Nr.2 - ALPA - Albanian Papers

Krasniqi & KokaDefinitions and Acronymsn gNumber of generators in thepower system.P DReal Power.Q DReactive Power.P QLoad Buses.P GReal Power Generated.θVoltage Phase.Y busThe admittance matrix of apower system.p.uPer unitMATLAB Is a numerical computingenvironment and programminglanguage.MATPOWER Is a package of MATLAB M-filesfor solving power flow andoptimal power flow problems.PROBLEM STATEMENTThe Power Flow ProblemThe goal of a Power Flow study is to obtaincomplete voltage angle and magnitudeinformation for each bus in a power system forspecified load and generator real power andvoltage condition. Once this information isknown, real and reactive power flow on eachbranch as well as generator reactive poweroutput can be analytically determined. Due to thenonlinear nature of this problem, numericalmethods are employed to obtain a solution thatis within an acceptable tolerance.The solution to the Power Flow problem beginswith identifying the known and unknownvariables in the system. The known and unknownvariables are dependent on the type of bus. A buswithout any generators connected to it is called aLoad Bus. With one exception, a bus with at leastone generator connected to it is called aGenerator Bus. The exception is one arbitrarilyselectedbus that has a generator. This bus isreferred to as the Slack Bus.Equivalent Circuit ModelThe equivalent circuit model that we are using forour simulation is shown in Figure 1.Schematic, indicating the input and output to thebuses along with their transformer ratios inbetween.Figure 1: Equivalent Circuit Model|V k | = voltage magnitude at bus k,δ k = voltage phase angle at bus k,I k = current flowing from bus k,I m = current flowing from bus m,G k = generator at bus k,S GK = generator complex power at bus k,P GK = generator real power,Q GK = generator reactive power,S LK = load complex power at bus k,P LM = load real power,Q LK = load reactive power,Z km = line impedance,B cap = line shunt susceptance,a = normalized transformer turns ratio.Newton Raphson Solution MethodThere are several different methods of solvingthe resulting nonlinear system of equations. Themost popular is known as the Newton-RaphsonMethod. This method begins with initial guessesof all unknown variables (voltage magnitude andangles at Load Buses and voltage angles atGenerator Buses). Next, a Taylor Series is written,with the higher order terms ignored, for each ofthe power balance equations included in thesystem of equations. The result is a linear systemof equations that can be expressed as:AKTET Vol. IV, Nr 2, 2011 179