OPTIMAL ALLOCATION OF DG USING HARMONY SEARCH

ALGORITHM IN RADIAL DISTRIBUTION SYSTEM

A Dissertation submitted in fulfillment of the requirements for the Degree
of

MASTER OF ENGINEERING
In

Power Systems
Submitted by

Parul Singh
(801341014)
Under the Guidance of

Dr. Smarajit Ghosh

Professor, EIED

2015
Electrical and Instrumentation Engineering Department
Thapar University, Patiala
(Declared as Deemed-to-be-University u/s 3 of the UGC Act., 1956)

Post Bag No. 32, Patiala 147004

Punjab (India)

s,

ACKNOWLEDGEMENT
First of all, I would like to thank almighty God, who gave me opportunity and strength to carry
out this work.
Gratitude is accorded to all the authorities of Thapar University, Patiala for providing the
necessary facilities to complete my M.E thesis work.
I would like to express my sincere gratitude towards my supervisor Dr. Smarajit Ghosh,
Professor, EIED for his guidance and valuable advice throughout the progress. I thank him for
his untiring encouragement, trust and support. He was a guide in true sense both academically
and morally, throughout this work. It was a great experience working with him.
The paucity of words does not compromise to thank my parents, whose blessings have brought
me this far in life.

(PARUL SINGH)

ii

DEDICATED TO MY PARENTS

iii

ABSTRACT
In recent few years, the implementation of distributed generator into a distribution system has
been increasing rapidly in many parts of the world, due to the liberalization of the electricity
markets, constraints on constructing a new distribution network, transmission lines and
environmental concerns. Technical advancement in small generators, power electronics and
energy storage devices have promoted the use of DG unit. DG units, basically, are small
generating units, which are placed closer to the point of consumption. The utilization of a DG
unit placed on-site of the load demand in the system which provides evident power losses
reduction, stability improvement, and voltage profile improvement along with accelerating
sustainability of environmental issues. Distributed Generation is the power generation at the
point of consumption. Instead of providing power centrally, generating the power on-site
decreases the cost, less complex, independent, and efficient transmission and distribution. Using
this system, some of the controls such as distributed generation, distributed telephony i.e. using
mobile phone shifts to the consumer. It is, basically an electric power source connected to the
distribution system directly. Before the installation, its effects on line losses, voltage profile,
short-circuit current, amount of harmonics injected and the reliability should be computed. In
order to obtain the efficient compensated system factors like type of network, best technique
used, no. and capacity of units to be used, best location etc. should be taken into account. This
thesis work focuses on the minimization of real power loss and voltage profile improvement of a
radial distribution network using suitable DG units. Here, a 33-node radial distribution system
has been used as the test system and Harmony Search Algorithm has been implemented to find
the optimal location of DG unit and Loss sensitivity Method has been used to obtain the optimal
size of DG in order to reduce real power losses and improve voltage profile.

iv

TABLE OF CONTENTS
Page
DECLARATION

ACKNOWLEDGEMENT

ii

DEDICATION

iii

ABSTRACT

iv

TABLE OF CONTENTS

LIST OF FIGURES

vii

LIST OF TABLES

viii

NOMENCLATURE

ix

CHAPTER-1:INTRODUCTION

1-12

1.1

Electric Power Distribution System

1.2

Classification

1.3

Requirement of Power Distribution System

1.4

Distribution Generation

1.4.1 Definition of distributed generation

1.4.2 Advantages of distributed generating system

Load-Flow

1.5.1 Bus classification

1.5

1.6

Literature Review

1.7

Research Gap

12

1.8

Objective of Thesis Work

12

1.9

Organization of Thesis

12

CHAPTER-2: PROPOSED METHOD

8-11

13-16

2.1

Load-Flow Calculation

13

2.2

Power Loss Sensitivity Factor Method

13

2.3

Harmony Search Algorithm

14

CHAPTER-3: PROBLEM FORMULATION

15-36

3.1

Load-Flow Calculation

17

3.2

Formulation Of The Objective Function

3.3

Sizing Of DG At Various Locations

21

3.4

Placement of DG

22

20

CHAPTER-4: RESULTS

37

CHAPTER-5: CONCLUSIONS AND FUTURE SCOPE

40

5.1

CONCLUSION

40

5.2

FUTURE SCOPE

40

REFERENCES

41-44

APPENDIX-A: TEST SYSTEM DATA

45-47

vi

LIST OF FIGURES
Figure No.

Title

Page

Figure 2.1

Flow chart for HAS

16

Figure 3.1

Single-line diagram for a radial distribution network

17

Figure 3.2

Single-line diagram for 33-node radial distribution system

26

Figure 4.1

Plot showing improvement in bus voltages

32

Figure 4.2

Plot showing reduction in real power losses

35

Figure 4.3

Plot showing reduction in reactive power losses

37

vii

LIST OF TABLES

Table No.

Title

Page

Table 1.1 Showing known quantities for each type of bus

Table 4.1 Voltage magnitude at each node for Base Case without any DG

27

Table 4.2 Real and Reactive power losses for Base Case without any DG

28

Table 4.3 Node voltages at each node with 1 DG & 2 DGs

30

Table 4.4 Size of DGs

33

Table 4.5 Real Power Losses

33

Table 4.6 Reactive power losses

36

Table 4.7 Location of DG

38

Table 4.8 Comparison of Results for 33-bus system

38

viii

CHAPTER 1
INTRODUCTION
1.1 ELECTRIC POWER DISTRIBUTION SYSTEM
Distribution Systems is defined as the sequential flow of the activities, procedures and
systems designed and linked to facilitate along with monitoring the movement of services
and goods from the source to the consumer. Distribution is all about providing the products
and services to the end user whenever and where ever they require. The main objective of
power distribution system is to provide power to individual consumer area. The distribution
of electrical power is done with much low voltage level.
It is the final stage of electric power delivery. It carries electricity to individual consumers
from the transmission system. Distribution substations lowers the transmission voltage up to
a medium voltage range i.e. 2 kV-35 kV using transformers connecting them to
transmission system.
Primary distribution lines carry the medium voltage power to distribution transformer which
is located nearest to the customer's premises.
Distribution transformers further lowers the voltage value to the utilization level of
household

appliances

and

feed

several

customers,

typically,

through

the

secondary distribution lines at this voltage.

From secondary distribution lines commercial and residential customers are connected
through the service drops. Direct connection is provided for customers demanding a much
larger amount of power to the primary distribution or sub-transmission level.
Electric power distribution is done by distribution networks consisting following main
parts:

Distribution substation,

Primary distribution feeder

Distribution Transformer

Distributors

Service mains.
1

For primary distribution purpose, the electric power transmitted is stepped down in
substations and then this power is fed to the distribution transformer via primary
distribution feeders. Support to over-head primary distribution feeders is provided, mainly,
by supporting iron pole (preferably rail pole). The conductors used are, preferably, strand
aluminum conductors and are mounted on the arms of the pole using pin insulators. In
congested places, underground cables are used for primary distribution. Distribution
transformers are basically 3-phase pole mounted type. Secondary of the transformer is
connected with the distributors. Service mains feed electric power to different consumers.
These service mains are tapped from different distributor points. The distributors are further
categorized as distributors and sub-distributors. Distributors are directly connected with the
secondary of distribution transformers whereas sub-distributors are tapped from distributors.
Based on the position and agreement of consumers, service main of the consumers could be
connected either to distributors or sub distributors. Feeder and distributor both carry the
electrical load, but one basic difference is that feeder feeds power from one point to another
without any tapping from any intermediate point. And because of no-tapping point in
between, sending-end current is equal to that of receiving-end of the conductor. Whereas,
the distributors are being tapped at different points for feeding different consumers,
provides varying current along their entire length.
1.2 CLASSIFICATION
Distribution systems can be classified in various ways:
1.2.1 Based on the character of service:

General light and power

Industrial power

Railway

Street lighting etc.

1.2.2 Based on the type of construction the distribution systems

Overhead distribution system

Underground distribution system.

Due to low cost, overhead type system is generally employed. In case of impracticality,
Underground distribution system is used.

1.2.3 Based on the number of wires:

Two wire

Three wire

Four wire distribution systems

For DC supply, 3-wire distribution system is generally employed because of its

advantages over 2-wire distribution system. In case of the AC supply, 3-phase 3-wire
system is used for balanced loads like power loads.3-phase 4-wire system is
preferred for unbalanced loads like light and power loads combined and single-phase
2-wire system is employed for lighting and small power appliances.

1.2.4 Based on scheme of connections:

Radial

Ring

Inter-connected distribution systems

1. Radial System
It is the simplest and cheapest since the distributors are fed at one end only and it is
employed when the power station is situated at the center of the load and electrical energy is
generated at low voltage.
Because of following disadvantages, this system is rarely used:
There would be heavy loading at the end of the distributor nearest to the supply end.
In correspondence to the variations in load, the consumers at the farthest end of distributor
will experience serious voltage fluctuations.
All the consumers are dependent on a single feeder therefore when a fault occurs on
feeder or distributor they have to cuts-off the supply to all the consumers.

2. The Ring Main System

Each consumer is supplied via two feeders in this system and the arrangement of this
system is similar to two feeders arranged paralleled on different routes.
This system has following advantages:

Requirement of copper is less.

3

Fluctuations in voltage are less.

More reliable as during the fault on any one section, by isolating the faulty section, the
supply to all consumers can be maintained continuously.
Factors deciding number of feeders connected to the system are:

Maximum demand of the system

Total length of ring main distributors

Required voltage regulation

3. Interconnected System
In this system, there are two or more generating stations connected together and during
overload hours, any area could be fed from another power stations leading to following
advantages:

Reduction in required reserved capacity

More reliable supply

Improved load factor

Increased efficiency

1.3 REQUIREMENT OF POWER DISTRIBUTION SYSTEM

The basic requirements of a reliable and stable distribution system are:

Continuity in the power supply.

Specified consumer voltage should not vary more than the prescribed limits i.e. not
beyond 5 % of the specified voltage, as per the Indian Electricity Rules.

Efficiency of lines must be as high as possible.

There should not be any leakage in the system i.e., it should be safe from consumer
point of view must not be overloaded.

The layout must not affect the appearance of the site.

The system should be economical.

4

Mostly the AC transmission and distribution is used, still for some applications DC supply
is required, such as, electrochemical work, batteries, DC motors, electric traction etc.
Therefore, DC distribution is also equally important along with AC distribution. DC
generators are used in a DC distribution in the generating stations. Sometimes, AC is
converted into DC using the converters at the substations. Then, as per the consumer's
requirement, DC supply is distributed.

1.4 DISTRIBUTION GENERATION

It is the power generation at the point of consumption. Instead of providing power centrally,
generating the power on-site decreases the cost, less complex, independent, and efficient
transmission and distribution. Using this system, some of the controls such as distributed
generation, distributed telephony i.e. using mobile phone shifts to the consumer.
1.4.1 DEFINITION OF DISTRIBUTED GENERATION
Distributed generation (DG) basically refers to a small-scale (generally between 1 kW and
50 MW) electric power generators which produces electricity at a site that is close to
customers or which is tied to a distribution system.
These distributed generators includes induction generators, reciprocating engines, fuel cells,
wind turbines , solar photovoltaic, combustion gas turbines, synchronous generators , micro
turbines (combustion turbines which runs with high-energy fossil fuels like oil, natural gas,
propane, diesel or gasoline ).
1.4.2 ADVANTAGES OF DISTRIBUTED GENERATING SYSTEM:
Distributed generating system is really beneficial because of the following reasons:

Because of the small size the overall capital cost quite less of the system, although
the investment cost (per kVA) of one could be much higher in comparison to the
power plant.

Less need for the construction and up gradation of large infrastructure construction
as the DG could be constructed on the load location itself.

Reduction in pressure on the distribution and transmission lines since DG provides

5

power for local use.

Increment in power reliability as stand-by or back-up power to the customers.

Provide customers a choice to meet their energy requirement

1.5 LOAD-FLOW
In electrical power engineering, load-flow study is the numerical analysis of flow of electric
power in an interconnected system. In a power-flow study, usually, simplified notation such
as a one-line diagram and per-unit system are used and focus is on various aspects of AC
power parameters, like voltages, voltage angles, real power and reactive power. It analyzes
a power system in the normal steady-state conditions. It is an analysis of the system
capability to adequately supply connected load providing total system losses and individual
line losses.
Load-flow study is important for planning future expansion of the power systems as well as
to determine the best operation of the existing systems. The prime information obtained
from the load-flow study is magnitude and phase angle of the voltage at each bus also real
and reactive power flowing in each line.
Commercial power systems are, generally, too complex to allow a hand solution of the
power flow. Therefore, special purpose network analyzers were built in between 1929 and
1960in order to provide a laboratory-scale physical model of power systems. Analog
methods with numerical solutions were replaced by large-scale digital computers.
In addition to the load-flow study, computer programs perform many related calculations
such as short-circuit fault analysis, stability studies under transient & steady-state
conditions, economic dispatch and unit commitment. Specifically, some programs uses
linear programming to find out the optimal power flow and the conditions, which give the
lowest cost per kilowatt-hour delivered.
Load-flow study is, mainly, valuable for the systems with multiple load centers, like a
refinery complex. Performing a load-flow on an existing system provides the insight and
recommendations as to system operation and the optimization of control settings in order to
obtain the maximum capacity while minimizing the cost of operation. Results of such an
6

analysis are obtained in terms of real power, reactive power, magnitude of voltage and
phase angle.

1.5.1 BUS CLASSIFICATION

Load flow problem is concerned with finding the static operating conditions for an electric
power transmission system, while satisfying constraints are specified for the power and/or
voltage at network buses.
Generally, buses are classified as of 4 types as shown presented in Table 1.1.
Table 1.1: Showing known quantities for each type of bus

Bus Type

Specified Quantities

Swing/slack Bus

|V|

PV Bus

P
|V|

PQ or Load Bus

P
Q

Generator Bus

P
|V|
Qmax, Qmin

Each bus is modeled by two equations, for n numbers of buses and p numbers of PV and
generator buses 2n equations in 2n unknowns are there, which are |V| and for load buses,
Q and for generator and PV buses and the P and Q for slack bus. It requires only to obtain
the phase angle i.e. and voltage magnitudes i.e. V for all the buses and then dont need to
find any other unknowns. Since, slack bus is the reference bus a value of 0 degrees has been
assigned for its . The voltage magnitudes, V are already specified for the slack bus, the PV
buses and the generator buses. Therefore, the number of unknowns that required to be found
out is 2n 2 p. Once |V| and are evaluated for all the buses, P and Q at the slack bus and
Q for the generator and PV bus then can be calculated.

1.6 LITERATURE REVIEW

Alemi and Gharehpetian [1] introduced an analytical method to obtain minimized losses
and improved voltage profile by evaluating losses and voltage profile using load flow
method for radial a distribution network. This proposed method included the sizing and the
allocation of distribution generators (DGs).

Singh and Choudhury [2] represented the analysis of performance to place DG optimally
for power loss reduction and voltage profile improvements at nodes in the distribution
system. While optimally allocating DG to reduce the real power losses and sustaining the
voltage profile within already specified limits using GA in distribution network, that
method also presented the effect of change of loads along with voltage and frequency.

Parizad et al. [3] aimed at allocation of distribution generator to achieve improved voltage
profile, minimize losses and reduction in harmonic distortion for distribution network using
harmony search algorithm. The fast harmonics method load-flow method applied is based
on injection of equivalent current using BIBC and BCBV matrices

Amanifar [4] used heuristic optimization technique named Particle Swarm Optimization
(PSO).In that technique, power losses were minimized in addition to investment cost of
DGs. The proposed technique was basically hybrid of Particle Swarm Optimization (PSO)
and Harmonic Power Flow algorithm (HPF).That approach provided improvement in
voltage profile and reduction in THD and power losses.

Abu-Mouti and El-Hawary [5] used ABC algorithm to optimally place the DG-units, their
sizing and improved p.f. gave minimum real power loss of system. It is a meta-heuristic
optimization approach based on population, which was derived from intelligent foraging
behavior of the honeybee swarm. This technique found to be more efficient and able of
handling problems based on mixed integer non-linear optimization.

Reddy and Kumar [6] proposed a technique to optimally place capacitors on the primary
feeders of a RDS, used a new two-stage methodology, consisting fuzzy and Harmony
search algorithm (HSA) to get reduced the power losses and improved the voltage profile.
8

To find optimal capacitor locations, fuzzy approach was used and to find the optimal sizes
of the capacitors Harmony search algorithm used.

Hussain and Roy [7] used a new meta-heuristic approach which was population based
namely Modified Artificial-Bee-Colony algorithm (ABC), in order to reduce real power
losses and improve supply quality and the system reliability. It also reduced green-house
effects, improved voltage profile, and reduced line loss and environment impact. Better
solutions were achieved with the advantages of less time-consumption from CPUs and high
quality of solutions. That method was found to be superior and had more ability to solve
complex power system problems.

Nasiraghdam and Jadid [8] used an Improved Harmony Search algorithm to assess the
load model effect on the optimal sizing and allocation of distributed generation (DG). That
paper was successfully verified the effect of voltage dependent loads on system power
characteristics.

Shrivastava et al. [9] proposed a method to optimally locate and size multiple DG units in
an RDS, used classical grid-search based on successive load flow in order to minimize
active power losses and to improve the voltage profile. That technique was significant due
to the fact that there will be more decrement in total active power losses and maximum
voltage drop of the system is also decreased performing integration of DG units at various
locations.

Murthy and Kumar [10] presented a comparison of novel method, combined power loss
sensitivity, voltage sensitivity index, and the index vector methods to optimally allocate and
size the DG in RDS.
Nekooei et al. [11] presented a new approach named as Improved Multi-objective Harmony
Search by using a multiple objective framework of planning. In this approach, the optimum
sizes and the locations of DGs were found by taking objective functions as losses and the
voltage profile and qualitative comparison was made against Non-dominated Sorting
9

Genetic Algorithm II.

Baghaee et al. [12] presented a novel approach to optimally place multi-type FACTS
devices was presented in the first part of paper, which was based on HSA and in second
part, the HSA was proposed for the optimization of harmonic in multi-level inverters.
Implementation simplicity, precision, fast speed in the global convergence were some of the
advantages of HSA over GA.

Liu et al. [13] dealt with the optimization of DG planning to obtain minimized power loss,
reduced voltage deviation and maximum voltage stability margin. A meta-heuristic HSA
was improved with fast non-dominated sorting approach to solve comprehensive multiobjective harmony search (MOHS).

Naik. S et al. [14] used an analytical method for minimization of real power loss of
distribution networks. This was done by injection of power by the DG, operating at a given
p.f. The technique did not need Z-bus matrix calculation or calculation of inverse of Y-bus
matrix or Jacobean matrix and, therefore, taken less computation time.

Seker and Hocaoglu [15] aimed at placement of DG-unit and its sizing by performing a
meta-heuristic approach, which was derived from foraging behavior of the honey bee
swarms called Artificial-Bee-Colony (ABC) algorithm. The method successfully
implemented to determine the optimal place and size of DG-unit.

Sangeetha and Jalendiran[16] used a meta-heuristic HSA considering musical progression

of searching for a flawless harmony ceremonial, which described the sensitivity analysis for
proof of identity of optimal locations of distribution generation units to reduce the power
loss and improvement of voltage profile in the RDS. Objective function included constraints
of voltage profile, branch current and radial structure of the system.

Muttaqi et al. [17] discussed improvement of the voltage profile in RDS by the installment
of a DG at a suitable location and with most suitable size. Based on the algebraic equations
an analytical approach was developed for the uniformly distributed loads in order to
10

conclude optimal operation, the location and the size of DG to get required level of network
voltage profile. Proposed method was simple to use for the conceptual design and
distribution system expansion analysis with DG and it is suitable for the quick estimation of
the DG parameters in a RDS.

Naik et al. [18] used an analytical approach for optimum allocation and sizing of DG in
RDS to reduce real and reactive power losses. Suitable analytical expressions had been
derived for this purpose, which was based on change in active and reactive components of
branch currents caused by DG placement. Firstly, capacity of DG was determined causing
maximum benefit at different buses and the bus equivalent to the highest benefits was
designated as the best location. To determine the optimal size of DG unit(s), that method
needed the results for base case load-flow only.

Kaur et al. [19] aimed at the nonlinear and non-convex optimization problem of placement
DG using two methods, which are MINLP and heuristic approach created Improved
Harmony Search (IHS).Both of the algorithms were implemented for optimal placement of
DG units. Using MINLP formulation by sensitivity analysis the potential locations were
obtained to cut the search space and afterwards, for optimal sizes and locations the problem
is solved. Because of its non-monotonic solution surface results were also obtained with
HIS.

Biswas et al. [20] demonstrated artificial bee colony algorithm successfully utilized in order
to solve optimal DG placement problem, which considered both technical and economic
aspects. Technical objectives tried to minimize the line loss, effect of the voltage sag
problem, and variation in the node voltage deviation in a distribution network. Economic
objectives tried to minimize the operational cost of DG placement

11

1.7 RESEARCH GAP

Literature survey of the previous research work regarding the effect of distributed
generation in radial distribution system has been carried in chapter 2. From the discussion
carried out in chapter 2 it can be concluded that there is a still possibility to obtain optimum
location of DG units to be placed in a radial distribution network using harmony search
algorithm and a suitable analytical method can be implemented to obtain optimal size and
location of DG with reduced power losses and improved voltage profile.

1.8 OBJECTIVE OF THE DISSERTATION WORK:

The purpose of the work is to obtain the optimal location and size of Distribution Generator
in order to minimize the power losses and get an improved voltage profile in a Radial
Distribution Network. For optimal sizing and allocation of DG, an analytical method is used
for load-flow analysis to obtain power losses integrated with Harmony Search Algorithm in
order to reduce power losses and improve the voltage profile.
1.9 ORGANIZATION OF THE THESIS
CHAPTER 1: It includes an overview of distribution generation, literature review,
objective of the dissertation work and organization of thesis.
CHAPTER 2: Discusses the propose methods used to achieve the objective of the work.
CHAPTER 3: Illustrates problem formulation to compute the desired results.
CHAPTER 4: Gives the results for 33-node radial distribution system and discusses the
results obtained.
CHAPTER 5: Includes the conclusion of the work done and suggests the future scope.
References consists the papers studied and used in the thesis work.
Appendix-A represents the system data for a 33-node radial distribution system.

12

CHAPTER-2
PROPOSED METHOD
2.1 LOAD-FLOW CALCULATION
Load-flow techniques are very important for the analysis of power systems and are used in
operational and planning stages, as well. Some applications, specifically, in distribution
automation and optimization require repeated load-flow solutions. As the power distribution
networkismore complex, demand for efficient and reliable system operation increases.
Consequently, load-flow studies must be having the capability to handle the various system
configurations with adequatespeed and accuracy. In most cases, radial distribution systems
are unbalanced because of the single-phase, two-phase and three phase loads. Therefore,
load flow solution for an unbalanced situationis required and, hence a special treatment is
needed for solving such networks. In the present work, radial distribution system is assumed
to be balanced.
2.2 POWER LOSS SENSITIVITY FACTOR METHOD
This method is based on principle of linearization of non-linear equations around the
starting operating point, which helps to reduce the number of solution space or minimize the
search space.
Sensitivity factors are evaluated at each bus, firstly using the values obtained from the base
case power flow. The buses are ranked in descending order of the values of their sensitivity
factors to form a priority list. The top-ranked buses in the priority list are the first to be
studied alternatives location. This is generally done to take into account of the effect of
nonlinearities in the system. The first order sensitivity factor are based on linearization of
the original nonlinear equation around the initial operating condition and is biased towards
function, which has higher slope at the initial condition, that might not identify the global
optimum solution.
The sensitivity factor will reduce the solution space to less no. of buses, which constitute
the top ranked buses in priority list. Effect of number of buses taken in the priority will have
effect the optimum solution obtained for some system. For each bus in priority list, DG is
placed and the size is varied from minimum (0 MW) to a higher value until the minimum
13

system losses is found with the DG size. In this study, 30% of the total number of buses is
considered in preparing the priority list for each case. The process is computationally
demanding as one needs a large number of load flow solution.
The main steps of this algorithm are:
STEP 1: Run the base case load-flow.
STEP 2: Compute the sensitivity factor and rank the sensitivity in decreasing order to form
the priority list.
STEP 3: Select bus with highest priority and place DG at that bus.
STEP 4: Change the size of DG in very small step and calculate loss for each by running
load-flow.
STEP 5: Store size of DG with the minimum losses.
STEP 6: Compare the losses with the previous solution. If losses are less than previous
solution, store the new solution and discard the previous solution.
STEP 7: Repeat Steps 4, 5 and 6 for all buses in priority list.

2.3 HARMONY SEARCH ALGORITHM

It is a new meta-heuristic population search technique. The technique was derived from a
natural phenomenon of musicians behavior, when they all collectively play their musical
instruments i.e. population members to produce a pleasing harmony i.e. global optimal
solution. The state is determined by an aesthetic standard i.e. fitness function.
Although, the harmony estimation is aesthetic and subjective but there are several theorists
who have provided us with the standard of harmony estimation- a Greek mathematician and
philosopher, Pythagoras (582497BC) worked out the frequency ratios or string length
ratios with equal tension to found out that they had a particular mathematical relationship,
after researching what notes sounded pleasant all together.
In other words, it is the real parameter optimization algorithm which is derivative-free and
draws inspiration from the musical improvisation process to search for a perfect state of
harmony. Musical performances seeks for a best state i.e. fantastic harmony which is
determined by aesthetic estimation and as the optimization algorithms seek for the best state
i.e. global optimum minimum cost or maximum benefit or efficiency, which is determined
14

by the objective function evaluation. Whereas, the aesthetic estimation is determined by a

set of the sounds played by joined instruments, just the way, objective function evaluation is
determined by a set of the values produced by the component variables. The sounds for
better aesthetic estimation could be improved by practice after practice, just as the values
for a better objective function evaluation can be improved by iteration by iteration.
It is simple algorithm in concept which is less in parameters and easy in implementation. It
has already been successfully applied to various real-world and benchmark problems such
as pipe-network design [21], and structural optimization [22], the vehicle routing problem
[23], the combined heat [24] and the scheduling of a multiple dam system [25] and so on.
The basic steps of this algorithm are as follows:
1.Initializing the algorithm and problem parameters.
2. Initializing the harmony memory.
3. Improvising a new harmony.
4. Updating the harmony memory.
5. Checking the termination criterion.

15

START

Read the system data and specify the HSA, and Nmax

Generate initial harmony memory (HMS) and Size of DG units randomly,

setting iteration count i=1

Compute objective function and sort it in ascending order

Improvise New Harmony using HAS rules

Is New Harmony is better

than stored harmony in
HM
i=i+1

Update HM

i<Nmax

Output the Result

STOP

Figure 2.1 Flow chart for HSA

16

CHAPTER 3
PROBLEM FORMULATION
3.1 LOAD-FLOW CALCULATION
The prime assumption made here is that the taken three-phase radial distribution network is
balanced and they can be represented by their single-line diagrams by simply neglecting the
charging capacitances at the distribution voltage levels.

12

10

11

Figure 3.1: Single-line diagram for a radial distribution network [26]

17

Consider branch-1, the receiving-end node voltage can be written as:

V (2) = V(l) -I (1) Z(1)

(3.1.1)
Similarly, for branch-2:

V(3) =V(2) -I (2) Z (2)

(3.1.2)

Substation voltage V(1) is known, so if Z(l) is known i.e. current of branch-1, it would be
easy to calculate V(2) from eqn. (3.1.1).
Similarly, Once V(2) is calculated, if the current through branch-2 is known, it is easy to
calculate V(3) from eqn. (3.1.2)
Voltage at nodes 4, 5, ..., NB can be calculated, if all the branch currents are known.
Hence, a generalized equation for receiving-end voltage, sending-end voltage, branch
current and branch impedance is

V(m2) = V(m1) - I (jj) Z (jj)

(3.1.3)

m2 = IR (jj)

(3.1.4)

ml = IS (jj)

(3.1.5)

where,
jj is the branch number.
Eq. (3)could be evaluated for jj = 1, 2, ..., LN1 (LN1 = NB- 1 = number of branches).
Current passing through branch-1 is equal to the sum of load currents of all the nodes
beyond branch-1 add up the sum of the charging currents of all the nodes beyond the
branch-1, i.e.
I(1)=

(3.1.6)
18

The current passing through branch-2 is equal to the sum of load currents of all the nodes
which are beyond branch-2 plus sum of charging currents of all the nodes which are beyond
branch-2, i.e.

I(2) = IL(3) + IL(4) + IL(5) + IL(6)+ IL(10) + IL(11)

+ IC(3) + IC(4) + IC(5) + IC(6) + IC(10) + IC(11)

(3.1.7)

Therefore, if it is possible to identify nodes which are beyond all the branches, it is possible
to compute all branch currents.
The load current of node i is

i = 2, 3, .,N

IL(i) =

(3.1.8)

The charging current at node i is

IC(i) =

(i)V(i)

i = 2 , 3 , . . . , NB

(3.1.9)

Load currents and charging currents are calculated iteratively. Initially, flat voltage of all
the nodes is assumed and the load currents and the charging currents of all the loads are
computed using eq. (3.1.8) and eq. (3.1.9).
The active and reactive power loss of branch jj are given as:

LP(jj)=

R(jj)

(3.1.10)

LQ(jj)=

X(jj)

(3.1.11)

Once all the nodes beyond each branch are identified, the current flowing through each
branch can be calculated very easily. For this purpose, the load current and the charging
current of each node are computed by using eq. (3.1.8) and eq. (3.1.9). The expression of
branch current is given by:
19

I(jj)=

(3.1.12)

After calculating the new values of the voltages of all the nodes, convergence of the
solution is checked. In case, it does not converge, then load and charging currents are
calculated using the most recent values of the voltages and the whole procedure is repeated.
The convergence criterion of this proposed method is that if the maximum difference of
voltage magnitude i.e. DVm-axis less than 0.000lp.u., in successive iterations, the solution
has converged.

3.2 FORMULATION OF THE OBJECTIVE FUNCTION

In order to obtain minimized real power losses and improved voltage profile, the objective
function is formulated to maximize the real power loss reduction, which is given as
Maximize f = max (

subjected to
and

det(A)=1 or -1 (radial system)

det(A)=0 (not radial)

There are a number of techniques proposed for the optimal placement of DG in radial
distribution system.

20

3.3 SIZING OF DG AT VARIOUS LOCATIONS

Method used for siting of distributed generator is power loss sensitivity method and is
explained as follows:
The real power loss in a system is given by:

(3.3.1)

This is referred to as exact loss formula [1].

where,

and rij + jxij = Zij are the ijth element of [Zbus] matrix with [Zbus] = [Ybus]1.
The sensitivity factor of real power loss w.r.t. real power injection from DG is given by

(3.3.2)

The total power loss against injected power is a parabolic function and at minimum losses
the rate of change of losses with respect to injected power becomes zero.

(3.3.3)

It follows that

(3.3.4)

)]

(3.3.5)

21

where,
Pi is the real power injection at node i, which is the difference between real power
generation and the real power demand at that node:
Pi = ( P D G i - PDi )

where,
PDGiis the real power injection from DG placed at node i, and
PDi is the load demand at node i.
By combining eq.(3.3.4) and eq. (3.3.5) we can get eq.(3.3.6):

)]

(3.3.6)

The above equation gives the optimum size of DG for each bus i, for the loss to be
minimum. Any size of DG other than PDGi placed at bus i, will lead to higher loss. This
loss, however, is a function of loss coefficient and . When DG is installed in the system,
the values of loss coefficients will change, as it depends on the state variable voltage and
angle. Updating values of and again requires another load flow calculation. But
numerical result shows that the accuracy gained in the size of DG by updating and is
small and is negligible. With this assumption, the optimum size of DG for each bus, given
by eq. (3.3.6) can be calculated from the base case load flow (i.e. without GD case).

3.4 PLACEMENT OF DG
Here used is Harmony Search Algorithm and, in next 5 sections, its steps are explained
i) Algorithm and problem parameters initialization:
The optimization problem is formulated as:

Minimize f(x)
subjected to

,i= 1, 2, . . .,N.

where
f(x) is a scalar objective function to be optimized;
22

x is a solution vector composed of decision variables to

is the set of values for each decision variable to
and

, i.e.,

are lower and upper bounds for each decision variable, respectively;

N is the number of decision variables.

The control parameters of HSA are:

HM size (HMS) i.e., the number of solution vectors in the HM;

HM considering rate;

Pitch-adjusting rate;

Number of improvisations or stopping criterion.

ii) HM initialization

Each component of each vector in parental HM, i.e. size of HMS, initialized with a
uniformly distributed random number in between upper and lower bounds i.e.i[

],

where
1iN
This is done for ith component of jth solution vector using following equation:
=

+ rand(0, 1) (

where
j = 1, 2, 3 . . . , HMS.
rand(0, 1) is a uniformly distributed random number lies between 0 and 1.

iii) New harmony improvisation

A new harmony vector

=(

has been generated based on 3 rules:

1} memory consideration;
2} pitch adjustment;
3} random selection.
Generating a new harmony is called improvisation, the value of first decision variable for
23

new vector, in memory consideration, is chosen from anyavalue already existing in current
HM, i.e., froma{

,...,

},with probability HMCR. Theavalues of rest of the decision

variables

are also selectedain the same manner. HMCR, which

varies between 0 anda1, is rate of selecting one value fromaprevious set of values stored in
HM, when (1 HMCR) isarate of the randomly choosing a fresh value from possiblearange
i.e.,

} withaprobabilityof HMCR

also,

withaprobabilityof (1 HMCR)

E.g. an HMCR=0.70 shows that HS algorithm will choose a decisionavariable value from
already stored values inaHM with 70% of probability or fromaentire possible range with
30% of probability. Eachacomponent obtained by this memory considerationais examined
to decide whether it should be pitch adjusted or not. This process usesaPARasafollows:

Pitch-Adjusting Decision ::::

Also

rand(0, 1)*bw

withkprobability PAR

withkprobabilitya(1 PAR)

Where
bw shows an arbitraryadistance bandwidth
rand () represents aauniformly distributed random number betweena0 and 1.
This step is used toagenerate a new potential variation in algorithm andait is comparable to
mutation in standard EAs.a

24

iv) HM update

If newaharmony vector
=(

is betterathan worst harmony in HM, in terms of the objective function,anew harmony is

included in HM, and already existingaworst harmony is excluded from HM. This isaa
selection step of algorithm, whereaobjective function value is evaluated in order to
determineawhether the new variation should be included inaHM or not.

v) Check stopping criterion

If maximum NIais reached, the computation is terminated.

If not,nstep(iii) and step (iv) are repeated.

25

TEST SYSTEM

1
Figure 3.2: Single-line diagram for 33-node radial distribution system [27]

26

CHAPTER 4
RESULTS
Results have been obtained in order to improve voltage profile and minimize real power
losses for33-node radial distribution network considering radial distribution network is
balanced.
BASE CASE
Total no. of nodes or buses = 33
Total no. of branches = 32
Bus No. 1 taken as Reference Bus
Base MVA = 100
Base kVA = 12.66
Without using any DG, the voltage magnitude in per unit at each node of the test system is
shown in Table: 4.1
Table :4.1- Voltage magnitude at each node

Node No.
1
2
3
4
5
6
7
8
9

Voltage magnitude
(p.u.)
1
0.9968
0.9816
0.9736
0.9658
0.9463
0.9426
0.9375
0.9309
27

10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

0.9248
0.9238
0.9223
0.9158
0.9135
0.912
0.9106
0.9085
0.9078
0.9962
0.9921
0.9913
0.9836
0.9776
0.9702
0.9665
0.9443
0.9416
0.9295
0.9209
0.9171
0.9128
0.9118
0.9115

Bus with minimum voltage = 20

Minimum voltage = 0.9078 p.u.
Without using any DG, the Real and Reactive Power Losses at each branch of the test
system is shown in Table: 4.2
Table :4.2- Real and Reactive power losses for Base Case without any DG

Branch.No.

Real Power Losses

Reactive Power Losses

(kW)

(kVAR)

12.195

6.217

51.582

26.272
28

19.799

10.084

18.599

9.473

38.038

32.836

1.913

6.324

4.834

1.598

4.177

3.001

3.558

2.522

10

0.553

0.183

11

0.88

0.291

12

2.664

2.096

13

0.729

0.959

14

0.357

0.318

15

0.281

0.205

16

0.251

0.336

17

0.053

0.042

18

0.161

0.154

19

0.832

0.75

20

0.101

0.118

21

0.044

0.058

22

3.181

2.174

23

5.143

4.061

24

1.287

1.007

25

2.596

1.322
29

26

3.323

1.692

27

11.284

9.949

28

7.824

6.913

29

4.121

2.212

30

1.594

1.575

31

0.213

0.249

32

0.013

0.02

Total Real Power Losses = 202.18 kW

Total Reactive Power Losses = 135.011 kVAR

AFTER DG ALLOCATION
The voltage magnitude (in p.u.) at each node of the test system, using single and 2 DGs is
shown in Table: 4.3
Table: 4.3- Node voltages at each node.

Node No.

without DG

with 1 DG

with 2 DG

1
2
3
4
5
6
7
8
9
10
11
12

1
0.9968
0.9816
0.9736
0.9658
0.9463
0.9426
0.9375
0.9309
0.9248
0.9238
0.9223

1
0.998
0.9891
0.9854
0.982
0.9723
0.9688
0.9641
0.958
0.9523
0.9515
0.95

1
0.9985
0.9924
0.9887
0.9852
0.9754
0.972
0.9673
0.9612
0.9555
0.9547
0.9532
30

13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

0.9158
0.9135
0.912
0.9106
0.9085
0.9078
0.9962
0.9921
0.9913
0.9836
0.9776
0.9702
0.9665
0.9443
0.9416
0.9295
0.9209
0.9171
0.9128
0.9118
0.9115

0.944
0.9418
0.9404
0.9391
0.9371
0.9365
0.9975
0.9939
0.9932
0.9926
0.9855
0.9789
0.9756
0.9725
0.9728
0.9725
0.9728
0.9745
0.9705
0.9696
0.9693

0.9472
0.945
0.9436
0.9423
0.9403
0.9397
0.998
0.9944
0.9937
0.9931
0.9915
0.9902
0.9921
0.9756
0.9759
0.9754
0.9755
0.9771
0.9731
0.9722
0.972

31

1.2

Voltage magnitude in P.U.

0.8

without DG

0.6

with 1 DG
with 2 DG
0.4

0.2

0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Node numbers

Figure 4.1: Plot showing improvement in bus voltages

32

USING SINGLE DG:

Node with Minimum Voltage = 20
Minimum Voltage = 0.9365
USING 2 DGs:
Node with Minimum Voltage = 20
Minimum Voltage = 0.9397
Size of DGs used is shown in Table: 4.4
Table: 4.4- Size of DGs

No. of DG(s)

Size of DG(s)
(kW)

1456

1435 & 901

The Real Power Losses(in kW) for each branch of the test system, using single and 2 DGs is
shown in Table: 4.5
Table: 4.5 Real Power Losses

Branch
No.

Without DG

With 1 DG

With 2 DGs

(kW)
12.195

(kW)
6.1843

(kW)
4.2379

51.582

24.183

16.3812

19.799

7.4493

7.5242

18.599

6.7219

6.7888
33

38.038

13.5669

13.6975

1.913

1.8224

1.8103

4.834

4.6034

4.5726

4.177

3.9762

3.9494

3.558

3.3859

3.363

10

0.553

0.5264

0.5228

11

0.88

0.8376

0.8319

12

2.664

2.5346

2.5173

13

0.729

0.6932

0.6885

14

0.357

0.3395

0.3372

15

0.281

0.2676

0.2658

16

0.251

0.2392

0.2376

17

0.053

0.0505

0.0502

18

0.161

0.1606

0.1605

19

0.832

0.8305

0.8297

20

0.101

0.1006

0.1005

21

0.044

0.0435

0.0435

22

3.181

3.1414

0.5767

23

5.143

5.0787

0.933

24

1.287

1.2711

1.5908

25

2.596

1.5718

1.5239

26

3.323

2.2458

2.1718

27

11.284

8.5935

8.2919
34

28

7.824

6.7801

6.5311

29

4.121

4.7744

4.582

30

1.594

1.4251

1.4174

31

0.213

0.1906

0.1896

32

0.013

0.0118

0.0117

250

200

150
without DG
with 1 DG
100

with 2 DGs

50

0
1

11 13 15 17 19 21 23 25 27 29 31 33
Branch no.

Figure 4.2: Plot showing reduction in real power losses

35

The Reactive Power Losses (in kVAR) for each branch of the test system, using single and
2 DGs is shown in Table: 4. 6
Table: 4.6 Reactive power losses

Branch
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

without DG

with 1 DG

with 2 DGs

(kVAR)
6.217
26.272
10.084
9.473
32.836
6.324
1.598
3.001
2.522
0.183
0.291
2.096
0.959
0.318
0.205
0.336
0.042
0.154
0.75
0.118
0.058
2.174
4.061
1.007
1.322
1.692
9.949
6.913
2.212
1.575
0.249
0.02

(kVAR)
3.1525
12.3172
3.7938
3.4236
11.7116
6.0241
1.5213
2.8567
2.4
0.174
0.277
1.9942
0.9124
0.3021
0.1954
0.3194
0.0396
0.1533
0.7484
0.1175
0.0576
2.1465
4.0104
0.9946
0.8006
1.1434
7.5768
5.991
2.5626
1.4084
0.2222
0.0183

(kVAR)
2.1603
8.3434
3.832
3.4577
11.8243
5.9841
1.5111
2.8374
2.3837
0.1728
0.2751
1.9806
0.9062
0.3001
0.1941
0.3172
0.0393
0.1531
0.7476
0.1174
0.0575
0.3941
0.7367
1.2448
0.7762
1.1058
7.3108
5.771
2.4594
1.4008
0.221
0.0182

36

35

30

Power loss in kVAr

25

20
without DG
with 1 DG
15

with 2 DGs

10

0
1

9 11 13 15 17 19 21 23 25 27 29 31 33
Branch no.

Figure 4.3: Plot showing reduction in Reactive Power Losses

37

USING SINGLE DG:

Total Real Power Losses = 113.6014 kW
Total Reactive Power Losses = 79.3665 kVAR
USING 2 DGs:
Total Real Power Losses = 96.7303 kW
Total Reactive Power Losses = 69.0338 kVAR
The location of DGs used are shown in Table: 4.7
Table: 4.7- Location of DG

No. of DG(s)

Location of DG(s)
(Bus No.)

30

25 & 30

COMPARISON OF RESULTS
The Results obtained using the Proposed Method on 33-node Radial Distribution System
are compared with Voltage Sensitivity Index Method and shown in Table: 4.8
Table: 4.8 Comparison of Results for 33-bus system

METHODS
USED

Using Voltage
Sensitivity Index
Method

Using Proposed
Method
(1 DG)

Using Proposed
Method
(2 DGs)

210.9761

202.18

202.168

PARAMETERS

Total Real Power

Losses
without DG (kW)

38

Minimum Bus
Voltage without DG
(p.u.)

0.9040

0.9078

0.9078

DG Size (kW)

1000

1456

901 & 1435

DG Location (Bus
No.)

16

30

25 & 30

Total Real Power

Losses with DG
(kW)

136.7553

113.6014

96.7303

Minimum Bus
Voltage with DG
(p.u.)

0.9318

0.9365

0.9397

Loss Reduction
(%)

35.1797

43.8082

52.1535

Improvement in
Voltage Profile (p.u.)

0.0278

0.0287

0.0319

39

CHAPTER 5
CONCLUSION & FUTURE SCOPE
5.1 CONCLUSION
The results obtained, i.e. optimal location and size of DGs, by integrating power loss
sensitivity method and HSA in order to minimize real power losses and improve voltage
profile are much better than the previous methods.
5.2 FUTURE SCOPE
Further work could be done on this thesis is to integrate some other pair or algorithms to
obtain improved results.
Also, power factor could be considered in order to record results for different leading and
lagging p.f. conditions.

40

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44

APPENDIX-A
Table (A.1): Line Data for 33-Bus Radial Distribution System [28]
Branch Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

Sending-end
Bus
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
19
20
21
3
23
24
6
26
27
28
29
30
31
32

Receiving-end Bus
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

Branch
Resistance()
0.0922
0.4930
0.3660
0.3811
0.8190
0.1872
1.7114
1.0300
1.0040
0.1966
0.3744
1.4680
0.5416
0.5910
0.7463
1.2890
0.7320
0.1640
1.5042
0.4095
0.7089
0.4512
0.8980
0.8960
0.2030
0.2842
1.0590
0.8042
0.5075
0.9744
0.3105
0.3410

Branch Reactance
()
0.0477
0.2511
0.1864
0.1941
0.7070
0.6188
1.2351
0.7400
0.7400
0.0650
0.1238
1.1550
0.7129
0.5260
0.5450
1.7210
0.5740
0.1565
1.3554
0.4784
0.9373
0.3083
0.7091
0.7011
0.1034
0.1447
0.9337
0.7006
0.2585
0.9630
0.3619
0.5302

45

Table (A.2): Load Data for 33-Bus Radial Distribution System[28]

Bus Number

P(kW)

Q(kVAr)

0.0

0.0

100.0

60.0

90.0

40.0

120.0

80.0

60.0

30.0

60.0

20.0

200.0

100.0

200.0

100.0

60.0

20.0

10

60.0

20.0

11

45.0

30.0

12

60.0

35.0

13

60.0

35.0

14

120.0

80.0

15

60.0

10.0

16

60.0

20.0

17

60.0

20.0

18

90.0

40.0

19

90.0

40.0

20

90.0

40.0

21

90.0

40.0

22

90.0

40.0

23

90.0

50.0

24

420.0

200.0

25

420.0

200.0

46

26

60.0

25.0

27

60.0

25.0

28

60.0

20.0

29

120.0

70.0

30

200.0

600.0

31

150.0

70.0

32

210.0

100.0

33

60.0

40.0

(Base voltage = 12.66 kV, Base VA=100MVA)

47

48