Impact of AVR on Stability

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


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.


3/44


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


4/44


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


5/44


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


6/44


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.


7/44


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


8/44


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.


9/44


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


10/44


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


11/44


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.


12/44


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.


SYNC G1 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



0.4, -195

LINE BUS8 BUS9 1 P1 POWER MW





13/44


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


DATE 7 APR 2012 TIME15:54:50 JOBcasefault Simpow 11.0.009 Diagram:6

STRI Software


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


14/44


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


STRI Softw are



15/44


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


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


16/44


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


17/44


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


STRI Softw are


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



SYNC G1 SPEED p.u.

SYNC G2 SPEED p.u.

SYNC G3 SPEED p.u.

SYNC G4 SPEED p.u.


18/44


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


19/44


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.


20/44


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


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


Final (pu) 1.00056 1.00056 1.00056 1.00056


TR,G4=0.1S

All other gen

has

TR=0.01s


Final (pu) 1.00056 1.00056 1.00056 1.00056


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


All gen has

TR=0.2s


Final (pu) 1.00056 1.00056 1.00056 1.00056


All gen has

TR=0.3s


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


21/44


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


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


STRI Softw are



22/44


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


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


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


Final (pu) 1.00058 1.00058 1.00057 1.00057


KA,G4=60

All other gen

has KA=200


Final (pu) 1.00066 1.00066 1.00066 1.00066


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


All gen has

KA=60


Final (pu) 1.00059 1.00059 1.00059 1.00059

Settling time (s) 125 120 128 130

All gen has

KA=30


Final (pu) 1.00069 1.00069 1.00069 1.00069


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.


23/44


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




gen has TR=0.01s



All gen has TR=0.1s Before 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



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



KA,G4=10 All other

gen has KA=200



All gen has KA=10 Before 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 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


24/44


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


gen has TR=0.01s

Initial (MvaR 185 234 176 201

Final (Mvar) 206 286 200 262


gen has TR=0.01s

Initial (Mvar) 185 234 176 201

Final (Mvar) 205 285 200 261


gen has TR=0.01s

Initial (Mvar) 185 234 176 201

Final (Mvar) 205 285 200 261


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



KA,G3=10 All other

gen has KA=200



KA,G4=10 All other

gen has KA=200



All gen has KA=10 Initial value 185 MVar 234 MVar 176 MVar 201 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


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


25/44


24

gen has TR=0.02s Final (Mvar) 0 0 -8,9 -179


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.


26/44


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


27/44


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


28/44


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.


29/44


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


30/44


29

APPENDIX 1

Figure 1: Power flow at base case


31/44


30

Load flow result after increasing the compensation at bus 7 to improve the voltage at bus 8.

Figure 2: Improved power flow


32/44


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


33/44


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


STRI Softw are


-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


1 SYNCG4

2 SYNCG3

3 SYNCG2

4 SYNCG1


34/44


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


STRI Softw are

TR (0.01)


35/44


34



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


EXC G4 6


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


EXC G3 5


STRI Softw are

TR (0.01)


36/44


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


37/44


36

APPENDIX 5Eigen values by changing KA=10 of each generator one by one and on all generator at same time



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


EXC G1 2


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


EXC G2 3

DATE27 APR 2012 TIME11:26:12 Simpow 11.0.008Job casefault

STRI Softw are

KA (200)


38/44


37



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


EXC G3 5


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


EXC G4 6


STRI Softw are

KA (200)


39/44


38


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


40/44


39

APPENDIX 6speed:: by changing TR=0.1 s of each generator one by one and on all generator at same time



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



SYNC G1 SPEED p.u.

SYNC G2 SPEED p.u.

SYNC G3 SPEED p.u.

SYNC G4 SPEED p.u.


41/44


40

Appendix 7speed:: by changing KA=60 each generator one by one and on all generator at same time

Figure 1: change in Gen1



42/44


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


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


43/44


42

APPENDIX 9

Figure 1: eigen value analysis

Figure 2: Time domain Analysis


44/44


Appendix 10

Figure 1: eigen value analysis

Figure 2: Time domain Analysis

Impact of AVR on Stability

Documents

Transcript of Impact of AVR on Stability