International Journal of Advances in Electrical and Electronics Engineering
Available online at www.ijaeee.com & www.sestindia.org/volume-ijaeee/
211
ISSN: 2319-1112
Simultaneous Network Reconfiguration and Capacitor
Placement for Loss Reduction of Distribution Systems
by Ant Colony Optimization Algorithm
Divya M, Bindu R
Fr.CRIT, Vashi, Navi Mumbai
mdivya2@yahoo.com, rbinducrit@gmail.com
ABSTRACT: The objective of this study is to solve the simultaneous network reconfiguration and capacitor placement for
loss reduction in distribution systems. The work employs a meta-heuristic method called Ant Colony Optimization
(ACO). The ACO algorithm tries to emulate the behaviour of real ants by which they are able to identify the shortest path
between a food source and their nest. The proposed approach is demonstrated using a benchmark system from the
literature. Computational results obtained show that the loss reduction obtained using simultaneous application of
capacitor placement and network reconfiguration is higher compared to a case when they are applied separately. It is also
seen that along with loss reduction, voltage profile of the system is improved.
Keywords: Distribution system, network reconfiguration, capacitor placement, Ant Colony Optimization
I. INTRODUCTION
A distribution system is the most visible part of a supply chain. About 30 to 40% of total investments in the
electrical sector go to distribution systems. Ideally, losses in a power system should be around 3 to 6% of the total
power generated. However, in most of the developing countries, the percentage of active power losses is around
20%. There is a lot of scope for improvement in the field of power distribution which can serve as an effective step
towards meeting the ever increasing demand for power without increasing the installed capacity significantly.
Generally, distribution systems are designed to operate with maximum efficiency during peak load demand. The
efficiency of the system can be improved by reconfiguring it under part-load conditions. Hence, it is very important
to develop effective methods for network reconfiguration. Under normal operating conditions, the distribution
feeders can be reconfigured by switching operations for increased network reliability and reduced line losses. The
new configuration should be radial and should also meet the load requirements. Feeder reconfiguration is the
process by which the topology of a distribution system is changed by altering the open/closed status of the
sectionalizing switches and tie switches [1, 2].
Capacitors are commonly employed to provide reactive power compensation in distribution systems. They are used
to reduce power losses and to maintain voltage profiles within acceptable limits. The benefits of compensation thus
achieved depend greatly on how the capacitors are placed i.e. the location of capacitors and their size [3, 4]. Many
works are reported which handles capacitor placement and feeder reconfiguration separately [1- 5]. Many of the
later studies indicated that, for the same objective of minimizing real power losses of the system, combining
reconfiguration and optimal capacitor placement results in better solution. If this is done simultaneously it results in
optimal solution [6, 7]. J. J. Grainger and S. H. Lee [8] developed a procedure for optimizing the net monetary
saving associated with the reduction of loss by placing fixed and switched capacitors. The work was extended to
incorporate the effect of voltage variation along the feeder. Optimal sizes, locations, and switching times were
determined for a given number of fixed and switched capacitors, assuming capacitors are switched simultaneously
[8, 9]. M. E. Baran and F. F. Wu [10] formulated a non-linear programming problem to determine the optimal size
of capacitors placed on the nodes of a radial distribution system so that the real power losses will be minimized for a
given load profile.
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IJAEEE ,Volume1,Number 2
Divya M and Bindu R
Mathematically, distribution system reconfiguration problem is a complex, combinatorial, constrained optimization
problem. The complexity of the problem is due to the fact that, distribution network topology has to be radial and
power flow constraints are non-linear in nature. The radiality constraint and the discrete nature of the switch status
prevent the use of classical optimization techniques to solve the reconfiguration problem. Therefore, most of the
algorithms in literature are based on heuristic search techniques. A. Merlin and H. Back [5] proposed a branch-andbound type heuristic method to determine the network configuration for minimum line losses. S. Civanlar et al. [1]
suggested a branch-exchange type algorithm, where a simple formula has been derived to determine how a branch
exchange affects the losses. In [11, 12] the authors used genetic algorithm to find the minimum loss configuration.
Y. J. Jeon and J. C. Kim [13] proposed a loss minimum reconfiguration methodology using simulated annealing. In
[14, 15] the authors proposed solution procedure using particle swarm methods.
In this paper, a method employing ant colony optimization is used to solve the simultaneous capacitor placement
and network reconfiguration problem. The method has provisions built-in to prevent the method from converging to
a local optimum. In [16] the authors concluded that ant colony search algorithm is better than simulated annealing
and genetic algorithm methods in terms of the average solution obtained as well as the average computational time.
The paper is organized as follows: section 2 gives the problem formulation; ACO algorithm is discussed in section
3; the computational procedures are explained in section 4; an application example is demonstrated in section 5 and
section 6 gives the concluding remarks.
II. PROBLEM DESCRIPTION
This study presents the simultaneous capacitor placement and network reconfiguration of distribution systems. The
objective is to minimize the system power loss, subject to operating constraints under a certain load pattern. The
mathematical model of the problem can be expressed as follows:
(1)
Min F = min (PT , Loss + λV × S CV )
Subject to the constraint
(2)
Vmin ≤ Vi ≤ Vmax
where, PT , Loss is the total real power loss of the system. λV is the penalty constant, S CV is the squared sum of the
violated voltage constraints, Vi is voltage magnitude of bus i and Vmin ,Vmax are the minimum and maximum bus
voltage limits respectively.
Penalty constants are given by:
0, if voltage constraint is not violated
(3)
λV = 
1,
if
voltage
constraint
is
violated

Also the operating structure of the network should be radial in nature and there should be no nodes without a power
supply path present in the network.
A set of simplified feeder-line flow formulations is employed to avoid complex power flow computation. In figure1,
Pi and Qi are the real and reactive line powers flowing out of bus i respectively and PLi and QLi are the real and
reactive load powers at the bus. The resistance and reactance of the line sections between buses i and (i + 1) are
denoted by ri and xi respectively.
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Simultaneous Network Reconfiguration and Capacitor Placement for Loss Reduction of Distribution Systems
by Ant Colony Optimization Algorithm
Fig 1: One line diagram of radial network [2]
z i = ri + jxi
(4)
S Li = PLi + jQLi
(5)
Power flow in a radial distribution network is described by set of recursive equations called Distflow branch
equations. The Distflow forward update equations can be expressed as follows [2]:
P2 + Q2
(6)
Pi +1 = Pi − ri i 2 i − PLi +1
Vi
Qi +1 = Qi − xi
Pi 2 + Qi2
+ Q Li +1
Vi 2
Vi +21 = Vi 2 − 2(ri Pi + xi Qi ) + (ri2 + xi2 )
PLOSSi,i +1 = ri
(7)
Pi 2 + Qi2
Vi 2
Pi 2 + Qi2
Vi 2
(8)
(9)
n −1
PT , LOSS = ∑ PLOSSi ,i +1
(10)
i =0
In the above equations, Pi represents the real power, Qi is reactive power and Vi is the voltage magnitude at the
receiving end of a branch. PLoss ( i , i +1) is the power loss of the line section connecting buses i and (i + 1 ) . PT , Loss is
the total system power loss. These set of simplified power flow equations are widely used in reconfiguration
problems.
III. ANT COLONY OPTIMIZATION
Ant Colony Optimization (ACO) is one of the population based meta-heuristic optimization methods widely used
for finding approximate solutions to discrete optimization problems. The method was first applied to the Travelling
Salesman Problem (TSP) by M. Dorigo and L. M. Gambardella [17]. The method was successfully extended to
other optimization problems like vehicle routing problems [18, 19] and quadratic assignment problems [20]. The
method was derived from the behaviour of natural ants whereby, they identify the shortest possible path between
their nest and the food source without using any visual information. Ants follow the pheromone trail built by the
previous ant and reinforce it. The shortest path from the nest to food will have a stronger pheromone concentration
than the other paths. This is due to the fact that ants traversing the shortest path return to the nest than those
traversing the other paths.
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Divya M and Bindu R
ACO has some attractive features such as parallel search, shortest path finding, adaptability to changes in search
space, long term memory and information sharing. In ACO, a number of artificial ants build solutions for an
optimization problem and exchange information on their quality through a communication scheme that is similar to
the one adopted by real ants. E. Carpaneto and G. Chicco [21] introduced ant colony method to solve the network
reconfiguration problem.
A general algorithm for solving an optimization problem using ACO essentially consists of the following steps [22]:
1) Initialization step during which the problem variables are defined and initial ant population is generated and
distributed.
2) Evaluations of the objective function for all the ants. For the feeder reconfiguration problem this will
involve the estimation of the power loss for the chosen tie switch status.
3) Calculation of the probabilities for all available choices based on values obtained in step-2.
reconfiguration problem, this will involve choosing a switch based on the power loss calculations.
For a
4) Updating of the pheromone intensity for the step considering the evaporation factor.
5) Ants proceed to the next nodes.
6) The steps are repeated until the chosen criterion for stopping the calculation is achieved.
IV. COMPUTATIONAL PROCEDURES
Mathematical model of ACO can be explained as follows:
At first, each ant placed on a starting state, will build a full path from the beginning to the end state through
repetitive application of state transition rule which is given by:
 [τ (i, j )]α [η (i, j )]β

, if j ∈ J k (i )

α
β
(11)
pk (i, j ) =  ∑[τ (i, m)] [η (i, m)]

m∈J k (i )


otherwise 
 0,
In the above equation, τ (i, j ) is the pheromone content of the path from the element i of previous stage to element
j of the present stage η (i, j ) is the inverse of power loss of the corresponding path and J k (i ) is the set of elements
that remain to be visited in the present stage by ant k positioned at device i . The denominator of the expression is
the sum of probabilities of all the state options that are available for the k th ant for the present stage. The above
equation is called the state-transition rule. This process is continued until the ant reaches the last stage.
Once an ant completes its tour, the pheromone content of the complete path travelled by it is updated using the
following equations:
∆τ (i, j ) = ∆τ (i, j ) + q
Stage− n
∑ p (k )
Stage−1
Loss
τ (i, j ) = (1 − ρ )τ (i, j ) + ∆τ (i, j )
(12)
(13)
Where, ∆τ (i, j ) is the incremental change in pheromone for a path from device i of previous stage to device j of
the next stage, q is a heuristic parameter, ∑ pLoss (k ) is the power loss of the completed path from stage-1 to stage-
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Simultaneous Network Reconfiguration and Capacitor Placement for Loss Reduction of Distribution Systems
by Ant Colony Optimization Algorithm
n . ρ is the pheromone trail decay co-efficient, which is defined to diversify the search by shuffling the search
process.
Figure 2 shows the full search space for a simultaneous capacitor placement and feeder reconfiguration problem.
The left side of the figure is the search space of capacitor placement and the other side is the search space of ant
reconfiguration. Loop-1 of the ant reconfiguration search space contains k tie-switches; loop-2 contains m tieswitches and so on. For the system, j buses in loop-1 have capacitor banks connected to them. Each of these buses
may have different capacitor sizes. Since practical sizes available for switched capacitor banks are 300, 600, 900,
1200, 1500 and 1800 kVAr, they are included in the study. It may be noted that, this problem utilizes two categories
of ants 1) ants that choose the optimal tie at every stage (Type-1 ant) and 2) ants that choose the optimal set of
capacitors for every selected tie-switch of every stage (Type-2 ant).
Fig. 2: Full search space of capacitor placement and feeder reconfiguration
In the above figure, red lines indicate solution for optimal capacitor placement for loop-1 and red tie-switches
indicate the optimal solution for feeder reconfiguration.
For feeder reconfiguration part of the problem, all possible tie-switches for a given stage are represented by the
states in the search space. It may be noted that, the number of stages will be equal to the number of loops. For the
capacitor placement part, all the capacitor values for the capacitor bank connected to a given bus are represented by
the states in the search space.
Figure 3 shows the flow chart for the code developed for reconfiguration part of the simultaneous capacitor
placement and feeder reconfiguration. Movement of reconfiguration ants (Type-1) is from one loop to the next. In a
given loop, each Type-1 ant selects only one tie-switch. From the selected tie-switch of one stage, it moves to the
next stage’s selected tie-switch. Capacitor ants (Type-2) move within one loop. For a given loop, they select one
capacitor each for all nodes having capacitor banks. Opening of tie-switch in the last stage results in a complete
radial system. Once every reconfiguration has completed all stages, the solution provided by Type-1 ant with the
minimum real power loss is chosen as the optimal solution, both for tie-switches as well as optimal capacitor
placement.
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IJAEEE ,Volume1,Number 2
Divya M and Bindu R
Fig. 3: Flow chart for simultaneous reconfiguration and optimal capacitor placement
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Simultaneous Network Reconfiguration and Capacitor Placement for Loss Reduction of Distribution Systems
by Ant Colony Optimization Algorithm
V. APPLICATION EXAMPLE
To study simultaneous capacitor placement and network reconfiguration in distribution systems 14 bus, 3 feeder
system from the literature was used. Details of the data of the system can be found in [1]. The system is shown in
figure 4.
Fig 4: Civanlar 3-feeder system [1]
The system consists of three radial feeders, connected at the root node, thirteen sectionalizing switches and three tie
switches. The system load is assumed to be constant and the base values are 100 MVA and 23 kV . The original
system has 15, 21 and 26 as the tie switches.
To solve the simultaneous capacitor placement and network reconfiguration problem using ACO algorithm the
parameters were chosen as number of Type-1 ants to be 3, number of Type-2 ants to be 5, trail intensity factor,
α = 1 , visibility factor, β = 8 , pheromone trail decay co-efficient, ρ = 0.5 and heuristic parameter, q = 10 .
Figure 5 gives the voltages at all buses before and after the simultaneous reconfiguration and capacitor placement. It
can be seen from the figure that the voltage profile of the system has improved with simultaneous network
reconfiguration and capacitor placement. It can be seen from the figure that the maximum and minimum voltages of
the original system were 1.00 p.u (feeder nodes 1, 2 and 3) and 0.9053 p.u (node 11) respectively and the maximum
and minimum voltages of the new system are 1.00 p.u (feeder nodes 1, 2 and 3) and 0.9320 p.u (node12)
respectively.
The results obtained for simultaneous capacitor placement and network reconfiguration is compared with four
different cases of the system: original system, with capacitor placement only, with reconfiguration only and first
capacitor placement and then network reconfiguration. The comparisons of the results obtained for all the cases are
given in table 1. It can be observed from the table that lowest power loss of the system is for simultaneous capacitor
placement and network reconfiguration.
Bus voltages corresponding to all the cases are shown in figure 6. From the figure it can be noted that, voltage
profile of the system is considerably improved after carrying out simultaneous capacitor placement and network
reconfiguration.
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Divya M and Bindu R
1.02
Original
After simultaneous capacitor placement and reconfiguration
1
Voltage in per unit
0.98
0.96
0.94
0.92
0.9
2
4
6
8
Nodes
10
12
14
16
Fig. 5: Bus voltages before and after simultaneous reconfiguration and capacitor placement
Parameters
Tie-switches
Table 1: Comparison of results for different cases of Civanlar system
Original
Capacitor
Reconfiguration First capacitor
configuration
placement
only
placement then
only
reconfiguration
Simultaneous
capacitor
placement and
reconfiguration
15, 21, 26
15, 21, 26
19, 17, 26
19, 17, 26
19, 17, 26
Maximum voltage
(p.u)
1
1
1
1
1
Minimum voltage
(p.u)
0.9053
0.9231
0.9143
0.9320
0.9320
(4,1500)
(5,300)
(11,1200)
(13,300)
(16,300)
(4,1500)
(5,300)
(11,300)
(13,900)
(16,300)
Capacitors added
(Bus no., kVAr)
Power loss (kW)
(4,1500)
(5,300)
(11,1200)
(13,300)
(16,300)
612.3092
602.6223
438.8224
437.2928
432.7058
1.58
28.33
28.58
29.33
Loss reduction
(%)
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Simultaneous Network Reconfiguration and Capacitor Placement for Loss Reduction of Distribution Systems
by Ant Colony Optimization Algorithm
1
0.99
0.98
Voltage in per unit
0.97
0.96
0.95
0.94
0.93
Original
Capacitor
Reconfiguration
Separate
Simultaneous
0.92
0.91
0.9
2
4
6
8
Nodes
10
12
14
16
Fig. 6: Voltage profile for all the cases considered for Civanlar system
VI. CONCLUSION
In this paper simultaneous capacitor placement and network reconfiguration for loss reduction in distribution
systems has been presented. This was done using Ant Colony Optimization algorithm. ACO is a novel metaheuristic approach for the solution of combinatorial optimization problems. This method was inspired by
observation of the behaviors of ant colonies. From the application example it is observed that the simultaneous
capacitor placement and network reconfiguration reduces the power loss of the system. In addition, the voltage
profile of the system has been improved. Computational results show that simultaneously taking into account both
feeder reconfiguration and capacitor placement is more effective than considering only one technique.
VI. REFERENCES
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ISSN:2319-1112 /V1N2:211-220 ©IJAEEE
IJAEEE ,Volume1,Number 2
Divya M and Bindu R
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