Automatic Generation Control by Using ANN Technique

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Automatic Generation Control by Using ANN Technique Aysen Demiroren, Neslihan S. Sengor, H. Lale Zeynelgil Published online: 30 Nov 2010.

To cite this article: Aysen Demiroren, Neslihan S. Sengor, H. Lale Zeynelgil (2001) Automatic Generation Control by Using ANN Technique, Electric Power Components and Systems, 29:10, 883-896, DOI: 10.1080/15325000152646505 To link to this article: http://dx.doi.org/10.1080/15325000152646505

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A utomatic Generation Control by Using ANN Technique


AYSEN DEMIROREN NESLIHAN S. SENGOR H. LALE ZEYNELGIL Istanbul Technical University Electrical & Electronic Faculty Maslak, 80626, Istanbul, Turkey T his pape r investigates an applicatio n o f layered artic ial neural netwo rk for auto matic generatio n control o f the po we r syste m. Co mpute r simulatio ns o n the inte rconnec ted power syste m with two areas that include re heate r e Œec t and also the go vernor deadband e Œect show that the artic ial neural netwo rk control sche me pro po sed is e Œective in damping out o sc illatio ns re sulted by load pe rturbatio ns. O nly one artic ial neural netwo rk co ntro ller, which controls the inputs o f eac h area in the po we r syste m toge the r, is considered. By comparing the o btained re sults with co nventional controlle rs, it is shown that the pe rformance o f artic ial neural netwo rk co ntro ller is bette r than co nventional co ntro llers. In this pape r, back pro pagatio n-thro ugh-time algo rithm is used as neural network learning rule .

1

Introduction

Automatic generation control, sometimes called load-frequency control, is a very important issue in power system operation and control. T he automatic generation control ( AGC ) is implemented to solve the problems which occur due to sudden small-load perturbations which continuously perturbate the normal operation of power system. T he frequency must be xed at a nominal value to supply qualied power for consumers. Because components in a power system have various nonlinearities inherently, generally a linear model obtained by linearization at an operating point is used for the controller design [1–3]; however, the operating point of a power system can change very much because of load perturbations occurring in the power system. T herefore, a xed controller, which is optimal under one operating condition, can be unsuitable for another operating point. In literature, there are many variable controller structures which aim a sensitive control to the plant parameter changes [4, 5]; however, these methods need an exact state space representation, which generally is not available completely known. On the other hand, many adaptive control techniques have been introduced for automatic generation control [6–8]. Due to the requirement of the perfect model, which has to track the state variables and satises system constraints, it is rather

Manuscript received in nal form on 15 November 2000. Address correspondence to Aysen Demiroren.

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di cult to apply these adaptive control techniques to AGC in practical implementations. In this paper, articial neural network technique to control interconnected power system with two areas connected with a tie line to each other to supply different consumers is considered. In the power system considered, as the load varies at any area, rstly, the frequency related with this area is aŒected, and then the other area is also aŒected from this perturbation through tie-line. To return back to the steady-state value of the frequency after a given load perturbation, a control system has to be designed that acts on the setting of the steam admission valve of the unit turbine. T he frequency transients must be eliminated as rapidly as possible. It is known that in conventional cases, AGC systems include an integral controller. T he integrator gain is set to a level that compromise between fast transient recovery and low overshoot in dynamic response of the system [9]. In conventional system, the integral controller in governor conguration is used as secondary controller. So, this type of controller is considerably slow. T herefore, the controller operates by a given delay, and then the settling of variables takes a considerably longer time. T he model of nonlinear system to be controlled is given by a set of diŒerential equations ( i.e., the system is a continuous dynamical system modelled by state space equations) . For steam turbine in each area, including of the governor deadband effects in the state space, equations are very important, as the governor deadbands have the destabilizing eŒects on transient response. Moreover, the eŒects of generating rate constraints and reheater eŒects considered yield additional nonlinearity on state space equations. So, the control rule to be imposed must cope with these dynamics, and thus, articial neural network controller, which is suitable for this aim, is used to control the system. In this study, it is shown that the ANN conguration using back propagationthrough-time algorithm and applied for AGC at the power system gives better dynamic response in respect to conventional integral controller.

2

A utomatic Generation Control in Two-A rea Power System

A two-area power system, including two single areas connected through a tie-line, is considered as illustrated in Figure 1. Each area supplies its user pool, and tie-line allows electric power to ow between areas [10]. So, both areas aŒect each other ( i.e., a load perturbation in onearea aŒects the output frequencies of both areas as well as power ow on the tie-line) . Because of this, the control system of each area needs information about the transient situation in both areas to bring the local frequency to its steady state value. As the information about each area is found in its output frequency, the information about the other area is in the perturbation of tie-line power. So, tie-line power ow is needed in order to feed back the information in both areas. W hile the electric load increases in one area, the frequency of the same area decreases, and power transmitted from the other area to this area increases. T his has the same eŒect on the frequency of the other area as if its load increases. T he power system with two areas considered is shown in Figure 2. In conventional systems, the turbine reference power of each area is tried to be set to its nominal value by an integral controller [9]. T he input of the integral


Automatic Generation Control Using ANN Technique

885

Figure 1. Schematic diagram of power system.

controller of each area is B i D f i + D P t ie ( i = 1, 2) , and it is called area control error ( ACE ) . T he parameters of B i may be optimized, but here, they are chosen as 1=K pi + 1=R i as generally taken [9, 11]. Each of the areas in the power system contains governor deadband eŒects, reheater stage eŒects of steam turbines, and generation rate constraints. T he speed governor deadband has signicient eŒect on the dynamic performance of automatic generation control at the power system [11]. So all of the eŒects mentioned above must be considered in the state space model. To describe the governor deadband nonlinearity, describing function approach is used as explained below [11]. T he describing function approach is used to linearize the governor deadband in terms of change and rate of change in speed. T he governor deadband for each area is dened

Figure 2. T he detailed power system with two areas.

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as the total magnitude of a sustained speed change, which has no change in valve position, within. T he nonlinearity of hysteresis is expressed as: y = F (x , dx =dt ) .

( 1)

It has been known that the backlash nonlinearity tends to give a continuous sinusoidal oscillation with a natural period of about two seconds [11]. T herefore, to take x as a sinusoidal oscillation is a realistic assumption:


x º A sin!0 t,

( 2)

where A is amplitude of oscillation, !0 is the frequency of oscillation, and !0 = 2¼f 0 = ¼ with f 0 = 0 .5 Hz. F (x , dx =dt ) function can be evaluated as a Fourier series as follows: F (x , xÇ ) = F 0 + N 1x +

N2 !0

xÇ +

( 3)

.

For a reasonable approximation, it is enough to consider the rst three terms. As the blacklash nonlinearity is symmetrical about the origin, F 0 is zero and F (x , xÇ ) = N 1x +

N2 !0

"

N2 d

xÇ = N 1 +

!0 dt

#

x = D Bx,

( 4)

where D B represents deadband. As described in [5], the Fourier coe cients are found as N 1 = 0 .8 and N 2 = ¡ 0 .2. T he state space equations obtained by considering deadband eŒects and reheater eŒects, in discrete time domain, are given as below: D

³

f 1 (k ) =

¡ D P G 1 (k ) =

³ +

D P R 1 (k ) = D x E 1 (k ) =

D

f 2 (k ) =

³ ³

³

T

1¡

TP 1

´

D f 1 (k ¡

1) +

K P 1T TP 1

( D P G 1 (k ¡

1)

D P D 1 ( k ¡ 1) ¡ D P 12 ( k ¡ 1)) , ´ T D P G 1 ( k ¡ 1) + K R 1 D P R 1 ( k ) 1¡

( 5)

TR 1

³

T TR 1

´ ¡ K R 1 D P R 1 (k ¡

1¡

T TT 1

1¡

T

³

TG 1

´

´

1¡

u s 1 (k ) + T TP 2

´

(D P G 2 (k ¡

D P R 1(k ¡

1) ¡

TT 1 T

1) +

KAF 1 +

D f 2 (k ¡

T

1) +

D x E 1 (k ¡

³

1) ,

1 R1

1) +

TG 1

´

( 6) D x E 1 (k ¡

³

N1 +

D f 1 (k )

´

1) ,

N2 d !0 dt

( 7) ´ ( 8)

,

K P 2T

D P D 2 (k ¡

TP 2

1) ¡

a 12 D P 12 ( k ¡

1)) ,

( 9)

Automatic Generation Control Using ANN Technique ³ ´ T D P G 2 (k ) = 1 ¡ D P G ( k ¡ 1) + K R 2 D P R 2 ( k )

887

TR 2

³

+ D P R 2 (k ) =


D x E 2 (k ) =

³ ³

TR 2

TT 2 T

1¡

KR2

¡

T

1¡

³

T

TG 2

´

´

u s 2 (k ) ¡

´

D P R 2(k ¡

D P R 2(k ¡

1) +

D x E 2 (k ¡

1) +

³

KAF 2 +

D P 12 ( k ) = 2¼T 12 T ( D f 1 ( k ¡

1) ¡

1 R2

1) , T TT 2 T TG 2

´

( 10) D x E 2 (k ¡

³

N1 +

D f 2 (k )

D f 2 (k ¡

´

1) ,

N2 d !0 dt

( 11) ´ ( 12)

,

1)) + D P 12 ( k ¡

1) ,

( 13)

where parameter a 12 equals to ¡ 1. While the integral controllers are used, a new state variable is added for each area at the power system as follows: D P r e f 1 (k ) = D P r e f 1 (k ¡

1) ¡

K I 1B 1T D

f 1 (k ¡

1) ¡

K I 1 T D P 12 ( k ¡

D P r e f 2 (k ) = D P r e f 2 (k ¡

1) ¡

K I 2B 2T D

f 2 (k ¡

1) ¡

a 12 K I 2 T D P 12 ( k ¡

1) ,

( 14) 1) .

( 15)

In this case, in equations ( 8) and ( 12) , D P r e f 1 and D P r e f 2 are replaced with u s 1 and u s 2 . As a result, the state space equations of the power system, including two areas in discrete-time domain, are written as follows: x ( k ) = Ax ( k ¡

1) + B u ( k ¡

1) + G ,

( 16)

where G is a vector containing nonlinear terms. In the case of using conventional integral controllers, the state variables and control inputs are given as follows: x T = [D

f 1 , D P R 1, D P G 1 , D P r e f 1, D x E 1 , D

f 2 , D P R 2 , D P G 2 , D P r e f 2 , D x E 2 , D P 12 ],

u T = [D P D 1 , D P D 2 ].

On the other hand, in the case of using ANN controller, they take the following forms: x T = [D

f 1 , D P R 1, D P G 1, D x E 1 , D

f 2 , D P R 2 , D P G 2 , D x E 2 , D P 12 ],

uT = [u s 1 , u s 2 ].

T he variables used in the above equations are given in the list of symbols. Moreover, in order to project physical constraints, a generation rate limitation of 0.1 p.u. per minute is considered ( i.e., D P G· i µ 0 .1 p.u.MW / min = 0.0017 p.u. MW / sec. ( i = 1, 2)) [8].

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A rticial Neural Network Controller for the T wo-A rea Power System

In two-area power systems, frequency deviation in each area has to be brought back to their steady-state values. T he articial neural network controller can be used to provide control input, which succeeds this deed. As implied by the state space equations given in the previous section, the system model is nonlinear. So, to use a nonlinear controller would be more proper than using a linear one as conventional integral controller. Articial neural network controller is indeed an adaptive nonlinear controller with control strategy dened by the learning rule used in changing the weights of the synaptic connections. T he activation function is the sigmoid with unsymmetrical unipolar representation. In order to model the dynamics of the system properly, the block composed of controller and system equations are spread in time as shown in Figure 3 [10]. So, the learning rule used is the back propagation-through-time [12, 13]. In this paper, the weights in ANN conguration are updated on-line. T he ANN controller used in this work is a multilayer perceptron with three layers, as given in Figure 4. In the rst hidden layer there are 20 neurons, in the second hidden layer there are ten neurons, and in the output layer there are two neurons. Since the system behavior is modelled almost exactly by the given state space equations, there is no need for neural network emulator. To use the system equations instead of neural network emulator simplies the network, but then the problem of how to back propagate the error arises. T his problem is important because the only a priori known about desired values are the values of states. To solve this problem, an error has to be dened for the neural network controller; this new error function is formed as a linear combination of the errors related with states. T he inputs of ANN are nine state variables and two inputs D P D 1, 2 , and the outputs are two variables represented by u s 1, 2 , which become the control inputs of the power system. D P D 1 and D P D 2 are the variables, which enter to both power system and controller. In practice, they are obtained in per unit MW from the load perturbation in each area. In this work, the load perturbation is assumed in only the rst area of the system, so D P D 1 6= 0 and the other equals zero. Since all of the state variables of the system are physical, it is easy to measure them. T he back propagation rule denes how to change the weights in the articial neural network in order to minimize the error function given by E = 12 eT e [12]. T he adaptiveness of articial neural network is due to this process of weight change,

Figure 3. T he block composed of controller and system for ANN.


889


Figure 4. ANN controller for a two-area power system. which mimics the change of synaptic weights in human brain during supervised learning process. Due to back propagation rule, the weights change according to gradient descent method of optimization as follows: 1 D w ij =¡ ¹

@E 1 @w ij

,

( 17)

where wij1 is the weight connecting neuron i in layer l to the neuron j in the next layer. For the neural network controller used in this work there are three layers, two hidden layers and an output layer, so l is 1, 2, or 3. T he positive real number ¹ is the learning rate, which corresponds to step size in gradient-based optimization methods. T he gradient of the error function is easy to calculate at the output layer ( i.e., the third layer) , and it is equal to ej f j3 ¢ .

Sˆ J3 = ¡

( 18)

Here, f j2 ¢ is the derivative of the activation function of the j th neuron at the output layer. T he gradient of energy functions for the hidden layers ( i.e., second and rst layers) are as follows: ±j2 =

X

±n3 w j3n ,

( 19)

n

±j1 =

X

2 ±m w j2m .

( 20)

m

So the weights are changed according to the following rule for the output and hidden layers, respectively, as follows: 3 D w ij = ¡ ¹±j3 f 2 ( v ji ) ,

( 21)

2 D w ij = ¡ ¹±j2 f 2 ( v ji ) ,

( 22)

1

1

D w ij = ¡ ¹±j x i .

( 23)

In the following section, the simulation results using the above given ANN controller will be given, and these will be compared with the results obtained by integral controller. Furthermore, the ANN controller conguration can be used for multi-area power systems having areas with diŒerent characteristics by the same procedure. In this case, both the number of inputs and the number of outputs are increased. T hen, automatic generation control is implemented by the hierarchical control system conguration.

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Demiroren et al. Table 1 T he parameter values of the power system


K P 1, 2 T P 1, 2 T s 1, 2 K R 1, 2 T R 1, 2 T E 1, 2

4

120 20 s 0.002 s 0.333 10 s 0.3 s

T G 1, 2 K A F 1, 2 R 1, 2 !0

D PD 1 K I 1, 2

0.2 s 2 2.4 3.14 0.01 puMW 0.001

Simulations

In this study, the simulation results are obtained by using Matlab metales. It is not possible to benet from ANN toolbox of Matlab since back propagation-throughtime algorithm is used without emulator for the system, as mentioned before. Instead of ANN emulator for the plant, the system equations are used directly. T hese state space equations with nine states and two inputs are solved by using Euler method. T he sampling period represented by T is taken as 0.01 seconds. One of the inputs is from the ANN control output; the other is D P D i ( i = 1, 2) , namely a step-load perturbation. In here, it is assumed that a step-load perturbation occurs in only one area. In calculation related with the power system, the deadband of governor and the reheater in the turbine belonging to each area are considered and the rate of generating power belonging to each area is limited. T hese mentioned aspects give rise to the nonlinearities in the equations. T he parameter values belonging to the power system used during the simulation are given in Table 1. T he parameter values related to ANN are as follows: the learning rate ¹ = 0 .2, ®, which is a positive constant that controls the slope of the sigmoid function, is

Figure 5. Deviation of frequency at area 1 with ANN controller.



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Figure 6. Deviation of frequency at area 1 with conventional controller. assumed to be 5 for the rst hidden layer and 1 for the second layer, so the slope is a steep one. In order to model the nonlinear dynamical behavior of the power system 500 blocks formed by ANN controller and power system equations are used. It is well known that a criterion has to be imposed in order to stop back propagation algorithm. In this work, iteration number and an error criterion are both considered to stop the algorithm. In the beginning, the initial values of the state variables are taken to be zeros; the input D P D 1 in the rst area at the power system considered is the step load increasing of 0.01 p.u. MW as D P D 2 in the second area at the system equals zero. T hese values are applied both to the input of the ANN controller and to the power

Figure 7. Deviation of frequency at area 2 with ANN controller.


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Demiroren et al.

Figure 8. Deviation of frequency at area 2 with conventional controller. system. T he weights of the ANN controller are initially chosen as random values. After 700 iterations, the error obtained at the output of the whole system becomes approximately 0.0342, as observed in the simulation. T he simulation results are summarized in the gures. In all gures, 100 iterations equal to one second. All gures, which are given for the case of ANN controller, are the best results obtained about 100 testing. Figures 5, 7, and 9 include the deviations of the frequencies of rst and second areas, and tie-line power ow against a step-load perturbation in the rst area in the case of ANN controller, respectively.

Figure 9. Deviation of tie-line power with ANN controller.



893

Figure 10. Deviation of tie-line power with conventional controller.

In Figures 6, 8, and 10, the same deviations are given by using a conventional controller due to the same load perturbation. In the gures obtained for the case of using ANN controller, the beat frequencies are in tolerance limits acceptable. It has to be noted that the duration to reach the steady state is very short with ANN controller. In order to emphasize this, in Figures 11, 12, and 13, deviations of frequencies of rst and second areas and deviation of tie-line power ow between the areas are given in the same scale, respectively.

Figure 11. Deviation of frequency at area 1 with ANN and conventional controllers in the same scale.


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Figure 12. Deviation of frequency at area 2 with ANN and conventional controllers in the same scale.

5

Conclusions

T his study includes an application of ANN to automatic generation control in the power system. In this work, transient behavior of the frequency of each area and tie-line power deviation in the power system with two areas is considered under the step-load perturbation. T he power system considered is represented by the nonlinear state space equations because governor deadband eŒects, reheater eŒects, and generating rate constraints are included. T hese equations are used directly during the control of the power system by ANN. T his is not a usual method with

Figure 13. Deviation of tie-line power with ANN and conventional controllers in the same scale.


895


ANN controllers. W hen an ANN controller is used in order to back propagate the error, ANN emulator is used instead of the power system controlled. In this work, ANN conguration using back propagation is only used as controller and the power system is modelled by its state space equations. It is shown that the results obtained by using ANN controller outperform the results of the conventional controller. In practice, power systems generally include more than two areas, and each area is diŒerent. Because of this, the same ANN conguration for multiarea power system could be investigated later. Furthermore, it can be used as a recurrent ANN controller instead of multiplayer perceptron with back propagation-throughtime algorithm to AGC.

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Approach to Load-frequency Control,” IEEE Trans. O n P o we r A pparatus and System , Vol. PAS-90, pp. 2472–2482. N. N. Benjamin and W . C. Chan, 1978, “ Multilevel Load-frequency Control of Interconnected Power Systems,” P roc. IEE , Vol. 125, pp. 521–526. J. Nanda and B. L. Kavi, 1988, “ Automatic Generation Control of Interconnected Powers System,” P roc. IEE , Vol. 125, No. 5, pp. 385–390. N. N. Benjamin and W . C. Chan, 1982, “ Variable Structure Control of Electric Power Generation,” IEEE Trans. O n P o we r A pparatus and System , Vol. PAS-101, No. 2, pp. 376–380. A. Y. Sivaramaksishana, M. V. Hariharan, and M. C. Srisailam, 1984, “ Design of Variable Structure Load-frequency Controller Using Pole Assignment Techniques,” Int. Jo urnal o f C ontro l, Vol. 40, No. 3, pp. 437–498. I. Valk, M. Vajta, L. Keviczky, R. Haber, J. Hetthessy, and K. Kovacs, 1985, “ Adaptive Load-frequency Control of Hungarian Power System,” A uto matica , Vol. 21, No. 2, pp. 129–137. J. Kanniah, S. C. Tripathy, O. P. Malik, and G. S. Hope, 1984, “ Microprocessor-based Adaptive Load-frequency Control,” P roc. IEE., P t- C, G e neratio n Transmissio n and D istributio n, Vol. 131, No. 4, pp. 121–128. C. T. Pan and C. M. Liaw, 1989, “ An Adaptive Controller for Power System LoadFrequency Control,” IEEE Trans. on P owe r Syste m , Vol. 4, No. 1, pp. 122–128. O. I. Elgerd, 1971, Elec tric Ene rgy Systems T heory: A n Introductio n, McGraw-Hill Book Company. F. Beaufays, Y. A. Magid, and B. Widrow, 1994, “ Application of Neural Network to Load-Frequency Control in Power System,” Ne ural Ne two rks, Vol. 7, No. 1, pp. 183– 194. S. C. Tripathy, G. S. Hope, and O. P. Malik, 1982, “ Optimisation of Load-Frequency Control Parameters for Power Systems with Reheat Steam Turbines and Governor Deadband Non-Linearity,” IEE P roc ., Vol. 129, Pt. C, No. 1, pp. 10–16. S. Haykin, 1999, Neural Ne tworks: A C ompre hensive Foundatio n, 2nd Edition, Prentice Hall. D. H. Nguyen and B. W idrow, 1990, “ Neural Networks for Self-learning Control Systems,” IEEE Co ntr. Sys. Mag., pp. 18–23.

List of Symbols D f K P 1, 2

T he deviation Derivation of variable Frequency Transfer function gain of generator

896 T P 1, 2 P G 1, 2 P D 1, 2 N1 N2


!0

u s 1, 2 R 1, 2 P r e f 1, 2 x F (x ) E KI T K R 1, 2 T R 1, 2 P R 1, 2 T T 1, 2 X E 1, 2 T G 1, 2 K A F 1, 2 DB e w ¹ ± f¢ l i, j n m v

Demiroren et al. T ime constant of generator Fluctuation in turbine output power Electrical load perturbations Fourier series coe cent associated with x Fourier series coe cient associated with sx Angular frequency of natural sinusoidal oscillation Control input of power system Regulation parameter Output of integral controller State vector Nonlinear function of x Error function Integral controller gains Sampling period Transfer function gains of reheats of areas Reheat time constants Mechanical power during steam reheat T ime constant of turbine Governor valve position T ime constant of governor Proportional feedback gain Deadband of governor Error vector Weights of neural network Learning rate Error gradient Derivative of activation function Layer number Indices of neuron Numb er of the second layer inputs Numb er of the rst layer inputs Product of weights and inputs in each layer