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Identification of Voltage Stability Weak Points
in Bulk Power System
Presented to the NSF Applied Mathematics for Deregulated
Electric Power Systems Workshop, Washington DC
Tao He, Sujit Mandal, Floyd Galvan
Entergy
1
Entergy System
•
•
•
•
•
•
2
15,500 miles of
Transmission Lines
– 500 kV, 230 kV, 161
kV, 138 kV, 115 kV,
69 kV
1450 Substations
14 Interfaces with
neighboring companies
with over 75 tie lines
~22,000 MW of Load
~ 2.4 Million customers
in LA, MS, AR and TX
~45,000 MW of
available generation by
2005 !!
PV Curve Analysis - Disadvantages
•
PV curves are not very helpful to find the weak points in
a system
•
PV analysis is scenario-based. If the scenario changes, a
new PV curve analysis needs to be performed
•
PV analysis is very time consuming. It is not suited for
real-time operation purposes
3
Basic Concepts
• For simplified two bus system, assuming:
– The sending end is infinite bus, i.e. voltage = 1.0 p.u.
– The receiving end load increases, keeping Qr/Pr ratio constant
• For any particular Qr/Pr ratio, the equations for receiving
end voltage and power are
Es
Er
S=Pr+jQr
Simplified two bus system
cos(r   )
cos(r )
1 E
sin( r  2 )
Pr   s  (
 tan( r ))
2 X
cos(r )
(1)
2
Transmission line (jX)
Infinite Bus
Er  E s 
(2)
with
tan( r ) 
Qr
Pr
and θ is the angle difference between Es and Er
4
PV Curves
• Equations 1 & 2 show that the PV curve can be drawn
from Power-Angle and Voltage-Angle curves
Receiving End Voltage (PU)
1.20
(20, 0.94)
1.00
0.80
(45, 0.71)
0.60
0.40
(70, 0.34)
0.20
0.00
1.20
0
10
20
30
40
50
60
70
80
90
100
(0.64, 0.94)
Angle (Degree)
1.00
Voltage (PU)
0.80
(1.00, 0.71)
0.60
0.40
1.20
(0.64, 0.34)
0.20
(45, 1.00)
1.00
0.00
0.00
Power (p.u.)
0.80
(20, 0.64)
(70, 0.64)
0.40
0.20
0.00
10
20
30
40
50
60
70
80
90
0.40
0.60
Pow er (PU)
0.60
0
0.20
100
Angle (Degree)
5
0.80
1.00
1.20
Power & Voltage at the Knee Point
• Figure shows the relationship between voltage stability
and angle difference between the receiving and sending
end buses
• The analytical equations for Prmax and Ermax at the knee
point of the above PV curve can be derived from
Equations 1 & 2:
1 Es2
1

(
 tan( r ))
2 X cos(r )
Pr max
Er max 

 r )
2
Es
cos(r )
cos(
(3)
(4)
when

 max
 2
 r
2
for any particular ratio of Qr /Pr
6
(5)
VSMI
• The Voltage Stability Margin Index (VSMI), for any given
Qr/Pr ratio, can be defined as
 max  
VSMI 
 max
(6)
• Lower values of VSMI indicate closer proximity to voltage
collapse
• Above equations have been tested on simple two bus
system
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Application to Large Scale Power System
• If a large scale power system can be represented by a
simplified two bus system, then VSMI of every branch
can be calculated by Equation 6
8
Application to Large Scale Power System
• Such an equivalent two bus system can be found,
assuming:
– Sending end system can be represented by an infinite bus, whose
voltage is 1.0 p.u.
– The X/R ratio of source impedance is the same as that of the
interested branch
• The VSMI of every branch in the large scale power
system can be calculated by repeating the simplification
process for every branch
• The weak points can be found by comparing the VSMIs of
every branch
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Downstream of Gypsy Region
• Downstream of Gypsy region in Entergy system has a
voltage stability problem. There are five major 230 kV tie
lines and three major units at Ninemile and Michoud
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Ranking of Critical Lines
BRANCH
SND_VOL
SND_ANG
RCV_VOL
RCV_ANG
MW
MVAR
Q/P
INDEX
230 1
0.941
-0.161
0.914
-0.228
841.5
290.9
0.35
0.01
2 230 1
0.963
-0.047
0.958
-0.057
96.7
38.6
0.40
0.02
98555 6GYPSY
230 98557 6SNORCO
98569 6BGATEL
230 98544 6SORR
98606 69MILE
230 98691 6NAPOL
230 1
0.884
-0.431
0.876
-0.455
266.5
71.9
0.27
0.02
98586 6LABARE
230 98580 6PARIS
230 1
0.881
-0.418
0.878
-0.427
171.1
42.5
0.25
0.03
98606 69MILE
230 98687 6DERBI
230 1
0.884
-0.431
0.876
-0.458
244.2
61.9
0.25
0.03
98626 6KAISER
230 98630 6PACKHM
230 1
0.865
-0.499
0.865
-0.499
131.9
31.3
0.24
0.03
98633 6PACKAI
230 98626 6KAISER
230 1
0.865
-0.498
0.865
-0.499
131.9
31.3
0.24
0.03
98691 6NAPOL
230 98686 6MKTST
230 1
0.876
-0.455
0.875
-0.461
149.3
36.3
0.24
0.03
98504 6DNLDVL
230 98505 6BYVRET
230 1
0.984
-0.004
0.978
-0.018
187.5
61.6
0.33
0.06
98606 69MILE
230 98613 6ESTELL
230 1
0.884
-0.431
0.873
-0.471
219.5
50.1
0.23
0.07
98555 6GYPSY
230 98590 6UCITY
230 1
0.941
-0.161
0.895
-0.310
576.0
177.8
0.31
0.07
98555 6GYPSY
230 98589 6PONTCH
230 1
0.941
-0.161
0.888
-0.344
584.3
176.3
0.30
0.07
98545 6SLIDEL
230 50070 FRONTST6 230 1
0.909
-0.329
0.900
-0.359
323.5
84.9
0.26
0.07
98557 6SNORCO
230 98558 6PRSPCT
230 1
0.914
-0.228
0.912
-0.233
756.2
180.1
0.24
0.08
98613 6ESTELL
230 98614 6PTRSRD
230 1
0.873
-0.471
0.870
-0.486
182.5
32.0
0.18
0.09
98583 6SPORT
230 98655 6JOLIET
230 1
0.882
-0.431
0.879
-0.444
349.8
64.0
0.18
0.10
98558 6PRSPCT
230 98559 6GOODHP
230 1
0.912
-0.233
0.911
-0.238
721.6
165.0
0.23
0.10
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VSMI of Gypsy – South Norco 230 kV Line
Unit Output (MW)
Voltage (p.u.)
VSMI (%)
550
0.988
16.2
450
0.986
15.4
350
0.981
13.6
300
0.971
10.4
260
0.960
6.87
210
0.941
0.9
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Advantages of VSMI
• VSMI technique is much faster than PV curve technique
• VSMI will adjust with changing operating conditions
automatically
• VSMI calculation has the potential for being used in realtime operation
• This new approach can provide very useful information to
find the weak points in the system
• This new approach can estimate the proximity to voltage
collapse
13
Future Work
• VSMI index can be negative for transmission lines which
have heavy reactive power flow compared to real power
flow
• Transformer taps and negative impedance, such as series
cap compensation are not considered
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