Loading in 5 sec....

Newton-Raphson Power Flow Algorithm IIPowerPoint Presentation

Newton-Raphson Power Flow Algorithm II

- 85 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Newton-Raphson Power Flow Algorithm II' - buffy-fletcher

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### The End following power system assuming bus 1 is the slack bus, all bus voltages are approximately 1/

- During the last lecture, you (we) derived the functional form of the Jacobian entries:

- We laid out the mismatch equation ordering form of the Jacobian entries:P then Q and ordered the variable as then V to use LU factorization w/o pivoting:

- Recall that to avoid pivoting we needed positive definiteness
- numerically intensive to prove

- Or diagonal dominance
- easy to prove, but an overly restrictive requirement.

- Let’s investigate the approximate magnitude of each Jacobian entry.

- From our experience with power system data we know that for most branches:

- Also at the start of the iteration process:

- Entering these approximations into our Jacobian we get: most branches:

Jacobian is close diagonally dominant and it is not surprising that no pivoting is required.

Changing the order of the eqn’s or variables will destroy the near diagonal dominance property.

- Think-Pair-Square: Construct the Jacobian matrix for the following power system assuming bus 1 is the slack bus, all bus voltages are approximately 1/00 and the generator bus shown is not on VAR limits.

All line charging susceptances

are given by j0.02

2

1

0.02+j0.06 P.U.

0.02+j0.06 P.U.

0.02+j0.06 P.U.

3

Read Input, Construct Y following power system assuming bus 1 is the slack bus, all bus voltages are approximately 1/bus

Assume Flat Bus Voltage Profile E=1/00

Assume Gen’s not on VAR limits.

Update Bus Voltage Vq+1=Vq+Vq, q+1= q+ q

Iteration Index=q=0

Calculate Line Flows, Gen. Power and Mismatches

Y

Is q>3?

Perform bus type switching

Did buses

Switch Types?

N

N

q=q+1

Converged?

|Pqmax|, |Qqmax|<?

Y

Create Output

Y

N

Calculate Jacobian Entries and Solve Mismatch Eqn.

Determine optimal ordering for minimal fill. Permute input data.

Read following power system assuming bus 1 is the slack bus, all bus voltages are approximately 1/

Input

Solve

Write

Output

Optimal

Order

Permute

Input Data

Initial Estimate of

Bus Voltages

Line Flows

& Mismatches

Bus Type

Switching

Construct

Jacobian

Factorize

Jacobian

Solve for

q, Vq

Update

q+1, Vq+1

Permute

Output

Main Steering Routine

Download Presentation

Connecting to Server..