Reactive Power and Voltage Control Peter W Sauer

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 PSERC 1

15 years of interesting stuff • Proceedings: Bulk Power System Voltage Phenomena - Voltage Stability and Security, Potosi, MO, Sep 1924, 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

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

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

Instantaneous power (one phase)

Deomposed into two terms P (1 -cos(2 wt)) P =. 275 PU Watts - Q sin(2 wt)) Q = 0. 205 PU VARS

Steady-state frequency-domain model * S = V I = P + j. Q 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

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

What is voltage control? • Generator excitation • TCUL transformers • Switched capacitors and inductors • SVC and other FACTS devices PSERC 9

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

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

Opportunity costs 0

Challenges in voltage control • Determining AVR set points and supplementary input signals • Modeling what really happens when excitation systems hit limits • Optimal placement and control of SVC and other VAR sources PSERC 13

Optimal Power Flow Minimize total system costs subject to constraints

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

Inequality Constraints Generator Limits Line Limits Tap Limits Voltage Limits

Information from OPF solution • Marginal cost of real power in $/MWh at each system bus • Marginal cost of reactive power in $/MVARh at each system bus PSERC 17

Value of a Reactive Power Source • This example illustrates the use of a capacitor as a reactive power source for voltage control • It shows that a capacitor effects the available transfer capability • It shows the economic value of the VARS PSERC 18

Three-bus case with no area power transfer System Voltage Constraint 0. 96 < Vi < 1. 04 No power transfer Total Cost = $25, 743/hr

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

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

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

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

Six One Two Three Four Five No lights lights on on on 14 20 23 25 24 0 Wattstotal (some (roomgets light is dark) brighter) darker) in room) Voltagedrops is normal some more

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. PSERC 25 25

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. PSERC 26 26

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

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

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

Case 6: Five Lines Out System Collapse 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 PSERC 30 maintain the voltage at the East bus. 30

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

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

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

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

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

The challenge of security analysis • 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 failure PSERC 36