1. 1 PS ERC Reactive Power and Voltage Control Peter W. Sauer Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign NSF Workshop on applied mathematics for deregulated power systems: Optimization, Control and Computational Intelligence Nov 3-4, 2003, Alexandria, VA

2. 15 years of interesting stuff Proceedings: Bulk Power System Voltage Phenomena - Voltage Stability and Security, Potosi, MO, Sep 19- 24, 1988 Proceedings NSF Workshop on Bulk Power System Voltage Phenomena Voltage Stability and Security, Deep Creek Lake, MD, Aug. 4-7, 1991 Proceedings of the Bulk Power System Voltage Phenomena - III Seminar on Voltage Stability, Security & Control, Davos, Switzerland, August 22-26, 1994

3. 15 years of interesting stuff Proceedings of the Symposium on "Bulk Power System Dynamics and Control IV - Restructuring", Santorini, Greece, August 24-28, 1998 Proceedings Bulk Power Systems Dynamics and Control V - Security and Reliability in a Changing Environment, Onomichi, Japan, August 26-31, 2001 Proceedings Bulk Power Systems Dynamics and Control VI, Cortina, Italy, August 22-27, 2004

4. What is reactive power? It is all in the phase shift

5. Instantaneous power (one phase)

6. Deomposed into two terms P (1-cos(2wt)) - Q sin(2wt)) P =.275 PU Watts Q = 0.205 PU VARS

7. Steady-state frequency-domain model S = V I * = P + jQ Important thing here is that for a given amount of real power P, and a given voltage, the existence of Q causes current to be higher than necessary to provide P – i.e. VARS clog up the system

8. PQ capability curve 0 Shouldn’t just use fixed MVAR limit (MVAR limit is a function of MW dispatch)Shouldn’t just use fixed MVAR limit (MVAR limit is a function of MW dispatch) Perhaps unit commitment should consider VAR support capabilityPerhaps unit commitment should consider VAR support capability More on this laterMore on this later

9. 9 PS ERC What is voltage control? Generator excitationGenerator excitation TCUL transformersTCUL transformers Switched capacitors and inductorsSwitched capacitors and inductors SVC and other FACTS devicesSVC and other FACTS devices

10. 10 PS ERC Which is which and what is what? VARS are the problem and the solution for voltage controlVARS are the problem and the solution for voltage control – Transmission line losses (I 2 X) – Voltage drop (IX) – Local load compensation - current reduction ResponseResponse –Milliseconds to seconds –Zero to 1,000 MVARS –They do go long distances - just not very efficiently (Local supply is best)

11. 11 PS ERC A competitive environment VARS are a commodity?VARS are a commodity? Voltage control is a service?Voltage control is a service? How do you allocate VAR losses?How do you allocate VAR losses? How do you charge/compensate for voltage control?How do you charge/compensate for voltage control?

12. Opportunity costs 0

13. 13 PS ERC Challenges in voltage control Determining AVR set points and supplementary input signalsDetermining AVR set points and supplementary input signals Modeling what really happens when excitation systems hit limitsModeling what really happens when excitation systems hit limits Optimal placement and control of SVC and other VAR sourcesOptimal placement and control of SVC and other VAR sources

14. Optimal Power Flow Minimize total system costs subject to constraints

15. Equality Constraints The power flow equations Generator voltage set-points MW interchanges (contract agreements)

16. Inequality Constraints Generator Limits Line Limits Tap Limits Voltage Limits

17. 17 PS ERC Information from OPF solution Marginal cost of real power in $/MWh at each system busMarginal cost of real power in $/MWh at each system bus Marginal cost of reactive power in $/MVARh at each system busMarginal cost of reactive power in $/MVARh at each system bus

18. 18 PS ERC This example illustrates the use of a capacitor as a reactive power source for voltage controlThis example illustrates the use of a capacitor as a reactive power source for voltage control It shows that a capacitor effects the available transfer capabilityIt shows that a capacitor effects the available transfer capability It shows the economic value of the VARSIt shows the economic value of the VARS Value of a Reactive Power Source

19. Three-bus case with no area power transfer No power transfer Total Cost = $25,743/hr System Voltage Constraint 0.96 < V i < 1.04

20. Maximum power transfer = 244 MW Total Cost = $21,346/hr = savings of $4,397/hr Three-bus case with 15 MVAR support at load voltage constraint limits the power transfer

21. Three-bus case with 30 MVAR support at load Maximum power transfer = 325 MW Total Cost = $20,898/hr = additional savings of $448/hr voltage constraint limits the power transfer

22. Three-bus case with 45 MVAR support at load Maximum power transfer = 355 MW Total Cost = $20,849/hr = additional savings of $49/hr voltage constraint does not limit “economic” power transfer

23. Relationships between maximum power transfer and voltage control DC case - no VARS neededDC case - no VARS needed AC case - VARS do helpAC case - VARS do help AC case - even an infinite amount of VARS will not always helpAC case - even an infinite amount of VARS will not always help

24. No lights on 0 Watts total (room is dark) Voltage is normal One light on 14 Watts total (some light in room) Voltage drops some Two lights on 20 Watts total (room gets brighter) Voltage drops more Three lights on 23 Watts total (room gets brighter) Voltage drops more Four lights on 24 Watts total (room gets brighter) Voltage drops more Five lights on 25 Watts total (room gets brighter) Voltage drops more Six lights on 24 Watts total (room gets darker) Voltage drops more

25. 25 PS ERC Case 1: All Lines In-Service 3,000 MW transfer – 500 MW per line Voltage is 100% of rated voltage. (300 MVARs required by lines). East generator is below 1,200 MVAR limit. 25

26. 26 PS ERC Case 2: One Line Out 3,000 MW transfer – 600 MW per line Voltage is 100% of rated voltage (362 MVARs required by lines). East generator is below 1,200 MVAR limit. 26

27. 27 PS ERC Voltage is 100% of rated (453 MVARs required by lines). East generator is at 1,200 MVAR limit. Case 3: Two Lines Out 3,000 MW transfer – 750 MW per line 27

28. 28 PS ERC Voltage is only 99% of rated (611 MVARs required by lines). East generator is at 1,200 MVAR limit. Case 4: Three Lines Out 3,000 MW transfer – 1,000 MW per line 28

29. 29 PS ERC Voltage has dropped to 97% of rated voltage (957 MVARs required by lines). East generator is at 1,200 MVAR limit. Case 5: Four Lines Out 3,000 MW transfer – 1, 500 MW per line 29

30. 30 PS ERC This simulation could not solve the case of 3,000 MW transfer with five lines out. Numbers shown are from the model’s last attempt to solve. The West generator’s unlimited supply of VARs is still not sufficient to maintain the voltage at the East bus. Case 6: Five Lines Out System Collapse 30

31. Case 7: Two lines out - full voltage control 31 (452 MVARs required by lines).

32. Case 8: Three lines out - full voltage control 32 (606 MVARs required by lines).

33. 33 PS ERC Case 9: Four lines out - full voltage control 33 (922 MVARs required by lines).

34. Case 10: Five lines out - full voltage control 34 (2,000 MVARs required by lines).

35. Case 11: How much could this have handled? 35 4,900 MW

36. 36 PS ERC The challenge of security analysis Traditional security analysis uses N-1 criteria (withstand the outage of one thing)Traditional security analysis uses N-1 criteria (withstand the outage of one thing) A challenging and useful margin would be to compute the minimum number of things that can be lost without resulting in cascading failureA challenging and useful margin would be to compute the minimum number of things that can be lost without resulting in cascading failure