(IJIRMPS) A Unified Approach for the Transient Stability ...ijirmps.com/Volume 3/Issue 3/IJIRMPS1404201503_01.pdf · Analysis for a Multi machine System Using MatLab ... model used

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International Journal of Innovative Research in Engineering & Multidisciplinary Physical Sciences

(IJIRMPS)

Volume 3, Issue 3, October 2015

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A Unified Approach for the Transient Stability

Analysis for a Multi machine System Using

MatLab / Simulink Model Tefera Mekonnen, Dr HadadiSudheendra, Getnet_Zewde

School of Electrical and Computer Engineering, Jimma University, Jimma, Ethiopia

Abstract – Transient stability analysis has recently become a major issue in the operation of power systems due to the

increasing stress on power system networks specifically for a multi machine System. This problem requires evaluation of

a power system's ability to withstand disturbances while maintaining the quality of service. Many different techniques

have been proposed for transient stability analysis in power systems, especially for a multi machine system, these methods

include the time domain solutions, the extended equal area criteria, and the direct stability methods such as the transient

energy function. However, the most methods must transform from a multi-machine system to an equivalent machine and

infinite bus system. Transient stability well defined as the ability of a synchronous power system to return to stable

condition and maintain its synchronism following a relatively large disturbance arising from very general situations like

switching ‘on’ and ‘off’ of circuit elements viz the circuit breakers, relays or clearing of faults etc..More often than not,

the power generation systems are subjected to faults of this kind, and hence it’s extremely important for power engineers

to be well-versed with the stability conditions of the system without losing synchronism. Occurrence of fault in a power

system usually causes transients, which are due to sudden lightning, switching of lines etc, hence transient stability

analysis is extremely important for power engineers,. A classical model has been proposed for the study, for the faults

which are originating due to above said situations i.e. the ability of power system to deliver the power and maintain

synchronism when subjected to a severe transient disturbance is the Transient stability limit, such as a fault on

transmission facilitates the sudden loss of generation, or loss of a large load. In this research paper the transient model

of multi-machine power system is developed in MATLAB/SIMULINK using Simulator .A three–machine, six–bus power

system after subjected to a 3 Phase Short circuit (bolted fault) is studied. For studying the transient stability of this

system, the pre-fault load flow analysis, during fault and post fault analysis is calculated by using Kron’s elimination

method. For the simulation purpose, the Power System (SPS) set. Fault simulations at various clearing time is employed

to analyze for the critical clearing time. From the result obtained in the simulations for case study, the specific or the

exact fault clearing time for the system and the influence of fault clearing time is described.

Keywords: Multi machine, Transient stability, pre fault, during fault, post fault, Matlab/Simulink, Fault clearing

time (FCT), per unit value, Admittance parameter, Power angle, post fault admittance, Critical fault clearing time.

I. INTRODUCTION

Multi machine equations can be written similar to the one machine system connected to the infinite bus. In order

to reduce the complexity of the transient stability analysis, similar simplifying assumptions are made as follows.

A. Each synchronous machine is represented by a constant voltage source behind the direct axis transient

reactance. This representation Neglects the effect of saliency and assumes Constant flux linkages.

B. The governor’s action is neglected and the input powers are assumed to remain constant during the entire

period of simulation. -Using the prefault bus voltages.

The stability of power systems has been and continues to be of major concern in system

operation. Modern electrical power systems have grown to a large complexity due to

increasing interconnections, installation of large generating units and extra-high voltage tielines etc. Transient

stability is the ability of the power system to maintain synchronism when subjected to a severe transient

disturbance, such as a fault on transmission facilities, sudden loss of generation, or loss of a large load[1,2]. The

system response to such disturbances involves large excursions of generator rotor angles, power flows, bus

voltages, and other system variables. It is important that, while steady-state stability is a function only of

operating conditions, transient stability is a function of both the operating conditions and the disturbance(s).

This complicates the analysis of transient stability considerably. Repeated analysis is required for different

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disturbances that are to be considered. In the transient stability studies, frequently considered disturbances are

the short circuits of different types. Out of these, normally the three-phase short circuit at the generator bus is

the most severe type, as it causes maximum acceleration of the connected machine.

Simulink is an interactive environment for modeling, analyzing, and simulating a wide variety of dynamic

systems. Simulink provides a graphical user interface for constructing block diagram models using ‘drag and

drop’ operations. A system is configured in terms of block diagram representation from a library of standard

components. A system in block diagram representation is built easily and the simulation results are displayed

quickly. Simulation algorithms and parameters can be changed in the middle of a simulation with intuitive

results, thus providing the user with a ready-access learning tool for simulating many of the operational

problems found in the real world. Simulink is particularly useful for studying the effects of non- linearity on the

behavior of the system, and as such, is also an ideal research tool. I have considered its parent software package

Simulink as a main tool in my present study.

Excitation systems, turbine and governor blocks from power system block set (PSB) can be readily used with

Simulink blocks as and when required. The user also has access to numerous design and analysis tools provided

in MATLAB and its toolboxes [3].

The classical model of a multi machine may be used to study the stability of a power system for a period of time

during which the system dynamic response is dependent largely on the kinetic energy in the rotating masses.

The classical three-machine six-bus system is the simplest model used in studies of power system dynamics and

requires of minimum amounts of data. Hence such studies can be connected in a relatively short time under

minimum cost. Among various method of load flow calculation Newton Raphson method by usin Matlab

programming is chosen for computing of load flow study.

II. METHODOLOGY USED

In the case study in Fig 1, The study related to with the three- machine, six-bus system and The system data are

given in table 1&2. The system has been simulated with a classical model for the generators. The disturbance

initiating the transient is a three-phase fault being most severe case, the study proposes the classical model of

simulation ,fault being near to bus 6 at the end of line 4– 6.The fault is cleared by opening CBs in line 4–6 . If

The system, being small , is large enough to be nontrivial and thus permits and enhances the illustration of a

number of stability concepts and results with clear technical approach.

Fig 1; one line diagram of a three machine 6 bus power system

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Note; all values are given in Per unit

A . System modeling

The complete system has been represented in terms of Simulink blocks in a single integral model. It is self-

eplanatory with the mathematical model given below. One of the most important features of a model in

Simulink is its tremendous interactive capacity. It makes the display of a signal at any point readily available; all

one has to do is to add a Scope block or, alternatively, an output port. Giving a feedback signal is also as easy as

drawing a line. A parameter within any block can be controlled from a MATLAB command line or through an

m-file program. This is particularly useful for a transient stability study as the power system configurations

differ before, during and after fault. Loading conditions and control measures can also be implemented

accordingly.

From the given data in order to analyze the bus voltage across each bus, the power flow across the line and line

loss, formulation of Y bus matrix is the second step next to identification of the bus types. As it is indicated that

in the above figure 1, we have six buses

One Slack bus ( bus 1)

Two PV buses ( bus 2 &3)

Three load buses (bus 4,5 & 6)

After knowing the bus types it is possible to compute y bus matrixes.

B. Mathematical modeling

It is customary to have the following assumptions during our analysis for the Studies and the analysis made in

transient stability studies viz [1 - 4]:

1. The mechanical power input to each machine remains constant during the entire period of the swing curve

computation.

2. Damping power is negligible.

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3. Each machine may be represented by a constant transient reactance in series with a constant transient internal

voltage.

4. The mechanical rotor angle of each machine coincides with the electrical phase angle of the transient internal

voltage.

5. All loads may be considered as shunt impedances to ground with values determined by conditions prevailing

immediately prior to the transient conditions. The system stability model based on the above assumptions is

called the classical stability model, which is used to study system disturbances originating from three-phase

faults, and studies which use this model are called classical stability studies. The system conditions before the

fault occurs, and the network configuration both during and after its occurrence, must be known in any transient

stability study. Consequently, in the multi-machine case ,two preliminary steps are required viz:

1. The steady-state pre-fault conditions for the system are calculated using a power-flow program.

2. The pre-fault network representation is determined and then modified to account for the fault and for the post-

fault conditions. From the first preliminary step I , I propose to calculate the values of power, reactive power,

and voltage at each generator terminal and load bus with all angles measured with respect to the slack bus. The

transient internal voltage of each generator is

Where; Vt is the corresponding terminal voltage and I is the output current.

Each load is converted into a constant admittance to ground at its bus using the equation

Where, PL + jQL is the load and VL is the magnitude of the corresponding bus voltage. The bus admittance

matrix which is used for the pre-fault power-flow calculation is now augmented to include the transient

reactance of each generators and the shunt admittance of each load. In the second preliminary step the bus

admittance matrix is modified to correspond to the faulted and post fault conditions.

Once the Y matrix for each network condition (pre-fault, during and after fault) is calculated, we can eliminate

all the nodes except for the internal generator nodes and obtain the Y matrix for the reduced network. The

reduction can be achieved by matrix operation with the fact in mind that all the nodes have zero injection

currents except for the internal generator nodes. In a power system with n generators, the nodal equation can be

written as[1,5].

Where the subscript n is used to denote generator nodes and the subscript r is used for the remaining nodes.

Expanding eqn. (3),

From which we eliminate Vr to find

Thus the desired reduced matrix can be written as follows:

It has dimensions (n x n) where n is the number of generators. Note that the network reduction illustrated by

eqns. (3)–(5) is a convenient analytical technique that can be used only when the loads are treated as constant

impedances. For the power system under study, the reduced matrices are calculated. The resultant matrices for

the pre fault, Instant of the fault and Post fault are given below.

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The power into the network at node i, which is the electrical power output of machine i, is given by:

= negative of the transfer admittance between nodes i and j

= driving point admittance of node i

The equations of motion are then given by [7-,9]

And,

It should be noted that prior to the disturbance (t = 0) Pmi0 = Pei0; Thereby,

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The subscript 0 is used to indicate the pre-transient conditions. As the network changes due to switching during

the fault, the corresponding values will be used in above equations.

C Simulink Models

Classical system model

The complete 3-generator system, given in Fig. 1, has been simulated as a single integral model in Simulink.

The mathematical model given above gives the transfer function of the different blocks. Fig. 2 shows the

complete block diagram of a classical system representation for transient stability study. The subsystems 1, 2

and 3 in Fig. 2 are meant to calculate the value of electrical power outputs for different generators; for example

Fig. 3 shows the computation of the power output of generator 1.

The model also facilitates the choice of simulation parameters, such as start and stop times, type of solver, step

sizes, tolerance and output options etc. The model can be run either directly or from the MATLAB command

line or from an m-file program. In the present study, the fault clearing time, the initial values of parameters as

well as the changes in network due to fault, are controlled through an m-file program in MATLAB.

Fig 2; complete classical model for transient stability analysis of three machines

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Fig 3. Computation of electrical power output of generator # 1 by subsystem 1

Fig 4. Computation of electrical power output of generator # 2by subsystem 2

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Fig 5. Computation of electrical power output of generator # 3by subsystem 3

III. SIMULATION RESULT AND DISCUSSION

In order to observe the transient behavior of a three–machine, six–bus power system after subjected to a three

phase bolted fault, Simulation studies are carried out under different values of fault clearing time (FCT). The

following cases are considered;

Case 1; fault cleared at 0.2 second.

In Figs 6(a), (b), (c) and (d):-The angular position of individual generators, the relative angular positions,

electrical power output of each generator and Accelerating power of each generator. This shows the rotor of the

machines becomes swing together. The accelerating power of each machine and their combined effect is going

to zero value. This implies that the system is stable and will come to some acceptable steady state value.

Fig 6(a); Angular position of individual generators for critical clearing time of 0.2 sec.

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Fig 6(b); Relative angular position of δ21&δ31 of the machine with slack bus reference

Fig 6(c); plot of electrical power output of generator #1, 2&3 vs time

Fig 6 (d); plot of accelerating power of generator #1, 2 &3 vs time

Case 2; fault cleared at 0.41 second.

In Figs 7(a), (b) (c) and (d):- The system is unstable if the fault is cleared after 0.4 sec. from the critical fault

clearing time(0.4 sec.). The angular positions of the entire machines are increasing. This also shows that the

steady state operating power is greater than the maximum power output of the system during fault condition.

Therefore, the machines will be out of synchronism and the system is unstable during fault condition.

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Fig7(a); Angular position of individual generators for clearing time of 0.41 sec

Fig 7(b) ; Relative angular position of δ21&δ31 of the machine with slack bus reference

Fig 7(c) ; plot of electrical power output of generator #1 , 2&3 vs time

Fig 7(d); plot of accelerating power of generator #1, 2&3 vs time.

IV. CONCLUSION

This paper presents the difference in response of the transient behavior of a three –machine ,six – bus power

system .For the case study, a three phase fault is placed on one of the transmission lines (near bus #6) at

different fault clearing time. A complete classical model for transient stability study of a multi-machine power

system was developed using Simulink. System responses are given for different values of fault clearing time

(FCT).

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As it has been observed that the system response from the MATLAB model Simulink that, there is no stability

for clearing time of greater than 0.4seconds. Delaying the clearing time by few milli second make the system

out of synchronism or the system is not restored as before at steady state. Therefore It is proposed to have the

system fault clearing time to be 0.2 second. Accordingly the relay coordination setup is configured with this

fault clearing time.

REFERENCES [1] P. Kunder, ―Power system stability and control, EPRI Power system Engineering Series‖ (McGraw-Hill, New York,

1964).

[2] M. Anderson and A. A. Faud, Power System Control and Stability (Iowa State

University Press, Ames, IA, 1977).

[3] Simulink User’s Guide (The Math works, Natick, MA, 1999).

[4] Huynh ChauDuy, Transient stability analysis of a multi machine power system,HoChiMinh City University of

Technology, Vietnam, 2008.

[5] P. M. Anderson and A. A. Fouad, Power System Control and Stability (Iowa State University Press, USA,, IA, 1977).

[6] John J. Grainer, Willam D. Stevenson JR: Power System Analysis, McGraw-Hill International Editions, 1999.

AUTHORS PROFILE

Mr Tefera Mekonnen is the Head of the dept of School of Electrical and Computer engineering, Jimma University, JIT , Ethiopia, Having

vast experience in Electrical engineering teaching, Research, project guiding etc.,His main areas of research are Renewable energy, Power

systems, power Electronics,. Having good exposure to the simulation software applications, development and deployment as well power

system Stability studies. His main hobbies include Research, books, articles, writing, sports etc.

Dr Hadadi Sudheendra a senior member of IEEE having around 20 years of teaching and research experience .His main areas of Research

are Renewable energy, parallel processing, power systems, protection, stability analysis and spoof attack suppression by cryptography.. .

Mr. Getnet Zewde a senior Faculty member in the dept of ECE, JIT, Jimma Ethiopia, his main areas of interest are parallel computing,

power systems, having an experience of around 10 years in teaching and Research .

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(IJIRMPS) A Unified Approach for the Transient Stability ...ijirmps.com/Volume 3/Issue 3/IJIRMPS1404201503_01.pdf · Analysis for a Multi machine System Using MatLab ... model used