IEEE Transactions on Energy Conversion, Vol. 8, No. 2, June 1993 221

IMPLEMENTATION AND LABORATORY TEST RESULTS FOR A FUZZY LOGIC BASED SELF-TUNED POWER SYSTEM STABILIZER

M. A. M. Hassan * 0. P. Malik

Electrical & Computer Engineering Department The University of Calgary, Calgary

Alberta, T2N 1N4, Canada

* On Scientific leave from Cairo University, Giza, EGYPT

ABSTRACT : This paper describes the implementation of a fuz- zy logic based self-tuned controller to improve the stability of electric power systems. The stabilizing signal is computed using the standard fuzzy membership function depending on the speedacceleration state of the generator in the phase plane. The performance of the proposed stabilizer is demonstrated by practi- cal implementation using a digital signal processor mounted on a PC-AT. Results of the experimental tests on a physical model of a power system are presented.

KEYWORDS : On-line Computer Control, Excitation Control, Synchronous Alternator, Power System Stabilizer, Fuzzy Sets and Logic.

1. INTRODUCTION

Advances in computer technology have made available reli- able digital devices and microcomputers at low cost. As a result , real-time on-line computer control systems for electric generating units have become feasible and realizable. In the past decade, much effort has been directed towards the development of digital controllers based on advanced control strategies such as adaptive self-tuning control [l-31 to improve the overall power-system sta- bility. They can easily be implemented with high reliability.

Recently, alternative control schemes have been proposed. These are the rule-based stabilizer [4, 51 and the fuzzy logic con- trol [6-81. The operating conditions of the synchronous machine are expressed by the quantities of speed, deviation, and accelera- tion in the phase plane [4]. The supplementary stabilizing signal i s determined using fuzzy membership. Out of these schemes, fuzzy control appears to be the most suitable one, due to its robustness and lower computation burden. The fuzzy logic con- trollers could easily be constructed using a simple microcomputer associated with AID and D/A converters.

All the studies reported in Refs, [4-81 describe simulation results. First implementation and experimental verification Of a fuzzy logic based controller as a power system stabilizer is described in this paper. The fuzzy logic based self-tuned stabilizer proposed in Ref. [8] has been implemented on a Th4S32OC30 Digital Signal Processor (DSP) board, installed in a PC-AT with a capability of uninterrupted communication. To demonstrate its performance, several real-time tests have been performed on a physical model of a power system. Test results illustrate the effectiveness of the proposed controller and the non-dependability of the controller parameters on the operating point of the alternator. Also the computation time is less than that of the self-tuning [l-31.

92 SM 474-7 EC A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1992 Summer Meeting, Seattle, WA, July 12-16, 1992. Manuscript submitted January 20, 1992; made available for printing June 2. 1992.

2. THEORETICAL BACKGROUND

The physical model of the power system available in the laboratory consists of a generating unit, composed of a micromachine driven by a dc motor, connected to a constant vol- tage system ( infinite bus ). The supplementary stabilizing signal U is added to the excitation control loop as shown in Fig. 1. The required stabilizing signal is to be generated based on fuzzy logic and self-tuned parameter. The supplementary stabilizing signal, u(t), is given by

u ( f ) = U ( k ) ; kTs < f < (k+l)Ts (1)

where, Ts is the sampling period and

The value of U(k) is determined through the following steps [8] : k is an integer.

Sample the alternator speed deviation Am. Compute the scaled acceleration signal using :

A

As = Fa * A

=[ A N k ) - ANk-1) ]I TS (2) (3)

where, A is the acceleration , AS is the scaled acceleration, and FU is the scaling factor. Compute e&) and R(k), from the phase plane, as shown in Fig. 2. Determine the fuzzy membership functions Ns (0) and Ps (0) as described in Fig. 3 and in reference [8]. Compute the stabilizing signal U&) using :

where Gc(k) is the gain whose value is given by the discon- tinuous function shown in Fig. 4. The value of Gc&) is function in R ( 0 ) and Dr. Increase k by 1 and repeat steps 1 through 4.

The Main Tuning Parameters

The imDlemented self-tuned fuzzy logic controller dewnds mainly on &e basics of the fuzzy lo& controller introduced in reference [8]. However, a tuning process shapes the fuzzy membership functions and a self-tuning parameter, related to the magnitude of the disturbance, is also used.

The functions Ns(O)andPs(e) were introduced as standard fuzzy membership functions as given in references [7] and 181. Fig. 3 shows the membership functions Ns (e) and Ps(e ) , which are nonlinear continuous functions. These functions are used to indi- cate the degree of deceleration and acceleration control effort required to bring the system state to equilibrium after a distur- bance. In general, deceleration control is only needed when the machine state is in the first quadrant, deceleration and accelera- tion in the second and the fourth quadrant, and acceleration con- trol only in the third quadrant, as given in references [4 - 61. However, both membership values are used in the computation of the stabilizing signal as shown in equation (4).

0885-8969/93$03.00 0 1992 IEEE

222

F i g . 1 The l a b o r a t o r y s i n g l e mach ine i n f i n i t e bus s y s t e m '

The function Ps(e ) exists for e => 90 degrees in reference [6]. That means Ps(e ) = 0.0 for e < 90 degree. In this paper, as well as references [7-91, w e ) = 0.0 for 0 < ei, where Oi is con- sidered as a tuning factor. This factor will affect the shape of both functions Ps(8) and Ns(8). where Ns(8) = 1 - Ps(0 ) . The domain of the function w e ) will be (ei < e < 360). Also both functions will be symmetric around the average angle between ei and 360. It is clear that the functions chosen in reference [6] are the spe- cial case of the standard functions shown in Fig. 3.

2.1.1. The Self Tuning Parameter

In order to improve the performance of the fuzzy controller, the value of 'Dr' was introduced in [8] to be self tuned in pro- portion to the magnitude of the disturbance. A very low starting value (Dri) was assigned to 'Dr' at the initialization of the con- troller. This value of 'Dri' is not system specific. The parameter 'R' in the phase plane, as shown in Fig. 2, will be calculated at each sample and compared to 'Dr'. It is clear that the amount of disturbance is proportional to the value of 'R'. If the value of 'R' is less than 'Dr', the value of 'Dr' will remain the same, other- wise, the value of 'Dr' will be chosen as:

Dr = l.Ol(Sup(R)) (5 )

Equation (5) means that the algorithm will search for the highest value of ' R which corresponds to the magnitude of the current disturbance. During that search, if ' R is greater than 'Dr', 'Dr' will be updated to Dr = 1.01 ( Sup (R)). Before reach- ing the maximum value of ' R , 'Dr' will be very close to 'R', and hence the magnitude of the stabilizing signal will be very close to its upper limit. After reaching the peak value of 'R', R' will start to decrease, the value of 'Dr' will be kept constant, and the magnitude of the stabilizing signal will decrease until steady state is reached. Reaching steady state will reinitialize 'Dr' with its initial value. This will happen again for any later disturbance.

3. EXPERIMENTAL SET-UP

The proposed fuzzy logic based self-tuned PSS has been implemented using a DSP board, installed in a PC-AT. This board is used for measurement, filtering, control computation and displaying the output results on CRT as well as feeding the sbi- bilizing signal to the machine.

The laboratory model consists of a 3 kVA, 210 V, three phase micro-alternator, feeding a model representing a 500 kV, 300 km long double circuit transmission line. The parameters of the microaltemator and the transmission line are given in Appen- dix A. An overall schematic of the laboratory system is shown in Fig. 1. The PSS is connected in parallel with the AVR for sim- plicity and to be consistent with other literature in the field, as in references [2, 3, and 101.

A simple AVR with the transfer function :

was used to simulate a high gain, short time constant AVR. The AVR has been built using operational amplifiers.

bw

I 3rd

Fig.. 2 Generator C o n d i t i o n On the Phase-Plane

6 - E i 2

Fig. 3 Membership Functions Ns and Ps

1 Gc

I I

D r 0 t R

Gain F u n c t i o n F i g . 4

The input signal used for the PSS is the deviation in speed from the synchronous speed.

3.1. Speed Sensing

Since the speed is the most important input signal for the PSS, more attention was given to that signal. A photo interrupter was installed to detect the light crossing 4-holes in a disc mounted on the shaft of the altemator. The pulse train is first converted to a rectangular pulse train by a signal shaping circuit.

223

at: Ts = 9 msec, Fa = 1.0, 8,=80 d e g , and Dri = O.ooO1

It can be seen that the controller responded immediately.

were considered : a)

b) C)

d)

In the next stage of the tests, the following disturbances

Change in the input power. 5% change in the reference voltage. A 100 ms three-phase to ground fault with successful reclo- sure 450 ms after fault clearance. A 100 ms three-phase to ground fault with unsuccessful reclosure. Tests were conducted for various loads, and lagging and

leading power factor operating conditions. The test results presented in this paper are for the operating point :

P = . 6 l p u , P.F. =0.9 lead, and Vr = 1.01 p u

It was found from th: simulation studies in Refs. [7,8] that the optimal values of 'e, and 'Fa' are around 97 degrees and 0.1 respectively.

The results in this paper illustrate signals in real-time obtained using a storage oscilloscope interfaced to a PC. Also initial real-time tests showed that in a number of cases the sys- tem was oscillatory, or poorly damped, with no stabilizer or even with the conventional stabilizer. The conventional stabilizer is assumed to have a fixed transfer function as proposed by Ontario Hydro and is given in Appendix B.

The resulting pulses are introduced to the processor unit as an interrupt or other form of input, that can be activated by any one edge of the pulses. The processor counts the time between two consecutive speed pulses as pulse counts of an internally driven clock. The reciprocal of this count can be suitably scaled to obtain a measure of the speed. Four such speed measures were suitably averaged to reduce the effect of instrumentation noise. That means four pulses per revolution represent a fourth order moving-average filtering.

3.2. Hardware Requirements

In view of its suitability and ready availability in the Laboratory, TMS32OC30 was found to be the best and most con- venient processor to use. Using a clock frequency of 33.33 MHz, this processor has an instruction execution time of 60 ns [ll], and can execute programs at a speed of 33.3 MFLOPS. By a rough estimate, it was found that the implemented algorithm involves a little more than 1000 floating point instructions, which should take approximately 60 ps to execute. This DSP, unlike most microcontroller integrated circuits, does not have any specific on-chip features. Several of the on-chip peripherals have had to be programmed in order to run tasks such as output signal generation and speed sensing.

To implement real time tests on the above mentioned DSP, a real-time window monitor has been provided for the host PC. Using this window, it is possible to load files and study their execution through different facilities. It is also possible to leave the DSP program in execution and exit the monitor, so that the PC could be used for other purposes. However, this processor is a fast and powerful tool to investigate real-time algorithms. This board is also provided with an analog interface (through D/A and A/D devices) and a port connection [ 113.

3.3. Software Requirements

The software for the PSS was developed mainly using C programming language except for the speed sensing and signal U 0 routines which were written in Assembly. The procedure for the overall software algorithm for the implemented PSS is given below :

Start the Main Program. Initialize all parameters. Initialize the Clock and the Speed interrupt routines. Compute the speed using speed pulses interrupts. Wait for the sampling time interrupt. Get the speed deviation. Filter the speed deviation using software 2nd order filter. Then calculate the acceleration. Invoke the controller calculation once the tolerance in speed deviation is exceeded, and calculate the stabilizing signal using Fuzzy logic based self-tuned PSS. Output the new stabilizing signal and the speed deviation. Go To step 5). Step 4) is still in execution ( always in exe- cution ).

EXPERIMENTAL RESULTS

A number of real-time tests have been conducted in the laboratory with the fuzzy logic controller described in Sec. 2 and as programmed in Sec. 3.3. using the DSP.

The performance of the PSS as implemented was first moni- tored under steady state with no fault. During the periods when the system to which it was connected was also steady, both the speed deviation and the stabilizing signal were almost zero. At times the machine was subjected to random disturbances from the system caused by the changes in the operating conditions of other machines, which were in its proximity in the laboratory. The associated load, when changed, also contributed as another Source of light disturbances. Response to such disturbances were captured on the scope and is shown in Fig. 5. At this instant, the machine was operating under light load with the parameters set

4.1. Step Changes in Input Power

Change in input power was produced by changing the input current to the dc motor, which is working as a prime mover for the generator. Performance in response to a 0.3 pu step change in input power is shown in Fig. 6. As seen from this figure, the sta- bilizer has a strong effect on damping the oscillations.

4.2. 5% Change in the Reference Voltage

Performance of the stabilizer for a 5% change in the refer- ence voltage is shown in Fig. 7. It can be seen that with the PSS, the speed deviation signal, as well as the voltage signal, is damped out very quickly.

4.3. Three Phase Fault With Successful Reclosure

Response to a 3-phase to ground fault at the middle of one circuit of the transmission line is shown in Fig. 8. The faulted line was isolated by opening the breakers at both ends of the line 100 ms after the inception of the fault and reclosed successfully by closing the breakers 450 ms later. It can be seen that with the fuzzy logic controller the system recovered much more smoothly as compared to the conventional stabilizer.

4.4. Three Phase Fault With Unsuccessful Reclosure

In this test, a 3-phase to ground fault was applied at the middle of one circuit of the transmission line. The sequence of events is the same as in Section 4.3. In the end the breakers at both ends of the line were recloseed but dropped out after redo- sure leaving the faulted line open at both ends. System response for this test shown in Fig. 9 illustrates the effectiveness of the fuzzy logic based PSS in damping the oscillations.

4.5. Test Results With Changes In Parameters

The test described in Sec. 4.3. was repeated many times with different parameters such as : Sampling time ( Ts), Scaling Factor (Fa), and Initial Angle (e,). Test results for various Values of (e,) under the conditions :

Ts = 36 msec, Fa = 1.0, and Dri = O.oooo1

224

3 2

r( 1 . 5 0 0

0 1 -

0 . 5 - r:

I I I I 1 .5

U d - - random - -

half Id. --- 0 1 - full Id. - - - - - - - 0 . 5 m

Fig. 5 Performance of the proposed stabilizer under random disturbance, half load and full load changes ( Ts=9 ms.0i=80 deg, Fa=l.O, and Dri=O.OOOl )

?...

speed dev. - _ -

a,

- U

I I I I I I I I

1 2 3 4 5 6 7 8 9 10 2 - 2 -1 .5 I I I I I 1 I I ,

1 2 3 4 5 6 7 8 9 10 Time (sec.) Time (sec.)

a) 0.3 pu step Increase

6 I I I I I I I I

Vt - 5 - - 4 - - 3 - -

2 - - 1 I I I I I I I I

U id .r(

5

2 . 5

2

1 . 5

1

0 . 5

0

I I I I I I I I I

0 . 5 1 I I I I I I I I

1 2 3 4 5 6 7 8 9 10 Time (sec. )

I

a, ol

U

?...

U r(

0 - id ol cil

1 . 5

1

0 . 5

0

- 0 . 5

-1

-1 .5

I I I I I I I I I 1 2 3 4 5 6 7 8 9 10

Time (sec.)

b) 0.3 pu step Decrease

Fig. 6 Performance of the proposed stabilizer for a 0.3 pu step change in input power ( Ts=36 ms,f3,=80 deg, Fa=l.O, and Dri=O.ooOOl )

d 0 0

0 - c r( U id

.A

5

1.2 1

0 . 8 0.6 0 . 4 0 . 2

0

- 0 . 2

- 0 . 4

-0.6 - 0 . 8

speed dev. - - - -

- - -

1 2 3 4 5 6 7 8 9 10 Time (sec.)

a) Voltage response b) Speed deviation

Fig. 7 Performance of the stabilizers for a 5% step change in reference voltage ( T ~ = 3 6 m~.Oi=80 deg, Fa=l.O, and Dri=O.ooOOl )

2 -

3

rl 0 0

0 - c .ri U d .d

5 a a,

in

- 3

rl 0 0

0 - c

.r( U ld .r(

5 a m in

3

r( 0 0

0 I

C .r(

U 6 .ri

5 a m cn

I I I 1 propsd. - - convnt. --- no pss. - - - - -

propsd. - convnt. --- - no pss. - - - -

Fig. 8 Performance under a 3-phase to ground fault with successful reclosure ( Proposed, Conventional, and No stablizer )

( Ts=12 m,Bi=80 deg. Fa=l.O, and Dri=O.OOOO1 )

1 . 5 I I I I I 1 - U d 0 I

rl d m -6 in rl 0

U c

U - 2 ' I I I I I

0 2 4 6 8 10 Time (sec. )

I I I I I 1 -1 .5 0 2 4 6 8 10

Time (sec. )

Fig. 9 Performance of the stabilizers for a 3-pha.w to ground fault with unsuccessful reClOSUre ( Ts=36 ms,e,=80 deg, Fa=l.O, and Dn'=O.OOOOI )

I I I I I

2 t 1 . 5

1

0 . 5

0

0 . 5

-1

0 2 4 6 8 10 0 2 4 6 8 10 Time (sec. ) Time (sec. )

Fig. 10 Performance of the proposed stabilizer under a 3-phase to ground fault with successful reclosure for different values of Bi

( Ts=36 ms, Fu=l.O, andDri~.oooO1 )

are shown in Fig. 10. Comparing the responses in Fig. 10 for e, varying between 80 and 105 deg. including the optimal value of e, set at 95 deg., in respect of overshoot and damping of oscilla- tions, it can be seen that the proposed algorithm is robust as the fairly large variation in e, produces only a minimal variation in the performance.

Responses for sampling periods varying between 2 ms and 90 ms are shown in Fig. 11. The other parameters were set at :

Fa = 1 .O, 0, =80 deg , and DN' = O.oooO1

It is clear from the comparison of overshoots, the damped oscil- lation ( settling time ), and the stabilizer response, that the pro- posed controller responds very well over a wide range of sam- pling period.

Response for the scaling factor for acceleration (Fa) ranging between 0.1 and 10.0 is shown in Fig. 12. Other parameters were set at :

Ts = 12 msec, 8,=80 deg, and Dri = O.oooO1

Comparing the response again shows that the proposed controller is very robust as wide variations in the parameters can be tolerated without a major deleterious effect on system perfor- mance. However, a suitable value of (Fa) should be close to unity.

Response for two different values of (Dri), 0.0001 and 0.00001, is shown in Fig. 13. Other parameters were set at :

226

- 2 ?I 0 0

0 - C .4

U Q 4

5 a PI v)

CI

2 4 0 0

0 - c .4 U

.d

5 a 8

VI

- 3

3 0 0

0

C

.d

Y Q .rl

-

5 a PI v)

- 2 rl 0 0

0

C .d

U Q .4

-

5 a 8

v)

3 I I I I 1

2 t T s = 2- Ts = 6 --- Ts = 12 - - - -

I I I I I 0 2 4 6 8 10

Time (sec.)

3 I I I I 1 2 t Ts = 36 -

TS = 60 ---

I I I I

Time (sec.)

I 0 2 4 6 8 10

- U 7.

0 - d rb m -4 v)

d 0

U C

U

- U d

0 - d rb

m .4 rn 4 0

U c

U

1 . 5

1

0 . 5

0

- 0 . 5

-1

-.- 0 2 4 6 8 10

Time (sec.)

1 . 5

1

0 . 5

0

- 0 . 5

-1

- 1 . 5 ' I ' I I I 0

I

2 Time 4 (sec. 6 8 10

Fig. 1 1 Performance of the proposed stabilizer for different values of the sampling period ( €+=SO deg, Fa=l.O, and Dn=O.ooOOl )

2 2

1.5 ..-.

Fa = 0 . 5 --- Fa = 1 . 0 - - - - Fa = 1 0 . ........

- ; 1 1 7 0 . 5 c m o

B -1

-2 2 -1 .5

.4 0

- 0 . 5 -1

- 7 0 2 4 6 8 10

Time (sec.) 0 2 4 6 8 10

Time (sec. )

Fig. 12 Performance of the proposed stabilizer with various values of the acceleration scaling factor ( Ts=12 m,0i=80 deg, and Dri=O.ooOOl )

I I I I

Dri = 0.00010 - Dri = 0.00001 ---

2 - Dri = 0.00010 - - Dri = 0.00001 ---

-

6 8 10 0 2 4 6 8 10 0 2 4 Time (sec. ) Time (sec.)

Fig. 13 Performance of the proposed stabilizer for two different values of (Dn) ( Ts=12 ms,Bi=80 deg, and Fa=l.O )

Ts = 12 m e c , Oi=80 deg, and Fa = 1.0

Comparing the response again shows that the proposed controller is very robust. However, a very low value of (Dri) will be rea- sonable.

4.6. Discussion

Results given in Figs. 5 through 13 clearly show that the system response with the proposed stabilizer in general is very acceptable. The real-time test results show some differences from the simulation results reported in Ref. [8], specially for parameter settings. The implemented stabilizer shows robustness. Due to space limitations, results for only one operating point are included in this paper. The particular operating point chosen is in the leading power factor region where the margin of stability is low and is thus a more critical point.

5. CONCLUSIONS

Implementation of a fuzzy logic based self-tuned controller as a power system stabilizer is described in this paper. The sta- bilizing signal generated by the controller is computed using a standard fuzzy membership function and a self-tuned parameter. The calculation is based on the representation of the alternator state in the phase plane. Real-time test results have been per- formed for various operating conditions and disturbances. The results obtained demonstrate the effectiveness and improved response of the implemented PSS compared with the conven- tional stablizer. The proposed controller does not require any parameter identification in real time and has a much simpler algorithm than that for a self-tuning controller. The hardware implementation was done on a TMS32OC30 DSP because of its availability in the lab. However, the algorithm is so simple that it should be easy to implement it on a much cheaper 16 bit micro- controller. Other algorithms, such as rule-based, conventional digital based, etc. are being implemented now and a comparison of the performance with these algorithms will be reported in the future.

6. ACKNOWLEDGMENTS

The authors greatfully acknowledge the support from Cana- dian International Development Agency for financial support. They also acknowledge the help they got from Dr. S . Roy, Mr. P. Walsh, Mr. G. Hanckock and Mr. H. Kinawi during the prac- tical implementation. Dr. Hassan would also like to thank Cairo University, Giza - Egypt, for the scientific leave, during which this work was done.

REFERENCES

Malik, O.P., "Adaptive Control of Synchronous Machine Excitation", in Microprocessor-based control Systems by Sinha, N.K., 1986, pp. 61-79. Cheng, S . J., Chow, Y. S., Malik, 0. P., Hope, G.S, "An adaptive synchronous machine stabilizer", IEEE Trans. on Power Systems, 1986, Vol. PWRS-10). pp. 101-109. Chandra, A., Wong, K. K., Malik, 0. P., Hope, G. S., "Implementation and test results of a generalized self-tuning excitation controller", IEEE Trans. on Energy Conversion,

Hiyama,T., " Application of Rule-based Stabilizing Con- troller to Electrical Power System", IEE Proc. C, Vol. 136,

Hiyama,T., "Rule-Based Stabilizer for Multi-Machine Power System", IEEE Trans. on Power Systems, Vol. 5, No.2 , May 1990, pp. 403-411. Hiyama,T., Lim, C.M., " Application of Fuzzy Logic Con- trol Scheme for Stability Enhancement of A Power System", IFAC Symposium on Power Systems and Power Plant Con- trol, August 1989, Singapore.

March 1991, Vol. 6(1), pp. 186-192.

NO. 3, 1989, pp. 175-181.

227

Hassan, M.A.M., Malik,O.P., Hope, G.S.; "A Fuzzy Logic Based Stabilizer For A Synchronous Machine", IEEE Trans. on Energy Conversion, Vol. 6, No. 3, Sept. 1991, pp. 407- 413. Hassan, M.A.M., Malik,O.P., Hope, G.S.; "A Fuzzy Logic Based Self-Tuned Power System Stabilizer", Third Intema- tional Conference On Power System Monitoring and Con- trol, sponsored by IEE, London, UK, June 1991,Conference Publication No. 336,pp. 146-151. Hiyama,T., Sameshima, T., " Fuzzy Logic Control Scheme for on-line Stabilization of multi-machine Power System", Fuzzy Sets and Systems, Vol. 39, Mar. 1991, pp. 181-194.

[IO] Mao, C.X., Prakash, K.S, Malik, O.P., Hope, G.S., Fan, J.;"Implementation and Laboratory Test Results For an adaptive Power System Stabilizer Based on Linear Optimal Control", IEEE Trans. on Energy Conversion, Vol. 5, No. 4, Dec. 1990, pp. 666-672.

[11] Roy, S.; "Adaptive Techniques for the Speed Control of Diesel Driven Prime-Movers", Ph.D. Thesis, The University of Calgary, Calgary, CANADA, 1991.

8. APPENDICES

Appendix A: Micro-Machine Parameters

The parameters of the micro-machine alternator and the 500 KV transmission line model used for experimental studies are given below in per unit [ 2,3, 101 :

Alternator :

Rd=Rq =O.O026

Xkd =Ickq =I .25

Xd =Xq =1.2

Xmd =Xmq =l. 129

Rmd=Rmq=0.0083 Xf=l.27

Rf=O.000747 M3.18~

Each transmission line consists of six 50 Km equivalent x- sections. For each x section, the parameters are :

R = 0.036 X = 0.0706 B= 18.779

Appendix B: Parameters of the Conventional Stabilizer

The control signal for the conventional stabilizer, as pro- posed by Ontario Hydro, is calculated using the fixed parameter transfer function [2-51 :

This fixed transfer function was implemented in software on the DSP. The values of the parameters are :

K c = 100.0 TQ = 1.0 s T I = 0.1 T 2 = 0.0001 S

M. A. M. Hassan ( M'90 - SM'91 ) : graduated in 1977 and ob- tained M. Sc. and Ph. D from Cairo University, Egypt, in 1982 and 1988 respectively. During his Ph. D. program, he obtained the DAAD scholarship from FRG. Since 1988 he has been with Cairo University, Giza, Egypt, as an assistant professor. From October 1989 he is visiting the university of Calgary.

0. P. Malik ( M'66 - SM'69 - F'87 ) : graduated in 1952 and obtained M.E. in 1962. In 1965 he received Ph.D. from U of London. From 1952 to 1961 he worked with Electric Utilities in India. He is at present a professor at U of Calgary.

228

Discussion

P. K. Kalra and S. C. Srivastava (Indian Institute of Technology, Kanpur, India): We commend the work reported by authors for first time implementing Fuzzy Logic Based Self Tuned Power system Stabilizer (PSS). We appreciate authors response to the following questions:

(i).

(ii)

(iii)

( iv)

Authors may comment on comparison of results reported in this paper with any standard self tuning method to substantiate the superiority of fuzzy logic bases PSS? Can the phase-plane approach be used in multi-machines sys- tems? In most of the practical systems one has more than single machine. Authors have used “Learning through Examples” approach to adjust the parameters for dicision making using fuzzy theory to accomodate uncertainty in the system. Assuming that one is not sure about quality of measurement, will this method still be valid for bad measurements. Fuzzy based PSS self tunes for varying operating conditions. This paper has not reported how changes in system conditions are observed? There will be delays involved in measurements and detection in system conditions. Do these delays in detection and measurement affect the results?

(ii)

(iii)

(iv)

Manuscript received October 16, 1992.

M. A. M. Hassan, 0. P. Malik: The authors thank the discussers for their interesting comments. Response to their questions is given below:

(i). The authors have not done any direct comparison of perfor- mance between the fuzzy logic based PSS described in this paper Manuscript received September 16’ 1992’

and the self-tuning based PSS. Mathematically, the self-tuning algorithm is much more complicated requiring extensive comput- ing power, whereas the fuzzy logic based algorithm is very simple and easy to implement on a microcontroller. Comparing the performance of the self-tuning base PSS reported in the litera- ture to that reported in this paper with the fuzzy logic based PSS, it is seen that the two control algorithms can provide very similar performance. Yes, the phase plane approach can be used in multi-machine systems. Some simulation results are reported in references [5] and 191 of the paper, although no experimental implementation results have been reported so far. The fuzzy logic theory was originally developed to overcome uncertainty in the system. It approximates the human ability to work with imprecise information when effecting some form of control. Thus, it is not dependent on the quality of measure- ments. Measurements with normal errors and white or coloured noise will be acceptable. However, bad measurements i.e. abnor- mal errors may give misleading results. Due to the limitations of page length, the results for only one operating condition are reported in this paper. Tests were per- formed in the laboratory for various operating conditions with no degradation in results. As in all digital systems, there is some delay in the control output corresponding to the computation time. Using the digital signal processor, it was between one and two ms. Beyond that, no other delays in the detection of the system conditions or delays in the measurements were consid- ered. Considering the principal time constants of the controlled system and the frequency of oscillation to be damped, time delays of one or two sampling periods are not likely to have any significant effect on the overall performance.