to Society with varying Technological<br />
Improvements';'10% Investment Tax Credit, $0 Carbon<br />
Tax'},'fontsize',11,'fontweight','b');<br />
This code was adapted for all six graphs. Matrices Subsidy10, Subsidy30,<br />
et cetera were produced by a macro in Excel.<br />
A-10. Sample MATLAB code for graphing carbon tax, tax credit, and net<br />
savings to taxpayers in three dimensions (Chapter 5, multi-period):<br />
CarbonTax = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100];<br />
GovtITC = [0 10 20 30 40 50 60 70 80 90];<br />
figure(1)<br />
surf(GovtITC,CarbonTax,PVsocietycost);<br />
xlabel('Federal Tax Credit (%)','fontsize',11,'fontweight','b');<br />
ylabel('Carbon Tax ($/ton CO2)','fontsize',11,'fontweight','b');<br />
zlabel('Present Value of Cost to Society<br />
($)','fontsize',10,'fontweight','b');<br />
title({'Present Value of Cost to Society';'Gradual Decline in Tech<br />
Costs'},'fontsize',11,'fontweight','b');<br />
Matrix PVsocietycost was produced by a macro in Excel.<br />
132
A-11. Renewable Portfolio Standards, by state – <strong>April</strong> 2010 [88]<br />
Renewable Portfolio Standards<br />
State RPS Year Note<br />
Arizona 15% 2025<br />
California 20% 2010<br />
California 33% 2020<br />
Colorado 30% 2020 IOUs<br />
Colorado 10% 2020 Electric co-ops, Municipal utilities<br />
Connecticut 27% 2020<br />
Delaware 20% 2020<br />
DC 20% 2020<br />
Florida 7.5% 2015<br />
Hawaii 40% 2030<br />
Illinois 25% 2025<br />
Iowa 105 MW 2010 Renewable generating capacity minimum<br />
Kansas 20% 2020<br />
Maine 40% 2017<br />
Maryland 20% 2022<br />
Massachusetts 15% 2020<br />
Michigan 10% 2015<br />
Minnesota 25% 2025<br />
Missouri 15% 2021<br />
Montana 15% 2015<br />
Nevada 25% 2025<br />
New Hampshire 23.8% 2025<br />
New Jersey 22.5% 2020<br />
New Mexico 20% 2020 IOUs<br />
New Mexico 10% 2020 Electric co-ops<br />
New York 29% 2015<br />
North Carolina 12.5% 2021 IOUs<br />
North Carolina 10% 2018 Electric co-ops, Municipal utilities<br />
North Dakota 10% 2015<br />
Ohio 25% 2025<br />
Oregon 25% 2025<br />
Pennsylvania 18% 2020<br />
Rhode Island 16% 2019<br />
South Dakota 10% 2015<br />
Texas 5,880 MW 2015 Renewable generating capacity minimum<br />
Texas 10,000 MW 2025 Renewable generating capacity minimum<br />
Utah 20% 2025<br />
Vermont 20% 2017<br />
Virginia 15% 2025<br />
Washington 15% 2020<br />
West Virginia 25% 2025<br />
Wisconsin 10% 2015<br />
Note: IOUs are Investor-Owned Utilities<br />
Appendix<br />
133
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List of Chapter Images:<br />
1. http://www.electriccarsite.co.uk/<br />
2. http://www.sbc-‐technologies.com/sbc-‐technologies-‐renewableEnergy.php<br />
3. http://www.homeenergyadvisory.com/<br />
4. http://peopleandearth.com/faq.html<br />
5. http://green.venturebeat.com/2009/10/26/a-‐movement-‐toward-‐locally-‐grown-‐<br />
electricity/<br />
6. http://www.aabenergy.co.uk/renewable-‐energy-‐studies.php<br />
142