lecture5

# lecture5 - The Power Flow Solution Most common and...

This preview shows pages 1–6. Sign up to view the full content.

Power Systems I The Power Flow Solution Most common and important tool in power system analysis also known as the “Load Flow” solution used for planning and controlling a system assumptions: balanced condition and single phase analysis Problem: determine the voltage magnitude and phase angle at each bus determine the active and reactive power flow in each line each bus has four state variables: voltage magnitude voltage phase angle real power injection reactive power injection

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Power Systems I The Power Flow Solution Each bus has two of the four state variables defined or given Types of buses: Slack bus (swing bus) voltage magnitude and angle are specified, reference bus solution: active and reactive power injections Regulated bus (generator bus, P-V bus) models generation-station buses real power and voltage magnitude are specified solution: reactive power injection and voltage angle Load bus (P-Q bus) models load-center buses active and reactive powers are specified (negative values for loads) solution: voltage magnitude and angle
Power Systems I Newton-Raphson PF Solution Quadratic convergence mathematically superior to Guass-Seidel method More efficient for large networks number of iterations required for solution is independent of system size The Newton-Raphson equations are cast in natural power system form solving for voltage magnitude and angle, given real and reactive power injections

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Power Systems I Newton-Raphson Method A method of successive approximation using Taylor’s expansion Consider the function: f ( x ) = c , where x is unknown Let x [0] be an initial estimate, then Δ x [0] is a small deviation from the correct solution Expand the left-hand side into a Taylor’s series about x [0] yeilds ( ) c x x f = Δ + ] 0 [ ] 0 [ ( ) ( ) c x dx f d x dx df x f = + Δ + Δ + L 2 ] 0 [ 2 2 2 1 ] 0 [ ] 0 [
Power Systems I Newton-Raphson Method Assuming the error, Δ x [0] , is small, the higher-order terms are neglected, resulting in where

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/13/2011 for the course EEL 4213 taught by Professor Thomasbaldwin during the Spring '11 term at FSU.

### Page1 / 21

lecture5 - The Power Flow Solution Most common and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online