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Lecture Methods of Electric power systems analysis - Lesson 5: Power flow

Lecture Methods of Electric power systems analysis - Lesson 5: Power flow provide students with knowledge about two bus Newton-Raphson example; two bus solved values; two bus case low voltage solution; practical power flow software note; two bus region of convergence; power flow fractal region of convergence; modeling voltage dependent load; . | ECEN 615 Methods of Electric Power Systems Analysis Lecture 5 Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering Texas A amp M University overbye@tamu.edu Announcements Read Chapter 6 from the book Homework 1 will be due on Friday September 4 Homework 2 will be assigned next time due on Thursday September 17 1 Two Bus Newton-Raphson Example For the two bus power system shown below use the Newton-Raphson power flow to determine the voltage magnitude and angle at bus two. Assume that bus one is the slack and SBase 100 MVA. Line Z 0.1j One 1.000 pu Two 1.000 pu 0 MW 200 MW 0 MVR 100 MVR 2 j10 j10 x Ybus V2 j10 j10 2 Two Bus Example cont d General power balance equations n Pi Vi Vk Gik cos ik Bik sin ik PGi PDi k 1 n Qi Vi Vk Gik sin ik Bik cos ik QGi QDi k 1 Bus two power balance equations V2 V1 10sin 2 2.0 0 V2 V1 10cos 2 V2 10 1.0 0 2 3 Two Bus Example cont d P2 x V2 10sin 2 2.0 0 Q2 x V2 10cos 2 V2 10 1.0 0 2 Now calculate the power flow Jacobian P2 x P2 x V 2 J x 2 Q 2 x Q 2 x V 2 2 10 V2 cos 2 10sin 2 10 V2 sin 2 10cos 2 20 V2 4 Two Bus Example First Iteration 0 Set v 0 guess x 0 1 Calculate V2 10sin 2 2.0 2.0 f x 0 1.0 V2 10cos 2 V2 10 1.0 2 10 V2 cos 2 10sin 2 10 0 J x 0 0 10 10 V2 sin 2 10cos 2 20 V2 1 0 10 0 2.0 0.2 Solve x 1 1.0 1 0 10 0.9 5 Two Bus Example Next Iterations 0.9 10sin 0.2 2.0 0.212 f x 1 0.9 10cos 0.2 0.9 2 10 1.0 0.279 8.82 1.986 J x 1 1.788 8.199 1 0.2 8.82 1.986 0.212 0.233 x 2 0.9 1.788 8.199 0.279 0.8586 0.0145 0.236 f x 2 x 3 0.0190 0.8554 0.0000906 f x 3 Done V2 0.8554 13.52 0.0001175 6 Two Bus Solved Values Once the voltage angle and magnitude at bus 2 are known we can calculate all the other system values such as the line flows and the generator reactive power output 200.0 MW -200.0 MW 168.3 MVR Line Z 0.1j -100.0 MVR One 1.000 pu Two 0.855 pu -13.522 Deg 200.0 MW 200 MW 168.3 MVR 100 MVR PowerWorld Case Name Bus2_Intro Note most PowerWorld cases will be available on the course website 7 Two Bus Case Low .