An Implicit Self-tuning Regulator as a Power System Stabilizer

Copyright © IFAC Automation and Instrumentation for Power Plants, Bangalore, India, 1986

CONTROL HARDWARE

AN IMPLICIT SELF-TUNING REGULATOR AS A POWER SYSTEM STABILIZER N. C. Pahalawaththa, G. S. Hope and

o.

P. Malik

Department of Electrical Engineering, The University of Calgary, Calgary, Alberta, Canada T2N 1 N4

ABSTRACT

Use of adaptive control for generator stabilization has demonstrated the possibility of using microprocessors at lower levels of control hierarchy. (Kanniah, et.al. 1984, Ghosh, et.al. 1984).

Application of the generalized minimum variance control algorithm to damp power system oscillations is described in this paper, Modelling of the power system for on-line identification of the controller parameters using least-square identification techniques, and the self-tuning controller is discussed. This approach avoids the peaking of the controller output. It can also be used under non minimum phase conditions. The effectiveness of the stabilizer is evaluated over a wide range of operating conditions.

GENERALIZED SELF-TUNING CONTROL Application of the minimum variance control approach proposed by Astrom and Wittenmark (1973) to generator excitation control is described by Kanniah, et.al. (1984). The minimum variance control minimizes the variance of the output when the system is randomly disturbed, but the control algorithm demands large initial control action and causes actuator saturation. A further handicap of this algorithm is that it can not be used in non-minimum phase systems while retaining its simplicity.

Keywords

Self-tuning control; Power system stabilizer; Adaptive control.

Power systems can easily become non-minimum phase, and the actuator saturation for a long time can cause the system to become unstable. In such situations the minization of a general cost function which includes the input, set point and the output, as proposed by Clarke and Gawthrope (1975), can be used to control the system. For the application of this generalized minimum variance approach to the present problem, the power system is assumed to be of the form

INTRODUCTION With the use of low specific inertia generating units and long transmission lines the power system stabilization problem has become critical. A considerable degree of damping is often required for week transmission lines subjected to heavy loads . This situation is accentuated when attempting to transmit power over relatively week system ties during power system contingencies such as line outages or fuel shortages.

(1 + alz- 1 + a2z-2 + a3z-3) y(t) = z-l(b o + blz- I + b2z- 2)u(t)

+ ~(t)

Modem high speed exciter systems are used to improve the power system stability by rapidly restoring the voltage when the system is subjected to disturbances. However the high gains of these exciters sometimes introduce negative damping between the generator rotor and the power system. This results in oscillations of small magnitudes and low frequency which are often sustained for a long period of time.

or A(Z-I) yet) = B-I(z) u(t)

+ ~(t)

(1)

where ~(t) is uncorrelated random sequence of zero mean which disturbs the system, yet) = Pe, the electrical power output from the generator and u(t) is the stabilizer output injected at the avr summing point. A(z-I) and B(z-I) are the polynomials of lag operator z- I .

A power system stabilizer (PSS) provides damping against such low frequency oscillations. For that the stabilizer must produce a component of electric torque in phase with the speed variation of the rotor. To achieve this the stabilizer transfer function has to compensate for the gain and the phase characteristics of the excitation system, the generator and the power system. In general the transfer function of the PSS is strongly influenced by the voltage regulator gain, generator power level and ac system strength. Variations of the above conditions play a dominant role in power system stabilizer tuning and performance. (Larsen and Swann, 1981)

The control law minimizes the cost function 1= E{(y(t + 1) - w(t»2 + AU(t)2}

(2)

where wet) is the set point. The penalization of u(t) by a factor A in the cost function limits the control output, thereby avoiding the actuator saturation.

Power systems are nonlinear and non-deterministic. In every day operations the continuous variations of the operating conditions may change the above-mentioned factors which influence the PSS performance. This makes it difficult to tune a PSS to cover all operating conditions effectively.

It can be shown that minimizing (2) is same as minimizing (3)

where

An adaptive stabilizer adjusts its characteristics to suit the operating conditions. It may be more effective than a fixed parameter stabilizer in a power system because it can accommodate a wide range of variations in system operating conditions.


101

(4)

N. C. Pahalawaththa , C. S. Hope and O. P. Malik

102

The predicted value of
The arrangement of the identifier and the controller is shown in Fig 3. For the purposes of self-tuning control algorithm the system is considered to be of third order. The time varying parameters of the controller are identified as in eqn. (8). The out put of the system was sampled every 100 ms. The value of used in the cost function is 1.0. The controller parameters were identified using recursive least-squares algorithm, with variable forgetting factor (Fotescus, et.a!. 1981). The use of variable forgetting factor makes it possible to avoid the covariance matrix blow-up, since it approaches unity at steady state. It also gives fast parameter adaptation that is necessary to track the system with sudden disturbances and faults.

where

RESULTS

and 0 is any existing dc bias. In the control algorithm E{
The power system was subjected to the following disturbances.

The self-tuning control algorithm can be summarized as follows.

(1)

At t = 120.0s one line of the double-circuit transmission line was open-circuited.

(2)

At t = l30.0s the line was recJosed.

(3)

At t = l50.0s a three phase to ground fault was applied near the generator bus for a duration of O. Is. The fault was cleared by opening the faulted line.

(4)

At t = 170.0s the opened line was reclosed.

(5)

At t = 190.0s avr voltage reference was changed by 10%.

(6)

At t = 2l0.0s voltage reference was adjusted back to the original value.

(7)

At t = 230.0s, a load of 0.85 pf lag was suddenly applied on the generator bus.

(1)

Compute the auxiliary output from
(2)

+ M(t-l)

(7)

Identify the values of F,G,H and using the identification model

e + e(t)


(8)

where xT(t) = {y(t-l), '" yet - 3), u(t-l), '" u(t - 3), wet - 1), I}

and

The identified controller parameters shown in Figs. 4 and 5 demonstrate the effectiveness of using variable forgetting factor in tracking the parameters. (3)

Find the control u(t) according to the equation, The load angle response of the machine and the control output of the self-tuning stabilizer for the above disturbances are shown in Figs. 6 and 7 respectively. It can be seen that the output does not saturate the actuators for a long time.

+ gl u(t (4)

1)

+ g2 u(t -

2)

+ hw(t) + 0 = 0.0

Get the next sample and go to step (I) .

SYSTEM MODEL AND PARAMETER IDENTIFICATION Studies have been performed on a synchronous machine connected to an infinite-bus through a double-circu it transmission line. The machine is simulated on the computer by seven first order differential equations in d-q frame of reference. The avr used with the machine is that proposed in the IEEE Committee Report (1968) without saturation and is shown in Fig. 1. The governer used is a mechanical hydraulic govern er shown in Fig. 2 (IEEE Committee Report, 1973). System model and parameters are given in the Appendix.

Comparison of the system response with a fixed parameter stabilizer (FPS) (Dandeno, 1976) and the self-tuning stabilizer (STS) for a loss of line fault, and a three phase line-to-ground fault with subsequent opening of one line is shown in Figs. 8 and 9 respectively. These studies are for 0.85 pf lag operating condition and show comparable performance by the two stabilizers. Response of the machine with FPS and STS for loss of line fault and line to ground fault under leading power factor conditions are shown in Figs. 10 and I I respectively. At this operating point the STS shows a significantly superior performance over FPS, demonstrating the ability of the STS to adapt to the varying operating conditions. With the machine initially underexcited and supplying a load of 0.55 pu at 0 .91 pf load to the infinite bus, a load of 0.60 pu at 0.85 pf was suddenly connected to the machine terminals. This resulted in the machine primarily supplying the local load

An Implicit Self-tuning Regulator with very little load on the tie-line to the infinite bus. The machine field excitation adjusted automatically for a lagging pf operation. The load angle response with the self-tunning stabilizer has few oscillations as shown in Fig. 12.

103

APPENDIX

Generator connected to infinite bus representation.

CONCLUSIONS Use of the generalized minimum variance self-tuning approach for power system stabilization has been examined in this paper. The results described here show that a third order model with time-varying parameters can be used to successfully identify the controller parameters under both transient and steady-state conditions. The variable forgetting factor can be satisfactorily incorporated with recursive least-squares identification to have fast tracking of the parameters. Results show that by using the generalized self-tuning minimum variance controller appreciable damping can be achieved in power systems under different operating conditions.

REFERENCES [I]

K.J. Astrom, B. Wittenmark, (1973), "On self tuning regulators" . Automatica, Vol. 9, pp. 185-199.

[2]

D.W. Clarke, PJ. Gowthrop, (1975), "Self tuning controller". EE Proc . Vol. 122, pp. 929-934.

[3]

P.L. Dandeno, (1976), "Practical application of eigenvalue techniques in the analysis of power system dynamic stability problems". Can. Elec. Engg. J., Vol. 1(1), pp. 35-46.

[4]

T.R. Fortescue, L.S. Kershenbaum and B.E. Y dstie, (1981), "Implementation of self tuning regulators with variable forgetting factors". Automatica, Vol. 17(8), pp. 831-835.

[5]

A. Ghosh, G. Ledwich, O.P. Malik and G.S. Hope, (1984), "Power system stabilizer based on adaptive control techniques". IEEE Trans. on Power Apparatus and Systems, Vol. PAS-103, pp. 1983-1989.

A.kd

Lmd Lkd Lmd

ikd

A.f

Lmd Lmd Lf

if

00

= 000 - v

Ud = -em sin 8 - re id - x ei q ~ 000

8=v .

000

v=(T - T ) e

[6]

[7]

[8]

[9]

IEEE Committee Report, (1968), "Computer representation of excitation systems" . IEEE Trans. on Power Apparatus and Systems, Vol. PAS-87, pp. 1460-1464. IEEE Committee Report, (1973) , "Dynamic models for steam and hydro turbines in power studies" . IEEE Trans.: On Power Apparatus and Systems , Vol. PAS-92, pp. 19041915. J. Kanniah, O.P. Malik, G.S. Hope, (1984), "Excitation control of synchronous generators using adaptive regulators" . IEEE Trans. on Power Apparatus and Systems, Vol. PAS-103, pp. 897-904. E.V. Larsen and D.A. Swann, (1981), "Applying power system stabilizer; Parts I, 2 and 3 ". IEEE Trans. on Power Apparatus and Systems, Vol. PAS-lOO, pp. 3017-3046.

2H

m

System Parameters in p.u.: Generator Parameters :

ra = 0.007

xmd = 1.116

Xmq

= 0.6258

xd = 1.2329

Xq

= 0.7427

rf = 0.00089 rkd = 0.023 rkq = 0.023

xf= 1.331 xkd = 1.142

Transmission Line Parameters : Xe

= 0.25

re = 0.035

xkq = 0.6522

104

o. P.

N. C. Pahalawaththa, G. S. Hope and

Malik

Avr Parameters: Ka = 100.00 K. = 1.0 Kt =0.03 Vmax = 6.0 Ta = 0.02 T. = 0.8 Tt = 1.0 Vmin = -6.0

,. ~

CJ

I

i

I

1

Governer Parameters: Tg = 0.2

ilfo

1.$-

t:

0.5-+

= 0.04 T, = 5.0

~

Cmax = 0.1 PmJJ.X = 1.0

Tp = 0.04 /) = 0.34 Tw = 1.6 Cmin = -D. 1 Pmin = 0.0

n n n n n __ •

'1

•

2

___ n

--l-j...--r--~-r------~-----'--i I nO

-0.3-

r-t----1

-,-

Fixed Parameter Stabilizer:

_ _ _[

r-

-1.~}o----· m_----2·...,.O.,...0--::T:-im-e-s-~HO

Fig. 4 Controller parameters F and H K. = 0.03 , Tq = 1.5

v,

Tl = 0.1 T2 = 0.08

v....

l-

:~go I

----Lt - r - - E, K, + sr,

+

=--=4.- AW

w.

role

pooitiOll

limitl

limi"

I-ST.

T.

-H·--- -: 00

'

-------------· 6

-~j..--

Fig. 1 A VR model

: - ___ g L ____

n

__ ,

-- -- -

---

-

-

~

g2 ____

150

.-----

I

~

__ __

._ __ _ _+

200

2.50

Time s

I + ST.

Fig. 5 Controller parameters G and 8

-0.2+

Fig. 2 Governor model

v, AYR

SYNCHRONOUS

IIId

MACHINE

EXCITER

p.

i

u

I

-0 .7t

u...

J

IDENTIFlCAnON IIId

CONTROL

Fig. 3 Block diagram of machine and control system

_o.u~i:--____--:"!":""_ _ _ _ _-:!"':----;;;--;--------;:'. 100

150

200

Fig. 6 Load angle response

Time s

no

An Implicit Self-tuning Regulator O.l~

105

-0.1,

j

,

.',

:~

•

O.O,t

"

P.

i-:Jn'

r

r4

o

..,....

cS -O.D~

~

: -:: '

FPS

lk -

T

~- ;'~'!- 'TS" "=- ~---

\/

-O . H-

!

-O . l~~ .--­

-l .,L_. . . _ .__ + __ __

' so

~OO

250

Time s

200

" 7.'

120

---+:--:-<_ _ _ _'"'!-=--__~_, _--+ 122.' 12. Time s 127.5

Fig. 10 System response to a loss of line under leading power factor

Fig. 7 Control output

-D"t ;

- 0.' 1 ' - - - - - , :

\

.

" !.

I

-0.1 ...

I

-0.1_ .",

I, ,,

.... Q)

~ -O . 7~

. j11". t~-"-' ,,: .

,

«I Q

; ,V ,'

.

-0 .1-;

""

117 . 5

00

«I 0

..:l

STS

I

,

12.

Time s

t,

-1.2i 147.'

127.5

Fig. 8 System response to a loss of line under lagging power factor

,

"~~--.------

:/

~

t

-1~

-1.\

122 . 5

'20

\

•I

.",

.

/\"....,FPS

I

-0 .....

I

\

\

!

:;j

'.

-0.1'

-0 .• :

Cl)

......

\'

I

11

.",

«I

....

, A\

i

~

-0 .71

.",

• FPS

I

«I

...

I

,; "

150

t

"2 .5

'55

I

Time s

'H.'

Fig. 11 System response to a three-phase fault for leading power factor

-Ut

-0 .3'!

I

.",

«I

,t1\

-0.'

....

-O.4S~

Q)

~ -o .• l ~ I .",

«I

.3

," \ ,;," , ...

i

-0.,+ -0 .•

+

«I

00

\I "

147 . '

,I

1

0

..:l

...

I

-0 .1 ....

li: , "• 150

I

I

,

Time s

157 .'

/

:;

.",

Fig. 9 System response to a three phase line to ground fault for lagging power factor AI PP- H

-o.'S-t

:;j «I

,;

j - 11

if

.... Q)

......

\ 1I -D.' ' ;'

FPS

.",

\

..,- STS

,-- ------

-0.751 227.5

Fig. 12

,

230

, 232.5

u.•

, Time s

System response to a connection of a load

237.'