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Saroj Kumari Dr. Pratima Walde Asif Iqbal Akash Tyagi
Deptt of electrical engineering Deptt of electrical engineering Computer Science Division Electrical Engineering Division
Galgotias University Galgotias University Piro Technologies Pvt. Ltd. Piro Technologies Pvt. Ltd.
Greater Noida, (U.P), India Greater Noida, (U. P), India New Delhi, India New Delhi,India
Sarojk2701@gmail.com pratima.walde@galgotiasuniversity.edu.in asif@pirotechnologies.com akashtyagi0010@gmail.com
Abstract— This work presents a technique for the optimal
Phasor Measurement Units (PMUs) placement for complete
power network observability with number of PMUs as
minimum as possible. Due to the high installation cost of
PMUs it is necessary to make the system fully observable with
minimum PMUs. A binary particle swarm optimization
method (BPSO) is implemented on IEEE standard system
and Puducherry 17 bus system. The BPSO method of
Optimum PMU Placement can therefore be applied to any
power system to make the system fully observable with
different aspects of the power system. The obtained results
are compared with other techniques and it is found that
Adaptive GA, GILP, SA, TS, BSA and the proposed BPSO
method was found better.
Index Terms—Phasor measuring unit,Binary particle
swarm optimization, optimal PMU placement, observability.
I. INTRODUCTION
Synchronized measurements attracted the great attention to
the power system engineers. It provides the realization of
the real time monitoring, control and protection.
Synchronization can be achieved by real time sampling of
current and voltage waveforms with the help of Global
Positioning system (GPS). Basically through
synchronization voltage phase angle can be directly
measured which was not feasible earlier and also increases
the speed and accuracy of state estimation.
In power system, existing SCADA and EMS only
facilitates the steady state view of the power network.
SCADA measurements are obtained at slower rate and
does not measure the phase angle of voltage of power
system. Angle measurement are necessary to find possible
instabilities and allow the switching control to mitigate the
threating situation. It gives improved protection and
advance control of power system. For the above
advantages Phasor Measurement Unit (PMU) device is an
advance instrument that provides synchronized
measurement which is most accurate. The PMU at a bus
provides time synchronized measurement of current and
voltage phasors at that bus. A number of PMU already
installed in several utilities around the world because of its
various applications discussed in paper [2].
One of the most important issues is the cost of the PMU
which limits its installation, although an increased
demands in future might bring down its cost. Therefore a
method is required to find the optimal locations of such
synchronized measurement devices, in order to minimize
number of PMUs and make the system fully observable. A
power system is considered observable when all the states
in the system can be determined. A lot of research has been
done in determining the minimum number of PMUs
considering full system observability and finding their
optimal location. In [3], [4] & [5], the authors used integer
linear programming to find minimum number and optimal
locations of PMUs. In [6] graph theoretic method is
considered for placing PMUs which uses the concept of
spanning trees of the power system graph in order to
determine the optimal locations of PMUs. Simulated
annealing is used to solve the programmable
communication constrained PMU placement problem. In
[7] and [8] Genetic Algorithm procedure for solving OPP
problem is presented. In [9] Tabu search approach is
proposed which finds optimal number of PMUs by trial and
error method and their locations was determined by Tabu
search algorithm.
This approach has been successfully used in many
application of power system. BPSO based approach has
been used in this paper as an optimization tool to determine
the optimal number of PMUs for complete power network
observability. It is observed that BPSO successfully
optimizes the objective function and converges at global
optima at a rate faster than other methods. The simulations
are carried out using Binary PSO are listed below:-
Optimal Phasor Measuring Unit Placement
by Binary Particle Swarm Optimization
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1. Location of PMU in IEEE test system with and
without considering ZIBs.
2. Location of PMUs in a real system considering
ZIBs only.
II. PMU PLACEMENT PROBLEM
FORMULATION
In a power system, a bus is defined as observable when
node voltages of a bus can be calculated by the use of other
node voltages and branch currents. The basic rule in PMU
placement is that, the PMU can measure the voltage phasor
at the bus on which it is placed as well as at the adjacent
buses [10]. A bus without generation and load is called a
zero injection bus (ZIB). No PMU will be placed at ZIB in
any circumstance rather the voltage phasors can be
measured using KCL.
The PMU placement objective is to find the optimal
number of PMUs with full system observability. The
objective function can be defined as:
1. Optimal PMU placement without considering installation
cost :
Min
(1)
Subject to A(x) ≥ b (2)
2. Optimal PMU placement considering installation cost :
To find the total installation cost of PMU, an installation
cost factor ‘c’ is defined in this paper, its elements gives
the installation cost of PMUs in each bus of the power
system network. Optimal PMU placement problem
considering the installation cost criterion is given as
follows:
Min
(3)
Subject to the same constraint given in eq. (2)
Where,
Determines the feasibility installation of PMU at the ith
bus defined as follows:
=
(4)
N signifies the number of buses in a power network for
PMU installation, is the installation cost vector at the
bus k, x signifies binary decision vector having element ,
which decides the placement of PMU on the kth bus, A(x)
is the observability constraint or binary connectivity matrix
whose elements are given as:
Initially binary connectivity matrix A(x) is created
according to criterion given as follows:
A(k,l) =
(5)
b= [1 1 1 1 … … … NB times]
Due to the fact that, rather only considering the cost of the
PMU, installation cost of the current transformer and other
equipments should also be considered for each
transmission line connected to the bus. Because, of the
unavailability of equipment costs and other associated cost
of installation it is assumed the installation cost of one
PMU at a bus together with a connected transmission line
to be 1 p.u., defined as the base installation cost. The
installation cost will be further added by 0.1 p.u. for any
additional equipment connected to that bus. The next
section gives detail of the BPSO used in this paper.
III. BINARY PARTICLE SWARM
OPTIMIZATION
The proposed problem is mathematically formulated in
the previous sections and it was discussed that Meta
Heuristic technique has been very efficient with solving
Optimal PMU Placement (OPP) problem and on this basis
we decided to apply Binary form of one of the popular
Meta heuristic technique called Particle swarm
Optimization (PSO) technique.
Advantage of Particle swarm Optimization (PSO) is that it
has easy implementation, more efficient have control
parameters and have fewer parameters to adjust. However
the drawback of this technique is higher computation time
and that also increases with the increasing the dimensions
of solution i.e. number of buses and complexity of
constraints. Even though this problem is an offline
planning problem so we still propose BPSO method that
simultaneously make sure that the objective solution are
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within feasible region i.e. constraints are satisfied and also
convergence is accelerated.
A. Particle Swarm Optimization
Particle Swarm Optimization (PSO) was first introduced
by Kennedy and Eberhart in 1995. It is an evolutionary
computation technique which is inspired by the social
behavior of group of organisms like bird flocking.
It is a population search based method where individuals
called as particles that adjust their positions in search space
with the given velocities and direction. In this swarm of
birds that don’t have leader, so they find food by random
movement and follow one of the member of group whose
position is closest with food source. The group achieves
their best condition simultaneously by communicating with
the members who are already at better solution. So they
will move simultaneously to best position. This would
repeatedly happen until best food source/ condition has
discovered.
It’s an iterative method in which every particle adjusts its
velocity and position for best solution. Technically the
commutative cognitive occurrence of the swarm turns out
into the optimization technique. Mathematically let us
suppose we have N particles within the swarm in the
problem space. Each particle has position and velocity that
directs flying of particles and also has cost value that to be
minimized.
Position and velocity of the ith particle in jth dimension at
kth iteration are denoted by
and
:
(6)
(7)
Where j=1,2,3,………., up to n dimension
Swarm maintains its global best position:
(8)
= f () (9)
And each particle maintains its individual best position:
= f () (10)
At every iteration, velocity and position of each particle are
updated based on precious best position) and best
position calculated by information). An updated
formula is given as:
(11)
(12)
Where i is index of the particle, j is the index of the position
of the particles in the swarm, k is the iteration number.
is the inertia parameter and its ranges is in between 0.95 to
0.99. called cognitive parameter and has value around
2.0 called social parameter and its value equals to.
Parameters are random numbers consistently
distributed between 0 and 1.
B. Binary Particle Swarm Optimization
The BPSO technique was first introduced by Kennedy and
Eberhart in 1997. In BPSO each element of position vector
takes only binary values (0 or 1). Here velocity remains
unaltered but position is updated and rewritten by rule:
(13)
Where S is sigmoid function to transfer the velocity to the
possibility defined as:
=
(14)
And rand () is a random number with range [0, 1].
Here, it is shown that the BPSO successfully optimizes the
given test function with a faster rate of convergence at
global optima.
The updated velocity and the acceleration coefficients
decide the effect of and on the particles
current velocity vector. Better convergence can be obtained
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by making acceleration constant and inertia constant
dependent one each other as shown below:
(15)
= (16)
IV. CASE STUDIES
The proposed BPSO method is tested on IEEE 14 bus
system [14] and its effectiveness is evaluated by applying
the proposed approach on the Indian Utility-Puducherry-17
bus test system [15]. Software has been developed using
MATLAB to test the suggested BPSO technique and
simulations are carried out on a PC having Intel Core i3
Processor@2.20 GHz, 2 GB RAM. Also the presence of
ZIBs in PMU placement minimizes the required number of
PMUs for entire power network observability. Both the
cases with and without zero injection bus have been
performed. Single line diagram of the IEEE 14 bus system
and 17 bus system is shown in Fig. 1 and Fig. 2
respectively. Table 1 shows the number of zero injection
buses for the two test systems. Table 2 shows the
optimization parameters for the BPSO used in OPP
problem. These values of optimization parameters are
chosen after several runs of the program and gives the best
converging solution.
Number of buses defines the problem space dimension. To
achieve better search in the problem space, the BPSO
program is run number of times for each power system
which is mention in Table III and table IV for IEEE 14 bus
system and Puducherry 17 bus system.
Table III shows several alternative PMU locations for 14
bus system that result in full system observability but only
one out of several solutions will gives the minimum
installation cost of 4.6 p.u. Similarly for 17 bus system in
table IV, minimum installation cost is 7.1 p.u. The
program was run 100 of times for the two systems. In Table
V, according to the result it can be seen that by equipping
three PMUs in the 14 bus system, full observability will be
achieved at minimum installation cost. Similarly for 17 bus
system minimum six PMUs required at the defined location
to get full system observability at minimum installation
cost. The best achieved solution including PMU locations
along with installation cost are listed in table V and VI.
TABLE I
BASIC CONFIGURATION OF THE TEST SYSTEMS
Fig. 1. IEEE 14 bus test system [14]
1
2
3
4
5
6
7
8
9
10
0
15
0
11
0
16
13
17
14
12
Fig. 2. 17 bus system [15]
Test system
No. of
branches
No. of ZIB
Location of ZIB
IEEE 14-bus
system
20
1
7
Indian Utility
(Pondicherry)
17 bus
system
21
2
1 4
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TABLE II
BPSO Optimization parameters
Parameter names
Values
Population size
20
Cognitive parameter()
2.04
Social parameter ()
2.04
Inertia parameter()
0.95 - .099
Random parameter (and )
0 – 1
TABLE III
OPTIMUM PMU PLACEMENT CONSIDERING INSTALLATION
COST FOR 14 BUS SYSTEM
No. of
trials
Optimal PMU
location
No. of
PMUs
Installation
Cost (p.u.)
No. of
Buses
Observed
1
2 7 10 13
4
4.8
14
2
2 7 11 13
4
4.8
14
3
2 8 10 13
4
4.6
14
4
1 3 8 10 13
5
5.5
14
5
2 6 8 9
4
4.9
14
TABLE IV
OPTIMUM PMU PLACEMNT CONSIDERING
INSTALLATION COST FOR 14 BUS SYSTEM
No. of
trials
Optimal PMU
location
No. of
PMUs
Installation
Cost (p.u.)
No. of
Buses
Observed
1
1 4 5 9 16 17
6
7.1
17
2
2 7 8 11 12 14
17
7
7.7
17
3
1 4 5 10 13 16
6
7.3
17
4
2 4 5 8 16 17
6
7.3
17
5
1 4 5 9 16 17
6
7.2
17
TABLE V
NUMBER OF PMUs RESULTING FROM BPSO FOR 14 BUS
SYSTEM
Methods
No. of PMUs
PMU Locations
Cost
Excluding cost
factor (proposed)
4
2 6 8 9
4.9
Including cost
factor (proposed)
4
2 8 10 13
4.6
Considering ZIB
3
2 6 9
3.9
TABLE VI
OPTIMAL NUMBER OF PMUs FROM BPSO FOR 17 BUS SYSTEM
Methods
No. of
PMUs
PMU Locations
Cost
Excluding cost
factor
(proposed)
6
1 4 5 8 11 17
7.4
Including cost
factor
(proposed)
6
1 4 5 9 16 17
7.1
Considering ZI
Bus
6
2 8 11 12 14
17
6.7
TABLE VII
OPTIMAL NUMBER OF PMUs RESULTING FROM BPSO AND
OTHER OPTIMIZATION TECHNIQUES CONSIDERING ZI BUSES
Test Systems
Proposed Method
No. of
PMUs
Location of
PMU
Installation
Cost
IEEE 14 bus
system
3
2 6 9
3.9
Indian utility
17 bus
systems
6
2 8 11 12 14 17
6.7
Test
Systems
Graph
theoretic
procedure
[13]
Three
stage
method
[4]
SA and
TS [5]
BSA
[6]
GA
[7]
IEEE 14
bus
system
5
3
3
3
3
Indian
utility
17 bus
system
NR*
NR*
NR*
NR*
NR*
NR* means Not Reported
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Fig. 3.Convergence rate of BPSO for 14 bus system
Fig. 4. Convergence rate of BPSO for 17 bus system
V. CONCLUSION
A BPSO based methodology is proposed to find the
optimal location of PMUs in a network for its entire
observability at minimum installation cost. The proposed
method have higher rate of convergence to the global
solution with less execution time when compared to the
existing methods. The PMU placement problem has been
associated with different aspect with the presence of ZIBs.
Simulation results for the different power networks shows
the efficiency and the robustness of the proposed method
in achieving the complete network observability with
minimum number of PMUs at minimum installation cost.
This iterative process overcomes the limitations of
conventional optimization method such as integer linear
programming. And also its advantage of simplicity,
scalability to large systems, computation efficiency.
Future work will include additional
constraints
such as
measurement
uncertainty
and redundancy at the buses.
VI. REFERENCES
[1] Chakarbarti S, Kyriakides E, “Optimal pla cement of phasor
measurement units for power system observability,” IEEE Transaction on
Power Systems, vol. 23, No. 3, August 2008.
[2] Ree Jaime, Centeno V, Thorp J, Phadke, “Synchronized phasor
measurement applications in power system,” IEEE Transaction on Smart
Grid, vol. No. 1, June 2010.
[3] A Azizi S, Salehi Dobakhshari A, Nezam Sarmadi SA, Ranjbar AM,
Gharehpetian GB, “Optimal multi-stage PMU placement in electric power
systems using Boolean algebra,” Int Trans Electr Energy Syst 2014;
24(4):562–77.
[4] C. Jian and A. Abur, "Placement of PMUs to Enable Bad Data
Detection in State Estimation," Power Systems, IEEE Transactions on,
vol. 21, pp. 1608-1615, 2006.
[5] Gou B, “Optimal placement of PMUs by integer linear programming,”
IEEE Transactions on Power Systems, Vol. 23, No. 3, August 2008
[6] Nuqui R, Phadke A,” Phasor measurement unit placement techniques
for complete and incomplete observability,” IEEE Transaction on power
delivery, vol. 20, No. 4, October 2005.
[7] Abiri E, Ra shidi F, Niknam T,” An optimal PMU placement method
for power system observability under various contingencies,” Int Trans
Electr Energy Syst 2015; 25(4):589–606.
[8] Marin FJ, Garcia-Lagos F, Joya G, Sandoval F, “ Genetic algorithms
for optimal of SID placement of phasor measurement units in electrical
networks,” Electronics Letters September 2003; 39(19):1403–1405
[9] Amany El Zonkoly et al, ”Optimal placement of PMUs using
improved tabu search for complete observability and out-of-step
prediction,” Turkish Journal of Electrical Engineering & Computer
Sciences (2013) 21: 1376 -1393
[10] Chakrabarti S, Venayagamoorthy G, Kyriakides E, “PMU placement
for power system observability using binary particle swarm optimization.
2008
[11] Abiri E, Rashidi F, Niknam T. An optimal PMU placement method
for power system observability under various contingencies,” Int Trans
Electr Energy Syst 2015; 25(4):589–606
[12] T.L. Baldwin, L. Mili, M. B. Boisen, R. Adapa, “Power system
observability with minimum phasor measurement placement,” IEEE
Trans. Power System, vol. 20, pp. 707-715, May. 1993.
[13] B.Pal and B.Chaudhuri, “Robust control in Power systems,” Springer
Verlag, London, 2005.
[14] Power system test case archive
http://www.ee.washington.edu/research/pstca/. Last Accessed on 15-04-
2017 23:31.
[15] Raj P A. “Performance evaluation of swarm intelligence based power
system optimization strategies,” Phd, Department of Electronics and
Communication Engineering, Pondicherry, 2008
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