Newton-Raphson Power Flow Algorithm

1. Newton-Raphson Power Flow Algorithm Lecture #20 EEE 574 Dr. Dan Tylavsky

2. Formulate the Newton-Raphson Power-Flog Algorithm • Treat all buses as P-Q type buses. • Handle bus-type switching (i.e., P-Q to P-V and vice versa) by modifying the Jacobian. • Define the PG-PL=P (injected into the bus)

3. The real and reactive power balance equations are:

4. Working with the real power balance eqn. • Taylor’s expansion gives:

6. Writing the equation for all buses while interleaving the  & V variables gives: • The order of derivative is chosen to be  then V because the  derivative of the P function is not near zero under normal conditions.

7. We can perform a similar derivation for the reactive power balance equation. • Apply Taylor’s theorem.

9. Writing the  Q equation for all buses while interleaving the  & V variables gives:

10. Finally interleaving the P & Q equations gives:

11. Let’s find analytical expressions for each of the Jacobian entries:

12. Let’s find analytical expressions for each of the Jacobian entries:

13. Recall the definition of QCalc at bus i:

14. TEAMS: find the remaining derivatives:

15. Using the H, N, J, L notation we have for the mismatch equation:

16. The End