A NEW DISTRIBUTION SYSTEM RECONFIGURATION

APPROACH USING PARTICLE SWARM OPTIMIZATION

AND NEURAL NETWORK

M. W. Siti, B. P. Numbi, J. Jordaan and D. Nicolae

Department of Electrical Engineering, Tshwane Univeristy of Technology, 0001, Pretoria, South Africa

Keywords: Network reconfiguration, Mixed-integer programming, Binary particle swarm optimization, Neural

network.

Abstract: This paper uses artificial intelligent algorithms for reconfiguration of the distribution network. The problem

is formulated as an optimization problem where the objective function to be minimized is the power losses,

and the constraints are nodal voltage magnitude limits, branch current limits, Kirchhoff’s current law

(KCL), Kirchhoff’s voltage law (KVL) and the network radiality condition. While the state (on-off) of the

tie switch is considered as control or independent variable, the nodal voltage magnitude, branch current are

considered as state or dependent variables. These state variables are continuous whilst the switch state is an

integer (binary) variable. The problem being a mixed-integer programming one because of the state of

switch (on=closed=1 or off=open=0), a Binary Particle Swarm Optimization (BPSO) and Neural Network

are used separately to solve this problem. The effectiveness of proposed method is demonstrated through an

example.

1 INTRODUCTION

The energy in the system is wasted in the form of

power losses at the distribution level. Recent

advances in distribution automation technology have

made it possible to reduce these losses by applying

loss minimization techniques on a real time basis.

At the HV and MV levels, the load is usually

three-phase and balanced, although large single or

dual phase loads can be connected. Each feeder in a

distribution system usually supplies a mix of

residential, commercial and sometimes industrial

consumers with varying needs depending on the

season of the year (Chen and Cherng, 2000); (Liu et

al., 1989). Because of load changes and the diversity

of loads being on or off, the three phase imbalances

may be substantial. Balancing is accomplished by

selecting the phase of the supply for each load so

that the total load is distributed as evenly as possible

between the phases for each section of the feeder.

The balancing procedure must consider all possible

combinations of phase loads connecting to three

phases. There are a number of benefits that make

efficient load phase balancing a worthwhile

objective. Balancing reduces feeder losses for the

phases as the square of the current magnitude.

Loading on a feeder section is synonymous with the

most heavily loaded phase so that, in the case of

significant imbalance, feeder capacity is used

inefficiently. Balancing between phases tends to

equalize the phase loading by reducing the largest

phase peak load while increasing the load on the

other phases. This equates to releasing feeder

capacity that can be used for future load increases

without reinforcing feeder conductors. Released

feeder capacity provides more reserve loading

capacity for emergency loading conditions.

Balancing not only reduces feeder losses, but

also improves voltage on a feeder by equalizing the

voltage drops in each phase along the feeder. It is

realistic to assume that the benefits in improved use

of feeder capacity and voltage quality are significant

in terms of the value of reduction in loss except

when loading is already high (Ukil et al., 2006).

In past, many studies based on traditional

heuristic algorithms have been carried out on

network and feeder (Zhu, 2009); (Alexandre et al.,

2009). The problems were formulated and solved to

control the switching of sectionalize and tie switches

so as to achieve a better efficiency. However, they

218

W. Siti M., P. Numbi B. and Nicolae D..

A NEW DISTRIBUTION SYSTEM RECONFIGURATION APPROACH USING PARTICLE SWARM OPTIMIZATION AND NEURAL NETWORK.

DOI: 10.5220/0003681902180223

In Proceedings of the International Conference on Neural Computation Theory and Applications (NCTA-2011), pages 218-223

ISBN: 978-989-8425-84-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

did not guarantee the optimal solution although they

provide high quality suboptimal solution.

Recently new methods based artificial intelligent

such as genetic algorithm (GA) have been used in

the distribution network reconfiguration (Zhu,

2009). However, it has been shown in general that

PSO algorithm can provide better optimal solution

than GA (Zhu, 2009); (Yu et al., 2009) and it is also

requires lower computational time than GA (Zhu,

2009).

From the above background, the authors in this

paper have used a Binary particle swarm

optimization (BPSO) algorithm for the distribution

network reconfiguration loss minimization. Neural

network algorithm is used also in order to validate

the results obtained by BPSO algorithm.

2 PROBLEM DESCRIPTION AND

FORMULATION

2.1 Network Reconfiguration

The distribution system is the final stage in the

transfer of power to individual customers. Typically,

it commences from the sub transmission station

transformers, and normally will consist of two levels

primary distribution or medium voltage level

(Alexandre et al., 2009); (Siti et al., 2007).

There are two types of switch in primary

distribution systems: normally closed switch

connects line sections, and normally open switch on

the tie-lines which connects two primary feeders, or

two substation or loop-type laterals. Network

reconfiguration (or feeder reconfiguration) is the

process of altering the topological structures of the

distribution feeders by changing the open /closed

status of the sectionalizing and tie switches

(Alexandre et al., 2009), (Siti et al., 2007).

In general, distribution loads shows different

characteristics according to their corresponding

distribution lines and line sections. Therefore, load

levels for each time period can be regarded as non

identical. In the case of a distribution system with

some overloaded to less loaded feeders. The

maximum current which the feeder conductor can

take may be considered as the reference.

Nevertheless, the transfer of load must be such that

certain predefined objective is satisfied. In this case,

the objective is to ensure the network has minimum

real power loss.

The solution objective for a feeder is to obtain a

set of rearrangement of the connected loads at each

node (or consumer point) such that the objective

function is minimized. This is a non-linear problem

that will involve a number of trial and errors. It is

hereby proposed to solve this problem, where

iteratively, as changes are made, a method is used to

sense the relative loading of the phases, and another

method is used to edge towards the minimized

objective.

2.2 Mathematical Model for Optimal

Network Reconfiguration

This mathematical model has been discussed in

(Zhu, 2009); (Alexandre et al., 2009), (Siti et al.,

2007).The objective function to be minimized is the

total active power losses and is expressed in terms of

branch current as given below:

Min





bbbL

IRkP

NBb 

(1)

where

and

are respectively, the

total active power losses, the tie switch state of the

branch

(



if branch

is closed and



branch

is open), resistance and current magnitude

of the branch

, and

is the total number of

branches.

The operating constraints of the network are

given as follows:

2.2.1 Inequality Constraints

These constraints are nodal voltage and branch

current limits.

0.95 . . 1.05 . .

uV pu££

(2)

max

bbb

IIk 

(3)

where

is the voltage magnitude at node

max

(1.pu. in this paper) is the maximum branch current.

2.2.2 Equality Constraints

The fists equality constraint is the Kirchhoff’s

current law (KCL), given as follows:

()

hIb= iNÎ

(4)

The second equality constraint to be satisfied is the

Kirchhoff’s voltage law (KVL), given as follows:

()

hVb=

iNÎ

(5)

A NEW DISTRIBUTION SYSTEM RECONFIGURATION APPROACH USING PARTICLE SWARM

OPTIMIZATION AND NEURAL NETWORK

219

Another equality constraint is the one that ensure the

radiality condition of the network. This means that

the number of branches in the network must be

smaller than the number of nodes by one unit (

1 NNBk

) (Zhu, 2009). This can be expressed

by the following equation:







(6)

Any text or material outside the aforementioned

margins will not be printed.

2.3 Feeder Test System

In this case the suggestion is that the 66 kV be fed at

both ends instead of at one end only, since the total

voltage drop can be considerably reduced without

increasing the cross section of the conductor, and

also taking into account that the ends of distribution

are supplied with equal voltage. The system

distribution can be fed at both ends with the equal

voltage. Let S represent the sectionalizing switch

and T represent the tie switch as shown in Figure 1.

Figure 1: Network representation.

3 PROPOSED METHODS

3.1 Classical PSO

Particle swarm optimization is an intelligent

algorithm developed by Kennedy and Eberhart in

1995 as an alternative to genetic algorithm (GA)

(Zhu, 2009). The PSO algorithm motivation was the

social behaviour such as bird flocking and fish

schooling. This algorithm was used to solve many

nonlinear hard optimization problems (Zaraki and

Othman, 2009). The main advantage of the PSO

over traditional optimization algorithm is the fact it

does not need any gradient information about the

objective function when search for the global

optimal solution (Zhu, 2009); (Zaraki and Othman,

2009). Another advantage is the fact that it less

dependent on the initial starting point in the search

space (Numbi et al., 2011). Over other intelligent

algorithms such as GA, PSO can be easier to

program, to modify, inexpensive in terms of memory

and even computation time, etc. (Zhu, 2009);

(Mantawy and Al-Ghamdi, 2003). The general PSO

algorithm for real-valued numbers is explained as

follows:

From an initial position, a swarm of particles

starts flying in the search space exploring optimal

points. Each particle position represents a potential

solution. Therefore, the performance of each particle

position is evaluated by the fitness function which is

the objective function in this work. Our problem

having minimization purpose, the best particle is the

one with lower fitness value. During the flight

(iterations), the best experiences (positions) for each

particle is stored in its memory and called personal

best (Pbest). The lowest value of all the Pbests,

determines the global best (Gbest) of the swarm.

The velocity and the position of each particle are

updated using respectively, the following equations:

()

t t pbest t

ii ii

Gbest t

VwVCrX X

Cr X X

=+ -+

(7)

11 



VXX

(8)

with

: The Inertia weight (0.729 for clerc’s constriction

method) (Eberhart and Yuhui, 2001)

, C

: Acceleration coefficients (1.49445 for clerc’s

constriction method) (Eberhart and Yuhui, 2001)

, r

: Two separately generated uniformly

distributed random numbers in the range [0, 1]

added in the model to introduce stochastic nature.

3.1.1 Proposed Fitness of the Binary Particle

Swarm Optimization (BPSO)

With the purpose of dealing with constraints, all the

constraints given by (2)-(6) are penalized in the

main objective function given by (1). Exterior

penalty terms are used here. Since our problem has

binary control variables which are the states of tie

switch (on=1 or off=0), these tie switch states are

treated first as continuous number (real-valued

number) between 0 and 1. Secondly, the conversion

of continuous number to binary number is done as

follows:

-if the value of the particle position (tie switch state)

is less than 0.5 then this is set to zero,

-if the value of the particle position is greater than

0.5 then this set to one,

NCTA 2011 - International Conference on Neural Computation Theory and Applications

220

-otherwise, the PSO is reinitialized.

Therefore, the fitness of each particle in the swarm

is given as a penalty functions as expressed below:

()

{}

()

{}

()

{}

2 max

min max

1 2

1 1

max 0,

max 0, max 0,

ibbb bb

NB N

bb ii

b i

FX kRI k k

kk VV

= =

=+ - +

-+ - +

åå

()

{}

()

{}

min max

max 0, max 0,

NNB

ii bbb

VV kIImm

-+ - +

åå

(){} (){}

hIk hVkmm

åå

(9)

with

....



the penalty factors or coefficients for each

constraint violations. In order to reduce the number

of these penalty factors, all of them have been set to

a value of 10000.

The flowchart of BPSO is shown in figure 2

given below:

Figure 2: Flowchart of PSO algorithm.

3.2 Neural Networks

In the proposed strategy in this paper, the neural

network must control the switch-closing sequence of

each branch to achieve the minimum power loss

which will lead to the distribution network

reconfiguration. The inputs to the neural network are

the unbalanced branch currents while the outputs are

the switch closing sequences for each node.

The input layer of the network contains N input

neurons, N being the number of unbalanced branch

currents to be controlled. The following column

vector has been assumed as the input:





bNbSW

IIC .................



(10)

The output of the network is in the range {0,1} for

each switch, i.e., indicating which switch must be

open or close to reduce the power loss in the

network.

3.2.1 Neural Network Structure

For this application, we used the radial basis

network. Experiments with the back propagation and

the radial basis networks indicated faster training

and better convergence for the latter. Radial basis

networks may require more neurons than the

standard feed-forward back propagation networks,

but often they can be designed in a fraction of the

time needed to train the standard feed-forward

networks. They work best when many training

vectors are available. The Matlab

neural network

toolbox (Math Works; release 13) has been used for

the implementation. We experimented with different

kinds of radial basis networks, but a generalized

regression neural network (GRNN) produced the

best result (Ukil et al., 2006). Such a network is

often used for function approximation. It consists of

a radial basis layer and a special linear layer (Ukil et

al., 2006).

3.2.2 Neural Network Training

We have used the neural network-based operation

for the test data in the following structure: real and

simulated data for network presented in figure 1.

The real data set consisted of unbalanced network.

The test data set contained average load current

values per load in a specific network of the country

for the different times of each day in a month. We

selected a specific network as our test data for each

specific time, and we tested our result on 500 sets of

data. We consider the loads to be equally distributed

per phase, that is, we assume that the load flow

distribution in a loop is an optimal flow; the

corresponding network power losses will be

minimal. Thus the basic idea of the optimal flow



A NEW DISTRIBUTION SYSTEM RECONFIGURATION APPROACH USING PARTICLE SWARM

OPTIMIZATION AND NEURAL NETWORK

221

pattern is to open the switch of the branch that has

minimal current value in loop, with the optimal flow

pattern were to compute load flow of initial radial

network, it will follow by the closing of all normal

switches to produce loop networks, this will

continue by computing the equivalent injection

current at all nodes in loops through injecting

current method, and the replacement of the branch

impedance by corresponding branch resistance in the

loop and then compute the optimal flow, the network

will have a new reconfiguration by opening a switch

branch that has a minimal current value in loop. And

can again recomputed the load flow for the remained

network, this will end by opening the next branch

switch, and repeat the previous step discussed above,

until we have the radial network.

4 RESULTS AND DISCUSSION

The following case illustrates the loss reduction

through network reconfiguration of the tested system

of a 6 bus radial distribution. To evaluate the

proposed techniques, it has been applied to 6 bus

radial distribution system loss reduction. The results

obtained from the combination PSO, and as been

validated by Neural Network with the control of the

tie switch, it shows that it succeed in finding the

global solution with a high probability in the system

as represented in table 1

Table 1: Results of 6 bus radial distribution network

reconfiguration.

Description Initial State PSO

Neural

Network

Tie Switch open Switch 1-2 Switch 3-2

Switch 3-5

Switch 3-2

Switch 3-5

Total

Power

Loss

(MW)

Best ------------- 0.0096525 0.009652

Average ---------- 0.00117044 0.00117044

Worst 0.0095452 0.0035428 0.0035428

Average Power Loss

Reduction (%)

62.23 62.23

Minimum Voltage

Magnitude (p.u.)

0.894 0.978 0.978

5 CONCLUSIONS

Loss reduction is very important complement to

network and feeder reconfiguration. In this paper the

network and feeder reconfiguration problem was

formulated as loss minimization problem with the

view for its solution to control different switches

placed in the network. Two MATLAB based

solution methods have been proposed and

demonstrated. First is the PSO and the other is

neural network-base technique. The proposed

methods were successfully tested. From the practical

point of view these method can be very effective as

several model based approaches usually take very

long running time. The PSO has been found more

suitable and faster compared to neural network. But

both methods gives good results on loss reduction in

the network.

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A NEW DISTRIBUTION SYSTEM RECONFIGURATION APPROACH USING PARTICLE SWARM

OPTIMIZATION AND NEURAL NETWORK

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