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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
Three-bus case with 30 MVAR Three-bus case with 30 MVAR support at loadsupport at load
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
Three-bus case with 45 MVAR Three-bus case with 45 MVAR support at loadsupport at load
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
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.
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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
3,000 MW transfer – 750 MW per line
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).
East generator is at 1,200 MVAR limit.
Case 4: Three Lines Out
3,000 MW transfer – 1,000 MW per line
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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).
East generator is at 1,200 MVAR limit.
Case 5: Four Lines Out
3,000 MW transfer – 1, 500 MW per line
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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
(606 MVARs required by lines).
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
(922 MVARs required by lines).
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