Review, DCPF, and summary

11 outubro 2012, 11:00 • Luis Marcelino Ferreira

Review of PV buses

PVQ bus, P bus

Review of procedure

Review of FDPF

Where to get the idea of sepation of P,teta and Q, V

Direct current power flow, DCPF

Analogy with a resistive circuit and nodal current injections

The same B’, P injections; unknowns are teta

The ubiquitous role of a slack generator

Which power flow method is most used?

Why? Planning problems vs operations problems

A question of linearized and assume linearity pf vs linearized and successive linearizations

Summary of power flow problems and power flow methods

Neutra

9 outubro 2012, 11:00 • Luis Marcelino Ferreira

Não houve esta aula -- é a aula que fica vazia de 3 em 3 semanas

Newton, Quasi-Newton, decoupling, FDPF

9 outubro 2012, 09:30 • Luis Marcelino Ferreira

Complex pf eqs: Jacobi, Gauss, Seidel; no. of eqs

Real pf eqs: rectangular coordinates: Newton; no. of eqs

Real pf eqs: polar coordinates: Newton; no. of eqs

Experimentation with Newton Lab TE3: N and J zeroed; diagdiagN and diagdiagL; other experiments such as BB and diagdiagBB

Most simplified Newton (which works) vs Gauss: how they compare

Advantages and disadvantages of decoupling

Decoupling and not updating: keep Jacobian approximate and constant

Fast decoupling, Stott, approximation made in order to obtain B’ and B”

Why despite different Jacobians the solution remains exactly the same one

 How to test convergence properties for Lab exercise: further loading; network weakening

Observe number of iterations, Jacobian eigenvalues

PV bus: assumption may not hold; how to proceed

TE1 (cont) and TE2

8 outubro 2012, 08:00 • Luis Marcelino Ferreira

Review for TE1: results must be equal

Jacobi-Gauss vs solve()

TE2: discussion of problem, presentation of results

Again: Jacobi-Gauss vs solve()

Solution on a real parameter by trial and error (bissection, etc)

Powerflow eqs in real format and Newton's

4 outubro 2012, 11:00 • Luis Marcelino Ferreira

Powerflow eqs in real format

Based on separation of the matrix form of I=YV

Vectors P, Q; Matrices G and B

Polar form: V, theta

Rectangular form: Re(V), Imag(V)

Advantages and disadvantages of polar vs rectangular

Can Newton’s be used in rectangular form?

PV buses: how to handle them

Power flow without a I=YB matrix base: nodal power eqs

Newton’s method and the role of derivatives

Computation of dPi/dthetaj, dPi/dVj, dQi/dthetaj and dQi/dVj

Use (.)/dVj/Vj instead: historical advantages

Assembling J

inv(J) is merely symbolic: do not use it for Newton’s, not even in Matlab

Matrix factorization: review basics

Numerical example of a J