optimal neuro-fuzzy external controller for a statcom in

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Optimal Neuro-Fuzzy External Controller for a STATCOM in the Optimal Neuro-Fuzzy External Controller for a STATCOM in the

12-Bus Benchmark Power System 12-Bus Benchmark Power System

Salman Mohagheghi

Ganesh K. Venayagamoorthy Missouri University of Science and Technology

Ronald G. Harley

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Recommended Citation Recommended Citation S. Mohagheghi et al., "Optimal Neuro-Fuzzy External Controller for a STATCOM in the 12-Bus Benchmark Power System," IEEE Transactions on Power Delivery, Institute of Electrical and Electronics Engineers (IEEE), Jan 2007. The definitive version is available at https://doi.org/10.1109/TPWRD.2007.905837

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https://doi.org/10.1109/TPWRD.2007.905837

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2548 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 4, OCTOBER 2007

Optimal Neuro-Fuzzy External Controller for aSTATCOM in the 12-Bus Benchmark Power System

Salman Mohagheghi, Student Member, IEEE, Ganesh Kumar Venayagamoorthy, Senior Member, IEEE, andRonald G. Harley, Fellow, IEEE

Abstract—An optimal neuro-fuzzy external controller is de-signed in this paper for a static compensator (STATCOM) inthe 12-bus benchmark power system. The controller provides anauxiliary reference signal for the STATCOM in such a way that itimproves the damping of the rotor speed deviations of its neigh-boring generators. A Mamdani fuzzy rule base constitutes thecore of the controller. A heuristic dynamic programming-basedapproach is used to further train the controller and enable it toprovide nonlinear optimal control at different operating condi-tions of the power system. Simulation results are provided thatindicate the proposed neuro-fuzzy external controller is moreeffective than a linear external controller for damping out thespeed deviations of the generators. In addition, the two controllersare compared in terms of the control effort generated by eachone during various disturbances and the proposed neuro-fuzzycontroller proves to be more effective with smaller control effort.

Index Terms—Adaptive critic designs (ACDs), neuro-fuzzy sys-tems, optimal control, static compensator (STATCOM), supervi-sory level control.

I. INTRODUCTION

STATIC COMPENSATORs (STATCOMs) are power elec-tronics-based flexible ac transmission system (FACTS)

devices that are connected in parallel to the power network andcan control the voltage at the point of common coupling (PCC)[1]. Regulating the voltage at the PCC during slow changes tothe power system and/or controlling the active/reactive powerexchange with the network are some of the most commonmain control objectives for this device [1], [2]. However, manyresearchers have investigated the possibility of enhancing thedamping capabilities of the STATCOM by providing an externaladditional control loop that sends an auxiliary control signal tothe STATCOM in order to control it from a supervisory level.

Manuscript received August 8, 2006; revised January 16, 2007. This work wassupported in part by the National Science Foundation (NSF), USA, under GrantsECS 0400657 and ECS 0348221, and in part by the Duke Power Company,Charlotte, NC USA. Paper no. TPWRD-00465-2006.

S. Mohagheghi is with the Intelligent Power Infrastructure Consortium(IPIC), School of Electrical and Computer Engineering, Georgia Institute ofTechnology, Atlanta, GA 30332-0250 USA (e-mail: [email protected]).

G. K. Venayagamoorthy is with the Real-Time Power and Intelligent SystemsLaboratory, Department of Electrical and Computer Engineering, University ofMissouri-Rolla, Rolla, MO 65409-0249 USA (e-mail: [email protected]).

R. G. Harley is with the Intelligent Power Infrastructure Consortium(IPIC), School of Electrical and Computer Engineering, Georgia Institute ofTechnology, Atlanta, GA 30332-0250 USA and also with the University ofKwaZulu-Natal, Durban 4041, South Africa (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2007.905837

Most of these proposed external controllers employ a linearcontrol scheme, in the form of a simple proportional gain or aPI controller. Hingorani and Gyugyi [1] proposed a PI-basedexternal control structure for the STATCOM that enables it toincrease the damping of the power system. Patil et al. [3] de-signed a linear controller that provides auxiliary reference sig-nals for the line voltage control loop of a STATCOM connectedto a single machine infinite bus. By applying this auxiliary signalto the line voltage reference of the STATCOM, it is able to dampout the torsional oscillations in the power system more effec-tively. Also, Mathur and Karma [2] designed a linear externalcontroller for a STATCOM to improve the damping of the lowfrequency power oscillations in the power system.

The inherent disadvantage of the linear external controlschemes, i.e., being dependent on the operating conditions ofthe power system, is not as critical for the STATCOM externalcontrol as it is in the case of its internal controller. This isdue to the fact that the external controller does not normallyhave a role in the main quasi steady state control objective ofthe STATCOM. Rather, it is designed to improve the dampingcapabilities of the STATCOM during the transients and/or dy-namic disturbances. However, the efficacy of the linear externalcontroller can still be affected by a change in the operatingconditions of the power system or its topology. Moreover, asthe complexities of the power system to which the STATCOMis connected increases, linear control schemes become lessefficient in achieving the desired supervisory level controlobjectives.

Some external controllers have been proposed that incorpo-rate nonlinear or intelligent control schemes. Farsangi et al. [4]designed a robust controller to improve the transient sta-bility of a 4-bus 2-generator power system. Yixin et al. [5] de-signed a fixed structure fuzzy logic-based external controller fordamping out the inter-area oscillations in a two-area multima-chine power system. Qu and Chen [6] reported the successfulapplication of a fuzzy logic-based external controller, with afixed structure, for a STATCOM in a similar application. How-ever, these nonlinear control schemes have some disadvantagesassociated with them as well. Any nonlinear external controlscheme requires a mathematical model of the power system,which is tedious to derive. On the other hand, fuzzy logic-basedexternal controllers with fixed parameters lose their efficacy asthe dimensions of the power system increases, since there isno guarantee that a heuristic rule base, derived according to ahuman expert, can provide an optimal performance.

The powerful and well established theory of optimal controland dynamic programming can be used as an alternative. While

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MOHAGHEGHI et al.: OPTIMAL NEURO-FUZZY EXTERNAL CONTROLLER 2549

mathematically proven to provide an optimal control policy, thistechnique has its own disadvantages. Solving the dynamic pro-gramming algorithm in most of the cases is not feasible. Evena numerical solution requires overwhelming computational ef-forts, which increases exponentially as the size of the problemincreases (curse of dimensionality). These restrictive conditionslead the solution to a suboptimal control scheme with limitedlook-ahead policies [7]. The complexity level is even further ex-acerbated when moving from finite horizon to infinite horizonproblems, while also considering the stochastic effects, modelimperfections and the presence of the external disturbances.

Adaptive critic designs (ACD)-based controllers [8] can over-come the previously mentioned problems. These are powerfultechniques designed to perform approximate dynamic program-ming (ADP) in the presence of noise and uncertainties, even innon-stationary cases and provide optimal control over the in-finite horizon of the problem [8]. Such controllers do not needprior information of the plant to be controlled and can be trainedonline without any large amount of offline data.

This paper uses the ACD theory to implement an optimalneural network-based fuzzy (neuro-fuzzy) external controllerfor a STATCOM connected to the 12-bus benchmark powersystem [15]. The proposed controller uses the action depen-dent heuristic dynamic programming (ADHDP) method whichis a member of the ACD family, in order to provide nonlinearnear-optimal control.

Section II summarizes some of the key concepts behindACD-based controllers. The structure of the multimachinepower system and the conventional linear external controlscheme, used as the basis of comparison with the proposedneuro-fuzzy, appear in Section III of this paper. The structureof the proposed STATCOM neuro-fuzzy external controller isexplained in Section IV. Section V provides the details of thetraining process required for the proposed controller. Simula-tion results are provided in Section VI in order to compare theeffectiveness of the proposed neuro-fuzzy external controllerwith that of the conventional external controller during largescale disturbances. Some practical considerations are discussedin Section VII. Finally, the concluding remarks are given inSection VIII.

II. ADAPTIVE CRITIC DESIGNS

ACDs were first introduced by Werbos in [9] and later in [10],and by Widrow in the early 1970s [11]. Werbos later on pro-posed a family of ADP designs [12]. These are neural network-based techniques capable of optimizing a measure of utility orgoal satisfaction, over multiple time periods into the future, ina nonlinear environment under conditions of noise and uncer-tainty; in other words they perform maximization/minimizationof a predefined utility function over time [13], [14].

A utility function along with an appropriate choice ofa discount factor should be defined for the ACD controller. Ateach time step , plant outputs (a set of measured variables)are fed into the controller, which in turn generates a policy (con-trol signal ) in a way that it optimizes the expected valueof a user-defined utility function over the finite/infinite horizontime of the problem, which is known as the cost-to-go function

given by Bellman’s equation of dynamic programming [13]as follows:

(1)

where is the utility function and is a discount factor forfinite/infinite horizon problems . A discount factorof zero uses the present value of the utility function as the opti-mization objective (same as the minimization of one step aheaderror), while a discount factor of unity considers all the futurevalues of the utility function equally important and is most suit-able for the finite/infinite horizon problems.

The critic neural network accomplishes the task of dynamicprogramming by approximating the true cost-to-go functionwith no prior knowledge of the system. Moreover, it avoids thecurse of dimensionality that occurs in some cases of classicaldynamic programming-based optimal control [13].

Essentially, ACD-based controllers are based on three dif-ferent mathematical theories: approximate dynamic program-ming, optimal control and reinforcement learning. Two majorcategories of the ACD family include the model-based ACD de-signs, where a model of the plant to be controlled is requiredin order to train the controller, and the Action Dependent ACD(ADACD) designs, which is a model free approach. The ActionDependent HDP-based (ADHDP) ACD neuro-fuzzy controllerproposed in this paper includes two different parts:

• Critic network; a neural network trained to approximate thecost-to-go function required for optimization;

• Fuzzy logic controller; which functions as a controller andis trained to provide the near-optimal control signals to theSTATCOM, resulting in minimization/maximization of thefunction over the time horizon of the problem.

III. STATCOM IN THE 12-BUS BENCHMARK POWER SYSTEM

Fig. 1 illustrates the schematic diagram of the 12-bus powersystem with a STATCOM. The power system is a 12-bus3-generator network that is designed for evaluating the ef-fects of FACTS devices at the transmission level [15]. Theuncompensated system has low voltages at buses 4 and 5 [15].Preliminary simulation results by the authors showed thatinstalling a STATCOM at bus 4 can drastically improve thevoltage profile of the whole network [17], [24]. The detailsof the STATCOM internal control structure is provided in theAppendix.

A. STATCOM External Control

The external controller provides an auxiliary control for thereference signal of the line voltage controller (Fig. 1).The control objective of the external controller is to provideadditional damping for the two generators neighboring theSTATCOM, i.e., generators 3 and 4. Generator 2 is close tothe infinite bus and the simulation results indicate that it is notsignificantly affected by the STATCOM.

It is known that an active Var compensator with suitable in-ternal/external controller can improve the dynamic stability ofthe power system it is connected to [16]. In its simplest form,


Fig. 1. Schematic diagram of the 12-bus power system with a STATCOM.

this can be a bang-bang control scheme, where the compen-sator injects/withdraws reactive power into the network in re-sponse to the oscillations in the active power (or load angle).During the time that the transmission line active power and theload angle are increasing, reactive power injection into the net-work causes an increase in the PCC voltage which opposes thechange in the active power and the load angle. Similarly, a de-crease in the active power and load angle can be compensatedby withdrawing reactive power from the network and thereforedecreasing the voltage [1]. Although this control procedure iseffective in damping out the line active power flow and theload angle variations, it causes voltage deviations at the net-work buses. However, during large scale disturbances, wheremaintaining the system stability is of the highest priority, thesevoltage fluctuations can be ignored. Although care should betaken that at none of the buses the voltage falls outside the ac-ceptable range, which is normally [0.95, 1.05] p.u.

Since measuring and analyzing the speed deviations of thegenerators are simpler and more practical than the line activepower flows or the generator load angles, speed deviations ofgenerators 3 and 4, and are selected, respectively, asthe main inputs to the external controller. An increase in theload angle of any generator (and therefore the active powerflow of the neighboring lines) is caused by an increase in thecorresponding generator’s speed with respect to the steady staterotor speed and vice versa.

B. Linear External Controller

Generators 3 and 4 have inertia constants of 3.0 and 5.0MW.s/MVA, respectively, which result in the local swingswith frequencies of approximately 1 Hz for generator 3 and0.8 Hz for generator 4. The fact that generators 3 and 4 oscil-late at different frequencies complicates the external controlscheme, since the auxiliary control signal which is suitablefor generator 3 for example, might at times exacerbate thedynamic oscillations of the rotor of generator 4 and vice versa.It was reported in [17] that a linear control scheme as shown inFig. 2 can improve the dynamic stability of the two generators.However, due to the nonlinear nature of the power system, theperformance of the linear external controller in Fig. 2 is widely

Fig. 2. Schematic diagram of the STATCOM linear external controller.

affected by a change in the power system configurations or theoperating conditions [17]. Nevertheless, the parameters of thecontroller are fine tuned at a single operating point in order togive the “best” overall performance.

C. Alternative Solution: Neuro-Fuzzy Systems

In the nonlinear non-stationary power system in Fig. 1, thelevel of complexity to establish a relationship between the in-puts (the auxiliary reference signal to the STATCOM) and theoutputs (rotor speed of the two generators and ) is too highfor a linear controller. This is specifically causing difficulty fora conventional control scheme due to the fact that the oscilla-tions on generators 3 and 4 are out of phase. This problem canbe solved by using an intelligent control scheme, in which thecontroller exerts a control action while watching its effect onthe overall performance of the power system. An ACD-basedneuro-fuzzy controller is an excellent candidate for such a con-trol scheme, since:

• the relatively low number of inputs and outputs allows thecreation of an effective fuzzy rule base for the controller;

• introduction of neural networks enables the controller toperform in a near-optimal way by evaluating the effects ofits control actions on the response of the power system, andupdating the controller parameters accordingly.

Applications of connectionist learning systems such as artifi-cial neural networks to adaptively adjust the parameters of fuzzysystems have been discussed in the literature [18]–[20]. In a typ-ical neuro-fuzzy system, the parameters of the fuzzy controller,such as the membership functions and the consequent rules, areconsidered as the synaptic weights of a connectionist learningsystem. Neural network-based learning techniques are then ap-plied in order to adjust these parameters based on the perfor-mance of the system. Fig. 3 illustrates the schematic diagramof the neuro-fuzzy controller for the STATCOM, with the fuzzymembership functions and the fuzzy min/max operators as thenonlinear activation functions of the neurons.

IV. ACD NEURO-FUZZY EXTERNAL CONTROLLER STRUCTURE

Fig. 4 shows the schematic diagram of the proposedSTATCOM neuro-fuzzy external controller. It is an adaptivecritic designs-based fuzzy controller which is capable ofproviding near optimal results in the presence of noise anduncertainty in a nonlinear system, such as the power systemshown in Fig. 1.

The entire system of Figs. 1–4 is simulated in the PSCAD/EMTDC environment. A simulation step size of 50 is se-


Fig. 3. Schematic diagram of the neuro-fuzzy external controller.

Fig. 4. Schematic diagram of the STATCOM ACD-based neuro-fuzzy externalcontroller.

lected, while the sampling time for training the controller is 2.0ms (500 Hz).

The plant in Fig. 4 consists of the multimachine power systemin Fig. 1, the STATCOM and the controller. The input tothe plant is the modulation index generated by the con-troller and its output is the vector of the speed deviationsof generators 3 and 4. The proposed external controller consistsof two main components: the neuro-fuzzy controller (Fig. 3)and a critic neural network, which is trained to approximate thecost-to-go function (Fig. 4).

A. Neuro-Fuzzy Controller

The heart of the neuro-fuzzy controller is the fuzzy inferencesystem. A zero order Takagi-Sugeno fuzzy model is used for im-plementing the controller, which is a special case of the Mam-dani model [19]. The input to the fuzzy controller is the vectorof the selected states of the power system as in (2)

(2)

TABLE INEURO-FUZZY CONTROLLER RULE BASE

The neuro-fuzzy controller in return generates a controlsignal , which is added to the line voltage reference ofthe local controller (Fig. 1). At steady state, the hasa line voltage reference of 1.0 p.u. Therefore, the output of theneuro-fuzzy controller is clamped at 0.05 p.u., such that thevoltage at bus 4 does not fall outside the acceptable range of[0.95, 1.05] p.u.

Five membership functions are considered in Fig. 3 for therotor speed deviations of each generator, which are associatedwith the fuzzy terms Negative Big, Negative Small, Zero, Posi-tive Small and Positive Big; while the output variable hasseven fuzzy membership functions associated with it, namelyNegative Big, Negative Medium, Negative Small, Zero, Posi-tive Small, Positive Medium, and Positive Big. The rule baseimplemented for the neuro-fuzzy controller is shown in Table I.

Gaussian membership functions are used for each fuzzy inputvariable. The membership degree of variable in the fuzzy set

can be expressed as [19]

(3)

where and are the corresponding center and the widthof the fuzzy set, respectively. Singleton fuzzy sets are assigned


to the fuzzy output variable, where the membership degree at acertain singleton point is unity, but zero otherwise

(4)

The Mamdani min-max method is employed for the fuzzy in-ference mechanism and the centroid method is applied for de-fuzzification of the fuzzy output variable [19]. Therefore, thecrisp output of the controller can be expressed as (5)

(5)

where is the firing strength of the rule.

B. Critic Network

The parameters of the neuro-fuzzy controller are derived insuch a way that it performs well over a range of operating con-ditions and during different faults. This is also partly ensuredby the inherent robustness of the fuzzy controller. However, theperformance is yet far from optimal and therefore, the controlleris further trained so that it can perform near-optimal control ofthe plant over the horizon of the problem. The coefficients of thefuzzy output variable, i.e., the singleton parameters are con-sidered to be the adaptive parameters of the fuzzy controller. Anadaptive critic designs-based approach is applied in order to pro-vide appropriate training signals for the neuro-fuzzy controller.A critic network is trained in order to learn the cost-to-go func-tion associated with the power system. In other words, it evalu-ates how well the neuro-fuzzy controller is doing from momentto moment. Once sufficiently trained, the critic network can inturn provide the appropriate training signal for the fuzzy con-troller.

The utility function for the critic network is comprised of twoterms (decomposed utility function)

(6)

where

(7)

(8)

The two terms are necessary because the rotors of genera-tors 3 and 4 have different swings and therefore, the STATCOMshould try to improve the performance of both generators at thesame time. The cost-to-go function estimated by the critic net-work is

(9)

This can be further simplified as

(10)

Fig. 5. Schematic diagram of the STATCOM critic network.

Two subcritic networks are therefore used, where each onelearns one part of the cost-to-go function. Utility function de-composition speeds up the process of critic network learning,since each subcritic is estimating a simpler function [21]. Fig. 5shows the schematic diagram of the critic network. It consistsof two separate multilayer perceptron (MLP) neural networks[22], with 10 neurons in the hidden layer of each one and thesame input from the Action network, i.e., the neuro-fuzzy con-troller. The hyperbolic tangent is used as the activation functionof the hidden neurons.

V. NEURO-FUZZY CONTROLLER TRAINING

A. Critic Network Training

A period of forced training is carried out for training thecritic network. During this stage, pseudorandom binary signal(PRBS) disturbances are added to the STATCOM voltage refer-ence from an external source (switches and in Fig. 6are in position 1).

The PRBS disturbance applied to the system should be gen-erated in such a way that it excites the natural frequencies of thepower system. The frequency of the PRBS disturbance is there-fore heuristically chosen as a combination of 0.5, 1 and 2 Hzwhich are close to the natural frequencies of the power system,with the total PRBS signal magnitude limited to 5% of thevalue of at steady state [27]. The neuro-fuzzy con-troller tries to force the plant to follow the reference by injectingthe required amount of reactive power into the network. The re-sultant deviations in the values of the power system states in (2)along with are now fed into the critic network, whichgoes through backpropagation training to update its synapticweight matrices. The training procedure for the critic networkis discussed in more detail in the authors’ previous work [23].

The critic network training starts with a low discount factorof 0.2, which is gradually increased to 0.8 as the training pro-ceeds. This will help the weights of the critic network convergefaster [17]. Moreover, an annealing learning rate scheme is usedin which the critic network training starts with a learning rateof about 0.1, and gradually decreases to a value of 0.005. Thisensures that during the initial training stages the critic network


Fig. 6. STATCOM neuro-fuzzy external controller training.

adapts itself to the plant dynamics quickly, but as the learningprocess continues, the critic network does not have drastic re-actions to sudden changes in the plant dynamics. In this way itdoes not forget the previously learned information. Critic net-work training is repeated at various operating conditions until areasonable accuracy is achieved.

B. Neuro-Fuzzy Controller Training

The ACD-based neuro-fuzzy controller optimizes the overallcost over the time horizon of the problem [minimizing the func-tion in (9)] by providing an optimal control input to the plant.In order for the controller to be able to minimize the cost-to-gofunction over the horizon time of the problem, it should betrained with the following error signal:

(11)

where is the desired value for the cost-to-go function,which in the case of dealing with deviation signals is zero. Themean-squared error function in (12) is used as the error functionfor executing the backpropagation algorithm

(12)

A gradient descent learning algorithm is applied for adjustingthe values of the coefficients of the fuzzy output variable, i.e.,the singleton parameters , where each parameter is updated inthe negative direction of the gradient of the objective function

as follows:

(13)

where is the learning rate which is considered to be 0.005in this study. The partial derivative of the objective function

with respect to any parameter can be derived using the followingchain rule:

(14)

The first term on the right-hand side of (14) is equal toand the second term can be derived by backpropagating constant1.0 through the critic network [17]. The last term in (14) can alsobe simplified as follows:

(15)

In this study, only the singleton parameters of the neuro-fuzzy controller are updated. It is also possible to apply a fullupdating scheme where the parameters of the input member-ship functions in (3) are adaptively adjusted as well. However,a partial updating scheme is used here which considers all theparameters of the input fuzzy membership functions to be con-stant throughout the simulation. This approach is adopted sinceit is less computationally intensive. Moreover, the parameters ofthe input fuzzy sets are derived after closely studying the per-formance of the two generators during various natural faults ap-plied to the system.

The ACD neuro-fuzzy controller is trained by the cost func-tion defined in (9) using the update formula in (13) and (14),so that its output coefficients are adjusted for optimum per-formance. The neuro-fuzzy controller is trained online duringthe actual performance of the power system. At this stage theneuro-fuzzy controller is controlling the plant (switches and

in Fig. 6 are in position 2). Various faults and disturbancesare applied to the power network and the resultant error signalderived in (11) is used for updating the parameters of theoutput fuzzy sets.


Fig. 7. Rotor speed deviations of generator 3 during case study 1.


VI. SIMULATION RESULTS

Several tests are now carried out in order to evaluate the ef-fectiveness of the proposed neuro-fuzzy external controller andcompare its performance with the linear external controller forthe STATCOM, as well as the case where the STATCOM has noexternal controllers.

A. Case Study 1: Short Circuit Along the Transmission Line3–4

A 100 ms three phase short circuit is now applied to themiddle of one of the parallel transmission lines connecting theSTATCOM to generator 3. Figs. 7 and 8 show the effectivenessof the proposed neuro-fuzzy controller in damping out the rotorspeed oscillations and indicate that the proposed controller man-ages to improve the dynamic damping of both generators, eventhough the rotors of the two machines have different, and op-posing at times, excursions.

B. Case Study 2: Short Circuit Along the Transmission Line7–8

With the transmission line 3–4 remaining disconnected afterthe fault is cleared, a 100 ms three phase short circuit is now ap-plied to the transmission line connecting buses 7 and 8. This sec-tion of the power system is relatively weak and sensitive to dis-


Fig. 10. Reactive power injected by the STATCOM during case study 2.

turbances. Fig. 9 illustrates the effectiveness of the neuro-fuzzyexternal controller in restoring the system back to the steadystate condition. It shows that the linear controller, which wastrained at a different operating condition, cannot respond ef-fectively to the rotor speed deviations of generator 4. Fig. 10emphasizes the fact that the STATCOM, externally controlledby the neuro-fuzzy controller, injects less initial reactive powerinto the network when responding to the fault. Simulation re-sults indicate that the STATCOM controlled by the neuro-fuzzycontroller reduces the peak reactive power injection by almost14 MVar. Based on a typical conservative price of U.S.$50/kVar,this reduction results in approximate savings of U.S.$700 000.

It should be noted that during the normal steady state opera-tion of the power system the STATCOM already injects about290 MVar in order to maintain the desired voltage profile acrossthe power system. It is normally customary for a STATCOM tohave a safety margin in terms of reactive power, so that it is ableto respond to different loading conditions and/or disturbances.Clearly the amount of this safety margin is case dependent andis decided by the design engineers. The main objective of thispaper is to show that an intelligently controlled STATCOM isable to use less reactive power from the device safety marginin order to respond to different faults and improve the dynamicstability of the system. Fig. 10 clearly shows that a STATCOM


Fig. 11. Voltage at bus 4 in Fig. 1 during case study 2.

with 24% safety margin equipped with a neuro-fuzzy externalcontroller can respond well to the fault, whereas a STATCOMwith a linear external controller, even with 29% safety margin,cannot respond to the fault in the same manner.

Fig. 11 shows the voltage at bus 4 during the transient andit clearly shows that both external control schemes limit thevoltage within the acceptable range of 0.05 p.u. This voltagedeviation is normally allowed during dynamic and transient dis-turbances [1].

It should be noted that although the STATCOM external con-trol scheme proposed in this paper is effective in damping outthe line active power flow and the generator speed oscillationsduring disturbances, it causes temporary voltage deviations atthe network buses, specifically at bus 4 where the STATCOMis connected. However, during large scale disturbances, main-taining the system stability and improving the power systemdamping is normally a high priority, and as long as the voltagefluctuations that occur for a short duration of time are within theacceptable range of [0.95,1.05] p.u., there can be a tradeoff be-tween the rotor speed and the line voltage.

Examples of changing the line voltage reference (or the reac-tive power reference) of a shunt FACTS device during transientand dynamic disturbances has been shown for a STATCOM in[1], [2], and for a static var compensator (SVC) in [28].

C. Case Study 3: Transmission Line 2–5 Switch On/Off

In a different type of disturbance, the transmission line con-necting buses 2 and 5 is disconnected and is switched back intothe power system after 3 seconds. Fig. 12 shows the superi-ority of the proposed neuro-fuzzy external controller in dampingout the rotor speed deviations fast. Once again, Fig. 13 em-phasizes the fact that the neuro-fuzzy external controller re-duces the amount of three-phase reactive power injected by theSTATCOM and therefore its overall cost. Also, Fig. 14 illus-trates the voltage at the PCC (Fig. 1) during the fault.

D. Performance Measurement

In this section, the performance of the neuro-fuzzy externalcontroller is compared with the linear external controller and theuncompensated power system. A performance index is defined


Fig. 13. Reactive power injected by the STATCOM during case study 3.

Fig. 14. Voltage at bus 4 in Fig. 1 during case study 3.

for each case study 1–3 as in (16)

(16)


TABLE IIPERFORMANCE INDICES OF THE NEURO-FUZZY AND THE LINEAR

EXTERNAL CONTROLLERS FOR THE STATCOM

where represents the sample of the rotor speed de-viations of the generator and index represents the casestudy. During each fault/disturbance applied to the system, 100samples are taken from each rotor speed during the first 10 sof simulation. The overall performance index of each controlleris derived according to the performance indices , obtainedfrom various case studies, as in (17)

(17)

Table II summarizes the results. In the last row of the Table theoverall performance indices are normalized based on the overallperformance index of the uncompensated system. This showsthat the neuro-fuzzy controller improves the performance of thepower system by almost 40% during large scale disturbances.

VII. PRACTICAL CONSIDERATIONS

A. Hardware Implementation

The proposed ACD-based neuro-fuzzy controller can beimplemented on a digital signal processor (DSP) board. Ve-nayagamoorthy et al. [25], [27] have successfully implementeda neurocontroller on a turbogenerator. The authors have alsoreported successful implementation of a fuzzy controller fora STATCOM in a multimachine power system [26]. The con-troller, built on a DSP board, sends the control signals to thepower system which is implemented on a real-time digitalsimulator (RTDS).

B. Real-Time Development of the Neuro-Fuzzy Controller

Essentially, the training process of the fuzzy system is of thegreatest importance and delicacy. This is due to the fact that thetraining stages of the critic network can be conducted offline;however, the training process of the fuzzy controller should beexecuted online while it is controlling the plant.

In a real power system, applying the PRBS disturbances fortraining the neuro-fuzzy controller might not be desirable orpractical. In such cases, training data can be obtained from thenormal operation of the power system, as the network is exposedto natural changes to its operating condition and/or configura-tion, as well as possible large scale faults. Clearly, the critic net-work should be trained first. Once its weights have converged,the fuzzy controller can undergo training. In this way, the con-troller parameters will take a longer time to converge, but thiswill not cause any problems for the power system, since

• the initial parameters of the fuzzy controller (the member-ship function and the consequent parameters) are derived ina way that it stabilizes the power system. At worst case, thefuzzy controller acts as a nonlinear gain scheduling con-troller which is yet more effective than a PI controller [26].

• a critic network with its weights converged is guaranteedto provide optimal training signals to the controller [13].

It is possible in this case to define an adaptive learning rateparameter for the controller, which is increased when a changeoccurs in the value of its inputs and is a small number when theinput values are almost constant. This prevents the controllerweights/parameters from forgetting the previously learned in-formation.

C. Installment Cost

Implementing a neuro-fuzzy controller like the one proposedin this paper requires a larger amount of capital investment com-pared to a PI controller. However, it should be noted that theinstallment cost of a DSP-based neuro-fuzzy controller for aSTATCOM is negligible compared to the capital investment re-quired for the FACTS device itself.

Moreover, the neuro-fuzzy controller improves the overallperformance of the system by reducing the amount of reactivepower injected by the STATCOM, which in turn reduces the rat-ings of the inverter switches and hence its cost.

VIII. CONCLUSIONS

A near-optimal neuro-fuzzy controller has been designed inthis paper for external control of a STATCOM connected to the12-bus benchmark power system. Based on the speed deviationson the generators neighboring the STATCOM, the external con-troller generates an auxiliary control signal, which is appliedto the line voltage reference signal of the STATCOM in orderto improve the dynamic stability of the power system duringlarge scale disturbances. Using adaptive critic designs theory,the neuro-fuzzy controller is able to provide nonlinear near-op-timal control over the infinite horizon of the problem, with noneed to any mathematical model of the power system or theSTATCOM. Reinforcement learning is applied for training theexternal controller, which makes it largely insensitive to the sizeof the power system.

Simulation results have been provided that indicate that theproposed neuro-fuzzy external controller is more effective thana linear-based technique for damping the speed deviations of thegenerators neighboring the STATCOM. Moreover, it achievesthis with smaller amounts of reactive power injected by theSTATCOM as a result of the faults, which in turn could lead


Fig. 15. STATCOM internal control scheme.

to a smaller STATCOM size and therefore savings on the costof the FACTS device if it were to have a secondary function ofproviding system damping.

APPENDIX

STATCOM INTERNAL CONTROLLER

The STATCOM considered in this study is a voltage sourceinverter (VSI) type. It is essentially a voltage source inverter thatis connected to the power system through a step-up transformer.The internal controller of the STATCOM is shown in Fig. 15. Itconsists of two PI controllers for regulating the line voltage atthe PCC and the dc link voltage inside the STATCOM

. The deviations in the line voltage and the dc linkvoltage are passed through these two separate PI con-trollers in order to determine the inverter modulation indexand the phase shift , respectively. These signals are fed intothe PWM module that in turn generates the firing pulses appliedto the STATCOM switches. This control scheme was found tobe effective in responding to small scale as well as large scaledisturbances in the power system.

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Salman Mohagheghi (S’99) received the B.Eng. de-gree in power electrical engineering from the Univer-sity of Tehran, Tehran, Iran, in 1999, the M.Sc. de-gree from Sharif University of Technology, Tehran,in 2001, and the Ph.D. degree in power electrical en-gineering from the Georgia Institute of Technology,Atlanta, GA, in 2006.

Currently,heisaPostdoctoralFellowconductingre-search at the Georgia Institute of Technology. His re-search focuses on wide-area control in power systems,protective relaying, and distributed state estimation.


Ganesh Kumar Venayagamoorthy(S’91–M’97–SM’02) received the B.Eng. (Hons.)degree in electrical and electronics engineering fromthe Abubakar Tafawa Balewa University, Bauchi,Nigeria, in 1994, and the M.Sc.Eng. and Ph.D.degrees in electrical engineering from the Universityof Natal, Durban, South Africa, in 1999 and 2002,respectively.

He was a Senior Lecturer at the Durban Instituteof Technology, Durban, South Africa, prior to joiningthe University of Missouri-Rolla (UMR), Rolla, MO,

in 2002. Currently, he is an Associate Professor of Electrical and Computerand the Director of the Real-Time Power and Intelligent Systems Laboratory atUMR. His research interests are in power systems stability and control, com-putational intelligence, alternatives sources of energy, and evolvable hardware.He has published about 200 papers in refereed journals and international con-ference proceedings.

Dr. Venayagamoorthy is a recipient of the following awards: a 2004 NationalScience Foundation CAREER Award, the 2006 IEEE Power Engineering So-ciety Walter Fee Outstanding Young Engineer Award, the 2006 IEEE St. LouisSection Outstanding Section Member Award, the 2005 IEEE Industry Applica-tions Society (IAS) Outstanding Young Member Award, the 2005 South AfricanInstitute of Electrical Engineers (SAIEE) Young Achievers Award, the 2004IEEE St. Louis Section Outstanding Young Engineer Award, the 2003 Inter-national Neural Network Society (INNS) Young Investigator Award, a 2001IEEE Computational Intelligence Society (CIS) Walter Karplus Summer Re-search Award, and five prize papers with the IEEE Industry IAS and IEEE CIS.He is also a recipient of the 2006 UMR School of Engineering Teaching Excel-lence Award and the 2005 UMR Faculty Excellence Award. He is an AssociateEditor of the IEEE TRANSACTIONS ON NEURAL NETWORKS; senior member ofthe SAIEE; a member of INNS; the Institute of Engineering and Technology,U.K.; and the American Society for Engineering Education (ASEE). He is cur-rently the IEEE St. Louis CIS and IAS Chapter Chairs, the Chair of the TaskForce on Intelligent Control Systems, and the Secretary of the Intelligent Sys-tems subcommittee of the IEEE Power Engineering Society and the Chair of theIEEE CIS Task Force on Power System Applications. Dr. Venayagamoorthy islisted in the 2007 edition of Who’s Who in America.

Ronald G. Harley (M’77-SM’86-F’92) received theM.Sc.Eng degree (Hons.) in electrical engineeringfrom the University of Pretoria, Pretoria, SouthAfrica, in 1965, and the Ph.D. degree from LondonUniversity in 1969.

In 1971, he was appointed to the Chair of Elec-trical Machines and Power Systems at the Univer-sity of Natal, Durban, South Africa. At the Univer-sity of Natal, he was a Professor of Electrical En-gineering for many years, including the DepartmentHead and Deputy Dean of Engineering. Currently, he

is the Duke Power Company Distinguished Professor at the Georgia Institute ofTechnology, Atlanta, GA. His research interests include the dynamic behaviorand condition monitoring of electric machines, motor drives, power systems andtheir components, and controlling them by the use of power electronics and in-telligent control algorithms.

Dr. Harley has coauthored 380 papers in refereed journals and internationalconferences and three patents. Altogether, ten of the papers attracted prizes fromjournals and conferences. He is a Fellow of the British IEE and a Fellow of theIEEE. He is also a Fellow of the Royal Society in South Africa, and a FounderMember of the Academy of Science in South Africa formed in 1994. During2000 and 2001, he was one of the IEEE Industry Applications Society’s sixDistinguished Lecturers. He was the Vice-President of Operations of the IEEEPower Electronics Society (2003–2004) and Chair of the Atlanta Chapter of theIEEE Power Engineering Society. He is currently Chair of the DistinguishedLecturers and Regional Speakers program of the IEEE Industry ApplicationsSociety. He received the Cyrill Veinott Award in 2005 from the Power Engi-neering Society for “Outstanding contributions to the field of electromechanicalenergy conversion.”

optimal neuro-fuzzy external controller for a statcom in

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