sauer

1PSERC

Reactive Power and Voltage ControlReactive Power and Voltage Control

Peter W. SauerPeter W. SauerDepartment of Electrical and Computer EngineeringDepartment of Electrical and Computer Engineering

University of Illinois at Urbana-ChampaignUniversity 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

15 years of interesting stuff15 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

15 years of interesting stuff15 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?What is reactive power?

It is all in the phase shiftIt is all in the phase shift

-1.5

-1

-0.5

0

0.5

1

1.5

Voltage

Current

Instantaneous power (one phase)Instantaneous power (one phase)

-0.2-0.1

00.10.20.30.40.50.60.7

Power

Deomposed into two termsDeomposed into two terms

P (1-cos(2wt))

- Q sin(2wt))

P = .275 PU Watts

Q = 0.205 PU VARS

0

0.1

0.2

0.3

0.4

0.5

0.6

Real power

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Reactive power

Steady-state frequency-domain modelSteady-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

PQ capability curvePQ capability curve

(MVAR)Q

(MW)P

*min 1( )Q P

*max 1( )Q P

*1P0 *

3P*

2P

*max 2( )Q P

*max 3( )Q P

*min 2( )Q P

*min 3( )Q P

• Shouldn’t just use Shouldn’t just use fixed MVAR limit fixed MVAR limit (MVAR limit is a (MVAR limit is a function of MW function of MW dispatch)dispatch)

• Perhaps unit Perhaps unit commitment should commitment should consider VAR consider VAR support capabilitysupport capability

• More on this laterMore on this later

9PSERC

What is voltage control?What is voltage control?

• Generator excitation Generator excitation

• TCUL transformersTCUL transformers

• Switched capacitors and inductorsSwitched capacitors and inductors

• SVC and other FACTS devicesSVC and other FACTS devices

10PSERC

Which is which and what is what?Which is which and what is what?• VARS are the problem and the solution for VARS are the problem and the solution for

voltage controlvoltage control– Transmission line losses (ITransmission line losses (I22X)X)– Voltage drop (IX)Voltage drop (IX)– Local load compensation - current reductionLocal load compensation - current reduction

• ResponseResponse– Milliseconds to secondsMilliseconds to seconds– Zero to 1,000 MVARSZero to 1,000 MVARS– They do go long distances - just not very efficiently (Local They do go long distances - just not very efficiently (Local

supply is best)supply is best)

11PSERC

A competitive environmentA 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 How do you charge/compensate for voltage control?voltage control?

Opportunity costsOpportunity costs

(MVAR)Q

(MW)P

*min 1( )Q P

*max 1( )Q P

*1P0 *

3P*

2P

*max 2( )Q P

*max 3( )Q P

*min 2( )Q P

*min 3( )Q P

(MVAR)Q

*max 1( )Q P *

max 2( )Q P *max 3( )Q P*

min 1( )Q P*min 2( )Q P*

min 3( )Q P

$/MVAR

* * *1 2 3P P P

13PSERC

Challenges in voltage controlChallenges in voltage control

• Determining AVR set points and Determining AVR set points and supplementary input signalssupplementary input signals

• Modeling what really happens when Modeling what really happens when excitation systems hit limitsexcitation systems hit limits

• Optimal placement and control of Optimal placement and control of SVC and other VAR sourcesSVC and other VAR sources

Optimal Power FlowOptimal Power Flow

Minimize total system costsMinimize total system costs f x a b P c Pi i Gi i Gi

i( )

2

all system buses in ALL areas

subject to constraintssubject to constraints

P V V g b P P

Q V V g b Q Q

k k m km k m km k mm

N

Gk Lk

k k m km k m km k mm

N

Gk Lk

0

0

1

1

cos sin

sin cos

Equality ConstraintsEquality Constraints

The power flow equations The power flow equations

V VGi Gi setpo int 0Generator voltage set-pointsGenerator voltage set-points

P P P Pkminterchange sceduled interchangetie lines

sceduled interchange 0MW interchanges (contract agreements)MW interchanges (contract agreements)

Inequality ConstraintsInequality Constraints

P P P

Q Q QGi Gi Gi

Gi Gi Gi

min max

min max

t t tkm km km

km km km

min max

min max

S Skm km

2 20 max

V V Vi i imin max

Generator LimitsGenerator Limits Line LimitsLine Limits

Tap LimitsTap Limits Voltage LimitsVoltage Limits

17PSERC

Information from OPF solutionInformation 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

18PSERC

• This example illustrates the use of a This example illustrates the use of a capacitor as a reactive power source for capacitor as a reactive power source for voltage controlvoltage control

• It shows that a capacitor effects the It shows that a capacitor effects the available transfer capabilityavailable transfer capability

• It shows the economic value of the VARSIt shows the economic value of the VARS

Value of a Reactive Power SourceValue of a Reactive Power Source

Three-bus case with no area Three-bus case with no area power transferpower transfer

No power transferNo power transferTotal Cost = $25,743/hrTotal Cost = $25,743/hr

System VoltageConstraint0.96 < Vi < 1.04

1.04 PU0.9709 PU

502 MW194 MVR

413 MW 69 MVR

300 MW

Bus 1Bus 2

100 MW

1.04 PUBus 3

100 MVR

Area Two

Area One

14 MVR500 MW100 MVR

30 MVR

50.08 $/MWH 0.00 $/MVRH

20.26 $/MWH 0.00 $/MVRH

22.58 $/MWH 0.57 $/MVRH

74 MW 72 MVR

-73 MW 22 MVR

74 MW-15 MVR 239 MW

55 MVR

-72 MW-64 MVR

-228 MW-21 MVR

Maximum power transfer = 244 MWMaximum power transfer = 244 MWTotal Cost = $21,346/hr = savings of $4,397/hrTotal Cost = $21,346/hr = savings of $4,397/hr

Three-bus case with 15 MVAR Three-bus case with 15 MVAR support at loadsupport at load

1.04 PU0.9600 PU

271 MW290 MVR

668 MW 59 MVR

300 MW

Bus 1Bus 2

100 MW

1.04 PUBus 3

100 MVR

Area Two

Area One

14 MVR500 MW100 MVR

30 MVR

38.57 $/MWH 0.00 $/MVRH

25.35 $/MWH 0.00 $/MVRH

55.23 $/MWH54.75 $/MVRH

-27 MW112 MVR

-201 MW 78 MVR

214 MW-26 MVR 353 MW

55 MVR

30 MW-102 MVR

-330 MW 16 MVR

voltage constraint limits the power transfer


Maximum power transfer = 325 MWMaximum power transfer = 325 MWTotal Cost = $20,898/hr = additional savings of $448/hrTotal Cost = $20,898/hr = additional savings of $448/hr

1.04 PU0.9600 PU

198 MW323 MVR

754 MW 56 MVR

300 MW

Bus 1Bus 2

100 MW

1.04 PUBus 3

100 MVR

Area Two

Area One

28 MVR500 MW100 MVR

30 MVR

34.89 $/MWH 0.00 $/MVRH

27.07 $/MWH 0.00 $/MVRH

38.02 $/MWH13.42 $/MVRH

-60 MW122 MVR

-242 MW101 MVR

261 MW-25 MVR 393 MW

51 MVR

64 MW-109 MVR

-364 MW 36 MVR

voltage constraint limits the power transfer


Maximum power transfer = 355 MWMaximum power transfer = 355 MWTotal Cost = $20,849/hr = additional savings of $49/hrTotal Cost = $20,849/hr = additional savings of $49/hr

1.04 PU0.9631 PU

170 MW332 MVR

786 MW 51 MVR

300 MW

Bus 1Bus 2

100 MW

1.04 PUBus 3

100 MVR

Area Two

Area One

42 MVR500 MW100 MVR

30 MVR

33.52 $/MWH 0.00 $/MVRH

27.72 $/MWH 0.00 $/MVRH

32.82 $/MWH 1.05 $/MVRH

-73 MW122 MVR

-257 MW110 MVR

278 MW-24 MVR 408 MW

44 MVR

77 MW-107 MVR

-377 MW 49 MVR

voltage constraint does not limit “economic” power transfer

Relationships between maximum Relationships between maximum power transfer and voltage controlpower 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 AC case - even an infinite amount of VARS will not always helpVARS will not always help

No lights on0 Watts total(room is dark) Voltage is normal

One light on14 Watts total(some light in room)Voltage drops some

Two lights on20 Watts total(room gets brighter)Voltage drops more

Three lights on23 Watts total(room gets brighter)Voltage drops more

Four lights on24 Watts total(room gets brighter)Voltage drops more

Five lights on25 Watts total(room gets brighter)Voltage drops more

Six lights on24 Watts total (room gets darker)Voltage drops more

25PSERC

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU1150 MVR9000 MW

1150 MVR3000 MW

6000 MW1000 MVR

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

26PSERC

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU1176 MVR9000 MW

1186 MVR3000 MW

6000 MW1000 MVR

Case 2: One Line Out


Voltage is 100% of rated voltage(362 MVARs required by lines).

East generator is below 1,200 MVAR limit.

26

27PSERC

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU1253 MVR9000 MW

1200 MVR3000 MW

6000 MW1000 MVR

Voltage is 100% of rated (453 MVARs required by lines).

East generator is at 1,200 MVAR limit.

Case 3: Two Lines Out


27

28PSERC

EastWest

0.99 PU

6000 MW1000 MVR

1.00 PU1411 MVR9000 MW

1200 MVR3000 MW

6000 MW1000 MVR

Voltage is only 99% of rated (611 MVARs required by lines).


Case 4: Three Lines Out

3,000 MW transfer – 1,000 MW per line

28

29PSERC

EastWest

0.97 PU

6000 MW1000 MVR

1.00 PU1757 MVR9000 MW

1200 MVR3000 MW

6000 MW1000 MVR

Voltage has dropped to 97% of rated voltage(957 MVARs required by lines).


Case 5: Four Lines Out

3,000 MW transfer – 1, 500 MW per line

29

30PSERC

EastWest

0.77 PU

6000 MW1000 MVR

1.00 PU3500 MVR8926 MW

1200 MVR3000 MW

6000 MW1000 MVR

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

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU

1226 MVR9000 MW

1226 MVR3000 MW

6000 MW1000 MVR

Case 7: Two lines out - full voltage control

31

(452 MVARs required by lines).

Case 8: Three lines out - full voltage control

32

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU

1303 MVR9000 MW

1303 MVR3000 MW

6000 MW1000 MVR


33PSERC

Case 9: Four lines out - full voltage control

33

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU

1461 MVR9000 MW

1461 MVR3000 MW

6000 MW1000 MVR


Case 10: Five lines out - full voltage control

34

EastWest

1.00 PU

6000 MW1000 MVR

1.00 PU

2000 MVR9000 MW

2000 MVR3000 MW

6000 MW1000 MVR

(2,000 MVARs required by lines).

Case 11: How much could this have handled?

35

EastWest

1.00 PU

7900 MW1000 MVR

1.00 PU

4997 MVR10900 MW

5000 MVR3000 MW

6000 MW1000 MVR

4,900 MW

36PSERC

The challenge of security analysisThe challenge of security analysis

• Traditional security analysis uses N-1 Traditional security analysis uses N-1 criteria (withstand the outage of one thing)criteria (withstand the outage of one thing)

• A challenging and useful margin would be A challenging and useful margin would be to compute the minimum number of things to compute the minimum number of things that can be lost without resulting in that can be lost without resulting in cascading failurecascading failure

sauer

Documents

mvr bus

p mw qmin p

mw voltage constraint

mvr area

mvr maximum power transfer

real power p

mw total cost

function of mw dispatch