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1st International Conference on Engineering and Environmental Sciences, Osun State University. November 5-7, 2019.
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OPTIMAL PLACEMENT AND SIZING OF CAPACITOR IN
NIGERIAN RADIAL DISTRIBUTION NETWORKS USING CUCKOO
SEARCH ALGORITHM
Salimon, S. A.1*, Suuti, K. A.2 and Aderinko, H. A.3
1,3Department of Electrical and Electronic Engineering, Ladoke Akintola University of
Technology, Ogbomoso, Nigeria
2 Electrical and Electronic Engineering Department, University of Ibadan, Ibadan, Nigeria
*Email of Corresponding Author: sunnydexs.sa@gmail.com
ABSTRACT
Installation of capacitors in power networks are generally used for the improvement of the
network power factor, improvement of the voltage profile and the voltage stability index,
maximizing flow through cables and transformer, and minimization of total power loses due to
the compensation of the reactive component of power flow. These benefits depend to a very
large extent on the size and location of the capacitor in the radial distribution network as wrong
placement can lead to the opposite effects. Furthermore, the appropriate placement of
capacitors will reduce the total capacitor costs and the running expenses of Distribution
Companies (DISCOs). In this paper, the problem of optimal placement and sizing of capacitor
in the buses of Nigerian distribution network is addressed. The proposed methodology uses the
Cuckoo Search Algorithm (CSA) to determine the size and the location satisfying the operating
constraints. To demonstrate the capability of the proposed method, it was tested Imalefalafia
32 bus radial distribution network of the Ibadan Electricity Distribution Company (IBEDC).
The simulation results obtained with compensation was compared with that of the base case
(without compensation) and found to be encouraging.
Keywords: Cuckoo Search algorithm, Loss sensitivity factor, Radial distribution
network, Capacitors.
INTRODUCTION
Radial distribution networks consist of a main feeder and lateral distributors which act as a link
between high voltage transmission line and low voltage consumers. The low resistance to
reactance ratio of the radial distribution network leads to a high power losses compared to that
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of transmission networks (Moradi and Abednie, 2010). Research have revealed that installation
of capacitor banks in the radial distribution network has some advantages which include power
factor correction, improvement of the network voltage profile, power and energy loss
reduction, feeder and system capacity release as well as power quality improvement (Elsheikh
et al, 2014). The extent to which capacitor banks reduce power system loss, the cost of reactive
power compensation and improves the voltage profile depends on the size and location of the
capacitors. The reactive power supplied by the shunt capacitor affect the reactive power in the
network and enable it to provide voltage support. The support however depends on the
deliberate placement and size of capacitor to improve the voltage profile of the network, reduce
power loss and the reactive compensation cost (Ocha et al, 2006). Optimal placement and
sizing of capacitor is a complex combinatorial problem which can be solved with an
optimization technique.
Numerous optimization techniques and models have been proposed for the solution of the
optimal sizing and placement of capacitors in a radial distribution network for power loss
reduction and improvement of voltage profile by several researchers. The early proposed
approaches are the analytical numeric programming optimization techniques like local
variation method (Ponnavaiko and Prakassa Rao, 1989) and mixed integer linear programming
techniques (Baran and Wu, 1985; Khodr et al, 2008) have been used for solving the problem
of optimal placement and sizing of capacitor. In recent years, various meta-heuristics
population-based approaches have been introduced by researchers for capacitor placement
problem.
Raju et al. (2012) proposed direct search algorithm for optimal placement and sizing of
capacitors in a radial distribution system to maximize the savings and minimize the power loss.
The proposed method was tested on standard 22, 69 and 85 bus systems and the results were
compared with the results of PSO. Prakash et al. (2007) presented loss sensitivity factor and
particle swarm optimization for the placement of capacitor with the objective of minimization
of power loss. The method was implemented on standard 10-bus, 15-bus, 34-bus, 69-bus and
85-bus systems. Rao et al. (2011) proposed plant growth simulation algorithm for capacitor
sizing and placement in radial distribution systems with the objective of improving the voltage
profile and reduction of power losses. It was tested on 10, 34 and 85 bus standard IEEE radial
distribution systems. Ahmed et al. (2014) proposed a combination of LSF and fuzzy real coded
Genetic Algorithm for the optimal placement of capacitor on standard IEEE 33-bus. The
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objective of the work is minimization of power losses and total energy cost. Binary honey bee
foraging approach was proposed to solve optimal capacitor placement problem of radial
distribution systems by Sedighizadeh et al. (2012). The proposed method was implemented on
IEEE 9-bus test system and its performance was compared with Binary Particle Swarm
Optimization (BPSO) and Genetic Algorithm. Tamilselvan et al. (2015) used the clonal
selection algorithmic approach to minimize power loss and energy cost by optimal placement
and sizing of capacitor in radial distribution network. The feasibility of the method was tested
on standard 33 and 69 bus radial distribution systems.
All the aforementioned studies achieved encouraging results in solving the capacitor
placement problem in radial distribution system. The effectiveness of the various methods was
tested on standardized IEEE distribution systems. However, there is the need to use optimal
placement and sizing of capacitor to solve the inherent problems of real Nigerian radial
distribution system. This paper therefore focuses on optimal placement and sizing of capacitor
on the Imalefalafia 32-bus Nigerian radial distribution system Cuckoo Search Algorithm
(CSA) with the objective of minimizing the total power loss and the total cost of compensation.
METHODOLOGY
Load flow for radial distribution networks
Common load flow procedures like Newton-Raphson (NR) and Gauss-Seidel (GS) have less
accuracy and take many times to get convergence in distribution network, because the ratio of
resistance to reactance is high in respect of the distribution network. In order to analysis
capacitor effect on the network and calculating the active power loss of the grid, backward-
forward (BF) load flow method for distribution system (Moeini, 2010) is adopted for use in
this work. The main idea of Backward-forward load flow is based on Kirchhoff Voltage and
Current laws. This method derived from the single line diagram in Fig. 1 determines the current
of any feeder and the voltage of any node in four following stages:
Step 1- Node Injection Current
Whereas the load data are available it is possible to calculate injected current of each node by
=
(1)
Where - Given apparent load of the node, - the current of node in iteration k and
–The voltage of node in iteration k-1
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Step 2- Backward Sweep
In this step the current of all branches can be calculated from the end-customer nodes towards
the root node by:
=+ (2)
Where L is the branch index and
is the current of branch in iteration K
Step 3 – Forward Sweep
Update the voltage magnitude of all nodes by the computed current in step 2 using:
=
(3)
Where and
are the voltages of two nodes that
Fig. 1: Sample Radial Distribution Network
are connected through a branch with impedance equal to
Step 4 – Convergence Indexes
Calculate the apparent power of loads with new obtained voltages of all nodes. Computing the
active power and reactive power mismatch using equations (4), (5) and (6) respectively:
=
(4)
= Real (5)
Imag (6)
Where is active power mismatch in iteration k, is reactive power mismatch in iteration
k and is the apparent power of load.
Repeat step 1, 2, 3 and 4 until results satisfies the convergence indexes. BF Load flow program
is set to stop repetition when mismatch power and reach initially defined boundary.
The capacitor bank is a reactive source in any possible node which injects reactive power to
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the network. Active powers of the capacitors are taken to be zero. With capacitor imbedded
into the network, equation (1) should be revised to equation (7)
=
(7) Where is the capacitor assigned to node.
Power loss in the Lth line (where L is the branch index) between two immediate buses
‘i’ and ‘i+1’ is given by Eq. (8)
(8)
The total power loss, in the radial distribution network is given by Eq. (9)
(9)
Where is total buses in the distribution network.
Objective Function
The objective of the capacitor placement and sizing problem in the radial distribution network
is to minimize the total annual cost due to the network power losses and reactive power
compensation subject to the operating constraints. The cost of reactive power compensation
includes purchase, installation and operation cost of capacitors. As the location and size of
capacitors are to be treated discrete, the mathematical model can be expressed as constraint
nonlinear integer optimization problem:
Cost of power loss + Cost of reactive power compensation
x + α[x N) +
] + ( x N) (10)
Where is the total power losses, where is the annual cost per unit of power losses
(#/kW), is installation cost, N is the total number of candidate buses for capacitor
placement, is the purchase cost of capacitor, is the shunt capacitor size placed at bus
n and is the operating cost of the capacitor.
In order to measure the value of the voltage stability in the radial distribution network, the
Voltage Stability Index (VSI) is determined. Inspecting the VSI performance exposes the buses
which undergoing huge voltage drops are weak and within the condition of corrective actions.
VSI at line section ‘L’ between buses ‘i’ and ’i+1’ in the single line diagram shown in Fig. 1
can be calculated using Eq. (11) as given by (Tan et al, 2012).
VSI(i,i+1)=-4[]- 4 (11)
Where Vi, is the sending node voltage; while Pni, Qni, Rni, and Xni are real power, reactive
power, resistance, and impedance for the receiving node.
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The reactive power support provided by the capacitors also helps to enhance the voltage
stability of the distribution network.
3.3 Constraints
Each capacitor size minimizing the objective function, must satisfy the following constraints.
(i) Shunt capacitor limits
(12)
Where is the minimum compensation limit and is the maximum compensation limit
(ii) Bus bar voltage limits
(13)
In radial distribution networks and
(iii) Total reactive power injected
(14)
Where is the total reactive load
Overview of Cuckoo Search Algorithm
Cuckoo Search Algorithm (CSA) is a meta-heuristic optimization technique whose
birth was claimed from inspiration surrounding the brood parasitism of cuckoo species, which
lay their eggs in the nests of other host birds. CS Algorithm was developed by Yang and Deb
(2009) and it has been applied to various engineering optimization problems. The fundamental
ideas in modelling this algorithm was borrowed from the fact that if a host bird discovers
foreign egg in its nest, it will either abandon the nest and build a new elsewhere or throw the
foreign egg away.
Three rules are taken into account in cuckoo search algorithm as follows:
(i) At one time, each cuckoo only lays one egg, and
leaves it in a randomly chosen nest;
(ii) The algorithm will carry over the best nest with high quality eggs (solutions) to the next
generations;
(iii) A host bird can discover a foreign egg with a probability, = [0, 1] while the number
of available host nests is fixed. In this case, the host bird can either abandon its nest and build
a completely new nest elsewhere or simply throw the eggs away (Yang and Deb, 2010).
A Lévy flight is performed in other to produce new solutions, for a cuckoo i as given in
the equation.
= + α Levy() (17) (17)
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where α is the step size which should be associated to the problem of interests scales; α can be
set to value 1 in most situations (Yang and Deb, 2009). The random step length of Lévy flight,
which fundamentally provides a random walk, is derived from a Lévy distribution with an
infinite variance and infinite mean (Yang and Deb, 2010).
Levy~ u = (18)
Here, the sequential jumps of a cuckoo fundamentally form a random walk process with a
power law step length distribution with a heavy tail.
Application of Cuckoo Search Algorithm to Capacitor Placement
Application of CSA to the capacitor placement problem is discussed here. The available
discrete sized banks could be placed at any location and could be any size. Hence, capacitor
placement in a radial distribution network is a complex combinatorial problem which can be
solved with any suitable optimization algorithm. This paper reports the successful application
of CSA for capacitor placement problem in a practical Nigerian distribution system to minimize
the cost due to the system total power loss and reactive power compensation. The details of the
solution procedure are provided below:
(1) Input data: the data to be fed as input are listed below.
(a) Number of buses.
(b) Load demand active (kW) and reactive (kVAr) power at each bus.
(c) Bus voltage limit (
(d) Distribution lines’ impedances (resistance and reactance).
(e) CS parameters (number of nests, n=25, step size, α=1, maximum number of iterations,
probability to discover foreign eggs, ).
(2) Perform the initial load flow analysis using the Backward/Forward Sweep load flow for
radial distribution networks without capacitor compensation (base case). (3) Generate initial
population of the hoist nest (solution vector) X
An individual solution is defined as
[ ] where represents the location index for capacitor banks where 1 ≤≤ Lb, and Lb
is the highest location index; assuming that the location considered for capacitor placement are
numbered successively from 1, Lb is the index number of the last bus. The second part,
carries the integer representing size of the capacitor bank to be placed. To extract the size of
the capacitor bank, a multiplication factor is employed as in KVAr = *50 + 100.
1st International Conference on Engineering and Environmental Sciences, Osun State University. November 5-7, 2019.
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(19)
Each row of the solution vector is one complete solution having information on locations and
sizes of capacitor banks. Consider the a solution vector, say . The first part gives the
location and the second part gives the capacitor banks to be placed at the corresponding location
which implies that a capacitor bank of size 300kVAr (4*50 + 100) will be placed at bus 12 of
the radial distribution network.
(4) Evaluate the solutions X using load flow and get the following for each solution.
(a) the total active power losses,
(b) The voltage at each bus,
(c) Distribution line flows to determine the overloaded lines.
(5) Calculate the annual cost function for each nest (solution) using the objective function in
Eq. (10).
(6) Calculate the fitness function for each nest.
(20)
Where the penalty factor is assigned as follows for radial distribution systems.
(21)
(7) Generation of Cuckoo: A cuckoo, which is a new solution is generated by Levy flight
as given in Eq. (17).
(8) Evaluate the cuckoo, new solution, using the load flow to obtain its and line flows.
Calculate the annual cost function for the cuckoo using Eq. (10) and its fitness function, FF
using Eq. (20) to determine the quality of the cuckoo.
(9) Replacement: A nest is selected among n randomly, if the quality new solution in the
selected nest is better than the old solution, it is replaced by the new solution (cuckoo).
(10) Generation of new nest: The worst nest are abandoned based on the probability () and
new ones are built using Levy flight.
(11) The stopping criterion is set to a tolerance value of 1 and maximum generation of
100 iterations. If the maximum number of iterations is reached or specified accuracy level is
achieved, the iterative process is terminated and the result of the CSA displayed. Otherwise,
go to step 7 for continuation.
RESULTS AND DISCUSSION
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The network used to test the algorithm is the Imalefalafia 32-bus Nigerian radial
distribution networks. The data for the network were obtained from Ibadan Electricity
Distribution Company (IBEDC), Ibadan, Nigeria. The loads were modelled using steady state
values of the real and reactive power they consumed.
Imalefalafia 11-kV feeder is an outgoing feeder from Imaleafalafia, 33/11-kV
injection substation located at Ibadan Oyo State. Imaleafalafia 11-kV feeder has thirty-two
buses with thirty-one branches with a total real power loads and reactive power of 3.17 MW
and 1.04 Mvar respectively. The single-line diagram of the Imalefalafia 32-Bus feeder is as
depicted in Fig. 2.
To achieve the objective function, Backward-Forward sweep algorithm was utilized to
obtain the power flow solution, the total power losses and total annual cost. Matlab code was
written to add the capacitor bank to the network by suitably modifying the network bus data.
The loads are treated as constant power load and considered as balanced. Design period
of one year is taken at full load condition for the purpose of analysis. The various constant
assumed in the calculations are (Gnanasekaran et al, 2016): annual cost per unit of power
losses()=183,960 #/kW, purchase cost of capacitor =8,750 #/kVAr, Installation cost
= 560, 000 #/location and operating cost = 105,000 #/year per location. Depreciation
factor (α) of 10% is applied to installation and purchase cost of capacitor banks.
The total power loss and annual cost of operation of the system for the base case are 94.8842kW
and #17,454,897.40 respectively. The number of stages (number of iterations), Kmax = 100 and
the number of nest, n=25. The possible capacitor banks in discrete sizes are assumed to be from
150 kVAr up to 1000 kVAr in multiples of 50.
After running the algorithm, the returned optimal solution was given as X= [18 13] to
minimize the total annual cost of the radial distribution network. The physical meaning of this
is that 750 kVAr of capacitor bank placed at bus 18 will result in
the best reduction in the total annual cost of
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Fig. 2: Imalefalafia 32-bus
The distribution network. The total power loss and annual cost of operation of the system for
the optimum case are 84.20 kW and #16, 322, 506.77 respectively. The net cost saving per year
is #1,132,390.63. Table 1 summarises the results of the distribution network before and after
compensation. The voltage profile of the of the system before and after compensation are is
shown in Fig. 3; the voltage shows improvement after compensation. Figure 4 illustrates the
voltage stability index for the Imalefalafia 32-bus before and after compensation. It clearly
shows that VSI values in the radial distribution system were poor before compensation. After
compensation, the VSI values are improved. It is crystal clear from Table 1 that there is
significant reduction of cost and total power loss compared tobase case. Fig. 5 shows the
convergence characteristics of the CSA algorithm for the test system.
IMAFELAFIA
15MVA 33/
11KV S/S
ADEOYE
HOSP.
500KVA S/S FINA
BROWN
500KVA S/S OSANSAMI
1 500KVA S/
S
OLANIPEK
UN 500KVA
S/S OSANSAMI
11 500KVA
S/S EXTENSION
PUBLICATI
ON 100KVA
S/S
BATEYE
500KVA S/S
IBADAN
CENTRAL
300KVA S/S
WATER
COOPERATIO
N 200KVA S/S
MTN
100KVA S/S
ODUTOLA
500KVA S/S
IMALEFALAFIA
100KVA S/S
FAKEYE 11
100KVA S/S AYEGBUSI
500KVA S/S OGUNDEJI
500KVA S/S
TRIBUNE 1
300KVA S/S TRIBUNE 11
500KVA S/S
FALEWA 1
100KVA S/S
OLUSEYI 1
100KVA S/S
FALEWA 1
100KVA S/S OLUSEYI 1
100KVA S/S
AKURO 1
200KVA S/S AKUNRO 11
500KVA S/S
2.3km 0.2km 1.4km 0.1km 0.2km 0.1km MTN
100KVA S/S
T1 T2
T3
T4 T5 T6 T7
0.4km 0.1km 0.1km
0.3km
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Table 1: Summary of Results before and after Compensation for Imalefalafia 32-Bus
Base Case
After
Compensation
Optimal
Bus
----
18
Capacitor
Size (kVA)
----
750
Power Loss
(kW)
94.88
84.20
Total
Annual
Cost (#)
17,454,897.40
16,322,506.77
Annual Net
Saving
----
1,132,390.63
Min.
Voltage
0.9502
0.9654
Minimum
VSI
0.8152
0.8687
Loss
Reduction
(kW)
----
10.68
% Loss
Reduction
----
11.26
% Net
Annual
Saving
----
6.49
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Fig. 3: Voltage profile for Imalefalafia 32-bus
Fig. 4: Voltage stability index for Imalefalafia 32-bus
Fig. 5: Convergence characteristics for Imalefalafia 32 bus
CONCLUSION
A cuckoo search algorithm (CSA) for capacitor placement and sizing problem in the Nigerian
radial distribution system to reduce total annual compensation cost with imposed voltage
constrained is proposed in this paper. The CSA provides both optimal location and sizing of
1st International Conference on Engineering and Environmental Sciences, Osun State University. November 5-7, 2019.
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capacitor as the outputs. It is demonstrated that the proposed method is capable of saving a
significant amount of total annual compensation cost, reducing total power loss, attain
improvement in voltage stability, and voltage profile by comparing the results before and after
compensation in a practical Nigerian distribution network.
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