i

LOAD FLOW ANALYSIS OF RADIAL DISTRIBUTION NETWORK

Thesis submitted in partial fulfillment of the requirements for

the award of degree of

Master of Engineering in

Power Systems & Electric Drives

By:

Gurpreet Kaur

(801041008)

Under the supervision of:

Dr. Smarajit Ghosh

Head & Professor, EIED

June 2012

ELECTRICAL & INSTRUMENTATION ENGG

DEPARTMENT

THAPAR UNIVERSITY

PATIALA – 147004

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ACKNOWLEDGMENT

First of all, I thank the Almighty God, who gave me the opportunity and strength to carry out this

work.

I would like to thank Dr. Smarajit Ghosh, Prof. & Head, EIED for the opportunity to work

with him, and also for his encouragement, trust and untiring support. Dr. Smarajit Ghosh has

been an advisor in the true sense both academically and morally throughout this thesis work.

Gratitude is accorded to Thapar University, Patiala, for providing all the necessary facilities to

complete my M.E. Thesis work.

The paucity of words does not compromise for extending my thanks to my all family members

whose uninterrupted love, inspiration and blessings helped me in completing this research report.

I am also thankful to the previous researchers whose published work has been consulted and

cited in my dissertation.

Gurpreet Kaur

801041008

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Dedicated to My Parents

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ABSTRACT

In this thesis, a new method of load-flow technique for solving radial distribution networks by

sequential numbering scheme has been proposed. The aim of my thesis is to reduce data

preparation and propose a method to identify the nodes beyond each branch with less

computation. The simple transcendental equations have been used. Effectiveness of this load

flow method has been tested by taking an example of 69 node radial distribution networks) with

constant power (CP), constant current (CI), constant impedance (CZ) and composite load (CC)

modeling.

The superiority of the proposed method has been compared with the other method [19] available

in literature.

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TABLE OF CONTENTS

CERTIFICATE ii

ACKNOWLEDGEMENT iii

ABSTRACT v

LIST OF FIGURES viii

LIST OF TABLES ix

LIST OF SYMBOLS xi

1. INTRODUCTION 1-20

1.1 POWER DISTRIBUTION SYSTEMS 1

1.1.1 Global design of distribution networks 1

1.2 DISTRIBUTION SYSTEMS 2

1.2.1 Requirements of distribution system 3

1.2.2 Classification of distribution system 4

1.3 DISTRIBUTION SYSTEM TYPES 4

1.3.1 Radial type 5

1.3.2 Ring main type 6

1.3.3 Interconnected type 7

1.4 LOAD FLOW ANALYSIS 8

1.4.1 Choice of variables 11

1.4.2 Bus classification 12

1.4.3 Summary of variables in load flow analysis 14

1.4.4 Basic load flow equations 15

1.5 LITERATURE SURVEY OF LOAD FLOW 16

1.6 SCOPE OF THE RESEARCH 20

1.7 OBJECTIVES OF THE THESIS WORK 20

1.8 ORGANIZATION OF THESIS WORK 20

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2. PROPOSED METHOD 21-39

2.1 PROPOSED METHOD 21

2.2 ASSUMPTION 21

2.3 METHODOLOGY 21

2.4 IDENTIFICATION OF NODES BEYOND ALL BRANCHES 26

2.5 LOAD MODELLING 28

2.6 EXAMPLE 29

2.7 CONCLUSION 39

3. CONCLUSIONS AND FUTURE SCOPE OF WORK 40

3.1 CONCLUSION 40

3.2 FUTURE SCOPE OF WORK 40

REFERENCES 41-44

APPENDIX 45-50

A- Line and load data of 69 node Radial Distribution Network 45-49

B- Biography 50

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LIST OF FIGURES

FIGURE : CAPTION PAGE NUMBER NUMBER

Fig 1.1 : Single line diagram of distribution system 2

Fig 1.2 : Radial system 5

Fig 1.3 : Ring main system 7

Fig 1.4 : Interconnected system 8

Fig 2.1 : Single Line Diagram of Radial Distribution Network 22

Fig 2.2 : Branch of figure 2.1 23

Fig 2.3 : 69 Node Radial Distribution Network 30

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LIST OF TABLES

TABLE NUMBER : CAPTION PAGE NUMBER

Table 1.1 : Variables in Load Flow Analysis 14

Table 2.1 : Branch number (jj), Sending end node (m1 = IS(jj))

Receiving end node (m2 = IR(jj)) of figure 2.1 22

Table 2.2 : Nodes beyond Each Branch of Figure 2.1 25

Table 2.3 : Total Real power load and Reactive Power Load of 69- Node

Radial Distribution Network for CP, CI ,CZ, Composite load

modeling substation voltage 1.0 p.u. 31

Table 2.4 : Voltage of each node in p.u. of each node of 69-Node

Radial Distribution Network for CP, CI, CZ and CC load

modeling 32

Table 2.5 : Real power losses (kW) of each branch of 69-Node

Radial Distribution Network for CP, CI, CZ and CC load

modeling 34

Table 2.6 : Reactive power losses (kVAr) of each branch of 69-Node

Radial Distribution Network for CP, CI, CZ, CC load

modeling 36

Table 2.7 : Total real and reactive power losses of 69-Node Radial

Distribution Network for CP, CI, CZ and CC load

modeling 38

Table 2.8 : Node corresponding to minimum voltage of 69-Node

Radial Distribution Network for CP, CI, CZ and CC load

modeling 38

Table 2.9 : Comparison of relative CPU time and memory requirement

of the proposed method and method [19]. 39

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Table A.1 : Line Data of 69- Node Radial Distribution Network 45

Table A.2 : Load Data of 69-Node Radial Distribution Network 48

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LIST OF SYMBOLS

NB : Total no. of Nodes

LN1 : Total no. of Branches

jj : Branch no. i.e., jj = 1,2,3,………,LN1

m1 : IS(jj) be the Sending end Node of branch-jj

m2 : IR(jj) be the Receiving end Node of branch-jj

m2 : Set of the Receiving end nodes beyond the branch-jj.

N(jj) : Total number of nodes beyond branch-jj

IE(jj, i) : Receiving end node beyond branch-jj.

ISS(jj) : IS(jj) for all jj

IRR(jj) : IR(jj) for all jj

V(m1) : Voltage of Sending end Node of branch- jj

V(m2) : Voltage of Receiving end Node of branch -jj

R(jj) : Resistance of branch- jj

X(jj) : Reactance of branch -jj

Z(jj) : Impedance of branch- jj

I(jj) : Current through the Branch-jj

Ir(jj) : Real Component of I(jj)

Im(jj) : Imaginary Component of I(jj)

PL(m2) : Active Power Load at Node m2

QL(m2) : Reactive Power Load at Node m2

IL(m2) : Load Current at Node m2

LP(jj) : Real Power Loss of Branch- jj

LQ(jj) : Reactive Power Loss of Branch- jj

DVMAX : Maximum Voltage Difference

kVAr : Amount of reactive power

kW : kilo watts

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CHAPTER 1

INTRODUCTION

A planned and effective distribution network is the key to cope up with the ever increasing

demand for domestic, industrial and commercial load. The load-flow study of radial distribution

network is of prime importance for effective planning of load transfer. The power distribution

system and Load flow will be briefed in this introduction.

1.1 Power Distribution Systems

A Distribution network has typical characteristics of its own. Distribution networks design will

be introduced though this article along with clearly defining the differences between country and

urban distribution networks.

1.1.1 Global Design of Distribution Networks

The electric utility system is classified into the following three subsystems:

1. Generation

2. Transmission

Sub-transmission

3. Distribution

Sub-transmission is basically a subset of transmission as the voltage levels and protection

practices are almost similar, however it is sometimes treated as a Fourth Division. The

distribution system is further classified into the following:

Distribution Substation

Distribution Primary

Distribution Secondary

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The voltage is reduced at the distribution substation, it is distributed into smaller amounts

according to the customer requirements and is supplied to many customers thorough the same

distribution substation. Thereby making the total number of transmission lines involved in the

distribution system more than that in the transmission system. The distribution system is

considered as ‘unbalanced’ because of the fact that in a distribution system most of the

customers are connected to only one of the three phases available, thus making the power flow in

each line different, which makes it unbalanced. The load-flow studies related to distribution

network emphasize on this characteristic.

1.2 Distribution Systems

Distribution system is defined as the part of power system which distributes electric power for

local utilization.

Figure 1.1 Single line diagram of distribution system.

In other words, the electrical system between the substation fed by the transmission system and

the consumer’s meter is known as the distribution system. The basic elements of a distribution

system are feeders, distributors and the service mains. Figure 1.1 depicts the single line diagram

of a typical low tension distribution system.

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(i) Feeders: A feeder is essentially a conductor, connecting the localized generating station (or

the sub-station) to the desired area where power has to be distributed. In order to keep the current

in the feeder same throughout, generally no tappings are taken from the feeder. The current

carrying capacity is the main point of focus during design of a feeder.

(ii) Distributor: A distributor is basically a conductor from which tappings are taken for supply

to the consumers. In Figure1.1, AB, BC, CD, and DA represent the distributors. Since tapping

are taken at various places along the length of the distributor, the current through it is not

constant. The voltage drop across the length of the distributor is the main point of focus during

its design, as the statutory limit of voltage variations is ±10% of rated value at the consumer’s

terminal.

(iii) Service mains: A service mains is generally a small cable which connects the distributor to

the consumer terminals.

1.2.1 Requirements of a Distribution System

It is mandatory to maintain the supply of electrical power within the requirements of many types

of consumers. Following are the necessary requirements of a good distribution system:

1) Availability of power demand: Power should be made available to the consumers in large

amount as per their requirement. This is very important requirement of a distribution system.

2) Reliability: As we can see that present day industry is now totally dependent on electrical

power for its operation. So, there is an urgent need of a reliable service. If by chance, there is a

power failure, it should be for the minimum possible time at every cost. Improvement in

reliability can be made upto a considerable extent by

a) Reliable automatic control system.

b) Providing additional reserve facilities.

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3) Proper voltage: Furthermost requirement of a distribution system is that the voltage variations

at the consumer terminals should be as low as possible. The main cause of changes in voltage

variation is variation of load on distribution side which has to be reduced. Thus, a distribution

system is said to be only good, if it ensures that the voltage variations are within permissible

limits at consumer terminals.

4) Loading: The transmission line should never be over loaded and under loaded.

5) Efficiency: The efficiency of transmission lines should be maximum say about 90%.

1.2.2 Classification of Distribution System A distribution system may be classified on the basis of:-

i) Nature of current: According to nature of current, distribution system can be classified as

a) AC distribution system.

b) DC distribution system.

ii) Type of construction: According to type of construction, distribution system is classified as

a) Overhead system

b) Underground system

iii) Scheme of operation: According to scheme of operation, distribution system may be

classified as:

a) Radial system

b) Ring main system

c) Interconnected system

1.3 Distribution System Types

Here the distribution type has been discussed on the basis of scheme of operation. All

distribution of electrical energy is done by constant voltage system. In practice, the following

three types of distribution circuits are generally used in distribution system:

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1.3.1 Radial System

A schematic example of a radial distribution system is shown in Figure 1.2. In this system,

primary feeders take power from the distribution substation to the load areas by way of sub

feeders and lateral-branch circuits. This is the most common system used because it is the

simplest and least expensive to build. It is widely used in sparsely populated areas. A radial

system has only one power source for a group of customers

Radial feeders are characterized by having only one path for the power to flow from the source

(distribution substation) to each customer. If the distributor is connected to the supply system on

one end only, that system is called radial distribution system. A typical radial distribution system

is as shown below.

Figure 1.2 Radial System

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The radial system is employed when the power is generated at low voltage and the substation is

located at the center of the load.

The consumers at the end of distributor would be subjected to serious voltage fluctuations when

the load on distribution changes. The advantages of radial system are its simplicity, and low cost,

the amount of switching equipment required is small and protective relaying is simple. The

major disadvantage of radial system is its lack of security of supply.It is not the most reliable

system, however, because a fault or short circuit in a main feeder may result in a power outage to

all the users served by the system. Service on this type of system can be improved by installing

automatic circuit breakers that will reclose the service at predetermined intervals. If the fault

continues after a predetermined number of closures, the breaker will be locked out until the fault

is cleared and service is restored.

1.3.2 Ring main system

The loop (or ring) distribution system is one that starts at a distribution substation, runs through

or around an area serving one or more distribution transformers or load centres, and returns to

the same substation. The loop system shown in Fig 1.3 is more expensive to build than the radial

type, but it is more reliable and may be justified in areas where continuity of service is

required—at a medical centre, for example. In the loop system, circuit breakers sectionalize the

loop on both sides of each distribution transformer connected to the loop. A fault in the primary

loop is cleared by the breakers in the loop nearest the fault, and power is supplied the other way

around the loop without interruption to most of the connected loads. If a fault occurs in a

section adjacent to the distribution substation, the entire load can be fed from one direction over

one side of the loop until repairs are made.

The ring main system has the following advantages:

a) There are very less voltage fluctuations at consumer’s terminals.

b) The system is very reliable as each distributor is fed with two feeders. In case, of fault in any

section of feeder, the continuity of supply is maintained.

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Figure 1.3 Ring Main System

1.3.3 Interconnected system

The network system shown in Fig 1.4 is the most flexible type of primary feeder system. It

provides the best service reliability to the distribution transformers or load centres, particularly

when the system is supplied from two or more distribution substations. Power can flow from any

substation to any distribution transformer or load centre in the network system. The network

system is more flexible about load growth than the radial or loop system. Service can

readily be extended to additional points of usage with relatively small amounts of new

construction. The network system, however, requires large quantities of equipment and is,

therefore, more expensive than the radial system. For this reason it is usually used only in

congested, high load density municipal or downtown areas. When the feeder ring is energized by

two or more than two generating stations or sub stations, it is called inter-connected system.

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Figure1.4 Interconnected Systems

The ring main system has the following advantages:

a) It increases the service reliability.

b) Any area fed from one generating station during peak load hours can be fed from other

generating station. This helps in decreasing reserve power capacity and increases the efficiency

of the distribution system.

1.4 Load Flow Analysis

The operating state of an entire power system; i.e. network of generators, transmission lines, and

loads representing areas ranging from small municipality to several states; can be described with

load-flow analysis. If the amount of power generated and consumed at different locations is

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known then load flow analysis can be used to determine the other quantities. One of the

important quantities is voltage at different locations throughout the transmission system, for

which the alternating current (AC) consists of both magnitude and a time element or phase angle.

After determining the voltage at different locations, the current flowing through the entire

transmission link can be obtained. In a nutshell, if an amount of power delivered and where it

comes from is given, power flow analysis can be used to determine how it flows into its

destination. It is a very arduous task to determine what is happening at one part of a system for

given working conditions of another part of the system, even though their working is related by

deterministic laws of Physics. This is mainly because of the peculiar characteristics of AC

current and the complexity and size of a real power system; i.e. the elaborate topology including

many nodes and links, and large number of generator and loads. It is difficult to establish

relationships between all variables and obtain a formula, even for a small network of small

number of AC power sources and loads.

In mathematics, analytical solution cannot be obtained for it and a numerical solution is only

possible thorough a process of successive iterations. The entire system needs to be simulated to

find out the voltage or current at any given point. Earlier simulations were done through

miniature DC models of power system in use. DC power units were used to represent generators,

resistors for loads and appropriately sized wires for transmission lines. Then by measurement the

voltages and currents could be found out empirically. As an example, to find out the increase in

current on line A due to Generator X taking over power production from Generator Y, adjust the

values on X and Y and read the ammeter on line A. The DC model gives an approximation for

most practical purposes but not the exact match of the behavior of the AC system. Nowadays, a

computer can be used to represent both the DC and AC system, eliminating the need to build

these models physically, that accounts for peculiarities of the AC. Such a simulation uses load-

flow analysis.

Load flow utilizes a mathematical algorithm that approximates a solution through successive

iteration. These are basically a process of trial and error starting with an assumed value of array

of numbers for the entire system, it ten compares with the relationship of the numbers to the laws

of physics and continuously adjusts the numbers until the entire array is consistent with both

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physical law and the conditions stipulated by the user. Practically, it is a computer program

taking information about power system as input from the user, and provides the complete

working of the system as output. Different computational techniques are used and various types

of information are chosen as input and output for different programs. The straightforward load-

flow program simply calculates the variables pertaining to a single, existing system condition.

There are also more involved programs known as optimal power flow which analyze a multitude

of hypothetical situations or system conditions and rank them according to some desired criteria.

Planning, design and operation of distribution system for industrial facilities require load flow

study, which is used to evaluate the effects of additions or modifications to generators, motors, or

other electrical loads and various equipment configurations. Modern systems are complex and

power can flow through various paths or branches. The Kirchoff’s laws determine distribution of

electric power flow among these branches.

Typically the input data is divided into

Bus data

Branch data

Generator data

Transformer data

Load data

In order to document the system load configuration that the solution applies for , this data is

included with every load flow output file. The load flow study should have the following criteria

that the system evaluated must meet:

Voltage criteria

Power flows on cables and transformers must be within equipment ratings.

Generator reactive outputs must not be more than the limits defined by the generator

capability curves.

The load flow analysis designs a system that has a good voltage profile during normal operation

and that will continue to operate acceptably when one or more lines become inoperative due to

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line damage, lightning strokes, failure of transformers, etc. Also, load flow helps to study the size

and placement of power factor correction capacitors and the setting of generator scheduled

voltages and transformer tap positions.

The load flow study plays an important role in determining the best operation of existing systems

and planning the future expansion of power systems. In the nutshell, the load flow study gives

the magnitude and phase angle of the voltage at each bus and the real and reactive power flowing

in each line.

1.4.1 Choice of Variables

Since the load flow analysis deals with the known real and reactive power flows at each bus,

with known voltage magnitudes, the remaining voltage magnitudes and all the voltage angles can

be calculated from this information. The descriptive variables of the circuit should be organized

into ‘known variables’ and ‘unknown variables’ and then establish their relationships in terms of

equations. Then with the given information the equations should be manipulated to yield the

desired numerical results for the ‘unknown variables’. AC circuits utilize the dimension of time,

unlike in DC, where everything is static (except for the instant at which a switch is thrown), thus

AC describes an ongoing oscillation or movement. Each of the two main variables, voltage and

current, in an AC circuit has two numerical components: a magnitude component and a time

component. By convention, the magnitudes of AC voltage and current are described in terms of

root-mean-squared (r.m.s.) values and their timing in terms of a phase angle, which represents

the shift of the wave with respect to a reference point chosen in time. Thus, in order to describe

voltage or current at any given node in an AC circuit, it is essential to specify two quantities: a

voltage/current magnitude and a voltage/current angle.

While considering the amount of power transferred at any point of an AC circuit, two quantities

are taken into account: real and a reactive component. Thus, to completely determine an AC

circuit, exactly two pieces of information per node in is required. Lesser quantity will not lead to

a solution and more than two quantities would be redundant. Because of the nonlinear nature of

the load flow problem, it is impossible to find unique solution as more than one answer is

mathematically consistent with the given configuration. Thus, a ‘true’ solution is identified

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among the various mathematical solutions available based on physical plausibility and common

sense. Also, it is possible that there might be no solution, as the provided information might not

correspond to any physical situation. But two variables per node are needed to determine

everything that is happening in the system. Practically, current is unknown and current through

the various circuit branches is calculated at the end of load flow analysis. Voltage is known for

some buses only but the amount of power going in or out of the bus is known for all. Load flow

analysis takes into the account all the known real and reactive power flows at each bus, and the

voltage magnitudes that are explicitly known, and then calculates the remaining voltage

magnitudes and all the voltage angles. After this the current magnitudes and angles from the

voltages are calculated. Real and refractive power can be calculated from voltage and current as

power being the product of voltage and current, and the relative phase angle between voltage and

current gives the respective contributions of real and reactive power. Although it is

mathematically difficult but, voltage or current magnitude and angle can be calculated if real and

reactive power are given, as each value of real and reactive power would be consistent with

many different possible combinations of voltages and currents. Thus, to choose the correct

combination, each node is checked in relation to its neighboring nodes in the circuit and a set of

voltages and currents are determined that are consistent all the way around the system.

1.4.2 Bus classification

There are three types of bus in power system. Each bus in the system has four variables: voltage

magnitude, voltage angle, real power and reactive power. During the operation of the power

system, each bus has two known variables and two unknowns. And following are the bus types:

Slack or Swing Bus

This bus is considered as the reference bus. The swing/slack bus is distinguished from others by

the fact that real and reactive powers at this bus are not specified. Usually, there is only one bus

of this type in a given power system. It must be connected to a generator of high rating relative

to the other generators. During the operation, the voltage of this bus is always specified and

remains constant in magnitude and angle. In addition to the generation, this bus is also

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responsible for supplying the losses to the system. Here the voltage and the phase angle are

specified. Typically it is denoted as V1∠δ1 = 1∠0. The slack bus is numbered 1, for

convenience. Net power flows cannot be fixed in advance at every generating bus because the

network power losses are not known until the study has been completed. The generators at the

swing bus supply the difference between the specified real power into the system at the other

buses and the total system output plus losses. The power flow computes the real power P1 and

reactive power Q1.

Generator or Voltage Controlled Bus /PV Bus

During the operation the voltage magnitude at this bus is kept as constant. This bus has always a

generator connected to it where the voltage is controlled using the excitation and the power is

controlled using the prime mover control. Here the known are real power and voltage and

unknowns are reactive power and phase angle. PV buses comprise about 10% of all the buses in

a power system.

Sometimes, this bus is connected to a VAR device where the voltage can be controlled by

varying the value of the injected VAR to the bus.

Load Bus /PQ Bus

At this type of bus, the net powers real and reactive are known. The unknowns are voltage and

phase angle. A pure load bus (no generating facility at the bus)is a PQ bus. PQ buses are the

most common, comprising almost 80% of all the buses in a given power system.

Let us now articulate which variables will actually be given for each bus as inputs to the analysis.

Now we must distinguish between different types of buses. The two main types are generator

buses and load buses, for each of which it is required to specify concerned information. At the

load bus, we assume that the power consumption is given that is real and reactive power, for

each load bus. Referred to the symbols P and Q for real and reactive power, load buses are

denoted by PQ buses in load flow analysis.

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At the generator buses we could in principle also specify P and Q. Here it arises two problems.

However, the first has to do with balancing the power needs of the system, and the second with

the actual operational control of generators. Therefore, it turns out to be more convenient to

specify P for all but one generator, the slack bus, and to use the generator bus voltage, V, instead

of the reactive power Q as the second variable. Therefore generator buses are called PV buses.

1.4.3 Summary of variables in Load Flow analysis

To summarize, there are three types of buses in load flow analysis and these are PQ (load bus),

PV (generator bus), and θ V (slack bus). If we are given the two input variables per bus, and

knowing all the fixed values of the system (i.e., the impedances of all the transmission links, as

well as the AC frequency), we have all the information which is required to determine the

operating state of the system. This means that we can find values for all the variables that were

not originally specified for each bus: θ and V for all the PQ buses; θ and Q for the PV buses; and

P and Q for the slack bus. The known and unknown variables for each type of bus are shown in

Table 1.1.

Table-1.1: Variables in Load Flow Analysis

Type of bus Variables known Variables unknown

Generator Real power (P)

Voltage magnitude (V)

Reactive power (Q)

Voltage angle (θ)

Load or generator Real power (P)

Reactive power (Q)

Voltage angle (θ)

Voltage magnitude (V)

Slack Voltage angle (θ)

Voltage magnitude (V)

Real power (P)

Reactive power (Q)

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1.4.4 Basic Load Flow equations

Assuming a system having n buses, the injected current to the bus (node) k can be expressed as:

∑

Where is the proper element in the bus admittance matrix YBus

and,

| |∠ | |∠

The complex power at bus k ( k = 1,2, ..,n) is given as:

∑

| | ∑ | |

| |

| | ∑ | |

| |

where, Pk

and Qk

are the active and reactive power injection at bus k respectively. Thus, at each

bus we have two equations and four variables ( P, Q, δ, V ). Note that Y's and θ's are known from

network data. Actually, at each bus we have to specify two variables and solve for the remaining

two unknowns. Thus, for an N bus system 2N equations are solved. These 2N equations are

nonlinear equations as they involve products of variables as well as sine and cosine functions.

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1.5 Literature Survey of Load Flow

Load-flow analysis has always been the top most concern of electrical engineers. It is an

important area of activity as it is the final link between bulk power systems and consumers. A

few methods have been discussed in the literature for load-flow analysis of distribution system.

As the distribution network is radial in nature having high R/X ratio whereas the transmission

system is loop in nature having X/R ratio. Therefore, the variables used for load flow analysis of

distribution systems are different from that of transmission systems. The distribution networks

are known as ill-conditioned. The conventional Gauss Seidel (GS) and Newton Raphson (NR)

method does not converge for the distribution networks.

In the literature, there are a number of efficient and reliable load flow solution techniques, such

as; Gauss-Seidel, Newton-Raphson and Fast Decoupled Load Flow [1-7]. In 1967, Tinney and

Hart [1] developed the classical Newton based power flow solution method. Later work by Stott

and Alsac [2] made the fast decoupled Newton method. The algorithm made by [2] remains

unchanged for different applications. Even though this method worked well for transmission

systems, its convergence performance is poor for most distribution systems due to their high R/X

ratio which deteriorates the diagonal dominance of the Jacobian matrix. For this very reason,

various other types of methods have been presented. Those methods consist of back/forward

sweeps on a ladder system. The formulation and the algorithm of those methods were different

from the Newton’s power flow method, which made those methods hard to be extended to other

applications in which the Newton method seemed more appropriate.

Iwamoto and Tamura [8] proposed an algorithm that is based on the modification of

conventional Newton-Raphson method for the solution of ill-conditioned power systems. The

solution of load flow problem never diverges by this algorithm but this method was quite time

consuming and complex.

Tripathy et al. [9] presented a Newton like method for solving ill-conditioned power systems.

Their method showed voltage convergence but could not be efficiently used for optimal power-

flow calculations.

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Kersting [10] developed a technique for solving the load-flow problem in radial distribution

networks which is based on ladder network theory in the iterative routine. The solution was very

complicated and had many assumptions for a typical distribution system. In other words the

method was not designed to efficiently solve for meshed networks. Also Stevens et al. [11]

demonstrated that the ladder based technique was very fast but did not guarantee convergence.

Shirmohammadi et al. [12] presented a new compensation-based power flow method for radial

distribution system and then it was extended for the solution of weakly meshed distribution

system. The technique used is multiport compensation technique with some basic formulations

of Kirchoff’s law. The technique involves two step procedure in which first branch currents are

computed that is backward sweep and then bus voltages are updated that is forward sweep. This

method undoubtedly was more efficient than the Newton-Raphson power flow technique when

used for solving radial and weakly meshed distribution networks but needed a rigorous data

preparation. In improved version [13] branch power flow was used instead of branch complex

currents for weakly meshed transmission and distribution networks by Luo.

Renato [14] presented method in which the voltage magnitude at the receiving end is related to

the voltage at sending end and branch power flow. But the problem arises was that only voltage

magnitudes are computed not bus phase angles which was later used by Das et al. in [15].

Goswami and Basu [16] presented a direct method for solving radial and meshed distribution

networks where any node in the network could not be the junction of more than three branches.

Their method had the advantages of a no convergence problem, a guaranteed accurate solution

for any distribution system, and the ease with which composite loads could be represented. The

disadvantages were difficulty in numbering the nodes and branches. They had used sequential

branch and node numbering scheme.

Das et al. [17] had proposed a load-flow technique for solving radial distribution networks by

calculating the total real and reactive power fed through any node using power convergence with

the help of coding at the lateral and sub lateral nodes for large system that increased complexity

18

of computation. This method worked only for sequential branch and node numbering scheme.

They had calculated voltage of each receiving end node using forward sweep. They had taken the

initial guess of zero initial power loss to solve radial distribution networks. It can solve the

simple algebraic recursive expression of voltage magnitude and all the data can be easily stored

in vector form, thus saving an enormous amount of computer memory.

Haque [18] presented a new and efficient method for solving both radial and meshed networks

with more than one feeding node. The method first converted the multiple-source mesh network

into an equivalent single-source radial type network by setting dummy nodes. Then the

traditional ladder network method could be applied for the equivalent radial system. Unlike other

method effect of shunt and load admittances are incorporated in this method because of which it

can be employed to solve special transmission networks. This method has excellent convergence

for radial network.

Ghosh and Das [19] had proposed a load−flow method for solving radial distribution networks

which is based on the technique with nodes beyond branches using voltage convergence. Flat

voltage start had been considered. They had also shown that the proof of convergence. The

incorporation of charging admittances reduces losses and improves voltage profile. The main

drawback of this method was that it stores nodes beyond each branch. Computationally, the

proposed method is very efficient.

Eminoglu and Hocaoglu [20] presented a simple and efficient method to solve the power flow

problem in radial distribution systems which took into account voltage dependency of static

loads, and line charging capacitance. The method was based on the forward and backward

voltage updating by using polynomial voltage equation for each branch and backward ladder

equation. The proposed power flow algorithm has a robust convergence ability when compared

with the improved version of the classical forward-backward ladder method, i.e., Ratio-Flow.

Bijwe et al. [21] had proposed fuzzy based method for weakly meshed balanced and unbalanced

distribution systems. The method can handle simultaneous presence of several uncertainties in

19

input variables such as network parameters, load model coefficients, load forecast, and bus

shunts.

Sivanagaraju et al. [22] proposed a distinctive load flow solution technique which is used for

the analysis of weakly meshed distribution systems. A branch-injection to branch-current matrix

is formed (BIBC) and this matrix is formed by applying Kirchhoff’s current law for the

distribution network. Using the same matrix that is BIBC a solution for weakly meshed

distribution network is proposed.

Ghosh and Sherpa [23] proposed a method for load-flow solution of radial distribution

networks with minimum data preparation. Here the node and branch numbering need not to be

sequential like other available methods. This method only needs sending node, receiving node

and branch numbers if those were sequential. The presented method used the simple equation to

compute the voltage magnitude and had the capability to handle composite load modelling. This

method used the set of nodes of feeder, lateral(s) and sub lateral(s) if not sequential.

Aravindhababu et al. [24] proposed a simple and efficient branch-to-node matrix-based power

flow method for radial distribution systems but this method was unsuitable for optimal power

flow for which the NR method seems to be more appropriate. In that method any presence of sub

laterals complicates the matrix formation.

Augugliaro et al. [25] had proposed a method for the analysis of radial or weakly meshed

distribution systems supplying voltage dependent loads. The solution process is iterative and at

every step loads are simulated by impedances. Therefore it is necessary to solve a network made

up only of impedances; for radial systems, all the voltages and currents are expressed as linear

functions of a single unknown current and for mesh system two unknown currents for each

independent mesh. Advantages of this method are: its possibility to take into account of any

dependency of the loads on the voltage, very reduced computational requirements and high

precision of results.

20

1.6 Scope of the Research

Literature survey shows that a number of methods had been proposed for load-flow solution of

radial distribution networks. In some cases authors had used the data as it is without reducing

data preparation and in some cases authors have tried to reduce the data preparation. Since the

distribution system is radial in nature having high R/X ratio, the load flow methods become

complicated. There is a scope to propose software to compute the nodes beyond each branch

with less computation as compared to Ghosh and Das [19].

1.7 Objectives of the Thesis Work

The objective of this thesis work is to propose a new algorithm to identify nodes beyond each

branch without any rigorous computation technique. Hence load flow method will be faster and

require less memory.

1.8 Organization of Thesis Work

Chapter 1 shows the introduction of distribution system, literature survey on loadflow,

objectives of the research, scope of the research and organization of the research.

Chapter 2 presents the proposed method for loadflow analysis of radial distribution networks.

The assumption, solution methodology, load modelling, algorithms, examples and results and

the conclusion.

Chapter 3 presents the summary of conclusion and the future scope of further research work.

References present the list of previous papers published by researchers in load flow surveyed by

the author and also the books in this area.

Appendix A shows the line data and load data of 69 node radial distribution network available

in [4].

Appendix-B Biography

21

CHAPTER 2

PROPOSED METHOD

2.1 Proposed method

The distribution system is radial in nature whereas transmission system is loop in nature. The

distribution system has high R/X ratio whereas transmission system has high X/R ratio.

Convergence of load flow is utmost important. The load-flow methods proposed for transmission

systems do not converge for distribution systems. Literature survey of load-flow for radial

distribution networks has already been presented in Article 1.5 of Chapter1.

The voltage of each node is computed using simple transcendental equations. Although the

present method is based on forward sweep and backward sweep, it computes load-flow of any

radial distribution networks very efficiently.

A 69node radial distribution network with constant power (CP), constant current (CC),constant

impedance (CZ),composite has been considered .

2.2 Assumption

It is assumed that the three phase distribution network is balanced and the charging capacitance

has been neglected. The network can be represented by its single line diagram.

2.3 Methodology

Fig. 2.1 shows the single line diagram of a radial distribution network. Table 2.1 shows the

branch number, sendingend node and receivingend node of Figure 2.1.

22

Table 2.1: Branch number (jj), Sending end node (m1 = IS(jj)), Receiving end node

(m2 = IR(jj)) of Figure 2.1

Branch Number

(jj)

Sending end

m1 = IS(jj)

Receiving end

m2 = IR (jj)

1 1 2

2 2 3

3 3 4

4 4 5

5 5 6

6 3 7

7 7 8

8 8 9

9 5 10

10 10 11

1 2 3 4 5

6

7

8

9

10 Bold Numbers

represent

branch numbers

1 3 2 4 6 5

7

8

9

11

10

Figure 2.1 Single Line Diagram of Radial Distribution Network

S/S

23

Figure 2.2 shows a branch of Figure 2.1. For branchjj, m1 is the sendingend node and m2 is

the receivingend node.

Current through the branchjj is expressed by

2m 2)m(V

2)mjQ(2)mP(I(jj)

θZ

δ(m2)V(m2)δ(m1)V(m1)

where m2 are set of the receivingend nodes beyond the branchjj.

i.e.,

m22m 2)m(V

2)mjQ(2)mP(

(m2)V

jQ(m2)P(m2)

θZ

δ(m2)V(m2)δ(m1)V(m1)

i.e., jb)(a(m2)V

jQ(m2)P(m2)

θZ

δ(m2)V(m2)δ(m1)V(m1)

where

jjk

mr

m22m

(k)]jI(k)[I2)m(V

2)mjQ(2)mP(jba

i.e., θZ (m2)jb)V(aθZjQ(m2)][P(m2)(m2)Vδ(m2)V(m2)δ(m1)V(m1)

i.e., 0θZjQ(m2)][P(m2)θZ (m2)jb)V(a)δ(δV(m2)V(m1)V(m2) 21

2

i.e., 0jf)(e (m2)jd)V(c)δ(δV(m2)V(m1)V(m2) 21

2 (2.1)

where X(jj)] j[R(jj)](k)I j(k)[IθZjb)(ajdcjjk

mr

m1 m2

jj

Figure 2.2 Branch of figure 2.1

24

jjk

m

jjk

r

jjk

m

jjk

r R(jj) (k)IX(jj) (k)I jX(jj) (k)IR(jj) (k)I (2.2)

and X(jj)] jjj)jQ(m2)][R([P(m2)jfe

]Q(m2)R(jj))[P(m2)X(jj j Q(m2)X(jj)P(m2)R(jj) (2.3)

Putting 1 2 0 , we have from Eq. (2.1),

0fV(m2))sin ccos d(j

eV(m2))sin dcos c(V(m1)2

V(m2)

22

22

(2.4)

Equating real and imaginary parts of Eq. (2.4), we have

0eV(m2))sin dcos c(V(m1)2

V(m2) 22

(2.5)

0fV(m2))sin ccos d( 22 (2.6)

The roots of Eq. (2.5) will be real if

04e)sin dcos c(V(m1)2

22 (2.7)

where

jjk

m

jjk

r X(jj) (k)IR(jj) (k)Ic (2.8)

and Q(m2)X(jj)P(m2)R(jj)e (2.9)

The load current of any receivingend node m2 = IR(jj) of branchjj is expressed by

(m2)*V

jQL(m2)PL(m2)IL(m2)

(2.10)

The real and reactive power losses of branchjj are expressed by

R(jj)2

I(jj)LP (2.11)

25

and X(jj)2

I(jj)LQ (2.12)

respectively.

The current through branchjj is the sum of all load currents of all nodes beyond branchjj i.e.,

I(jj) =

N(jj)

1i

i)IE(jj,IL (2.13)

where N(jj) is the total number of nodes beyond branch jj and IE(jj, i) is the receiving-end node

beyond branchjj. Table 2.2 shows the nodes beyond each branch of Figure 2.1.

Table 2.2 Nodes beyond Each Branch of Figure 2.1

Branch

Number (jj)

Nodes beyond Branchjj Total Number of Nodes

beyond Branchjj

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

2 3,4,5,6,7,8,9,10,11 9

3 4,5,6,10,11 5

4 5,6,10,11 4

5 6 1

6 7,8,9 3

7 8,9 2

8 9 1

9 10,11 2

10 11 1

26

To compute the current through each branch, the storing of nodes beyond each branch is required

which is a tedious task for any network having large number of nodes and laterals and

sublaterals. To reduce the computational work a method is proposed below. This method only

needs the starting node of each lateral and sublateral.

2.4 Identification of Nodes beyond All the Branches

In Figure 2.1, the starting node of lateral 1 is 3 and that of lateral 2 is 5. The nodes of the

network shown in Figure 2.1 are S1={1,2,3,4,5,6,7,8,9,10,11}. The set of nodes of feeder is F =

{2,3,4,5,6}.The set of nodes of lateral 1 is L1 = {3,7,8,9} and that of lateral 2 is L2 = {5,10,11}.

If we look the Table 2.2, the nodes beyond branch-1 becomes all the nodes of S1 excluding the

source node of S1 i.e, the set becomes {2,3,4,5,6,7,8,9,10,11}. If we consider branch-2, the

nodes beyond it becomes all the nodes except node 2 of the previous set i.e.,

{2,3,4,5,6,7,8,9,10,11}. Hence the set becomes {3,4,5,6,7,8,9,10,11}. If we consider beanch-3,

the node number 3 is the sending-end node of branch-3. Hence node 3 cannot be taken into

account. Since the node 3 is also the source node of L1 and the lateral 1 consists of the nodes

3,7,8,9, the nodes beyond the branch-3 are 4,5,6,10,11 i.e., the elements of L1 have been

removed from the set {3,4,5,6,7,8,9,10,11}. Similarly, if we consider the branch-4, the nodes

beyond the branch-4 becomes all the nodes beyond the branch-3 excluding the node 4 i.e., 5,6

10,11. If we consider the branch-5, the sending-end node of this branch becomes 5, which is also

the source node of lateral 2. The other nodes of this lateral is 10 and 11. Hence the nodes beyond

the branch-5 become 6 only. The nodes of lateral 2 have been removed from the set {5,6 10,11}.

The nodes beyond the branch-6 are 7,8 and 9 i.e, all the nodes of L1 except the source node of

it. The nodes beyond the branch-7 are 8,9. The node beyond the branch-8 is 9 only, which is the

last element of L1. The second node of L2 is 10 i.e., 9 + 1 i.e., the end node of L1 +1. The nodes

beyond the branch-9 are all the nodes of L2 except the source node of L2. Hence the nodes

beyond the branch-9 are 10 and 11. The nodes beyond the branch-10 is the last element of L2

i.e., the node 11. From above we see that three sets are required here instead of 10 sets. Hence

this method needs reduced storage of memory.

27

The algorithm of proposed software to identify the nodes beyond each branch is shown below.

Step 1 : Start

Step 2 : Read total number of branches (jj) and total number of nodes (NB).

Step 3 : Read the set of all nodes, set of nodes of laterals and sublaterals.

Step 4 : k = 1

Step 5 : Check the first element of the main set of nodes (M) and the first

element of laterals and sublaterals.

Step 6 : If it does not match, remove the first element of the of the main set

of nodes and get the subset (SB). Otherwise, remove the elements

of the set with which the first element of M matches and get the

subset (SB).

Step 7 : M is replaced by SB in the first iteration and in all other iteration

SB(old) is replaced by SB(new).

Step 8 : k = k +1

Step 9 : If k ≤ jj , go to Step 5 else go to Step-10.

Step 10 : Stop

The complete algorithm for computation of voltage of each node and losses of the network is

shown below.

The algorithm for computation the value of VSI at all nodes and identification of most sensitive

node is presented below.

Step 1 : Read the system data

Step 2 : Set V(i) =1.0 + j 0.0 for all i i.e., i =1,2,….,NB

Set VV(i) = V(i) for all i i.e., i = 1,2,…….,NB

Step 3 : Set ISS(jj) = IS(jj) and IRR(jj) = IR(jj) for

jj = 1,2,3,………,LN1

Step 4 : Set iteration count m =1

Step 5 : Set kMAX = 100(say)

28

Step 6 : Set DVMAX = 0.0 and = 0.00001

Step 7 : Identify the nodes beyond each branch using proposed method.

Step 8 : Compute load currents IL(m2) for all the node m2 i.e., for

m2 =2,3,4,….,NB using Eq. (2.10).

Step9 : Compute the current through each branch i.e., I(k) for all k i.e.,

k = 1,2,3,…..,jj using Eq. (2.13).

Step 10 : Set jj =1

Step 11 : Set m1 = ISS(jj) and m2 = IRR(jj). Compute receivingend voltage

V(m2) for all m2 using the feasible root of Eq. (2.5).

Step 12 : Compute the absolute change in voltage at node m2 i.e.,

DV(m2) = ABS(|V(m2)| |VV(m2)|)

Step 13 : jj = jj + 1

Step 14 : If jj < LN1, go to Step11, otherwise go to Step15

Step 15 : Find max value of DV(m2) from DV(m2) for m2 =2,3,4,….,NB.

Step 16 : DVMAX = DV(m2)

Step 17 : If DVMAX < go to Step21 else go to Step8.

Step 18 : m = m + 1

Step 19 : Set VV(m2) = V(m2) for m2 = 2,3,……….,NB.

Step 20 : If m < kMAX, go to Step8, otherwise go to Step22.

Step 21 : Print “Solution has converged”. Display the result.

Step22 : Print “Does not converge”.

2.5 Load Modeling

Load modeling has a crucial role in voltage stability analysis of a distribution network system.

Every load depends upon the voltage and frequency in the distribution system. A balanced load

is being considered in this thesis that can be represented either as constant power, constant

current, constant impedance or as an exponential load. The method of load-flow analysis must

have the capability to handle all types of load modeling. Equation (2.14) and (2.15) shows the

load modeling.

29

( ) ( )

(2.14)

( ) [ ( ) ( )

( )] (2.15)

where, and are nominal real and reactive power respectively and V(FN(i,j)) is the voltage at

node m2.

For all the loads, Eq. (2.14) and Eq. (2.15) are modeled as

(2.16)

(2.17)

For constant power (CP) load = = 1 and = = 0 for i = 1, 2, 3. For constantcurrent (CI)

load = = 1 and = = 0 for i = 0, 2, 3. For constant impedance (CZ) load = = 1 and

= = 0 for i = 0, 1, 3. Composite load modeling is combination of CP, CI and CZ. For

composite load = = 0 and = = 1 for i = 0, 1, 2. For exponential load = = 1 and

= = 0 for i = 0, 1, 2 and e1 and e2 are 1.38 and 3.22 respectively.

2.6 Example

One example has been considered to demonstrate the effectiveness of the proposed method. The

example is 69-node radial distribution network (nodes have been renumbered with Substation as

node 1) shown in Figure 2.3. Data for this system is available in [4] shown in Appendix-A. Table

2.3 shows the total load on the system for constant power (CP), constant current (CI), constant

impedance (CZ) and composite load modeling (CC) respectively. Table 2.4 shows the voltage of

each node in p.u. for constant power (CP), constant current (CI), constant impedance (CZ) and

composite load modeling (CC) respectively. Real power losses (kW) of each branch for this

system for CP, CI, CZ and Composite load (40% CP + 30% CI + 30% CZ) modeling is shown

in Table 2.5.

Reactive power losses (kVAr) of each branch for this system for CP, CI, CZ and Composite load

(40% CP + 30% CI + 30% CZ) modeling are shown in Table 2.6.

Table 2.7 shows the total losses of the system. Table 2.8 shows the node number of this system

having minimum voltage and its value in p.u. Table 2.9 shows the relative values of CPU time

and memory requirement. Base values for this system are12.66 kV and 100 MVA respectively.

30

S/

S

1 2

3

4 5 6 7 8 9 10 11 12 13 14 15 16 17

28

29

30

31

32

33

34

35

36 37 38 39 40 41 42 43 44 45 46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

18

19

20

21

22

23

24

25

26

27

Figure 2.3 69 node radial distribution network

31

Table 2.3: Total Real power load and Reactive Power Load of 69node radial distribution

networks for CP, CI, CZ, Composite load modelling for substation voltage 1.0 pu

Type of load modelling

69node

radial distribution network

Real power load

(kW)

Reactive power load

(kVAr)

Constant Power 3801.89 2692.59

Constant Current 3633.45 2573.05

Constant Impedance 3495.96 2475.52

Composite load 3651.92 2586.17

32

Table 2.4 Voltage of each node in p.u. of each node of 69-node radial distribution network for

CP, CI, CZ and CC load modelling

Node

Number

Voltage (p.u.)

for CP load

Voltage (p.u.)

for CI load

Voltage (p.u.)

for CZ load

Voltage (p.u.)

for CC load

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

33

34

35

36

37

38

39

40

1.0000

0.9999

0.9999

0.9998

0.9990

0.9900

0.9807

0.9785

0.9774

0.9724

0.9713

0.9681

0.9652

0.9623

0.9595

0.9589

0.9580

0.9580

0.9576

0.9573

0.9568

0.9568

0.9567

0.9566

0.9564

0.9563

0.9563

0.9999

0.9998

0.9997

0.9997

0.9996

0.9993

0.9990

0.9989

0.9999

0.9997

0.9995

0.9995

0.9995

1.0000

0.9999

0.9999

0.9998

0.9990

0.9907

0.9820

0.9800

0.9789

0.9741

0.9730

0.9700

0.9672

0.9644

0.9617

0.9612

0.9603

0.9603

0.9599

0.9596

0.9591

0.9591

0.9591

0.9589

0.9587

0.9587

0.9587

0.9999

0.9998

0.9997

0.9997

0.9996

0.9993

0.9990

0.9989

0.9999

0.9997

0.9995

0.9995

0.9995

1.0000

0.9999

0.9999

0.9998

0.9991

0.9912

0.9831

0.9811

0.9801

0.9755

0.9744

0.9715

0.9688

0.9662

0.9635

0.9630

0.9622

0.9622

0.9618

0.9615

0.9611

0.9611

0.9610

0.9608

0.9607

0.9606

0.9606

0.9999

0.9998

0.9997

0.9997

0.9996

0.9993

0.9990

0.9989

0.9999

0.9997

0.9995

0.9995

0.9995

1.0000

0.9999

0.9999

0.9998

0.9990

0.9906

0.9819

0.9798

0.9788

0.9739

0.9729

0.9698

0.9670

0.9642

0.9614

0.9609

0.9601

0.9601

0.9596

0.9593

0.9589

0.9589

0.9588

0.9587

0.9585

0.9584

0.9584

0.9999

0.9998

0.9997

0.9997

0.9996

0.9993

0.9990

0.9989

0.9999

0.9997

0.9995

0.9995

0.9995

33

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

0.9988

0.9985

0.9985

0.9985

0.9984

0.9984

0.9997

0.9985

0.9947

0.9941

0.9785

0.9785

0.9746

0.9714

0.9669

0.9625

0.9401

0.9290

0.9247

0.9197

0.9123

0.9120

0.9116

0.9097

0.9091

0.9712

0.9712

0.9678

0.9678

0.9988

0.9985

0.9985

0.9985

0.9984

0.9984

0.9997

0.9985

0.9947

0.9942

0.9799

0.9799

0.9764

0.9734

0.9693

0.9653

0.9448

0.9347

0.9308

0.9262

0.9195

0.9192

0.9189

0.9171

0.9166

0.9730

0.9730

0.9697

0.9697

0.9988

0.9985

0.9985

0.9985

0.9984

0.9984

0.9998

0.9985

0.9947

0.9942

0.9811

0.9811

0.9778

0.9750

0.9712

0.9676

0.9486

0.9392

0.9356

0.9314

0.9252

0.9249

0.9246

0.9230

0.9225

0.9744

0.9744

0.9712

0.9712

0.9988

0.9985

0.9985

0.9985

0.9984

0.9984

0.9997

0.9985

0.9947

0.9941

0.9798

0.9798

0.9762

0.9732

0.9691

0.9650

0.9443

0.9341

0.9301

0.9255

0.9187

0.9184

0.9181

0.9163

0.9158

0.9728

0.9728

0.9695

0.9695

34

Table 2.5 : Real power losses (kW) of each branch of 69-node radial distribution network for

CP, CI, CZ and CC load modelling

Branch

Number

For CP load For CI load For CZ load For CC load

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

33

34

35

36

37

38

0.074951

0.074951

0.194856

1.936011

28.23028

29.33776

6.892022

3.373739

4.769865

1.013138

2.187400

1.282614

1.243801

1.204575

0.223837

0.320393

0.002604

0.104118

0.066933

0.107403

0.000536

0.005139

0.011185

0.006048

0.002495

0.000350

0.000347

0.002583

0.005829

0.001029

0.005143

0.012293

0.010403

0.000479

0.001405

0.015079

0.017323

0.005001

0.067705

0.067705

0.174678

1.683517

24.54849

25.50846

5.983242

2.915603

4.434904

0.941392

2.022315

1.176562

1.140558

1.104336

0.205210

0.293591

0.002385

0.095303

0.061266

0.098308

0.000490

0.004701

0.010233

0.005532

0.002282

0.000320

0.000347

0.002580

0.005818

0.001027

0.005134

0.012272

0.010382

0.000478

0.001403

0.015048

0.017282

0.004989

0.062190

0.062190

0.159379

1.495764

21.81073

22.66122

5.308249

2.576439

4.155425

0.881549

1.884989

1.088764

1.055105

1.021381

0.189795

0.271419

0.002204

0.088016

0.056582

0.090791

0.000453

0.004340

0.009446

0.005105

0.002106

0.000295

0.000346

0.002577

0.005808

0.001025

0.005125

0.012250

0.010362

0.000477

0.001400

0.015017

0.017242

0.004978

0.068501

0.068501

0.176892

1.711073

24.95031

25.92638

6.082432

2.965631

4.469410

0.948788

2.039418

1.187627

1.151333

1.114800

0.207155

0.296390

0.002408

0.096225

0.061859

0.099259

0.000495

0.004747

0.010333

0.005586

0.002304

0.000323

0.000347

0.002581

0.005819

0.001027

0.005135

0.012274

0.010384

0.000478

0.001403

0.015051

0.017287

0.004991

35

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

0.000199

0.048714

0.020117

0.002661

0.000514

0.006080

0.000013

0.023259

0.582158

1.631481

0.115753

0.001757

0.000044

5.781147

6.711319

9.124545

8.789956

49.68372

24.48876

9.505527

10.67081

14.02600

0.112051

0.134930

0.661155

0.041211

0.002624

0.000015

0.023324

0.000037

0.000198

0.048561

0.020053

0.002652

0.000512

0.006060

0.000013

0.023018

0.576136

1.613364

0.114405

0.001682

0.000042

4.833170

5.608976

7.611742

7.320890

41.38007

20.39595

7.916867

8.872423

11.66214

0.092768

0.111650

0.547084

0.034067

0.002476

0.000014

0.021849

0.000035

0.000197

0.048408

0.019990

0.002644

0.000510

0.006041

0.000012

0.022783

0.570257

1.595685

0.113090

0.001620

0.000040

4.153267

4.818533

6.528377

6.270060

35.44043

17.46834

6.780491

7.588098

9.973995

0.079058

0.095108

0.466027

0.028995

0.002351

0.000014

0.020611

0.000033

0.000198

0.048576

0.020059

0.002653

0.000512

0.006062

0.000013

0.023043

0.576742

1.615189

0.114541

0.001690

0.000042

4.937270

5.730026

7.777884

7.482258

42.29217

20.84552

8.091372

9.070159

11.92205

0.094894

0.114218

0.559669

0.034855

0.002490

0.000015

0.021999

0.000035

36

Table 2.6 :Reactive power losses (kVAr) of each branch of 69-node radial distribution network

for CP, CI, CZ, CC load modelling

Branch

Number

For CP load For CI load For CZ load For CC load

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

33

34

35

36

37

38

39

0.179883

0.179883

0.467655

2.267678

14.37738

14.94216

3.513286

1.717664

1.576560

0.335007

0.722881

0.423387

0.411026

0.398034

0.074005

0.105942

0.000886

0.034420

0.022025

0.035497

0.000176

0.001699

0.003698

0.001999

0.000825

0.000116

0.000851

0.006317

0.001927

0.000340

0.001700

0.004126

0.003439

0.000158

0.003450

0.036872

0.020235

0.005840

0.000232

0.162492

0.162492

0.419228

1.971928

12.50229

12.99185

3.050026

1.484414

1.465847

0.311283

0.668325

0.388380

0.376909

0.364911

0.067847

0.097080

0.000812

0.031506

0.020160

0.032491

0.000161

0.001554

0.003383

0.001828

0.000754

0.000106

0.000851

0.006310

0.001923

0.000339

0.001697

0.004119

0.003432

0.000158

0.003444

0.036797

0.020187

0.005826

0.000231

0.149256

0.149256

0.382510

1.752010

11.10798

11.54170

2.705940

1.311737

1.373472

0.291495

0.622942

0.359398

0.348670

0.337500

0.062750

0.089748

0.000750

0.029097

0.018619

0.030007

0.000149

0.001435

0.003123

0.001687

0.000696

0.000097

0.000850

0.006302

0.001920

0.000339

0.001694

0.004112

0.003425

0.000158

0.003437

0.036722

0.020140

0.005813

0.000230

0.164403

0.164403

0.424541

2.004205

12.70693

13.20469

3.100589

1.509885

1.477252

0.313728

0.673977

0.392032

0.380469

0.368369

0.068490

0.098005

0.000820

0.031810

0.020355

0.032805

0.000163

0.001569

0.003416

0.001846

0.000762

0.000107

0.000851

0.006310

0.001924

0.000339

0.001697

0.004120

0.003433

0.000158

0.003444

0.036804

0.020192

0.005828

0.000231

37

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

0.056915

0.023511

0.003102

0.000648

0.007665

0.000017

0.057463

1.424953

3.992005

0.283187

0.000896

0.000015

2.943734

3.418475

4.645748

4.477784

16.67685

8.218125

3.143511

3.239109

7.144279

0.057061

0.068674

0.336765

0.020990

0.000797

0.000005

0.007709

0.000013

0.056735

0.023436

0.003092

0.000646

0.007641

0.000017

0.056869

1.410212

3.947675

0.279889

0.000858

0.000014

2.461028

2.856986

3.875507

3.729411

13.88965

6.844629

2.618135

2.693209

5.940227

0.047241

0.056826

0.278663

0.017351

0.000752

0.000004

0.007222

0.000012

0.056557

0.023362

0.003082

0.000644

0.007617

0.000017

0.056289

1.395822

3.904418

0.276672

0.000826

0.000014

2.114825

2.454366

3.323914

3.194097

11.89595

5.862160

2.242332

2.303354

5.080350

0.040259

0.048406

0.237375

0.014768

0.000714

0.000004

0.006813

0.000011

0.056753

0.023444

0.003093

0.000646

0.007643

0.000017

0.056929

1.411697

3.952143

0.280222

0.000861

0.000014

2.514035

2.918644

3.960098

3.811615

14.19580

6.995499

2.675845

2.753232

6.072614

0.048324

0.058133

0.285073

0.017752

0.000756

0.000004

0.007271

0.000012

38

Table 2.7 :Total real and reactive power losses of 69-node radial distribution network for CP, CI,

CZ and CC load modelling

Losses

Type of Load

Real Power Losses

(kW)

Reactive Power

Losses(kVAr)

Constant Power 224.93 102.13

Constant Current 191.44 87.76

Constant Impedence 167.11 77.30

Composite Load

(40%CP+30%CI+30%CZ)

195.11 89.34

Table 2.8 : Node corresponding to minimum voltage of 69-node radial distribution network for

CP, CI, CZ and CC load modelling

Losses

Type of Load

Node Number Voltage (p.u.)

Constant Power 65 0.9091

Constant Current 65 0.9166

Constant Impedance 65 0.9225

Composite Load

(40%CP+30%CI+30%CZ)

65 0.9158

39

Table 2.9 : Comparison of relative CPU time and memory requirement of the proposed method

and method [19].

Relative Values→

Method

↓

Relative CPU time Relative memory

consumption

Proposed Method 1 1.49

Ghosh and Das [19] 1 2.18

2.7 Conclusion

In this thesis work an attempt has been made to propose a method, which can identify the nodes

beyond the branches in a simple way with less memory requirement. Using simple

transcendental equations, the expression for voltage without neglecting the voltage angle has also

been derived. The method has also been tested for constant power (CP), constant current (CI),

constant impedance (CZ) and composite (CC) load modelling. The superiority of the proposed

method with the existing method [19] has also been compared in terms of relative CPU time and

memory requirement.

40

CHAPTER 3

CONCLUSIONS & FUTURE SCOPE OF WORK

3.1 Conclusions

A method of loadflow analysis has been proposed for radial distribution networks based on the

new method to identify the nodes beyond each branch in a simple way. This has reduced the

computation. Effectiveness of the proposed method has been tested by one example 69 node

radial distribution networks with constant power load, constant current load, constant impedance

load and composite load. The voltage convergence has assured the satisfactory convergence in

all these cases. The superiority of the proposed method in terms of speed has been checked by

comparing with the other existing methods. The proposed method consumes less amount of

memory compared and less CPU time.

3.2 Future Scope of Work

The following are the scopes of future work

(i) Fuzzy loadflow analysis for unbalanced systems.

(ii) Loadflow analysis using Genetic Algorithms for unbalanced systems.

41

REFERENCES

[1] W.Tinney and C.Hart, “Power Flow Solution by Newton's Method”, IEEE Transactions on

Power Apparatus and Systems, Vol.PAS-86, no.11, pp.1449- 1460, November. 1967.

[2] B.Stott and O.Alsac, “Fast Decoupled Load-flow”, IEEE Transactions on Power Apparatus

and Systems, Vol.PAS-93, no.3, pp.859-869, May 1974.

[3] F. Zhang and C. S. Cheng, “A Modified Newton Method for Radial Distribution System

Power Flow Analysis”,IEEE Transactions on Power Systems, Vol.12, no.1,pp.389-397, February

1997.

[4] H. L. Nguyen, “Newton-Raphson Method in Complex Form”, IEEE Transactions on Power

Systems, Vol.12, no.3, pp.1355-1359, August 1997.

[5] Whei-Min Lin, Jen-HaoTeng, “Three-Phase Distribution Network Fast-Decoupled Power

Flow Solutions”, Electrical Power and Energy SystemsVol.22, pp.375-380, 2000.

[6] T. H. Chen, M. S. Chen, K. J. Hwang, P. Kotas, and E. A. Chebli, “Distribution System

Power Flow Analysis- A Rigid Approach”, IEEE Transactions on Power Delivery, Vol.6, no.3,

pp.1146-1153, July1991.

[7] J. H. Teng, “A Modified Gauss-Seidel Algorithm of Three-phase Power Flow Analysis In

Distribution Networks”, Electrical Power and Energy Systems Vol.24, pp.97-102, 2002.

[8] S.Iwamoto and Y.A.Tamura,“ Load-flow Calculation Method for Ill−Conditioned Power

Systems”, IEEE Transactions on Power Apparatus And Systems, Vol. PAS−100, no.4,

pp.1706−1713, April 1981.

42

[9] S.Tripathy,G.Prasad, O.Malik and G.Hope, “Load-Flow Solutions for Ill- Conditioned Power

Systems by a Newton-Like Method,” IEEE Transactions on Power Apparatus and Systems,

Vol.PAS-101, no.10, pp.3648-3657, 1982.

[10] W.H.Kersting, “A Method to Teach the Design and Operation of a Distribution System”,

IEEE Transactions on Power Apparatus and Systems; Vol.PAS-103, no.7, pp.1945-1952, 1984.

[11]R.A.Stevenset al., “Performance of Conventional Power Flow Routines for Real Time

Distribution Automation Application”, Proceedings 18th Southeastern Symposium on Systems

Theory: IEEE Computer Society: pp.196-200, 1986.

[12] D.Shirmohammadi, “A Compensation Based Power Flow Method for Weakly Meshed

Distribution and Transmission Network”, IEEE Transactions on Power Systems, Vol. 3, no. 2,

pp.753-762,1988.

[13] G. X. Luo, A. Semlyen, “Efficient Load Flow for Large Weakly Meshed Networks”,IEEE

Transactions on Power Systems, Vol.5, no.4, pp.1309-1316, 1990.

[14] C.G.Renato, “New Method for the Analysis of Distribution Networks”, IEEE Transactions

on Power Delivery; Vol.5, no.1, pp.391-396, January 1989.

[15] D. Das, D.P. Kothari, A Kalam, “Simple and Efficient Method for Load FlowSolution of

Radial Distribution Networks”, Electrical Power & Energy Systems, Vol.17, no.5, pp.335-346,

1995.

[16] S.Goswami and S.Basu, “Direct Solution of Distribution Systems”, IEE Proceedings on

Generation, Transmission and Distribution, Vol.138, no.1, pp.78- 88, January 1991.

43

[17] D.Das, H.S.Nagi and D.P.Kothari, “Novel Method for Solving Radial Distribution

Networks”, IEE Proceedings on Generation, Transmission and Distribution, Vol.141, no.4,

pp.291-298, July 1994.

[18] M.H.Haque, “Efficient Load-flow Method for Distribution Systems with Radial or Mesh

Configuration”, IEE Proceedings on Generation, Transmission, Distribution, Vol.143, no.1,

pp.33-39, January 1996.

[19] S.Ghosh and D.Das, “Method for Load−Flow Solution of Radial Distribution Networks”,

IEE Proceedings on Generation, Transmission and Distribution, Vol.146, no.6, pp.641–648,

November 1999.

[20] U.Eminoglu and M.H.Hocaoglu, “A New Power Flow Method For Radial Distribution

Systems Including Voltage Dependent Load Models”, Electric Power Systems Research Vol.76

pp.106–114, 2005.

[21] Bijwe PR, Vishwanadha Raju GK., “Fuzzy distribution power flow for weakly meshed

systems”, IEEE trans Power Syst. 2006;21(4):1645-52.

[22] S. Sivanagaraju, J. Viswanatha Raoand M. Giridhar,“A loop based loop flow method for

weakly meshed distribution network”, ARPN Journal of Engineering and Applied Sciences Vol.

3, no. 4, August 2008 ISSN 1819-6608.

[23] S. Ghosh and K.Sherpa, “An Efficient Method for Load−Flow Solution of Radial

Distribution Networks’’, Proceedings International Journal of Electrical Power and Energy

Systems Engineering, Spring 2008.

[24] A.Kumar and Aravindhababu, “An Improved Power Flow Technique for Distribution

Systems”, Journal of Computer Science, Informatics and Electrical Engineering Vol.3 Issue 1,

2009.

44

[25] Augugliaro A, Dusonchet L, Favuzza S, Ippolito MG, Riva Sanseverino E,“A Backward

sweep method for power flow solution in distribution networks”, Electrical Power and Energy

Systems 32 (2010) 271–280

[26] ME thesis by Apoorva Saxena ,“Load-flow analysis of Radial Distribution Networks with

Reduced Data Preparation”, from Thapar University under the supervision of Dr. Smarajit Ghosh

(Head & Professor, EIED) in June 2008.

[27] ME thesis by Amarinder Singh from Thapar University under the supervision of Dr.

Smarajit Ghosh (Head & Professor, EIED) in June 2008.

45

APPENDIX A

LINE & LOAD DATA OF 69 NODE RADIAL

DISTRIBUTION NETWORK

Table A.1 Line Data of 69 Node Radial Distribution Network

Branch

Number

Sendingend Receivingend Branch

Resistance ()

Branch

Reactance ()

1 1 2 0.0005 0.0012

2 2 3 0.0005 0.0012

3 3 4 0.0015 0.0036

4 4 5 0.0251 0.0294

5 5 6 0.3660 0.1864

6 6 7 0.3811 0.1941

7 7 8 0.0922 0.0470

8 8 9 0.0493 0.0257

9 9 10 0.8190 0.2707

10 10 11 0.1872 0.0619

11 11 12 0.7114 0.2351

12 12 13 1.0300 0.3400

13 13 14 1.0440 0.3450

14 14 15 1.0580 0.3496

15 15 16 0.1966 0.0650

16 16 17 0.3744 0.1238

46

17 17 18 0.0047 0.0016

18 18 19 0.3276 0.1083

19 19 20 0.2106 0.0696

20 20 21 0.3416 0.1129

21 21 22 0.0140 0.0046

22 22 23 0.1591 0.0526

23 23 24 0.3463 0.1145

24 24 25 0.7488 0.2475

25 25 26 0.3089 0.1021

26 26 27 0.1732 0.0572

27 3 28 0.0044 0.0108

28 28 29 0.0640 0.1565

29 29 30 0.3978 0.1315

30 30 31 0.0702 0.0232

31 31 32 0.3510 0.1160

32 32 33 0.8390 0.2816

33 33 34 1.7080 0.5646

34 34 35 1.4740 0.4873

35 3 36 0.0044 0.0108

36 36 37 0.0640 0.1565

37 37 38 0.1053 0.1230

38 38 39 0.0304 0.0355

39 39 40 0.0018 0.0021

40 40 41 0.7283 0.8509

41 41 42 0.3100 0.3623

42 42 43 0.0410 0.0478

47

43 43 44 0.0092 0.0116

44 44 45 0.1089 0.1373

45 45 46 0.0009 0..0012

46 4 47 0.0034 0.0084

47 47 48 0.0851 0.2083

48 48 49 0.2898 0.7091

49 49 50 0.0822 0.2011

50 8 51 0.0928 0.0473

51 51 52 0.3319 0.1114

52 9 53 0.1740 0.0886

56 53 54 0.2030 0.1034

53 54 55 0.2842 0.1447

54 55 56 0.2813 0.1433

55 56 57 1.5900 0.5337

56 57 58 0.7837 0.2630

57 58 59 0.3042 0.1006

58 59 60 0.3861 0.1172

59 60 61 0.5075 0.2585

60 61 62 0.0974 0.0496

61 62 63 0.1450 0.0738

62 63 64 0.7105 0.3619

63 64 65 1.0410 0.5302

64 11 66 0.2012 0.0611

65 66 67 0.0047 0.0014

67 12 68 0.7394 0.2444

68 68 69 0.0047 0.0016

48

Table A.2 Load Data of 69 Node Radial Distribution Network

Node

Number

PL(kW) QL(kVAr) Node

Number

PL(kW) QL(kVAr)

1 00.00 00.00 36 26.00 18.55

2 00.00 00.00 37 26.00 18.55

3 00.00 00.00 38 00.00 00.00

4 00.00 00.00 39 24.00 17.00

5 00.00 00.00 40 24.00 17.00

6 2.600 2.200 41 1.200 1.000

7 40.40 30.00 42 00.00 00.00

8 75.00 54.00 43 6.000 4.300

9 30.00 22.00 44 00.00 00.00

10 28.00 19.00 45 39.22 26.30

11 145.0 104.0 46 39.22 26.30

12 145.0 104.0 47 00.00 00.00

13 8.000 5.000 48 79.00 56.40

14 8.000 5.500 49 384.7 274.0

15 00.00 00.00 50 384.7 274.0

16 45.50 30.00 51 40.50 28.30

17 60.00 35.00 52 3.600 2.700

18 60.00 35.00 53 4.350 3.500

19 00.00 00.00 54 26.40 19.00

20 1.000 00.60 55 26.00 17.20

21 114.0 81.00 56 00.00 00.00

49

22 5.000 3.500 57 00.00 00.00

23 00.00 00.00 58 00.00 00.00

24 28.00 20.00 59 100.0 72.00

25 00.00 00.00 60 00.00 00.00

26 14.00 10.00 61 1244.0 888.0

27 14.00 10.00 62 32.00 23.00

28 26.00 18.60 63 00.00 00.00

29 26.00 18.60 64 227.0 162.0

30 00.00 00.00 65 59.00 42.00

31 00.00 00.00 66 18.00 13.00

32 00.00 00.00 67 18.00 13.00

33 14.00 10.00 68 28.00 20.00

34 19.50 14.00 69 28.00 20.00

35 6.000 4.000

BASE kV = 12.66 and BASE MVA = 100

50

APPENDIX B

BIOGRAPHY

PERSONAL INFORMATION

Name Gurpreet Kaur

D.O.B. 26/12/1988

Address House No. 250/12, Central Town, Sutehri Road, Hoshiarpur-

146001 (Punjab)

India

Contact No. 09041772923 (Mob.)

Mail Id gk_26_88@yahoo.com

gurforu@gmail.com

ACADEMIC QUALIFICATION

Pursuing M.E in Power System and Electrical Drives from Thapar University securing 9.82

(with Distinction) CGPA.

B.E in Electrical & Electronics Engg. from University Institute Of Engg. & Tech., Panjab

University, Chandigarh securing 78.2 %( with honors).

Higher Secondary from P.S.E.B securing 75.55 % (with distinction)

High School from P.S.E.B securing 79.53% (with distinction)

CAMPUS PLACEMENT

TCS Ltd.