Distribution Network Performance Enhancement Through Optimal

Sizing and Placement of D-STATCOM using Particle Swarm

Optimization Technique (case study-Woldya Distribution Network)

ESUBALEW FIKRU GETAHUN, ASEFA SISAY YIMER, WONDWOSSEN ASTATIKE HAILE

Electrical and Computer Engineering Department,

Kombolcha Institute of Technology, Wollo University

KOMBOLCHA, ETHIOPIA.

Corresponding Author

Abstract: This article presents the use of distribution static synchronous compensator (D-STATCOM)

to improve distribution network performance by maintaining voltage profile, stability and reducing

power losses. The study was conducted on a 7.2 MW Gonder ber feeder, which had an unacceptable

voltage profile and high active and reactive power losses. Two methods were applied to assign the

power control variables: bus-based voltage stability index analysis and particle swarm optimization

(PSO). The optimal allocation was tested in different system cases. The results showed that a single

installation of D-STATCOM improved system performance; with an improved voltage profile between

0.95 and 1.05p.u, increased voltage stability indices and reduced active and reactive power losses. Cost

analysis of the proposed compensation scheme indicated a payback period of 1.8 years.

Keywords: D-STATCOM, power loss, voltage profile, PSO, voltage stability index, MATLAB Software.

Received: April 21, 2024. Revised: October 11, 2024. Accepted: November 13, 2024. Published: December 10, 2024.

1 Introduction

Today, the main problem is to balance the energy demand

with the voltage magnitude while minimizing power

losses. Distribution systems must provide diverse

customers with varied demand patterns. Inductive loads

cause significant power losses in long radial networks,

operating close to voltage instability limits. This causes

network overload, increased power losses, reduced voltage

profile and associated problems. The energy generated

leads to high losses in transmission and distribution. Based

on several studies carried out around the world, the amount

of losses on the distribution side is estimated at 13% of the

total energy produced [1] . Proper compensation methods

are essential to maintain the voltage profile in distribution

systems. Two commonly used techniques are series

voltage regulators and shunt capacitors. Series regulators

step down voltage, generate reactive power, and have a

slow response. Shunt capacitors have limitations in terms

of continuously variable reactive power and natural

oscillatory behavior [2] .

2 Related works

Different researchers have proposed several ways to solve

the problem of voltage drop, power loss and voltage

instability in distribution systems. Some of them are

reviewed as follows: Khan, BaseemRedae, Kalay Gidey,

Esayas Mahela, PrakashTaha, Ibrahim

B.M.Hussien,Mohammed G uses the Improved Bacterial

Foraging Algorithm (IBFA) to optimize the sizing and

placement of DSTATCOM in the distribution subdivision,

minimizing the power losses and improving stability and

voltage profile.[3] .E. Ijmtst demonstrates the use of a

back-propagation control algorithm to perform a three-

stage delivery static compensator (DSTATCOM),

including load balancing and zero-voltage management of

reactive power compensation under nonlinear loads [4] .

IM Mehedi et al., Mehédi et al. propose a FACTS-based

method to minimize fault current in systems, improve the

performance of switchgear and protection equipment, and

enable higher power transmission via static synchronous

series compensators and power flow controllers unified [5]

. AA Abou El-Ela, RA El-Sehie my, AM Kinawy and MT

Mouwafi, This study proposes a two-step procedure for

identifying optimal locations and sizes of capacitors in

radial distribution systems. It uses loss sensitivity analysis

and an ant colony optimization algorithm, taking into

account energy losses and capacitor costs. The study also

considers fixed and practical switches and capacitor

combinations [6]. OE Olabode, IK Okakwu, AS Alayande

and TO Ajewole, the paper presents a two-step approach to

sizing shunt capacitors and identifying their Optimal

placement in radial distribution systems. It uses a multi-

objective function to minimize power losses and improve

the bus voltage profile, a weighted approach and the

Cuckoo search algorithm for load flow analysis [7] .

Search algorithm. G. Niazi and M. Lalwani This paper

discusses the research and development of particle swarm

optimization (PSO) algorithm for distributed generation

optimal placement (ODGP) problems, reviewing various

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models and methods [8] . Wondossen. A. and P.

Chandrasekar, this article deals with the study of design

and analysis of micro grids in a rural village using

HOMER Pro software. The hybrid system, consisting of

wind turbines, diesel and solar panels, aims to provide

reliable and cost-effective electrical energy [9] . Chitransh

Shrivastava, Manoj Gupta, Dr. Atul Koshti PG This paper

presents an approach based on a forward-backward

scanning method for load flow analysis in a radial

distribution system to improve voltage stability and

minimize losses on transmission lines, taking into account

takes into account the cost function for planning the entire

power system, and has been tested on the IEEE-33

standard. bus system tested on IEEE-33 bus system [10] .

Moufid, Ismail El Markhi, Hassane El Moussaoui, Hassan

Tijani and Lamhamdi This article discusses the use of a

synchronous static compensator (STATCOM) to improve

the voltage in the IEEE 14 bus power system network. The

study analyzes the system using standard test data and

STATCOM, by comparing the results with the original

power flow to determine the optimal STATCOM location

for improved voltage profiles [11] .Yuvaraj, T.Ravi, K.

Devabalaji, K. R, This study uses curve fitting technique to

optimize placement and sizing of DSTATCOM, thereby

helping distribution network operators select size based on

load changes on IEEE 33 and 69 bus radial distribution

systems. Literature on optimal allocation methods has

limitations, including single objective functions, long

simulation times, and theoretical assumptions. This

research aims to fill these gaps by focusing on optimal D-

STATCOM placement and sizing, multi-objective

optimization, fast convergence characteristics, economic

preferences and system constraints for PSO simulation [12]

.

3 Problem formulation

3.1 Minimize active power losses

Active power losses in the distribution system should be

minimized as much as possible for reliable power transfer.

The total line losses in the distribution system can be

calculated as follows:

2

1

*

NBr

ii

i

F R I





(1)

Where F 1 is the first term of the objective function

associated with the system losses, Ii is the current of line i,

R i is the resistance of the i th line and NBr is the number

of branches of the system [13] .

3.2 Minimize bus voltage deviations

It is important to keep the bus voltage within the limit and

the deviation from the rated voltage can be the second

objective function. The objective function to improve the

voltage profile is

 

2

1

Nbus

i

F V V







(2)

Where F 2 is the second term of the objective function, V i

is the bus voltage and V is the reference voltage which is 1

pu [14] .

3.3 Improved voltage stability

There are many indices used to check the safety level of

the electrical system. In this section, a new steady-state

voltage stability index is used to identify the node that has

the highest risk of voltage collapse. The voltage stability

index at each node is calculated using equation 3. The node

which has the low value of VSI is the weakest node and

the voltage collapse phenomenon will start from this node.

The VSI is calculated from the load flow for all buses in

the given system and the values are ranked in descending

order. Therefore, to avoid the possibilities of voltage

collapse, the VSI of the nodes must be maximized [15] .

3.4 Choosing weighting values

This research study focuses on effectively reducing power

losses in multi-objective functions to reduce total operating

costs. The weights are assumed to be positive and limited

to 0.5-0.8, 0.1-0.4 and 0.1-0.4, respectively. The real

power loss reduction index is given more emphasis, while

all three indices are taken into account. The condition W 1

+ W 2 + W 3 =1 must be satisfied in each case [16] .

3.5 System constraints

From the results presented in Table 1 above, the weight

combination chosen is the one that gives the best minimum

physical condition. Thus, the weights chosen. W 1 = 0.8

for power loss reduction, W 2 = 0.1 for voltage profile

improvement and W 3 = 0.1 for voltage stability index and

the MOF was given by eqn.(3) [13] :

12

3

1

0.8* 0.1* 0.1*F F F F



(3)

3.5.1 Voltage deviation limit

System voltage in all buses must be within an acceptable

range

min max

m m m

V V V

(4)

The system voltage is limited to 0.95pu ≤ Vm ≤1.05 Pu

[13] .

3.5.2 Reactive power compensation

The reactive power injected by D-STATCOM to the

system is limited by a lower and upper limit as shown

below.

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min max

mm

Q Qm Q

(5)

The reactive power injected by D -STATCOM is limited

by 100KVar ≤Qm≤1250KVAr [17] .

3.5.3 Thermal limit

The energy flow crossing the lines is limited by the

thermal capacity of the lines:

min maxij ij

SS

(6)

The power flow through the lines is limited with S ijmax

=100MVA [17] .

4 Load flow analysis of radial

distribution systems

For a given set of load conditions, load flow analysis of

power networks is important to acquire data on voltage,

active and reactive power of the system. It is a beneficial

analysis, investigation of problems and optimal utilization

of the distribution system. Newton Raphson, Gauss Seidel

and decoupled load flow analysis are the most

conventional and widely applicable methods in distribution

and transportation systems. Nowadays, due to the radial

nature of power lines, unbalanced loading, high R/X ratio,

large number of buses, wide impedance range, problems

convergence and related problems, conventional methods

of load flow analysis become unsuitable for distribution

systems. Following this forward/backward scanning charge

flow analysis using Kirchhoff's laws, it becomes more

suitable for distribution systems and was used in this work

[18] .

4.1 Forward/Backward Sweep Load flow

method

This method uses forward and backward scanning

processes to calculate node voltages and branch current in

radial network topologies. It forms two derivative matrices

called bus injection matrix to branch current (BIBC) and

branch current to bus voltage matrix (BCBV) using

Kirchhoff's current law and Kirchhoff's voltage law. The

BIBC matrix can be expressed as a complex power

absorbed by the load [18] .

Li Li Li

S P jQ

(7)

Or

1....iN

Step 1: The backward sweeping branch currents are

grouped from the charges to the origin for each iteration k.

To find the branch current, the current injected on each bus

and the bus injection to the branch current (BIBC) are

taken into account.

   

k r k i k ii

i i i i i k

i

P jQ

I I V jI V V





   



(8)

Where

k

i

V

and

r

i

I

are respectively the bus voltage and the

equivalent

th

i

bus current injection at

th

k

the iteration.

r

i

I

And

i

I

are respectively the real and imaginary parts of the

equivalent current injection of bus i at iteration

th

k

. Figure

1 below is an example of radial distribution system.

Fig. 1: Example of radial distribution system

From equation 2, the injected currents are obtained. By

applying Kirchhoff's current law (KCL) to the distribution

network, the current branches are calculated. A simple

distribution system, shown in Figure 1, is used as an

example test system. Bypass currents can be formulated

based on equivalent current injections. The bypass currents

B1, B 2 , B 3 , B 4 and B 5 can be expressed as follows:

1 23456

2 3456

3 4 5

45

56

B I I I I I

B I I I I

B I I

BI

    

   





 

12

12 23

12 23 34

12 23 34 45

12 23 34 45 56

0 0 0 0

000

00

0

Z

ZZ

BCBV Z Z Z

Z Z Z Z

Z Z Z Z Z











The general form of the bus voltage at (k+1 ) th iteration

can be expressed as

    

1

k

V V BCBV B



(9)

In general form, with i and k denoting the node and

iteration number respectively

1, , 1

k k k

i i i i i

I I I





(10)

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1

1 1, 1',

*

k k k

i i i i I I

V V Z I 

  



(11)

4.2 Procedure to form the BIBC and BCBV

matrix

As seen above, the BIBC and BCBV matrices are

developed based on the topological structure of the

distribution systems. The BIBC matrix represents the

relationship between bus current injections and bypass

currents. The corresponding variations in branch currents,

generated by variations in bus current injections, can be

calculated directly by the BIBC matrix. The BCBV matrix

represents the relationship between shunt currents and bus

voltages. The corresponding variations in bus voltages,

generated by variations in branch currents, can be

calculated directly by the BCBV matrix. Thus, the BIBC

and BCBV training procedures are presented below[18] .

Step 1: For a distribution system with a branch section m

and a bus n, the dimension of the BIBC matrix is mx (n-1).

Step 2: If a line section (B k ) is located between bus i and

bus j, copy the column of the i th bus from the BIBC

matrix into the column of the j th bus and fill in a 1 at the

position of k th line and the jth bus column.

Step 3: Repeat step (2) until all row sections are included

in the BIBC matrix.

4.3 Power loss calculation

Line losses can be calculated in the distribution system in

primary and secondary feeders. The active and reactive

power loss in the distribution system per phase can be

calculated as follows:

   

2

1

*

nb

loss i

P I i R i





(12)

 

2

1

* ( )

nb

loss i

Q I i X i





(13)

The total active and reactive power loss of the distribution

systems is obtained by adding the losses of each branch

current line:

 

1

,1

nb

TLoss Loss

t

P P t t







(14)

4.4 Voltage drop calculation

All equipment connected to the electrical network is

designed to be used under a certain defined voltage. It is

not practical to serve every customer on an electrical

distribution at the same voltage exactly matching the

nameplate voltage, because voltage drops exist in every

part of the electrical system, from generation to the

customer's meter. The voltage drop in the distribution

system can be calculated as follows [19] .

 

1

3 Cos sin

n

i i i i

i

V I R X L





  



(15)

4.5 Load flow with D- STATCOM

D-STATCOM is a shunt device that uses force-switched

power electronics to control power flow and improve

transient stability on power networks. It is also part of the

so-called flexible AC transmission system devices. The

D_STATCOM is a three-phase shunt-connected Voltage

Source Converter (VSC), designed for use in the

distribution network to compensate for bus voltage to

provide better power factor and reactive power. The device

is capable of injecting or absorbing active and reactive

current at the point of common coupling (PCC). The

limiting constraint linked to energy storage makes it

practically impossible for D_STATCOM to inject active

power over a long period. Thus, operation is primarily

steady state, with reactive power being the power exchange

between D-STATCOM and the system. Figure 2 shows a

schematic diagram of D-STATCOM incorporated into a k

bus [20] .

Fig. 2: D-STATCOM connected to a certain bus k [20]

4.6 Components of D-STATCOM

D-STATCOM consists of a three-phase inverter (usually a

PWM inverter) using SCRs, MOSFETs or IGBTs, a DC

capacitor which supplies the DC voltage to the inverter, a

link choke which connects the output of the inverter to the

AC power side, a filter Components to filter high

frequency components due to the PWM inverter. From the

DC side capacitor, a three-phase voltage is generated by

the inverter. This is synchronized with AC power. The link

inductor connects the system voltage to the AC power side

[21] .

4.7 Basic working principle of D-STATCOM

The voltage of the D-STATCOM is injected in phase with

the mains voltage and in this case, there is no energy

exchange with the network, but only the reactive power is

to be injected (or absorbed) by the D -STATCOM. The

reactive power exchange with the network is achieved by

varying the amplitude of the output voltages. The output

voltage of Vd is controlled in phase with the system

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voltage Vs. If Vd is greater than Vs then the D-STATCOM

will act as a capacitor and generate reactive power

(capacitive mode). On the other hand, if Vs is greater than

Vd then the D_STATCOM will act as an inductor and

consume reactive power (inductive mode). ). If V d is

equal to Vs then D-STATCOM neither generates nor

absorbs reactive power and the reactive power is zero (no-

load mode)[22] .

4.8 Applications of D-STATCOM

D-STATCOMs are typically used in long distance

transmission systems, electrical substations and heavy

industries where voltage stability is the primary concern.

Furthermore; Synchronous static compensators are

installed at selected points in the electrical system to

perform the following basic functions. The basic functions

of D-STATCOM include: Voltage regulation and reactive

power compensation of harmonic currents. Power factor

correction, Voltage flicker mitigation and uninterrupted

power supply when used as an energy storage device[14] .

4.9 Reasons to choose D-STATCOM

There are two main conventional ways of controlling

voltage on distribution systems: Series voltage regulator

and shunt capacitors are the two conventional ways of

keeping distribution system voltages within an acceptable

range, but these devices have some disadvantages that

conventional series voltage regulators cannot generate

reactive power and have quite slow response due to their

step-by-step operations. The reason why D-STATCOM

was chosen as a compensation device over other FACTS

shunt equipment is: to autonomously control the voltage,

resulting in much faster power factor correction.

continuously variable output without steps, without

harmonics, without transients, it can generate and absorb

reactive power and reacts practically instantly [23] .

4.10 D-STATCOM modeling

The steady-state mathematical modeling of D-STACOM is

explained as follows. A simple two-bus radial distribution

system is shown in Figure 3.

Fig. 3: Two-bus radial distribution system

The voltage equation for the two-bus system is given as

follows

 

m

I

n m m m m

V V R jX



    

(16)

The schematic of two-bus radial distribution

system with D-STATCOM is shown in Figure 4.

Fig. 4: Two-bus radial distribution System with D-

STATCOM

By installing D-STATCOM, the voltage values on the bus

where it is installed and on the neighboring bus change.

The new tensions are

'

n

V

on the candidate bus and

'

m

V

on

the previous neighboring buses. The current changes and

'

m

I

corresponds to the sum of Im and IDS. Here, I DS is the

current injected by D-STATCOM and is in quadrature with

the voltage. Therefore, the expression of the new voltage

after installing D-STATCOM is given as follows:

 

' ' ' '

m

I2

n n m m m m DS n

V V R jX I



   



        





(17)

Here

'

n



,

'

m



and are the phase angles of Vn,

'

m

V

and

m

I

respectively. Separating the real and imaginary parts of the

above equations, we obtain

 

' ' ' ' ' '

m

cos Re Re I cos sin

22

n n m m m m DS n m DS n

V al V al Z R I X I



    

   

       

   

   

(18)

 

' ' ' ' ' '

m

sin Im Im I cos sin

22

n n m m m m DS n m DS n

V ag V ag Z R I X I



    

   

       

   

   

(19)

So the bus voltage angle is

The current angle and amplitude of the D-STATCOM are

1

2sin

22

DS

I x t





    

(20)

1

1''

43

cos

sin cos

nn

DS

nn

Vh

Ix

hh











(21)

Finally, the reactive power injected is:

 

' ' '

.2

DS n n DS n

jQ V I







   





(22)

Where * denotes the conjugated complex.

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5 Optimization technique used to

solve power loss and voltage drop

Optimization consists of finding the best solution to a

problem under predefined constraints. Intelligent

techniques such as bee colony, particle swarm, firefly,

cuckoo search, ant lion, genetic algorithm, whale

optimization, simulated annealing and harmony search

have been applied to incorporate shunt compensation

devices into electrical distribution systems. Recent efforts

have focused on solving the problem of optimal placement

of fact devices.

5.1 Analytical methods

Although analytical methods suffer from many drawbacks,

they are still used to optimize the location and size of

FACTS in distribution systems. Indeed, they are easy to

use and their logical analysis can be easily followed[ 24] .

5.2 Computational methods

Although these methods are fast compared to other classes

of techniques, their disadvantage is that they are complex

and reproducing their results can be difficult, or sometimes

impossible[25] .

5.3 Artificial intelligence methods

Artificial intelligence (AI) is increasingly being used to

solve optimization problems, with techniques such as

particle swarm optimization (PSO) and genetic algorithms

(GA) under development. These methods aim to obtain

more precision in the optimization process. PSO is chosen

as the most effective technique to optimize the location and

size of FACTS in power distribution systems, ensuring

reduced power losses and improved voltage profiles [25] .

Researchers used PSO as an optimization technique for

exploration, followed by an improved version

incorporating crossover and mutation parameters for

exploitation. They compared GA and PSO to resolve

distribution losses and distribution line voltage deviations.

The theoretical background of the most used optimization

algorithms is discussed below [25] .

5.3.1 Particle Swarm Optimization

Particle swarm optimization is a population-based meta-

heuristic optimization approach, created in 1995 by James

Kennedy and Russell Eberhart and motivated by flocks of

birds or schools of fish[26] . PSO is initialized with a

random number of solutions called particles which are left

free on a “search space”. Each particle is a possible

solution to the problem and has a fitness value. Physical

condition is assessed and must be optimized. A velocity is

defined that directs the position of each particle and is

updated with each iteration. The particles end up moving

towards the optimum due to their best location and the best

solution this group has ever encountered. A particle's

velocity is updated based on three factors: the particle's

previous velocity, the best position the particle has ever

been in, and the best position the entire swarm has ever

been in[27 ] . Particles track their coordinates in the search

space, linked to their best solution (fitness) so far. Personal

best (Pbest) and Gbest (best value) are tracked by the

Particle Tracking System (PSO). PSO uses random

weighted acceleration to accelerate particles toward their

Pbest and Gbest positions at each time step. The dominant

speed is calculated using the previous speed and distance

between Pbest and Gbest [27] .

   

1

12

k k k k

id id bestid id bestid id

V wV c r P S c r G S

    

(23)

11k k k

id id id

S S V





(24)

Where i=1, 2 ……..n & d=1, 2 ………..m

The following weight function is used

max min

max

.

kWW

W W k

K











(25)

Where W min, and W max are the minimum and

maximum weights respectively. K and K max are the

current and maximum iteration.

How particles update their speed in a PSO is indicated in

Figure 5.

X

Y

SK

SK+1

V

VK+1

Vpbest

VG best

Fig. 5: Updating Speed in PSO

5.3.1.1 PSO parameter selection and optimization

process

For any given optimization problem, certain parameters of

the PSO algorithm can affect its effectiveness. Certain

values and choices of these parameters have a significant

impact on the performance of PSO techniques, while

others have little or no impact. The basic parameters of

PSO are [27] :

Swarm size refers to the number of agents in a swarm, with

larger swarms generating more particles and covering more

search space per iteration. Reducing the number of

iterations can increase the computational complexity and

time consumption. The particle velocity is constrained by

the parameters, which determine the resolution or

adequacy of the regions between the current and target

positions. High 𝑉𝑖𝑑𝑚𝑎𝑥 can cause particles to overtake

good solutions, while low 𝑉𝑚𝑎𝑥 can cause particles to

take longer to reach the desired solutions.

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Speed components play a crucial role in updating an

agent's speed, with three terms: inertia, cognitive, and

social. Inertia provides information about the agent's recent

history, while cognitive measures performance based on

past performance. Social measures performance based on a

group of agents, guiding each agent to the best position

found by their neighborhood.

The accelerating coefficients C1 and C2 play a crucial role

in determining the optimal values for the PSO.

Initialization of C1 and C2 is crucial to obtain the optimal

values, and incorrect assumptions can result in cyclical

behavior. It is recommended to use C1 and C2 = 2 for

optimal results[27].

Inertia Weight: The inertia weight determines how much

of the previous time step's velocity should be retained.

However, the best results were obtained by adopting an

inertia mass that increases from 0.9 to 0.4 throughout the

first simulation course. This setting allows the PSO to

search a large region at the beginning of the simulation

when the inertia weight is high, and then refine the search

later when the inertia weight is lower. Another advantage

of adopting a decreasing inertia mass is that it damps the

oscillations of particles close to gbest. Additionally,

damping particle oscillations around gbest is another

advantage obtained by using decreasing inertia mass.

These oscillations are recorded when a large constant

inertial mass is used. As a result, removing these

oscillations helps the particles in the swarm converge

toward the best overall solution. According to, the value of

inertia weight (w) should drop linearly from 0.9 to 0.4

during the experiment [27] .

In general, the inertia weight ( w ) is adjusted according to

equation (2.3) above. The appropriate values for 𝑤 𝑚𝑖𝑛

and 𝑤 𝑚𝑎𝑥 are 0.4 and 0.9, respectively. Termination

Criterion: After the initial phase, several iterations of

update and evaluation steps are performed until a

termination condition is met. Generally, the stopping

condition is the achievement of a predefined maximum

number of iterations or the achievement of a certain

precision in the solution. PSO has the following

advantages including [27] .

1. PSO is based on swarm intelligence. It can be applied to

both scientific research and engineering.

2. PSO has the advantage of fast convergence rate

compared to most optimization techniques, including

genetic algorithm.

3. PSO has no overlap or mutation calculation. The

velocity of the particle can be used to perform the search,

for example relative to GA.

4. PSO has a stronger memory capacity than GA since

each particle remembers its own previous best value as

well as the neighboring best value.

5. PSO is more effective at maintaining swarm diversity

than GA because bad solutions are discarded and only

good ones are kept, resulting in a population that revolves

around a subset of the best individuals because all particles

use the information from the most successful particle to

improve. The main disadvantages of PSO are:

1. The approach is prone to partial optimism, which causes

it to be less precise in regulating its speed and direction.

2. The method may not properly solve the problems of the

uncoordinated system, such as the solution to the energy

field and the Variable rules of particles in the energy field.

In the PSO algorithm, the population has n particles which

represent candidate solutions. Each particle is a real-valued

vector of m dimensions where m is the number of

optimized parameters. Therefore, each optimized

parameter represents one dimension of the problem space

[27] . The proposed PSO technique for the optimization

algorithm is described using the following steps and shown

in Figure 6.

Initialize the particles

Calculate the fitness value

of the particles

Is the current fitness

better than p-best?

Keep previous p-

best

Assign current

fitness as new p-best

Maximum iteration

reached

END

Update the position and velocity of particles

Read system

data

Yes No

NO

Yes

Assign best particle p-best as g-best

Fig..6: PSO optimization flow chart

Step 1: Initialization: Set all parameters and generate n

random particles, each particle in the initial population is

evaluated using the objective function f. Set iteration

counter k = 1. Randomly generate an initial population

(array) of n particles. The initial velocity of each particle is

randomly generated for the evaluation of the objective

function. Kmax, Win, Wmax, C 1 and C 2 are assigned. In

this step, the lower and upper bounds of the regional

constraints are also specified.

Step 2: Calculate the objective function: Calculate the

objective function and find the fitness value of each

particle.

Step 3: Comparison of fitness values: The fitness value of

each particle in the first iteration becomes its best p . In the

previous iteration, if the new value of p best is obtained as

well as the previous one, it is modified otherwise it

remains the same.

Step 4: Assign the best personal value as the best overall

value: The best fitness value among all P bests is denoted

by G best .

Step 5: Changing the Speed: Change the speed of each

particle using the following equation:

Then generate the new particles based on the following

equation:

11

Sk k k

id id id

SV





(26)

i=1, 2…..…n and d=1, 2….….m

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Step 6: Update Iterations: Update the iteration counter, k =

k+1.

Step 7: If the stopping criteria are met, go to step 8,

otherwise go to step 2.

Step 8: Stop. The particle that generates the last iteration is

the optimal PSO solution

5.3.1.2 Benefits of PSO

1. Based on swarm intelligence. It can be applied to both

scientific research and engineering.

2. PSO has the advantage of fast convergence rate

compared to most optimization techniques, including

genetic algorithm.

3. PSO has no overlap or mutation calculation. The search

can be done by the velocity of the particle, for example in

comparison with GA.

4. During the development of several generations, only the

most optimistic particle can transmit information to other

particles, and the search speed is very fast.

5. The calculation in PSO is very simple. Compared to

other calculations in development, it occupies a larger

optimization capacity.

6. PSO adopts the actual digital code, and it is decided

directly by the solution. The dimension number is equal to

the solution constant. The main disadvantages of PSO are:

1. The method easily suffers from partial optimism, which

makes the regulation of its speed and direction less precise.

2. The method may not properly solve problems of

uncoordinated systems, such as the solution of the energy

field and the rules for moving particles in the energy field.

6 Case study

Woldya, located in the northern part of Ethiopia, is one of

the oldest cities in the country. The city has many shopping

centers, small industries and densely populated residents.

The old and mobile substations of Woldya are structured to

supply the city. An incoming 230KV line from the

Dorogbir mobile substation and an incoming 66KV line

are fed from the Dessie substation. These two substations

have a total of thirteen feeders, seven of which are 15KV

feeders and the rest are 33KV feeders.

The data required for this thesis work was collected from

Woldya distribution substation, Ethiopian Electric Utility

(EEU) engineering office and Ethiopian Electric Power

(EEP). The data was collected from the recorded feeder

loading data (peak load) of the substation and the

conductor impedance and other important data are

collected.

1. Old Woldya substation: This substation is located at

kebele-03, near Woldya bus station. It has a dual bus bar

system comprising a single transformer with 6.3/8.4 MVA,

66/15 KV and 8.4 MVA, 66/33/15 KV three-phase

transformers. There are three 15KV feeders and three

33KV feeders in this substation.

2. New Woldya substation: it has two 230/33/15KV power

transformers with a nominal power of 50MVA each and

supplies four 15KV feeders and three 33KV feeders. The

substations can be modeled using Microsoft Office Visio

software and the single line diagram is shown in Figure 7

below combining the two substations.

6.1 Analysis of the loading capacity of existing

Woldya 15 and 33KV power lines

All existing feeder lines in the city are used to distribute

medium voltage level of 15 and 33 KV from substations to

distribution centers over long distance coverage.

According to substation data, both substations operate with

a power factor of 0.8. Peak load power (MW) and peak

load current (A) data are available and the maximum

reactive power load can be calculated using the following

equations.

22

S P Q

(27)

3 cosP VI





(28)

3 sinQ VI





(29)

Where: P, Q and S are respectively the active, reactive and

apparent powers, V is the starting voltage 15KV; I is the

current reading and

cos



power factor of the substation.

Among the thirteen 15 and 33 KV feeders of the Woldya

Distribution substation, the Gonder ber feeder (F 7 ) is

selected for this case study for the following reasons: high

energy demand, high peak load current, long distance

covered and departure Gonder ber has 69 knots, and a total

capacity of 7.2 MW.

6.2 Gonder ber Distributor Analysis

Gonder ber feed emanates from Dorogbir mobile

substation and this feed is one of the heavily loaded feeds

of Woldya town covering large areas from Dorogbir to

Gonder ber up to Tikur Wuha River. In this area there are

some load centers which require very reliable energy like

health station, oil factory, Yeju mars Process, Poly technic

collage, Teacher College, milk processes, Mifa powder

factory, Yeju powder factory, Yegna plastic factory and

small industry etc.

6.3 Bus and branch numbering system

The bus and branch numbering system is very important

for the study of a given electrical system. Even though the

numbering scheme has no effect on the calculation

efficiency of departures, it must be assigned schematically,

including the laterals. It starts from the substation by

assigning it the bus number 1. The departures starting from

the substation and going to the ends are main departures

while the branches emanating from the main departure and

not from the substation are called lateral. For example, in

Figure 7, is the single-line schematic representation of the

Gonder ber charger drawn using Microsoft Office Visio.

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SS

123

456 7 8910 11

12 13 14 15 16 17 18 19 20 21 22

23

24 25 26 27

28 29 30 31 34

32 33

35 36 37 38 39 40 41 42 43 44 45 46 47

48 49 52

53 54

50 51

55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Fig. 7: Single-line diagram of the Gonder ber distributor

6.4 per-Unit value (p.u)

It is a dimensionless value of any quantity obtained by

dividing the actual value by the base value in the same

unit. This makes the calculation easier since all values are

taken in the same unit (p.u).

Unit value=Actual val./Base val. (30)

Based on the basic base values (S base, and V base), the

derived base values can be

base

S

IV



(31)

2

base

V

ZS



(32)

Now taking the common base power (100 MVA) and

system voltage (15 KV) as base values

100 6.6667

15

base

SMVA

I KA

V KV

  

(33)

 

2

215 2.25

100

base

KV

V

ZS MVA

   

(34)

The ratio of active power to base power and reactive power

to base power gives the unit values of active and reactive

power respectively.

6.5 Overhead line impedance calculation

The inductance of a transmission line depends on the

material, dimensions and configuration of the wires and the

length and spacing between them. A conductor's AC

resistance is always greater than its DC resistance due to

the skin effect forcing more current near the exterior.

Conductor surface. The higher the frequency of the

current, the more noticeable the skin effect will be. Wire

manufacturers usually provide tables of resistance per unit

length at common frequencies (50 or 60 Hz). The

conductors used in distribution feeders are stranded

conductors. The inductive reactance is calculated at a

frequency of 50 Hz and over a length of one kilometer. .

Thus, the impedances are given by [28] .

0.06283ln /

aa D

Z R j km

GMR

  

(35)

.GMR k r

(36)

3ab bc ac

D D D D

(37)

6.6 Sixty Nine Bus Gonder ber Radial

Distribution Distributor

It consists of a total number of sixty -nine power buses of

which bus-1 is taken as the reference node or slack bus, 11

nodes are common coupling nodes and 57 nodes are

connected to the loads through a transformer of step-down

distribution. The single line diagram of the Gonder feeder

is shown in Figure 3.2. The power line is a stranded

conductor of type AAC-50 and AAC-95 with a total length

of 31.2 km. These overhead lines are used to distribute

medium voltage power (15 kV) from Woldya Mobile

Substation to distribution transformers.

7 Result and Discussion

In this section, the results obtained using the load flow,

PSO and VSI methods were presented. The algorithm

described in the previous section is applied and

programmed in Mat lab 2019a.The implementation

parameters of the PSO algorithm are shown below in the

Table 1:

Table 1. Parameter value for PSO simulation

Population

Size

Number

of

iterations

Wmin.

Wmax.

C1

C2

40

20

0.4

0.9

2

Based on the collected data, a backward sweeping load

flow algorithm was performed, and from there, the

preliminary power loss, bus voltage and voltage stability

index of the feeder had been obtained. To obtain the best

location and size of D-STATCOM, a bus-based voltage

stability index analysis guided by the PSO algorithm was

simulated. The simulation results for the suggested system

are tested in four cases: Case 1: system without D-

STATCOM, Case 2: system with only one D-STATCOM

7.1 Case 1: System without D-STATCOM

The base case real and reactive power losses, voltage

profile and voltage stability index of the Gonder ber feeder

were simulated via Mat lab Software. The actual power

loss, reactive power loss, minimum voltage amplitude,

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minimum voltage stability index amplitude of the charger

are 172.8202 kW, 42.4213 KVAr, 0.9453pu and 0.7985

P.u without installing D-STATCOM. The base case

voltage profile and stability index are shown in Figures 8

and 9, respectively.

Fig. 8: Voltage profile for the base case scenario

Fig. 9: Voltage stability index for the base scenario

7.2 Case 2: System with a single D-

STATCOM

In case 2, the real and reactive power losses, voltage

profile and voltage stability index of the Gonder ber feeder

were simulated. The actual power loss, reactive power loss,

minimum voltage amplitude and minimum voltage

stability index amplitude of Gonder ber charger are

35.8184 kW, 29.4665 KVAr, 0.9802pu respectively and

0.9230 P.u with single installation of D-STATCOM. The

voltage profile of Case 2, stability index, active power loss

and reactive power loss are shown in Figures 10, 11, 12

and 13, respectively.

Fig. 10(a): Voltage profile without and with D-STATCOM

Fig. 10(b): Voltage profile without and with D-STATCOM

Fig. 11(a): Voltage stability index without and with D-

STATCOM

Fig. 11(b): Voltage stability index without and with D-

STATCOM

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Fig. 12(a): Active power loss of all buses for case 2

Fig. 12(b): Active power loss before and after

compensation for case 2

Fig. 13(a): Reactive power loss of all buses for case 2

Fig. 13(b): Reactive power loss before and after

compensation for case 2

Table 2, shows that the comparison of real power loss,

reactive power loss, voltage profile, voltage stability index,

location, optimal size of the D -STATCOM, of the

percentage reduction in active and reactive power losses

for case 2.

Table 2. Performance evaluation for Case 2

8. Conclusion

This paper demonstrates the effectiveness of a PSO

optimization technique to reduce system power loss,

improve voltage profile, and increase voltage stability

index by optimizing the location and size of D-

STATCOM. The bus-based voltage stability index was

used to reduce the search space of the algorithm. A direct

load flow analysis method was applied to determine

system voltage and active and reactive power losses. A

multi objective function was formulated for the

optimization algorithm, which was tested on the Woldya

Gonder ber Feeder (F7). The simulation results showed a

significant reduction in real power losses and reactive

power losses, resulting in a total annual cost reduction of

1,478,771.22 Birr and a payback period of 1.8 years. A

No

Parameters

Base case

PSO (Case 2)

1

Loss of active power

177.9424KW

36.4801KW

2

Loss of reactive power

144.2124 KVAr

29.5017 KVAr

3

Minimum VSI

0.7942pu

0.9193pu

4

Minimum voltage

0.9440pu

0.9792pu

5

Location of D-STATCOM

……………

@ Bus number 1

6

Size D-STATCM

……………

1250KVAr

7

% active power loss

……………

79.498900

8

% reactive power loss

……………

79.542900

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Sino pack company offered a better price for a D-

STATCOM supplier of size 1250KVAr, which resulted in

a total installation and the price of D -STATCOM is

2,652,242.857 Birr.

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Contribution of individual authors to the creation

of scientific article

The authors equally contributed to the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of funding for research presented in a

scientific article or scientific article itself

No funding was received for conducting this study

Conflict of interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

Creative commons attribution licence 4.0

(attribution 4.0 international, CC BY 4.0)

This article is published under the terms of the

creative commons attribution licence 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_U

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