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lecture5 - Power Systems I The Power Flow Solution l Most...

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Unformatted text preview: Power Systems I The Power Flow Solution l Most common and important tool in power system analysis u also known as the “Load Flow” solution u used for planning and controlling a system u assumptions: balanced condition and single phase analysis l Problem: u determine the voltage magnitude and phase angle at each bus u determine the active and reactive power flow in each line u each bus has four state variables: n voltage magnitude n voltage phase angle n real power injection n reactive power injection Power Systems I The Power Flow Solution u Each bus has two of the four state variables defined or given l Types of buses: u Slack bus (swing bus) n voltage magnitude and angle are specified, reference bus n solution: active and reactive power injections u Regulated bus (generator bus, P-V bus) n models generation-station buses n real power and voltage magnitude are specified n solution: reactive power injection and voltage angle u Load bus (P-Q bus) n models load-center buses n active and reactive powers are specified (negative values for loads) n solution: voltage magnitude and angle Power Systems I Newton-Raphson PF Solution l Quadratic convergence u mathematically superior to Guass-Seidel method l More efficient for large networks u number of iterations required for solution is independent of system size l The Newton-Raphson equations are cast in natural power system form u solving for voltage magnitude and angle, given real and reactive power injections Power Systems I Newton-Raphson Method l A method of successive approximation using Taylor’s expansion u Consider the function: f ( x ) = c , where x is unknown u Let x [0] be an initial estimate, then ∆ x [0] is a small deviation from the correct solution u Expand the left-hand side into a Taylor’s series about x [0] yeilds ( 29 c x x f = ∆ + ] [ ] [ ( 29 ( 29 c x dx f d x dx df x f = + ∆ + ∆ + L 2 ] [ 2 2 2 1 ] [ ] [ Power Systems I Newton-Raphson Method...
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This note was uploaded on 11/27/2011 for the course EEL 4213 taught by Professor Thomasbaldwin during the Spring '11 term at FSU.

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lecture5 - Power Systems I The Power Flow Solution l Most...

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