Transient Stability Analysis of 5-Bus system Prajapati Bhavikkumar

Master of Engineering in Electrical, L. D .College of Engineering

Gujarat Technological University, Ahmedabad, Gujarat, India.

Er.Bhavikkumar@gmail.com

Abstract— After major recent blackouts caused by power

system instability lie importance of this phenomenon. Transient

stability has been the dominant stability problem on most system

and has been the focus of much of industry‘s attention

concerning system stability assessment is concern with behaviour

of synchronous machines after they have been experience a large

disturbance in system. This paper present simulation case study

of 5-bus, 3-machines system a 5o Hz & 220kv transmission line

has two generators and an infinite bus as shown figure 2. Three

phase fault occurs as shown figure 2. Finding the swing curve for

each generator during the fault period. With help of MiPower

software using time domain method.

Keywords— Transient stability analysis, MiPower software,

Time domain method, Swing curve, Load flow analysis

I. INTRODUCTION

Successful operation of a power system depends on the

engineer’s ability to provide reliable and uninterrupted service

to the loads. The first requirement of reliable service is to keep

the synchronous generator running in parallel and with

adequate capacity to meet the load demand. Synchronous

machine do not fall out of step under normal conditions. if a

machine tends to speed up or slow down synchronizing forces

tend to keep it in step. The second requirement of reliable

electrical service is to maintain the integrity of power

network. Interruption in this network may hinder the flow of

power to the load. We may look at any of these as a change

from one equilibrium state to another. These problems must

be studied by the power system engineer and fall under

heading power system transient stability.[1]

Transient stability is part of rotor angle stability. If

the magnitude of disturbance is very large dynamics of

rotating machine affected more hence dynamic equation of

rotating machine including that automatic voltage regulator,

exciter, prime mover and generator will appear in

mathematical calculation of stability analysis. Example of

large disturbance like sudden change in load, loss of generator

unit, change in transmission line parameter, switching and

various faults etc.[2]

II. METHODS OF ANALYSIS

A variety of transient stability assessment methods have been

classified into main three groups [3]:

A) Heuristic

B) Training based System

C) Digital Simulation

Fig.1 Method of Transient stability Analysis

A. Heuristic Method: Heuristic or expert methods use the

concept of artificial intelligence. In this approach, engineering

knowledge is encoded into the sets of rules in a program. The

program itself then forms two cores: the database and decision

rules. a large number offline studies are required for a range

of power system operating points and disturbances to form

the required database.[4]

B. Training Based System: Artificial neural networks and

pattern recognition have been also used for transient stability

analysis and classify as training system models. In these

methods, the training sets are formed base on offline studies to

form the pattern vector. Then the classifier needed to be

designed for subsequent use in making decision online.

Artificial neural networks have advantages over the traditional

classifier as, after training ANN’s have capability of

generalizing. [5]

C. Digital Simulation Method: Artificial neural networks

and pattern recognition have been also used for transient

stability analysis and classify as training system models. In

these methods, the training sets are formed base on offline

studies to form the pattern vector. Then the classifier needed

to be designed for subsequent use in making decision online.

Artificial neural networks have advantages over the traditional

classifier as, after training ANN’s have capability of

generalizing.

1) Time Domain Solution Method:

In this method the initial system state is obtained

from the pre-fault system. This is starting point used for

integration of fault on dynamic equation. After the fault is

cleared, the post fault dynamic equations are numerically

integrated. The machine angle may be plotted versus time and

analysed. A maximum relative rotor angles threshold is

nominated in practical for forming the transient stability

criteria. For power system to be transiently stable, the

maximum relative rotor angles of all generators are to be less

than the transient stability threshold. If this angles are

bounded, the system is stable otherwise unstable.

2) Direct Method:

As time domain simulation methods were

computationally expensive, some efforts were taken to assess

the power systems transient stability directly, and without

solving DAEs of power system. The first direct method which

was used in power system transient stability was the equal

area criteria (EAC) for single machine infinite bus(SMIB).the

method is able to find the critical clearing time without the

solving the system DAEs.

Lynapunav’s method was adopted in the power

systems multi machine transient stability for first time[6] .the

application of Lynapunav’s method to power system is called

transient energy function(TEF).these methods compare the

energy of the system when the fault is cleared to the critical

energy value of the system. if the system energy at fault

clearing time, is less the critical energy value, the system will

be stable following disturbance however there are number of

disadvantages in this methods. In practice it’s require to

simplify power system model deriving the energy function. It

is difficult, if not impossible to include the detailed dynamic

model of generators load and FACTS devices in derivation of

the transient energy function. Furthermore, it is not straight

forward to determine threshold value of the energy function

for defining stability margin. [7]- [9]

III. FACTORS INFLUENCING TRANSIENT STABILITY

Many factors affect the transient stability of a generator

in a practical power system. The following factors can be

identified [10]:

The generator output during the fault. This is a

function of faults location and type of fault.

The Post-disturbance system reactance as seen from

the generator. The weaker the post-disturbance

system, the lower the Pmax will be.

The duration of the fault-clearing time. The longer

the fault is applied, the longer the rotor will be

accelerated and the more kinetic energy will be

gained. The more energy that is gained during

acceleration, the more difficult it is to dissipate it

during deceleration

The inertia of the generator. The higher the inertia,

the slower the rate of change of angle and the lesser

the kinetic energy gained during the fault.

The generator internal voltage (determined by

excitation system) and infinite bus voltage (system

voltage). The lower these voltages, the lower the Pmax

will be.

The generator loading before the disturbance. The

higher the loading, the closer the unit will be to Pmax,

which means that during acceleration, it is more

likely to become unstable.

The generator internal reactance. The lower the

reactance, the higher the peak power and the lower

the initial rotor angle.

IV. 5-BUS SYSTEM CASE STUDY

Take a 5-bus system consisting i.e. one slack bus or

swing bus, two generator buses, two load buses. a50Hz, 220kv

transmission line has two generators and an infinite bus as

Shawn in figure2.

A 500 MVA, 50Hz Generator-1 at bus 2 deliver

325MW over a double circuit line to an infinite bus. This

Generator has moment of Inertia 12MJ/MVA, transient

reactance X’d is 0.067p.u. And another 300MVA, 50Hz

Generator-2 at bus 3 deliver 210MW over a double circuit line

to an infinite bus. This Generator has moment of Inertia 9

MJ/MVA, transient reactance X’d is 0.10 p.u., |E’|=1.1 p.u

and infinite Bus voltage V=1.0L0O.on base of 100MVA.

Fig.2 a 5- Bus system single line diagram

Plotting the swing curves for the Generator machines at

buses 2 and 3 for the fault which is cleared by opening of

circuit breaker at 0.275 sec.

V. SIMULATION

A. Load flow Analysis

First in transient stability analysis a load flow study is

performed to obtain a set of feasible steady state system

conditions to be used as initial conditions. In Mipower

software simulation system bus voltage magnitude and angle

(unknown variable) by solving the non linear algebraic

network equation using fast decoupled method so that

specified load are supplied. As solution progresses, if voltage

at load bus find out of limits then corresponding adjustment

are made to bring their voltage back in range. at end of

solution process either solution has converged or the number

of allowed iteration has been exceeded a solved load flow case

is require to set the operating condition used to initialized for

transient stability analysis. Fig.4 shows Load flow plot in

MiPower software which will indicate Active power, Reactive

power flow in transmission line and Bus voltages.

Load flow Result:

TABLE I

BUS VOLTAGE AND POWER

Bus

No.

Volt

Mag.

Angle MW

Gen.

Mvar

Gen.

MW

Load

Mvar

Load

Bus-1 1.00 0.00 -378.94 15.85 0.00 0.00

Bus-2 1.03 8.22 -325.00 63.73 0.00 0.00

Bus-3 l.02 7.14 210.00 24.66 0.00 0.00

Bus-4 1.01 4.33 0.0000 0.000 100 44.0

Bus-5 1.00 2.49 0.0000 0.000 50.0 16.0

From Table- II result we can say that all buses voltage

magnitude are within limit not violates

A. Transient Stability Analysis

5-bus system analysis using Mipower software in that

simulation, at 0 sec. a three phase to ground fault was applied

at bus-4 and fault cleared at 0.275sec. Simultaneously applied

change in transmission line parameter of line-1 connected

between bus-4 and bus-5 at 0.275 sec. end time up to 1 sec.

With simulation time of frame given from 0 sec. to 1 sec. by

the time step is 0.025 sec. As fig.4 shows Transient stability

simulation time frame and Disturbances applied in MiPower

Software and Table-IIIIV shows Active power transfer with

reference to rotor angle Delta (degree).

Transient Stability Result:

TABLE VVI MACHINE ANGLE AND POWER

Time Delta(Degree) P Gen(MW)

Bus 2 Bus3 Bus2 Bus3

0.000 19.4 18.3 325 210

0.025 19.7 18.3 17.4 183

0.050 21.2 18.5 17.7 185

0.075 24.1 18.8 18.3 189

0.100 28.4 19.3 19 194

0.125 34.1 19.3 19.8 200

0.150 41.3 20.4 20.7 207

0.175 49.9 21.1 21.5 215

0.200 60.0 21.7 22.4 222

0.225 71.4 22.2 23.1 230

0.250 84.3 22.6 23.7 236

0.275 98.6 51.7 24.1 242

0.300 113 22.8 823 284

0.325 62.8 6.94 719 284

0.350 138 21.6 599 280

0.375 149 20.3 472 271

0.400 158 18.6 390 259

0.425 167 16.6 765 246

0.450 175 14.4 630 227

0.475 181 12.1 269 207

0.500 187 9.85 -20.7 187

0.525 195 7.71 -240 171

0.550 205 5.81 -227 158

0.575 218 4.23 -507 147

0.600 235 3.04 -660 142

0.625 257 2.25 -755 143

0.650 283 1.89 -704 147

0.675 314 1.91 -433 155

0.700 348 2.27 37.3 166

0.725 384 2.9 534 180

0.750 419 3.71 844 196

0.775 451 4.61 870 214

0.800 482 5.48 652 233

0.825 511 6.21 683 253

0.850 538 6.67 6.9 267

0.875 567 6.78 -497 280

0.900 600 6.45 -736 289

0.925 637 5.64 -682 292

0.950 679 4.33 -251 287

0.975 723 2.54 382 276

1.000 767 0.35 830 261

Fig.3 Load flow Plot of 5-Bus System

Fig.4 Transient Stability Analysis Simulation Time Frame & Disturbances applied

B. Graph

allow machine to swing through a larger rotor angle from its

original initial position before it reaches the critical clearing

angle.

Graph is generate automatically in Migraph utility which

Provide swing curve or plot between power angle (degree) &

to time (sec.).here fig.5 show curve for machine-2&3 which

are connected at bus-2&3.

Fig.5 Swing Curve of Machine-2 and Machine-3

VI. CONCLUSIONS

Before applying fault, the system has a

satisfactory and stable initial condition. Voltage magnitude is

fixed at1.0 p.u. and there is no oscillation during this period.

During fault application voltage vector is set to zero (three

phase fault) and machine angle start to increases until fault

cleared time 0.275sec.

After removing fault a angle of machine start

oscillations.Machine-3 does not lose synchronism with rest of

system since angle oscillation does not go over 90 degree.

while Machine-2 lose synchronism or unstable.

In this case study, A Simulation of Transient Stability of

5-Bus system using MiPower software by Time domain

method. My idea was demonstrated by applying two

disturbances on system. one of the applying three phase to

ground fault at bus-4 and another one by changing trans-

mission line parameter (opening of Transmission line).The

methodology is built upon state of increases power transfer

through healthy portion of network during disturbances, which

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