Application of fuzzy logic stabilisers in a multimachine power system environment

K.A. El-Metwally O.P. Malik

Indexing terms: Power systeni stahili.r.ers, Fzizzy logic, Control, Multimuchine power cystmi

Abstract: Application of fuzzy logic based power system stabilisers (FLPSS) in a multimachine environment is described. A five-machine power system representing two generation areas is used. The proposed FLPSS uses machine speed deviation and accelerating power as the inputs. The performance of the FLPSS when the system exhibits multimode oscillation phenomenon is illustrated. Simulation tests and results for different operating conditions and disturbances are discussed.

1 Introduction

Electric power systems are highly complicated systems that contain nonlinear and time varying elements. Since interconnected power systems can encompass entire countries, and continents, they can involve a large number of interacting systems with an immense array of variables. This highly interconnected nature of power systems makes their operation and control a complex process.

Conventional power system stabilisers (CPSSs) have been developed using linear control theory to damp the oscillation of synchronous machines under transient conditions [ I ] . Power systems are highly nonlinear and stochastic in nature, so the controller parameters which are optimum for one set of operating conditions may not be optimum for another set of operating condi- tions. Therefore, various investigators are studying the use of modern control techniques to improve overall system performance.

Fuzzy logic based controllers have been suggested as an appropriate choice to control non-linear systems [2], and are being investigated as an alternative to conven- tional control. The basic feature of fuzzy logic control- lers (FLCs) is that the control strategy can be simply expressed by a set of rules which describe the behav- iour of the controller using linguistic terms. Proper control action is then inferred from this rule base. In addition, FLCs are relatively easy to develop and sim- ple to implement.

Some initial investigations have been performed in

0 IEE, 1996 IEE Pvoceedings online no. 19960193 Paper received 30th August 1995

The authors are with the Deudrtinent of Electrical & Coinouter Ens4neer- ing, University of Calgary. 2500 University Drive N W , Calgary. Alberta, Canada T2N 1N4

the area of fuzzy logic based power system stabilisers (FLPSS) [3-5]. As these investigations are limited to single mode oscillations, there is a need for further investigations to study the FLPSS performance with multimode oscillations. Multimode oscillations appear in an interconnected multimachine power system in which the generating units have quite different inertias and they are weakly connected by transmission lines.

An FLPSS and its effectiveness in a single machine infinite-bus system is described in [6]. The objective of this paper is to extend the application of this FLPSS to a multimachine power system and study its effective- ness in damping local and interarea modes of oscilla- tion. An additional objective is to observe the coordination between the CPSS and the FLPSS when both are present in a system.

2

The basic configuration of an FLC can be simply rep- resented in four parts: the fuzzifier, the knowledge base, the inference engine and the defuzzifier as shown in Fig. 1. The fuzzifier maps the FLC input crisp val- ues into fuzzy variables using normalised membership functions and input gains. The fuzzy logic inference engine then infers the proper control action based on the available fuzzy rule base. The fuzzy control action is in turn translated to the proper crisp value through the defuzzifier using normalised membership functions and output gains [7].

Fuzzy logic power system stabiliser

inference engine

Fig. 1 Schemmt dugutn of t k FLC bddcng hlotks

For the current application, speed deviation, Am, and active power deviation, AP,, of the synchronous machine are chosen as the FLPSS inputr The output control signal from the FLPSS, Ups?, is injected to the summing point of the automatic voltage regulator (AVR).

261 IEE Pro?.-Gmer. lrunsnz. Distrih., Vol. 143, No. 3, May 1996

Each of the FLPSS input and output fuzzy variables; (XI = {Am, AP, Up,,}) is interpreted into seven linguistic fuzzy subsets varying from, Negative Big (NB) to Posi- tive Big (PB). Each subset is associated with a triangu- lar membership function to form a set of seven normalised and symmetrical triangular membership functions for each fuzzy variable [6] . The input gains K,, Kp and the output gain, K,, are used to properly scale the fuzzy input and output variables.

A symmetrical fuzzy rule set is used to describe the FLPSS behaviour as shown in Table 1. Each entity in the table represents a rule of the form 'if antecedent then consequence', e.g.

Using the correlation product inference and the centre of gravity defuzzification method the appropriate crisp control is then generated [7, 81.

if Aw is NB and AP is NB then L-p,, is NB

Table 1: A sample set of 7 by 7 rules

NB N M NS Z PS PM PB

NB NB NB NB NB N M NS Z

N M NB NB N M N M NS Z PS

NS NB N M N M NS Z PS PM

Z N M N M NS Z PS PM PM

PS N M NS Z PS PM PM PB

PM NS Z PS PM PM PB PB

PB Z PS PM PM PB PB PB

3 Multimachine system model

A five-machine power system without infinite bus, as shown in Fig. 2, was used to test the proposed FLPSS. The configuration was chosen to represent two physi- cally far power generation areas. The interconnections between the two areas can be considered weak in com- parison to the connection within the individual subsys- tems.

bus7 bus1

bus 5

load 1

kbus w Fig. 2 Five machine power system model

Generators # I , #2 and #4 have much larger capaci- ties than generators # 3 and #5. Generators #2, # 3 and #5 may be considered to form one area and generators #I and #4 a second area. The two areas are connected together through a tie line connecting buses #6 and #7. Under normal operation, each area serves its own load and is almost fully loaded with a small load flow over the tie line. Parameters for all generating units, trans- mission lines, loads and operating conditions are given in the Appendix.

The system configuration in Fig. 2 is specially

264

designed such that multimode oscillations appear in the system when disturbances occur. With the system at operating point # I (see Table 6), a 0.25p.u. step decrease in the mechanical input torque reference of generator # 3 is applied at 1 s, and the system returns to the original condition at 10s. System response given in Fig. 3 shows the local mode at about 1.3Hz and the interarea mode at about 0.65Hz under the above men- tioned disturbance without any PSSs installed. The local mode frequency differs significantly from the interarea mode frequency due to the very different iner- tias of the generators. As can be seen, the speed devia- tion between generators #2 and #3 exhibits mainly local mode oscillations. The speed deviation between generators #1 and #2 exhibits mainly the interarea mode oscillations. Both the local and interarea mode oscillations exist in the speed deviation between genera- tors #1 and #3.

020, ' I

8 -0 201 1 U

0 1 0

g 0 5 - - - 0

-0 5 U

-1 01 0 5 10 15 20

time, s J!4iihiinode oscilicrtion qf the $five-muchine ~ O M J ~ F system (Opt. # I ) Fig. 3

Top. # I - # ? : middle: #1-#1; bottom: #2-#3

The system is simulated using a dynamic simulation package developed in [9]. The simulation package sim- ulates the real-time interaction between the machines and the stabilisers using the interprocess communica- tion facilities available in the Unix operating system. The model equations used in the simulation are given in the Appendix.

A number of tests have been performed with the multimachine model to study the effectiveness of the FLPSS in comparison with a conventional PSS. Tests described in Sections 5.1 - 5.5 are conducted using the operating point given in Table 6 which represents oper- ation close to the full capacity of the system, Tests in Section 5.6 are conducted using the operating point given in Table 7 which represents light load conditions.

4 environment

Tuning of FLPSS for multimachine

Previous expericnce with the controlled system is hclp- ful in providing information to assign the initial values of the FLC gains. If such information is not available, assigning values for the FLC gains can become a tedi- ous trial and error process. Some studies have been reported to automate the process of tuning the FLC parameters at the design phase to get an optimal or near-optimal performance [10-12].

Tuning fuzzy logic controllers in a multimachine system is automatically carried out off-line by using a tuning software extension module to the multimachine

IEE ProicGener. Trmrm. Dislrih., Vol. 143, No. 3, Mnv 1996

simulation package. This tuning module hierarchically lies on top of the simulation package and uses a blind search algorithm to locate optimum, or near-optimum FLPSS gains that minimise certain system performance indices (PIS).

A brief description of the tuning algorithm [lo] fol- lows. Assuming that the synchronous machine speed deviation between machines #1 and #2 is Awl?, the tuning module uses the overshoot (OS) and J 1 (where J , = C A O ~ , ~ ) as the system PIS to calculate the FLPSS input gains, K,, and K,,, at generator # l . The tuning module iteratively simulates the system with the con- troller for incremental values of K, and Kp and com- putes the corresponding system PIS. The FLPSS gains selected by the module are those which minimise a weighted sum of the system PIS. Presently, all system indices are equally weighted.

The FLPSS gains selected with the help of the above tuning module for the current multimachine simulation are given in the Appendix in Table 8 .

5 Simulation studies

5. I Generator #3 is of much smaller capacity than genera- tor #2 in the same area. It acts as a source of the local mode of oscillations when subjected to a disturbance. The proposed FLPSS is first installed on generator #3 only to study its effect on the dynamic behaviour of the system. None of the other generators has any PSS. The machine speed deviation and the terminal power devia- tion of generator #3 are sampled at the rate of 5OHz and used as inputs to the FLPSS. The control signal output of the FLPSS is added to the generator AVR summing injection. The sample and control process is similar to the physical process.

A 0.25p.u. step decrease in the mechanical input torque reference of generator #3 is applied at l s , and the system returns to the original condition at 10s. The FLPSS damps the local mode oscillations very effec- tively as shown in Fig. 4.

Only one PSS installed

1 0 1 I

-1 01 I

-0 201 I 0 5 10 15 20

time,s System response. to step decrease in torque with PSSs installed ou Fig.4

generator #3 (Opt. # I ) FLPSS (solid line); CPSS (broken line); 0.25 input torque disturbance

For comparison, a conventional AP type PSS (CPSS) with the following transfer function [9] was designed under the same conditions as for the FLPSS develop- ment.

After careful parameter tuning, the CPSS installed on generator #3 with the following parameter set pro- duced almost the same results as the FLPSS.

K S = 1.0, TI = Td = 0.3, T2 7'4 = 0 10, Ts = 0 4 The system response with the CPSS is also shown in Fig. 4. Similar conclusions for the system with the CPSS can be drawn as in the case of FLPSS.

A PSS installed on generator #3 has little influence on the interarea mode oscillations. This is because the rated capacity of generator #3 is much less than that of generators #I and #2, and the interarea mode oscilla- tions are introduced mainly by these large generators. Generator #3 does not have enough power to control the interarea mode oscillations. To damp the interarea mode oscillations, PSSs must be installed on generators #1 or #2 as well.

5.2 Two PSSs installed To damp both the local and interarea modes of oscilla- tions, PSSs were installed on generators #2 and #3. System response to the same disturbance as in Section 5.1 given in Fig. 5 for the case of two FLPSSs and two CPSSs shows damping of the interarea mode as com- pared to Fig. 4.

' 1

2 - 0 5 1 V -1 01

0.1 0 I I

. _ 0 5 10 15 20

time, s Fig.5 System response to step decrease in torque with ESSs irrstalled on generutors #2 and #3 (Opt. #1) FLPSS (solid line); CPSS (broken line)

5.3 Three PSSs installed System response with FLPSSs installed on generators #1, #2 and #3 for a 0.25p.u. step decrease in the mechanical input torque reference of generator #3 applied at 1s and the system returning to the original condition at lOs, is given in Fig. 6. The system response shows that both modes of oscillations are damped very effectively.

Response of the power system with three CPSSs is also shown in Fig. 6. The additional CPSSs installed on generators #1 and #2 were carefully tuned to damp the interarea mode of oscillation. The CPSS parameters for generator #1 and #2 are Ks = 0.9, T, = T3 = 0.1, T2 = T4 = 0.08, and T, = 0.5. It is clearly seen from Fig. 6 that the FLPSS not only damps both modes of oscillations but also reduces significantly the overshoot in the speed difference between machines #1 and #2.

5.4 Three phase to ground fault test With the power system operating at the same operating conditions as in Section 5.1, a three phase to ground fault was applied at the middle of one transmission line between buses #3 and #6 at 1 s and cleared lOOms later

265 IEE Pro?.-Cener. Tvrmsm. Dtwih., Vol. 143, No. 3, May I996

by disconnecting the faulted line. At IOs, the faulted transmission line was restored. The response of the sys- tem with no PSS, with the FLPSSs only and with CPSSs only installed on generators # I , #2 and # 3 is shown in Fig. 7. It shows that even though the CPSS can improve the system performance to some extent. the FLPSS can improve the system performance even further.

L

I N 3 4

-1.0 t 1

-0 10 1 0 5 10 15 20

System re,rponse to step decrease in torque with PSSs installed on time,s

Fig.6 generator.r # I , #2 and #.? (Opt. #IJ FLPSS (solid line); CPSS (broken line)

0.6 I I

1 0 5 1 iv ' I

3 U

- 1 .o 0 5 10 15 20

time, s Fig. 7 System response to a three phase fault with PSSs installed on gen- erators # I , #2 and #3 (Opt. #l) FLPSS (solid line); CPSS (broken line); NO PSS (dotted line): 3-phase to ground fault

5.5 Coordination between FLPSS and CPSS In most situations, the newly installed FLPSS will have to work together with CPSSs which already exist in a power system. System response with FLPSSs and CPSSs working together has been also investigated. For the five-machine power system, the proposed FLPSS was installed on generators #2 and #3, with a CPSS of proper parameter set on generator # l . The response of the system to the same step disturbance in torque under this configuration is shown in Fig. 8. Response to a three phase to ground short circuit on line 3-6 with the same combination of PSSs is shown in Fig. 9.

It can be seen from Figs. 8 and 9 that the two types of PSSs can work cooperatively. The response with the FLPSS and CPSS combination is better than the response with three CPSSs in the corresponding Figs. 6 and 7, respectively.

266

a' - 0 5 V

- 1 0 1 0 OL, I

L I

-0. OLi i 0 5 10 15 20

time, s S3,steni response to step decrease in torque with FLPSS on genera- Fig. 8

tors #1, #3 and CPSS on generator # I (opt. # I )

O 4 r . . 1

3 : q -0 6

-0 81 1 1 0 1 1

-1 0 t 1

0 5 10 15 20 time, s

System response to a 3-phase short circuit with FLPSS on genera- Fig.9 toilc #I, #2 und CPSS on generator # I (opt. #l)

5.6 Different operating condition test To test the behaviour of the proposed FLPSS and the CPSS under other operating conditions, the operating point of the power system was changed to that given in Table 7. First, the same disturbance as in Section 5.1, 0.25 p.u. mechanical input torque step change, was applied to generator #3. The closed loop response with FLPSSs only and CPSSs only installed on generators #1 #2 and #3, is shown in Fig. 10. The system response for a three phase to ground fault as in Section 5.4 with no stabiliser, and with FLPSSs only and CPSSs only on generators #1, #2, # 3 is shown in Fig. 11. It can be seen that the system response with the FLPSSs is better than with CPSSs in both cases.

6 Conclusions

The objective of this paper is to show the effectiveness of the FLPSS in damping multimodal oscillations and this has been illustrated on a multimachine system that exhibits such a phenomenon. The results show that the proposed FLPSS can damp both modes of oscillations effectively. The results also show that the FLPSS can work cooperatively with the CPSS.

The simulation tests show that each FLPSS can damp the specific mode of oscillation introduced by the generator on which it is applied. To damp both local and interarea modes of oscillations, PSSs have to be installed on generators which are the main cause of the two modes of oscillations.

IEE ProcGener Tiansm. Dislrib., Vol. 143, No 3. Muy 1996

1 0, 1 1 1

-1 0 7 0 20

Ln

- 0.201 0 5 10 15 20

time, s System response to step decrease in torque with PSSs installed Fig. 10

on generators # I , #2 and #3 (Opt. #2) FLPSS (solid line); CPSS (broken line)

0.61 I

-1.01 0 5 10 15 20

time, s Sy,stem response to a three-phase fault with PSSs installed on Fig. 11

generators #1, #2 and #3 (Opt. #2) FLPSS (solid line): CPSS (broken line); NO PSS (dolled line)

It is well known that the effectiveness of the PSS in damping oscillations depends upon its location, and the appropriate location of the FLPSSs in a large multima- chine system can be determined by the same techniques as used for CPSS [13].

The FLC algorithm is simple and it is possible to realise the controller efficiently and quickly as illus- trated by implementation and experimental results on a physical model given in [14]. Lack of on-line compli- cated mathematical computations makes it more relia- ble for real-time applications where small sampling time may be required.

7 Acknowledgments

The authors would like to thank the Canadian Tnterna- tional Development Agency for financial support.

8 References

1 LARSEN, E.V., and SWANN, D.A.: ‘Applying power system stabilizers, Part 1: general concepts’, ZEEE Trans., 1981, PAS- 100, (6), pp. 3017-3024

2 DRIANKOV, D., HELLENDOORN, H, and REINFRANK, M.: ‘An introduction to fuzzy control’ (Springer-Verlag, 1993)

3 HANDSCHIN, E., HOFFMANN, W., and RAYER, F.: ‘A new method of excitation control based on fuzzy seL thcory’, IEEE Trans. Power Systems, 1994, 9, (I) . pp. 533-539

4 HASSAN, M.A., MALIK, O.P., and HOPE, G.S.: ‘A fuzzy logic based stabilizer for a synchronous machine’, ZEEE Trans. Energy Conversion, 1991, 6 , (3 ) , pp. 407413

IEE Proc.-Gener. Transm. Dlrtrih., Vol. 143, No. 3, May I996

/ 1

5 HIYAMA, T.: ‘Application of rule-based stabilizcr control to electric power system’, IEE-Pmc. C, 1989, 136, ( 3 ) , pp. 175-181

6 EL-METWALLY, K.A., and MALIK, O.P.: ‘Fuzzy logic power system stabilizer’, IEE Proc. Generation, Transmission and Distri- bution, 1995, 1421 (3), pp. 277-281 LEE, C.C.: ‘Fuziy logidin cOntrol syqtems: fuzzy logic controller - Parts IJI’, IEEE Tr ns Systems, Man and Cybern., 1990, 20,

KOSKO, B.: ‘Neural qietworks,and fuzzy systems: A dynamic approach to machine intelligende’ (Praice-Hall, 1992) CHEN. G.: ‘An adaptive self-optimizing power system stabilizer’. PhD thesis, University of Calgary, Calgary, Alberta, Canada, June 1994

10 EL-METWALLY, K.A., and MALIK, O.P.: ‘Parameter tuning for fuzzy logic controller’. Proceedings IFAC 12th world congress on Automatic conlrol, July 1993, Sydney, Australia, Vol. 2, pp, 581-586

11 ZHANG, B.S., and EDMUNDS, J.:,:gelf-organizing fuzzy logic controller’. IEE Proc. D, 1992, 139, (5 ) ; pp. 460464

12 MEADA, M., and MURAKAMI, S.: ‘A self tuning fuzzy logic controller’, Fuzzy sets and systems, 1992, 51, pp. 29-40

13 ZHOU, E.Z., MALIK, O.P., and HOPE, G.S.: ‘Theory and method for selection of power system stabilizer location’, IEEE Trans. Energy Conversion, 1991, 6, (l), pp. 170-176

14 EL-METWALLY, K.A., HANCOCK, G., and MALIK, O.P.: ‘Implementation of fuzzy logic PSS using Intel 8051 micro-con- troller’. IEEEiPES 95 SM 445-7 EC, July 1995

7

(2), pp. 404-435 4 . 8

9

9 Appendix

Each generating unit is modelled by five first-order dif- ferential equations given below:

6 = w o . w (2)

Table 2: Parameters of the generators

Gen#l Gen#2 Gen#3 Gen#4 Gen#5

0.1026

0.0658

0.0339

0.0269

0.0335

5.6700

0.6140

0.7230

80.000

0.1026

0.0658

0.0339

0.0269

0.0335

5.6700

0.6140

0.7230

80.000

1.0260

0.6580

0.3390

0.2690

0.3350

5.6700

0.6140

0.7230

10.000

0.1026

0.0658

0.0339

0.0269

0.0335

5.6700

0.6140

0.7230

80.000

1.0260

0.6580

0.3390

0.2690

0.3350

5.6700

0.6140

0.7230

10.000

Table 3: Parameters of AVRs and simplified STIA excit- ers

Gen#l Gen#2 Gen#3 G e n M Gen#5

T, 0.0400 0.0400 0.0400 0.0400 0.0400

Ka 190.00 190.00 190.00 190.00 190.00

Ta 10.000 10.000 10.000 10.000 10.000

Tc 1.000 1.000 1.000 1.000 1.000

Kc 0.0800 0.0800 0.0800 0.0800 0.0800

The output of all exciters is limited within -6.7 to 7.8 p.u.

Table 4: Parameters of the governors

Gen#l Gen#2 Gen#3 Gen#4 Gen#5 TQ 0.25000 0.25000 0.25000 0.25000 0.25000

a -0.00015 -0.00015 -0.00133 -0.00015 -0.00133

b -0.01500 -0.01500 -0.17000 -0.01500 -0.17000

261

Table 5: Parameters of transmission lines in p.u. Table 7: Operating point #2

Bus# R X B12 Bus# R X 612 1-7 0.00435 0.01067 0.01536 2 6 0.00468 0.0468 0.00404 3-6 0.01002 0.03122 0.03204 3-6 0.01002 0.03122 0.03204

443 0.00524 0.01184 0.01756 5-6 0.00711 0.02331 0.02732

6-7 0.04032 0.12785 0.15858 7-8 0.01724 0.04153 0.06014

Gen#l Gen#2 Gen#3 Gen#4 Gen#5

P(p.u.) 3.1558 3.8835 0.4055 4.0670 0.4501

0 (P.u.) 2.9260 1.4638 0.4331 2.1905 0.2574

V(p.u.) 1.0500 1.0300 1.0250 1.0500 1.0250

8 (rad.) 0.0000 0.1051 0.0943 0.0361 0.0907

Table 6: Operating point #I

Gen#l Gen#2 Gen#3 Gen#4 Gen#5

P(p.u.) 5.1076 8.5835 0.8055 8.5670 0.8501

Q (P.u.) 6.8019 4.3836 0.4353 4.6686 0.2264

V(p.u.) 1.0750 1.0500 1.0250 1.0750 1.0250

0 (rad.) 0.0000 0.3167 0.2975 0.1 174 0.3051

Load admittances in p.u. L, = 7.5 - j5.0 L, = 8.5 - j5.0 L, = 7.0 - j4.5

Load admittance in p.u. L, = 3.755 - j2.5 L, = 4.25 -j2.5 L3 = 3.5 - j2.25

Table 8: FLPSS parameters used in simulation

Gen#l Gen#2 Gen#3

Kw 5 5 0.45

K, 3.3 3.3 2.0

K,, 0.1 0.1 0.1

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