An Adaptive Fuzzy Controller Gain Scheduling For Power ... - CiteSeerX

2004 lEEE International Conference on Industrial Technology (ICIT)

An Adaptive Fuzzy Controller Gain Scheduling For Power System Load-Frequency Control M. Masiala, M. Ghnbi and A. Kaddouri Department of Electrical Engineering Universite de Moncton, New Brunswick, Canada {Emm1097, Ghribim, Kaddoua}@umoncton.ca

Abstract

- In this paper, an adaptive fuzzy controller

gain scheduling scheme for power system load-frequency control is designed tu damp the frequency oscillations and to track its error to zero at steady state, A Sugeno type inference system is used in the proposed controller to adapt the scaling gains of a single fuzzy controller through a classical on-line monitoring of the most sensitive parameters of the system. The proposed controller avoids excessive patterns and training time compared to neural network based adaptive schemes. A typical single-area nonreheat power system is considered. Simulation results indicate that the proposed controller is insensitive to parameter changes in a wide range of operating condition, and to the generation rate constraints. Furthermore, it is simple io implement.

Keywords: Power systems, Load-Frequency Control, Fuzzy logic controlkr, Gain scheduling 1 Introduction During the past decades Load-Frequency Control (LFC) has gained a lot of interests in the literature [I-121. The main objective of LFC is to ensure a sufficient and reliable supply of,power-with good quality. Load fluctuations and abnormal conditions such as the generation outages; cause the system frequency to decay from the desired value. To ensure the quality of the power supply, it is necessary to regulate the generator loads depending on the optimal frequency value with a proper LFC design. Therefore, in designing the controller, the nonlinear effects due to the physical components of the system, the load change inherent Characteristics and the parametric uncertainty and disturbances should be taken into account [I]. Based on cIassica1 linear control theories, various control strategies have been proposed for designing LFC in order to achieve a better dynamic performance. Despite its poor dynamic performance evidenced by large overshoots and oscillations when applied to systems with nonlinear effects, the proportional-integral (PI) controller remains the most widely used type [ 1-51. The PI controller poor performances are due to the fact that the loading of a power system is never constant. Consequently, its operating point changes constantly during a daily cycle [2]. As a result, a fixed gain

0-7803-8662-0/04/$20.00 02004 IEEE

controller, which is optimal at a nominal operating point (nominal regime), fails to provide best control performances in various states [ f -41. In order to take the parametric uncertainty and the nonlinear constraints into account, and to keep the system performance near its optimal operating condition, different approaches have been applied in the past, Wang [ 11 and Pan 121 used adaptive schemes with self-adjusting gain scheduling. Fosha [3] and Begiamin [4] have applied the concept of Variable-Structure Systems (VSS) in order to improve the dynamic performance of the system by making the controller insensitive to the plant parameter disturbances. Despite the promising results achieved by the adaptive and the VSS schemes, their control algorithms are complicated and require the on-line identification or monitoring of the overaIl system. In the past decades, fuzzy logic controllers (FLCs) have been successfully developed for analysis and control of nonlinear systems [X-lo]. The fuzzy reasoning approach is motivated by its ability to handle imperfect information, especially uncertainties in available knowledge.

Stimulated by the success of FLCs, Talaq [SI, Yesil [6] and Chang [7] proposed different adaptive fuzzy scheduling schemes for conventional PI andor PLD controllers. These methods provide good performances but the system transient responses are relatively oscillatory.

In view of this, this paper proposes an adaptive FLC gain scheduling scheme for LFC. The underlying idea is to point out the behavior of the standard FLC when the plant parameters are time varying. In addition, we demonstrate that the proposed scheme exhibits good transient and steady state responses, and is robust to load and parameter changes, and to Generation Rate Constraints (GRC), in a very wide range of operating conditions. The remaining of this paper is organized as following, In section 2 we briefly introduce the power system investigated and the related concepts. Section 3 describes the idea underlying the approach and the design procedure of the proposed controller. The simulation results that illustrate the behavior of our scheme, taking into account the parameter disturbances and the GRC are provided and compared in section 4. Finally, conclusions and recommendations based on simulation results are drawn in section 5.

1515

2 Power system model Power systems can be modeled by their power balance equations, linearized around the operating point. Since power systems are only exposed to small changes in load during their normal operation, a h e a r mode1 can be used to design LFC. We consider the same single-area nonreheat power system model reported in El] and [2] as shown in Fig. 1. The investigated system consists of a speed-governor, a turbine that produces mechanical power, PE,and the rotating mass (or power system). In steady state, P, is balanced by the electrical power output, P,, of the generator. Any imbalance between Pg and P, produces accelerating power and thereby creates an incremental change in frequency, A$ Each parameter is determined as following [2]: - integral control gain - speed regulation due to = 2.4 [Hz.p.u./MW] govemor action T, - governor time constant = 0.08 [sec] T, - turbine time constant = 0.3 [sec] K, - electric system static gain = 120 [Hz.p.u./MW] T, - electric time constant = 20 [sec] bf - frequency deviation [Hz p.u.1 APL - load demand change [p.u.MW] AP, - incremental generation change [p.u.MW] A X E - incremental change in governor [p.u.MW] valve position APc - incremental change in the speed Ip.u.MW] changer position

K; R

(7) such that the closed loop eigenvalues become insensitive to variations of the system parameters {2].

3.1 FLC schemes

-1/q

-

wt

(1)

0

0

1/T,

-pg-pg (3 1

B = [O 0 l/Tg

Or

It is we11 known that FLC consists of three main stages, namely the fuzzification interface, the inference rules engine

and the defiwification interface. The reader is refereed to [13-151 for details on FLC design theories. For LFC the process operator is assumed to respond to variables error (e) and change of error (ce) [%lo].

where:

0

(4)

. Similarly to the controller shown in fig. 1, the variable error is equal to the real power system frequency deviation (AA. The frequency deviation, AA is the difference between the nominal or scheduled power system frequency f &)and the real power system frequency Ifl.

In literature, the FLC that responds to the system error and its change is called standard or proportional-derivative FLC (PD-FLC) [14]. Taking the scaling gains into account, the global function of the PD-FLC output signal can be written as following [13]: APC = Ftne

F=[-Kp/Tp 0 0 c'= [l 0 0 01

k(t)

Assume that.the supplementary controller of the investigated power system is assured by a FLC of the same type as [SI or ~91.

y(r) = Cx(0

A=

-

3 Design of adaptive FLC gain scheduling

expressed as following:

+

The time constant, T,, in the governor model is quite small and often it is neglected, which means that the govemor is assumed to act very fast compared to the change in speed or frequency [ 171. This leads to a second order dynamic power system model. But for accuracy and comparison purposes, Tg is considered. In linear control system theory, it is required that a state feedback controller APC =

The investigated model consists of a tandem-compound single nonreheat turbine. The state space model can be

xtt) = Ax(t) + BU(t) FAPL

Fig.1: Bloc diagram of the investigated power system with integral controller

op (6)

e o 9

%ect.Ck)l

18)

where ne and nueare the error and the change of error scaling gains, respectively, and F is a fuzzy nonlinear function. It can be seen from (8) that PD-FLC is dependant to its inputs scaling gains.

1516

Table 1. Fuzzy inference rules for the PD-FLC

The block diagram of the PD-FLC used for the investigated power system is shown in Fig.2, where n, is the output control gain.

A label set corresponding to the linguistic variables of the input control signals, efi) and ce(k), with a sampling time of 0.01. sec is as follows: L(e, ce) = {NB, NM, ZE, PM, PB} where, NB - Negative Big, NM - Negative Medium, ZE Zero, PM - Positive Medium and PB - Positive Big. The membership fbnctions (MFs) for the input variables are shown in Fig.3. The universe of discourse of each control variable (inputs/output) is normalised from -1 to 1. The output variable uses the singleton MFs labelled as follows: L(u) = {-1.0, -0.5, 0.0, 0.5. 1.0). The center ofgravity (COG) defuzzification method is used to compute the output control (21) as following:

i

where wi is the grade of ith output MF, yi is the output label for the value contributed by the ith MF, and m is the number of contributions from the rules. The associated fuzzy matrices are shown in table 1. The fourth-order Runge-Kutta method is used to compute the output (AA of the investigated power system. The performance of the proposed PD-FLC is evaluated by the integral of the time multiplied by the absolute value of the error criterion (ITAE) defined as following:

where the stop time (Tstup) corresponds to the simulation period.

Fig. 2. Block diagram of a PD-FLC

ZE

PM

PB

-0.5 0 +0.5 +1.0 Fig.3 MFs for the control inputs variables -1.0

NB NM ZE ZE

ZE NM

NM ZE PM PM

PM NM

ZE PM PB PB

P3 ZE ZE PM PB PB

A system designed by the ITAE criterion is known to exhibit small maximum overshot (OS) and few oscillations [6]. In view of this, for a step load change A P L = 0.01 p.u.MW during the nominal operating regime, the optimal scaling gains were found ne = 5.00, ncp = 2.20 and n,,= 0.1865.

(9)

2Y,

NM

ce@)

NB NM ZE PM PB

NM NE NB NM PM ZE

3.2 Fuzzy Gain scheduling control strategy

u=n, '

NB

eo NB NB

Recall that the FLC designed in the previous sub-section is a fixed gain PD-FLC. Its performance has been proven to be more robust compared to that of a PI controller [$, 91. However, the common drawback of fixed gain controllers is that their performances deteriorate as a result of changes in system operating conditions [5]. In order to maintain the quality optimal or near the optimal operating condition, it is highly recommended to adapt the gains according to the online system information.

On the other hand, it is known that the performance of the FLC is affected by the variables (inpukdoutputs) scaling gains, the types and the shapes of the corresponding membership functions and the inference rules. However, as stated in [14], [l5] and [16], the change in the scaIing gains has a very significant influence on the performance of the resulting FLC, as it can be seen in (8). Therefore, they are the convenient tuning parameters for the optimization of FLCs [14, 151. The calibration of FLC scaling gains is still under investigation. This is due to the nonlinear relations between the input and the output variables of FLC. So far, the main approaches are the heuristic tuning based on human knowledge of the controlled system [ 161. Neural network has been used in [ 111 to adapt the element of a gain matrix by monitoring three parameters of power systems. For every value of the monitored parameters, a training set of patterns are generated based on the design of an optimal controller. Neural network requires a large number of patterns and the network training procedure is usually long and slow. In view of this, [5] proposed a Sugeno type fuzzy inference system to adapt the gains of a PI controller by monitoring the same set of parameters as in [I 11. Since the adaptation is based on the optimal gains of a PI controller, the responses obtained in nominal regime are identical to those of a conventional PI controller, In addition, Talaq [5] did not consider the GRC effect.

1517

In view of this, a new adaptive method for the input scaling gains of a PD-FLC is proposed in this paper. Our gain scheduling FLC (GS-FLC) aims to point out the behavior of the FLC scaling gains when the system parameters are time varying. In other words, we aim to deduce relations, even nonlinear ones, between the parameters (R, Tg, T,,T,, K,,) of the system and the scaling gains. The results obtained can be used to generate adaptive rules for the FLC scaling gains according to various operating conditions of the system, through a classical monitoring of the parameters. Therefore, the scaling gains must be determined according to the prefixed performance indicator defined in (10). Consequently, two fuzzy based LFC are proposed in this work, The fust one is the main PD-FLC with fixed gains, described in the previous sub-section. The second one, also a FLC, automatically adjusts the scaling gains of the main PDFLC according to monitored parameter. Fig. 4 shows the block diagram for the proposed controller (GS-FLC). The proposed scheme requires fewer training patterns and, as we will see, its design is simple. In addition, only the most sensitive parameters need to be monitored, Table 2 shows the off-line values of the PD-FLC scaling gains for 10% alternative parameter disturbances in the range of 130% fiom their nominal values. It can be seen fiom table 2 that the scaling gains are more sensitive to the system static gain (KJ perturbations than to any other parameter.

Therefore, according to the proposed scheme, K, is the parameter to monitor in order to generate the on-line fuzzy tuning rules for ne and rice. The parameter Kp depends on the load frequency characteristic, D [p.u./Hz] as following: Kp = I/D

(1 11

The parameter D is expressed as percent change in load divided by percent change in frequency. So, by simply monitoring the power system frequency and load deviations, the on-line value of D can be deduced [171.

3.3 Fuzzy inference rules for n, and nCe The rules for n, and n,., are determined as follows:

%e

=f('J

(13)

From table 2, it can be seen that (12) and (13) are nonlinear functions of Kp. Therefore, it is very difficult, even approximately, to find their mathematical forms. In our approach, fuzzy logic reasoning is used to adjust the values of ne and U,, for every on-line monitored value of Kp, To do so, Kp must be expressed in a fuzzy (linguistic) form by means of MFs. So, each monitored value of Kp is divided into 7 fuzzy set, labelled as L(K,) = (NE, NM, NS, ZE, PS, PM, PE); where NS - Negative Small and PS - Positive Small. Fig. 5 shows the MFs €or the variable K,. A Takagi single input multi outputs (SIMO) type is used to generate the fuzzy rules for ne and n,, as folIowing:

GS-FLC

IF Kp is A , THEN{ ne is

and n, is Gz,~)

(1 4)

where K, is the monitored parameter at a particular operating condition, A, are fuzzy sets of the ith rule, and GI,,,GIT1are optimal scaling gains for ne and rice, respectively.

I

Scheduler

I

It is assumed that Kp vanes within a prescribed universe of discourse [Kpmn,Kpm].

Table 3 shows the fuzzy inference rules used to determine the optimal values of the gains based on the results of table 2. Table 2: Off-line scaling gain values during parameters disturbance

NE

NM

NS

ZE

PS

PM

96

108

120

132

144

PB

%

T, Tt T, 8.0 5.20 5-10 5.22 7.0 5.18 5.09 5.13 5.5 5.15 5.05 5.08 5.0 5.00 5.00 5.00 4.6 5.14 4.90 5.11 3.9 5.20 4.48 5.12 3.8 5.20 4.47 5.13

- K, -30 -20 -10 0 10

20 30

R 5 5 5 5 5 5 5

I(p T, 3.15 2.10 2.80 2.16 2.40 2.20 2.20 2.20 2.10 2.30 1.85 2.32

Tt

1.81 1.95 2.09 2.20 2.30 2.39 1.80 2.40 2.47

Tg 2.12 2.14 2.18 2.20 2.28 2.30 2.45

R 2.40 2.35 2.25 2.20 2.15 2.10 2.05

84

156

Kp

Fig. 5 : Membership functions for Kp

Table 3. Fuzzy matrix rules for ne and %c ISp n,. U,.,

1518

NG 1.0

NM 0.6

NP 0.2

ZR 0.0

PP -0.2

PM -0.6

PG -1.0

4 Simulation results To verify the effectiveness of the proposed controller, suppose that the investigated power system is subjected to a sudden step load change, Fur comparison purpose with other control strategies, we consider the same step load change magnitude as reported in [1-9]; that is, APL = 0.01 p.u. MW. The maximum frequency deviation due to APL occurs at exactly the same time for different values of APL. This indicates that the time of maximum frequency deviation is not a function of the disturbance magnitude [17]. Fig 6 shows the results of the frequency deviation, AA at the nominal operating regime. The results of the VSS designed in [4] and that of the PD-FLC, previously designed, are also shown for comparison purpose.

Now assume the same parameter disturbances as reported in [Z], i.e. simultaneous changes of 50% for K,,, T, and 20% for T,, TI, R. Fig. 7 plots the response of the frequency deviation, AJ under this off-nominal operating conditions. The responses obtained by the adaptive PI controller (MI) proposed in [ 2 ] and by the PD-FLC are also plotted in the same figure for comparison purpose.

PQ-FLC >

-?a0

.,

GS-FLC

.

05

I

I

I

1

15

2

Time [ s e c ]

2.5

3

Fig.7: The frequency deviation for 0.01 p.u. MW load change under parameter disturbances without GRC.

-

-1

Next, assume a +50% simultaneous change of all parameters (R, T,. T,, T, and Kp). Fig, 8 shows the response of the frequency deviation of the proposed controIler (GSFLC) and that of the PD-FLC and the MI. In practice, a maximum limit on rate of change in the generating power of a steam turbine is imposed to avoid a wide variation in process variables (such as temperature and pressure) for the safety of equipment. Previous analysis [ 1,2, 9, 121 indicate that in the presence of the Generation Rate Constraint (GRC), the dynamic response of the system experiences Iarger overshoot and longer stabilizing time, compared to the case without GRC.

I

a5

1

Time lsecl

0.5

1

1.5

2

2.5

Time [sec]

3

3.5

4

4.5

5

Fig. 6: Frequency deviation A f of a typical single-area power system for 0.01 p.u.MW load change at nominal regime without GRC.

2

2.5

I

Fig.8: The fiequency deviation for 0.01 p.u. MW load change for 50% parameter disturbances without GRC. Hence, if the parameters of the controller are not adjusted properly, the system may become unstable under GRC. A GRC is taken into account in the plant shown in Fig. 1 by adding limiters tu the turbine, as shown in fig 1. A GRC of 10% p.u. MW / min is usually applied to typical nonreheat steam turbines 12, 121, i.e.

AP'

'-0

1.5

5 O.lp.u.MW/min

(16)

For diesel-electric generator, for example, the typical value of GRC is set to 0.02Xp.u.MW/s [9]. As pointed out in [ 121, the earlier studies adopted a strict GRC of 0.00 17p.u.MWis. In practice, the boiler can afford to keep its pressure to be constant for a long period of time. Thus, it is possible to increase the GRC up to 1.2 p.u./min of normal power during the first tens of seconds. Fig. 9 shows the response of the system with and without a CRC of 0.002p.u.MW/s. It is observed from Figs 6-8 that the responses of Af with our proposed controller are less oscillatory and settle faster

1519

[3] C.E. Fosha and 0.1. Elgerd, “The megawatt frequency

141

[5]

[6] 0

0.5

1

1.5

Time [sec]

2

2.5

3

Fig.9: Frequency deviation of the proposed controller €or 0.0lp.u. MW load change at nominal regime with and without GRC than those obtained by the PD-FLC, the APl controller and the VSS controIler, in a very wide range of operating conditions, when only Icp is monitored. In addition, the proposed controller still yields good control performance when GRC is applied to the plant turbine. The performance of the proposed controller can be improved by monitoring more than one system parameter.

[7] 181

[9]

[lo]

5 Conclusions In this paper, a new method to adapt the scaling gains of a fuzzy controIler for load - fiequency control have been used to damp the power system fiequency oscillations and to track i t s error to zero in steady state. A simple on-line monitoring of the system static gain enables the easy implementation of the proposed controller. Extensive digital siInuIations for a typical single-area nonreheat power system, taking into account the generation rate constraints, have verified the effectiveness of our scheme over the conventional variable-structure system, the conventional adaptive P1 controller and the standard fuzzy controller, in a very wide range of operating conditions. Despite the promising results of the proposed controller, its performance can be improved by including other parameters in the monitoring and gain scheduling mechanism.

[ll]

[12]

[I31

[14] [15]

References Y. Wang, R. Zhoii and C. Wen, “New Robust Adaptive Load-Frequency Control with system parametric uncertainties,” IEE Proc. Generation, Distribution and Transmission, vol. 14 1, May 1994, pp. 184-1 90. C.T. Pan and C.M. Lian, “An adaptive controller for 121 power system Load - Frequency Control,” IEEE Trans. Power Systems, vol. 4, Feb. 1989, pp. 122-128. [l]

[16]

[17]

control problem: a new approach via optima1 control theory,” IEEE Trans. Power Apparat2rs and Systems, vol. PAS-89(4), April 1970, pp. 563-577. N.N. Bengiamin and W.C. Chan, “Variable structure control of electric power generation,” IEEE TramPower Apparahrs and Systems, vol. 10, 1982 pp. 376-380. J. Talaq and F. Al-Basri, “Adaptive fuzzy gain scheduling for load frequency control,” IEEE Trans. Power Systems, vol. 14, Feb. 1999, pp. 145-150. E. Yesil, M. Guzelkaya and 1. Eksin, “Self tuning fuzzy PID type load and frequency controller,” Energy Conversion and Mmagement, vol. 45, 2004, pp. 377390. C.S. Chang and W. Fu, “Area load-frequency control using gain scheduling of PI controllers. EZectric Power Systems Research,” vol. 42, 1997, pp. 145-1 52. C.S. lndulkar and B. Raj, “Application of h z z y controller to automatic generation control,” Electricul Machines and Power Systems, vol. 23, 1995, pp. 209220. Y.L. Karnavas and D.P. Papadopoulos, “AGC for autonomous power system using combined intelligent techniques,” Electric Power Systems Research, vol. 62, 2002, pp. 225-239. ‘ G.A. Chown and R.C. Hartman, “Design and experiment with a fuzzy controller for automatic generation control (AGC),” IEEE Trans. Power Systems, vol. 13, Aug: 1998, pp. 965-970. M. Djukanovic et al., (+Conceptual development of optimal load frequency control using artificial neural networks and fuzzy set theory,” International Journal of Engineering intelligent Systems for Electrical Engineering Br Communication, vol. 3, 1995, pp. 95108. Y.-H. Moon et al, “Extended integral control for load frequency control with consideration of generation-rate constraints,” Electrical Power and Energy Systems, vol. 24,2002, pp. 263-269. L.-X. Wang, A cozrrse in fuzzy Systems and control, New Jersey: Prentice Hall, 1997. K.M. Passino and S. Yourkovich, Fuzzy Control, Menlo Park, California: Addison Wesley Longman, 1998. H.-X. Li and H.B. Gatland, “Conventional fuzzy control and its enhancement,” IEEE Trans. Systems, Man and Cybernetics - Part B: Cybernetics, vol. 26, Oct. 1996, pp. 791-797. S. Ouattara, P. Loslever and T.M. Guerra, “Towards a methodology for selecting good scaling factors for a fbzzy controller,” Fuzzy Sets and Systems, vol. 83, 1996, pp. 2 7 4 2 . P.M. Anderson, Power System Protection, New York, New York: IEEE Press, 1999

I

1520