TJPRC: International Journal of Power Systems
& Microelectronics (TJPRC: IJPSM)
Vol. 2, Issue 1, Jun 2016, 39-50
© TJPRC Pvt. Ltd.
OPTIMAL PLACEMENT OF TCSC FOR REACTIVE POWER
RESERVE MANAGEMENT WITH REACTIVE POWER LOSS
MINIMIZATION USING HYBRID PSOGSA
L. N. MRUNALINI DEVI1 & A. SURYA PRAKASH RAO2
1
2
Research Scholar, Department of E .E. E, Sir C. R. REDDY College of Engineering, Andhra Pradesh, India
Sr.Assistant Professor, Department of E.E.E, Sir C. R. REDDY College of Engineering, Andhra Pradesh, India
ABSTRACT
This paper presents a novel heuristic optimization method inspired by law of gravity to reduce the reactive power
losses in the system by incorporating series compensating FACTS device, TCSC using a hybrid method based on particle
swarm optimization (PSO) and gravitational search algorithm (GSA).This algorithm named as hybrid PSOGSA combines the
social thinking feature in PSO with the local search capability of GSA. A power system during disturbances is at a risk of
voltage instability due to insufficient reactive power reserve. The optimal placement and parameter setting of multiple TCSCs
with proposed algorithm ensures reactive power reserve management which is the suboptimal solution of reactive power loss
convergence, robustness and most significantly its optimal search behavior. The effectiveness of the proposed work is tested
for IEEE 30 bus test system. It is observed that the proposed algorithm can be applied to larger systems and do not suffer with
computational difficulties.
KEYWORDS: Facts Devices, Hybrid PSOGSA, TCSC, Reactive Power Reserve and Reactive Power Loss
Original Article
minimization. Experimental results justify the superiority of the approach over PSO and GSA techniques in terms of its fast
Received: Jan 07, 2016; Accepted: Jan 10, 2016; Published: Jan 18, 2016; Paper Id.: TJPRC: IJPSMJUN20164
INTRODUCTION
The reactive power demand of a power system increases dramatically whenever the system is overloaded or
subjected to sudden disturbances or contingencies. If the sufficient amount of reactive power is not supplied to the
system then there will be a drop across terminal bus voltages and has been found responsible for system block outs in
many countries across the world [1].Hence, adequate reactive power reserves are must for the system to overcome
voltage instability problem.
In a deregulated power system environment, the optimum bidders are chosen based on real power cost
Characteristics, so it results in reactive power shortage and hence loss of voltage stability of the system.
The reactive power reserves of a power system at generators can be improved by reducing the reactive power
losses of the system. As the losses in the system are reduced the reactive power conserved can act as reserve capacity
of the generators.
Voltage profile improvement alone cannot ensure the voltage stability. The authors [2-3] discuss methods to
access voltage stability of a power system to find the possible ways to improve the voltage stability. The amount of
reactive power reserves at the generating stations is found to be the measure of degree of voltage stability and it
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40
L. N. Mrunalini Devi & A. Surya Prakash Rao
stressed the importance of reactive power management from generators point of view which so far paid less attention rather
than the load’s perspective.
In [4] T. Manezes et al. proposes a strategy to improve voltage stability by dynamic var sources scheduling. In [5]
a methodology to reschedule the reactive power injection from generators and synchronous condensers with the aim of
improving the voltage stability margin is proposed.
An alternative approach for optimal reactive power dispatch based on iterative techniques is considered in [7-8].
H. Yoahida et al. has adopted easy to implement search algorithm PSO for reactive power and voltage control. Reactive
power reserve management rather than reactive power scheduling is proposed to enhance voltage stability (Feng Dong et
al. 2005).
The difficulty in controlling the modern power systems due to increased power flows is resolved by the advent of
fast acting, self commutated power electronics converters well known as FACTS Controllers introduced by Hingorani
[12].which are useful in taking fast control actions to ensure security of power systems.
Thyristor controlled series capacitor (TCSC) is a
series compensating FACTS device inserted in transmission
lines to vary its reactance and thereby reduces the reactive power losses and increases transmission capacity of the system.
As other FACTS devices, TCSC is also a costly device and hence it is important to place it at optimal location and to find
optimal size.
In recent times, many heuristic and hybrid approaches such as genetic algorithm (GA), particle swarm
Optimization (PSO), differential evolution (DE), GA-PSO and DE-PSO have been proved effective in optimally locating
FACTS devices.
A new population based hybrid algorithm PSOGSA is implemented to optimally locate TCSC with an aim to
minimize reactive power losses of the system. The PSOGSA algorithm incorporates some features of particle swarm
optimization algorithm into gravitational search algorithm i.e. exploitation ability of PSO with ability of exploration in
GSA to unify their strength.
PROBLEM FORMULATION
•
Reactive Reserves
The different reactive power sources of a power system are synchronous generators and shunt capacitors. During a
disturbance the real power demand does not change considerably but reactive power demand increases dramatically. This
is due to increased voltage decay with increasing line losses and reduced reactive power generation from line charging
effects
Sufficient reactive power reserves should be made available to supply the increased reactive power demand and
hence improve the voltage stability limit. The reactive power reserve can be improved by reducing the reactive power
losses in the system.
The reactive power reserve of a generator is the ability of the generator to support bus voltages under increased
load condition or system disturbances.
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Optimal Placement of TCSC for Reactive Power Reserve Management
with Reactive Power Loss Minimization Using Hybrid PSOGSA
•
41
Modeling of TCSC
TCSC (Thyristor controlled series capacitor) is a series compensation FACTS device which consists of a series
capacitor bank shunted by thyristor controlled reactor. The basic idea behind power flow control with the TCSC is to
decrease or increase the overall lines effective series transmission impedance, by adding a capacitive or inductive reactance
correspondingly.
Figure 1: TCSC as a Variable Reactance Incorporated in the System
The TCSC is modeled as variable reactance, where the equivalent reactance of line Xij is defined as
= + (1)
Where,
= ∗ (2)
−0.8' ≤ ≤ 0.2' (3)
= !"!
Where, Xline is the transmission line reactance, and XTCSC is the TCSC reactance. The level of the applied
compensation of the TCSC usually varies between 20% inductive and 80% capacitive.
•
Objective Function
The goal of reactive power planning is to minimize the reactive power losses of the system there by minimizing
the reactive power generated by optimally placing TCSC. Hence, the objective function can be mathematically expressed
as
* = +(,'-.. + /0 1'2 + /3 ,'2 )
(4)
Where,
7
8
,'-.. = ∑9:0
,6'-.. 1'2 =
,'2 =
>?@
∑ABC <= D<=8EF
<=GHI D<=GEJ
>
M L DL 8EF
∑ABC
=
=
GHI DL GEJ
L=
=
(5)
(6)
(7)
Where,16'2 ,6'2 are defined as
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42
L. N. Mrunalini Devi & A. Surya Prakash Rao
16'2 = O
16PQR 16 > 16PQR U
16P 16 < 16P
,PQR ,6 > ,6PQR U
,6'2 = O 6P
,6 ,6 < ,6P
Equation (5) is the expression for total reactive power loss of the system and NL represents total number of
transmission lines in the system.The second and third terms in the ojective function are normalized violations of load bus
voltages and generator reactive power outputs. NPQ and NG are number of load buses and generator buses
respectively./0 /3 are penality coefficients set to 10.
The objective function is subjected to both equality and inequality constraints.
constraint 1: Real power balance equation
7
Y
1 1Z [Z (
) cos_`Z + Z − a = 0
VW − VX − ∑Z:0
(8)
Constraint 2: Reactive power balance equation
7
Y
,W − ,X − ∑Z:0
1 1Z [Z (
) sin_`Z + Z − a = 0
(9)
Constraint 3: Reactance limits of TCSC
P
PQR
≤ ≤ (10)
HYBRID PSOGSA
PSOGSA is formulated by S. Mirjalili et al. [17]. The basic concept behind the hybridization is to combine the
ability of social thinking (gbest) in PSO using the local search capability of GSA.
The proposed algorithm considers N agents in the system. The algorithm starts with randomly defining all agents
in search space. It considers agents as objects and the position of ith agent is given by
= (e0 , … . , eh , … . e ) i=1, 2….N (11)
Where, Xi is the position in the dth dimension of the ith agent.
In this problem each agent is defined as a vector containing the line number and the size of TCSC in terms of
reactance. Hence the dimensionality of the problem is two.
Agent: [@ Φ]
Where
@: is the TCSC line location number.
Φ: is the TCSC size.
The gravitational forces from agent j on agent i at a specific time t is defined as
*Zh () = i()
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PE (j)×Pl (j)
mEl (j)n∈
peZh () − eh ()q
(12)
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Optimal Placement of TCSC for Reactive Power Reserve Management
with Reactive Power Loss Minimization Using Hybrid PSOGSA
43
Where,
Mi (t) and Mj(t) are masses of objects i and j,G(t) is the gravitational constant at time t, Rij(t) is the Euclidean
distance between i and j, ε is a small constant
Gravitational constant G(t) is initialized randomly in the beginning and is reduced with time to control the search
accuracy.
i() = ir × exp p−v ×
jw
2QRjw
q
(13)
It means G is the function of time t and initial value G0, where G0 is the initial value of gravitational constant, α is
the user specified descending coefficient, iter is the current iteration, and maxiter is maximum number of iterations.
Let the total force acting on agent i in the dimension d is calculated as
h
*h () = ∑7
Z:0,Zx Z *Z ()
(14)
The acceleration of ith agent at iteration t having d dimension is given according to the law of motion i.e., the
acceleration of an agent is proportional to the resultant force and inverse of its mass, so the acceleration of all agents
should be calculated as
h () =
yEz (j)
PE (j)
(15)
The velocity of the agents is given as
1h ( + 1) = { × 1h () + 0′ × × h () + × × p| − eh ()q
(16)
Where, vid is the velocity of agent i at iteration t in dimension d, cj1 is a weighting factor, w is a weighting
function, gbest is the best solution found so far.
At each, iteration the position of an agent is updated as
h () = h () + 1h ( + 1)
(17)
Where, vid (t+1) is the velocity of next agent and xid is the position of ith agent in dth dimension at iteration t.
The value of masses of agents are calculated by comparison of fitness
() =
}~wwjj..E (j)Dr.€€∗-w.j(j)
‚.j(j)D-w.j(j)
† (ˆ)∗‰
M„ (t) = ∑‹ ‡
ŠBC †Š (ˆ)
(18)
(19)
Where, current-fitnessi(t) is the fitness value of the agent i at any time t, and best (t) and worst (t) are the
minimum and maximum fitness value of all agents.
The agents exploring in the search space are attracted towards other agents by means of gravity force. The heavier
mass represents a good solution.
Here gbest help them in finding the optima around a good solution. The optimal solution is found by using the
exploitation ability of PSO. Global search and local search balance is accomplished by adjusting the values C1 and C2.
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44
•
L. N. Mrunalini Devi & A. Surya Prakash Rao
Flow Chart of PSOGSA
Figure 2: Flow chart of hybrid PSOGSA
CASE STUDIES
The optimal reactive power reserve management is formulated with primary objective of minimization
minimi
of reactive
power losses. The search space is bounded by violation limits to avoid unfeasible solutions.
The objective
ective function (4) with reactive power losses along with equality and inequality constraints is solved by
proposed algorithm to locate TCSC in most suitable line.
The system (Figure 3) represents IEEE 30 bus test system it has 6 generator buses, 24 load buses and 41 branches.
Figure 3: IEEE 30 Bus Test Systems
For a TCSC to be placed in the line, the lines with tap changing transformers are not considered. Each time when
the particle’s new position includes a line with tap setting transformer, the position is changed to the geographically closest
line (line without transformer).
In order to limit the sizes of the TCSC units, the restrictions on level of compensation is applied to the particles
using Equation (3) so that the power
ower flows
flow does not diverge giving worst solutions.
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Optimal Placement of TCSC for
or Reactive Power Reserve Management
with Reactive Power Loss Minimization Using Hybrid PSOGSA
P
45
The
he reduction in reactive power loss by implementation of the proposed algorithm with one, two and three TCSC
devices is tabulated as in Table 1.
Table 1: Simulation Results of Reactive Power Loss
Optimal
Location of
TCSCs (Line
Number)
IEEE 30
BUS
SYSTEM
Without
TCSC
With 1
TCSC
With 2
TCSCs
With 3
TCSCs
Line Reactance
With
Out
With
TCSC
TCSC
Q LOSS
(MVAR)
% Loss
Reducti
on
-
-
-
22.2444
-
5
0.1983
0.09915
14.4833
34.89
5,1
0.0575
0.0287
6.296
71.7
5,1,2
0.1852
0.0926
1.2919
94.1922
TCSC device is installed on different branches one by one based on the proposed algorithm and further the model
has been applied to multiple TCSC devices.
The optimal location of single TCSC at which the value of objective function is minimum, can be found as line
number 5. That means locating a TCSC in this line gives best optimum value for the objective function.
When only one TCSC is incorporated, the reactive power loss reduction is from 22.244 MVAR to 14.4833
MVAR, which is about 34%. For two TCSCs the reduction is
i about 71% and for three TCSCs it is 94% which shows
maximum improvement.
The
he total reactive power loss in the system with and without installation
installation of TCSCs is illustrated in Figure 4.
Figure
igure 4: Reduction in Total Qloss with PSOGSA
The reactive power generation, before and after positioning of TCSC, from all 6 generator buses and 2 SVC buses
(bus10 and bus 24) are tabulated in Table II.
Table 2:
2 Reactive Power Generation at Different Buses
Given bus
No
1
2
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Q gen
Without
TCSC in
MVAR
-17.021
48.822
Q gen With
1 TCSC in
MVAR
Q gen With 2
TCSC in
MVAR
Q gen With 3
TCSC in
MVAR
-17.967
41.001
-20.192
27.296
-11.917
16.371
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L. N. Mrunalini Devi & A. Surya Prakash Rao
5
8
10
11
13
24
35.975
30.975
19
16.119
10.432
4.3
Total Q g
(MVAR)
148.4442
Table 2: Contd.,
38.401
35.856
29.709
38.029
19
19
15.961
16.804
10.279
11.402
4.3
4.3
140.6831
132.4960
34.735
37.085
19
16.740
11.178
4.3
127.4920
SVC buses (10 and 24) are not considered for minimization of reactive power generation and therefore there is no
change in Qgen at those buses. Therefore the candidate buses considered for reactive power generation reduction are only
the generator buses of 1, 2,5,8,11 &13.
The effective reactance of the line is reduced with TCSC in the system. When three TCSCs are used, reactive
power generation is reduced from 148.442 MVAR to 127.492 MVAR (about 14%).That is the reactive power reserve is
increased by 14%, making the system more voltage secured in terms of additional capability of generators to generate more
reactive power during disturbance or contingency.
Figure 5: Reduction in Total Qgen with PSOGSA
The total
otal reactive power generation (Qgen) from all the generator buses is shown in Figure 5. It is observed from
the plot that the reduction in Qgen is encouraging and the reactive power reserve of the system is improved.
In addition to the principle objective of reactive power reserve management, the three TCSC
T
locations (lines 5, 1
and 2) which are major power transmitting channels in the IEEE 30 bus test system are expected to be with increased
power handling capacity as the effective reactance of the line is reduced.
Comparative Analysis
The effectiveness of the proposed algorithm is proved by comparing the simulation results of PSOGSA with that
of PSO and GSA and results for IEEE 30 bus test system are tabulated as follows.
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Optimal Placement of TCSC for Reactive Power Reserve Management
with Reactive Power Loss Minimization Using Hybrid PSOGSA
47
Table 3: Comparison of Reactive Power Losses
Parameters
PSO
With 1
TCSC
Step by
With 2
Step
TCSCs
Placement
With 3
TCSCs
Simultaneous
Placement of three
TCSCs
Qloss (MVAR)
GSA
PSOGSA
14.6724
14.4833
14.4833
6.4582
6.2960
6.2960
1.421
1.4061
1.292
9.1018
6.2592
6.1095
Multiple TCSCs can be optimally placed in the system either simultaneously or step by step. The reactive power
losses in both the cases is shown in Figure 6
Figure 6: Reduction in Qloss with Three TCSCs
From the figure it is observed that step by step placement gives better results compared to simultaneous placement
and it also shows that in both the cases PSOGSA gives the improved performance over the other two methods.
In case of step by step placement the reactive power loss minimization using PSOGSA is about 94% where as for
PSO and GSA it is 93.60% and 93.68% respectively. Hence, the percentage of loss minimization is more with hybrid
PSOGSA.
The total reactive power generation of the system, computed using all three methods is tabulated as follows
Table 4: Comparison of Simulation Results
Qgen(MVAR)
Parameters
With 1
TCSC
With 2
TCSCs
With 3
TCSCs
PSO
GSA
PSOGSA
140.8724
140.6831
140.6831
132.6582
132.4960
132.4960
127.6210
127.6061
127.4920
The total reactive power reserve of the system improves with reduction in reactive power generation and it is
more in the case of PSOGSA. Hence, from the results it is evident that step by step placement of multiple TCSCs with
PSOGSA gives optimum results.
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L. N. Mrunalini Devi & A. Surya Prakash Rao
Figure 7: Convergence Characteristics with Single TCSC
Figure 8: Convergence Characteristics with Two TCSCs
Figure 9: Convergence Characteristics with Three TCSCs
The convergence characteristics of PSO, GSA and PSOGSA in each case are shown in the above figures. From
the obtained convergence characteristics it is observed that the PSOGSA exhibits better convergence when compared with
other two methods.
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Optimal Placement of TCSC for Reactive Power Reserve Management
with Reactive Power Loss Minimization Using Hybrid PSOGSA
49
CONCLUSIONS
The problem of optimal placement of TCSC to minimize reactive power losses with the aim of reactive power
reserve management for improved operation of power system is solved by using hybrid PSOGSA in this paper. The
simulation results show that multiple TCSCs can be used for minimizing reactive power losses leaving sufficient amount
of reactive power reserves at generator buses. The security margin increases with the number of TCSCs but there should be
a limit on the number of devices due its cost constraint.
The feasibility of the proposed method is verified by using IEEE 30 bus test system and the results are compared
with PSO and GSA. From the simulation results, it is evident that the proposed algorithm has the ability to find the better
solution with improved convergence characteristics and computational efficiency. Hence the proposed hybrid PSOGSA
algorithm is proved to be a promising alternative approach to solve complex optimization problems in power systems.
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