Adaptive-Network-Based fuzzy.pdf

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013 2799

Stability Enhancement of a Power System With aPMSG-Based and a DFIG-Based Offshore

Wind Farm Using a SVC With anAdaptive-Network-BasedFuzzy Inference System

Li Wang, Senior Member, IEEE, and Dinh-Nhon Truong

Abstract—This paper presents the stability-improvement re-sults of a synchronous generator (SG)-based one-machineinfinite-bus system with a permanent-magnet SG (PMSG)-basedoffshore wind farm (OWF) and a doubly fed induction generator(DFIG)-based OWF using a static VAR compensator (SVC). Theoperating characteristics of the studied two OWFs are simulatedby an equivalent aggregated PMSG driven by an equivalent windturbine (WT) and an equivalent aggregated DFIG driven by anequivalent WT through an equivalent gearbox, respectively. Adamping controller of the SVC is designed by using adaptive-network-based fuzzy inference system (ANFIS) to contributeadequate damping characteristics to the dominant modes of thestudied SG under various operating conditions. A frequency-domain approach based on a linearized system model usingroot-loci technique and a time-domain scheme based on a nonlin-ear system model subject to various disturbances are both utilizedto examine the effectiveness of the proposed control scheme. Itcan be concluded from the simulation results that the proposedSVC joined with the ANFIS damping controller is capable of im-proving the stability of the studied SG system subject to differentdisturbances.

Index Terms—Doubly fed induction generator (DFIG), offshorewind farm (OWF), permanent-magnet synchronous generator(PMSG), stability, static VAR compensator (SVC).

I. INTRODUCTION

S TATIC VAR compensators (SVCs) have played impor-tant roles in voltage support and stability improvement of

power systems for several years due to their simple structuresfor reactive power compensation. A novel SVC was proposed in[1] to replace fixed capacitor compensating devices of a windfarm system, and the voltage level of the studied system was

Manuscript received January 27, 2012; revised March 31, 2012, June 26,2012, August 10, 2012, and August 26, 2012; accepted September 4, 2012.Date of publication September 27, 2012; date of current version February 28,2013. This work is supported by National Science of Council (NSC) of Taiwanunder Grant NSC 100-3113-P-006-014, Grant NSC 100-3113-E-006-013, andGrant NSC 100-ET-E-006-005-ET.

L. Wang is with the Department of Electrical Engineering as well as theResearch Center for Energy Technology and Strategy, National Cheng KungUniversity, Tainan 70101, Taiwan (e-mail: [email protected]).

D.-N. Truong is with the Department of Electrical Engineering, NationalCheng Kung University, Tainan 70101, Taiwan (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/TIE.2012.2218557

stable through using a voltage feedback control strategy. With anew winding structure, the proposed SVC can improve voltagestability of the studied wind farm connected to the grid [1].A new topology structure of a SVC, i.e., a low-cost improvedthyristor-controlled reactors (TCR) by removing series circuitelements, proposed in [2] was used to correct the unbalancedproblems and improve the reliability of power systems. Ahybrid SVC presented in [3] was utilized to improve reactivepower control capability of wind farms fed to an ac grid incase of low-voltage conditions. For damping subsynchronous-resonance oscillations due to torsional interactions as wellas induction generator effects, a SVC with a simple voltageregulator was connected to the induction-generator terminalsfor dynamic reactive power support when the studied systemwas subjected to a severe fault [4]. A SVC and a thyristor-controlled series compensator (TCSC) were employed in asingle-machine infinite-bus system to improve transient voltagestability of an asynchronous wind farm [5]. The SVC was ableto offer reactive power to maintain the transient stability whilethe TCSC was able to promote the terminal voltage and effec-tively improve low-voltage ride through (LVRT) capability [5].A SVC was located at the middle point of the tie line todamp out inter-area oscillations occurred in a two-area four-machine system [6], [7]. Comparing to the performance of aSVC, a static synchronous compensator (STATCOM) gave alarger contribution to transient margin and LVRT capability ofsquirrel-cage induction generator-based wind farms using bothcalculations and simulations [8]. However, the main drawbacksof using a STATCOM were larger harmonics injected into sys-tems, higher investment, and operational costs. With the samestudied power system in [6] and [7], a STATCOM with fuzzycontroller was used to enhance power-system stability [9]. In[9], the fuzzy supplementary controller was designed by using alook-up table method to damp the inter-area power oscillationsand enhancing dynamic stability of the interconnected powersystems. The fuzzy controller offered better damping perfor-mance under changed system operation conditions. The newproposed fuzzy logic (FL) controller replaces the existing PIusing the error between the reference voltage and the measuredvoltage to determine the required susceptance of SVC is usedto maintain the voltage bus constant has been proposed in [10].

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2800 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013

However, the drawbacks of the fuzzy inference system werecompletely based on the knowledge and experience of thedesigner. Since both FL and artificial neural network (ANN)have their relative advantages, a powerful processing toolwith both advantages can be obtained by combining themtogether. The architecture and learning procedure underlyingadaptive-network-based fuzzy inference system (ANFIS) wasproposed in [11]. This ANFIS incorporated the self-learningability of ANN with the linguistic expression function of fuzzyinference. By using a hybrid learning procedure, i.e., least-square estimation and back-propagation, the proposed ANFIScan construct an input-output mapping based on both humanknowledge and stipulated input-output data pairs. In which,human knowledge can be transformed by using “If—then”rules of a fuzzy inference system. Since no standard meth-ods for transforming human knowledge exist, ANFIS can beconsidered as an effective method for tuning the membershipfunctions to minimize the measured output errors. In addition,ANFIS is also an adaptation and robustness method since itcombines the advantages of ANN and FLC. According to theapplications of ANFIS to power systems, in [12], both rotorangle stability and system voltage profile were enhanced byusing a TCSC-based controller with ANFIS. A SVC with anindirect adaptive FL control was also coordinated with gen-erator excitation system of a multi-machine power system fortransient stability enhancement was presented in [13]. In similarfields with this paper, several papers focused on the hybridsystem such as a hybrid wind-hydro generation system [13],a hybrid offshore wind farm (OWF) and tidal farm [14], and ahybrid OWF and marine-current farm [15]. The authors of thesepapers considered a power grid as an infinite bus. However,an actual large power system may include many synchronousgenerators (SGs) whose stability can be affected by new addedrenewable-energy systems such as an OWF. In order to studythe practical performance of actual power systems, the studiedsystem in this paper uses a large equivalent SG connected to thepoint of common coupling (PCC) for simulating the stabilitycharacteristics of an actual power system. The control schemeis proposed in this paper to design a damping controller using anANFIS [16] to suppress oscillations of the SG system in orderto maintain system stable.

This paper is organized as below. System configurationand employed models for the studied system containing theintegrated two OWFs with SVC are introduced in Section II.The design procedure and design results for the PID controllerand the ANFIS controller of the proposed SVC are shownin Section III. Comparative transient responses of the studiedsystem with and without the designed PID damping controllerand the ANFIS controller subject to a severe disturbance aredescribed in Section IV. Finally, specific important conclusionsof this paper are drawn in Section V.

II. CONFIGURATION OF THE STUDIED SYSTEM

Fig. 1 shows the configuration of the studied SG-based one-machine infinite-bus (OMIB) system with a permanent-magnetSG (PMSG)-based OWF, a doubly fed induction generator(DFIG)-based OWF, and a ±50-MVAR SVC. The 80-MW

Fig. 1. Configuration of the studied SG-based OMIB system with a PMSG-based OWF, a DFIG-based OWF, and a SVC.

OWF #1 is represented by a large equivalent aggregated PMSGdriven by an equivalent aggregated variable-speed wind turbine(WT). The 80-MW OWF #2 is represented by a large equivalentaggregated DFIG driven by an equivalent aggregated variable-speed WT through an equivalent gearbox (GB). The two OWFsare connected to a common ac bus through correspondingconnection lines and transformers. The equivalent capacitanceCbus is also connected to the common ac bus that is fed tothe PCC of an onshore SG-based OMIB system through a23/161-kV offshore step-up transformer and undersea cables.The proposed SVC is connected to the PCC for supplyingadequate reactive power to maintain voltage profile and todamp oscillations of the SG. The 1230-MVA SG is fed to thePCC through a 15/161-kV step-up transformer. The PCC isconnected to a power grid through two parallel transmissionlines (TL1 and TL2) [17], [18]. The employed mathematicalmodels of the studied system are described as below.

A. WT Model

The captured mechanical power (in W) by a WT can bewritten by

Pmw =1

2ρw ·Arw · V 3

W · Cpw(λw, βw) (1)

where ρw is the air density (kg/m3), Arw is the blade im-pact area (m2), VW is the wind speed (m/s), and Cpw is the

WANG AND TRUONG: POWER SYSTEM WITH A PMSG-BASED AND A DFIG-BASED OFFSHORE WIND FARMS 2801

Fig. 2. Two-inertia reduced-order equivalent mass-spring-damper model ofthe WT coupled to the rotor shaft of the studied wind PMSG.

dimensionless power coefficient of the WT. The power coeffi-cient of the WT Cpw is given by

Cpw(ψkw, βw)=c1

(c2ψkw

−c3 ·βw−c4 ·βc5w −c6

)exp

(− c7ψkw

)

(2)

in which

1

ψkw=

1

λ+ c8 · βw− c9

β3w + 1

(3)

λw =Rbw · ωbw

VW(4)

where ωbw is the blade angular speed (rad/s), Rbw is the bladeradius (m), λw is the tip speed ratio, βw is blade pitch angle(degrees), and c1 − c9 are the constant coefficients for powercoefficient Cpw of the studied WT. The wind speed VW ismodeled as the algebraic sum of a base wind speed, a gustwind speed, a ramp wind speed, and a noise wind speed [19].The power coefficients of the WT can be referred to [20]. Thecut-in, rated, and cut-out wind speeds of the studied WT ofthe PMSG-based OWF #1 (DFIG-based OWF #2) are 3 (4),13 (14), and 23 (24) m/s, respectively. When wind speed VW islower than the rated wind speed of the WT (VW rated), βw = 0◦.When VW > VW rated, the pitch-angle control system of theWT activates, and the pitch angle of the WT (βw) increases.

B. Mass-Spring-Damper Systems for Two OWFs

The two-inertia reduced-order equivalent mass-spring-damper model of the WT directly coupled to the rotor shaft ofthe wind PMSG is shown in Fig. 2 [19]–[21]. Except employedparameters, this model can also be applied to the equivalentmass-spring-damper model of the WT coupled to the rotor shaftof the wind DFIG through an equivalent GB whose effect canbe properly included in this model.

C. PMSG Model and Control of Power Converters

The d–q axis equivalent circuit model of the studied windPMSG can be expressed by [22]

vqsw1 = − rsw1iqsw1 +p(Ψqw1)

ωb+

ωrw1

ωbΨdw1 (5)

vdsw1 = − rsw1idsw1 +p(Ψdw1)

ωb− ωrw1

ωbΨqw1 (6)

in which

Ψqw1 = − (Xmqw1 +Xlsw1)iqsw1 = −Xqw1iqsw1 (7)Ψdw1 = − (Xmdw1 +Xlsw1)idsw1 +Xmdw1i

′m1

= −Xdw1idsw1 +Xmdw1i′m1 (8)

where Ψ is the p.u. flux linkage, vs is the p.u. stator-windingvoltage, is is the p.u. stator-winding current, Xm is the p.u.

Fig. 3. Control block diagram of the VSC converter and the VSC inverter ofthe wind PMSG.

magnetization reactance, Xl is the p.u. leakage reactance, i′mis the p.u. magnetization current, ωr is the p.u. rotationalspeed, ωb is the p.u. base speed, and subscript w1 denotesthe quantities of the studied OWF #1. The input d–q axis p.u.voltages of the VSC converter of the PMSG can be expressed byvcond = kmcondVdc1 and vconq = kmconqVdc1, respectively,where Vdc1 is the dc-link voltage, and kmcond and kmconq arethe d- and q-axis modulation indices of the VSC converter, re-spectively. The output d–q axis p.u. voltages of the VSC inverterof the PMSG can be written by vinvd = kminv sin(αinv)Vdc1

and vinvq = kminv cos(αinv)Vdc1, respectively, where kminv

and αinv are the modulation index and the phase angle ofthe VSC inverter, respectively. The fundamental control blockdiagram of the VSC converter and the VSC inverter of the windPMSG can be referred to Fig. 3. According to the operationof Fig. 3, it is seen that αinv is responsible to control therotor speed of the wind PMSG (ωrw1) for maximum powerextraction, kminv is used to control the output reactive powerof the PMSG (Qw1), kmcond is employed to control the dc-link voltage (Vdc1), and kmconq is utilized to control the stator-winding voltage of the PMSG (vsw1).

D. DFIG Model and Control of Power Converters

The one-line diagram of the studied wind DFIG of the OWF#2 was shown in Fig. 1. The stator windings of the windDFIG are directly connected to the low-voltage side of the0.69/23-kV step-up transformer while the rotor windings of theDFIG are connected to the same 0.69-kV side through a rotor-side converter (RSC), a dc-link, a grid-side converter (GSC), astep-up transformer, and a connection line.

For normal operation of a wind DFIG, the input ac-sidevoltages of the RSC and the GSC can be effectively controlledto achieve the aims of simultaneous output active-power and


Fig. 4. Control block diagram for the RSC of the studied wind DFIG.

Fig. 5. Control block diagram for the GSC of the studied wind DFIG.

reactive-power control [23]–[25]. Fig. 4 shows the controlblock diagram of the RSC of the studied DFIG, and theoperation of the RSC requires iqrw and idrw to followthe varying reference points that are determined by maintainingthe output active power and the stator-winding voltage at thesetting values, respectively. The required voltage for the RSC(vrw) is derived by controlling the per-unit q- and d-axiscurrents of the RSC. The control block diagram of the GSCof the studied wind DFIG is shown in Fig. 5. The per-unitq- and d-axis currents of the GSC, iqgw and idgw, have to trackthe reference points that are determined by maintaining the dc-link voltage Vdc2 at the setting value and keeping the outputof the GSC at unity power factor, respectively. The requiredper-unit voltage of the GSC (vgw) is derived by controlling theper-unit q- and d-axis currents of the GSC.

E. SVC Model

The proposed SVC in this paper is for regulating the volt-age at its terminals by compensating the proper amount ofreactive power delivered to or absorbed from the connectedpower system. The single-phase equivalent circuit of the SVCwith TCR-fixed capacitor (TCR-FC) type was shown in Fig. 1[6]–[8]. Fig. 6 shows the control block diagram for the equiv-alent susceptance BL of the studied SVC. When the systemvoltage is lower than the reference value, the value of BL of theSVC is positive to inject reactive power to the system; whenthe system voltage is higher than the reference value, the BL

of the SVC is negative to absorb reactive power from the powersystem. The employed system parameters for the models of thispaper are listed in Appendix.

Fig. 6. Control block diagram of the employed SVC including (a) the de-signed PID damping controller and (b) the designed ANFIS controller.

III. DESIGN OF A PID DAMPING CONTROLLER AND AN

ANFIS CONTROLLER FOR THE PROPOSED SVC

A. Design of a PID Damping Controller for the SVC

This section describes the procedure and results to design thePID damping controller of the proposed SVC shown in Fig. 6(a)to achieve stability improvement of the studied SG-based sys-tem using a unified approach based on modal control theory. Todesign a PID damping controller for the proposed SVC in thispaper can be refereed to the detailed design procedure listedin [15], and only the important design steps and results arelisted as below. The nonlinear system equations developed inthe previous section are linearized around a selected nominaloperating point to acquire a set of linearized system equationsin matrix form of

pX =AX+BU+VW (9)

Y =CX+DU (10)

where X is the state vector, Y is the output vector, U is theexternal or compensated input vector, W is the disturbanceinput vector while A, B, C, and D are all constant matrices ofappropriate dimensions. To design the PID damping controllershown in Fig. 6(a), W in (9) and U in (10) can be ignoredby setting D = V = 0. The state vector X can be partitionedinto five substate vectors as X = [XWT−PMSG,XWT−DFIG,XOMIB,XLOCAL,XSVC]

T , where XWT−PMSG,XWT−DFIG,XOMIB,XLOCAL, and XSVC are referred to the system statevectors of the WT-PMSG system of OWF #1, the WT-DFIGsystem of OWF #2, the SG-based OMIB system, the local load,and the SVC, respectively. Because wind speed VW seldomreaches the rated wind speed of the WTs of the two OWFs, VW

of 12 m/s is properly selected as the nominal operating pointsfor designing the PID SVC damping controller.


TABLE IEIGENVALUES (rad/s) [DAMPING RATIOS] OF THE STUDIED SYSTEM UNDER NOMINAL OPERATING CONDITIONS

The eigenvalues of the studied SG-based OMIB system con-taining the two OWFs without and with the SVC under PSG =0.9 p.u., VSG = 1.0 p.u., PFSG = 0.9 lagging, and VW =12 m/s are listed in the third column and the fourth columnof Table I, respectively. The eigenvalues Λ1–Λ16 and Λ17–Λ38

listed in Table I relate to the modes of the WT-PMSG of OWF#1 and the WT-DFIG of OWF #2, respectively. The eigenvaluesΛ39–Λ58 and Λ59–Λ61 listed in Table I refer to the modes of theSG-based OMIB system and the SVC, respectively. It is seenthat the damping ratio of the mechanical mode (Λ51,52) can beslightly improved by the proposed SVC, but the damping ratioof the exciter mode (Λ55,56) is slightly reduced by the SVC.

The control block diagram of the inductive susceptance BL

of the SVC including the PID damping controller was shown inFig. 6(a). The PID damping controller with a first-order wash-out term senses the rotor-speed deviation of the SG (Δω) togenerate a damping signal Vs in order to improve the dampingratios of both mechanical mode and the exciter mode of the SG-based OMIB system listed in Table I. Hence, the output signalin (10) is Y = Δω and U = Vs is the input vector. The transferfunction H(s) of the proposed PID SVC damping controllerwith a first-order wash-out term in s domain is given by

H(s)=U(s)

Y(s)=

Vs(s)

Δω(s)=

sTW

1 +sTW

(KP +

KI

s+sKD

)(11)

where TW is the time constant of the wash-out term whileKP , KI , and KD are the proportional gain, integral gain, and

derivative gain of the PID damping controller, respectively.Taking the Laplace transformation of (9), (10), an algebraicequation of the closed-loop system containing the PID SVCdamping controller can be acquired. The input signal in sdomain can be expressed by

U(s) = H(s)Δω(s) = H(s)Y(s) = H(s)CX(s). (12)

Combining (20) and (21), it yields

sX(s) = {A+B [H(s)C]}X(s). (13)

The characteristic equation of the closed-loop system includingthe PID damping controller is given by

det {sI− [A+BH(s)C]} = 0. (14)

When two pairs of the specified mechanical mode and excitermode (Λ51,52 and Λ55,56) are substituted into (14), the fourparameters of the PID controller can be solved. The designresults of the PID SVC damping controller are given as below.Prespecified Eigenvalues

Λ51,52 = − 2.3± j9.8 (Mechanical mode)Λ55,56 = − 2.5± j1.6 (Exciter mode).

Parameters of the Designed PID Controller for SVC

KP = −1.23,KI = −3.63,KD = 0.16, TW = 0.64 s.


Fig. 7. Structure of the proposed ANFIS model.

The system eigenvalues of the studied SG-based OMIBsystem containing the two OWFs with the proposed SVC joinedwith the designed PID damping controller are listed in thefifth column of Table I. It can be clearly observed that bothΛ51,52 and Λ55,56 have been exactly positioned on the desiredlocations on the complex plane. The damping ratios of Λ51,52

and Λ55,56 have been increased from 0.055 to 0.228 and from0.349 to 0.842, respectively. According to the eigenvalue resultslisted in the fifth column of Table I and the four parameters ofthe designed PID damping controller of the SVC shown above,it can be concluded that the design results are appropriate to thestudied system.

B. Design of an ANFIS Controller for the SVC

The control block diagram of the employed SVC includingthe designed ANFIS damping controller was shown in Fig. 6(b).The rotor-speed deviation of the SG (Δω) and the voltagedeviation of PCC (ΔVPCC) are fed to the ANFIS controllerto generate a control signal V s to modulate the inductivesusceptance BL of the SVC. To design the ANFIS controllerfor the SVC, the following basic steps are employed: 1) datageneration, 2) rule extraction and membership functions,3) training and testing, and 4) results. The design procedure andassociated results of the ANFIS will not be discussed here, andthey can be referred to [10], [11]. The structure of the proposedANFIS is the Sugeno-type, in which the structure rules aregiven as follows:

If(x1=Ai) and (x2=Bi) then (fi=pix1+qix2+ri) (15)

where x1 and x2 are the inputs while (x1 = Δω) and (x2 =ΔVPCC) are used in this paper; Ai and Bi are the fuzzy sets; fiis the output within the fuzzy region specified by the fuzzy rule;pi, qi, and ri are the designed parameters that are determinedduring the training process; and i is the number of membershipfunctions of each input.

Three linguistic variables, i.e., NEG (Negative), ZER (Zero),and POS (Positive), for each input variable and two inputvariables for the proposed ANFIS are employed in this paper.Hence, nine linguistic variables for the output variable areproduced. The structure and control surface of this designedANFIS model are shown in Figs. 7 and 8, respectively. InFig. 7, five layers are presented. In which, each neuron inthe first layer (Inputs) corresponds to a linguistic variable andthe output equals the membership function of this linguistic

Fig. 8. Output of training data and control surface of the proposed ANFIS.(a) Output of training data; (b) Control surface.

variable. In the second layer (input membership function), eachnode multiplies the incoming signals and sends the product outthat represents the firing strength (wi) of a rule. Each node inthe third layer (Rules) estimates the ratio (w̄i) of the ith rulefiring strength to sum of the firing strength of all rules. In thefourth layer (Output membership function), the output is theproduct of the previously found relative firing strength ofthe ith rule and the rule fi. The final layer (Output) computesthe overall output as the summation of the incoming signals.

The ANFIS is checked by using the ANFIS Editor toolboxin MATLAB. With the type of membership function is Gauss,the number of epochs is 30, and the sample data for trainingthe ANFIS are taken from the transient responses of thestudied system with the designed PID controller under the mostsevere disturbance condition, i.e., a three-phase short-circuitfault at the infinite bus. A hybrid learning algorithm, i.e., amixed least-square and back-propagation scheme, is used fortraining the proposed ANFIS. The detailed parameters of theproposed ANFIS are: number of nodes = 35, number of linearparameters = 9, number of nonlinear parameters = 12, totalnumber of parameters = 21, number of training data pairs =1257, and number of fuzzy rules = 9.

Fig. 8(a) plots the output of the designed PID controller as theoutput training data for ANFIS (blue circles) and the responseafter training the designed ANFIS (red asterisks). It can beobserved from this figure that the output signal after trainingthe designed ANFIS (red asterisks) exhibits better dampingperformance. Fig. 8(b) shows the control surface between thetwo inputs (ΔωSG = Δω and ΔVPCC) and the correspondingoutput (Vs). It is seen from Fig. 8 that the rotor-speed deviation


Fig. 9. Transient responses of the studied system under a three-phase short-circuit fault. (a) δSG; (b) ωrSG; (c) PSG; (d) QSG; (e) PWF1; (f) QWF1;(g) PWF2; (h) QWF2; (i) VWF1; (j) VWF2; (k) VPCC; (l) BL.

of the SG (Δω) is varied from −4× 10−3 pu to 6× 10−3 puand the voltage deviation of PCC (ΔVPCC) is changed from−0.5 to 0 p.u. while the resultant output signal or dampingsignal Vs ranges from −0.2 to 0.8 pu. Using the proposedANFIS with these input/output relationships, the studied systemsubject to various disturbances can be effectively stabilized.

IV. TIME-DOMAIN SIMULATIONS

The nonlinear system model developed in Section II is em-ployed in this section to compare the damping characteristicscontributed by the proposed SVC joined with the two dampingcontrol schemes on stability improvement of the studied systemsubject to a severe disturbance. It is assumed that the two OWFsare operated under a wind speed of 12 m/s while the SG is oper-ated at PSG = 0.9 pu, VSG = 1.0 pu, and PFSG = 0.9 lagging.Simulation results of the proposed system using MATLAB/Simulink toolbox are presented and analyzed as below.

Fig. 9 plots the comparative transient responses of the studiedsystem without the proposed SVC (blue lines), with the SVCjoined with the designed PID controller (red lines), and withthe SVC joined with the proposed ANFIS system (black lines)under a three-phase short-circuit fault at the power grid. Thefault is suddenly applied at t = 1 s and is cleared at t = 1.1 s. Itis clearly observed from the comparative simulation results thatthe transient responses of the SG-based OMIB system shownin Fig. 9(a)–(d) exhibit good damping performance when theproposed SVC with the designed PID damping controller andthe SVC with the ANFIS system are, respectively, included inthe system. When the fault is suddenly applied to the studiedsystem, the system responses oscillate for a while, and thenreach their steady-state values at around 6, 4, and 3 s whenthe system is without SVC, with SVC and the PID controller,and with SVC and the ANFIS, respectively. Although theproposed ANFIS system is trained from the transient responsesof the studied system with the proposed SVC joined with


the designed PID controller, the responses of the system withthe proposed SVC joined with the ANFIS system give thebest damping performance in three cases. In other words, thetransient responses of the system with the SVC and the ANFISreaching their steady-state values are the fastest. The remainingtransient responses also have similar features that the proposedSVC joined with the ANFIS system can contribute the bestdamping characteristics to the studied system in three cases. Forexample, the active power and reactive power of the PMSG-based OWF #1 shown in Fig. 9(e) and (f) and the activepower and reactive power of the DFIG-based OWF #2 shownin Fig. 9(g) and (h) have similar results. Since the SVC is tocontrol the voltage profile of the studied system, the voltagesof OWF #1 and OWF #2 shown in Fig. 9(i) and (j) and thevoltage of PCC shown in Fig. 9(k) still show the similar resultsthat the SVC with the ANFIS contributes the best damping tothe studied system. The studied system with the SVC and theproposed ANFIS only needs about 1.5 s (from 1 to 2.5 s) toreach the steady-state value after the severe fault is cleared (seeblack line). However, the proposed ANFIS can result in largervariations on BL than the PID controller as shown in Fig. 9(l)when the fault is applied to the studied system. As shown inFig. 9, the peak values of the studied system with the SVC andthe ANFIS are the same as the ones of the studied system withthe SVC and the PID controller. This is due to the fact that thetraining data for ANFIS are generated from the responses of thesystem with the designed PID controller.

The transient results shown in Fig. 9 are convincing theimportant effectiveness of ANFIS on damping improvement ofthe studied system since ANFIS is a very powerful approachfor building complex and nonlinear relationship between a setof input and output data. Also, in ANFIS, both numerical andlinguistic knowledge can be combined into a fuzzy rule base byemploying fuzzy methods. By using the error back-propagationalgorithm in this study, the fuzzy membership functions canbe tuned optimally. Other advantages of the ANFIS include itsnonlinear ability, its capacity for fast learning, and its adaptationcapability.

With the advantages of ANFIS mentioned above, Fig. 8(a)presents the output of the designed PID controller as thetraining data for the ANFIS (blue circles) and the outputresponse (red asterisks) after training the designed ANFIS. Itcan be observed from Fig. 8(a) that the output signal of theANFIS after training (red asterisks) exhibits better dampingperformance. Thus, the stability of the studied system can beeffectively improved and the transient results shown in Fig. 9are convincing.

V. CONCLUSION

This paper has presented the stability improvement of twoparallel-operated OWFs connected to a SG-based OMIB sys-tem using a SVC joined with a designed PID damping con-troller and an ANFIS controller. The SVC is proposed and isconnected to the PCC of the OMIB system to supply adequatereactive power. A PID damping controller has been designedfor the SVC by using a unified approach based on modal controltheory to assign the mechanical mode and exciter mode of the

TABLE IISYSTEM PARAMETERS

studied SG. An ANFIS controller has been designed by usingthe transient-response data of the studied system with the SVCand the PID controller under a three-phase short-circuit fault.Since the mechanical mode and exciter mode of the studied SGdominant the significant characteristics of the studied system,the proposed SVC joined with the designed PID dampingcontroller has the ability to improve the performance of thestudied system. Time-domain simulations of the studied systemsubject to a three-phase short-circuit fault at the grid havebeen performed to compare the effectiveness of the proposedSVC joined with the designed PID damping controller andthe proposed SVC joined with the designed ANFIS dampingcontroller on suppressing inherent SG oscillations of the studiedsystem and improving system stability. It can be concludedfrom the simulation results that the proposed SVC joined withthe designed ANFIS damping controller offers better dampingperformance of the studied two OWFs connected to a SG-basedpower system under a severe disturbance condition. The ANFISis a nonlinear controller that can face the different operatingpoints of the system. Moreover, the proposed ANFIS is alsoan adaptation and robustness method since it combines theadvantages of ANN and FLC.

APPENDIX

See Table II.


REFERENCES

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Li Wang (S’87–M’88–SM’05) received the Ph.D.degree from the Department of Electrical Engineer-ing, National Taiwan University, Taipei, Taiwan,in 1988.

He has been an Associate Professor and a Pro-fessor at the Department of Electrical Engineering,National Cheng Kung University, Tainan, in 1988and 1995, respectively. He was a visiting scholar ofthe School of Electrical Engineering and ComputerScience, Purdue University, West Lafayette, IN, fromFebruary 2000 to July 2000, and the School of

Electrical Engineering and Computer Science, Washington State University,Pullman, from August 2003 to January 2004. He was a Research Scholar ofthe Energy Systems Research Center, the University of Texas at Arlington,Arlington, from July 2008 to January 2009. His current research interestsinclude power systems dynamics, power system stability, ac machine analyses,and renewable energy.

Dinh-Nhon Truong was born in Quang namProvince, Vietnam, on December 3, 1979. He re-ceived the B.S. and M.S. degrees in electrical andelectronics engineering from the University of Tech-nical Education, Ho Chi Minh, Vietnam, in April2003 and May 2005, respectively. Currently, he isworking toward the Ph.D. degree at the Departmentof Electrical Engineering, National Cheng KungUniversity, Tainan, Taiwan.

He has been a Lecturer in the Department ofElectrical and Electronics Engineering, University of

Technical Education, Ho Chi Minh, Vietnam, since 2005. His research interestsare grid-connected wind power systems, marine-current energy conversionsystems, and FACTS devices.

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