Variable-structure-system control appliedto AGC of an interconnected power

systemAshok Kumar. B.E., M.E., Prof. O.P. Malik. M.E., Ph.D., C.Eng.. F.I.E.E., Sen.

Mem. I.E.E.E., andProf. G.S. Hope. B.Sc. Ph.D.. C.Eng.. M.I.E.E.. Sen. Mem. I.E.E.E.

Indexing terms: Power systems and plant, Control equipment and applications, Mathematical techniques

Abstract: A control scheme based on a variable-structure-system concept is applied to the problem of auto-matic generation control of interconnected power systems. The proposed algorithm is simple and easy to imple-ment. The effect of generation-rate-constraint nonlinearity on the dynamic performance of the system forreheat- and nonreheat-type steam turbines is also studied. A comparison of the conventional and the proposedvariable-structure control strategies shows that, with the application of the proposed algorithm, the systemperformance is improved significantly.

List of symbols

Ttl,Trl,

Tt2

Z,Tp

APn

APcl

K,

P2

APl2

APc2

= governor time constants= turbine time constants= reheater time constants= electric system time constants= speed regulation due to governor action= reciprocal of load-frequency constant= change in loads= speed gear changer deviation= proportional gain constant= integral gain constant

Introduction

For reasons of economy and system reliability, neighbour-ing power systems are interconnected, forming an aug-mented system referred to as 'power pool'. The net powerflow on the tie lines connecting a system to the externalsystem is frequently scheduled by an a priori contractbasis. System disturbances caused by load fluctuationsresult in changes in tie-line power and system frequencywhich give rise to a load-frequency control (LFC) problem.

The load-frequency control is based on an error signalcalled area control error (ACE) which is a linear com-bination of net-interchange and frequency errors. The con-ventional control strategy used in industry is to take theintegral of ACE as the control signal [1-10]. It has beenfound [5] that the use of ACE as the control signal reducesthe frequency and tie-line power errors to zero in thesteady state, but the transient response is not satisfactory.

To improve the transient response, linear optimalcontrol theory has been used in References 11-14. Therealisation of such a controller is difficult, cumbersome andexpensive because the feedback portion of the optimal con-troller is a function of the complete state vector of thesystem. Generally, all the state variables are not accessible.Even if state estimation techniques are used to estimate theinaccessible state variables, the data needs to be trans-ferred over long distances. This involves additional cost oftelemetering. For the realisation of the optimal controller,it is also necessary to know the new steady states, which, inturn, are a function of load demand. Thus, there is aproblem of estimating the load demand through a load

Paper 3562C (P9), first received 22nd February and in revised form 3rd October1984

The authors are with the Department of Electrical Engineering, University ofCalgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4

estimater which again is a complicated and expensiveproposition. On the other hand, the generating units areunable to respond as fast as the optimal controllerdemands in view of the time lag associated with the char-acteristics of boilers, steam flow and auxiliaries. This isknown as the unit rate constraint.

Recently, variable structure system (VSS) concept hasbeen used by some of the investigators [15-18] to copewith the LFC problem. The VSS controller proposed inthese references has an even more complex structure thanthe linear optimal controller. Implementation of this con-troller is very difficult and expensive.

In view of the above, an alternative formulation of thecontroller based on VSS concept is described in this paper.The proposed algorithm requires only two measurablevariables, i.e. frequency deviation and deviation in tie-linepower. The proposed structure is practically as simple asthat of the conventional controller and can be implement-ed with very little additional cost. The VSS controller isapplied to a two-area interconnected power system.Studies have been conducted for reheat- and nonreheat-type steam power systems, with and without generation-rate constraints. Simulation results show the effectivenessof the proposed VSS controller.

2 Power system model

2.1 AssumptionsFor small changes in the power demand, the two prob-lems, load-frequency control and reactive-power/voltagecontrol, are decoupled and can be considered separately[5].

The individual electrical connections within an areamust be strong enough so that the considered area may berepresented by a single frequency.

2.2 Model for simulation studyBecause the system is exposed to a small change in loadduring its normal operation, the linear model will be suffi-cient for its dynamic representation. The block-diagramrepresentation shown in Fig. 1 for load-frequency controlfor equal areas with reheat steam turbines has been takenfrom Reference 6. For the nonreheat turbine, the values ofKrl and Kr2 are set to unity and system state equations aremodified accordingly. Therefore, the block diagram shownin Fig. 1 may be used for the representation of both reheatand nonreheat turbines. The block designated by 'control-ler' has been modified to that shown in Fig. 2 in the case ofthe proposed control scheme. The system dynamics for

1EE PROCEEDINGS, Vol. 132, Pt. C, No. 1, JANUARY 1985 23

AF,

Fig. 1 Block diagram representation fortwo-area thermal power system

u,.u2

ACE><f

Fig. 2 Block diagram for VSS controller

reheat- and nonreheat-turbine power systems are describedby the following state differential equations:

(a) Nonreheat turbine

Xi = = X-% T Di Xj

X2 — — T X2 —

x3 = - x8)

' P i ' P i ' p i ' P i

x7 = a 1 2 x 3 + B2x9

X 8 - rp X 8

Xi — ~Z Xo -r Xin — i\r

X 1 0 — ry, X 10

x,, =1 Krl K.

The above state differential equations are solved to studythe dynamic performance of the system.

X5 = + — X2 - —hi hi

X 6 = -

• -Oil _ LX 8 ~~ rp X 3 rp Xt

• __L _LX9 ~ Tp~ X7 ~ Tf~ X9

hi hi(b) Reheat turbine

1 1x-, = —

x3 = 2nTl2(xA -x9)

x = - ^ i x - —Tpi Tpl

'92

K

3 Proposed control algorithm

With the present practice of using integral control [5], thesystem has no steady-state error in response to a stepinput; besides, this improves the speed of response of thesystem, which is desirable. If the gain of the integrator K,is sufficiently high, overshoot will occur, increasing sharplyas a function of the gain; this is highly undesirable. In theabsence of integral control, one can sharply increase thegain of the closed-loop system and thereby improve thesystem response. However, the system will then display asteady-state error. Thus, some investigators [19] proposeda compromise, making the control a linear combination as

(1)u(t) = C. • ACE + — • ACE • dt

' p i

where ACE is the error signal, and the gains Cp

(proportional gain) and 1/7^ (TN, time constant) are givensome average value which guarantees satisfactory responseand not too large oscillations in the system. However, sub-sequent work [20] showed that the best known results areobtained with the existing control structure. This is also

24 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 1, JANUARY 1985

corroborated by the results of studies with a proportional-plus-integral controller.

The same model as discussed in Section 2.2 was used tostudy the system response with proportional-plus-integralcontrol action as given by eqn. 1. The results presented inFig. 3 for the reheat turbine were obtained with typical

0.01

-0.008

Fig. 3 System response with reheat turbineCp = 0.3, TN = 100 sa Frequency deviation area 1b Tie-line power deviation

proportional plus integralintegral

values proposed in Reference 20, i.e. Cp = 0.3 and TN =100 s. It can be observed that the response with integralcontrol is much better than that with proportional-plus-integral control of eqn. 1. The study was repeated withoptimum values of proportional and integral gain con-stants obtained by trial and error. Frequency deviation ofarea 1, plotted in Fig. 4, shows that the system response

0.01

-0.030 10

time, s15 20

Fig. 4 Frequency deviation in area I with reheat turbineCp = 0.3, Tv = 1.5 s

proportional plus integralintegral

with proportional-plus-integral action is more oscillatorythan with pure integral control.

It is observed that the compromise solution of usingproportional-plus-integral control does not eliminate theconflict between the static and dynamic accuracy. Thisconflict may be resolved by employing the principle ofvariable structure [21]. If the control law applied at thefirst stage of the transient (as long as the error is sufficient-ly large) is chosen as

u(t) = Kp ACE for|ACE|>£ (2)

where e > 0 is some constant, but when the error is smallthe control law is

u(t) = K, ACE • dt (3)

where | ACE | > £ for t ^ te, then, if the parameters Kp, K,and e are suitably selected, one can ensure a high-qualitytransient response, distinguished by good dynamic andsteady-state characteristics. Indeed, taking Kp sufficientlylarge, one can make sure that the speed of the system ishigh; thus, the error ACE in response to a step inputrapidly enters the region |ACE|^e. At the instant te,when the error has fallen to e, the structure of the control-ler is changed by switching to an integral control, whicheliminates the steady-state error remaining in the system.

4 Results

A unit-step input disturbance reveals useful informationabout the speed of response of the system. The transientperformance of a system is, therefore, usually characterisedby the use of step disturbances. For the studies describedin this paper, a small step load change in area 1 has beenconsidered.

Depending on the type of steam turbine used, two casesare demonstrated. For comparative study between the con-ventional (pure integral) controller and the proposed con-troller, the same values of the system parameters [5, 9] asgiven in Table 1 are used.

Table 1 : System parameters

TP1 = TPTry = Tr.Tn = Tt.fl, =/?2

l2 = 20 s y2 = 1 0 s /2 = 0.3s ;= 2.4 Hz/p.u.MW ^

<pi = Kp.Kry = /Cr 2

r , = r 2» 1 2 = ~ 1

2 = 12O Hz/p.u.MW= 0.5

, = 0.08 s

The constant parameters Kp, K,, e, APn and APl2 areselected as shown in Table 2. A generation rate constraint(GRC) [9] of 10% per minute is considered for both cases.Simulation results for nonreheat- and reheat-type systems,with and without GRC, are shown in Figs. 5-8, when theload in area 1 is suddenly increased by the value given inTable 2.

Table 2: Controller parameters

Type of turbine

Nonreheatno GRCwith GRC

Reheatno GRCwith GRC

0.0010.01

0.30.01

K,

0.750.075

0.670.1

E

0.0010.001

0.0020.001

p.u.

0.010.005

0.010.005

5 Discussion5.1 Nonreheat turbineResults for the nonreheat-turbine system without GRCand with GRC are shown in Figs. 5 and 6, respectively. It

IEE PROCEEDINGS, Vol. 132, Pi. C, No. I, JANUARY 1985 25

can be observed that, even though the settling time withthe proposed control strategy is much shorter than thatwith the conventional controller in both cases, theimprovement is particularly significant in the case of GRC.

As seen in Fig. 5e, the tie-line power deviation isreduced to about one-half with the proposed switchinglogic as compared to the conventional controller, with aconsequent increase in the power generation in area 1 (Fig.5b) in which the disturbance occurs. This shows that, with

0.002

0.005

0

£-0.005

< -0 .010

-0.015

-0.02015 20

.-0.002

-0.004 -i

-0.00610

time, se

15 20

Fig. 5 System responses with nonreheat turbine, no constraint

conventional controllerVSS controller

a & c Frequency deviation, b & d power deviation, e tie-line power deviation

the proposed control strategy, each area tries to meet itsown demand and minimises the effect on the adjoiningareas.

Without GRC the maximum frequency deviation isreduced by about 40% in area 1 and by about 50% in area2. In the case of GRC (Fig. 6) there is no difference in thefirst swing because of the constraints; however, there is atremendous improvement in the overall settling time.

Responses for all the studies performed are not includedin the paper. However, these studies showed that, withGRC also, the effect on the interconnected areas of a dis-turbance in one area was considerably reduced.

5.2 Reheat turbineSystem responses for studies with the reheat-turbinesystem without GRC and with GRC are shown in Figs. 7and 8, respectively. Results obtained in this case are, in

0.005 -

-0.02020

26 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 1, JANUARY 1985

0.001

0

i -0.0015

^-0.0024;

< -0-003

-0.004

-0.005

l\

i i i

0.002 r

15 20

0.04

Fig. 6 System responses with nonreheat turbine and generation rateconstraint

• conventional controllerVSS controller

a Frequency deviation area 1b Frequency deviation area 2c Tie-line power deviationd ACE area 1

0.01

-0.03

0.02

0.010

iO.005cou

0

- : n

n

f —•

A i

10 20time, s

e

Fig. 7 System response with reheat turbine, no constraint

conventional controllerVSS controller

a Frequency deviation area Ib Frequency deviation area 2c Tie-line power deviationd ACE area 1

proportionalintegral

e Switching modes area I/ Switching modes area 2

general, very similar to those for the nonreheat-turbinecase. The settling time is much smaller with the proposedcontroller, and this effect is particularly significant in thecase of GRC. The controller again tends to counteract thedisturbance by fast action within the disturbed area, and,thereby, reduces the effect of the disturbance on the adjoin-ing areas.

Control u(t) for the proposed algorithm, as determinedby the switching action, is also shown in Figs. 7 and 8. Itswitches between proportional and integral as the magni-tude of the corresponding ACE changes.

IEE PROCEEDINGS, Vol. 132, Pt. C, No. 1, JANUARY 1985 27

0.004

0.002

10time, s

b

15 20

0.003

I 0.0 02r>d.(VI

§0.001

-0.012

0.004

0.002

10time, s

f

15 20

Fig. 8 System response with reheat turbine and generator rate con-straint

• conventional controllerVSS controller

a Frequency deviation area 1b Power deviation area 1c Frequency deviation area 2d Power deviation area 2

ACE area 1proportionalintegral

/ Switching modes area 1

5.3 GeneralA significant improvement in the system performance isobtained with the simple switching logic proposed in thispaper, particularly in the presence of generation rate con-straint. The improvement obtained is comparable to thatshown in Reference 16 with a much more complicated VSScontrol algorithm.

The switching vector required for the control schemebased on VSS concept proposed in References 15-17 wasdetermined by trial and error [16, 17]. Although a methodof determining the switching vector is proposed in Refer-ence 18, it has an even more complex structure than thelinear optimal controller developed in Reference 11. Evenif one has obtained the switching vector, all state variablesfor that area need to be known online for practical realis-ation. All variables are not directly measurable and willhave to be estimated using mathematical observer algo-rithms. Furthermore, no direct method is given for calcu-

lating the values of the feedback gains. This makes theimplementation of the controller proposed in References16 and 17 very difficult and uneconomical.

The controller proposed in this paper has a very simplealgorithm and is easy to implement.

6 Conclusions

A control algorithm based on the variable-structureconcept has been investigated for automatic generationcontrol of interconnected power systems. It is shown thatthe proposed control algorithm is effective and providessignificant improvement in system performance.

The proposed control algorithm is very simple in struc-ture and easy to implement as it requires only one variablei.e. ACE, already available in the conventional controller.The dotted line portion of the VSS controller in Fig. 2becomes functional only when ACE exceeds a prespecified

28 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 1, JANUARY 1985

limit given in Table 2. Small random load fluctuations aretaken care of by the conventional controller.

7 Acknowledgments

The work described in this paper was supported under anoperating grant provided by the Natural Sciences andEngineering Research Council of Canada.

8 References

1 CONCORDIA, C, and KIRCHMAYER, L.K.: 'Tie-line power andfrequency control of electric power system', Trans. Amer. Inst. Elect.Engrs., 1953, 72, Part III-A, pp. 562-572

2 KIRCHMAYER, L.K.: 'Economic control of interconnected systems'(Wiley, New York, 1959)

3 ROSS, C.W.: 'Error adaptive control of interconnected powersystems', IEEE Trans., 1966, PAS-85, pp. 742-749

4 AGGARWAL, R.P., and BERGSETH, F.R.: 'Large signal dynamicsof load frequency control systems and their optimization using non-linear programming', ibid., 1968, PAS-87, pp. 527-538

5 ELGERD, O.I., and FOSHA, C.E.: 'Optimum megawatt frequencycontrol of multi-area electric energy system', IEEE Trans., 1970,PAS-89, pp. 556-563

6 ELGERD, O.I.: 'Electric energy systems theory' (McGraw-Hill, 1971),pp. 315-389

7 GLOVER, J.D., and SCHWEPPE, F.C.: 'Advanced load frequencycontrol', IEEE Trans., 1972, PAS-91, pp. 2095-2103

8 WILLIAMS, J.L.: 'Sensitivity analysis of the optimum performance ofconventional load-frequency control', IEEE Trans., 1974, PAS-93,pp.1287-1291

9 NANDA, J., and KAUL, B.L.: 'Automatic generation control of aninterconnected power system', Proc. IEE, 1978, 125, (5), pp. 385-390

10 HIYAMA, T.: 'Optimisation of discrete-type load-frequency regula-tors considering generation-rate constraints', IEE Proc. C, Gen.,Trans. & Distrib., 1982,129, (6), pp. 285-289

11 FOSHA, C.E., and ELGERD, O.I.: 'The megawatt-frequency controlproblem: a new approach via optimal control theory', IEEE Trans.,1970, PAS-89, pp. 563-577

12 MINIESY, S. M., and BOHN, E.V.: 'Optimal load-frequency contin-uous control with unknown deterministic power demand', IEEETrans., 1972, PAS-91, pp. 1910-1915

13 MOORTHI, V.R., and AGGARWAL, R.P.: 'Suboptimal and near-optimal control of a load-frequency-control system', Proc. IEE, 1972,119, (11), pp. 1653-1660

14 CAVIN, R.K., BUDGE, M.C., and RASMUSSEN, P.: 'An optimallinear system approach to load frequency control', IEEE Trans., 1971,PAS-90, pp. 2472-2482

15 HSU, Y.Y., and CHAN, W.C.: 'Control of power systems using theconcept of variable structure'. Proceedings of the first symposium onelectrical power, Taiwan, 1980, pp. 19-37

16 CHAN, W.C., and HSU, Y.Y.: 'Automatic generation control ofinterconnected power systems using variable-structure controllers',IEE Proc. C, Gen., Trans. & Distrib., 1981, 128, (5), pp. 269-279

17 BENGIAMIN, N.N., and CHAN, W.C.: 'Variable structure controlof electric power generation', IEEE Trans., 1982, PAS-101, pp.376-380

18 HSU, Y.Y.: 'Variable structure control of interconnected powersystem'. Ph.D. thesis, Graduate Institute of Electrical Engineering,National Taiwan University, May 1982

19 GLAVITSCH, H., and GALIANA, F.D.: 'Load frequency controlwith particular emphasis on thermal power stations', in HAND-SCHIN, E. (Ed.): 'Real-time control of electrical power systems'(Elsevier Publ. Co., 1972)

20 GLAVITSCH, H., and STOFFEL, T.: 'Automatic generationcontrol'. Transcripts of the state-of-the-art lecture delivered at theIFAC symposium on computer applications in large-scale systems,New Delhi, India, August 1979

21 ITKIS, U.: 'Control systems of variable structure' (Wiley, New York,1976)

ErratumWILLIAMS, A., and WARREN, R.H.J.: 'Method of usingdata from computer simulations to test protectionequipment', IEE Proc. C, Gen., Trans. & Distrib., 1984, 131,(7), pp. 349-356

On p. 349, Section 2, the second paragraph should read asfollows:

The PTL equipment is based around a general-purposeminicomputer which calculates and stores the digital datarepresenting the power-system voltages and currents. Theminicomputer controls conversion of the digital data intoanalogue signals and it monitors and controls the relaysbeing tested.

3639C

IEE PROCEEDINGS, Vol. 132, Pt. C, No. I, JANUARY 1985 29