1. ECEN 460 Power System Operation and Control
Lecture 12: Power Flow
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
Texas A&M University

2. Announcements Finish reading Chapter 6
Homework 5 is 6.38 (except change the line’s impedance to 0.02+j0.08), 6.39 (except use the 0.02+j0.08 line impedance, and just do one iteration), 6.44, 6.48, 6.52, 6.53
Lab 5 next week is again in CVLP 319
Lab 6 and the following labs will be back in WEB 115

3. Power Flow Application PJM Control Center
Their generation capacity is about 177 GW 2

4. The N-R Power Flow: 5-bus Example
400 MVA
15 kV
15/345 kV T1 T2
800 MVA
345/15 kV
520 MVA
80 MW
40 Mvar
280 Mvar
800 MW
Line kV
Line 2
Line 1
345 kV 100 mi
345 kV 200 mi
50 mi 1 4 3 2 5
Single-line diagram 3

5. Five Bus System Ybus 4 4

6. Ybus Details
Elements of Ybus connected to bus 2 5 5

7. Here are the Initial Bus Mismatches6 6

8. And the Initial Power Flow Jacobian7 7

9. And the Hand Calculation Details!8 8

10. Five Bus Power System Solved9 9

11. Five Bus System With Capacitor
A capacitor has been added at bus 2 to fix its low voltage 10

12. Example: ERCOT Competitive Renewable Energy Zones (CREZ) Study
In 2005 Texas Legislature ordered a grid study in order to accommodate more renewable generation in West Texas; reactive compensation was a key aspect
Starting System Topology
Shunt Additions (< 0=caps) 11
Source:

13. Chapter 6 Design Case 1 Example
System has 37 bus, plus one new bus 12 12

14. Good Power System Operation
Good power system operation requires that there be no reliability violations for either the current condition or in the event of statistically likely contingencies
Reliability requires as a minimum that there be no transmission line/transformer limit violations and that bus voltages be within acceptable limits (perhaps 0.95 to 1.08)
Example contingencies are the loss of any single device. This is known as n-1 reliability.
North American Electric Reliability Corporation (N ERC) now has legal authority to enforce reliability standards (and there are now lots of them). See 13 13

15. Design Case 1 Line Outages
Playing around with the power flow can help gain an intuitive feel for how the system operates 14

16. Design Case 1: Voltage Control15

17. Power System Operation Over Time
Movie shows the hourly system variation over the course of one week for a 500 bus synthetic grid 16

18. Synthetic Texas 2000 Bus System
As is the case with actual grids, as the system load changes with time there is a need for lots of reactive power control device
changes to keep the voltages in range 17