Speed deviation driven adaptive neural network based power system stabilizer

Electric Power Systems Research 38 (1996) 169 175

ELSEVIER

ELEC?RIC POUJ|R SWSTEm$ RE$ElqflCH

Speed deviation driven adaptive neural network based power system stabilizer M.K. E1-Sherbiny*, G. E1-Saady, E.A. Ibrahim Department of Electrical Engoteering, Faculty, of Engineering, Assiut Unit~ersity, Assiut, Egypt

Received 29 March 1996

Abstract

The paper presents an online adaptive artificial neural network (ANN) based power system stabilizer (PSS). The proposed controller is first trained offline using a pole placement based state feedback gain technique at different operating points. The trained ANN parameters (weights and biases) are updated and tuned online using the speed deviation as the reinforcement signal. The proposed PSS is tested at different operating conditions and a variety of regulator gains. The digital results validate the effectiveness and reliability of the new PSS in terms of fast system response under different loading conditions compared with the conventional PI controller and the modern control theory approach of pole placement. Keywords: Artificial intelligence; Power system stability; Adaptive control; Stabilizer design; Neural networks

I. Introduction

An additional signal to the excitation and/or mechanical system of a synchronous machine is currently being used for improving the damping characteristics of the machine under disturbance conditions. The classical controllers with filters fed from speed signals are well known and used in practice [1,2]. Design of such controllers was first made through a trial-and-error approach depending on experience and simple methods. Modern optimal control theory has now been used in this field [3-5], but the controllers obtained suffer from difficulties in calculations and realization. Generally, the design of such optimal feedback controllers is obtained through the minimization of a quadratic performance index and the solution of a nonlinear algebraic Riccati equation which depends upon two arbitrary chosen weighting matrices Q and R [3-5]. The pole placement technique has been applied to allocate the dominant system poles to specified locations [6-9]. The controller parameters obtained are variable and related to the loading conditions at which they are calculated, so if the operating point is changed there will be a drift in the system poles as a result of change in the system * Corresponding author. 0378-7796/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved

parameters. Although the pole placement technique can minimize this deviation in the system poles [7-9], it still suffers from difficulties in the calculation of the feedback matrix and large computation time. Other types of power system stabilizer (PSS), such as lead-lag PSSs and the fixed-gain PI PSS [10], have been widely used by power system engineers. Normally, the parameters of these stabilizers are calculated at a nominal operating point to give good performance. However, the system dynamic response may deteriorate when the operating point changes. Self-tuning and adaptive control [11-13] have been developed to adapt PSS parameters in real time due to any change in the operating conditions. However, these techniques require model identification in real time which requires large computation times. New techniques such as expert systems, fuzzy logic [14] and artificial neural networks have been used in power systems applications [15-18]. The present paper introduces a novel PSS controller based on a multilayer feedforward artificial neural network (ANN). A feature of the proposed A N N controller is that the A N N parameters can be adapted online in real time according to generator loading conditions. Time domain simulations with specified state disturbances for a synchronous machine connected to an infinite bus through an external transmission line are employed to prove the effectiveness of the proposed

M.K. EI-Sherbiny et al.//'Electric Power Systems Research 38 (1996) 169 175

170

ANN based controller under a wide range of variations of the operating conditions and a variety of exciter gains. The results obtained show that the proposed adaptive ANN based controller can enhance the damping characteristics of the power system over a wide range of variations of the operating point and regulator gain in comparison with the pole placement based controller and fixed-gain PI controller.

A.~/

\

CONTROLLER

~qd

PI CONTROLLER

~

I~AC~3,IgI~

~o d~.l'd ~Eq Three separate pOWersystem stmblizers

CONTROLLER

2. System representation

L. ,

for comparison

The synchronous machine under study is provided with a thyristorized excitation system and assumed to be connected through a short line to an infinite-bus system. A Heffron-Phillips model for the synchronous machines is used in which the loading variation appreciably changes the model gains K t - K 6. The model is shown in Fig. 1 and the block diagram is given in Ref. [9]. The dynamic behavior of the synchronous machine can be described by [9] Ac~= 314 Ao9 1

Ad) = ~

A/~q -

(1) (2)

( A T m -- K 1 A 6 - K 2 AE'q)

/£4 1A 1 ~-7~doA6 - -~ ~o - ~do AEfd

(3)

AEfa = ~-~ (Aeref- Aet + Upss)

(4)

Aet = K5 Ad + K6 A/~'q

(5)

It

[ I I t ' I I I

Fig. 2. Schematic diagram of power system control.

(ii) a proportional-integral (PI) PSS based controller; (iii) an artificial neural network (ANN) based controller. The parameters of the pole placement feedback based controllers and fixed-gain PI controllers are determined at a certain operating point. Therefore, the system closed-loop poles will drift as a result of a change in the operating conditions. In order to maintain good damping characteristics over a wide range of operating conditions, an ANN will be developed to adapt the PSS parameters according to online measured system loading conditions.

3. ANN based controller for a synchronous machine where T = K3T'do. The system A matrix elements are functions of the machine gains (KL-K6) which are all load dependent. In some cases, even small changes in the values of the system parameters may affect the system behavior appreciably. Since the design of controllers is usually based on nominal values of these parameters, it has become necessary to adapt the parameters of these controllers as a result of variation in operating conditions. To enhance the system damping, the generator is equipped with three types of PSS controller as shown in Fig. 2. These controllers comprise the following: (i) a controller design using the pole placement technique;

•

The proposed ANN based PSS controller consists of three layers, namely, an input layer, a hidden layer and an output layer. The input layer has four nodes. The best number of nodes for the hidden layer has been found by trial and error to be seven, with a nonlinear tansigrnoid activation function. The last layer (output layer) has one node whose activation function is tansigmoid. The present ANN structure is shown in Fig. 3 and the following steps describe its operation.

input l a y e r

v o u t p u t layer

Fig. 1. System under study.

Fig. 3. Multilayer feedforward neural network.

M.K. El-Sherbiny et al./ Electric Power Systems Research 38 (1996) 169-175

start

l train

the

ANN u s i n g

the

state

gain matrix based on p o l e t e c h n i q u e and u s e t h e w e i g h t s as i n i t i a l values

feedback

placement and b i a s e s

initialize the state variables of simulated system / calculate

the

control

signal

ANN-based c o n t r o l l e r

using

[Eqns.(6)-(9)]

s o l v e t h e s t a t e e q u a t i o n s of t h e s y s t e m u s i n g t h e Runge K u t t a m e t h o d and g e t t h e next state variables

I I

Yes

using error

U

signal to the excitation system (A Upss), as shown in Fig. 2. The statistical data for the A N N training are as follows: No. of training data = 1000 No. of iterations = 9000 Sum of squared error = 1 E - 05 Learning rate = 0.001 Momentum constant = 0.95 The resulting weight matrix between the hidden and input neurons is given by -0.5631 -0.9015 0.3603 0.3610 0.8702 -0.2354 0.0406

0.6619 -0.9308 -0.8931 0.0594 0.3423 -0.9846 -0.2332

the next speed deviation state as signal to modify the weights and

b i a s e s of t h e t h r o u g h (13)

trained

ANN u s i n g

171

Eqns.(10)

10

xlO

-0.8663 -0.165 0.3736 0.1780 - 0.8609 0.6923 0.0539

-0.7977 0.2259 -0.2148 0.3585 0.8065 0.5691 -0.5083

-3

I Fig. 4. F l o w c h a r t of the digital s i m u l a t i o n using the p r o p o s e d A N N b a s e d controller.

v ~o ¢3

Step I. Nodes of the input layer receive signals from the outside world. Step 2. Output signals from the input layer pass to hidden nodes through weighted links which amplify or attenuate signals. Step 3. Output signals from the hidden nodes result from input signals passing through their tansigmoid activation function. Step 4. Hidden layer output signals are sent to the output node via weighted connections between the hidden nodes and the output node. Step 5. The ANN output signal is obtained using the tansigmoid transfer function of the output node. It is well known that the important application of an A N N is to map or represent any linear or nonlinear function. To make an ANN accommodate an approximate function, it is trained using input-output pair data. The present paper attempts to train an ANN to emulate a power system controller. The input-output data are collected from a state feedback pole placement controller at a nominal operating point. The ANN input vector comprises the following: rotor angle deviation A6; generator speed deviation Am; exciter field voltage deviation AEfd; q-axis voltage deviation AE'q. The ANN desired output signal is the additional

i

-5 < 10 "3

1 2 time (sec.) ~a)

...........................

i ............................i...........................

0

3

10

v

0

x 10"~

2 time (see.~

3

(b)

10

..........................

...........................

i ............................

v

0

....

0

2

3

time (sec.)

(o) Fig. 5. D y n a m i c response o f A6 for different o p e r a t i n g c o n d i t i o n s (Qg = 0.0 p.u. a n d K E = 50): - - , a d a p t i v e A N N controller; - - pole p l a c e m e n t controller; - • - , fixed-gain PSS controller. (a) Pg = ' 0.2 p.u.; (b) Pg = 0.6 p.u.; (c) Pg = 1.2 p.u.

M.K. El-Sherbiny et at./Electric Power Systems Research 38 (1996) 169-175

172

adaptive A N N PSS controller. The following steps describe the m e t h o d for calculating and updating the weights and biases o f the A N N controller: Step I. C o m p u t e the input to the hidden layer, X,s(t):

x 10 s

/ i\

.-?

' ~ ~

Ot 3

-5

i

0

4 X,j(t)

.........i..........................

1 2 time (sac.)

,--,i 0 .............. z

=

E i=,

W, ijXi(t) -~ Olj

3

i

1 - exp[ - Xlj(t)] Yt/(t) = 1 + exp[ - Xv(t)]

0

1 2 time (sec

(7)

f\

i

7

3

X2j(t) = ~ W2j Ylj(t) + 02

i

!

i ~-

i

(8)

j= 1

(b)

x 10 "s

0

(6)

Step 3. C o m p u t e the input to the o u t p u t layer, Xzj(t):

[ '

"2.

j = 1, 2 ..... 7

where X~(t) is the input vector to the A N N , Wlu are the connection weights between the input layer and the hidden layer, O,s are the biases o f nodes in the hidden layer, and t the sampling interval. Step 2. C o m p u t e the output o f the hidden layer, Y,;(t):

(=)

x 10 s

~.

"~'!. . . . ~"-

2,111;ii

t

-10

i

where W2j are the connection weights between the hidden layer and the output layer, and 02 is the bias o f the node in the o u t p u t layer. Step 4. C o m p u t e the o u t p u t o f the o u t p u t layer,

-5

r2(t):

3

"~ -10 Y2(t) 0

1

2

time (sac.) (c)

3

1 - exp[ - X2(t)] 1 + exp[ - Xz(t)]

(9)

Step 5. U p d a t e the weights from the hidden to the o u t p u t layer, W2s(t + 1):

Fig. 6. Dynamic response of Am for different operating conditions (Qg = 0.0 p.u. and KE = 50): - - , adaptive ANN controller; pole placement controller; - - -, fixed-gain PSS controller. (a) Pg = 0.2 p.u.; (b) Pg = 0.6 p.u.; (c) Pg = 1.2 p.u.

W2j(t + 1) = W2j(t ) + AW2/(t)

(10)

where

AW2/(t ) = I16, Yu(t) 6 , = Ao~ [1 -

The hidden node biases are

r}(t)]

and ~/ is the learning rate. Step 6. Update the weights from thc input to the hidden layer, Wm(t + I):

- 0.8665 0.3133 - 0.4225

Wlu(t + 1) = W,u(t ) + A W w ( t )

0.1627

(11)

where

0.4655

A W,~j(t) = q 6 j X i ( t )

1.0255 - 0.3120

6; = 6, W2/[1 -- Y,~(t)]

The connection weights between the output neuron and the hidden neurons are

Step 7. U p d a t e the biases f r o m the hidden to the o u t p u t layer, 02(t + 1):

[ -0.301 0.8301 1.0448 0.3671 ]

O2(t + 1) = 02(t ) + v/6,

0.5344

0.4076

0.1294

-

The bias o f the output neuron is 0.5465. The above weights and biases o f the trained A N N are used as the initial values o f the p r o p o s e d online

(12)

Step 8. U p d a t e the biases f r o m the input to the hidden layer, O,/(t + 1): O,/(t + 1) = O,s(t) + ,I6j

(13)

173

M.K. El-Sherbiny et a l . / Electric Power Systems Research 38 (1996) 169-175

4. D i g i t a l computer simulation results x 1 0 "s

Consider the synchronous machine connected to an infinite bus through a transmission bus, as shown in Fig. 1. The parameters of the system are given in Ref. [11]. First, the A N N is trained using the results of the pole placement technique. The M A T L A B Neural Network Toolbox is used in training the A N N controller described in Section 4. It is noted that in both the hidden layer and the output layer the tansigmoid function is used. The input and output training data are obtained from the digital simulation results of closedloop state feedback pole placement of the synchronous machine at different operating conditions covering a wide variation of lagging and leading power factor operations. All the computations are performed offline using the generalized delta rule [15]. Once the A N N is trained offline, the weights and biases of the A N N are updated online with the synchronous machine using the speed error signal to yield desired A N N parameters for any generator operating conditions, as shown in the flowchart of Fig. 4. Thus, the A N N parameters are adapted in real time based on online measured generator operating conditions. The effectiveness of the proposed A N N controller is demonstrated by studying the time domain simulations for the synchronous machine under a wide range of

x 10 -3 10

=

5 ......................... 4....................... ~............................

5 ! U>'~, ........ ~ .......... ~

0

-5

-

0

i -~_~,~

i

i

1

2

time lO-a

--

3

(sac.)

(a)

iiiiii!

10

~

II 1

2

-10

="

0

1 2 time (see.)

10

3

(a)

.s

5 ............,,:............. ~....................... -J............................. .....,

-"

!

.~'. . . . . . . -s

,I~.................i.............................'~........................... i

~

h

7;i

-lo

i

i

0

2

3

time (sac.) (b)

Fig. 8. Dynamic response of Aw for different operating conditions (Pg = 0.6 p.u. and KE = 50): - - , adaptive ANN controller; - - -, pole placement controller; - • -, fixed-gain PSS controller. (a) Qg = 0.6 p.u.; (b) Qg = - 0 . 6 p.u. variations of the operating conditions (Pg----0.2 to 1.2 p.u. and Q g - - 0 . 6 to - 0 . 6 p.u) and a variety of exciter gains (KE varying between 10 and 400). Only the results for Pg = 0.2, 0.6 and 1.2 and Qg = 0.6, 0.0 and - 0 . 6 p.u. for the generator loading and KE = 10, 50 and 400 for the exciter gain are presented. The dynamic response of the system states A6 and Ao~ for a 1% disturbance in state variable A~ is traced in Figs. 5 - 8 for different operating conditions. The two groups of responses are repeated for regulator gain variations between l0 and 400 in Figs. 9 and 10. Figs. 5 and 6 show the response for two extreme cases of active power loading (0.2 and 1.2 p.u.), as well as with the value P = 0.6 p.u. at which the controller has been designed, while Figs. 7 and 8 show the response for two extreme cases of reactive power variation (0.6 and - 0.6 p.u.).

[ 0

5 .............. ,,~,4 ;'~"~ ! ........................... :!............................

3

time (see.) (b)

Fig. 7. Dynamic response of A8 for different operating conditions (Pg = 0.6 p.u. and KE= 50): - - , adaptive ANN controller; - - -, pole placement controller; - . -, fixed-gain PSS controller. (a) Qg = 0.6 p.u.; (b) Qg = --0.6 p.u.

F o r the sake of comparison, the responses of the system with the following controllers are also given. (i) A controller based on the pole placement technique is designed to assign the closed-loop eigenvalues of the system at ( - 3.00 _+j5.26, - 16.00 and - 18.00), ( = 0.5 [9], at a nominal loading condition Pg = 0.6 p.u. and Qg = 0.0 p.u with K E = 50. The M A T L A B software package is used to obtain the desired feedback matrix as follows: K = place(A, B, P )

M.K. El-Sherbiny et a l . / Electric Power Systems Research 38 (1996) 169-175

174

where A and B are the system matrices and P is a vector containing the above specified eigenvalues. (ii) A fixed-gain PI excitation controller of the following form [18]:

xlO

-4

1 t ..................l--:~.i ..................................................... ,, i ~

g~(s) - 1 + ar-------~ Kp +

]I

A~o(s)

0.01S ( 1 5 7 6 . 0 3 + 4 1 ; . 2 7 ) - 1 + 0.01S A~o(s)

&

r,

,~ !.

o

k

/i.

~i~ ~, i '~

~"~

. .

/

., i'. i ~,

.

,,

/k,

/1/

(14)

li;

3

where the controller parameters Kp and K~ are computed at a nominal operating condition Pg = 0.6 p.u. and Qg = 0.0 p.u. with K~ = 50 to allocate the poles of the closed-loop system at ( - 3.00 +j5.26, -16,00, 18.00). From the simulation results shown in Figs. 5-10, it can be seen that the system with the proposed adaptive ANN based controller gives a better dynamic response to load variations than the other controllers (fixed-gain PI controller and controller based on the pole placement approach). Furthermore, the deviation in the system response due to changes in the operating condition is kept within a very narrow range while the variation in the system parameters covers a wide range of load variations. On the other hand, the system responses are significantly affected by the load variations when the other controllers are used. Also, the effectiveness of the proposed ANN based controller has

\

....'W, / ,. i'~' ."

i '., ,:

\;

,"

,.'.-v"

,,

,

.,

~

4

,.

, ."

.LI..~....... ~..........:.................:...........................

-1

0

1

2

3

time ('sec.) x 1 0 "s

J 0

................

(a)

.. ": . . . . . . .

'

......

& v

3

-5

-10

0

2

3

time (sec.)

(b)

-3

xlO 10 _,~,...

o e~

~,.,

.........

it

0 ..... t l ~ '

--"'";t. "--~

............ i;::::ii

xq ! ',i, \,. ..' :,

','./

/

f~-.. ,! "l

, ~

Fig. 10. D y n a m i c r e s p o n s e o f A~o f o r d i f f e r e n t o p e r a t i n g c o n d i t i o n s (Pg = 0.6 p.u. a n d Qg = 0.0 p.u.): - - , adaptive ANN controller; - - - , p o l e p l a c e m e n t c o n t r o l l e r ; - . - , f i x e d - g a i n PSS c o n t r o l l e r . (a) . . . . . . . . . . . . . .

,

,/,

K E = 10; (b) K E = 400. _

"',

-5 i

10

xlO

i

1 2 time (s~.)

0

-3

3

been checked for a variety of exciter gains KE from 10 to 400. The proposed A N N controller gives a better dynamic response than the other two controllers, especially at low values of the exciter gain (KE = 10).

(.)

5. Conclusions

V,

i

~t ~ -5 0

.""

-" k

-'

1

2

3

time (sec.) (b) Fig. 9. D y n a m i c r e s p o n s e o f A6 f o r d i f f e r e n t o p e r a t i n g c o n d i t i o n s (Pg = 0.6 p . u . a n d Qg = 0.0 p.u.): - - , adaptive ANN controller; - - - , p o l e p l a c e m e n t c o n t r o l l e r ; - • - , f i x e d - g a i n PSS c o n t r o l l e r . (a)

K E = 10; (b) K E = 400.

An adaptive A N N based controller has been developed to be included in a power system in order to improve the dynamic response due to any variations caused by changing the operating conditions and/or voltage regulator gain. The inputs to the A N N are the rotor angle deviation, angular speed deviation, field voltage deviation and q-axis voltage deviation. The output of the A N N is the desired additional signal. The A N N feedforward multilayer based controller is used and is trained offline using the results of the pole placement approach. The A N N trained parameters (weights and biases) are then tuned online to compen-

M.K. EI-Sherbiny et al./Electric Power Systems Research 38 (1996) 169-175

sate for any change in the power system parameters by using the speed deviation signal due to any change in the operating point or exciter gain. The digital simulation results validate the robustness and fast dynamic response of the ANN based controller compared with the fixed-gain PI controller and the pole placement controller which require adjustment of the parameters with changes in the operating conditions.

References [1] R.J. Fleming, M.A. Mahan and K. Parvatisam, Selection of parameters for stabilizers in multimachine power systems, 1EEE Trans. Power Appar. Syst., PAS-IO0 (1981) 2329-2333. [2] M.J. Gibbard, Co-ordinated design of multi-machine power system stabilizers based on damping torque concepts, IEE Proc. C, 135 (4) (1988) 276-284. [3] O.A. Solheim, Design of optimal control systems with prescribed eigenvalues, Int. J. Control, 15 (1) (1872) 143-160. [4] Y.N. Yu and H.A.M. Moussa, Optimal stabilization of a multimachine system, IEEE Trans. Power Appar. Syst., PAS-91 (1972) 1174-1182. [5] Y. Bar-Ness, Optimal closed-loop pole assignment, Int. J. Control 27 (3) (1978) 421-430. [6] N. Munro, Pole assignment, Proc. Inst. Electr. Eng., 126 (6) (1979) 549-554. [7] H.M. Soliman and A. Bahgat, Minimum sensitivity pole placer, Dynamics Stability Syst., 3 (I-2) (1988) 51-56. [8] H.M. Soliman and M.M. Sakr, Wide range power system pole placer, Proc. IEE C, 135 (3) (1988) 195-201.

175

[9] E.A. Ibrahim, Design of controller for power system under different operating conditions using pole placement technique, M.Sc. Thesis, Faculty of Engineering, Assiut University, Assiut, Egypt, 1990. [10] Y.Y. Hsu and C.Y. Hsu, Design of a proportional-integral power system stabilizer, IEEE Trans. Power Syst., PWRS-1 (1986) 46-53. [11] D. Xia and G.T. Heydt, Self-tuning controller for generator excitation control, IEEE Trans. Power Appar. Syst., PAS-I02 (1983) 1877-1885. [12] Y.Y. Hsu and K.L. Liou, Design of self-tuning PID power system stabilizers for synchronous generators, IEEE Trans. Energy Convers., EC-2 (1987) 343-348. [13] S.J. Cheng, Y.S. Chow, O.P. Malik and G.S. Hope, An adaptive synchronous machine stabilizer, IEEE Trans. Power Syst., P W R S - I (3) (1986) 101-109. [14] Y.Y. Hsu and C.H. Cheng, A fuzzy controller for generator excitation control, IEEE Trans. Syst. Man Cybern., 23 (2) (1993) 532-539. [15] D.E. Rumelhart, G.E. Hinton and R.J. Williams, Learning internal representations by error propagation, in D.E. Rumelhart and J.I. McClelland (eds.), Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1, Foundations, MIT Press, Cambridge, MA, Ch. 8.

[16] C.R. Chen and Y.Y. Hsu, Synchronous machine steady-state stability analysis using an artificial neural network, IEEE Trans. Energy Convers., 6 (1) (1991) 12-20. [17] D.J. Sobajic and Y.H. Pao, Artificial neural-net based dynamic security assessment for electric power systems, IEEE Trans. Power Syst., 4 (l) (1989) 220-228. [18] Y.Y. Hsu and C.R. Chen, Tuning of power system stabilizers using an artificial neural network, IEEE Trans. Energy Convers., 6 (4) (1991) 612-619.