optimal allocation of shunt capacitor in the radial distribution network using … ·...

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]

2, [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

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 15901-15917ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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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

International Journal of Pure and Applied Mathematics Special Issue

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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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