OPTIMAL ALLOCATION OF SHUNT CAPACITOR IN THE RADIAL
DISTRIBUTION NETWORK USING BIO INSPIRED BAT ALGORITHM
K.Sukraj1, T.Yuvaraj
2, R. Hariharan
3
P.G. Scholar, Department of Electrical and Electronics Engineering, Saveetha School of Engineering, Saveetha
Institute of Medical And Technical Science, Chennai 1
Assistant Professor, Department of Electrical and Electronics Engineering, Saveetha School of Engineering,
Saveetha Institute of Medical And Technical Science, Chennai 2,3
[email protected], [email protected]
3
ABSTRACT
This paper introduces a new method of scheduling for optimal placement and sizing of capacitor
in the radial distribution network with the objective of minimizing losses. Voltage stability index
is used to identify the location where in the capacitor can to be installed. Recently developed bio
inspired Bat algorithm is proposed to calculate the optimal size of the capacitor. To check the
feasibility of the proposed method, it has been tested on two standard IEEE buses such as 34 and
85 bus radial distribution systems.
Key words: Shunt capacitor, Radial distribution network, Voltage stability index (VSI), Bat
algorithm
1. INTRODUCTION
In modern power distribution network, losses are considered as one of the major challenge
towards the overall efficiency of the power system. The losses in power system are expressed in
terms of I2R [1]. It is known that losses in distribution network are considerably high compared
to that of a transmission network. Studies as on date indicated that almost 10-13% [2-4] of the
total power generated is consumed as losses at the distribution level in power system. In addition
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to that, the distribution network also has a specific drawback of voltage reduction at nodes while
moving away from substation. Such losses and poor voltage profile also have a direct impact on
the financial issues as well as the overall efficiency of the power utilities. Therefore, the need of
improving the overall efficiency of the power delivery has forced the power utilities to reduce
the losses and improve the voltage profile at distribution level. [34-37] The ultimate reason for
the losses in power system is inadequate amount of reactive power in distribution system.
Reactive power support is provided to the power system in order to reduce the power losses and
increase the overall efficiency of the power system. Many arrangements can be followed to
reduce losses like network reconfiguration, shunt capacitor placement, distribution generator
placement etc. Moreover, It is not possible to attain zero losses in a power system but it is
possible to keep them to a minimum to reduce the system overall cost [5-7].
Innumerable methods had been adopted for solving this problem with a view to minimizing
losses have been suggested in the literature based on both traditional mathematical methods and
more recent heuristic approaches. An elaborated survey of the literature from the last decade
focusing on various heuristic optimization techniques applied to evaluate optimal capacitor
placement (OCP) and size is presented in [8].
Through Bi-level programming Co-ordinated optimal allocation of DGs, Capacitor banks and
SOPs is made possible in Active Distribution Network [9]. An allocation Bacterial foraging
optimization algorithm was used for optimal location and sizing of capacitor placement
methodology for placement of capacitor in Unbalanced Distribution Systems to achieve loss
minimization with an adequate voltage profile is described in [10]. Implementation of bat
algorithm is explained in [11]. Bacterial foraging optimization algorithm was used to determine
optimal location and size of capacitor in radial distribution system [12]. Chu-Sheng Lee, Helon
Vicente Hultmann Ayala and Leandro Dos Santos Coelho employed Particle Swarm
Optimization method for a new capacitor placement in Distribution System [13]. A Clustering
Based Optimization (CBO) is proposed for the Discrete Optimization Problem of fixed shunt
capacitor placement and it‟s sizing [14]. Genetic algorithm is used to determine the optimal size
of the fixed and switched capacitor in radial distribution system [15-18]. Fuzzy based GA was
used to calculate the optimal size with the multi objective of minimizing the energy cost and to
enhance the voltage profile of the system [19]. Direct search algorithm was used to determine the
optimal location and size of fixed and switched capacitor and it is test executed on IEEE 22, 69,
85 bus distribution system to maximize net savings and to minimize the power loss [20]. Taher
and Bagherphor proposed hybrid honey bee colony colony optimization algorithm for the
placement of the shunt capacitor in IEEE 25, 37 bus radial distribution system with the objective
of minimizing power loss and maintaining total harmonic distortion [21]. Antunes et al.
proposed non-dominated sorting genetic algorithm to solve the optimal capacitor placement in
radial distribution system to compensate reactive power [22]. Baran and Wu introduced mixed
integer programming for the placement of capacitor [23]. Chis et al. have chosen more sensitive
nodes of optimal location and sizing through heuristic search strategies to maximize net savings
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[24]. Prakash and Sydulu introduced Particle swarm optimization to calculate the optimal size of
the capacitor bank and to minimize the power loss [25]. Sayyad nojavan et al. proposed mixed
integer nonlinear programming approach to identify the optimal location and to determine the
size of the capacitor to minimize the power loss and increase the net benefits [26]. Plant growth
optimization was used for optimal placement of capacitor with the goal of voltage profile
improvement and power loss reduction [27].
The present work targets to develop a quick and affordable technique to calculate the size of the
capacitor and to determine the optimal location for the placement of capacitor to minimize power
loss in radial distribution system. In this paper, the optimal location of the capacitor is identified
using the voltage stability index. Bat algorithm has been proposed to minimize the objective
function by calculating the size of capacitor at candidate location.
2. PROBLEM FORMULATION
2.1. Power flow analysis
The traditional load flow studies such as Newton-Raphson, Gauss-Seidal and Fast De-Coupled
are not an appropriate for finding the voltages and line flows in radial distribution systems
because of a high resistance to reactance ratio(R/X). A Direct Approach for Distribution System
Load Flow Solution has been executed in [28]. The single line diagram of simple distribution
system is shown in Fig. 1.
From Fig. 1, the equivalent injected current at node t is given as
= ( + ) / ( ) (1)
Kirchoff‟s current law is applied to calculate the branch current in the line section between buses
t and t+1 and it is given as,
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= + (2)
By using the Bus Injected to the Branch Current Matrix (BIBC) the eqn. (2), is formed into
matrix format
[J] = [BIBC][I] (3)
Kirchoff‟s voltage law was applied to calculate the voltage at buses t+1, which is given as
= – ( + ) (4)
The real and reactive power loss in the line section between buses t and t+1 can be calculated as
= ( +Q2t,t+1) / ((| |2) * ( )) (5)
= ( +Q2t,t+1) /( (| |2) * ( )) (6)
The total power loss of the distribution system is calculated by adding all the losses in line
sections, which is given by
= (Loss, t , t+1) (7)
2.2. Objective function
The objective of capacitor placement in radial distribution system is to minimize the total power
loss while satisfying the equality and inequality constraints. The mathematical formulation of the
objective function (F) is given by
Minimize (F) = Min ( ) (8)
The considered equality and inequality constraints in the present problem are as follows:
2.2.1. Voltage deviation limit
≤ | | ≤
2.2.2. Power balance constraints
+ ∑ = ∑
Where, PD(t) is the power demand at bus t and PCapacitor(t) is the power generation using capacitor.
2.2.3. Reactive power compensation
≤ ≤ t = 1, 2,…..,nb
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Where, is the minimum reactive power of the limits of the compensated bus t and
is the maximum reactive power of the limits of the compensated bus t
2.6. Voltage stability index (VSI)
There are many indices to check the power system security level. In this section new steady state
Voltage Stability Index(VSI) is used in order to identify the node which has more chances to
voltage collapse [29, 12]. Voltage stability at each node is calculated using eqn. 11. The node
which has low value of VSI has more chance of getting capacitor installed to it. Hence, the VSI
should be maximized to prevent the possibilities for voltage collapse.
VSI(t+1)=| |4-4[ * - * ]2-4[ * + * ]| |2 (11)
2.6. Net savings calculation of capacitor
Net savings of the capacitor is determined by eqn. (12) and for all calculations, the rates
furnished in table 1are used for the purpose of obtaining net savings of the capacitor with the
assumption that capacitor‟s cost purchase is linearly proportional to the capacitor size.
Net saving / year = {Total Cost of Energy Reduction – σ × {Cost of Installations + Cost of
Purchase - Operating Cost / year} (12)
Table 1. Constants for the rates using a long with simulated test cases
SNo Item Proposed Rate
1 Average energy cost $0.06/kwh
2 Depreciation factor (γ) 20%
3 Purchase cost $25/KVAr
4 Installation cost $1600/location
5 Operating cost $300/year/location
6 Hours per year 8760
3. BAT ALGORITHM
3.1. Overview of Bat algorithm
In recent years, nature inspired algorithms are one of the most powerful for tougher power
system optimization problems. Based on the echolocation characteristic of natural bats in
locating their foods, a new nature inspired meta-heuristic algorithm called “Bat Algorithm” has
been proposed by Yang [30-32, 11, 4]. Bats are the only interesting animals, which has the
mammals having wings and advanced echolocation ability to find their prey. Basically, it
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generates a sound signal called echolocation to detect the objects surrounding them and to find
their way even in full darkness[38].
Bat algorithm can be developed by idealizing some of the specific behaviours of bats. The
approximated or idealized three rules are given below:
1. Each bat makes use of the echolocation characteristic to sense the distance and also to know
the difference between food or prey and background obstacles in some magical way through its
echolocation property.
2. Each bat flies randomly with velocity , position with a frequency , a varying
wavelength λ and a loudness Ao to seek their prey (or wavelength) of emitted pulse and regulate
the rate of pulse emission r in the range of [0,1] relying on the proximity of its aim.
3. Even though the loudness varies in different ways we assume that the loudness varies from a
large positive to a minimum constant value .
3.1.1. Initialization of population
Initially, the population is the number of virtual bats for bat algorithm which is generated
randomly. The number of virtual bats should be anywhere between 10 and 40 and after getting
the initial fitness of the population for given function the values are updated based on loudness,
movement and pulse rate.
3.1.2. Movement of virtual bats
In bat algorithm we have to define the rules for updating the position and velocities of the
virtual bats. These are given by
= +( - )β (13)
= +( - ) (14)
= + (15)
Where, β ϵ [0,1] is a random vector drawn from a uniform distribution, and here x is the current
global best location (solution) among all the „n‟ bats. Locally, generated new solution for all bats
using random walk is given by (16)
= +ƐAt
(16)
Where, Ɛ is the random number in the range [0,1], while = ) is the average loudness of all
the bats at this time step.
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3.1.3. Loudness and pulse emission
Based on the iteration and loudness Ai and the rate of pulse emission are updated as a bat
which reaches to its prey and the pulse emission increases while the loudness decreases. Then,
the equation for convergence can be taken as
= α (17)
= [1-exp(-λt)] (18)
Where α and λ are constant values.
For any value of 0 < α < 1 and γ > 0 we have
→0, → as t→∞
The initial values of loudness can be typically in the range of [0,1] and on the other hand the
initial value of emission rate can be in the range of [0,1].
Table 2. Input parameters of the Bat Algorithm
Sr. No Parameters Quantity
1 Population Size 20
2 Number of Generations 50
3 Loudness 0.5
4 Pulse Rate 0.5
The selected parameters for bat algorithm are given in Table 1. Based on the above approximation and idealization the step by step implementation of bat algorithm for the
optimization process can be described in the following steps:
Step 1: First, read input data of the system (bus data and load data). Step 2: Run the distribution load flow of base case and calculate the real and reactive power
losses, voltages and Voltage Stability Index (VSI).
Step 3: Identify the candidate bus for placement of the Capacitor using VSI. Step 4: Set the lower and upper bounds for the constraints as bat algorithm control parameters
(pulse frequency, pulse rates and loudness) and maximum number of iteration.
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Step 5: Generate the initial bat population randomly in the feasible area. Each bat indicates an encouraging optimal size (kVAr) for the Capacitor devices in the distribution network.
Step 6: Evaluate the fitness function. In this step, the expected value of the active and reactive
power losses and the voltage deviation of the objective function can be determined by using Direct Load Flow method for each solution or bat.
Step 7: Choose the best bat in the population (minimum power loss value).
Step 8: Update the population of Bat. Step 9: Now, run the load flow and calculate the active power loss and reactive power loss with
the updated population.
Step 10: Check the termination criterion. The termination criterion can be the maximum number of iterations to update the Bat Algorithm population or a specific value which the objective function should reach to a minimum value. If it is satisfied then finish the algorithm or else
return to step no 5.
Step 11: Display the optimal solutions. These steps will be followed in order to minimize the objective function.
4. RESULTS AND DISCUSSION
4.1. IEEE 34-bus radial distribution system
In this case IEEE 34-bus radial distribution system is analyzed. The data for this system are taken from [24, 11]. The single line diagram of this system is shown in Fig. 2. The total real and reactive power loads of the system are 4636.5 kW and 2873.5 kVAr, the base values are Sbase
100 MVA, Vbase 11 kV. The total real and reactive power loss of the base case is 221.286 kW and 65.0980 kVAr respectively. In the proposed method the optimal location for the capacitor
placement is 19, 22, 20 and the optimal size optimal size of the capacitor which is to be located is calculated using Bat algorithm. The optimal size obtained using Bat algorithm is dramatically small in comparison with the existing methods. The optimal capacitor size, optimal capacitor
location, total real and reactive power loss, minimum voltage magnitude before and after capacitor installation is shown in Table 3. The proposed method results are compared with
Heuristic method [24], PSO [25], PGS [27], and MINLP [26]. The optimal size obtained using Bat algorithm is dramatically small when compared to the existing methods. The real and reactive power loss obtained from the proposed method are 159.89 kW and 47.03 kVAr
respectively and this value is less when compared to 162.9 kW, 47.3 kVAr by MINLP [26], 168.7 kW, 48.9 kVAr by PGS [27], 168.5 kW, 48.90 kVAr by PSO [25], 167 KW, 48.3 KVAr
by Heuristic Based[24]. Net savings of the proposed method is $ 17268 along with the high % of reduction of PLoss and QLoss as 27.75% and it is proved to be better than all the other methods used in this paper.
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The minimum voltage obtained from this method is 0.9505 p.u. and this voltage is better when compared to the base case of 0.9420 p.u. Also Table 3 shows that the proposed method having
significant improvement in all specifications while comparing with the other existing methods.
Fig.2 IEEE 34-Bus Radial Distribution System
Table 3. Simulation result of 34-bus system
Base
Case
Heuristic
Based[24]
PSO[25] PGS[27] MINLP[26] Proposed
Method
Optimal size
and Location
---------- 1400(26) 750(11)
300(17) 250(4)
781(19) 803(22)
479(20)
1200(19) 639(22)
200(20)
300(4) 600(10)
100(14) 500(18) 300(22)
1000(27)
720(11) 800(18)
720(24)
PLoss(KW) 221.286 167 168.5 168.7 162.9 159.89
% Reduction
in PLoss
--------- 24.53% 23.85% 23.76% 26.38% 27.75%
QLoss(KVAr) 65.09 48.3 48.90 48.9 47.3 47.03
% Reduction
in QLoss
--------- 25.8% 24.88% 24.88% 27.34% 27.75%
VMin(p.u) 0.9420 0.9515 0.9500 0.9496 0.9513 0.9504
Net
savings/Year
($)
--------- 12553 15569 15584 12968 17268
34 bus test systems
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Fig. 3 Voltage profile improvement of 34 bus system
The above figure 3 shows the voltage profile improvement of the 34 bus system i.e with the usage of capacitor and without the usage of capacitor. In order to reduce the losses in the radial
distribution network capacitor was allocated at the appropriate place with the right size through Voltage Stability Index and bat algorithm. Moreover, with reference to the output received in the
waveform format clearly explains the improvement in the voltage profile with the usage of capacitor and without the usage of capacitor in radial distribution system of the 34 bus system.
Hence, this method proves to be successful for the implementation.
4.2. IEEE 85-bus radial distribution system
In this case IEEE 85-bus radial distribution system is analyzed. The line data and bus data are available from [33, 11] with a real and reactive power loads of 2570.28 kW and 2621.936 kVAr.
The base values are Sbase 100 MVA, Vbase 11 kV. The single line diagram of this system is shown in Fig. 4. The total real and reactive power losses of the base case are 315.3278 kW and 198.1867 kVAr. The optimal location of this system is chosen as 9, 33 and 61, then the optimal
size is obtained using Bat algorithm. The total kVAr is used in the proposed method is less when compared with other existing techniques at the same time the real and reactive power reduction
are also found to be better. The real and reactive power loss obtained from the proposed method are 150.98 kW and 93.42 kVAr respectively and this value is less when compared to 159.87 kW, 97.10 kVAr by MINLP [27], 174.01 kW, 103.76 kVAr by PGS [30], 163.32 kW, 98.9 kVAr by
PSO [26]. Net savings of the proposed method is $ 70801 along with the high % of reduction of PLoss and QLoss as 52.12 and 52.82 respectively and it is proved to be better than all the other
methods used in this paper.
5 10 15 20 25 300.9
0.92
0.94
0.96
0.98
1
Bus Number
Voltage(p
u)
without Capacitor
with Capacitor
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Fig. 4 IEEE 85-bus radial distribution system Table 4. Simulation result of 85-bus system
Base Case PSO[25] PGS[27] MINLP[26] Proposed
Method
Optimal size
and Location
--------- 324(7) 796(8)
901(27) 453(58)
200(7) 1200(8)
908(58)
300(7) 700(8)
900(29) 500(58)
950(9) 650(33)
650(61)
PLoss(KW) 315.3278 163.32 174.0048 159.87 150.98
% Reduction
in PLoss
--------- 48.21% 44.82% 49.30% 52.12%
QLoss(KVAr) 198.18 98.18 103.76 97.10 93.42
% Reduction
in QLoss
--------- 50.09% 47.64% 51.01% 52.82%
VMin(p. u) 0.8708 0.9153 0.9089 0.9089 0.9209
sNet
savings/Year
($)
--------- 65045 60879 67229 70801
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85 bus test systems
Fig. 5 Voltage profile improvement of 85 bus system
The above figure 5 shows the voltage profile improvement of the 85 bus system i.e with the usage of capacitor and without the usage of capacitor. In order to reduce the losses in the radial
distribution network capacitor was allocated at the appropriate place with the right size through Voltage Stability Index and bat algorithm. Moreover, with reference to the output received in the waveform format clearly explains the improvement in the voltage profile with the usage of
capacitor and without the usage of capacitor in radial distribution of the 85 bus system. Hence,
this method proves to be successful for the implementation.
5. CONCLUSION
Capacitor placement in the distribution system is used to compensate the reactive power which would ultimately leads to the minimization of the power loss, enhance the voltage profile, improve the overall system stability, etc., It is necessary to place the capacitor in right location
with optimal size to ensure the maximum benefits of the distribution system. In this article, Voltage Stability index is used to identify the location of the capacitor and the optimal size is
determined by using Bat algorithm. The proposed method is applied on IEEE 34-bus and 85-bus radial distribution system. The simulated results are compared with the results of MINLP, PGS, PSO, HS-based methods. The result obtained by the proposed method of Bat algorithm is found
to be better than the other existing techniques. Hence, the proposed method can be easily applied to any kind of radial distribution system.
10 20 30 40 50 60 70 800.85
0.9
0.95
1
Bus Number
Voltage(p
u)
without Capacitor
with Capacitor
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