Abstract— A new Object-Oriented Design (OOD) for unbalanced distribution system is proposed and employed for developing short circuit analysis software. The difficulty associated with the procedure-oriented implementation of short circuit analysis program is overcome with a new object-oriented implementation. The purpose of using Object-Oriented Methodology (OOM) for unbalanced distribution system is to achieve a flexible software model for the complex nature of the system involving three-phase, two-phase and single-phase components. Considerable reduction in the programming complexity can be obtained by the proposed method. The method was successfully tested on benchmark systems like IEEE 13-bus and IEEE 34-bus systems.

Index Terms— Distribution System, Unbalanced Network, Short Circuit Analysis, Phase Frame Method, Object-Oriented Methodology

I. INTRODUCTION

istribution system is one of the most complex systems in power system domain. Distribution system analysis is gaining more importance in recent days due to the

expansion of distribution system network and automation of its operation [1]. Short circuit analysis is a vital tool for determining the ratings of the protective devices in the distribution system. Distribution systems are generally unbalanced. A typical distribution system may be radial or weakly meshed; balanced or unbalanced; single-phase, two-phase or three-phase system[2]. Unbalanced distribution system consists of several components of different types, which require an efficient software modeling technique for analysis. Shunt devices used for reactive power compensation and loads in the distribution system may be either single-phase or three-phase. Single-phase loads and shunts may be connected either between a phase and neutral or between two phases. Three phase loads and shunts may be either star connected or delta connected. Transmission lines and cables may be single-phase, two-phase or three-phase. Transformers are usually either YGYG (both primary and secondary star connected and neutral grounded) or YGD (primary star connected neutral grounded and secondary delta connected) type. Distribution transformers may be connected in any other configuration (YY, YGY, YYG, DY, DYG, YD, DD)

M.P. Selvan is a lecturer in the department of Electrical and Electronics

Engineering, National Institute of Technology, Tiruchirapalli, Tamil nadu, India – 620 015. (Corresponding author :- phone: 91-431-2503262; fax: 91-431-2500133; e-mail: selvanmp@ nitt.edu).

K.S. Swarup is an associate professor in the department of electrical

engineering, Indian Institute of Technology-Madras, Chennai, Tamil nadu, India - 600 036 (e-mail: swarup@ee.iitm.ac.in).

depending on the requirement [3], [4]. Representation of such a system involving different types of components and performing various analyses on the system with traditional programming becomes more complex. An elegant and mature design can be obtained using object-oriented approach.

Object-oriented approach was applied for the development of efficient sparse matrix computation tools [5], [6], network topology processor [7], [8], load flow analysis [9], [10], and dynamic simulation [11]. Recently, object-oriented models for radial, weakly meshed distribution systems and distribution system with dispersed generation were proposed [12], [13]. Only load flow analysis of balanced distribution system was discussed and the more realistic unbalanced distribution system was not addressed. Object-oriented software models of unbalanced distribution system components were proposed by the present authors [14]. In this paper, those software models were employed to obtain a complete design for unbalanced distribution system involving three-phase, two-phase and single-phase components.

The proposed object-oriented design of unbalanced distribution system has been used for developing short circuit analysis software. Since the distribution system lines are not transposed, there exists an unequal mutual coupling between the phases, which introduce mutual impedances in the sequence network impedance matrix. Consequently, the advantages obtained from the symmetrical component analysis are lost and phase frame method has been chosen for the short circuit analysis of unbalanced distribution system. This involves tracing the path connecting the faulted bus and the substation, to find the equivalent impedance [15]. Tracing the path is a tedious process in traditional procedure-oriented implementation of the short circuit analysis program, which is usually developed using Fortran or C languages. This paper introduces a new method of tracing the path using the association relationship of object-oriented methodology

II. UNBALANCED DISTRIBUTION SYSTEM SHORT CIRCUIT ANALYSIS

The computation of short circuit currents for unbalanced faults can be performed using symmetrical components. However, this method is not suitable for a system, which is inherently unbalanced, such as a system with unequal mutual coupling and unbalanced loads. This is because the sequence impedances in the unbalanced system are not decoupled as in balanced system, which can be described as follows:

Unbalanced Distribution System Short Circuit Analysis – An Object-Oriented Approach

M P Selvan, K S Swarup

D

aa ab acabc

ba bb bc

ca cb cc

Z Z ZZ Z Z Z

Z Z Z

⎡ ⎤⎢ ⎥⎡ ⎤ =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(1)

Equation (1) is the phase impedance matrix of a three-phase transmission line. Assuming that the three-phase system loads are balanced and the transmission lines are transposed, the phase impedance matrix (1) is modified such that the three diagonal terms are equal ( sZ ) and all of the off-diagonal terms are equal ( mZ ). The modified phase impedance matrix is given by equation (2).

s m mabctransposed m s m

m m s

Z Z ZZ Z Z Z

Z Z Z

⎡ ⎤⎢ ⎥⎡ ⎤ =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(2)

Sequence impedance, given by the equation (5), of the balanced system can be obtained using the matrix ‘A’ given by equation (3).

2

2

1 1 111

A a aa a

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

(3)

[ ] [ ]1012 abctransposed transposedZ A Z A−⎡ ⎤ ⎡ ⎤=⎣ ⎦ ⎣ ⎦ (4)

00

01211

22

0 00 00 0

transposed

ZZ Z

Z

⎡ ⎤⎢ ⎥⎡ ⎤ =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(5)

where

00

11

22

2s m

s m

s m

Z Z ZZ Z ZZ Z Z

= += −= −

For an untransposed distribution system, assuming all the diagonal elements in the phase impedance matrix in equation (1) are equal and the off diagonal elements

1ab ba mZ Z Z= = ,2bc cb mZ Z Z= = ,

3ac ca mZ Z Z= = ,the equation (1) can be modified as given in equation (6).

1 3

1 2

3 2

s m mabcuntransposed m s m

m m s

Z Z ZZ Z Z Z

Z Z Z

⎡ ⎤⎢ ⎥⎡ ⎤ =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(6)

Using equation (4), the sequence impedance for the untransposed transmission line can be written as given in equation (7).

00 01 02012

10 11 12

20 21 22

untransposed

Z Z ZZ Z Z Z

Z Z Z

⎡ ⎤⎢ ⎥⎡ ⎤ =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(7)

( )( )( )

where

00 1 2 3

201 2 1 3

202 2 3 1

3 2s m m m

m m m

m m m

Z Z Z Z Z

Z Z aZ a Z

Z Z aZ a Z

= + + +

= − + +

= − + +

( )( )

( )

210 2 3 1

11 1 2 3

212 1 2 3

220 2 1 3

221 1 2 3

22 1 2 3

3

2( )( )

2( )3

m m m

s m m m

m m m

m m m

m m m

s m m m

Z Z aZ a Z

Z Z Z Z Z

Z aZ Z a ZZ Z aZ a ZZ a Z Z aZZ Z Z Z Z

= − + +

= − + +

= + +

= − + +

= + += − + +

From equation (7), it can be observed that the unequal mutual coupling between the phases causes mutual coupling between sequence networks. Due to this mutual coupling between the sequence networks, no advantage is obtained using symmetrical components. Another technique called “phase frame method” is used to analyze faults in unbalanced three-phase distribution feeders 15. This section briefly describes the phase frame short circuit analysis. Figure 1 shows the radial distribution system model considered during the faulted condition.

In Fig. 1, ⎡ ⎤⎣ ⎦abcTOTZ is the three-phase impedance matrix that

represents the total equivalent impedance between the fault bus and the system equivalent generator.

⎡ ⎤ = + +⎣ ⎦abcTOT line ss systemZ Z Z Z

Where, lineZ = Total line impedance from the faulted bus back to the substation.

ssZ = Substation transformer impedance.

systemZ = System equivalent impedance as determined

at the high voltage side.

aE , bE and cE are Thevenin equivalent voltages at the

faulted bus. The following relationship can be written from

0 00 00 0

a aa ab ac a f a ax xg

b ba bb bc b f b bx xg

c ca cb cc c f c cx xg

E Z Z Z I Z I V VE Z Z Z I Z I V VE Z Z Z I Z I V V

⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= + + +⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦

(8)

Equation (8) can be written in matrix form as equation (9)

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= + + +⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦abc abc abc abc abc abcx xg

TOT fE Z I Z I V V (9)

Equation (9) can be written as,

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= − −⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦abc abc abc abcx xgEQZ I E V V (10)

where, ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= +⎣ ⎦ ⎣ ⎦ ⎣ ⎦abc abc abcEQ TOT fZ Z Z and

[ZTOTabc]

Ea Eb Ec

g

Faulted Bus [Iabc]

[Zfabc] x

Vxg

Vcx

Vbx

Vax

Fig.1 Radial system model for faulted condition.

let 1−⎡ ⎤ ⎡ ⎤=⎣ ⎦ ⎣ ⎦

abc abcEQ EQY Z

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= − −⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦abc abc abc abc abcx abc xg

EQ EQ EQI Y E Y V Y V (11)

Let ⎡ ⎤ ⎡ ⎤ ⎡ ⎤=⎣ ⎦ ⎣ ⎦ ⎣ ⎦abc abc abcT EQI Y E

Equation (11) becomes ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= − −⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

abc abc abc abcx abc xgT EQ EQI I Y V Y V (12)

Equation (12) can be expanded as,

a Ta aa ab ac ax aa ab ac xg

b Tb ba bb bc bx ba bb bc xg

c Tc ca cb cc cx ca cb cc xg

I I Y Y Y V Y Y Y VI I Y Y Y V Y Y Y VI I Y Y Y V Y Y Y V

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= − − ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(13)

From Equation (13)

( )a Ta aa ax ab bx ac cx a xgI I Y V Y V Y V Y V= − + + − (14a)

( )b Tb ba ax bb bx bc cx b xgI I Y V Y V Y V Y V= − + + − (14b)

( )c Tc ca ax cb bx cc cx c xgI I Y V Y V Y V Y V= − + + − (14c)

Where,

a aa ab acY Y Y Y= + +

b ba bb bcY Y Y Y= + +

c ca cb ccY Y Y Y= + +

Equations (14a), (14b) and (14c) are the general equations that are used to simulate all types of short circuits. Expressions for line-to-line fault are only described here for the purpose of illustration.

a) Line to Line fault

Assuming fault between phases b and c,

00

0

bx cx

b c

a

V VI II

= =+ ==

From equations (14a), (14b) and (14c),

0a Ta aa ax a xgI I Y V Y V= − − = (17a)

b Tb ba ax b xgI I Y V Y V= − − (17b)

c Tc ca ax c xgI I Y V Y V= − − (17c)

From equation (17a)

Ta aa ax a xgI Y V Y V= + (18a)

Adding (17b) and (17c)

0b cI I+ = =>

( ) ( ) ( )Tb Tc ba ca ax b c xgI I Y Y V Y Y V+ = + + + (18b)

Equations (18a) and (18b) can be written in matrix form as follows

axTa aa a

xgTb Tc ba ca b c

VI Y YVI I Y Y Y Y⎡ ⎤⎡ ⎤ ⎡ ⎤

= ⎢ ⎥⎢ ⎥ ⎢ ⎥+ + +⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (19)

11 12

21 22

⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥ +⎣ ⎦ ⎣ ⎦⎣ ⎦

ax Ta

xg Tb Tc

V IZ ZV I IZ Z

(20)

Where 1

11 12

21 22

−⎡ ⎤⎡ ⎤

= ⎢ ⎥⎢ ⎥ + +⎣ ⎦ ⎣ ⎦aa a

ba ca b c

Y YZ ZY Y Y YZ Z

In general, for a fault between phases ‘i’ and ‘j’, and with ‘k’ as the healthy phase.

0 0 0ix jx kV V I= = =

11 12

21 22

⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥ +⎣ ⎦⎣ ⎦ ⎣ ⎦

kx Tk

xg Ti Tj

V IZ ZV I IZ Z

(21)

Where, 1

11 12

21 22

−⎡ ⎤⎡ ⎤

= ⎢ ⎥⎢ ⎥ + +⎣ ⎦ ⎣ ⎦

kk k

ik jk i j

Y YZ ZY Y Y YZ Z

Similar expressions for other types of faults can also be derived.

III. SHORT CIRCUIT ANALYSIS IN PROCEDURE ORIENTED IMPLEMENTATION

Computation of the equivalent impedance between the fault point and the source of fault current is the most involved part in the short circuit analysis. The equivalent impedance includes the total line impedance from the fault bus back to the substation, substation transformer impedance and system equivalent impedance as determined at the high voltage bus of the substation. This calculation involves tracing the path connecting the fault point and the substation. This path may consist of several feeders, which are the aggregation of branches such as transmission lines, transformers and switches. The remaining part of this section explains the method of tracing the path in the procedure-oriented implementation, where the data is kept global and is passed as arguments into the functions for performing the desired task.

650

646 645 632 633 634

611 684 671 692 675

652 680

Fig.2 Network diagram of IEEE 13-bus unbalanced distribution system. Fig. 2 shows the IEEE 13–bus unbalanced radial

distribution system. Assuming a fault at bus 692, the path to be traced follows the switch 692-671 and the transmission lines 671-632, 632-650. In traditional methods, if the data structure used to store the branch data does not capture the

radial topology of the distribution network, then it will be inflexible to find the path connecting the fault point and the substation. Hence, it is required to create an ordered list of line segments while reading the line data. The ordered list for the IEEE 13-bus is system is shown in Table 1.

TABLE-I

ORDERED LIST OF LINE SEGMENTS FOR IEEE 13-BUS SYSTEM

To Bus From Bus To Bus From Bus

652 684 671 632

611 684 634 633

684 671 633 632

680 671 646 645

675 692 645 632

692 671 632 650

The logic to trace the path from the ordered list of line segments is as follows:

1. Find the faulted bus in the “To bus” list. 2. Find the corresponding entry in the “From bus” list. 3. Search down the “To bus” list to find the bus that

matches the present “From bus”. 4. Find the corresponding entry in the “From bus” list. 5. Repeat the above steps (3 & 4) till reaching the

source bus. Following are the drawbacks of procedure-oriented implementation

1. Preparation of the ordered list of line segments is a tedious programming task, which involves several conditional statements and logical loops.

2. Since distribution system is subjected to switching operations leading to frequent topology changes, every time after the new topology is identified by the topology processor, the ordered list of line segments need to be prepared.

These drawbacks were identified by the authors and eliminated in the proposed object-oriented approach. The subsequent sections brief the object-oriented methodology and its application to the present problem.

IV. OBJECT-ORIENTED METHODOLOGY (OOM)

The basic principle of OOM is to represent each component of the problem domain by an element called object. A class represents a collection of similar objects and is effectively a template, from which the objects are instantiated. Objects have data or attributes and behaviors or methods [16]. Classes and objects provide a computable representation of the physical system that is convenient for engineers, who naturally think of systems as collection of objects. Object-oriented approach generally leads to more flexible, modular and reusable code. Using this approach, programs can be written in a more general way. The main features of the object-oriented methodology are abstraction, encapsulation, inheritance and polymorphism. The important relationships of OOM are

generalization, association, aggregation and composition. The present paper employs the UML (unified modeling language) class diagram [17] for representing the proposed object-oriented design of unbalanced distribution system.

V. OBJECT-ORIENTED DESIGN OF UNBALANCED DISTRIBUTION SYSTEM

Unbalanced distribution system has three-phase, two-phase and single-phase components, where the connected phases (a-b, b-c, c-a for two-phase and a, b, c for single-phase) have to be taken into consideration. Three-phase and two-phase objects are modeled as a composition of three and two single-phase objects respectively. In order to represent the connected phases, an additional attribute is included in the single-phase objects. The unbalanced distribution system has been modeled as an object of class UBDistSys (UnBalanced Distibution System), which is an aggregation of all three-phase feeders, two-phase feeders, single-phase feeders, three-phase, two-phase and single-phase buses etc [14]. Fig.3 shows the class diagram of a three-phase unbalanced distribution system. Only important base and derived classes are shown to improve the clarity.

UBDISTSYS

BUS FEEDER

SERIESBRANCH

TP FEEDER

DP FEEDER

SP FEEDER

TP SERIESBRANCH

DP SERIESBRANCH

SP SERIESBRANCH

TPTRANSMISSIONLINE

TP SWITCH

TP CABLE

TP TRANSFORMER

SPTRANSMISSIONLINE

SP SWITCH

SP CABLE

SP TRANSFORMER

DPTRANSMISSIONLINE

DP SWITCH

DP CABLE

SP BUS

DP BUS

TP BUS

TP ROOTNODE

TP FORKNODE

TP TERMINALNODE

DP FORKNODE

DP TERMINALNODE

SP FORKNODE

SP TERMINALNODE

TP LOAD

PP LOAD

PN LOAD

0..n

0..n

0..n

1..n

1..n

1..n

3

3

3

2

2

2

TP YGYGTRANSFORMER

TP YGDTRANSFORMER

CONCENTRICNEUTRAL CABLE

TAPE SHIELDEDCABLE

3 2

DSCOMPONENT1..*

BRANCH

SHUNTBRANCH

TP - Three PhaseDP - Two\Double PhaseSP - Single PhasePP - Phase to PhasePN - Phase to Neutral

Generalization/ Inheritance

Aggregation

CompositionAssociation

Fig.3 Class diagram of unbalanced distribution system

VI. SHORT CIRCUIT ANALYSIS IN OBJECT-ORIENTED IMPLEMENTATION

In traditional procedure oriented methods, if the data structure used to store the branch data does not capture the radial topology of the distribution network, then it will be inflexible to find the path connecting the fault point and the substation. But, in object-oriented methodology, the association relationship between the objects, which reflects the real world physical connection of the branches, makes the task simpler. Each Bus object has a list of the addresses (pointers) of the connected SeriesBranch objects. Similarly, each SeriesBranch object has the addresses of its “frombus” and “tobus”. The steps involved in tracing the path using this association is as follows:

1. Find the faulted bus.

Ratings IEEE 13-bus System [19]

IEEE 34-bus system [19][15]

Substation Transformer

5000 kVA, 115 kV-Δ /4.16 kV-GrY

2500 kVA, 115 kV-Δ /24.9 kV-GrY

Transformer Impedance 1.0+j8.0 %. 1.0+j8.0 %.

Short circuit MVA on the 115kV bus

1800 MVA at an angle of 85 degrees.

1800 MVA at an angle of 85 degrees.

Fault impedance for the present study

2 ohms 40 ohms

2. Choose the address of the branch, to which this bus is 'tobus', from the list of addresses of the connected branches.

3. Get the address of the 'frombus' of that branch. 4. Repeat the steps 2 and 3 till the ‘frombus’ becomes the

source bus.

In object-oriented implementation, a task is performed by the collaboration of objects with one another by sending messages. Messages are modeled in UML sequence diagrams that models the sequential logic; in effect, the time ordering of messages between objects [16], [17]. The sequence diagram for the equivalent impedance calculation is shown in Fig.4.

ubd : UBDistSys tpbus : TPBus tpfeeder : TPFeeder tpbranch : TPBranch

readData ( )

establishLinks ( )

readFaultedBusNo ( )

getOwnFeeder ( )

feeder address

getZtotalFromBus ( tpbus )

Ztotal

getStartingNode ( )

tpbus address

getBranchImpedance ( )

Zbranch

check if the tpbus is sourcenode. Stop if Yes.

1

2

3

4

56

7

8

TP - Three-Phase

Methodinvocation

box

Fig.4 Sequence diagram for equivalent impedance calculation

The execution of equivalent impedance calculation is briefly described by the following 8 steps. Each step is indicated in Fig.4 by the numerals.

1. “ubd” object reads the system data when “readData( )” method is invoked.

2. Associations between the objects are established by “establishLinks()” method of “ubd”.

3. “ubd” reads the fault bus number. 4. The object “ubd” obtains the feeder number along

which the fault bus is located, by invoking “getOwnFeeder ()” method.

5. “ubd” sends a message to the particular feeder to find the total impedance between the given “tpbus” and its starting node.

6. “tpfeeder” invokes the “getBranchImpedance ()” method of all its branches and calculates the total impedance.

7. “tpfeeder” gives its starting node address as a response to the “getStartingNode ()” message.

8. If the given “tpbus” is the root node then “ubd” stops the process. Otherwise it again invokes the “getOwnFeeder( )” method of “tpbus”.

Once the equivalent impedance of the path connecting the fault point and the substation is computed, “ubd” calculates the fault current for a particular type of fault using the

associated mathematical relationship given in the section unbalanced distribution system short circuit analysis.

VII. CASE STUDY AND RESULTS

The short circuit analysis program developed in C++, an object-oriented programming language, has been tested using 4.16 kV IEEE 13-bus system[19] shown in Figure 2 and 24.9 kV IEEE 34-bus distribution system[19] shown in Figure 5. Balanced and unbalanced fault analyses have been performed on the IEEE 13-bus and IEEE 34-bus systems. The ratings of both the systems are given in Table 2.

800 802 806 808

810

812 814 850

816

824 826

818

820

822

858

864

832

852

828 830 854 856

888 890

834 860

836

862

838

840

842

844

846

848

Fig.5 IEEE 34-bus Radial Distribution System

Fault is created at bus 671 of IEEE 13-bus system and the fault currents in three phases for various faults are tabulated in Table 3. Similarly, all types of faults are simulated at bus 854 of IEEE 34-bus system and the results are tabulated in Table 4.

TABLE-II RATINGS OF THE SYSTEMS UNDER STUDY

TABLE III

FAULT CURRENT FOR DIFFERENT FAULTS AT BUS 671 OF IEEE 13-BUS SYSTEM.

Fault Type Phases Involved

Fault Current in p.u. Phase A Phase B Phase C

3 Phase ABC 24.88 25.67 24.61 3Ph-Ground ABCG 24.65 25.78 24.73

LL AB 21.83 21.83 0 LL BC 0 21.59 21.59 LL CA 21.68 0 21.68

LLG ABG 21.89 26.19 0 LLG BCG 0 22.342 25.51 LLG CAG 25.74 0 22.19 LG AG 22.77 0 0 LG BG 0 22.78 0 LG CG 0 0 22.82

Fault Type Phases Involved

Fault Current in p.u. Phase A Phase B Phase C

3 Phase ABC 21.55 22.00 21.29 3Ph-Ground ABCG 21.39 22.09 21.36

LL AB 18.86 18.87 0 LL BC 0 18.59 18.59 LL CA 18.71 0 18.71

LLG ABG 19.05 22.19 0 LLG BCG 0 19.24 21.65 LLG CAG 21.85 0 19.18 LG AG 19.13 0 0 LG BG 0 19.14 0 LG CG 0 0 19.14

TABLE IV FAULT CURRENT FOR DIFFERENT FAULTS AT BUS 854 OF

IEEE 34-BUS SYSTEM.

VIII. CONCLUSION

This paper proposed an object-oriented design for unbalanced distribution system. The development of short circuit analysis software using the proposed methodology was demonstrated. A new method for tracing the path connecting the faulted bus and the substation using the association relationship between the objects has been introduced. The flexibility of using the proposed method over traditional procedure-oriented method has also been discussed. The method was successfully tested for different benchmark systems like IEEE 13-bus and IEEE 34-bus system.

IX. REFERENCES [1] W R Cassel, ‘Distribution Management Systems: functions

and payback’. IEEE Transactions on Power Systems, vol. 8, no. 3, pp. 796-801, 1993.

[2] Gonen, T., ‘Electric Power Distribution System Engineering’. McGraw Hill, 1986.

[3] Chen, M. S. and Dillon, W. E. ‘Power System Modeling’. Proceedings of the IEEE, vol. 62, no. 7, pp. 901-915, 1974.

[4] Chen, T. H. and Chen, M. S. ‘Three Phase Co-generator and Transformer Models for Distribution System Analysis’. IEEE Transactions on Power Delivery, vol. 6, no. 4, pp. 1671-1681, 1991.

[5] Hakavik, B. and Holen, A. T., ‘Power System Modeling and Sparse Matrix Operations using Object-Oriented Programming’. IEEE Transactions on Power Systems, vol. 9, no. 2, pp. 1045-1051, 1994.

[6] Pandit, S., Soman, S. A. and Khaparde, S. A., ‘Design of Generic Direct Sparse Linear System Solver in C++ for Power System Analysis’. IEEE Transactions on Power Systems, vol. 16, no. 4, pp. 647-652, 2001.

[7] Foley, M. and Bose, A. ‘Object-Oriented On-Line Network Analysis’. IEEE Transactions on Power Systems, vol. 10, no. 1, pp. 125-132, 1995.

[8] Pandit, S., Soman, S. A. and Khaparde, S. A., ‘Object-Oriented Network Topology Processor’. IEEE Computer Applications in Power, pp. 42-46, April 2001.

[9] Neyer, A. F., Wu, F. F. and Imhof, K., ‘Object-Oriented Programming for Flexible Software: Example of a Load Flow’. IEEE Transactions on Power Systems, vol. 5, no. 3, pp. 689-696, 1990.

[10] Fuerte-Esquivel, C. R., Acha, E., Tan, S. G. and Rico, J. J., ‘Efficient Object-Oriented Power Systems Software for the Analysis of Large-Scale Networks Containing FACTS-Controlled Branches’. IEEE Transactions on Power Systems, vol. 13, no. 2, pp. 464-472, 1998.

[11] Manzoni, A., Se. A. Silva and Decker, I. C., ‘Power Systems Dynamics Simulation Using Object-Oriented Programming’. IEEE Transactions on Power Systems, vol. 14, no. 1, pp. 249-255, 1999.

[12] Losi, A. and Russo, M., ‘Object-Oriented Load Flow for Radial and Weakly Meshed Distribution Networks’. IEEE Transactions on Power Systems, vol 18., no 4., pp.1265-1274, 2003.

[13] Losi, A. and Russo, M. ‘Dispersed Generation Modeling for Object-Oriented Distribution Load Flow’. IEEE Transactions on Power Delivery, vol. 20, no. 2, pp 1532-1540, 2005.

[14] Selvan, M. P. and Swarup, K. S., ‘Object modelling of balanced and unbalanced distribution systems for power flow analysis’, Electric Power Components and Systems, vol. 34, no. 2, pp. 191-215, 2006.

[15] Kersting, W. H. and Phillips, W. H., ‘Distribution System Short-Circuit Analysis’. Proceedings of 25th Intersociety Energy Conversion Engineering Conference, Reno, NV, pp. 310-315, 1990.

[16] Ambler, S. W., ‘The Object Primer - The Application Developer’s Guide to Object- Orientation and the UML’. Cambridge University Press, 2001.

[17] Rumbaugh, J., Jacobson, I. and Booch. G., ‘The Unified Modeling Language Reference Manual’. Addison Wesley, 1999.

[18] Kersting, W. H. and Phillips, W.H., ‘Distribution Feeder Line Models’. IEEE Transactions on Industry Applications, vol 31, no 4, pp 715-720, 1995.

[19] Radial Test Feeders- IEEE Distribution System Analysis Subcommittee. http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders.html