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 abirchfield@tamu.edu Material gratefully adapted with permission from slides by Prof. Tom Overbye.

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 www.nerc.com/pa/stand/pages/reliabilitystandards.aspx 1

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

Design case 1: voltage control

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

Synthetic Texas 2000 bus system

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

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

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

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

Extreme control example: 42 bus tornado scenario

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

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

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

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 64.7 MW drop on the flow from 1 to 3. Expressed as a percent, 30.3/95 =32% and 64.7/95=68%

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

Analytic sensitivities

Three bus sensitivity example

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

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 116.1-121.4 MW, so the sensitivity is -0.53. Of course this is just an approximation!

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 117.5-121.4 MW, so the sensitivity is 0.39 (note sign is positive because increasing the generation would increase the flow)

Lab six example So shifting 10 MWs from Pear69 to Orange69, should decrease the line flow (0.39+0.53)*10= 9.2 MW This is very close to the actual change with little impact on the slack bus

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

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

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!

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

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 1973-74 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

Zion nuclear power plant

Lab 6 reactive power optimization