1. ECEN 460 Power System Operation and Control
Lecture 13: Power flow control, sensitivities, and voltage control
Adam Birchfield
Dept. of Electrical and Computer Engineering
Texas A&M University
Material gratefully adapted with permission from slides by Prof. Tom Overbye.

2. 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 (NERC) now has legal authority to enforce reliability standards (and there are now lots of them). See 1

3. Design case 1 line outages
Playing around with the power flow can help gain an intuitive feel for how the system operates

4. Design case 1: voltage control

5. Power system operation over time
Movie shows the hourly system variation over the course of one week for a 500 bus synthetic grid

6. Synthetic Texas 2000 bus system

7. Contingency analysis
Contingency analysis provides an automatic way of looking at all the statistically likely contingencies. In this example the contingency set is all the single line and transformer outages 6

8. Design case 1: serving new load
Assume we need to serve a new 70 MW, 20 Mvar load at 69 kV

9. Solving large power systems
The most difficult computational task is inverting the Jacobian matrix
inverting a full matrix is an order n3 operation, meaning the amount of computation increases with the cube of the size
this amount of computation can be decreased substantially by recognizing that since the Ybus is a sparse matrix, the Jacobian is also a sparse matrix
using sparse matrix methods results in a computational order of about n1.5.
this is a substantial savings when solving systems with tens of thousands of buses
We’ll return to large systems once we cover economic dispatch and optimal power flow

10. Power system control
A major issue with power system operation is the limited capacity of the transmission system
lines/transformers have limits (usually thermal)
no direct way of controlling flow down a transmission line (e.g., there are no valves to close to limit flow)
open transmission system access associated with industry restructuring is stressing the system in new ways
We need to indirectly control transmission line flow by changing the generator outputs
Similar control issues with voltage

11. Extreme control example: 42 bus tornado scenario

12. Power system control
A major issue with power system operation is the limited capacity of the transmission system
lines/transformers have limits (usually thermal)
no direct way of controlling flow down a transmission line (e.g., there are no valves to close to limit flow)
open transmission system access associated with industry restructuring is stressing the system in new ways
We need to indirectly control transmission line flow by changing the generator outputs
Similar control issues with voltage

13. Indirect transmission line control
What we would like to determine is how a change in
generation at bus k affects the power flow on a line
from bus i to bus j.
The assumption is
that the change
in generation is
absorbed by the
slack bus

14. Power flow simulation - before
One way to determine the impact of a generator change is to compare a before/after power flow.
For example below is a three bus case with an overload

15. Power flow simulation - after
Increasing the generation at bus 3 by 95 MW (and hence decreasing it at bus 1 by a corresponding amount), results in a 30.3 MW drop in the MW flow on the line from bus 1 to 2, and a MW drop on the flow from 1 to 3.
Expressed as a percent, 30.3/95 =32% and 64.7/95=68%

16. Analytic calculation of sensitivities
Calculating control sensitivities by repeat power flow solutions is tedious and would require many power flow solutions. An alternative approach is to analytically calculate these values

17. Analytic sensitivities

18. Three bus sensitivity example

19. Larger system example: Lab six 37 bus system with two lines out
With two lines out, there is an overload on a line between Pear69 and Pecan69.
We will approximate the impact of generation changes on this line flow by looking at the results of changing the generation in the power flow

20. Lab six example
Increase generation at Orange69 by 10 MW, noting that this change is absorbed at the slack bus
The change in the line flow is MW, so the sensitivity is Of course this is just an approximation!

21. Lab six example
Decrease the generation at Pear69 by 10 MW, noting that this change is also absorbed at the slack bus
The change in the line flow is MW, so the sensitivity is 0.39 (note sign is positive because increasing the generation would increase the flow)

22. Lab six example
So shifting 10 MWs from Pear69 to Orange69, should decrease the line flow ( )*10= 9.2 MW
This is very close to the actual change with little impact on the slack bus

23. PowerWorld analytic sensitivities
Select Tools, Sensitivities, Flow and Voltage Sensitivities to see lots of sensitivities. The below image shows values for our example.

24. Contour of the line flow to bus injection sensitivities
Image shows how a change in injection at a bus affects the flow on the Pear69-Pecan69 line
This is a contour of the bus field: Sensitivity or Injection Value dValue/dP

25. Lab 6, part B: Can you save Texas?
You’ll be using a 2000 bus model of a synthetic grid that is supplying a load that matches the actual Texas population. A tornado takes out two lines, and you need to fix the overloads before the grid fails!

26. Reactive power optimization
Reactive power controllers include switched shunts, static var compensators (SVCs), LTC transformers, sometimes generator voltage setpoints
Goal is to maintain adequate system voltages and reduce losses
Reactive power control is much less linear than real power control; this is partially due to the much higher reactive power losses because for high voltage transmission lines X is usually much larger than R
Losses are vary nonlinear

27. Zion nuclear power plant
The Zion nuclear power plant, located on Lake Michigan, on the Illinois/Wisconsin border, use to be a 2000 MW generator, commissioned in
In 1997 a control-room operator inserted control rods too far during a shut down, then withdrew them without following procedures
NRC also said there were too many people in the control room
ComEd ended up shutting down both units because it was too costly to fix the damage (estimated at $435 million!)
However, the plant was used for many years as a source of reactive power for North Illinois

28. Zion nuclear power plant

29. Lab 6 reactive power optimization