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
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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
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
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
Figure 4.4 Relative rotor angles when fault at bus 7 and fct = 0.077 seconds
24
Figure 4.5 Terminal voltage when fault at bus 7 and fct = 0.05 seconds
Figure 4.6 Terminal voltage when fault at bus 7 and fct = 0.077 seconds
25
Figure 4.7 Relative rotor angles when fault at bus 7 and fct = 0.08 seconds
Figure 4.8 Relative rotor angles when fault at bus 7 and fct = 0.2 seconds
26
Figure 4.9 Terminal voltage when fault at bus 7 and fct = 0.08 seconds
Figure 4.10 Terminal voltage when fault at bus 7 and fct = 0.2 seconds
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.
Figure 4.21 Rotor angle variation for multiple contingency case 2
35
Figure 4.22 Frequency variation due to multiple contingency case 2
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.
Figure 4.23 Rotor angle variation for multiple contingency case 3
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
Figure 4.26 Frequency variation due to multiple contingency case 3
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"