Online monitoring of voltage stability margin using PMU measurements

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 2, April 2020, pp. 1156~1168
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i2.pp1156-1168  1156
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Online monitoring of voltage stability margin using
PMU measurements
Pankaj Sahu, M. K. Verma
Department of Electrical Engineering, Indian Institute of Technology (BHU), India
Article Info ABSTRACT
Article history:
Received Apr 15, 2019
Revised Oct 11, 2019
Accepted Oct 20, 2019
With the growing smart grid concept it becomes important to monitor health
of the power system at regular intervals for its secure and reliable operation.
Phasor Measurement Units (PMUs) may play a vital role in this regard.
This paper presents voltage stability monitoring in real time framework using
synchrophasor measurements obtained by PMUs. Proposed approach
estimates real power loading margin as well as reactive power loading
margin of most critical bus using PMU data. As system operating conditions
keep on changing, loading margin as well as critical bus information is
updated at regular intervals using fresh PMU measurements. Simulations
have been carried out using Power System Analysis Toolbox (PSAT)
software. Accuracy of proposed Wide Area Monitoring System (WAMS)
based estimation of voltage stability margin has been tested by comparing
results with loading margin obtained by continuation power flow method (an
offline approach for accurate estimation of voltage stability margin) under
same set of operating conditions. Case studies performed on IEEE 14-bus
system, New England 39-bus system and a practical 246-bus Indian power
system validate effectiveness of proposed approach of online monitoring of
loading margin.
Keywords:
Critical bus
Online monitoring
Phasor measurements units
Voltage stability
Wide area monitoring system
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Pankaj Sahu,
Department of Electrical Engineering,
Indian Institute of Technology (BHU),
Varanasi 221005, India.
Email: psahu.rs.eee13@itbhu.ac.in
1. INTRODUCTION
Voltage stability has been considered as an important threat against secure operation of power
system [1]. Several incidences of voltage instability initiated grid failures have been observed in different
parts of the world [2]. Various approaches for offline estimation of voltage stability have been well
documented [3]. Offline assessment of voltage stability is quite useful in advance planning of preventive and
corrective measures against instability. However, secure operation of a system in real time framework
requires its online monitoring against instability. A forecasting-aided state estimation has been proposed for
online monitoring of voltage stability [4]. Online assessment of voltage stability margin based on available
reactive power reserve has been suggested [5]. Yiwei Qiu et. al. proposed parametric polynomial
approximation of static voltage stability region boundaries based on Galerkin method and, suggested real
time determination of left and right eigen vectors associated with zero eigen value at the estimated saddle-
node-bifurcation space for online monitoring and control of voltage stability [6].
With advancement in wide-area monitoring system (WAMS) technology, online monitoring of
voltage stability through time stamped measurements by Phasor Measurement Units (PMUs) seems possible.
In comparison to Supervisory Control and Data Acquisition (SCADA) System the utilization of PMUs shows
improved decision making and operation [7, 8]. Many researchers proposed online monitoring of voltage
stability margin by obtaining Thevenin’s equivalence of network across a critical load bus based on real time

Int J Elec & Comp Eng ISSN: 2088-8708 
Online monitoring of voltage stability margin using PMU measurements (Pankaj Sahu)
1157
measurements by PMUs. Online estimation of voltage stability margin through matching of critical load
impedance with PMU measurements based Thevenin’s impedance of the rest of the network has been
proposed [9–12]. Representation of whole network connected across a critical load bus may be suitable for
voltage stability monitoring of radial networks. However, interconnected power system may have a critical
area comprising of a set of critical load buses prone to voltage collapse. Thevenin’s equivalent of critical load
area based on PMU measurements at its surrounding buses has been proposed [13, 14]. All the buses in
the critical load area have been merged to replace these by a fictitious load bus. A critical load area is fed by
multiple tie-lines, in general. Some of these may have over flows that may lead to voltage instability in
the area. Replacing all the buses in the area with a single equivalent bus merges all the tie-lines too into
a fictitious equivalent tie-line. Therefore, tie-lines of original network having overflows and hence being
responsible for instability cannot be detected. In order to address this issue, online monitoring of voltage
stability margin of a load area based on tie-line flows has been proposed [15]. Tie-line flows have been
obtained through phasor measurements performed by PMUs placed at boundary buses of the critical load
area. However, critical load areas are dependent upon operating conditions and topology of the network.
Change of network topology due to occurrence of contingencies may lead to emergence of new critical load
areas where PMUs are not placed.
Distributed linear algorithm has been proposed for online computation of voltage stability proximity
indices (VCPI) based on local phasor measurements performed at all the load buses [16].
PMU measurements based online monitoring of critical buses using Q-V (reactive power-voltage magnitude)
and P-Ө (real power-voltage angle) sensitivities has been proposed [17]. However, assumption of Q-Ө and
P-V decoupling are not valid near nose point. A normalized P-index has been proposed for online monitoring
of voltage stability using phasor measurements [18]. However, P-index has been developed assuming
constant power factor under increased demand which is not valid for real time systems.
Online monitoring of voltage stability based on Thevenin’s equivalent of the network [9-15], as well
as sensitivity based real time estimation of voltage stability margin [16-18] may fail to produce satisfactory
results in case of large disturbances due to highly non-linear behavior of power systems. An Artificial Neural
Network (ANN) based monitoring of voltage stability based on phasor measurements has been
proposed [19]. Proper training of ANN is still a challenge. Enhanced-Online-Random-Forest (EORF) model
has been proposed based on voltage phasor measurements for online monitoring of voltage stability [20].
EORF model updates voltage stability information under change in operating conditions/network topology
using fresh PMU measurements at important load buses. EORF model may lead sometimes to erroneous
estimation of voltage stability margin due to non-consideration of voltage phasor information of remaining
buses. A general method to adjust loads at the receiving end has been applied to determine the proximity to
voltage collapse [21]. Here, it is concluded that the intermediate load adjustment improves the accuracy of
the indices. In this the PMUs are not placed optimally in the system. In most of the research the statistical
information obtained from PMUs has not actionably used to improve the voltage stability. In [22], the new
method has been suggested that gauges and improves the voltage stability of a system using statistical data
obtained from PMUs.
In this paper, real time determination of nose curve of all the load buses based on three successive
PMU measurements and pseudo-measurements is performed. Minimum out of maximum loadability of all
the load buses has been considered as the loading margin of the system. Voltage stability information is
updated with new PMU measurements obtained. Thus, proposed approach is capable of monitoring voltage
stability of real time systems as change in system operating conditions and network topology is considered by
updated PMU measurements performed at regular intervals. PMUs have been optimally placed in the system
based on result of binary integer linear programming ensuring full network observability even in case of loss
of few PMUs under contingencies [23]. Paper is structured as follows: Section II presents methodology
proposed for online monitoring of voltage stability margin using PMU measurements based quadratic fitting
of nose curves. Section III validates effectiveness of proposed approach based on case studies performed on
standard IEEE 14-bus system, New England 39-bus system and a practical 246-bus Indian system
representing power network of nine states and union territories of India. Section IV concludes summarizing
important contributions of the proposed work.
2. METHODOLOGY
Proposed approach of online monitoring of voltage stability margin using phasor measurements is
presented: Real power demand ( iDP ) versus voltage magnitude iV curve (P-V curve) of bus-i shown in
Figure 1 may be approximately obtained by solution of quadratic equation,

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 2, April 2020 : 1156 - 1168
1158
2
1 2 3iD i i i i iP a V a V a   (1)
where, 1ia , 2ia and 3ia are constants
Differentiating iDP
with respect to iV ,
1 22iD
i i i
i
dP
a V a
dV
  (2)
At nose point of P-V curve, iD
i
dP
dV
= 0. Therefore, from (2),
2
12
np i
i
i
a
V
a
  (3)
where,
np
iV = voltage magnitude of bus-i at the nose point of P-V curve shown in Figure1. From (1) and (3),
2
2
3
14i
n i
D i
i
a
P a
a
   (4)
where,
i
n
DP = Real power demand of bus-i at the nose point of P-V curve shown in Figure 1.
Figure 1. P-V curve of bus-i
Reactive power demand ( iDQ ) versus voltage magnitude ( iV ) curve (Q-V curve) of bus-i shown in
Figure 2 may be approximately obtained by solution of quadratic equation,
2
1 2 3iD i i i i iQ b V b V b   (5)
where, 1ib , 2ib and 3ib are constants.

1159
Figure 2. Q-V curve of bus-i
Differentiating iDQ with respect to iV ,
1 22iD
i i i
i
dQ
b V b
dV
  (6)
At the nose point of Q-V curve, iD
i
dQ
dV
= 0, Therefore, from (6),
2
12
nq i
i
i
b
V
b
  (7)
where,
nq
iV = voltage magnitude of bus-i at the nose point of Q-V curve shown in Figure 2. From (5)
and (7),
2
2
3
14i
n i
D i
i
b
Q b
b
   (8)
where, i
n
DQ = Reactive power demand of bus-i at the nose point of Q-V curve shown in Figure 2. Constants
1ia , 2ia and 3ia were obtained by solution of equations:
1 1 2 1
1 2 3( )iD i i i i iP a V a V a   (9)
2 2 2 2
1 2 3( )iD i i i i iP a V a V a   (10)
3 3 2 3
1 2 3( )iD i i i i iP a V a V a   (11)
where,
1
iV ,
2
iV ,
3
iV shown in Figure 1 and in Figure 2 correspond to voltage magnitude of bus-i at
operating points 1, 2 and 3, respectively, and
1
iDP ,
2
iDP and
3
iDP shown in Figure 1 correspond to real power
demand of bus-i at operating points 1, 2 and 3, respectively.
Evaluated constants 1ia , 2ia and 3ia were used to find real power loading margin of bus-i
using (4). Constants 1ib , 2ib and 3ib are obtained by solution of equations:
1 1 2 1
1 2 3( )iD i i i i iQ b V b V b   (12)

 ISSN: 2088-8708
1160
2 2 2 2
1 2 3( )iD i i i i iQ b V b V b   (13)
3 3 2 3
1 2 3( )iD i i i i iQ b V b V b   (14)
where,
1
iDQ ,
2
iDQ and
3
iDQ shown in Figure 2 correspond to reactive power demand of bus-i at operating
points 1, 2 and 3, respectively.
Evaluated constants 1ib , 2ib and 3ib were used to find reactive power loading margin of bus-i
using (8). Constants a1i, a2i, a3i, b1i, b2i and b3i for each of the load buses were evaluated using voltage
magnitude, real power demand and reactive power demand obtained by PMU measurements/pseudo
measurements performed at operating points 1, 2 and 3, respectively. Evaluated constants predict real power
loading margin as well as reactive power loading margin of each bus using (4) and (8), respectively.
Minimum out of maximum real power loadability of all the load buses present in the system is considered as
real power loading margin of the system, and corresponding bus was considered as the most critical bus
based on real power loading margin. Minimum out of maximum reactive power loadability of all the load
buses present in the system was considered as reactive power loading margin of the system, and
corresponding bus was considered as the most critical bus based on reactive power loading margin criterion.
A flow chart for finding loading margin as well as most critical bus based on PMU measurements is shown in
Figure 3. Since, loading margin of a real time system keeps on changing with change in operating conditions;
it is proposed to update loading margin as well as most critical bus information based on new PMU
measurements obtained, at regular intervals. Flowchart shown in Figure 3 assumes very high initial loading
margin of 10,000 MW and 10,000 MVAR, respectively, keeping in mind such values to be higher than
loading margin of any of the load buses present in the system, and keeps on reducing these till real power
loading margin as well as reactive power loading margin of the most critical bus are obtained. Pseudo
measurements were performed using following network observability rules:
a. If voltage and current phasor at one end of a branch are known, voltage phasor at the other end of
the branch can be calculated using Ohm’s law.
b. If voltage phasors at both the ends of a branch are known, branch current can be calculated
c. If there exists a zero-injection bus with all branch currents known except for one, the unknown branch
current can be calculated using Kirchhoff’s Current Law (KCL).
3. CASE STUDIES
Proposed approach of online monitoring of voltage stability margin was tested on IEEE 14-bus
system, New England 39-bus system and 246-bus Northern Region Power Grid (NRPG) system of India with
the help of Power System Analysis Toolbox (PSAT) software [24]. Simulation results obtained on three
systems are presented below:
3.1. IEEE 14-Bus System
IEEE 14-bus system consists of two synchronous generators (at bus numbers 1 and 2),
three synchronous condensers (at bus number 3, 6 and 8) and 20 transmission lines including three
transformers [25]. This system has a zero-injection bus at bus number 7. PMUs were placed at bus numbers
2, 4, 5, 6 and 9 based on results of binary integer linear programming [23] ensuring full network
observability even in case of loss of few PMUs. Voltage magnitude, real power demand and reactive power
demand of all the load buses were obtained at three operating points (viz. points 1, 2 and 3, respectively)
using combination of PMU measurements and pseudo measurements for the system intact case. Constants a1i,
a2i and a3i were calculated using (9), (10) and (11) for each of the load buses. Evaluated constants were used
to find nose point real power demand ( i
n
DP ) of each load bus using (4). Minimum out of nose point real
power demand of all the load buses was considered as real power loading margin
xMa
DP of the intact system,
and bus having minimum
i
n
DP value was considered as the most critical bus requiring attention as far as
system real power loadability is concerned. In order to update loading margin information under change in
operating scenario, PMU measurements as well as pseudo measurements obtained at three operating points
under all the single line outage cases were used for evaluation of updated a1i, a2i, a3i for all the load buses, and
new
xMa
DP were calculated under these conditions using flow chart shown in Figure 3.

1161
Figure 3. Flowchart for determining loading margin of system using proposed approach
Measured voltage magnitude and real power demand of the most critical bus at the three operating
points, 𝑃𝐷
𝑀𝑎𝑥
calculated using proposed approach and real power loadability based most critical bus number
have been shown in Table 1 for the system intact case and few critical contingency cases. In order to validate
real power loading margin obtained by proposed approach, real power demand versus voltage magnitude
curve (P-V curve) of most critical bus was plotted using continuation power flow (CPF) method [26] for
the system intact case and all the single line outage cases. For obtaining P-V curve of the most critical bus
using CPF method, its real power demand 𝑃𝐷 𝑗
was varied as per following:
𝑃𝐷𝑗 = 𝑃𝐷 𝑗
1
(1 + 𝜆𝑗𝑝) (15)
where, 𝜆𝑗𝑝= fraction of real power demand increase at bus-j
Real power loading margin (𝑃𝐷
𝑀𝑎𝑥
) of the most critical bus obtained by CPF method (real power
demand at the nose point of its P-V curve) have also been shown in Table 1 for the system intact case
and few critical contingency cases. It is observed from Table 1 that real power loading margin obtained
by proposed approach closely matches with real power loading margin found by continuation power
flow method.

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1162
Table 1. Real power loading margin under critical contingencies (IEEE 14-bus system)
C.C.
M.C.B
(Bus-j)
Point 1 Point 2 Point 3
xMa
DP (MW)
1
jV
(p.u.)
1
jDP
(MW)
2
jV
(p.u.)
2
jDP
(MW)
3
jV
(p.u.)
3
jDP
(MW) P.A. CPF
Intact 5 1.03 7.60 0.96 36.16 0.90 37.09 39.44 40.20
1-2 5 1.03 7.60 0.95 17.71 0.91 16.26 17.78 16.49
2-3 4 1.03 47.8 0.95 177.82 0.90 187.85 189.7 188.3
2-4 5 1.03 7.60 0.96 30.40 0.90 30.86 32.76 32.91
1-5 5 1.02 7.60 0.95 37.32 0.92 34.50 37.39 34.50
2-5 5 1.02 7.60 0.95 33.14 0.90 33.21 35.64 35.26
C.C. = critical contingency, M.C.B. = most critical bus number, P.A. = proposed approach
P-V curve of bus 4 (most critical bus) obtained by proposed quadratic fitting of nose curves using
PMU measurements/pseudo measurements at three operating points as well as continuation power flow based
P-V curve of same bus have been shown in Figure 4 for the outage of line 2-4. It is observed from Figure 4
that nose point real power loadability obtained by proposed approach closely matches with real power
loading margin of the bus obtained by continuation power flow method.
Figure 4. P-V curve of critical bus 5 obtained using proposed approach and by CPF method
for line outage 2-4 (IEEE 14-bus system)
Constants b1i, b2i and b3i were calculated for each of the load buses using (12), (13) and (14) for
the system intact case and all the single line outage cases using PMU measurements/pseudo measurements.
Evaluated constants were utilized to determine nose point reactive power demand, i
n
DQ of each bus using (8).
Minimum out of nose point reactive power demand ( i
n
DQ ) of all the load buses was considered as reactive
power loading margin 𝑄 𝐷
𝑀𝑎𝑥
of the system, and bus having minimum i
n
DQ value was considered as most
critical bus requiring attention as for as reactive power loading margin is concerned. In order to validate
reactive power loading margin obtained by proposed approach, reactive power demand versus voltage
magnitude curve (Q-V curve) of the most critical bus was obtained by CPF method for the system intact case
and all the single line outage cases. For obtaining Q-V curve of the most critical bus using CPF method,
its reactive power demand was varied using:
𝑄 𝐷 𝑗
= 𝑄 𝐷 𝑗
1
(1 + 𝜆𝑗𝑞) (16)
where, 𝜆𝑗𝑞= fraction of reactive power demand increase at bus-j
Measured voltage magnitude and reactive power demand of most critical bus at three operating
points, reactive power loading margin (𝑄 𝐷
𝑀𝑎𝑥
) obtained by proposed approach as well as by CPF method
have been shown in Table 2, for the system intact case and few critical contingency cases. Reactive power
7.6 11.4 15.3 19.2 23.1 27 30.9 34.8
0.8
0.85
0.9
0.95
1
1.05
Active Power P (MW)
V(p.u.)
Proposed Approach
CPF

1163
loadability based most critical bus number has also been shown in Table 2 for all these cases. It is observed
from Table 2 that
xMa
DQ obtained by proposed approach closely matches with
xMa
DQ obtained by
CPF method.
Table 2. Reactive power loading margin under critical contingencies (IEEE 14-bus system)
C.C M.C.B.
(Bus-j)
Point 1 Point 2 Point 3 xMa
DQ (MVAR)
1
jV
(p.u.)
1
jDQ
(MVAR)
2
jV
(p.u.)
2
jDQ
(MVAR)
3
jV
(p.u.)
3
jDQ
(MVAR)
P.A. CPF
Intact 5 1.03 0.32 0.96 3.81 0.90 7.81 0.85 0.86
1-2 5 1.03 0.32 0.95 1.86 0.91 3.42 0.56 0.54
2-3 4 1.03 0.78 0.95 7.25 0.90 15.33 3.10 3.07
6-13 13 1.01 1.16 0.95 3.20 0.91 6.50 5.57 6.04
9-14 14 1.02 1.00 0.96 3.93 0.92 7.26 4.68 5.22
9-10 10 1.02 1.16 0.96 3.49 0.91 6.99 5.64 6.10
Q-V curve of bus 4 (most critical bus) obtained by proposed quadratic curve fitting of nose curves
using PMU measurements/pseudo measurements obtained at three operating points as well as CPF based Q-V
curve of same bus have been shown in Figure 5 for the outage of line 2-3. It is observed from Figure 5 that
nose point reactive power loadability of bus 4 obtained by proposed approach closely matches with CPF
based nose point reactive power demand.
Figure 5. Q-V curve of critical bus 4 obtained using proposed approach and by CPF method
for line outage 2-3 (IEEE 14-bus system)
3.2. New England 39-Bus System
The New England 39-Bus System has 10 generators and 46 transmission lines with 12 zero-injection
buses at bus numbers 1, 2, 5, 6, 9, 10, 11, 13, 14, 17, 19 and 22 [27]. Binary integer linear programming was
used to optimally place PMUs in the system ensuring full network observability even in case of loss of few
PMUs [23]. It results PMU placement at bus numbers 4, 8, 12, 16, 18, 20, 23, 25, 26, 27, 29, 30, 31, 32, 33,
34, 35, 36, 37, 38 and 39.
Real power loading margin 𝑃𝐷
𝑀𝑎𝑥
was calculated as per flow chart shown in Figure 3 for the system
intact case and all the single line outage cases, as in case of IEEE 14-bus system. Measured voltage
magnitude and real power demand of the most critical bus at the three operating points, 𝑃𝐷
𝑀𝑎𝑥
calculated
using proposed approach and real power loadability based most critical bus number have been shown in
Table 3 for the system intact case and few critical contingency cases. In order to validate real power
loadability obtained by proposed approach, real power demand versus voltage magnitude curve (P-V curve)
of most critical bus was plotted using continuation power flow (CPF) method [26] for the system intact case
and all the single line outage cases. For obtaining P-V curve of the most critical bus, its real power
demand was varied as per (15). Real power loading margin ( 𝑃𝐷
𝑀𝑎𝑥
) of the most critical bus obtained by CPF
0.78 1.17 1.56 1.95 2.34 2.73 3.12
0.85
0.9
0.95
1
1.05
Reactive Power Q (MVAR)
V(p.u.)
Proposed Approach
CPF

 ISSN: 2088-8708
1164
method (real power demand at the nose point of its P-V curve) have also been shown in Table 3 for
the system intact case and few critical contingency cases. It is observed from Table 3 that real power loading
margin obtained by proposed approach closely matches with real power loading margin found by
continuation power flow method.
Table 3. Real power loading margin under critical contingencies (New England 39-bus system)
C.C. M.C.B
(Bus-j)
DP (MW)
1
jV
(p.u.)
1
jDP
(MW)
2
jV
(p.u.)
2
jDP
(MW)
3
jV
(p.u.)
3
jDP
(MW)
P.A. CPF
Intact 29 1.03 283.5 0.96 1227.56 0.90 1360.80 1363.64 1686.83
28-29 29 1.02 283.5 0.95 768.29 0.89 853.34 856.17 989.42
29-38 20 1.00 680 0.97 2380 0.96 2380 2420.8 2380
21-22 23 1.05 247.5 0.95 868.73 0.91 905.85 908.33 930.60
22-35 29 1.03 283.5 0.98 1097.15 0.96 1097.15 1108.49 1099.98
10-32 29 1.03 283.5 0.98 1102.82 0.96 1102.82 1114.16 1102.82
C.C=critical contingency, M.C.B.=most critical bus number, P.A.=proposed approach
PMU measurements/pseudo measurements obtained at three operating points as well as continuation power
flow based P-V curve of same bus have been shown in Figure 6 for the outage of line 29-38. It is observed
from Figure 6 that nose point real power loadability obtained by proposed approach closely matches with real
power loading margin of the bus obtained by continuation power flow method.
Figure 6. P-V curve of critical bus 20 obtained using proposed approach and by CPF method for line outage
29-38 (New England 39-bus system)
Reactive power loading margin (𝑄 𝐷
𝑀𝑎𝑥
) was calculated as per flow chart shown in Figure 3 for
the system intact case and all the single line outage cases, as in case of IEEE 14-bus system. In order to
validate reactive power loading margin obtained by proposed approach, reactive power demand versus
voltage magnitude curve (Q-V curve) of the most critical bus was also obtained by CPF method for
the system intact case and all the single line outage cases. For obtaining Q-V curve of the most critical bus,
its reactive power demand was varied as per (16). Measured voltage magnitude and reactive power demand
of most critical bus at three operating points, reactive power loading margin (𝑄 𝐷
𝑀𝑎𝑥
) obtained by proposed
approach as well as by CPF method have been shown in Table 4, for the system intact case and few critical
contingency cases. Reactive power loadability based most critical bus number has also been shown in
Table 4 for all these cases. It is observed from Table 4 that
xMa
DQ obtained by proposed approach closely
matches with
xMa
DQ obtained by CPF method.
680 1020 1360 1700 2040 2380
0.95
0.955
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
Active Power P (MW)
V(p.u.)
Proposed Approach
CPF

1165
Table 4. Reactive power loading margin under critical contingencies (New England 39-bus system)
C.C.
M.C.B.
(Bus-j)
xMa
DQ (MVAR)
1
jV
(p.u.)
1
jDQ
(MVAR)
2
jV
(p.u.)
2
jDQ
(MVAR)
3
jV
(p.u.)
3
jDQ
(MVAR) P.A. CPF
Intact 29 1.03 25.38 0.96 274.74 0.91 609.12 122.08 151.01
28-29 29 1.02 25.38 0.95 171.95 0.89 381.97 76.65 88.58
29-38 20 1.00 20.60 0.97 180.25 0.96 360.50 73.34 72.10
15-16 15 1.02 30.60 0.96 76.50 0.92 153 142.60 168.90
2-25 25 1.03 9.44 0.95 23.60 0.91 47.20 42.10 51.26
10-32 29 1.03 25.38 0.98 246.82 0.96 493.64 99.74 98.73
using PMU measurements/pseudo measurements at three operating points as well as CPF based Q-V curve of
same bus have been shown in Figure7 for the outage of line 10-32. It is observed from Figure 7 that nose
point reactive power loadability of bus 29 obtained by proposed approach closely matches with CPF based
nose point reactive power demand.
Figure 7. Q-V curve of critical bus 29 obtained using proposed approach and by CPF method for line outage
10-32 (New England 39-bus system)
3.3. NRPG 246-Bus System
The 246-bus Northern Regional Power Grid (NRPG) system covers power network of seven states
(Jammu and Kashmir, Himachal Pradesh, Punjab, Haryana, Rajasthan, Uttarakhand and Uttar Pradesh) and
two union territories (Chandigarh and New Delhi) of India [28]. It consists of 42 generators, 36 transformers
and 376 transmission lines. It has 15 zero-injection buses at bus numbers 63, 75, 81, 102, 103, 104, 107, 122,
155, 180, 210, 226, 237, 241, and 244. Binary Integer linear Programming was run to optimally place 97
PMUs in the 246-bus NRPG system to ensure complete observability even in case of loss of few PMUs [23].
xMa
DP was calculated for the system as per flow chart shown in Figure 3 for the system intact case and all
the single line outage cases, as in case of IEEE 14-bus system and New England 39-bus system. Measured
voltage magnitude and real power demand of the most critical bus at the three operating points, real power
loadability based most critical bus number and 𝑃𝐷
𝑀𝑎𝑥
calculated using proposed approach have been shown in
Table 5 for the system intact case and few critical contingency cases. In order to validate real power loading
margin obtained by proposed approach, real power demand versus voltage magnitude curve (P-V curve) of
most critical bus was plotted using continuation power flow (CPF) method [26] for the system intact case and
all the single line outage cases. CPF based P-V curve was obtained by varying real power demand at the bus
as per (15). Real power loading margin (𝑃𝐷
𝑀𝑎𝑥
) of the most critical bus obtained by CPF method (real power
demand at the nose point of its P-V curve) have also been shown in Table 5 for the system intact case and
few critical contingency cases. It is observed from Table 5 that real power loading margin obtained by
proposed approach closely matches with real power loading margin found by continuation power flow
method.
25.38 38.07 50.76 63.45 76.14 88.83 101.52
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
V(p.u.)
Proposed Approach
CPF

 ISSN: 2088-8708
1166
PMU measurements/pseudo measurements at three operating points as well as continuation power flow based
P-V curve of same bus have been shown in Figure 8 for the outage of line 194-198. It is observed from
Figure 8 that nose point real power loadability obtained by proposed approach closely matches with real
power loading margin of the bus obtained by continuation power flow method.
𝑄 𝐷
𝑀𝑎𝑥
was calculated for the system intact case and all the single line outage cases, as in case of
IEEE 14-bus system and New England 39-bus system. In order to validate reactive power loading margin
obtained by proposed approach, reactive power demand versus voltage magnitude curve (Q-V curve) of the
most critical bus was also obtained by CPF method for the system intact case and all the single line outage
cases. CPF based Q-V curve was obtained by varying reactive power demand at the bus as per (16).
Measured voltage magnitude and reactive power demand of most critical bus at three operating points,
reactive power loading margin (𝑄 𝐷
𝑀𝑎𝑥
) obtained by proposed approach as well as by CPF method have been
shown in Table 6, for the system intact case and few critical contingency cases. Reactive power loadability
based most critical bus number has also been shown in Table 6 for all these cases. It is observed from Table 6
that
xMa
DQ obtained by proposed approach closely matches with
xMa
DQ obtained by CPF method.
using PMU measurements/pseudo measurements at three operating points as well as CPF based Q-V curve of
same bus have been shown in Figure9 for the outage of line 156-158. It is observed from Figure 9 that nose
point reactive power loadability of bus 158 obtained by proposed approach closely matches with CPF based
nose point reactive power demand.
Table 5. Real power loading margin under critical contingencies (NRPG 246-bus system)
C.C. M.C.B.
(Bus-j)
DP
(MW)
1
jV
(p.u.)
1
jDP
(MW)
2
jV
(p.u.)
2
jDP
(MW)
3
jV
(p.u.)
3
jDP
(MW)
P.A.
CPF
Intact 174 1.01 169.8 0.95 419.41 0.90 485.63 487.33 641.84
173-174 174 1.01 169.8 0.96 249.61 0.90 264.89 269.98 344.69
40-41 174 1.01 169.8 0.96 382.05 0.94 384.35 388.84 383.75
166-173 174 1.01 169.8 0.95 339.60 0.90 383.70 385.45 434.69
156-158 158 1.01 174.7 0.97 468.20 0.96 459.46 473.44 476.93
194-198 174 1.01 174.7 0.95 468.20 0.90 459.46 506.63 518.86
C.C=critical contingency, M.C.B.=most critical bus number, P.A.=proposed approach
Figure 8. P-V curve of critical bus 174 obtained using proposed approach and by CPF method
for line outage 194-198 (NRPG 246-bus system)
174.7 208.8 244.58 279.52 314.46 349.4 384.34 419.28 454.22 489.16 524.1
0.85
0.9
0.95
1
1.05
Active Power P (MW)
V(p.u.)
Proposed Approach
CPF

1167
Figure 9. Q-V curve of critical bus 158 obtained using proposed approach and by CPF method
for line outage 156-158 (NRPG 246-bus system)
Table 6. Reactive power loading margin under critical contingencies (NRPG 246-bus system)
C.C.
M.C.B.
(Bus-j)
xMa
DQ
(MVAR)
1
jV
(p.u.)
1
jDQ
(MVAR)
2
jV
(p.u.)
2
jDQ
(MVAR)
3
jV
(p.u.)
3
jDQ
(MVAR) P.A. CPF
Intact 174 1.01 13.52 0.95 83.49 0.90 193.34 38.80 51.11
173-174 174 1.01 13.52 0.96 49.69 0.90 105.46 21.50 27.45
40-41 174 1.01 13.52 0.96 76.05 0.94 151.42 30.96 30.56
166-173 174 1.01 13.52 0.95 67.6 0.90 152.8 30.69 34.61
156-158 158 1.01 12.48 0.97 50.86 0.96 164.11 33.82 34.07
63-70 156 1.01 17.74 1.01 44.35 1.01 88.7 19.51 19.33
4. CONCLUSION
Online monitoring of voltage stability margin using PMU measurements has been proposed in this
work. Proposed approach estimates voltage stability margin based on measurements obtained at three
operating points. Due to highly dynamic nature of power systems, voltage stability margin keeps on
changing. Therefore, proposed approach suggests computation of updated voltage stability margin at regular
intervals based on new PMU measurements obtained. Change in operating scenario has been simulated in
PSAT software considering different single line outage cases. Accuracy of proposed approach has been
validated by comparing voltage stability margin obtained by proposed approach with margin estimated
using continuation power flow method under same set of operating conditions. Case studies performed on
three test systems show that real power loading margin as well as reactive power loading margin of
the system obtained by proposed approach closely matches with loading margin obtained by continuation
power flow method.
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Proposed Approach
CPF

 ISSN: 2088-8708
1168
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BIOGRAPHIES OF AUTHORS
Pankaj Sahu received his B.Tech degree in electrical engineering from Harcourt Butler
Technological Institute, Kanpur, India in 2007 and M.Tech degree in electrical engineering from
Motilal Nehru National Institute of Technology, Allahabad, India in 2010. He is currently
persuing for PhD degree at Indian Institute of Technology (BHU), Varanasi, India. His research
interests include control system, instrumentation and voltage stability studies.
M. K. Verma received his B.Sc (Eng.) degree in electrical engineering from Regional
Engineering College, Rourkela (presently National Institute of Technology, Rourkela), India in
1989, M.Sc (Eng.) degree in electrical engineering from Bihar Institute of Technology, Sindri,
India in 1994 and PhD degree in electrical engineering from Indian Institute of Technology (IIT),
Kanpur, India in 2005. He is currently working as Professor in electrical engineering department
at Indian Institute of Technology (BHU), Varanasi, India. His current research interests include
voltage stability studies, application of FACTS controllers, power quality, wide area monitoring
system and smart grid

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