Upload
mannat-mrjn
View
216
Download
0
Embed Size (px)
Citation preview
7/31/2019 Impact of AVR on Stability
1/44
TET 4180 Electric Power System Stability [Year]
IMPACT OF AVR
Linda Aino-Maija Rekosuo 733028Mamta Maharjan 729299
7/31/2019 Impact of AVR on Stability
2/44
TET 4180 Electric Power System Stability
1
1 SUMMARYThe system contains eleven buses and two areas, connected by a weak tie between bus 7 and 9. Totally
two loads are applied to the system at bus 7 and 9. The system has the fundamental frequency 60 Hz.
The system comprises two similar areas connected by a weak tie. Each area consists of two generators,
each having a rating of 900 MVA and 20 kV. In order to analyse this system called KUNDUR twoAREA system following steps are carried out.
Power-flow calculation Linear Analysis and Modal Analysis Time-domain simulation
For carrying out KUNDUR Two Area system, Simulation software called SIMPOW is used. In part 1,
power flow calculation is done by using kundur.optpow file and single line diagram is drawn. By
using casefault.dynpow file, dynamic simulation is carried out. At 1s, there is three phase short circuit
in bus 8. Assuming fault to be small signal disturbance, linear analysis is carried out and Eigen values
are calculated. Linear analysis and the information provided by eigenvalues and eigenvectors are very
useful when doing system studies. Time domain simulations (in SIMPOW) using the non-linear
models are further used to verify the responses.
Automatic voltage regulator (AVR) and the field excitation system of the generators have an impact
on system stability. In part 2 there is analysis of AVR by changing its gain and time constant. The
whole part 2 is analysed by removing Power system Stabilizer (PSS). PSS helps in stability
enhancement. In this part also linear analysis is carried out, Eigen values are calculated. The
parameters which affect the stability of the system is gain and time constant. So analysis is done to see
how these value influence the stability.
7/31/2019 Impact of AVR on Stability
3/44
TET 4180 Electric Power System Stability
2
Table of Contents................................................................................................................................................................. 0
1 SUMMARY ....................................................................................................................................... 1
2 INTRODUCTION ............................................................................................................................... 4
3 BASICS OF POWER SYSTEM DYNAMICS AND SIMPOW (PART 1) .................................................... 5
3.1 INITIAL POWER FLOW COMPUTATION ................................................................................... 5
3.2 LINEAR ANALYSIS ..................................................................................................................... 5
3.3 MODAL ANALYSIS .................................................................................................................... 7
3.4 SENSITIVITY ANALYSIS ............................................................................................................. 8
3.5 DATA SCANNING...................................................................................................................... 9
3.6 DYNAMIC SIMULATION OF BASE CASE .................................................................................. 10
3.6.1 PREDEFINED PLOT ......................................................................................................... 10
3.6.2 POWER TRANSFER BETWEEN BUS 8 AND BUS 9 ........................................................... 11
3.6.3 Relation between generator power and power angle/generator speed ...................... 12
3.7 EIGEN VALUE AFTER FAULT ................................................................................................... 13
4 IMPACT OF AVR ( part 2) ............................................................................................................... 15
4.1 INSERTION OF EXC_HTC WITH KA=200, TR=0.01S ................................................................ 15
4.2 IMAPCT OF CHANGING KA and TR of AVR ............................................................................. 18
4.2.1 Changing time constant ................................................................................................. 18
4.2.2 Changing Gain constant ................................................................................................. 18
4.3 TIME DOMAIN ANALYSIS ....................................................................................................... 19
4.3.1 CHANGING TIME CONSTANT ......................................................................................... 19
4.3.2 CHANGING GAIN ............................................................................................................ 20
4.4 PRE AND POST FAULT STEADY STATE VOLTAGE AND REACTIVE POWER EXCHANGE ........... 22
4.4.1 Steady state voltage ...................................................................................................... 22
4.4.2 reactive power ............................................................................................................... 234.4.3 EXCHANGE OF REACTIVE POWER .................................................................................. 23
4.5 MORE ADVANCED AVR .......................................................................................................... 24
4.5.1 KA=200 TR=0.005 TA=1.0 TB=10.0 ............................................................................. 25
4.5.2 KA=200 TR=0.005 TA=0.5s TB=10.0 ........................................................................... 25
4.5.3 KA=200 TR=0.005 TA=0.5s TB=5.0 ............................................................................. 26
5 CONCLUSION: ................................................................................................................................ 28
APPENDIX 1 ........................................................................................................................................... 29
APEENDIX 2 ............................................................................................................................................ 31
7/31/2019 Impact of AVR on Stability
4/44
TET 4180 Electric Power System Stability
3
Appendix 3 ............................................................................................................................................. 32
APPENDIX 4 ........................................................................................................................................... 33
APPENDIX 5 ........................................................................................................................................... 36
APPENDIX 6 ........................................................................................................................................... 39
Appendix 7 ............................................................................................................................................. 40
APPENDIX 8 ........................................................................................................................................... 41
APPENDIX 9 ........................................................................................................................................... 42
Appendix 10 ........................................................................................................................................... 43
7/31/2019 Impact of AVR on Stability
5/44
TET 4180 Electric Power System Stability
4
2 INTRODUCTIONThe KUNDUR two area systems consists of two generating and load areas consisting of 2 generators
in each area and is connected by a duplex tie line between bus 7 and 9 as depicted in fig 1.
Part 1 is exercise meant to give idea of the simulation tool SIMPOW and some ideas about thedynamics of the power system. Power flow, linear analysis, Eigen values, sensitivity, data scanning,
modal analysis are carried out to have better insight of Kundur two area system. There is some slight
understanding of stability, inter area mode of oscillation, electromechanical oscillation.
In part 2 AVR is introduced to all the generators. Exciter called high transient gain exciter is equipped
to the all generators. Parameter like KA, TR of the exciter is changed and its impact on stability is
studied. More advance exciter Transient gain reduction is used and its parameters are tuned in order to
improve the stability of the system.
There is three phase short circuit on bus 8.Pre fault and Post fault values of steady state voltage and
reactive power is calculated and analysed. After the fault is removed on bus 8, one of the lines
between bus 8 and bus 9 is tripped. The reactive power exchange, before and after fault are alsostudied and the results are analysed.
The results are discussed and tried to associate with the general theory and from the course book
Power system Stability.
Figure 1 :Kundur two area system
7/31/2019 Impact of AVR on Stability
6/44
TET 4180 Electric Power System Stability
5
3 BASICS OF POWER SYSTEM DYNAMICS AND SIMPOW (PART 1)3.1 INITIAL POWER FLOW COMPUTATIONThe optimal power flow using SIMPOW is carried out using base case. The figure 1 in the Appendix 1
represents the power flow result of the kundur case in tabular format. This is the total overview of the
system. The Kundur two area system consists of ten buses in which bus 1,2,5,6,7 lies in the AREA 1
and rest of the bus lies in AREA 2 except for bus 8 which lies in the tie between AREA 1 and AREA
2 via bus 7 and bus 9. Here bus 3 is swing bus and rest of generator bus 1, 2 and 4 is PV bus. Bus 7
and 9 is the load bus or PQ bus and load is modelled as constant power character. it is done by
making MP=MQ=0 in SIMPOW. This result is also displayed in single line diagram in Appendix 2.
The voltage of Bus 9 is lower than the permissible value as seen in figure 1 of Appendix 1.. So it has
been improved by using the shunt compensation at bus 7 and 9 . The improved power flow is also
shown in figure 2 of Appendix 1.
The summary of power flow result is tabulated below.
BUS V (PU) TETA (DEG) P(MW) Q(MVAR)
1 (PV) 1.03 20.17 700.0 184.8
2 (PV) 1.01 10.41 700.0 234.2
3(SW) 1.03 -6.8 718.9 175.7
4(PV) 1.01 -16.99 700.0 201.4Table 1. Summary of Power flow
The summary of power transfer between area 1 and area two via the duplex transmission line is as
follows:
Merit P (MW) Q (MVAR)
Power transmitted from Area 1(from Bus 7) 400.848 16.855
Power received at Area 2(at Bus 9) 382.316 -97.12
Loss in Tie line 18.352 113.975
Table 2: Summary of Power transfer between AREA 1 and AREA 2
3.2 LINEAR ANALYSISLinear Analysis is done for the small disturbance in the system. Linear analysis reduces the
complexity of the power system. The computation of eigenvalues, and performing frequency scanning,
data scanning and modal analysis is carried out in linear analysis which can be done easily in
SIMPOW. The alter command features to connect and disconnect the power components, the
connection and disconnection time as per the requirement in analysis of the system. The figure 1 in
Appendix 3 shows the eigen values of the kundur 2 area system before the 3 phase fault occurs at bus
8. All the eigen values have negative real part indicating the stable system. But of all the eigen values,
only one of those eigen values whose imaginary part in the range of 0.2-2Hz are chosen as only the
electromechanical mode is studied. The eigen value (-0.599,0.66) is chosen as the initial value and the
eigen values are improved. It is done because for the numerical method problem the initial value
matters which is shown in figure 2.
7/31/2019 Impact of AVR on Stability
7/44
TET 4180 Electric Power System Stability
6
Figure 2: pre fault improved eigen values
The filtered eigen values are tabulated as below in table 3. Only those eigen values which has
frequency in the range 0.2-2Hz is taken into consideration. It is because these values represent the
electromechanical mode which is the interest of this project.
-0.60
-0.40
-0.20
0.20
0.40
0.60
-1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 0.20
Eigenvalues at time=0 seconds
STRI Softw are
DATE 27 APR 2012 TIME 12:06:57 Job casefault Simpow 11.0.008
7/31/2019 Impact of AVR on Stability
8/44
TET 4180 Electric Power System Stability
7
Real parts Imaginary parts
21 -2.258673 1.366046
22 -2.58675 -1.366046
23 -2.202345 1.315472
24 -2.202345 -1.315472
29 -0.599853 0.660476
30 -0.599853 -0.660476
35 -1.758968 0.216461
36 -1.758968 -0.216461
Table 3: Eigen value with imaginary part between 0.2-2 Hz
As all the eigen values lie in the negative half plane the system is stable before the fault occurs. The
damping ratio is given by
If the Eigen values have negative real part then damping ratio is positive and the system is stable.
3.3 MODAL ANALYSISModal analysis means the eigen vector of any given eigen value. The figure 3 shows the modal
analysis for the Eigen value no. 29. For the particular Eigen value the eigen vector of 4 different
generator is plotted in this figure. For the eigen vector no. 29,(-0.59985, 0.66048) the generator 1
and 2 which is of the AREA1 is oscillating against AREA 2. This is called inter area interaction and is a
positive quality for an integrated large network. And figure2 in Appendix 3 shows the model analysis
for eigen value no. 21.
7/31/2019 Impact of AVR on Stability
9/44
TET 4180 Electric Power System Stability
8
Figure 3: MODAL ANALYSIS for eigen value no. 29
3.4 SENSITIVITY ANALYSISSensitivity analysis means how much sensible the eigen values are to the control parameters like
Inertia Constant, Damping ratio. By changing these control parameters, sensitivity analysis shows how
the eigen values are changed. Hence this gives idea about how these control parameters effect on the
stability of the system.
It is seen from the sensitivity table 4 that if inertia constant of synchronous generator is increased then
there is increase in real part and decrease in imaginary part because the sensitivity is positive for real
part and negative for imaginary part. Assuming initially, the eigen value is in negative half plane, For1 pu change in inertia constant the eigen value change by 0.03484 1/s in positive direction bringing it
near to the origin so the stability decreases. In contradiction increase in pu of damping constant of
synchronous generator 3, there is decrease of real part of eigen value taking it more far from the origin
so the stability increase.
Taking the second order model of synchronous generator the eigen value are represented by
Where , so the result is compatible with the formula. The equation says that if inertia
constant is increased real part comes closer to origin. i.e the system would be less stable. And if
Damping Constant is increased then eigen values move far away from the origin and system increase
stability.
parameter Eigen value sensitivity
Sync gen 3, H -0.599 1/s, 0.66 Hz 0.03484 1/s/pu, -0.0173 Hz/pu
Sync gen 3, D -0.599 1/s, 0.66 Hz -0.0134 1/s/pu, -0.00035 Hz/pu
Table 4. sensitivity for H=6.175
-1,00
1,00
-1,00 -0,50 0,50 1,00
4
3
21
Eigenvalue: -0.599852 1/s + j0.660476 Hz at Time=0 seconds
STRI Softw are
DATE 9 APR 2011 TIME 15:54:42 Job casefaul Simpow 11.0.009
1 SYNCG3
2 SYNCG4
3 SYNCG1
4 SYNCG2
7/31/2019 Impact of AVR on Stability
10/44
TET 4180 Electric Power System Stability
9
3.5 DATA SCANNINGData Scanning is the graphical approach of verifying the sensitivity analysis. Here also eigen values
are initially in negative half plane. From the graph obtained by data scanning of H from 4 to 8 in step
of 0.5 in figure 4, it is seen that increase in inertia constant decrease the imaginary part and increase
the real part of eigen value. The real part determines the state of stability. The system is stable if the
eigen value is located far away from the origin in negative x axis. But increase in H is taking the eigen
value nearer to the origin so the stability is decreasing on increase in H. If it is done for damping
constant D then it looks as in figure 5
Figure 4 change in eigen value by changing H
Figure 5 change in eigen value by changing D
7/31/2019 Impact of AVR on Stability
11/44
TET 4180 Electric Power System Stability
10
Figrue 5 shows that increase in D is taking the eigen value away from the origin in negative x axis so
stability margin is increasing. Data scanning shows the exact value of eigen value on increasing or
decreasing of system parameter but Sensitivity analysis shows only the slope of eigen value with
respect to system parameters.
3.6 DYNAMIC SIMULATION OF BASE CASEWith casefault.dynpow file, additional file called casefault.dynpost is also attached. This dynpost file
consists of some predefined plot which are listed below .
3.6.1 PREDEFINED PLOT
Figure 6 :plot of voltage of bus 8 during outage of line 1 at base case
Figure 7 plot of speed of generators during outage of line 1 at base case
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
TIM E SECONDS
0,00
0,20
0,40
0,60
0,80
1,00
case fault - A three -phase fault close to BUS8 with dis connection of a line.
DATE 7 APR 2012 TIME 15:54:50 JOB casefault Simpow 11.0.009 Diagram:1
STRI Software
NODE BUS8 U POS. p.u. 230.000/ SQRT[3] kV
0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00
TIME SECONDS
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 7 APR 2012 TIME 15:54:50 JOB casefault Simpow 11.0.009 Diagram:2STRI Software
SYNC G1 SPEED p.u.
SYNC G2 SPEED p.u.
SYNC G3 SPEED p.u.
SYNC G4 SPEED p.u.
7/31/2019 Impact of AVR on Stability
12/44
TET 4180 Electric Power System Stability
11
Figure 8. : plot of power output(MW) of generators during outage of line 1 at base case
The dynpow file casefault.dynpow shows that there is three phase fault at bus 8 at 1s and the fault is
removed at 1.05 s. In figure 6 the voltage of bus 8 is zero during the fault and regained after fault is
removed. Figure 7 is speed response of the all generator which shows that there is oscillation in all
the generator after fault but the system finally became stable after the removal of fault. It is also seen
that during fault, generator 1 and 2 of AREA 1 is oscillating against generator 3 and 4 of AREA 2.
This is called inter area mode of interaction. The same type of oscillation is also felt by power outputof generators which is shown in figure 8.
3.6.2 POWER TRANSFER BETWEEN BUS 8 AND BUS 9
Figure 9: power flow between bus 8 and bus 9 of line 1 and line 2
LINE 1 LINE 2
0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00
TIM E SECONDS
0,500
0,600
0,700
0,800
0,900
1,000
0,500
0,600
0,700
0,800
0,900
1,000
0,600
0,650
0,700
0,750
0,800
0,850
0,600
0,650
0,700
0,750
0,800
0,850
0,900
0,950
case fault - A thr ee-phase fault close to BUS8 with disconnection of a line.
DATE 7 APR 2012 TIME 15:54:50 JOB casefault Simpow 11.0.009 Diagram:3STRI Software
SYNC G1 P POWER p.u. 900.000 MW
SYNC G2 P POWER p.u. 900.000 MW
SYNC G3 P POWER p.u. 900.000 MW
SYNC G4 P POWER p.u. 900.000 MW
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
TIME SECONDS
-150
-100
-50
0
0
50
100
150
-400
-350
-300
-250
-200
-150
-100
-50
0
0
50
100
150
200
250
300
350
400
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 23 APR 2012 TIME 19:43:06 JOB casefault Simpow 11.0.008 Diagram:4STRI Software
0.4, -195
LINE BUS8 BUS9 1 P1 POWER MW
LINE BUS8 BUS9 1 P2 POWER MW
LINE BUS8 BUS9 2 P1 POWER MW
LINE BUS8 BUS9 2 P2 POWER MW
7/31/2019 Impact of AVR on Stability
13/44
TET 4180 Electric Power System Stability
12
AREA 1 AREA 2 AREA 1 AREA 2
Initial (MW) -195 191 -195 191
Final (MW) 0 0 -395 367
With simpow, some graphs can be plotted manually. The figure 9 consists of graph which representsthe exchange of active power between the bus 8 and bus 9. There are duplex line between bus 8 and
bus 9. After the fault, line 1 is cut off so the active power transfer by the line 1 after the fault is zero.
So all the power must be exchanged by line 2.Line 2 is exchanging the same power as line 1 before
fault
3.6.3 Relation between generator power and power angle/generator speed
Figure 10 power vs power angle for generator 3
Figure 11 power vs speed for generator G3
Power versus power angle and speed is plotted for the swing bus G3. Because of fault, both the speedand angle increase and after some time it is seen to be stabilized because of removal of fault.
105.3406
4.589564.37174.15384
3.71811 3.500253.39132
3.282393.17346
2.706742.5668
2.496842.42687
2.35692.286942.216972.1005
447
1.774951.68193
1.63542
1.58892
1.53253
1.50434
1.47615
1.44796
1.41977
1.39158
1.36339
1.32024 1.27537
1.230491.18562
1.142
1.11612
1.0710
1.0571
1.050
1.049
1.00
0
-0,850 -0,800 -0,750 -0,700 -0,650 -0,600 -0,550 -0,500
SYNC G3 TETA RADIANS RELATIVETO G1
0,600
0,650
0,700
0,750
0,800
0,850
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 7 APR 2012 TIME15:54:50 JOBcasefault Simpow 11.0.009 Diagram:6
STRI Software
SYNC G3 P POWER p.u. 900.000 MW
100
0.99940 0.99960 0.99980 1.00000 1.00020 1.00040 1.00060 1.00080 1.00100
SYNC G3 SPEED p.u .
550
600
650
700
750
800
case fault - A three-phase fault close to BUS8 with disconnection of a line.
DATE22 MAR 2012 TIME 15:40:37 JOB casefault Simpow 11.0.008 Diagram:10STRI Software
SYNC G3 P POWER MW
7/31/2019 Impact of AVR on Stability
14/44
TET 4180 Electric Power System Stability
13
3.7 EIGEN VALUE AFTER FAULTThe figure 12 represents the eigen value after the fault. But all the eigen values do not represent the
electromechanical mode of oscillation. Only those eigen values which have 0.2-2 Hz is considered as
the electromechanical mode.
Figure 12 eigen value after fault
The list of filtered electro-mechanical mode of eigen values are:
Eigenvalue no 21: -2.19124 1/s , 1.29966 Hz
Eigenvalue no 22: -2.19124 1/s , -1.29966 HzEigenvalue no 23: -2.24210 1/s , 1.34514 Hz
Eigenvalue no 24: -2.24210 1/s , -1.34514 Hz
Eigenvalue no 29: -0.570887 1/s , 0.528683 Hz
Eigenvalue no 30: -0.570887 1/s , -0.528683 Hz
Eigenvalue no 35: -1.76428 1/s , 0.216604 HzEigenvalue no 36: -1.76428 1/s , -0.216604 Hz
From the figure 13, the period of oscillation is T=1.8 sec i.e. frequency f = 1/1.8 s = 0.55 Hz which is
very close to the frequency of oscillation computed by SIMPOW in eigenvalue no. 29. And from thereal part of the same eigenvalue, the damping period is T=1/0.57091 =1.75 seconds. Practically, it
takes around 5 cycles to decay the oscillations that equals to 5*1.75 s = 8.75 seconds which can also
be observed in the figure 13.
-1.00
-0.50
0.50
1.00
-1.50 -1.00 -0.50 0.50
Eigenvalues at time=10 seconds
STRI Softw are
DATE 27 APR 2012 TIME 10:43:52 Job casefault Simpow 11.0.008
7/31/2019 Impact of AVR on Stability
15/44
TET 4180 Electric Power System Stability
14
Figure 13: Power angle curve of Generator G4
By inspection of the Eigen value also the stability of the system can be found out. But after converting
to the time domain it is seen that due to fault at 1s, rotor angle swings and after some oscillation it
final settles down to another equilibrium value. The system is stable.
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
TIM E SECONDS
-1,100
-1,050
-1,000
-0,950
-0,900
-0,850
-0,800
-0,750
-0,700
-0,650
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 9 APR 2011 TIME 15:54:42 JOB Simpow 11.0.009 Diagram:11STRI Software
2,0, -1,102
3,8, -1,004
SYNC G4 T ETA RADIANS RELATIVE TO G1
7/31/2019 Impact of AVR on Stability
16/44
TET 4180 Electric Power System Stability
15
4 IMPACT OF AVR ( part 2)Before the effect of AVR in stability is discussed, it is useful to explain some theory regarding the
control system. For the control system as shown below
Figure 14. General control system
If the transfer function is
, Damping constant = and natural frequency wn= . For the
system to be stable damping constant must be high. i.e T(time constant) must be less and K(gain) must
be less.
Automatic voltage regulator is designed to automatically maintain a constant voltage level usually by
varying the field voltage. Part 2 is the analysis of regulated system so every generator is equipped
with the AVR. When any disturbance occurs for instant the short circuit then voltage of the node goes
down, AVR maintains the voltage of the generator terminals constant by adjusting the value of the
excitation voltage. If AVR is fast then it tries to maintain the generator stable despite the occurrence of
the fault. Stability means ability to come in the original position even after disturbance. So the
parameters of AVR have huge impact on generator stability.
Exciter EXC_HTG is introduced to all the generators. It is thyristor static exciter with a high transient
gain which is shown in figure 15
Figure 15: EXC_HTC exciter
This type of exciter is called static exciter. High value of KA is desirable from the viewpoint of
overall excitation control design and performance. KA=200 is chosen. All the analysis is done by
disconnecting PSS. PSS is power system stabilizer. Part 1 is analyzed with PSS. PSS is a device which
provides additional supplementary control loops to the AVR system. System stabilizes faster when
PSS is used. It is one of the most cost effective methods of enhancing power system stability. PSS is
removed in SIMPOW by making SWS=0.
4.1 INSERTION OF EXC_HTC WITH KA=200, TR=0.01SInserting the EXC_HTG for all the generators, casefault.dynpow is analysed linearly and the eigenvalues are calculated which is shown in figure 16.. All the generator has KA=200, TR=0.01s
7/31/2019 Impact of AVR on Stability
17/44
TET 4180 Electric Power System Stability
16
Figure 16 eigen value for KA=200, TR=0.01S
The eigen values are liste as:
Eigenvalue 17 (-0.74222 1/s , 1.1186 Hz)
Eigenvalue 18(-0.74222 1/s , -1.1186 Hz)
Eigenvalue 19 (-0.73589 1/s , 1.1495 Hz)
Eigenvalue 20 (-0.73589 1/s , -1.1495 Hz)
Eigenvalue 21 (-0.87935E-01 1/s , 0.52029 Hz)
Eigenvalue 22 (-0.87935E-01 1/s ,-0.52029 Hz)
Eigenvalue 34: ( -1.3541 1/s , 0.12096 Hz)
Eigenvalue 35 ( -1.3541 1/s ,-0.12096 Hz)
All the eigen values are in negative half plane which means that the system is stable. Any eigen values
has real part and imaginary part. Real part indicates the damping nature of the disturbance while theimaginary part indicates the oscillation of disturbance. So the negative real part of eigen value means
that oscillation is decreasing and the system is stable. The eigen values analysis is frequency domain
analysis. The system behaviour is more illustrative in time domain analysis which is shown below in
figure 17.
-1.00
-0.50
0.50
1.00
-2.00 -1.50 -1.00 -0.50
Eigenvalues at time=55 seconds
STRI Softw are
DATE 27 APR 2012 TIME 10:55:24 Job casefault Simpow 11.0.008
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0 55,0
TIM E SECONDS
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99900
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 22 APR 2012 TIME 16:07:41 JOB casefault Simpow 11.0.009 Diagram:2STRI Software
SYNC G1 SPEED p.u.
SYNC G2 SPEED p.u.
SYNC G3 SPEED p.u.
SYNC G4 SPEED p.u.
7/31/2019 Impact of AVR on Stability
18/44
TET 4180 Electric Power System Stability
17
Figure 17: Speed Response
This graph shows there is disturbance at 1s and after it is cleared the disturbance dies out gradually
and after around 40s the system is stable again but in the different value than the pre fault condition. It
can also be seen that the generator 1 and 2 of area 1 is oscillating against generator 3 and 4. The initial
value, final value and settling time is tabulated below.
G1 G2 G3 G4
Initial 1 pu 1 pu 1 pu 1pu
final 1.00056 pu 1.00056 pu 1.00056 pu 1.00056 pu
Settling time 41s 41s 46s 46sTable 5: time response for KA=200 TR=0.01s
All the generators are oscillating in 1pu before fault. After the fault, all the generator settles down in
another value 1.00057 but it happens in different settling time. G1,G2 of area 1 settles down in 41s
while generator G3,G4 of area 2 settles down in 46s.
Figure 18: Voltage response
Figure 18 shows the voltage analysis in time domain. The voltage of all the generator goes down to
zero during fault at 1s and after the fault is cleared the voltage is again risen and finally becomes
stable. The initial, final values are as indicated below.
G1 G2 G3 G4
Initial value (KV) 11.89 11.66 11.89 11.66
Final value (KV) 11.89 11.66 11.89 11.66Table 6: initial and final steady state voltage for KA=200, TR=0.01s
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0 55,0
TIME SECONDS
11,00
11,50
12,00
12,50
10,00
10,50
11,00
11,50
12,00
12,50
10,50
11,00
11,50
12,00
12,50
9,00
9,50
10,00
10,50
11,00
11,50
12,00
12,50
case fault - A thr ee-phase fault close to BUS8 with disconnection of a line.
DATE 22 APR 2012 TIME 16:07:41 JOB Simpow 11.0.009 Diagram:4STRI Software
27,7, 11,66
SYNC G1 U POS. kV
SYNC G2 U POS. kV
SYNC G3 U POS. kV
SYNC G4 U POS. kV
7/31/2019 Impact of AVR on Stability
19/44
TET 4180 Electric Power System Stability
18
Here it is seen that the initial and final value is same because the gain is very high KA=200 and the
steady state error is zero.
4.2 IMAPCT OF CHANGING KA and TR of AVRIn this section, value of KA and TR of generators are change one by one and to all the generator at the
same time. In this way it can be seen how the stability of generator is affected by these parameter.
Originally the value of KA=200 and TA=0.01 s.
This figures 1 to 4 in Appendix 4 shows how the Eigen values change, when TR is change from 0.01s
to 1s one by one in all four generator keeping KA constant at 200.Fig 1 to fig 4 is the result of data
scanning. Data scanning is done for the eigen value (-0.87935E-01 1/s ,-0.52029 Hz). This
particular eigen value is chosen because the time response of figure 17 shows that Time period of
oscillation is 2s which means frequency of oscillation is nearly 0.5Hz.
4.2.1 Changing time constantIt is seen that when TR of generator 1 and 2 is changed then eigen values are moving towards origin
decreasing stability and finally lie in right half plane if TR is further increased making the system
unstable. On contrary, eigen values of generator 3 and 4 of area 2 are moving away from the origin
increasing stability. And the figure 5 in appendix 4 shows the effect on Eigen values when TR is
changed in all generator at the same time. TR is voltage transducer time. It is seen that when TR is
increased the Eigen values are tilting more and more to the origin. That means the stability is
decreased when TR is increased. From the table 1 in appendix 5, it can be seen that when TR is
increased to 0.5s and more than that, then the eigen value lie in right half plane making it unstable.
Increasing TR means that the AVR is getting slow. It is mentioned in the textbook in 5.5.1.2 (pg 199)that if AVR is slow acting i.e it has large time constant then it may be assumed that following a small
disturbance the AVR will not react during the transient state and the regulated and unregulated
systems will behave in a similar manner. It means that if AVR cannot respond when disturbance
occurs then there is no meaning of keeping AVR, as the system will get unstable as the unregulated
system.
4.2.2 Changing Gain constantNow TR is made constant and gain is decreased from KA=200 to KA=10 one by one in all the
generator and at last in all the generator at the same time. The result of data scanning are plotted in
appendix 5. Fig 1 and fig 2 represents the gen 1 and gen 2 respectively which shows that when gain is
decrease from 200 to 50 then eigen values are moving near to origin. If further decreased then eigen
values are moving away from the origin. While opposite is happening in gen 3 and gen 4. From fig5 in
appendix 5, it is seen that when KA decrease then stability is decreased by shifting the eigen value to
the origin but when it is decreased more than 50, then stability increased.
7/31/2019 Impact of AVR on Stability
20/44
TET 4180 Electric Power System Stability
19
4.3 TIME DOMAIN ANALYSIS4.3.1 CHANGING TIME CONSTANTTo illustrate more, time domain analysis is done. The figure 1 and figure 2 in appendix 6 below
represent speed for all the generators by changing TR=0.01 to TR=0.1 s of generator 1 and on all
generator at same time respectively. This is done by keeping gain KA constant at 200.
In the table below, Initial value, final value and settling time of the speed response is presented by
changing TR=0.1 s one by one in all the generator.
KA=200 G1 G2 G3 G4
TR,G1=0.1S
All other gen
has
TR=0.01s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) 43 43 48 48
TR,G2=0.1S
All other genhas
TR=0.01s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056Settling time (s) 56 53 60 58
TR,G3=0.1S
All other gen
has
TR=0.01s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) 39 40 44 44
TR,G4=0.1S
All other gen
has
TR=0.01s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) 41 38 42 41
Table 7: Initial value, final value and settling time for all generator one by one
Settling time is the measure of stability. It means the time system takes to come to final value. Stable
system will have less settling time. In this case TR is increased more than 0.01s. Table5 above shows
the case for TR=0.01s.If this table7 is compared with table 5, it is seen that if TR of generator 1 and
generator 2 is increased then the system is decreasing stability. On contrary, if TR of generator 3 and
4, is increased then system is increasing stability. This result is well matched with eigen value
analysis done before IN IMPACT OF CHANGING TR. Generator 3 and 4 of area 2 act oppositely to
generator 1 and 2 of area 1.
Now, TR of all the generator is changed and the effect is seen which is shown in table 8.
All gen hasTR=0.1s
Initial (pu) 1 1 1 1Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) 53 50 56 54
All gen has
TR=0.2s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) 76 73 80 79
All gen has
TR=0.3s
Initial (pu) 1 1 1 1
Final (pu) 1.00056 1.00056 1.00056 1.00056
Settling time (s) unstable unstable unstable unstableTable 8: Initial value, final value and settling time for all generator
Increase in TR means AVR is slow so it takes longer time to settle down the disturbance or it is
relatively becoming less stable. The instability increases with increase in TR. Below is the example
7/31/2019 Impact of AVR on Stability
21/44
TET 4180 Electric Power System Stability
20
given the figure 19, when TR=0.5s. The speed response shows that the system is unstable because the
oscillation is growing.
Figure 19: speed response for TR=0.5s
If frequency analysis is also done in this case then eigen values will lie in positive half plane as shown
in figure 20
Figure 20: eigen value in positive half plane for TR=0.5s
4.3.2 CHANGING GAINThe time domain analysis is done. The figure 1 and figure 2 in appendix 7 represent speed for all the
generators by changing KA=200 to KA=60 of generator 1 and on all generator at same time
respectively. This is done by keeping gain TR constant at 0.01s.
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0 55,0
TIME SECONDS
0,9900
0,9950
1,0000
1,0050
1,0100
1,0150
0,9900
0,9950
1,0000
1,0050
1,0100
1,0150
0,9900
0,9950
1,0000
1,0050
1,0100
1,0150
0,9900
0,9950
1,0000
1,0050
1,0100
1,0150
case fault - A three-phase fault close to BUS8 with disconnection of a line.
DATE22 APR 2012 TIME17:12:43 JOB casefault Simpow 11.0.009 Diagram:2STRI Software
1,4, 0,9992
SYNC G1 SPEED p.u.
SYNC G2 SPEED p.u.
SYNC G3 SPEED p.u.
SYNC G4 SPEED p.u.
-1.00
-0.50
0.50
1.00
-1.50 -1.00 -0.50 0.50 1.00
Eigenvalues at time=55 seconds
STRI Softw are
DATE 27 APR 2012 TIME 11:53:50 Job casefault Simpow 11.0.008
7/31/2019 Impact of AVR on Stability
22/44
TET 4180 Electric Power System Stability
21
In the table below, Initial value, final value and settling time of the speed response is presented by
changing KA=60 one by one in all the generator.
TR=0.01 G1 G2 G3 G4
KA,G1=60
All other genhas KA=200
Initial (pu) 1 1 1 1
Final (pu) 1.00057 1.00057 1.00057 1.00057Settling time (s) 60 59 62 65
KA,G2=60
All other gen
has KA=200
Initial (pu) 1 1 1 1
Final (pu) 1.00065 1.00065 1.00065 1.00065
Settling time (s) 115 113 118 120
KA,G3=60
All other gen
has KA=200
Initial (pu) 1 1 1 1
Final (pu) 1.00058 1.00058 1.00057 1.00057
Settling time (s) 39 37 41 42
KA,G4=60
All other gen
has KA=200
Initial (pu) 1 1 1 1
Final (pu) 1.00066 1.00066 1.00066 1.00066
Settling time (s) 36 33 38 40
Table 9: Initial value, final value and settling time for all generator one by one
Settling time is the measure of stability. It means the time, system takes to come to final value. Stable
system will have less settling time. In this case KA is decreased less than 200 which is the default .
table 5 above shows the case for KA=200.If this table 9 is compared with table 5, it is seen that if KA
of generator 1 and generator 2 is decreased then the system is decreasing stability. On contrary, if KA
of generator 3 and 4, is decreased then system is incresing stability. This result is well matched with
eigen value analysis done before that generator of Area 2 act oppositely to generator of Area 1.
Now, KA of all the generator is changed and the effect is seen which is shown in table 10
All gen has
KA=200
Initial (pu) 1 pu 1 pu 1 pu 1pu
Final (pu) 1.00056 pu 1.00056 pu 1.00056 pu 1.00056 puSettling time (s) 41 41 46 46
All gen has
KA=100
Initial (pu) 1 pu 1 pu 1 pu 1pu
Final (pu) 1.00058 pu 1.00058 pu 1.00058 pu 1.00058 pu
Settling time (s) 76 73 80 82
All gen has
KA=60
Initial (pu) 1 1 1 1
Final (pu) 1.00059 1.00059 1.00059 1.00059
Settling time (s) 125 120 128 130
All gen has
KA=30
Initial (pu) 1 1 1 1
Final (pu) 1.00069 1.00069 1.00069 1.00069
Settling time (s) 94 90 97 100
All gen hasKA=10
Initial (pu) 1 1 1 1Final (pu) 1.0008 1.00079 1.00078 1.00078
Settling time (s) 15 12 18 20Table 10: Initial value, final value and settling time for all generator
It is seen that from the table that if KA of all the generator is decreased from 200 to 60 then the system
is decreasing stability by having larger settling time. But if KA is further decreased then instead of
being unstable the system slowly increases stability. This is exactly the result received from the topic
IMPACT OF CHANGING KA as shown in figure 5 of appendix 5. Another thing that should is
noticed here is that when the KA is decreasing then final steady state value is increasing bringing more
steady state error in the system.
7/31/2019 Impact of AVR on Stability
23/44
TET 4180 Electric Power System Stability
22
4.4 PRE AND POST FAULT STEADY STATE VOLTAGE AND REACTIVEPOWER EXCHANGE
4.4.1 Steady state voltageThe casefault.dynpow consists of three phase short circuit fault occurring at 1s on bus 8 and the fault
is removed at 1.05s and at the very instant line 1 between bus 8 and bus 9 is removed. Actually there is
two lines between bus 8 and bus 9. So after the fault if one of the line is removed then obviously, the
power flowing between area 1 and area 2 is changed. In the following section, the change in voltage
and reactive power of all the generator bus is analysed. In addition the reactive power exchange
between bus 8 and bus 9 before and after fault is also studied.
4.4.1.1 Changing time constantKA=200 G1 G2 G3 G4
TR,G1=0.1s All other
gen has TR=0.01s
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.89 kV 11.65 kV
TR,G2=0.1sS All othergen has TR=0.01s
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kVAfter fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
TR,G3=0.1S All other
gen has TR=0.01s
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
TR,G4=0.1S All other
gen has TR=0.01s
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
All gen has TR=0.1s Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
In this table , before and after fault voltage is studied in all the generator with constant KA=200 and by
changing TR=0.1s one by one in all generator and on all generator at the same time. It is seen that
voltage is constant before and after fault. But not much difference is seen in all the five case above. It
means that pre and post fault voltage is independent of time constant of AVR until the system is
stable. From the appendix8, FIG 1 it is seen that the system is stable. Obviously there is change in
settling time by varying TR of the generator but in this section, the concern is not about the stability in
this section but the concern in the voltage before and after fault by changing TR.
4.4.1.2 CHANGING GAINTR=0.01s G1 G2 G3 G4
KA,G1=10 All other
gen has KA=200
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.88 kV 11.66 kV 11.89 kV 11.66 kV
KA,G2=10 All othergen has KA=200
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kVAfter fault 11.89 kV 11.60 kV 11.89 kV 11.66 kV
KA,G3=10 All other
gen has KA=200
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
KA,G4=10 All other
gen has KA=200
Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.89 kV 11.66 kV 11.87 kV 11.66 kV
All gen has KA=10 Before fault 11.89 kV 11.66 kV 11.89 kV 11.66 kV
After fault 11.87 kV 11.60 kV 11.86 kV 11.58 kV
In this table, before and after fault voltage is studied in all the generator with constant TR. Those
generator which has reduced KA , has less voltage. And in the last case all the generator has reducedKA, so every generator has reduced voltage level than pre fault voltage. When one of the line is
7/31/2019 Impact of AVR on Stability
24/44
TET 4180 Electric Power System Stability
23
tripped then the impedance of the line is increased so the voltage level of each generator is also
decreased.
4.4.2 reactive power4.4.2.1
changing time constant
reactive power by changing TR=0.1s of each generator one by one and on all generator at same time
KA=200 G1 G2 G3 G4
TR,G1=0.1S All other
gen has TR=0.01s
Initial (MvaR 185 234 176 201
Final (Mvar) 206 286 200 262
TR,G2=0.1S All other
gen has TR=0.01s
Initial (Mvar) 185 234 176 201
Final (Mvar) 205 285 200 261
TR,G3=0.1S All other
gen has TR=0.01s
Initial (Mvar) 185 234 176 201
Final (Mvar) 205 285 200 261
TR,G4=0.1S All other
gen has TR=0.01s
Initial (Mvar) 185 234 176 201
Final (Mvar) 204 284 199 261All gen has TR=0.1s Initial (Mvar) 185 234 176 201
Final (Mvar) 204 284 199 261
Here not much difference is seen in five cases. Only the result that can be concluded is that after the
fault, there is weak tie between Area 1 and Area 2. So to compensate, generator must generate more
reactive power.
4.4.2.2 CHANGING GAINReactive power by changing KA=10 of each generator one by one and on all generator at same time
TR=0.01 G1 G2 G3 G4
KA,G1=10 All other
gen has KA=200
Initial value 185 MVar 234 MVar 176 MVar 201 MVar
Final value 203 MVar 288 MVar 200 MVar 262 MVar
KA,G2=10 All other
gen has KA=200
Initial value 185 MVar 234 MVar 176 MVar 201 MVar
Final value 215 MVar 278 MVar 201 MVar 264 MVar
KA,G3=10 All other
gen has KA=200
Initial value 185 MVar 234 MVar 176 MVar 201 MVar
Final value 205 MVar 284 MVar 197 MVar 264 MVar
KA,G4=10 All other
gen has KA=200
Initial value 185 MVar 234 MVar 176 MVar 201 MVar
Final value 204 MVar 283 MVar 209 MVar 249 MVar
All gen has KA=10 Initial value 185 MVar 234 MVar 176 MVar 201 MVar
Final value 210 MVar 279 MVar 206 MVar 256 MVar
As it is seen in the section 4.4.1.2 that those generator which has less KA has less voltage it is because
generator is inducing less reactive power as seen in this section.
4.4.3 EXCHANGE OF REACTIVE POWER4.4.3.1 CHANGING TIME CONSTANT
LINE 1 LINE 2
KA=200 AREA 1 AREA 2 AREA 1 AREA 2
TR,G1=0.1S All other
gen has TR=0.02s
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -8,9 -180TR,G2=0.1S All other Initial (Mvar) 24.3 -53 24,3 -53
7/31/2019 Impact of AVR on Stability
25/44
TET 4180 Electric Power System Stability
24
gen has TR=0.02s Final (Mvar) 0 0 -8,9 -179
TR,G3=0.1S All other
gen has TR=0.02s
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -8,9 -180
TR,G4=0.1S All othergen has TR=0.02s Initial (Mvar) 24.3 -53 24,3 -53Final (Mvar) 0 0 -8,9 -180
All gen has TR=0.1s Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -8,9 -181
After the fault, line 1 is cut off so the reactive power transfer by the line 1 after the fault is zero. So all
the power must be exchanged by line 2, which was exchanging the same power as line 1 before fault.
But not much difference can be made from the five cases because KA is same in all the case.
4.4.3.2 Changing gainTR=0.01 G1 G2 G3 G4KA,G1=10 All other
gen has KA=200
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -8,8 -180
KA,G2=10 All other
gen has KA=200
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -7,7 -185
KA,G3=10 All other
gen has KA=200
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -9,1 -179
KA,G4=10 All other
gen has KA=200
Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -10,6 -175
All gen has KA=10 Initial (Mvar) 24.3 -53 24,3 -53
Final (Mvar) 0 0 -9,7 -179
Here also after fault , line 2 carries more reactive power than the pre fault condition because line 1 is
tripped.
4.5 MORE ADVANCED AVRIn this section more advanced AVR called EXC_TGR is used. It means Thyristor excitor with
transient gain reduction.
Figure 21: exc_tgr exciter
The default value given to us was KA=200 , TR=0.01, TA=1.0, TB=10.0. One of the task is to tune
the parameters so that stability can be improved.
7/31/2019 Impact of AVR on Stability
26/44
TET 4180 Electric Power System Stability
25
Before tuning, the default value gives the eigen value as shown in figure 1, time domain analysis in
figure 2 in appendix 9 and the result of time domain analysis is tabulated in table just below.
G1 G2 G3 G4
Initial 1 pu 1 pu 1 pu 1pufinal 1.00056 pu 1.00056 pu 1.00056 pu 1.00056 pu
Settling time 115s 108 133 128
it is seen that the disturbance takes long time to settle down. It was seen in the previous examples that
stability can be improved by decreasing TR so in the next step TR is decreased to 0.005s
4.5.1 KA=200 TR=0.005 TA=1.0 TB=10.0The eigen values, time domain anlaysis is shown in fig 1and fig2 respectively in appendix 10. And the
result is tabulated in table just below.
G1 G2 G3 G4Initial 1 pu 1 pu 1 pu 1pu
final 1.00056 pu 1.00056 pu 1.00056 pu 1.00056 pu
Settling time 109 108 122 123
Settling time is little bit improved. So in next case TA is decreased from 1 to 0.5s
4.5.2 KA=200 TR=0.005 TA=0.5s TB=10.0Again the eigen values and time domain analysis is plotted in fig 22 and fig 23 respectively.
Figure 22: eigen value
7/31/2019 Impact of AVR on Stability
27/44
TET 4180 Electric Power System Stability
26
Figure 23: Speed response
G1 G2 G3 G4
Initial 1 pu 1 pu 1 pu 1pu
final 1.00056pu 1.00056 pu 1.00056 pu 1.00056 pu
Settling time 22 21 33 32
In this case there is huge improvement in stability. The settling time is much lesser which means that
system comes to stabilise much faster than in previous two cases. But in the fig 22 it is seen that one
of the eigen value is nearly touching origin. So this must be the point to stop. But further analysis is
done to confirm this in next section.
4.5.3 KA=200 TR=0.005 TA=0.5s TB=5.0
Figure 24:Unstable speed response
7/31/2019 Impact of AVR on Stability
28/44
TET 4180 Electric Power System Stability
27
Figure 25: eigen value in postive half plane
So this case is unstable. So in order to tune this exciter case 4.5.2 is the better option. So the
parameters for EXC_TGR is chosen as KA=200 TR=0.005 TA=0.5s TB=10.0 in order to tune this
excitor to improve the stability properties. All the final value is same 1.00056 pu because in all the
cases KA=200. To improve steady state, high gain is needed. When KA=300 is made but it increased
settling time to a very large value. Again KA=250 is used but it did not much affected the final value.
So ultimately, KA is chosen 200. So the parameters chosen is KA=200 TR=0.005 TA=0.5s
TB=10.0 to tune both steady state and stability properties.
7/31/2019 Impact of AVR on Stability
29/44
TET 4180 Electric Power System Stability
28
5 CONCLUSION:Frequency domain analysis and time domain analysis can be done to check the stability. In frequency
domain, Eigen values indicates if the system is stable or not. For the system to be stable all the eigen
values must be located in negative half plane. By changing any system parameters, if the eigen values
are moving away from origin in negative axis, then stability is improved. Among all the eigen values
only those eigen values whose imaginary part is 0.2-2 Hz is taken because here the concern is only the
electromechanical mode.
Linear analysis can be carried out only when the disturbance is small. On increasing inertia constant,
system is becoming less stable whereas the stability is increased if Damping constant is increased.
Also if the time constant of AVR is increased system would be less stable. And if the gain of AVR is
reduced then there is steady state error in the system. Increasing time constant of AVR means it is
slow acting i.e it has large time constant then it may be assumed that following a small disturbance the
AVR willnot react during the transient state and the regulated and unregulated systems will behave in
a similar manner
7/31/2019 Impact of AVR on Stability
30/44
TET 4180 Electric Power System Stability
29
APPENDIX 1
Figure 1: Power flow at base case
7/31/2019 Impact of AVR on Stability
31/44
TET 4180 Electric Power System Stability
30
Load flow result after increasing the compensation at bus 7 to improve the voltage at bus 8.
Figure 2: Improved power flow
7/31/2019 Impact of AVR on Stability
32/44
TET 4180 Electric Power System Stability
31
APEENDIX 2
00
2
1
2
100
BUS1
U = 1.03p.u.
FI= -6.8degrees
P= 6.81291E-013MW
Q= -8.12391E-014Mvar
G1
P= -8.1755E-013
MW
Q= 9.74869E-014
Mvar
BUS5
U = 1.03p.u.
FI= -6.8degrees
P= 7.88828E-013MW
Q= 3.55534E-012Mvar
P= -6.81291E-013
MW
Q= 8.12391E-014
Mvar
0
BUS6
U = 1.03p.u.
FI= -6.8degrees
P= -7.88828E-013
MW
Q= -3.55534E-012
Mvar
P= -2.4978E-013MW
Q= 9.37993E-012Mvar
P= -6.49913E-013MWQ= -5.45033E-012Mvar
BUS2
U = 1.03p.u.
FI= -6.8degrees
P= 6.49913E-013
MW
Q= 5.45033E-012
Mvar
0
G2
P= -7.79895E-013
MW
Q= -6.5404E-012
Mvar
BUS7
U = 1.03p.u.
FI= -6.8degrees
0
P = 0MW
Q= -0Mvar
P= 2.4978E-013MW
Q= -9.37993E-012
Mvar
P= -2.00391E-012MW
Q= -4.06686E-013Mvar
P= -2.00391E-012MW
Q= -4.06686E-013Mvar
0
P = 0MW
Q= -0Mvar
BUS8
U = 1.03p.u.
FI= -6.8degrees
P= 2.00391E-012
MW
Q= 4.06686E-013
Mvar
P= 2.00391E-012
MW
Q= 4.06686E-013
Mvar
P= -2.03599E-012MW
Q= -2.95135E-012Mvar
P= -2.03599E-012MW
Q= -2.95135E-012Mvar
BUS9
U = 1.03p.u.
FI= -6.8degrees
0
P = 0MW
Q= -0Mvar
P= -2.7213E-012MW
Q= 1.92529E-011MvarP= 2.03599E-012
MW
Q= 2.95135E-012
Mvar
P= 2.03599E-012
MW
Q= 2.95135E-012
Mvar
0
P = 0MW
Q= -0Mvar
BUS10
U = 1.03p.u.
FI= -6.8degrees
P= -5.67742E-012MW
Q= -2.4707E-012Mvar
P= 2.7213E-012MW
Q= -1.92529E-011
Mvar
P= -7.1267E-013MW
Q= 5.61281E-012Mvar
BUS4
U = 1.03p.u.
FI= -6.8degrees
P= 7.1267E-013MW
Q= -5.61281E-012
Mvar
0
G4
P= -8.55204E-013
MW
Q= 6.73537E-012
Mvar
BUS11
U = 1.03p.u.
FI= -6.8degrees
P= 5.67742E-012
MW
Q= 2.4707E-012
Mvar
P= -3.40646E-012MW
Q= 4.06195E-013Mvar
BUS3
U = 1.03p.u.
FI= -6.8degrees
P= 3.40646E-012
MW
Q= -4.06195E-013
Mvar
0
G3
P= -2.4903E-012
MW
Q= 6.93034E-012
Mvar
7/31/2019 Impact of AVR on Stability
33/44
TET 4180 Electric Power System Stability
32
Appendix 3
Figure 1: Eigenn value before fault
Figure 2: Modal analysis for eigen value no. 22
-0.60
-0.40
-0.20
0.20
0.40
0.60
-1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 0.20
Eigenvalues at time=0 seconds
STRI Softw are
DATE 27 APR 2012 TIME 12:06:57 Job casefault Simpow 11.0.008
-1.00
-0.50
0.50
1.00
-1.00 -0.50 0.50 1.004
321
Eigenvalue: -2.25867 1/s + j1.36605 Hz at Time=0 seconds
STRI Softw are
DATE 27 APR 2012 TIME 12:06:57 Job casefault Simpow 11.0.008
1 SYNCG4
2 SYNCG3
3 SYNCG2
4 SYNCG1
7/31/2019 Impact of AVR on Stability
34/44
TET 4180 Electric Power System Stability
33
APPENDIX 4Eigen values: by changing TR=0.1 s of each generator one by one and on all generator at same time
Figure 1: change in Gen 1
Figure 2: For change in Gen 2
1
0.91
0.51
-0.080 -0.060 -0.040 -0.020 0.000 0.020 0.040 0.060 0.080
Real 1/s
-0.5300
-0.5290
-0.5280
-0.5270
-0.5260
-0.5250
-0.5240
-0.5230
-0.5220
-0.5210
Imag.Hz
Eigenvalue: -0.087935 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G1 2
DATE 27 APR 2012 TIME 10:57:11 Simpow 11.0.008Job casefault
STRI Softw are
TR (0.01)
0.91
0.81
0.71
0.610.41
0.31
0.21
1
-0.050 0.000 0.050 0.100 0.150 0.200 0.250 0.300
Real 1/s
-0.5300
-0.5250
-0.5200
-0.5150
-0.5100
Imag.Hz
Eigenvalue: -0.087935 1/s+/-j-0.520292 Hz at Time=55 secondsEXC G2 3
DATE 27 APR 2012 TIME 10:57:11 Simpow 11.0.008Job casefault
STRI Softw are
TR (0.01)
7/31/2019 Impact of AVR on Stability
35/44
TET 4180 Electric Power System Stability
34
Figure 3: For change in Gen 3
Figure 4: For change in Gen 4
0.91
0.81
0.71
0.61
0.51
0.31
-0.350 -0.300 -0.250 -0.200 -0.150 -0.100
Real 1/s
-0.5200
-0.5150
-0.5100
-0.5050
-0.5000
-0.4950
Imag.Hz
Eigenvalue: -0.087935 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G4 6
DATE 27 APR 2012 TIME 10:57:11 Simpow 11.0.008Job casefault
STRI Softw are
TR (0.01)
0.91
0.81
0.71
0.61
0.41
-0.1500 -0.1400 -0.1300 -0.1200 -0.1100 -0.1000 -0.0900
Real 1/s
-0.52000
-0.51900
-0.51800
-0.51700
-0.51600
-0.51500
-0.51400
-0.51300
Imag.Hz
Eigenvalue: -0.087935 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G3 5
DATE 27 APR 2012 TIME 10:57:11 Simpow 11.0.008Job casefault
STRI Softw are
TR (0.01)
7/31/2019 Impact of AVR on Stability
36/44
TET 4180 Electric Power System Stability
35
Figure 5: change in all generator
TIME CRITICAL EIGEN VALUE
0.01 (-0.87935E-01 1/s ,-0.52029 Hz)
0.1 (-0.75659E-01 1/s ,-0.52195 Hz)
0.3 -0.38646E-01 1/s ,-0.52635 Hz
0.5 ( 1.108 1/s , 0.000 Hz)
0.7 ( 3.292 1/s , 0.000 Hz)
1 ( 3.379 1/s , 0.000 Hz)
Table 1: change in eigen values
7/31/2019 Impact of AVR on Stability
37/44
TET 4180 Electric Power System Stability
36
APPENDIX 5Eigen values by changing KA=10 of each generator one by one and on all generator at same time
Figure 1: For change in Gen 1
Figure 2: For change in Gen 2
170
130
100
70
30
20
-0.0850 -0.0800 -0.0750 -0.0700 -0.0650 -0.0600
Real 1/s
-0.5200
-0.5180
-0.5160
-0.5140
-0.5120
-0.5100
-0.5080
-0.5060
Imag.Hz
Eigenvalue: -0.0879347 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G1 2
DATE 27 APR 2012 TIME 11:26:12 Simpow 11.0.008Job casefault
STRI Softwar e
KA (200)
190170
150
130
110
90
70
50
40
30
20
-0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 -0.0400 -0.0300
Real 1/s
-0.5200
-0.5150
-0.5100
-0.5050
-0.5000
-0.4950
-0.4900
-0.4850
-0.4800
Imag.Hz
Eigenvalue: -0.0879347 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G2 3
DATE27 APR 2012 TIME11:26:12 Simpow 11.0.008Job casefault
STRI Softw are
KA (200)
7/31/2019 Impact of AVR on Stability
38/44
TET 4180 Electric Power System Stability
37
Figure 3: For change in Gen 3
Figure 4: change in Gen 4
140
100
70
20
-0.1020 -0.1000 -0.0980 -0.0960 -0.0940 -0.0920 -0.0900 -0.0880
Real 1/s
-0.52500
-0.52450
-0.52400
-0.52350
-0.52300
-0.52250
-0.52200
-0.52150
-0.52100
-0.52050
Imag.Hz
Eigenvalue: -0.0879347 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G3 5
DATE 27 APR 2012 TIME 11:26:12 Simpow 11.0.008Job casefault
STRI Softw are
KA (200)
170150
130
110
90
70
0
40
30
20
-0.1100 -0.1050 -0.1000 -0.0950 -0.0900 -0.0850 -0.0800
Real 1/s
-0.5360
-0.5340
-0.5320
-0.5300
-0.5280
-0.5260
-0.5240
-0.5220
Imag.Hz
Eigenvalue: -0.0879347 1/s+/-j-0.520292 Hz at Time=55 seconds
EXC G4 6
DATE 27 APR 2012 TIME 11:26:12 Simpow 11.0.008Job casefault
STRI Softw are
KA (200)
7/31/2019 Impact of AVR on Stability
39/44
TET 4180 Electric Power System Stability
38
Figure 5: change in all generator
KA EIGEN VALUE
200 (-0.87935E-01 1/s ,-0.52029 Hz)
150 (-0.72947E-01 1/s ,-0.51867 Hz)
100 (-0.50837E-01 1/s ,-0.51131 Hz)
50 (-0.2829E-01 1/s ,-0.4834 Hz)10 (-0.1409 1/s , 0.000 Hz)
Table 1: change in eigen value
7/31/2019 Impact of AVR on Stability
40/44
TET 4180 Electric Power System Stability
39
APPENDIX 6speed:: by changing TR=0.1 s of each generator one by one and on all generator at same time
Figure 1: change in Gen 1
Figure 2: change in all generator
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0 55,0
TIM E SECONDS
1,00000
1,00050
1,00100
1,00150
1,00200
1,00000
1,00050
1,00100
1,00150
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
0,99950
1,00000
1,00050
1,00100
1,00150
1,00200
1,00250
case fault - A thre e-phase fault close to BUS8 with disconnection of a line.
DATE 23 APR 2012 TIME 17:31:46 JOB casefault Simpow 11.0.009 Diagram:5STRI Software
SYNC G1 SPEED p.u.
SYNC G2 SPEED p.u.
SYNC G3 SPEED p.u.
SYNC G4 SPEED p.u.
7/31/2019 Impact of AVR on Stability
41/44
TET 4180 Electric Power System Stability
40
Appendix 7speed:: by changing KA=60 each generator one by one and on all generator at same time
Figure 1: change in Gen1
Figure 2: change in all generator
7/31/2019 Impact of AVR on Stability
42/44
TET 4180 Electric Power System Stability
41
APPENDIX 8
Figure 1: change in voltage when ka=200, tr=0.1S IN GEN 1
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0
TIME SECONDS
11,00
11,50
12,00
12,50
10,00
10,50
11,00
11,50
12,00
12,50
10,50
11,00
11,50
12,00
12,50
9,00
9,50
10,00
10,50
11,00
11,50
12,00
12,50
case fault - A three-phase fault close to BUS8 with disconnection of a line.
DATE22 APR 2012 TIME17:10:54 JOB casefault Simpow 11.0.009 Diagram:1STRI Software
SYNC G1 U POS. kV
SYNC G2 U POS. kV
SYNC G3 U POS. kV
SYNC G4 U POS. kV
7/31/2019 Impact of AVR on Stability
43/44
TET 4180 Electric Power System Stability
42
APPENDIX 9
Figure 1: eigen value analysis
Figure 2: Time domain Analysis
7/31/2019 Impact of AVR on Stability
44/44
TET 4180 Electric Power System Stability
Appendix 10
Figure 1: eigen value analysis
Figure 2: Time domain Analysis