Transient stability analysis and enhancement of ieee 9 bus system

Electrical & Computer Engineering: An International Journal (ECIJ) Volume 3, Number 2, June 2014
DOI : 10.14810/ecij.2014.3204 41
TRANSIENT STABILITY ANALYSIS AND
ENHANCEMENT OF IEEE- 9 BUS SYSTEM
Renuka Kamdar1
, Manoj Kumar2
and Ganga Agnihotri3
1,3
Department of Electrical Engineering, MANIT, Bhopal, India
ABSTRACT
System stability study is the important parameter of economic, reliable and secure power system planning
and operation. Power system studies are important during the planning and conceptual design stages of the
project as well as during the operating life of the plant periodically. This paper presents the power system
stability analysis for IEEE- 9 bus test system. The fault is created on different busses and transient stability
is analyzedfor different load and generation conditions. The critical clearing time (CCT) is calculated by
using time domain classical extended equal area criterion method. The system frequency and voltage
variation is observed for different fault locations and CCT. The IEEE-9 bus test system is simulated and
stability is analyzed on ETAP software.
KEYWORDS
Critical Clearing Time (CCT), ETAP, Extended Equal Area Criterion (EEAC), Frequency Stability, IEEE-9
Bus Test System, Load Flow Study, Load Shedding, Transient Stability.
1. INTRODUCTION
Electric power system stability analysis has been recognized as an important and challenging
problem for secure system operation. When large disturbances occur in interconnected power
system, the security of these power systems has to be examined. Power system security depends
on detailed stability studies of system to check and ensure security.
In order to determine the stability status of the power system for each contingency of any
disturbance occurs in power system, many stability studies are defined [1]. Power system stability
analysis may involve the calculation of Critical Clearing time (CCT) for a given fault which is
defined as the maximum allowable value of the clearing time for which the system remains to be
stable. The power system shall remain stable if the fault is cleared within this time. However, if
the fault is cleared after the CCT, the power system is most likely to become unstable. Thus, CCT
estimation is an important task in the transient stability analysis for a given contingency. In this
paper for the Transient Stability Analysis, an IEEE 9 Bus system is considered.
Critical clearing time (CCT) in a way measures the power systems Transient stability. It denotes
the secure and safe time margin for clearing the contingency, usually three-phase ground-fault.
The larger the value of CCT, the power system has ample time to clear the contingency. CCT
depends on generator inertias, line impedances, grid topology, and power systems operating
conditions, fault type and location. For a single machine infinite bus power system, CCT
calculation is straightforward. While for the case of multi-machine power systems, CCT is always

42
obtained by repeating time-domain simulations, and hence the evaluation of CCT can only be
done off-line The Load Flow study and Transient Stability study is discussed and performed for
the IEEE-9 Bus test system simulated on ETAP 7.5.1.
2. POWER SYSTEM STABILITY
Power system stability is defined as the capability of a system to maintain an operating
equilibrium point after being subjected to a disturbance for given initial operating conditions [4].
Power system stability is categorized based on the following considerations:
i. The nature of the resulting instability mode indicated by the observed instability on certain
system variables.
ii. The size of the disturbance which consequently influences the tool used to assess the system
stability.
iii. The time margin needed to assess system stability.
The classification of power system stability as shown in Fig.1
Fig. 1 Classification of Power System Stability
3. SWING EQUATION
The swing equation governs the motion of the machine rotor relating the inertia torque to the
resultant of the mechanical and electrical torques on the rotor i.e.[5]
‫ܯ‬௜
݀ଶ
ߜ௜
݀‫ݐ‬ଶ
= ܲ௠௜
− ܲ௘௜
, ݅ = 1,2,3, … … … … . . , ݊(1)
Where,
ܲ௘௜ = |‫ܧ‬௜|ଶ
‫ܩ‬௜௜ + ∑ ൣ|‫ܧ‬௜|ห‫ܧ‬௝หห‫ܩ‬௜௝ห cos(ߜ௜ − ߜ௝) + |‫ܧ‬௜|ห‫ܧ‬௝หห‫ܤ‬௜௝ห sin(ߜ௜ − ߜ௝)൧௡
௝ୀଵ (2)

43
With:
ߜ௜= rotor angle of the i-th machine;
‫ܯ‬௜= inertia coefficient of the i-th machine;
ܲ௠௜
, ܲ௘௜
= mechanical and electrical power of the i-th machine;
‫ܧ‬௜ = voltage behind the direct axis transient reactance;
‫ܩ‬௜௝, ‫ܤ‬௜௝= real and imaginary part of the ij-th element of the nodal admittance matrix reduced at
the nodes which are connected to generators
The following steps are taken for stability studies of multimachine system[6]:
1. From the pre-fault load flow data determined ‫ܧ‬௞voltage behind transient reactance for all
generators. This establishes generator emf magnitudes |‫ܧ‬௞|which remain constant during
the study and initial rotor angle ߜ௞
଴
= angle (‫ܧ‬௞). Also record prime mover inputs to
generators, ܲ௠௞ = ܲீ௄
଴
.
2. Augmented the load flow network by the generator transient reactance. Shift network
buses behind the transient reactance.
3. Findܻ஻௎ௌfor various network conditions-during, post fault (faulted line cleared), after line
reclosure.
4. For faulted mode, found generator outputs from power angle equation ܲ௘௜ = |‫ܧ‬௜|ଶ
‫ܩ‬௜௜ +
|‫ܧ‬௜|ห‫ܧ‬௝หหܻ௜௝ห cos(ߜ௜ − ߜ௝ − ߠ௜௝) and solve swing equations.
5. The above step is repeated for post fault mode and after line reclosure mode.
6. Examined ߜ(‫)ݐ‬ plots of all generators and established the answer to the stability question.
The following preliminary calculation steps are needed for transient stability analysis of
multi-machine system[4]:
1. Prepare the system data generally at 100 MVA base.
2. Loads are represented by equivalent shunt admittances.
3. Calculate the generator inter voltages and their initial angles.
4. Calculate the admittance bus matrix ܻ஻௎ௌ for each network condition.
5. Except for the internal generator nodes, eliminate all the nodes and obtain the ܻ஻௎ௌ
matrix for the reduced network. The reduced ܻ஻௎ௌ matrix is obtained as shown below :
Let ‫ܫ‬ = ܻܸ
‫ܫ‬ = ቂ
‫ܫ‬௡
0
ቃ
ቂ
‫ܫ‬௡
0
ቃ = ൤
ܻ௡௡ ܻ௡௥
ܻ௥௡ ܻ௥௥
൨ ൤
ܸ௡
ܸ௥
൨
Where n denotes generator nodes and r denotes remaining nodes.
‫ܫ‬௡ = ܻ௡௡ܸ௡ + ܻ௡௥, 0 = ܻ௥௡ܸ௡ + ܻ௥௥ܸ௥
From which we eliminateܸ௥,
‫ܫ‬௡ = ൫ܻ௡௡ − ܻ௡௥ܻ௥௥
ିଵ
ܻ௥௡൯ܸ௡

44
The matrix ൫ܻ௡௡ − ܻ௡௥ܻ௥௥
ିଵ
ܻ௥௡൯ is the desired reduced ܻ஻௎ௌ matrix. It is (݊ × ݊) matrix where ݊
is the number of generators.
When large disturbances occur in power system, there is no availability of generalized criteriafor
determining system stability. Hence the experimental approach for the solution of transient
stability problem is all about listing of all important severe disturbances along with their possible
locations to which the system is likely to be subjected.
A plot of power angle ߜand t (time) is called the swing curve which is obtained by numerical
solution of the swing equation in the presence of large severe disturbances. If ߜ starts to decrease
after reaching a maximum value, it is normally assumed that the system is stable and the
oscillation of ߜaround the equilibriumpoint will decay and finally die out. Important
severedisturbances are a short circuit fault or a sudden loss of load [3].
4. CRITICAL CLEARING TIME CALCULATION USING EEAC
Since the time EEAC was proposed in literature, a great interest has been raised on it [7-11],
because it is able to yield fast and accurate transient stability analysis. In order to determine the
stability of the power system as a response to a certain disturbance, the extended equal area
criterion (EEAC) method described in [10] decomposes the multi-machine system into a set of
critical machine(s) and a set of the‘remaining’ generators. In order to form an OMIB system, the
machines in the two groups are aggregated and then transformed into two equivalent machines.
Some basic assumptions for EEAC are : (i) The disturbed system separation depends upon the
angular deviation b/w the following two equivalent clusters: the critical machine group(cmg) and
the remaining machine group(rmg), (ii) The partial centre of angles (PCOA) of the critical
machine group (ߜ௖௠௚) and The partial centre of angles (PCOA) of the remaining machine
group(ߜ௥௠௚):
ߜ௖௠௚ =
∑ ‫ܯ‬௜ߜ௜௜ఢ௖௠௚
‫ܯ‬௖௠௚
(3)
‫ܯ‬௖௠௚ = ෍ ‫ܯ‬௜
௜ఢ௖௠௚
(4)
ߜ௥௠௚ =
∑ ‫ܯ‬௝ߜ௝௝ఢ௥௠௚
‫ܯ‬௥௠௚
(5)
‫ܯ‬௥௠௚ = ෍ ‫ܯ‬௝(6)
௝ఢ௥௠௚
On the basis of above assumption, a multi-machine system can be transformed into equivalent
two-machine system. After which, the two machine equivalent is reduced to a single machine
infinite bus system. The equivalent One-machine-Infinite-Bus (OMIB) system model is given by
the following equation:
‫ܯ‬
݀ଶ
ߜ
݀‫ݐ‬ଶ
= ܲ௠ − ܲ௘ = ܲ௠ − ሾܲ௖ + ܲ௠௔௫ sin(ߜ − ߛ)ሿ (7)

45
Where,
‫ܯ‬ =
‫ܯ‬௖௠௚‫ܯ‬௥௠௚
‫ܯ‬்
‫ܯ‬் = ෍ ‫ܯ‬௜
௡
௜ୀଵ
δ = δୡ୫୥ − δ୰୫୥
ܲ௖ =
‫ܯ‬௥௠௚ ∑ ‫ܧ‬௜‫ܧ‬௞‫ܩ‬௜௞௜,௞ఢ௖௠௚ − ‫ܯ‬௖௠௚ ∑ ‫ܧ‬௝‫ܧ‬௟‫ܩ‬௝௟௝,௟ఢ௥௠௚
‫ܯ‬்
ܲ௠ =
‫ܯ‬௥௠௚ ∑ ܲ௠௜௜ఢ௖௠௚ − ‫ܯ‬௖௠௚ ∑ ܲ௠௝௝ఢ௥௠௚
‫ܯ‬்
ܲ௠௔௫ = ඥ‫ܥ‬ଶ + ‫ܦ‬ଶ
ߛ = tanିଵ
൬
‫ܥ‬
‫ܦ‬
൰
‫ܥ‬ =
‫ܯ‬௥௠௚ − ‫ܯ‬௖௠௚
‫ܯ‬்
෍ ‫ܧ‬௜‫ܧ‬௝‫ܩ‬௜௝
௜ఢ௖௠௚,௝ఢ௥௠௚
‫ܦ‬ =
‫ܯ‬௥௠௚ − ‫ܯ‬௖௠௚
‫ܯ‬்
෍ ‫ܧ‬௜‫ܧ‬௝‫ܤ‬௜௝
௜ఢ௖௠௚,௝ఢ௥௠௚
The accelerating and decelerating areas are given by [12]:
‫ܣ‬௔௖௖ = (ܲ௠ − ܲ௖஽)(ߜ௖௥ − ߜ଴) + ܲ௠௔௫஽ሾcos(ߜ௖௥ − ߛ஽) − cos(ߜ଴ − ߛ஽)ሿ (8)
‫ܣ‬ௗ௘௖ = (ܲ௖௉ − ܲ௠)(ߨ − ߜ௖௥ − ߜ௉ + 2ߛ௉) + ܲ௠௔௫௉ሾcos(ߜ௖௥ − ߛ௉) + cos(ߜ௉ − ߛ௉)ሿ(9)
Where 0 denotes original (pre-fault), D during fault, and P post-fault, ߜ௖௥ is the critical clearing
time.
The transient stability margin: ߤ = ‫ܣ‬௔௖௖ − ‫ܣ‬ௗ௘௖, at the critical clearing time ‫ݐ‬௖௥, ߤ = ‫ܣ‬௔௖௖ −
‫ܣ‬ௗ௘௖ = 0
Solving the equations (13) & (14), the critical clearing angle ߜ௖௥ can be computed. The value of
critical clearing time (CCT) can be computed [17] by following formula:
‫ݐ‬௖௥ = ට
ଶெ
ఠబ௉೚
(ߜ௖௥ − ߜ଴) (10)
Where,
ܲ௢ = generator output before fault
ߜ଴ = pre-fault angle

46
5. SYSTEM SIMULATION AND LOAD FLOW ANALYSIS
In this paper IEEE 9 bus system is used as the test system, which is simulated on ETAP 7.5.1.
Fig. 2 Single Line Diagram of IEEE 9 Bus test system
The single line diagram (SLD) of the simulated test system on ETAP is shown in Fig 2. For this
test system generator and load parameters are given in appendix. The total generation is 313MW
and total load is 312.5MW. The test system contains 6 lines connecting the bus bars in the system
with the generator connected to network through step-up transformer at 230kV transmission
voltage.
It is good practice to have periodic and updated load flow study for every installation. The
purpose of load flow study is
i. To calculate bus voltage levels tocompare to equipment ratings anddistribution system
operatingrequirements
ii. To calculate branch current flows for comparing it to equipment ampacity ratings and
protective device triplevels.
Depending upon the type of plant there can be many load flow cases to study. The objective is to
identify the best and worst operating conditions. Several load flow solution algorithms used in
industry such as Gauss-Seidel, Newton-Raphson and current injection. There is requirement of at
least one swing bus in the network for all the Load flow solution algorithms. The utility point of
service is always modeled as swing bus.
The result of load flow analysis when all generators and loads are operating at rated power is
given in Table.1. Calculation of critical clearing time (CCT) by using EEAC for different
generation and loading condition at the different fault locations are shown in Table. 2.

47
This CCT is then used to operate the circuit breakers near the faulted bus and hence the
corresponding generators are removed from the system. This creates the generation – load
imbalance and hence the system frequency is affected.
When the frequency of the system crosses the permissible limit after the fault has occurred, the
frequency protection scheme is activated. The frequency stability of the system is enhanced using
Load Shedding.
Table.1 Load Flow Report
Bus
No.
Bus
KV
Voltage
Mag.(%)
(%)
Voltage
Angle
Gen.
(MW)
Gen.
(Mvar)
Load
(MW)
Load
(Mvar)
1 16.5 100.0 1.0 73.831 9.738 0 0
2 18.0 100.0 0.3 155.00 92.091 0 0
3 13.8 100.0 -0.2 85.00 41.951 0 0
4 230 98.940 -4.3 0 0 0 0
5 230 98.827 -4.3 0 0 123.947 49.550
6 230 98.834 -4.3 0 0 89.247 29.726
7 230 99.132 -4.3 0 0 0 0
8 230 98.884 -4.3 0 0 99.284 34.790
9 230 99.005 -4.3 0 0 0 0
Table.2CCT for different generation – loading conditions
Cases Fault Bus CCT(sec)
1 Bus 1 0.361109
2 Bus 2 0.31693
3 Bus 3 0.317587
For the above mentioned generation – loading conditions, load shedding was performed till the
system frequency stability is regained. The bus frequency and bus voltage plots for the three cases
are shown in Fig. 3- Fig 8.
Fig.3 Bus voltage when the fault has occurred at bus 1
At t= 1.0 sec 3phase faultoccurred at bus 1, the circuit breaker 1 and 4 are operated before the
CCT calculated for the case i.e. at 1.36 sec. As a result generator 1 is removed from the system
0 5 10 15 20 25 30
50
60
70
80
90
100
110
120
Time(sec)
%BusVoltage

48
and the power imbalance condition arises. Due to this the load shedding scheme is activated and
an amount of 68 MW load is curtailed to regain the system stability. Similarly when the fault
occurs at bus 2 and 3 leading to generator 2 and 3 outage respectively, the load of 150MW and 84
MW is shed from the system.
Fig.6 Bus frequencyafter load shedding when fault has occurred at bus1
0 5 10 15 20 25 30
20
30
40
50
60
70
80
90
100
110
120
Time(sec)
%Busvoltage
0 5 10 15 20 25 30
40
50
60
70
80
90
100
110
Time(sec)
%BusVoltage
0 5 10 15 20 25 30
97.5
98
98.5
99
99.5
100
100.5
101
101.5
102
Time(sec)
%Frequency

49
Fig.7 Bus frequency after load shedding when fault has occurred at bus2
Fig.8 Bus frequency after load shedding when fault has occurred at bus3
6. CONCLUSION
Transient stability analysis has been performed on ETAP software. The Critical Clearing time
(CCT) i.e. the maximum allowable value of the clearing time for which the system remains to be
stable is calculated for a given fault. System frequency and voltage is analyzed for different
loading conditions and faults on busses. The excess amount of load has to be shedded to maintain
system stability.
APPENDEX
Generator data of IEEE 9 bus system
Parameter G1 G2 G3
Operation mode Swing Voltage control Voltage
control
Rated MVA 80 220 110
KV 16.5 18 13.8
Power factor 0.90 0.85 0.85
Type Hydro Thermal Thermal
Speed 1500 1500 1500
'
doT 5.6 5.6 5.6
'
qoT 3.7 3.7 3.7
0 5 10 15 20 25 30
97
98
99
100
101
102
103
Time(sec)%Busfrequency
0 5 10 15 20 25 30
97
98
99
100
101
102
103
Time(sec)
%BusFrequency

50
Load data of IEEE 9 bus system
Load id Rating
(MVA)
Rated KV
Lump1 71.589 230
Lump2 53.852 230
Lump3 55.902 230
Lump4 31.623 230
Lump5 20.616 230
Lump6 25.495 230
Lump7 31.623 230
Lump8 20.616 230
Lump9 25.495 230
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[4] IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, “Definitions and Classification of
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51
[16] Krishna, D.R., Murthy, K., Rao, G.G., "Application of Artificial Neural Networks in Determining
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Authors
Renuka Kamdar was born in Bhopal, India in 1987. She has received her BE degree
(Electrical and Electronics Engineering) from Oriental Institute of Science and
Technology, Bhopal in 2009 and M. Tech degree (Power System) from MANIT Bhopal
in 2013. She is presently working as a JRF in MANIT, Bhopal
Dr. Ganga Agnihotri (M92118974) received BE degree in Electrical engineering from
MACT, Bhopal (1972), the ME degree (1974) and PhD degree (1989) from University of
Roorkee, India. Since 1976 she is with Maulana Azad College of Technology, Bhopal in
various positions. Currently she is Professor. Her research interest includes Power System
Analysis, Power System Optimization and Distribution Operation.

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