Handbook of Energy Storage for Transmission or ... - W2agz.com
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Handbook of Energy Storage for Transmission or ... - W2agz.com

Handbook of Energy Storage for Transmission or ... - W2agz.com Handbook of Energy Storage for Transmission or ... - W2agz.com

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28.01.2015 Views

EPRI Proprietary Licensed Material generally in the range of 1 Hz to ~ 100 Hz. This occurs because the capacitance itself is very large. The inductance is generally small for this technology. So the frequency range of interest for large electrochemical capacitors is generally below 1 kHz. Figure 28 shows the magnitude of the impedance versus the frequency for a series-RLC circuit. For large electrochemical capacitors presently available, the frequency at which Xc = ESR, is less than 10 Hz. Thus, these devices are completely unsuitable for 60-Hz power filtering applications. Stated differently, the dissipation factor of large commercial electrochemical capacitors at 60-Hz frequency is greater than 100%, making them behave more as a resistor than a capacitor. Thus, electrochemical capacitor technology does not compete with electrolytic capacitors in common dc filtering applications. Figure 28 Magnitude of the impedance as a function of frequency for a series-RLC circuit. As described above, the minimum impedance value occurs at the self-resonant frequency and is equal to the value of the ESR. This ESR value (R s ) along with the operating voltage, determines the maximum power capability of the capacitor. The maximum power (Pmax) that can be delivered by the capacitor into a matched load is Pmax =V 2 /4R s . When operating the capacitor at this maximum power point, the amount of energy that is delivered is equal to the amount dissipated internally within the capacitor. For many applications, particularly where efficiency is important, or where repetitive operation may lead to an unacceptable temperature rise, it is undesirable to operate a capacitor at this maximum power condition. Deviations from Ideal Behavior Because of the porous electrodes in an electrochemical capacitor, the power-energy relationship is more complicated than that described by a series-RC circuit. The equivalent circuit model used to describe the response of an electrochemical capacitor can be used to derive this energy-power relationship in Ragone plots. For example at very low discharge powers, when P ave /P max is

EPRI Proprietary Licensed Material the RC model and the actual performance increase as the power level approaches its maximum value. 1 0.9 0.8 E dis / E del 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Electrochemical Capacitor Series RC 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P ave / P max Figure 29 Energy dissipated as a function of power for series RC circuit versus a typical electrochemical capacitor A rule of thumb for capacitor operation, where efficiency or self-heating is important, is to restrict operation to a P ave /P max ratio of less than 0.1. At this power level, ~90% of the stored energy can be extracted from the capacitor. There are some applications where operation at higher power levels is appropriate. These applications generally are not cyclic in nature since operating at such high levels does cause a temperature rise within the capacitor. Two-Terminal Response The behavior of a typical electrochemical capacitor cell can be represented by the equivalent circuit model shown in Figure 30. Circuit elements include a series resistance, R s , and a capacitor, C, in parallel with a leakage current source. The equilibrium leakage current has exponential voltage dependence, which is observed for all electrochemical capacitors. The series resistance of a cell, R s , is responsible for establishing the voltage of that cell in a series string during transient operation. During steady state operation, the leakage current element establishes the voltage in a cell. During intermediate rate operation, that is during charge/discharge cycling, all three elements can play a role in establishing the voltage of each cell. Electrochemical Capacitors 59

EPRI Proprietary Licensed Material<br />

generally in the range <strong>of</strong> 1 Hz to ~ 100 Hz. This occurs because the capacitance itself is<br />

very large. The inductance is generally small <strong>f<strong>or</strong></strong> this technology. So the frequency<br />

range <strong>of</strong> interest <strong>f<strong>or</strong></strong> large electrochemical capacit<strong>or</strong>s is generally below 1 kHz.<br />

Figure 28 shows the magnitude <strong>of</strong> the impedance versus the frequency <strong>f<strong>or</strong></strong> a series-RLC<br />

circuit. F<strong>or</strong> large electrochemical capacit<strong>or</strong>s presently available, the frequency at which<br />

Xc = ESR, is less than 10 Hz. Thus, these devices are <strong>com</strong>pletely unsuitable <strong>f<strong>or</strong></strong> 60-Hz<br />

power filtering applications. Stated differently, the dissipation fact<strong>or</strong> <strong>of</strong> large <strong>com</strong>mercial<br />

electrochemical capacit<strong>or</strong>s at 60-Hz frequency is greater than 100%, making them behave<br />

m<strong>or</strong>e as a resist<strong>or</strong> than a capacit<strong>or</strong>. Thus, electrochemical capacit<strong>or</strong> technology does not<br />

<strong>com</strong>pete with electrolytic capacit<strong>or</strong>s in <strong>com</strong>mon dc filtering applications.<br />

Figure 28 Magnitude <strong>of</strong> the impedance as a function <strong>of</strong> frequency <strong>f<strong>or</strong></strong> a series-RLC circuit.<br />

As described above, the minimum impedance value occurs at the self-resonant frequency<br />

and is equal to the value <strong>of</strong> the ESR. This ESR value (R s<br />

) along with the operating<br />

voltage, determines the maximum power capability <strong>of</strong> the capacit<strong>or</strong>. The maximum<br />

power (Pmax) that can be delivered by the capacit<strong>or</strong> into a matched load is Pmax<br />

=V 2 /4R s<br />

. When operating the capacit<strong>or</strong> at this maximum power point, the amount <strong>of</strong><br />

energy that is delivered is equal to the amount dissipated internally within the capacit<strong>or</strong>.<br />

F<strong>or</strong> many applications, particularly where efficiency is imp<strong>or</strong>tant, <strong>or</strong> where repetitive<br />

operation may lead to an unacceptable temperature rise, it is undesirable to operate a<br />

capacit<strong>or</strong> at this maximum power condition.<br />

Deviations from Ideal Behavi<strong>or</strong><br />

Because <strong>of</strong> the p<strong>or</strong>ous electrodes in an electrochemical capacit<strong>or</strong>, the power-energy<br />

relationship is m<strong>or</strong>e <strong>com</strong>plicated than that described by a series-RC circuit. The<br />

equivalent circuit model used to describe the response <strong>of</strong> an electrochemical capacit<strong>or</strong><br />

can be used to derive this energy-power relationship in Ragone plots. F<strong>or</strong> example at<br />

very low discharge powers, when P ave /P max is

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