Power System Stabilisation with ANN

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 2, MAY 2011 669

Power System Stabilization Using Adaptive NeuralNetwork-Based Dynamic Surface Control

Shahab Mehraeen, Student Member, IEEE, Sarangapani Jagannathan, Senior Member, IEEE, andMariesa L. Crow, Fellow, IEEE

AbstractIn this paper, the power system with an excitationcontroller is represented as a class of large-scale, uncertain,interconnected nonlinear continuous-time system in strict-feed-back form. Subsequently, dynamic surface control (DSC)-basedadaptive neural network (NN) controller is designed to overcomethe repeated differentiation of the control input that is observedin the conventional backstepping approach. The NNs are utilizedto approximate the unknown subsystem and the interconnectiondynamics. By using novel online NN weight update laws withquadratic error terms, the closed-loop signals are shown to belocally asymptotically stable via Lyapunov stability analysis, evenin the presence of NN approximation errors in contrast with otherNN techniques where a bounded stability is normally assured.Simulation results on the IEEE 14-bus power system with gener-ator excitation control are provided to show the effectiveness ofthe approach in damping oscillations that occur after disturbancesare removed. The end result is a nonlinear decentralized adaptivestate-feedback excitation controller for damping power systemsoscillations in the presence of uncertain interconnection terms.

Index TermsAdaptive control, decentralized control, dynamicsurface control, excitation control, power system stabilization.

I. INTRODUCTION

I N the recent years, the competitive market for power gen-eration and energy services demands a more reliable powernetwork. Due to offshore wind generation plants and solar cells,a noticeable uncertainty in the load flows will occur in a powersystem, thus impacting the dynamic behavior and stability.Therefore, excitation control, power system stabilizer (PSS),static VAR compensators, and other power system controllerscan play an even more important role in maintaining dynamicperformance and power system stability, thus increasing relia-bility. Centralized control strategies for ensuring performanceand stability are not viable due to the sheer size of the powernetwork which causes time delays in acquiring power systembus voltages and currents.

Decentralized control (DC) techniques [1][6], on the otherhand, have been evolving for power systems so that they canachieve transient stability as well as steady-state behavior interms of damping oscillations caused by faults/disturbances.

Manuscript received September 14, 2009; revised September 15, 2009, Jan-uary 20, 2010, and April 15, 2010; accepted May 26, 2010. Date of publicationSeptember 16, 2010; date of current version April 22, 2011. This work was sup-ported in part by NSF ECCS#0624644. Paper no. TPWRS-00730-2009.

The authors are with the Department of Electrical and Computer Engineering,Missouri University of Science and Technology, Rolla, MO 65409 USA (e-mail:[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2010.2059717

Under the DC techniques, load and frequency control methodsof a multi-area interconnected power system are studied in[1] and [2]; however, linear power system model is used todesign turbine and exciter voltage controllers, and the methodtacitly assumes that the network variables remain in the neigh-borhood of the desired operating point. In [3], a linear matrixinequality (LMI) approach is chosen and sequential linearmatrix inequality programming is utilized to design a powersystem stabilizer (PSS.) In [4], by considering nonlinear powersystem representation, a suboptimal performance for all admis-sible variations of generator parameters is achieved using anLMI-based control approach which depends on the existenceof LMI solutions.

By contrast, in [5], a decentralized neural network (NN) con-trol of a general class of nonlinear systems in strict-feedbackform has been proposed for power systems by using backstep-ping technique while relaxing the matching condition (wherethe interconnected terms appear in the input domain only). Themethod is applied to design excitation and steam turbine con-trols rendering state boundedness due to NN reconstruction er-rors while encountering repeated differentiation of the controlsignal resulting from the standard backstepping design. In [6], alinear parameter varying (LPV) representation of the nonlinearpower system is chosen at each operating point obtained via lin-earization and subsequently, a decentralized PSS is designed. Inthis approach a linear time-varying model of power system isused instead of the nonlinear model.

Dynamic surface control (DSC) [7], on the other hand, hasbeen receiving attention in this decade [7][9]. In the DSCscheme, the well-known problem of repeated differentiation ofthe control signal in the backstepping design is replaced by a se-ries of algebraic terms which simplifies the implementation fornonlinear systems in strict-feedback form. Consequently, theDSC scheme results in the asymptotic stability in a semi-globalmanner [7] provided the system dynamics are accuratelyknown. Further attempts in [8] provide asymptotic stabilizationfor a class of uncertain nonlinear systems using adaptive DSCprovided the control gain coefficient matrix being unity and thesystem uncertainties are assumed to be linear in the unknownparameters (LIP). Hence, NN universal approximation propertyis asserted in [9] to relax this LIP assumption for subsystemuncertainties in order to ensure state boundedness.

In this paper, the large-scale power system with generator ex-citation control is represented as a nonlinear uncertain, intercon-nected system, in strict-feedback form. Subsequently, the DSCdesign framework is proposed while relaxing the matching con-dition (i.e., the interconnected terms appear in several dynamicequations as opposed to the one where the actual control input

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670 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 2, MAY 2011

appears). Next, NNs are introduced to approximate both sub-system and the interconnection dynamics. Novel NN weight up-date laws are derived which render asymptotic stability evenin the presence of NN approximation errors and interconnec-tion terms. Finally, simulation results on a 14-bus five-gener-ator power system with generator excitation control confirm thesatisfactory performance of this controller in damping the oscil-lations after a disturbance has occurred.

This paper is organized as follows. First, background infor-mation is given in the next section. Subsequently, power systemmodel development as well as excitation control is introducedin Section III. The DSC state feedback design is introduced inSection IV. A numerical example is presented in Section V.Conclusions are given in Section VI.

II. BACKGROUNDConsider the dynamical system , where

represents the state vector and is the input vector. Let theinitial time be , and the initial condition be . Thestate is considered as an equilibrium point of the system if

.

Definition 1: An equilibrium point is locally asymptoti-cally stable at if there exists a compact set suchthat, for every initial condition , as

. If the compact set can be made arbitrarily largeand if as , then the equilibrium pointis semi-globally asymptotically stable.

Next, a brief background on NN is given. A general func-tion where can be written as

with NN denotes functional recon-struction error vector, and representtarget NN weight matrices.

III. POWER SYSTEM AS AN INTERCONNECTED SYSTEMIn this section, a decentralized representation of a power

system is obtained for nonlinear controller development. Wheneither a three-phase to ground fault or a disturbance occursthe generator angles and speeds deviate from their normaloperating range. Unless there is a controller to mitigate theoscillations, which bounce back and forth among multiple gen-erators, the power system will not return to its normal operatingstate after the fault is removed. Generator excitation control isa means to alleviate the power system oscillations. Since thedisturbance is a function of the power network voltages andangles as well as generator states, it is generally hard to design acentralized damping controller for the complex interconnected

Fig. 1. Power system.

power network. Thus, in this paper, we aim at a decentralizedexcitation controller to mitigate the oscillations by using locallymeasurable states of the generator as well as its bus voltagesand angles. For this controller development, the large-scalepower system has to be represented in a decentralized form,which is discussed next.

A. Model DevelopmentA power system is usually modeled using a combination of

differential and algebraic equations. The differential equationsrepresent generator states (i.e., angles, speeds, and voltages

and ) whereas the algebraic equations represent bus ac-tive and reactive power balance relationships. For the purpose ofcontroller design, it is desirable to have pure dynamical equa-tions. In [12], authors have proposed an algebraic-free powersystem representation based on the classical generator model.In order to incorporate the generator flux-decay states, the pro-posed model is extended herein.

A two-axis model [13] is chosen for the purpose of powersystem representation. As a consequence, the generator dynam-ical equations are given as (1) at the bottom of the page, where

is the rotor angle of the th machine, is the difference be-tween the generator angular speed and synchronous speed,and are generators variables as defined in [13], isthe excitation voltage, and and are the generator busvoltage and phase angle, respectively, as depicted by Fig. 1. Inaddition

(2)where represents the reactance of the admittance matrix,being the number of generators, and denotes the number ofnon-generator buses in the power system as shown in Fig. 1.The bus voltage and phase angles of the power system buses areillustrated in Fig. 1 which are constrained by the set of algebraic

(1)

MEHRAEEN et al.: POWER SYSTEM STABILIZATION USING ADAPTIVE NEURAL NETWORK-BASED DYNAMIC SURFACE CONTROL 671

power balance equations (neglecting resistances) as shown in(3) at the bottom of the page. Then, taking the derivative of (3)to obtain and as

(4)

and

(5)

By using (1) for and and solving (4) and (5) forand , we obtain a new set of dynamic equations as

(6)

where ,, and

is the generators speederror vector. Define ,

,

, ,

, and. The entries for ,

, , , , , and can bederived by collecting the corresponding coefficients. Equation(6) can be rewritten in a more appropriate way as

(7)

It is important to note that this step is needed only for modeldevelopment and is not required for implementation.

B. Generator Representation

Next, the flux-decay model [13] of the generator is given as

(8)

where is the active load at each bus, and isthe th machine inertia. In addition, the following equalities arevalid:

(9)

and

(10)

Moreover, the power balance (3) will be simplified by em-ploying the flux-decay assumption

(11)

In this design, we assume that the mechanical poweris slowly changing compared to the other control vari-

ables; thus, . Now define

(12)

(3)


Fig. 2. Generator flux-decay model.

where and . Consequently, thegenerator dynamics (8) can be rewritten in the state-space formas

(13)

The electrical diagram of the generator using theflux-decay model is depicted in Fig. 2 [13] where thevoltage source and injected current are representedas , and

. According to the figure and (11), thevoltage source in Fig. 2 can be represented as

.

Then, by applying to the power net-work, where and

, we

obtain

(14)

which yields

(15)

and

(16)

Remark 1: Here may contain nonlinear impedances (in-cluding constant loads). Consequently, even if the systemis reduced to an matrix, non-generator bus voltages andangles are involved in computations. Thus, conventionalreduction techniques cannot be applied to overcome non-gener-ator nodes.

C. Decentralized Nonlinear System Representation

The dynamical representation of the power system from (13)can be rewritten as a general class of interconnected nonlinearsubsystems in strict-feedback form as

.

.

.

(17)

where index , , represents the subsystem (gener-ator) number, is the number of subsystems (generators) inthe power system, , , shows the generator statenumber, is the order of the power system according to(13), and , represent unknown nonlinearities, de-notes interconnected terms, with ,

, , andis the subsystem output for and . Thenonlinear function in (17) satisfies forand . By comparing the power system representation(13) and the general system description given by (17), it followsthat , , ,

, and . Also, , with

(18)(19)

and

(20)

In the following, we find and as a function of the state , ,and . Equations (15) and (16) yield expressionsand as functions of , , and , which in turn yields

and to be functions of , and as

(21)

Consequently, by using (9), (10), and (21), the variables andas well as can be represented as functions of and as

(22)


Now, (11) and (21) (for ) along with the nodalpower flow (3) give solutions for and in terms of for

as

(23)

D. Interconnection TermsIn order to address the interconnection terms, the following

fact is used for analyzing their upper bound.Remark 2: The excitation voltage, , satisfies the fol-

lowing inequality [14] defined by

(24)where is a positive constant. Consequently, by (10) and (21),we have

(25)Also, by employing (6), (11), (21), and (25), we conclude that

(26)where and are positive nonlinear functions and

. Then, by using (22) and (23), we ob-tain

(27)where and are positive nonlinear functions. Now, by con-sidering the interconnection term (18) along with (10), (23),(24), and (27), it can be shown that for

. This step is only for model development and is notnecessary for practical implementation.

Next, we show that and are zero at steady-state con-dition. Obviously, at steady state, we have .Consequently, by using (18) at steady state, we obtain

where the index stands for steady-state conditions. At steadystate, the state variables , , and in (12) are zero. Theterm is zero for round rotors and it is a small value forsalient pole rotors. Therefore, . Also, since atsteady state, we have . In addition, and

. Consequently, at steady stateand we have .

IV. DECENTRALIZED CONTROLLER DESIGNIn this section, the design of the DSC controller is now ad-

dressed. Equation (17) represents a nonlinear system in strict-feedback form where a standard backstepping design can be ap-plied. In the backstepping design, the repeated differentiation

Fig. 3. Controller block diagram.

of virtual control inputs is necessary in the consecutive designsteps. This, in turn, renders the design more involved as the de-sign progresses where the virtual control becomes more complexin the consecutive steps, especially when adaptive terms (such asadaptive neural networks) are involved in the control design toovercome the system uncertainties. The dynamic surface controlmethod, on the other hand [7], is a robust control design method-ology that has been introduced to relax the need for the derivativeof virtual control in the backstepping method. In this method, afirst-order filter is utilized to produce the derivative of the vir-tual control and to overcome the complexity involved in the re-peated differentiation. However, the DSC method can stabilizethe system in semi-global manner [15] whereas backstepping re-sults in global stability when the system dynamics are known.Also, DSC adds extra first-order filters to the design, which inturn increases the overall order of the system.

In DSC control design, due to the filter, additional error termsappear (i.e., in Fig. 3) which complicates the stability anal-ysis. The variables used in Fig. 3 are and

where and are introduced in Fig. 3for and .

Fig. 3 illustrates the NN DSC controller design steps for thegeneral system (17) where the interconnection and unknownnonlinear functions are present in each state dynamics. There-fore, one cannot use the assumption of matching condition. In-stead, these terms have to be explicitly taken into account in thecontroller design which further complicates the stability anal-ysis. Moreover, to deliver asymptotic stability, the NN weightshave to be tuned appropriately. Finally, it is shown that if thefollowing Assumptions are satisfied, the procedure shown inFig. 3 can (semi-globally) stabilize the interconnected system(17) asymptotically where , , and are considered un-known as shown in Theorem 2.

Assumption 1: In a compact set , assume that the inter-connection terms in (17) satisfy


where are unknown functions with forand .Remark 3: This assumption is considered mild in comparison

with the assumption that the interconnection terms are boundedabove with a constant upper bound.

Assumption 2: The control gains for andsatisfy .

Remark 4: Assumptions 2 is standard in the control litera-ture since practical systems including power systems obey thisassumption.

A. Error Dynamics

The DSC controller design procedure is explained now. Sincethere are no unknown terms in the generator state dynamicsand , no NNs are utilized in the first two steps.Step 1) Define the error as and

, where is the desired set point for regulation.Now define , where is thedesired virtual input to make as . Forthe stabilization problem, the desired values become

. Next, the intermediate virtualinput is obtained by passing the desired virtualinput through a first-order filter consistent withthe DSC literature [7] as

(28)

Also, define and .Thus

(29)

Then, from (13) and (29), the error dynamic be-comes

(30)

Step 2) Define . By using (28), we get; thus, .

Similarly, the intermediate virtual input is ob-tained by passing through a first order filter as

(31)

Define and toobtain

(32)

Thus, from (17) and (32), we have

(33)

Step 3) Due to the presence of unknown interconnectionterms in , we use an NN approximator in thedesired virtual control to approximate the unknownnonlinear dynamics. Since it is assumed that othersubsystems (generators) states are not availablein subsystem (generator) , the NN approximatoris only a function of available states through

, i.e., , whereis part of unknown nonlinear function in

. In addition, the target NN weights andapproximation error term (for and

) are not known; thus, a tunable weightmatrix is utilized [15] to calculate which resultsin .Accordingly, we define the desired virtual controlas . From(31), we obtain ; thus,

. Passingthrough a first-order filter results in the intermediatevirtual input to be

(34)

Define and toobtain

(35)

and

(36)

Step 4) Similar to step 3, in the last step, the desired virtualinput is defined as

(37)

by using (34) to replace for . Note that, ac-cording to [7], there is no need for filtering the de-sired virtual input in the last step. Thus, dy-namics can be written as

(38)

Before proceeding, define, , and , where

for and .

B. Stability AnalysisHere, we discuss a novel NN weight update law by using

the projection scheme [16] since NNs are utilized for nonlinearfunction approximation. An interesting property of updating theNN weights using the proposed projection scheme is the bound-edness of the NN weights which when combined with the error


dynamics will result in asymptotic stability in a semi-globalmanner when the subsystem and interconnection dynamics areunknown. Subsequently, by using the NN weight update law, theoverall stability of the closed-loop system is stated.

Theorem 1: Assume that single-layer NNs are utilized to ap-proximate the unknown nonlinearities of the system dynamicsand the interconnection terms in (17). Let the NN weight tuningfor the th subsystem be provided by

(39)

where if or; if

; if

for all and , with

denoting the user selected bound for the weights . Then,the weight estimates remain within the user selected boundsuch that for provided the initial weights

start within the set defined by .The NN weight update law is a variant of the projection al-

gorithm [17] wherein a quadratic term of the error is employedalong with a new term for relaxing the persistency ofexcitation (PE) condition. This ensures asymptotic stability inerror dynamics and for all and .The user selected bound on the NN weights can play an im-portant role for the function approximation. Conservative boundselection (i.e., small ) can result in significant reconstruc-tion errors, which should be avoided since this causes the weightestimates to stay away from the actual weights . Never-theless, the system errors regulate asymptotically to zero whilethe weight estimation are bounded.

Theorem 2: Consider the nonlinear interconnected systemgiven by (17). Consider the Assumptions 1 and 2 hold and letthe unknown nonlinearities in the subsystems and interconnec-tion terms be approximated by NNs. Let the NN weight updatebe provided by (39), then there exist a set of control gainsand filter time constants, , associated with the given controlinputs such that the states and approach to zero asymp-totically (local) for all and .

It is shown in [16] that if the Assumptions 1 and 2 hold and theunknown nonlinearities in the subsystems and interconnectionterms are approximated by NNs, the states and approachzero asymptotically for all and providedthat the NN weight update is provided by (39) and control gains

and filter time constants, are chosen properly. In addi-tion, from Section III, a power system satisfies Assumptions 1and 2.

V. SIMULATION RESULTSThe method introduced in Section III is utilized to design

damping controller for generator excitation control. The pro-

TABLE IDSC NN DESIGN PROCEDURE

posed design is summarized in Table I and a comparison of de-sign complexity with backstepping method is given. Note theincreased complexity when dealing with the term inbackstepping (in row 11). In the table, is the stabilizing de-sign gain for where is the number of generatorsin the multi-machine power system and . Also, isthe filter time constant at each step for . In addition,

and are the NN weight estimate matrix whileand are the NN activation function vector. Since there areno unknown terms in the first- and second-state dynamics, onlytwo NN are utilized per generator. In other words, the generatorangle and speed dynamics do not require NN approximators.

The IEEE 14-bus, five-generator power system shownin Fig. 4 with a three-phase disturbance is considered. Thegenerator data [19] are given as , ,

, , , forwhereas for , and

for . Each generator in the network rep-resents an aggregation of several generators and the inter-areaoscillations are investigated. Two generation/load levels, asgiven in Tables II and III, are studied where the powers indi-cated in the tables are the generation power minus load powerat each generator bus and the load power at each load bus. Allthe generators have speed governors and the excitation controlis implemented by employing the DSC-based NN controlleras proposed in (37) and (39). The power system loads areconsidered as constants. The control objective is to damp thegenerators oscillations caused by a three-phase fault.

Although the stability analysis is based on the lossless powersystem dynamical model as described in (6), the simulations are


Fig. 4. IEEE 14-bus, five-generator power system.

TABLE IIPOWER SYSTEM LOADS AND GENERATIONS (HIGH GEN./LOAD LEVEL)

TABLE IIIPOWER SYSTEM LOADS AND GENERATIONS (LOW GEN./LOAD LEVEL)

performed using a complete power system dynamic representa-tion with line resistances and two-axis generator model in orderto evaluate the effectiveness of the representation and the con-troller design.

The power system modes are 11.3561, 5.9101, 2.6977, and2.1026 Hz. A three-phase disturbance is injected to the bus 1,6, and 11 at and removed at s. Generators1 through 5 are chosen for control. The control inputs andweight estimate 10 1 (i.e., 10 neurons are used in the outputlayer) matrices and (for ) are obtainedby using (37) and (39), respectively, where the NN weights aretuned throughout the simulations by using online learning. Thevoltage is calculated using (20) and is subjected to hardlimits such that the voltage satisfies to avoidany impractical excitation voltages .

The design gains and filter time constants are chosen as fol-lows: ; ;

; ; ;

Fig. 5. (a) Excitation/PSS+ AVR controller with (b) IEEE PSS2A block dia-grams.

; ;; ; ;

; ; ;; for and

. The weight estimate matrices and are ini-tialized randomly for . Moreover, no offline trainingis used to tune the weights in advance and no initial knowledgeabout the power system dynamics, complete knowledge of in-terconnection dynamics, or power system topology are neededfor the controller design. The NN activation function is chosenas [16] for whereis chosen at random initially and held fixed afterwards to forma set of basis functions needed for the NN approximation [10].

For comparison, the results from the DSC design are com-pared with the IEEE PSS2A [20] power system stabilizer, wherethe ramp-tracking filter is bypassed, combined with automaticvoltage regulator , shown in Fig. 5(a) and (b), inthe presence of steam governor. The design recommendationsin [20] are changed in order to obtain a stable controller in thesimulations. The PSS2A parameters are selected as

; ;; ; ; for

, where is generator number. The AVR is definedby [13] for . In addition,

and are employed.Two generation/load conditions are selected to investigate the

effectiveness as well as the robustness of the proposed method.First the generation/loading schedule shown in Table II is se-lected and the proposed DSC controller is compared with the


Fig. 6. Generator speeds with control when fault is on bus1; generation/load levels are selected according to Table II.


PSS/AVR controller. Figs. 68 depict that a significant oscil-lation damping is observed for a medium-size power networkby using both controllers with the proposed method having aslightly faster damping effect.

Fig. 9 shows that the variations in excitation voltages, ,have fast transients as well as slow dynamics where the fasttransients are damped in the first few seconds whereas the slowdynamics are due to the generator speed controller (governor)and are damped in a longer time. The NN weight estimates inFig. 10 are bounded as expected. In addition, the control effortsof the two controllers are compared through comparison of thevoltages for in Figs. 11 and 12, where it is shownthat the DSC controller control effort is in a reasonable range.Overall, from these results, the proposed control is very effectivein damping the oscillations even in the presence of numerousmodes.

Next, by using the generation/loading schedule shown inTable III, the performance of the proposed controller is com-pared with PSS/AVR without changing the design parameters


Fig. 9. Generator internal voltages with fault on buses 1, 6, and 11 when theDSC controller is used; generation/load levels are selected according to Table II.

used in the previous generation/loading level (i.e., Table II).Figs. 1315 depict that the proposed method has a betterdamping effect over the PSS/AVR with the new generation/loadlevel. This can be explained by the robustness of the proposeddesign and the presence of the adaptive NN with online learningthat is able to learn and accommodate for the changes in thepower system dynamics.

According to Figs. 68 as well as Figs. 1315, the DSC con-troller is robust when dealing with faults and generation/loadlevels where the proposed controller is able to damp oscillationsfrom the faults occurring at different locations without changingthe gains and filter time constants even when the power systemdynamics and interconnection effects are unknown. Note, how-ever, that damping performance varies with the fault location.This is due to different after-fault conditions imposed on thecontroller.

In order to investigate the ability of the DSC controller to mit-igate the oscillations when renewable energy sources are presentin the power system, a wind turbine is connected to bus 14. The


Fig. 10. Neural network weight estimates with fault on bus 6; generation/load level are selected according to Table II.

Fig. 11. Generator voltages with fault on buses 1, 6, and 11 when the DSCcontroller is used; generation/load levels are selected according to Table II.

Fig. 12. Generator voltages with fault on buses 1, 6, and 11 when thePSS+AVR is used; generation/load levels are selected according to Table II.

wind turbine is modeled as an induction generator where its pa-rameters are given as , , ,

Fig. 13. Generator speeds with control when fault is onbus 1; generation/load levels are selected according to Table III.


, , , and where all the valuesare in p.u. The wind turbine steady state power is 0.9 p.u. Then,a three-phase disturbance is injected to bus 6 at andremoved at s.

The damping performance of the DSC controller is shown inFig. 16 which is found to be satisfactory. However, in order toprecisely address the renewable energy sources and mathemati-cally assure the stability of the overall system, the proposed ap-proach requires a DSC stabilizing controller on each subsystemincluding the wind turbine. The wind turbine controller designis out of scope of this paper.

VI. CONCLUSIONSIn this paper, the power system is represented as a large-scale

interconnected nonlinear system with uncertainties in both sub-



Fig. 16. Synchrounus generators speeds with DSC controller with a wind tur-bine connected to bus 14 and fault on bus 6.

system and the interconnection terms where the system doesnot satisfy the matching condition. By using a new variant ofthe projection scheme and dynamic surface control with NNs,the need for the repeated differentiation in the backstepping de-sign procedure was overcome. The neural network approxima-tion property is used to approximate the nonlinearities of thesubsystems and interconnection terms in the power system. Itis shown that the closed-loop system is asymptotically regu-lated to zero with state feedback control, even in the presence ofNN function reconstruction errors. Simulation results on powersystem with generator excitation control shows the effectivenessof the approach in damping oscillations that occurs after faultsin power systems. Also, the proposed controller is shown to berobust when dealing with different fault locations and genera-tion/load levels.

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[20] IEEE Recommended Practice for Excitation System Models for PowerSystem Stability Studies, IEEE Std. 421.5-1992, 1992.

Shahab Mehraeen (S08) received the B.S. degreein electrical engineering from Iran University of Sci-ence and Technology, Tehran, Iran, in 1995, the M.S.degree in electrical engineering from Esfahan Uni-versity of Technology, Esfahan, Iran, in 2001, andthe Ph.D. degree in electrical engineering from Mis-souri University of Science and Technology, Rolla, in2009.

He joined the Louisiana State University, BatonRouge, as an Assistant Professor in 2010. Hisresearch interests include renewable energies, power

system control, decentralized control of large-scale interconnected systems,nonlinear, adaptive, and optimal controllers for dynamic systems.


Sarangapani Jagannathan (M89SM99) re-ceived the B.S. degree in electrical engineering fromCollege of Engineering, Guindy at Anna University,Madras, India, in 1987, the M.S. degree in electricalengineering from the University of Saskatchewan,Saskatoon, SK, Canada, in 1989, and the Ph.D.degree in electrical engineering from the Universityof Texas, Austin, in 1994.

During 1986 to 1987, he was a junior engineer atEngineers India Limited, New Delhi, as a ResearchAssociate and Instructor from 1990 to 1991, at the

University of Manitoba, Winnipeg, MB, Canada, and worked at Systems andControls Research Division, Caterpillar Inc., Peoria, IL, as a consultant during1994 to 1998. During 1998 to 2001, he was at the University of Texas at SanAntonio, and since September 2001, he has been at the University of Missouri,Rolla, where he is currently a Rutledge-Emerson Distinguished Professor andSite Director for the NSF Industry/University Cooperative Research Center onIntelligent Maintenance Systems. He has coauthored over 78 peer reviewedjournal articles, 150 IEEE conference articles, several book chapters, and threebooks entitled Neural Network Control of Robot Manipulators and NonlinearSystems (London, U.K., Taylor & Francis, 1999), Discrete-Time Neural NetworkControl of Nonlinear Discrete-Time Systems (Boca Raton, FL: CRC, 2006), andWireless Ad Hoc and Sensor Networks: Performance, Protocols and Control(Boca Raton, FL: CRC, 2007). He holds 17 patents with several pending. His

research interests include adaptive and neural network control, computer/com-munication/sensor networks, prognostics, and autonomous systems/robotics.

Prof. Jagannathan received NSF Career Award in 2000, Caterpillar ResearchExcellence Award in 2001, Boeing Pride Achievement Award in 2007, andmany others. He served as an Associate Editor for the IEEE TRANSACTIONSON NEURAL NETWORKS, IEEE TRANSACTIONS ON CONTROL SYSTEMSTECHNOLOGY, and IEEE SYSTEMS JOURNAL. He served on a number of IEEEConference Committees.

Mariesa L. Crow (M80SM94F10) received theB.S.E. degree from the University of Michigan, AnnArbor, and the Ph.D. degree from the University ofIllinois, Chicago.

She is presently the Director of the Energy Re-search and Development Center and the F. FinleyDistinguished Professor of Electrical Engineering atthe Missouri University of Science and Technology,Rolla. Her research interests include developingcomputational methods for dynamic security assess-ment and the application of power electronics in

bulk power systems.

Documents

Power System Stabilisation with ANN