transient stability analysis of nine bus system with multiple contingencies

TRANSIENT STABILITY ANALYSIS OF THREE–MACHINE NINE–BUS SYTEM WITH MULTIPLE CONTINGENCIES

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENT FOR THE BACHELOR OF

ENGINEERING DEGREE IN ELECTRICAL AND

ELECTRONICS ENGINEERING

By

V. Shashank 2451-10-734-024

M. Saikiran 2451-10-734-025

B.Ritvik Kranti 2451-10-734-040

V. Arun 2451-10-734-057

T. Ajay Kumar 2451-09-734-021

Under the Esteemed guidance of

Dr. D. Venu Madhava Chary

DEPARTMENT OF ELECTRICAL AND

ELECTRONICS ENGINEERING

MVSR ENGINEERING COLLEGE, NADERGUL,

HYDERABAD

2013-2014

MVSR ENGINEERING COLLEGE NADERGUL(P.O), HYDERABAD

CERTIFICATE

This is to certify that the thesis entitled, “Transient Stability Analysis of three-machine nine-bus

system with multiple contingencies” submitted by V. Shashank, M. Saikiran, B. Ritvik

Kranthi, V. Arun and T. Ajay Kumar at the MVSR Engineering College, Nadergul,

Hyderabad (Affiliated to Osmania University) is an authentic work carried out by them under my

supervision and guidance.

To the best of my knowledge, the matter embodied in the thesis has not been submitted to any

other University / Institute for the award of any Degree or Diploma.

Dr. D. Venu Madhava Chary

Head of Department, EEE

Date: MVSR Engineering College

Acknowledgement:

We wish to express our deep sense of gratitude to our Head of Electrical and Electronics department,

Dr.D.Venu Madhava Chary, MVSR Engineering College, for duly steering the course of action and

also for his guidance and encouragement throughout our project.

We would like to extend our gratitude and our sincere thanks to our honourable Principal

Dr. P.A. Sastry for letting us do the project in the college and for being a source of constant

motivation.

We would like to thank other staff members for their valuable guidance and highly interactive

attitude without which the completion of the project would have been a difficult task.

Finally, we express our gratitude to all other members who are involved either directly or indirectly

for the completion of this project.

Contents

ABSTRACT ............................................................................................................................................. 1

INTRODUCTION .................................................................................................................................... 2

1.1 BACKGROUND ............................................................................................................................. 3

1.2 POWER SYSTEM STABILITY: ........................................................................................................ 4

1.3 CLASSIFICATION OF POWER SYSTEM STABILITY: ....................................................................... 4

TRANSIENT STABILITY: AN OVERVIEW ................................................................................................ 6

2.1 TRANSIENT STABILITY .................................................................................................................. 7

2.2 MECHANICAL ANALOGY .............................................................................................................. 8

2.3 ELEMENTARY VIEW OF TRANSIENT STABILITY .......................................................................... 10

2.4 SWING EQUATION .................................................................................................................... 12

2.5 EQUAL AREA CRITERION ........................................................................................................... 13

POWERWORLD SIMULATOR: INTRODUCTION ................................................................................. 15

TRANSIENT STABILTY ANALYSIS OF THREE MACHINE NINE BUS SYSTEM ....................................... 19

4.1 IMPORTANCE OF TRANSIENT STABILITY ANALYSIS .................................................................. 20

4.2. CASE STUDY OF A THREE-MACHINE NINE-BUS SYSTEM .......................................................... 21

4.2.1 CASE 1: LINE FAULT ........................................................................................................... 23

4.2.2 CASE 2: LOSS OF GENERATION .......................................................................................... 28

4.2.3 CASE 3: LOSS OF LOAD ...................................................................................................... 30

4.2.4 CASE 4: SIMULTANEOUS LOSS OF GENERATION AND LOSS OF LOAD .............................. 32

4.2.5 CASE 5: LOSS OF GENERATION AND LOSS OF LOAD ......................................................... 34

4.2.6 CASE 6: BUS FAULT, LOSS OF GENERATION, LOSS OF LOAD ............................................. 36

RESULTS AND DISCUSSION ................................................................................................................ 39

6.1. RESULTS .................................................................................................................................... 40

6.1.1 CASE 1: ............................................................................................................................... 40

6.1.2 CASE 2: ............................................................................................................................... 41

6.1.3 CASE 3: ............................................................................................................................... 41

6.1.4 CASE 4: ............................................................................................................................... 42

6.1.5 CASE 5: ............................................................................................................................... 42

6.1.6 CASE 6: ............................................................................................................................... 43

CONCLUSION ...................................................................................................................................... 44

7.1. CONCLUSION ............................................................................................................................ 45

7.2. ASPECTS OF FUTURE WORK ..................................................................................................... 45

REFERENCES ....................................................................................................................................... 46

APPENDIX ........................................................................................................................................... 47

System data ..................................................................................................................................... 47

1

ABSTRACT Power-system stability is a term applied to alternating-current electric power systems, denoting a

condition in which the various synchronous machines of the system remain in synchronism, or

"in step," with each other. Conversely, instability denotes a condition involving loss of

synchronism, or falling "out of step." Occurrence of a fault in a power system causes transients.

A PowerWorld Simulation is done to study the transient stability of a three machine nine bus system

for both single and multiple contingencies.

2

Chapter 1

INTRODUCTION

3

1.1 BACKGROUND

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 nine-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 is usually chosen for calculation of load flow study.

If the oscillatory response of a power system during the transient period following a disturbance is

damped and the system settles in a finite time to a new steady operating condition, we say the system

is stable. If the system is not stable, it is considered unstable. This primitive definition of stability

requires that the system oscillations should be damped. This condition is sometimes called

asymptotic stability and means that the system contains inherent forces that tend to reduce oscillation.

Transient stability of a transmission is a major area of research from several decades. Transient

stability restores the system after fault clearance. Any unbalance between the generation and

load initiates a transients that causes the rotors of the synchronous machines to “swing” because

net accelerating torques are exerted on these rotors. If these net torques are sufficiently large to

cause some of the rotors to swing far enough so that one or more machines “slip a pole” and

synchronism is lost. So the calculation of transient stability should be needed. A system load flow

analysis is required for it .The transient stability needs to be enhanced to optimize the load ability

of a system, where the system can be loaded closer to its thermal limits.

Occurrence of fault may lead to instability in a system or the machine fall out of

synchronism. Load flow study should be done to analyse the transient stability of the power

system. If the system can’t sustain till the fault is cleared then the fault instabilise the whole

system. If the oscillation in rotor angle around the final position go on increasing and the change

in angular speed during transient condition go on increasing then system never come to its final

position.

4

1.2 POWER SYSTEM STABILITY: Power system stability as the ability of an electric power system, for a given initial operating condition

to regain a state of operating equilibrium after being subjected to a physical disturbance ,with most

system variables bounded so that the practically the entire system remains intact.

To understand stability well another factor that is to be taken into consideration is the stability limit of

the system. The stability limit defines the maximum power permissible to flow through a particular

point or a part of the system during which it is subjected to line disturbances or faulty flow of power.

Having understood these terminologies related to power system stability let us now look into the

different types of stability.

1.3 CLASSIFICATION OF POWER SYSTEM STABILITY:

The synchronous stability of a power system can be of several types depending upon the nature of

disturbance, and for the purpose of successful analysis it can be classified into the following 3 types as

shown below:

1) Steady state stability.

2) Transient stability.

3) Dynamic stability.

Figure 1.1 Classification of power system stability

5

The steady state stability of a power system is defined as the ability of the system to bring itself back

to its stable configuration following a small disturbance in the network.

Transient stability of the system refers to the ability of the system to reach a stable condition following

a large disturbance in the network condition. [1][2]

Dynamic stability of a system denotes the artificial stability given to an inherently unstable system by

automatic controlled means. It is generally concerned to small disturbances lasting for about 10 to 30

seconds.

In general practice studies related to transient stability in power system are done over a very small

period of time equal to the time required for one swing, which approximates to around 1 sec or even

less. If the system is found to be stable during this first swing, it is assumed that the disturbance will

reduce in the subsequent swings, and the system will be stable thereafter as is generally the case.

6

Chapter 2

TRANSIENT STABILITY: AN OVERVIEW

7

2.1 TRANSIENT STABILITY

Each generator operates at the same synchronous speed and frequency of 50 hertz while a

delicate balance between the input mechanical power and output electrical power is maintained.

Whenever generation is less than the actual consumer load, the system frequency falls. On the

other hand, whenever the generation is more than the actual load, the system frequency rise. The

generators are also interconnected with each other and with the loads they supply via high

voltage transmission line.

An important feature of the electric power system is that electricity has to be generated when it

is needed because it cannot be efficiently stored. Hence using a sophisticated load

forecasting procedure generators are scheduled for every hour in day to match the load. In

addition, generators are also placed in active standby to provide electricity in times of

emergency. This is referred as spinning reserved.

The power system is routinely subjected to a variety of disturbances. Even the act of switching

on an appliance in the house can be regarded as a disturbance. However, given the size of the

system and the scale of the perturbation caused by the switching of an appliance in comparison

to the size and capability of the interconnected system, the effects are not measurable.

Large disturbance do occur on the system. These include severe lightning strikes, loss of

transmission line carrying bulk power due to overloading. The ability of power syste m to

survive the transition following a large disturbance and reach an acceptable operating condition

is called transient stability.

The physical phenomenon following a large disturbance can be described as follows. Any

disturbance in the system will cause the imbalance between the mechanical power input to the

generator and electrical power output of the generator to be affected. As a result, some of the

generators will tend to speed up and some will tend to slow down. If, for a particular generator,

this tendency is too great, it will no longer remain in synchronism with the rest of the system and

will be automatically disconnected from the system. This phenomenon is referred to as a

generator going out of step.

8

Acceleration or deceleration of these large generators causes severe mechanical stresses.

Generators are also expensive. Damage to generators results in costly overhaul and long

downtimes for repair. As a result, they are protected with equipment safety in mind. As soon as a

generator begins to go out-of-step, sensor in the system sense the out-of-step condition and trip the

generators. In addition, since the system is interconnected through transmission lines, the

imbalance in the generator electrical output power and mechanical input power is reflected in a

change in the flows of power on transmission lines. As a result, there could be large oscillations

in the flows on the transmission lines as generator try to overcome the imbalance and their output

swing with respect to each other.

2.2 MECHANICAL ANALOGY

A mechanical analogy to this phenomenon can be visualized in fig. 1. Suppose that there is a set

of balls of different sizes connected to each other by a set of strings. The balls represent

generators having a specific mechanical characteristic (that is, inertia). The strings represent the

transmission line interconnecting the generators.

Fig.2.1. Mechanical Analogy of Transient Stability

9

Now suppose that there is a disturbance in which one of the balls is struck with a cue.

The ball now begins to swing, and as a result, the string connected to the ball also

oscillates. In addition, the other strings to which this string is connected are also affected,

and this in turn affects the other balls connected to these strings. As a result, the entire

interconnected system of balls is affected, and the system experiences oscillations in the

strings and motion of the balls. If these oscillations in the strings become large, one of the

strings may break away from the rest, resulting instability. On the other hand if the

oscillation dies down and the entire system comes back to rest as in the situation prior to

the ball being struck. This condition is analogous to a power system being “transiently

stable”.

In a power system, an additional important characteristic in the operating condition, as the

loading on the system increases, the system becomes more stressed and operates closer to

its limits. During these stressed condition, a small disturbance can make the system

unstable. Dropping a marble into a pitcher of water provides a suitable analogy to

understand why the operating condition makes a difference in maintaining transient

stability.

1. Take a pitcher and fill it with the water to quarter its capacity. Now drop a marble

in the pitcher. The dropping of the marble is akin to a disturbance in the power

system. In this situation no water from the pitcher will splash out, indicating the

system is stable.

2. Now fill the pitcher with water close to it brim and drop the same marble into the

pitcher. In this case, water will splash out, indicating the system is unstable.

In these two situations, the same disturbance was created. However, the system was

operating at different conditions, and in the latter situation, the system was more stressed.

Again, this analogy illustrates that the degree of stability is dependent on the initial

operating condition.

10

2.3 ELEMENTARY VIEW OF TRANSIENT STABILITY

Fig. 2.2. Simple two machine power system Fig.2.3. Phasor diagram of the different

parameters

Consider the very simple power system of Fig. 2.2, consisting of a synchronous generator

supplying power to a synchronous motor over a circuit composed of series inductive

reactance XL. Each of the synchronous machines may be represented, at least

approximately, by a constant- voltage source in series with a constant reactance. Thus

the generator is represented by Eg and Xg; and the motor, by EM and XM. Upon

combining the machine reactance and the line reactance into a single reactance, we have

an electric circuit consisting of two constant-voltage sources, Eg and EM, connected

through reactance X =XG + XL + XM . It will be shown that the power transmitted

from the generator to the motor depends upon the phase difference 8 of the two voltages

EG and EM. Since these voltages are generated by the flux produced by the field

windings of the machines, their phase difference is the same as the electrical angle

between the machine rotors.

The vector diagram of voltages is shown in figure. 2.3 Vectorially,

EG = EM + jXI

(The bold-face letters here and throughout the book denote complex, or vector, quantities)

Hence the current is

11

The power output of the generator and likewise the power input of the motor, since there is

no resistance in the line is given by

This equation shows that the power P transmitted from the generator to the motor varies

with the sine of the displacement angle δ between the two rotors, as plotted in Fig. 2.3.

The curve is known as a power angle curve. The maximum power that can be transmitted

in the steady state with the given reactance X and the given internal voltages EG and EM is

and occurs at a displacement angle δ= 90°. The value of maximum power may be

increased by raising either of the internal voltages or by decreasing the circuit reactance.

12

2.4 SWING EQUATION

The electromechanical equation describing the relative motion of the rotor load angle (δ)

with respect to the stator field as a function of time is known as Swing equation.

When the synchronous generator is fed with a supply from one end and a constant load is

applied to the other, there is some relative angular displacement between the rotor axis

and the stator magnetic field, known as the load angle δ which is directly proportional to

the loading of the machine. The machine at this instance is considered to be running

under stable condition.

Now if we suddenly add or remove load from the machine the rotor decelerates or

accelerates accordingly with respect to the stator magnetic field. The operating condition

of the machine now becomes unstable and the rotor is now said to be swinging w.r.t the

stator field and the equation we so obtain giving the relative motion of the load angle δ

w.r.t the stator magnetic field is known as the swing equation for transient stability of

power system.

M d2δ/dt

2 = Pt− Pu

M= inertia constant

Pt =Shaft power input corrected for rotational losses

Pu = Pmax sin δ = Electrical power output corrected for rotational losses

Pmax = Amplitude for the power angle curve

δ = Rotor angle with respect to a synchronously rotating reference

Fig.2.4. Power-angle curve of the system

http://www.electrical4u.com/alternator-or-synchronous-generator/

http://www.electrical4u.com/what-is-magnetic-field/

http://www.electrical4u.com/what-is-magnetic-field/

13

2.5 EQUAL AREA CRITERION

Consider the power angle curve shown in following figure. Suppose the system is operating

in the steady state delivering a power of Pm at an angle of δ0 when due to malfunction of the

line, circuit breakers open reducing the real power transferred to zero. Since Pm remains

constant, the accelerating power Pa becomes equal to Pm. The difference in the power gives

rise to the rate of change of stored kinetic energy in the rotor masses. Thus the rotor will

accelerate under the constant influence of non-zero accelerating power and hence the load

angle will increase. Now suppose the circuit breaker re-closes at an angle δc. The power will

then revert back to the normal operating curve. At that point, the electrical power will be

more than the mechanical power and the accelerating power will be negative. This will

cause the machine decelerate. However, due to the inertia of the rotor masses, the load angle

will still keep on increasing. The increase in this angle may eventually stop and the rotor

may start decelerating, otherwise the system will lose synchronism.

Figure 2.5 Equal area criterion

Note that

Hence multiplying both sides of above equation by and rearranging we get

14

Multiplying both sides of the above equation by dt and then integrating between two

arbitrary angles δ0 and δc we get

Now suppose the generator is at rest at δ0. We then have dδ / dt = 0. Once a fault occurs, the

machine starts accelerating. Once the fault is cleared, the machine keeps on accelerating

before it reaches its peak at δc , at which point we again have dδ / dt = 0. Thus the area of

accelerating is given as

In a similar way, we can define the area of deceleration. The area of acceleration is given

by A1 while the area of deceleration is given by A2 . This is given by

Now consider the case when the line is reclosed at δc such that the area of acceleration is

larger than the area of deceleration, i.e., A1 > A2 . The generator load angle will then cross

the point δm , beyond which the electrical power will be less than the mechanical power

forcing the accelerating power to be positive. The generator will therefore start accelerating

before is slows down completely and will eventually become unstable. If, on the other

hand, A1 < A2 , i.e., the decelerating area is larger than the accelerating area, the machine

will decelerate completely before accelerating again. The rotor inertia will force the

subsequent acceleration and deceleration areas to be smaller than the first ones and the

machine will eventually attain the steady state. If the two areas are equal, i.e., A1 = A2 ,

then the accelerating area is equal to decelerating area and this is defines the boundary of the

stability limit. The clearing angle δc for this mode is called the Critical Clearing Angle and

is denoted by δcr. By by substituting δc = δcr

We can calculate the critical clearing angle from the above equation. Since the critical

clearing angle depends on the equality of the areas, this is called the equal area criterion.

15

Chapter 3

POWERWORLD SIMULATOR: INTRODUCTION

16

PowerWorld Simulator is an interactive power system simulation package designed to

simulate high voltage power system operation on a time frame ranging from several

minutes to several days. The software contains a highly effective power flow analysis

package capable of efficiently solving systems of up to 100,000 buses.

The electric power system is considered the backbone of modern information society.

Without safe, reliable and economic supply of electricity many other infrastructures and

services including telephone, airlines, railways, computing, banking, hospitals will not be

operating properly.

Therefore the power system infrastructure is considered the most critical one and its

operation needs to be assured on a daily basis. Simulation programs like PowerWorld are

essential for planning and operation of modern power systems.

The simulator is actually a number of integrated products. At its core is a comprehensive,

robust Power Flow Solution engine capable of efficiently solving systems of up to 100,000

buses. This makes the simulator quite useful as a stand-alone power flow analysis package.

System models may be modified on the fly or even built from scratch using Simulator’s

full-featured graphical case editor. Transmission lines may be switched in or out of service,

new transmission or generation may be added, and new transactions may be established, all

with a few mouse clicks. The simulator’s extensive use of graphics and animation greatly

increases the user’s understanding of system characteristics, problems, and constraints, as

well as of how to remedy them.

The simulator also provides a convenient medium for simulating the evolution of the power

system over time. Load, generation, and interchange schedule variations over time may be

prescribed, and the resulting changes in power system conditions may be visualized. This

functionality may be useful, for example, in illustrating the many issues associated with

industry restructuring.

In addition to these features, Simulator boasts integrated economic dispatch, area

transaction economic analysis, power transfer distribution factor (PTDF) computation,

short circuit analysis and contingency analysis, all accessible through a consistent and

colourful visual interface.

PowerWorld offers several optional add-ons like Available Transfer Capability (ATC),

Distributed Computing, Geomagnetically Induced Current (GIC), Integrated Topology

Processing, Optimal Power Flow Analysis Tool (OPF), Voltage Stability Analysis,

Automation Server (SimAuto), Transient Stability.

Transient Stability addon is used in this project. It is accessible within the familiar

PowerWorld Simulator interface

Figure 3.1 Transient stability addon in PowerWorld Simulator

17

Variety of Dynamic models can be assigned to the power system elements.

Figure 3.2 Generator modelling in PowerWorld Simulator

Figure 3.3 Model Explorer in PowerWorld Simulator

18

Various types of faults can be created and the simulation can be run after inputting the time

of occurrence of the fault, time of clearance of fault if any and simulation time values.

Clicking on the Run Transient Stability button on the top left of the window starts the

simulation.

Figure 3.4 Transient stability analysis window in PowerWorld Simulator

Figure 3.5 Example Plots obtained using PowerWorld Simulator

Plots can be obtained from the plots tab in the left side plane of the transient stability

analysis window.

PowerWorld Simulator is a powerful tool in Power Systems analysis and design. Lot of

computational effort and time in solving complex power system related problems can be

saved using simulator software such as PowerWorld Simulator.

19

Chapter 4

TRANSIENT STABILTY ANALYSIS OF THREE MACHINE NINE BUS SYSTEM

20

4.1 IMPORTANCE OF TRANSIENT STABILITY ANALYSIS

The stability of power systems continues to be major concern in system operation. Modern

electrical power systems have grown to a large generating units and extra high voltage tie-

lines, etc. The transient stability is a function of both operating conditions and disturbances.

Thus the analysis of transient stability is complicated.

Synchronous machines will respond to close-up faults with rotor swings that depend upon

the machine loading, excitation control, the fault location and the speed and action of

protective gear. Excessive rotor oscillations result in large current flows between the

machine and system and lead to eventual tripping of the machine from the system. Modern

excitation systems are effective in damping oscillations to a certain extent but the

configuration of the network and loading conditions are significant factors in determining

stability. For most cases, the size of the generator compared to the capacity of the

distribution feeder source to which it is connected is small. However, if machine size

approaches the feeder source capacity, the implications of fault disturbances or the loss of

the machine have to be considered much more carefully and will almost certainly result in

the imposition of a limit on generator size.

In practical terms, transient stability analysis for a distribution system is not as significant a

problem as for a transmission system. Generators are typically isolated onto individual

feeders supplied from separate substations. Consequently, the impedances between

generators imposes a limit on the the synchronizing power that can flow between machines

and a fault affecting one machine has very limited impact on another. Synchronizing power

almost invariably flows from the supply source to stabilize the machine.

A common regulatory requirement imposed by most supply utilities is that a generator

connected at distribution level be removed from the system in the event of machine

operation that jeopardizes the integrity of the system. Under and overvoltage protection is

commonly applied to disconnect the machine from the system. Another example of a

suitable device is a rate-of-change of frequency protective device that removes the machine

from the network in the event that the instantaneous frequency difference between

generator and system exceeds a certain value. In many cases, the complications of

accommodating all eventualities raise technical and cost issues and tripping the machine off

the supply system is the only practical resort.

21

4.2. CASE STUDY OF A THREE-MACHINE NINE-BUS SYSTEM

The following three-machine nine-bus system is used for the transient stability analysis

studies.

Fig.4.1 3-machine 9-bus system which has to be simulated

22

The system data is provided in appendix.

The above system is modelled in PowerWorld and the power flow solution is obtained as

follows

Figure 4.2 Simulated model

23

4.2.1 CASE 1: LINE FAULT

A fault is created on the line between buses 5 and 7 near the terminal of bus 7, which is

cleared after fault clearing time fct = 0.077 seconds by opening the bus 5 to 7 line.

Figure 4.3 Relative rotor angles when fault at bus 7 and fct = 0.05 seconds


24

Figure 4.5 Terminal voltage when fault at bus 7 and fct = 0.05 seconds


25



26



27

These characteristic indicates that the generators are unstable for the fault clearing times of

0.08s and 0.2 seconds. The critical clearing time for this case is 0.079 seconds. The

voltages at buses 1,2,3 for fault clearing time 0.05 seconds and 0.077 seconds are shown in

figures 4.5 and 4.6 respectively. From these figures, it is observed that the bus bar voltage is

collapsed at the fault clearing times of 1.050 and 1.077 seconds. After that, the bus bar

voltages swing together with the time, which indicates the generators are becoming stable.

In figures 4.9 and 4.10, the bus bar voltages do not swing together with time after fault

clearance causing the unstable condition.

28

4.2.2 CASE 2: LOSS OF GENERATION

The generator connected to bus bar 3 is opened at t = 1 second.

This is a severe contingency since more than 25% of the system generation is lost resulting

in a frequency dip of almost 1 Hz. Notice that the frequency does not return to 60 Hz.

Turbine governors are used for the generators in plotting these results.

Figure 4.11 Frequency variation with generator 3 open at t = 1 second with turbine governors

Figure 4.12 Mechanical Power input variation with generator 3 open at t = 1 second

29

Figure 4.13 Frequency variation with generator 3 open at t = 1 second with slower hydro

governors

The slower hydro governors result in much more frequency dip of almost 1.5 Hz. In actual

operation this frequency decline may have been interrupted by under frequency relays.

30

4.2.3 CASE 3: LOSS OF LOAD

The load connected to bus 8 is opened at t = 1 second. The rotor angle variation due to this

disturbance is shown in figure 4.14

Figure 4.14 Relative rotor angles for loss of load on bus 8 at t = 1 second

Figure 4.15 Output Power variation with loss of load on bus 8 at t = 1 second

31

Figure 4.16 Frequency variation with loss of load on bus 8 at t = 1 second

As part of the system load is suddenly removed at t = 1 second, the frequency rises and

settles at a value slightly above 60 Hz.

32

4.2.4 CASE 4: SIMULTANEOUS LOSS OF GENERATION AND LOSS OF LOAD MULTIPLE CONTINGENCY CASE 1 In this case both the generator at bus 3 and load on bus 8 are removed at t = 1 second.

Figure 4.17 Rotor angle variation for multiple contingency case 1

\

Figure 4.18 Terminal voltage variation for multiple contingency case

33

Figure 4.19 Mechanical Power input variation for multiple contingency case 1

In this case, the decrease in shaft input due to loss of load is approximately compensated by

the increase in mechanical power input required due to loss of generation. Hence the

Mechanical power inputs of both the generators 1 and 2 remain almost constant.

Figure 4.20 Frequency variation due to multiple contingency case 1

The frequency dip in figure 4.20 is due to the loss of generation while the subsequent rise in

frequency is due to the loss of load. The frequency finally settles slightly above 60 Hz.

34

4.2.5 CASE 5: LOSS OF GENERATION AND LOSS OF LOAD

MULTIPLE CONTINGENCY CASE 2

To visualise the effects of loss of load and loss of generation in change in frequency more

clearly, the faults are slightly separated in time. The load on bus 8 is opened at t = 1 second

while the generator at bus 3 is opened at t = 2 seconds.


35


Since the load is opened at t = 1 second, the frequency starts to rise at t = 1 second.

Generator on bus 3 is now opened at t = 2 seconds, as visible from the plot, the frequency

now starts to fall. Frequency dips below 60 Hz and finally settles slightly above 60 Hz.

36

4.2.6 CASE 6: BUS FAULT, LOSS OF GENERATION, LOSS OF LOAD MULTIPLE CONTINGENCY CASE 3

A balanced three phase fault is created on bus 5 at t = 1 second and is cleared at t = 1.1

seconds.

The load on bus 8 and generator connected to bus 3 are also opened at t = 1 second.


37

Figure 4.24 Mechanical Power input variation for multiple contingency case 3

Figure 4.25 Terminal voltage variation for multiple contingency case 3

38


39

Chapter 6

RESULTS AND DISCUSSION

40

6.1. RESULTS

The transient stability studies of nine bus system under different fault conditions have been

studied. Multiple contingencies have been simulated on test system. The PowerWorld

simulation results are shown in figures 4.2 to 4.26

6.1.1 CASE 1:

In this a line fault is created between buses 5 and 7 near terminal of bus 7.

In figure 4.3 and figure 4.4 rotor angle is plotted v/s time when fault is cleared before

critical clearing time.

During fault, the rotor angle undergoes sudden change and reaches peak value.

Post fault clearance, the relative variation of rotor angle starts to damp out and finally settles

at steady state value.

In figure 4.5 and figure 4.6 the variation of terminal voltage of the generators with time are

studied when the fault is cleared before critical clearing time

During fault, the terminal voltage collapses to very low value

Post-fault, after clearing the fault the bus bar voltages swing together with time indicating

that the generators are becoming stable.

In figure 4.7 and figure 4.8 the fault is cleared after critical clearing time. Hence the rotor

angle is unbounded indicating unstable system.

In figure 4.9 and figure 4.10 the voltage collapses during the fault but after clearing of fault

the voltages do not swing together indicating an unstable system.

41

6.1.2 CASE 2:

Generator connected to bus bar 3 is opened at t = 1 second.

In figure 4.11 the variation of frequency is plotted with time. It is observed that the

frequency reduces almost by 1Hz immediately after the occurrence of the fault. The

frequency rises back due to governor action and finally settles slightly below 60Hz.

In figure 4.13 hydro governors are used for the generators instead of turbine governors .it is

observed that the frequency dip is higher in case of hydro governors compared to turbine

governors.

In figure 4.12 the variation in mechanical power input to the generators is plotted against

time. The generator 3 is opened at t=1second, hence the mechanical power input to the

generator 3 falls to zero at t=1second. The shaft inputs to the remaining two generators

increases to share the system load.

6.1.3 CASE 3:

The load connected to bus 8 is removed at t = 1 second.

The variation of rotor angles with time is plotted in figure 4.14. The rotor angles undergoes

damped oscillations after the occurrence of the fault and settles to stable value.

In figure 4.15 output power of the generators is plotted against time. The load on bus 8 is

removed at t=1second. The power output falls and undergoes damped oscillations and

finally settles to value less than initial value .

In figure 4.16 frequency is plotted against time. The frequency starts to rise when the load is

removed at t = 1 second and reaches a peak value of about 61.5Hz and then falls to stable

value slightly above 60Hz.

42

6.1.4 CASE 4:

Generator 3 and load on bus bar 8 are removed at t = 1 second.

In figure 4.18 the variation of terminal voltage of the generators with time is observed when

both loss of load and generation occurs. Since the 85 MW generator 3 is suddenly opened at

t=1 second along with 100 MW load at bus 8, the terminal voltages of the generators rise

initially. The voltages at bus 1 and bus 2 settles back to initial values since they are

generator buses and voltage at bus 3 settles at a value higher than its initial as it is far open

end.

In figure 4.19, the mechanical power input is plotted against time and it is observed that the

generator 3’s mechanical power input falls to zero as it is opened at t = 1second. The net

load on the system is reduced due to the removal of 100 MW load and 85 MW generator,

hence the mechanical power inputs of other two generators are slightly reduced.

In figure 4.20, the frequency undergoes oscillation and settles above initial value of 60 Hz

due to net loss of load.

6.1.5 CASE 5:

Load on bus bar 8 is opened at t = 1 second and generator 3 is opened at t = 2 seconds.

Unlike the previous case, in this case the opening of load on bus 8 and opening of generator

3 are simulated to occur one second apart to study the action of each on variation of

frequency.

In figure 4.21, the rotor angles of generators 1 and 2 are seen to rise after the opening of

generator 3 at t = 2 seconds. This is expected as the remaining two generators now have to

share the system load and the mechanical power input to the two generators increases

correspondingly.

43

As seen in figure 4.22, the frequency rises at t = 1second when the load is removed and

subsequently when the generator is removed at t = 2 seconds, the frequency decreases,

undergoes oscillation and finally settles above 60 Hz due to net loss of load

.

6.1.6 CASE 6:

Balanced three phase fault is created on bus 5 at t = 1 second and is cleared at t = 1.1

seconds, generator 3 and load connected to bus 8 are opened at t = 1 second.

In figure 4.23, the variation of rotor angle due to the multiple contingency is simulated. The

rotor angles of generators 1 and 2 settle at higher rotor angle than compared to pre-fault

condition similar to previous case.

Mechanical power input plot in figure 4.24 is almost same as that of figure 4.19 except with

a small dip in at t = 1second for generators 1 and 2 due to the fault on bus 5.

Plot of generator bus bar voltages in figure 4.25 is similar to figure 4.18 except with voltage

collapse at t = 1 second due to the three phase fault on bus 5. The voltage recovers after the

clearance of fault at t = 1.1 seconds. The voltages of bus 1 and bus 3 settle at initial value as

they are generator buses and voltage of bus 3 increases compared to its initial value of 1.025

per unit as it is far open end.

Frequency variation due to the multiple contingency is observed in figure 4.26. Rapidly

oscillating deviations occur in the speeds of generators 1 and 2. The frequency settles to a

value slightly higher than 60 Hz due to net loss of load.

44

Chapter 7

CONCLUSION

45

7.1. CONCLUSION

The transient stability studies are used to determine speed deviations, system electrical

frequency , real and reactive power flow of the machines ,the machine power angles as well

as the voltage levels of the bus and power flows of lines and transformers in the system.

System stability is assessed with these system conditions. Dynamic performance of a power

system is critical in design and operation of the system. The results can be printed or plotted

and are displayed on the one -line diagram. The total simulation time for each study case

should be long enough to obtain a definite stability conclusion.

7.2. ASPECTS OF FUTURE WORK

To date the computational complexity of transient stability problems have kept them from

being run in real –time to support decision making at the time of disturbance. If a transient

stability program could run in real time or faster than real time, then power system control

room operators could be provided with detailed view of the scope of cascading failure. This

view of unfolding situation could assist an operator in understanding the magnitude of the

problem and its ramifications so that pro-active measure could be taken to limit extent of the

incident. Faster transient stability simulation implementation may significantly improve

power system reliability which in turn directly or indirectly affects:

1) Electrical utility company profits.

2) Environment impact.

3) Customer satisfaction.

In addition to real time analysis, there are other areas where transient stability analysis could

become an integral part of daily power system operations.

1) System restoration analysis.

2) Economic/Environmental dispatch.

3) Expansion planning.

46

REFERENCES

[1] Power System Analysis by Hadi Saadaat, second edition, McGraw-Hill Higher

Education, 2002

[2] Modern Power System Analysis by D P Kothari and I J Nagrath

[3] S. B. GRISCOM, "A Mechanical Analogy of the Problem of Transmission Stability"

Elec. Jour., vol. 23, pp. 230-5, May, 1996.

[4] "PowerWorld Simulator 17" PowerWorld Corporation, 2014

http://www.powerworld.com/

[5] PowerWorld Simulator User’s Guide, PowerWorld Corporation, 2011

47

APPENDIX

System data The data is represented in per unit on 100 MVA base.

Time quantities are in seconds.

Line data

From Bus

number

To Bus

number

Series

Resistance (Rs)

pu

Series

Reactance (Xs)

pu

Shunt

Susceptance

(B) pu

1 4 0.0000 0.0576 0.0000

4 6 0.0170 0.0920 0.1580

6 9 0.0390 0.1700 0.3580

9 3 0.0000 0.5860 0.0000

9 8 0.0119 0.1008 0.2090

8 7 0.0085 0.0720 0.1490

7 2 0.0000 0.0625 0.0000

7 5 0.0320 0.1610 0.3060

5 1 0.0100 0.0850 0.1760

Machine data

Variable Machine 1 Machine 2 Machine 3

Xd 0.1460 0.8958 1.3125

X'd 0.0608 0.1198 0.1813

Xq 0.0969 0.8645 1.2578

X'q 0.0608 0.1198 0.1813

T'do 8.9600 6.0000 5.8900

T'qo 0.3100 0.5350 0.6000

H 23.64 6.40 3.01

D 0.0254 0.0066 0.0026

48

Bus data for the system

Pg Qg PL QL

1 Swing - - 0.0000 0.0000 1.0400

2 PV 1.6300 - 0.0000 0.0000 1.0253

3 PQ 0.8500 - 0.0000 0.0000 1.0253

4 PQ 0.0000 0.0000 0.0000 0.0000 -

5 PQ 0.0000 0.0000 1.2500 0.5000 -

6 PQ 0.0000 0.0000 0.9000 0.3000 -

7 PQ 0.0000 0.0000 0.0000 0.0000 -

8 PQ 0.0000 0.0000 1.0000 0.3500 -

9 PQ 0.0000 0.0000 0.0000 0.0000 -

Load (pu)Generation (pu) Voltage

MagnitudeBus no. Bus Type

Excitation System Data

Varaibale Exciter 1 Exciter 2 Exciter 3

Ka 20 20 20

Ta 0.2 0.2 0.2

Ke 1 1 1

Te 0.314 0.314 0.314

Kf 0.063 0.063 0.063

Tf 0.35 0.35 0.35

transient stability analysis of nine bus system with multiple contingencies

Documents

bachelor of engineering

electronics department

head of electrical

esteemed guidance of

multiple contingencies

valuable guidance

ajay kumar

hyderabad certificate