automatic reactive power control of isolated wind diesel hybrid power systems

1116 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006

Automatic Reactive-Power Control of IsolatedWind–Diesel Hybrid Power Systems

R. C. Bansal, Senior Member, IEEE

Abstract—This paper presents an automatic reactive-powercontrol of an isolated wind–diesel hybrid power system having aninduction generator (IG) for a wind-energy-conversion system andsynchronous generator (SG) for a diesel-generator (DG) set. Tostudy the effect of the size of the wind-power generation on thesystem performance, three examples of the hybrid system areconsidered with different wind-power-generation capacities. Themathematical model of the system using reactive-power-flow equa-tions is developed. Three different types of static var compensators(SVCs) commonly used in conventional power system along withIEEE type-I excitation are considered to compare their perfor-mance in a hybrid system.

Index Terms—Diesel-generator (DG) set, induction generator(IG), isolated wind–diesel hybrid power system, reactive-powercontrol, static var compensator (SVC), synchronous generator(SG), wind-energy-conversion system.

NOMENCLATURE

[A], [B], [C] System, control, and disturbance ma-trix, respectively.

x, u, p State, control, and disturbance vector,respectively.

EM Electromagnetic energy stored in in-duction generator (IG).

∆EM Small change in the stored electro-magnetic energy of IG.

∆Efd, ∆Eq, ∆E ′q Small change in the voltages of

the exciter, internal armature understeady state, and transient conditions,respectively.

KA, KE, KF, KR, Kα Voltage regulator, exciter, stabilizer,var regulator, and thyristor-firing gainconstants, respectively.

KP, KI Proportional and integral controllergain of the var regulator, respectively.

η Performance index.ηIG Efficiency of IG.Pin, PIG, QIG Real power input, real power gener-

ated and reactive power required byIG, respectively.

PSG, QSG Real and reactive powers gener-ated by a diesel generator (DG),respectively.

Manuscript received December 29, 2004; revised May 5, 2005. Abstractpublished on the Internet May 18, 2006.

The author is with the Electrical and Electronics Engineering Division,School of Engineering and Physics, The University of the South Pacific, Suva,Fiji (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2006.878322

PL, QL Real- and reactive-power-load de-mands, respectively.

QSVC Reactive power generated by staticvar compensator (SVC).

BSVC Reactive susceptance of the SVC.∆BSVC Small change in reactive susceptance

of the SVC.Td SVC average dead time of zero cross-

ing in a three-phase system.Tα Thyristor-firing delay time.T1, T2, T3, T4 Time-constant lead-lag type of SVC

regulator.α, αo Thyristor-firing angle and nominal

thyristor-firing angle.∆α Small deviation in thyristor firing

angle.δ Power angle between terminal volt-

age and armature internal EMF.r1, x1, r′2, x′

2 Stator resistance, stator reactance,rotor resistance, and rotor reactancereferred to the primary side of IG,respectively.

Req, Xeq, Xm Equivalent resistance, equivalent re-actance, and magnetizing reactanceof the IG, respectively.

SIG Apparent power delivered by the IG.s Slip of IG.TE, TF, TR Exciter, stabilizer, and regulator time

constants, respectively.T ′

do Direct-axis open-circuit transienttime constant.

V System terminal voltage.∆V , ∆Vref , ∆Va, ∆Vf Small change in the voltages of ter-

minal voltage, reference voltage, am-plifier output voltage, and exciterfeedback voltage, respectively.

xd, x′d Direct-axis reactance of synchronous

generator (SG) under steady-stateand transient-state conditions,respectively.

Qc Rating of the SVC.QR System reactive-power rating.

I. INTRODUCTION

THE OPTIMUM utilization of the resources for providingpower to the community at large has resulted in large

interconnected power systems. The demand to provide power to

0278-0046/$20.00 © 2006 IEEE

BANSAL: AUTOMATIC REACTIVE-POWER CONTROL OF ISOLATED WIND–DIESEL HYBRID POWER SYSTEMS 1117

all by a large interconnected system in developing countries likeIndia remains unfulfilled due to the nonavailability of sufficientfunds, constraints on the right of way for additional transmis-sion lines, and rapid growth in load with the developments,but on the other hand, the gap between supply and demandincreases day by day. Not only to reduce the gap between gen-eration and load, but because of the limited life of conventionalsources with high pollution rate, more explorations have beencarried out on alternative sources of energy during the last threedecades. During this period, the assessment of the potential ofthe sustainable eco-friendly alternative sources and refinementin technology has taken place to a stage so that economical andreliable power can be produced. Different renewable sourcessuch as wind, mini/micro hydro, etc., are available at differentgeographical locations close to loads, therefore the latest trendis to have a distributed or dispersed power system [1]–[3].Examples of such are the wind–diesel, wind–diesel–micro-hydro systems, etc. These systems are known as isolated hybridpower systems.

In general, in any hybrid energy systems, there may be morethan one type of electrical generators [4], [5]. In such circum-stances, it is normal, although not essential for generator(s),usually on the diesel to be synchronous, and on wind-turbinegenerator(s) to be asynchronous (induction) [4]. An IG offersmany advantages over a conventional SG as a source of isolatedpower supply. Reduced unit cost, ruggedness, brushless (insquirrel-cage construction), absence of separate dc source, easeof maintenance, self-protection against severe overloads andshort circuits, etc., are the main advantages [6]–[13]. A majordisadvantage of an IG is that it requires a reactive power for itsoperation. In the case of a grid-connected system, an IG can getthe reactive power from the grid/capacitor banks, whereas inthe case of an isolated/autonomous system, reactive power canonly be supplied by capacitor banks/SG. In addition, generally,most of the loads are also inductive in nature. The mismatch ingeneration and consumption of the reactive power can causea serious problem of large voltage fluctuations at generatorterminals.

A detailed literature survey [6], [10] shows that there is agreat need to improve the reactive-power-control strategy ofthe autonomous hybrid power system to maintain the voltagewithin the specified limits. SVC [14]–[20] is one of the flexibleac transmission systems (FACTS), which is commonly usedfor reactive-power control in the power system. The primarypurpose of SVC is to regulate the voltage of the transmissionsystems. In a stand-alone hybrid power system, the reactive-power device has to fulfill the variable reactive-power require-ments of the IG and of the load. In the absence of properreactive device and controls, the system may be subjected tolarge voltage fluctuations, which is not desirable.

This paper presents a new innovative automatic reactive-power-control scheme that is similar to automatic generationcontrol [21], [22] for isolated hybrid power systems. The sys-tem state equations have been derived with transfer-functionblock-diagram representation of the control system. The volt-age deviation signal is used as the reactive-power-control errorto eliminate the reactive-power mismatch in the system. Tostudy the effect of the size of the wind unit on the system

Fig. 1. Schematic diagram of general isolated wind–diesel hybrid powersystem.

performance, three wind–diesel hybrid systems are consideredwith different wind-generation capacities. The mathematicalmodel of the system using reactive-power-flow equations isdeveloped. Three different types of SVCs [14]–[19] commonlyused in conventional power system are considered in orderto compare their performance in the hybrid system. Finally,the dynamic responses of the hybrid power systems with anoptimum gain setting are presented.

II. MATHEMATICAL MODELLING OF

WIND–DIESEL SYSTEM

A wind–diesel system, as shown in Fig. 1, is considered formathematical modeling, where the SG considered with IEEEtype-I excitation system connected on the DG set acts as alocal grid for the IG connected on the wind energy-conversionsystem. The system also has an SVC to provide the requiredreactive power in addition to the reactive power generated bythe SG. Wind–diesel system data are given in Appendix I.Small changes in the real power are mainly dependent uponthe frequency, whereas a small change in the reactive poweris mainly dependent on the voltage [21]. The excitation timeconstant is much smaller than the prime-mover time constant,and its transient decays much faster and does not affect theload-frequency-control (LFC) dynamic. Thus, cross couplingbetween the LFC and the automatic-voltage-regulator (AVR)loop is negligible. The reactive-power balance equation of thesystem under steady-state condition is

QSG + QSVC = QL + QIG (1)

where QSG = reactive power generated by DG set (per unit(pu) kilovolt-amperes reactive); QSVC = reactive power gen-erated by SVC (per unit kilovolt-amperes reactive); QL =reactive-power-load demand (per unit kilovolt-amperes re-active), and QIG = reactive power required by generator (perunit kilovolt-amperes reactive).

For the incremental reactive-power-balance analysis of thehybrid system, let the hybrid system experience a reactive-power-load change of magnitude ∆QL. Due to the action of


Fig. 2. Small-signal models of thyristor-controlled SVC schemes. (a) Type-I. (b) Type-II. (c) Type-III.

the AVR and SVC controllers, the system reactive-power gen-eration increases by an amount ∆QSG + ∆QSVC. The reactivepower required by the system will also change due to a changein voltage by ∆V . The net reactive-power surplus in the system,therefore, equals ∆QSG + ∆QSVC − ∆QL − ∆QIG, and thispower will increase the system voltage in two ways:

1) by increasing the electromagnetic-energy absorption(EM) of the IG at the rate d/dt (EM);

2) by an increased reactive load consumption of the systemdue to an increase in voltage.

This can be expressed mathematically as

∆QSG + ∆QSVC − ∆QL − ∆QIG

= d/dt(∆EM) + DV∆V. (2)

The electromagnetic energy stored in the IG is given by

EM =12LMIM

2 =12LM(V/XM)2 (3)

where IM, LM, and XM are the current drawn, inductance, andreactance of the IG, respectively.

Equation (3) can be further written as

EM = V 2/(4πfXM) (4)

where f is system frequency. From (4), ∆EM can be written as

∆EM = EM − EoM = 2 (Eo

M/V o) ∆V (5)

where V o and EoM are the nominal values of terminal voltage

and electromagnetic energy stored in the IG. With the increasein voltage, all the connected reactive-power-loads experience

an increase by DV = ∂QL/∂V (per unit kilovolt-amperesreactive/per unit kilovolt). The reactive-power loads can beexpressed in the exponential voltage form as [23]

QL = C1Vq (6)

where C1 is the constant of the load, and the exponent qdepends upon the type of load. For small perturbations, (6) canbe written as

∆QL/∆V = q (QoL/V

o) (7)

where QoL is the nominal value of the reactive-power-load

demand. In (2), DV can be calculated empirically using (7).Let QR be the system reactive-power rating.

Using (5), (2) can be written as

∆QSG + ∆QSVC − ∆QL − ∆QIG =2Eo

M/(V oQR)d/dt(∆V ) + DV∆V. (8)

In (8), QR divides only one term as all the other terms arealready in pu kilovolt-amperes reactive. The term Eo

M/QR canbe written as

EoM/QR = 1/(4πfkR) = HR (9)

where HR is the constant of the system, which has a unit of“s,” and kR is the ratio of the system reactive-power rating torated magnetizing reactive power of IG. Substituting the valueof Eo

M/QR from (9) in (8), we get

∆QSG + ∆QSVC − ∆QL − ∆QIG

= 2HR/Vod/dt(∆V ) + DV∆V. (10)


Fig. 3. Transfer-function block diagram for the reactive-power control of the wind–diesel hybrid power system.

In Laplace form, the state differential equation from (10) canbe written as

∆V (s) =KV/(1 + sTV )× [∆QSG(s)+∆QSVC(s)−∆QL(s)−∆QIG(s)]

(11)

where

TV =2HR

DVV o(12)

and

KV =1DV

. (13)

Under transient condition, QSG is given by [21]

QSG = (E ′qV cos δ − V 2)/X ′

d. (14)

For small perturbation, (14) can be written as

∆QSG = (V cos δ/X ′d)∆E ′

q

+{(E ′

q cos δ − 2V)/X ′

d

}∆V. (15)

In Laplace transform, (15) can be written as

∆QSG(s) = K3∆E ′q(s) + K4∆V (s) (16)

where

K3 = (V cos δ)/X ′d (17)

and

K4 =(E ′

q cos δ − 2V)/X ′

d. (18)

The reactive power supplied by the SVC is given by[20], [25]

QSVC = V 2BSVC. (19)

For small perturbation, (19) in the Laplace-transform formcan be written as

∆QSVC(s) = K6∆V (s) + K7∆BSVC(s) (20)

where

K6 = 2V BSVC


TABLE IOPTIMUM GAIN SETTINGS OF SVCS FOR DIFFERENT HYBRID

POWER SYSTEMS CONSIDERED

Fig. 4. Optimization of the amplifier gain of SVC type-I for the wind–dieselhybrid power system. (a) System data-I. (b) System data-II. (c) System data-III.

and

K7 =V 2. (21)

The flux linkage equation [24] of the round rotor synchronousmachine for small perturbation is given as

d/dt(∆E′q) = (∆Efd − ∆Eq)/T ′

do. (22)

In (22), ∆Eq is given by

∆Eq =xd

x′d

∆E ′q −

(xd − x′d)

x′d

cos δ∆V. (23)

For small changes, (22), using (23) in the Laplace-transformform, can be written as

(1 + sTG)∆E ′q(s) = K1∆Efd(s) + K2∆V (s) (24)

where

TG = (X ′dT

′do) /Xd (25)

K1 =X ′d/Xd (26)

K2 = {(Xd −X ′d) cos δ} /Xd. (27)

IG equations for constant slip model [8], [25] for small per-turbation, reactive power absorbed by IG, QIG in terms ofgenerator terminal voltage, and generator parameters can bewritten as

∆QIG(s) = K5∆V (s) (28)

where

K5 =2V Xeq

R2Y + X2

eq

(29)

RY =RP −Req (30)

and

RP =R′

2

s(1 − s) . (31)

The transfer-function models of the three different SVCmodels considered are shown in Fig. 2. The basic differencein the transfer-function block diagrams is the type of varregulator used. In SVC type-I [14], [15], the var regulatoris an amplifier with a gain and time constant. The regulatorin SVC type-II [16], [17] model is a twin lead-lag type forproviding compensation for the time delays in the firing circuitand due to phase-sequence dead-time delay of the zero crossing.The var regulator is proportional plus integral in SVC type-III[18], [19] model.

The block diagram of the system using the Laplace transferfunction (11), (16), (20), (24), and (28) with SVC type-1 andIEEE type-I excitation system is shown in Fig. 3. The state-space equations in a standard form can be written as

x = [A]x + [B]u + [C]p (32)

The vectors are given as

x = [∆Efd ∆Va ∆Vf ∆E ′q ∆BSVC ∆B′

SVC ∆α ∆V ]T

(33)u = [∆Vref ] (34)p = [∆QL]. (35)

The block diagrams with SVC types-II and III can be ob-tained by replacing the dotted portion of Fig. 3 with Fig. 2(b)and (c), respectively. The elements of the associated matricescan be obtained from the mathematical modeling of hybridpower system, and from Figs. 2 and 3 are given in Appendix II.

III. TRANSIENT RESPONSES OF THE

WIND–DIESEL SYSTEMS

In this section, transient responses of isolated wind–dieselhybrid power systems are presented. To study the effectof the size of the wind-turbine unit of the system on thetransient performance, three examples of the hybrid system are


Fig. 5. (a)–(h) Transient responses of the wind–diesel hybrid power system (System Data-I) with SVC type-I for a 1% step increase in the reactive-power load.

considered with different wind-power generation capacities.Three SVC configurations for reactive-power control areconsidered along with the IEEE type-I excitation controlsystem of SGs. Transient responses are compared in terms ofthe first-swing amplitude and settling time, etc.

The values of the constants have been calculated using thedata given in Appendix I. For the wind–diesel systems, thedata-I constants are given as

K1 =0.15K2 =0.793232K3 =6.22143K4 =−7.358895K5 =0.126043K6 =1.478K7 =1.0KV =0.6667Kα =0.446423TV =0.000106 s.

The values of the constants for the wind–diesel system data-IIare given by

K2 = 0.7589468K3 = 5.952524K4 =−7.823439K5 = 0.1067734K6 = 1.3364Kα = 0.403279.

The other constants remain the same as for system data-I.The values of the constants for wind–diesel system data-III

are given byK2 =0.673608K3 =5.2832K4 =−8.906K5 =0.052182K6 =0.996Kα =0.30056.

The other constants remain the same as for system data-I.


Fig. 6. (a)–(h) Transient responses of the wind–diesel hybrid power system (System Data-II) with SVC type-I for a 1% step increase in the reactive-power load.

Fig. 7. (a)–(h) Transient responses of the wind–diesel hybrid power system (System Data-III) with SVC type-I for a 1% step increase in the reactive-power load.


TABLE IIMAXIMUM DEVIATIONS OF DIFFERENT PARAMETERS OF WIND–DIESEL SYSTEMS FOR 1% STEP INCREASE IN THE REACTIVE-POWER LOAD

Fig. 8. Optimization of the amplifier gain of the wind–diesel hybrid powersystem for system data-I. (a) SVC type-II. (b), (c) SVC type-III.

The gains are optimized using the Lyapunov technique forcontinuous linear systems with the performance index (η) usingan integral square error criterion (ISE) and is given as

η =∫

[∆V (t)]2 dt. (36)

The optimum value of the parameters corresponds to theminimum value of the η. The SVC type-I amplifier-regulatorgain parameter KR is optimized, and the values are givenin Table I. The loci for η against KR for the three systemexamples are shown in Fig. 4. It is observed that as theunit size of the wind-power generation decreases, the valueof the optimum gain setting increases. It is because of the

decrease in the SVC rating with the decrease in the unit size ofthe wind-power generation, therefore, higher gain is requiredto offset the reactive-power mismatch during the transientcondition.

The transient performance for a 1% step increase in thereactive-power load for system data-I, II, and III with SVCtype-I are shown in Figs. 5–7, respectively. Table II shows themaximum deviations of the main parameters of wind dieselfor a 1% step increase in the reactive-power load. It is foundthat the peak deviation in the terminal bus voltage decreaseswith the decrease in the size of the wind-power genera-tion/IG, but the settling time of the oscillations remainsthe same.

The deviations in the field excitation (∆Efd), internal ar-mature voltages under steady-state (∆Eq), and transient con-ditions (∆E′

q) also follow the same trend. It indicates thatas the ratio of the SG size to the IG size increases, a bettercontrol of the terminal voltage is obtained. The peak deviationin the firing angle (α) of the thyristor-controlled-reactor (TCR)unit of the SVC increases with the decrease in the size ofthe wind-power generation, but the settling time of the oscil-lations remains the same for the three examples of the hybridpower systems.

There is no steady-state error in the terminal voltage ofthe system with SVC control; therefore, the deviation in thereactive power required by the IG vanishes. It is observed thatthe increase in the reactive-power load is purely met by SVC.In all of the three examples of the system, it is found that theoscillation vanishes in about 0.25 s.

The different loci for η against various gain parametersare shown in Fig. 8 for the system data-I with SVC types-IIand III. The transient performance for 1% step increase inthe reactive-power load for the system examples-I, with SVCtype-II and SVC type-III, are shown in Figs. 9, and 10, re-spectively. It can be seen from Table II and Figs. 5, 9, and10 that the system performance is best with SVC type-IIin terms of the minimum first swing and damping of thesubsequent oscillations in comparison to the other types ofSVCs under consideration. In case of SVC type-II, the transientperformance improves considerably but due to the absence ofthe integral action, steady-state error persists following a stepdisturbance.

IV. CONCLUSION

A dynamic voltage stability study has been presented inthis paper for the isolated wind–diesel hybrid power system


Fig. 9. (a)–(h) Transient responses of the wind–diesel hybrid power system (System Data-I) with SVC type-II for a 1% step increase in the reactive-power load.

Fig. 10. (a)–(h) Transient responses of the wind–diesel hybrid power system (System Data-I) with SVC type-III for a 1% step increase in the reactive-power load.


TABLE IIIWIND-DIESEL SYSTEM DATA

considering a transfer-function model based on a small sig-nal analysis. The automatic reactive-power-control model us-ing reactive-power-flow equations have been developed forhybrid systems. It is observed that as the unit size of thewind-power generation decreases, the value of the optimumgain setting increases. It can be seen that the system per-formance is best with the SVC type-II in terms of theminimum first swing and damping of the subsequent os-

cillations in comparison to the other types of SVCs underconsideration.

APPENDIX I

The data of the isolated three different wind–diesel hybridpower system, SG, IG, load, reactive-power data, excitationcontrol, and three different types of SVC are given in Table III.


TABLE IVELEMENTS OF MATRICES FOR WIND-DIESEL SYSTEM

APPENDIX II

See Table IV(a)–(c).

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R. C. Bansal (S’99–A’02–SM’03) received the M.E.degree from Delhi College of Engineering, Delhi, In-dia, in 1996, the M.B.A. degree from Indira GandhiNational Open University, New Delhi, India, in 1997,and the Ph.D. degree from Indian Institute of Tech-nology (IIT), Delhi, India, in 2003.

He is with the faculty of the Electrical and Elec-tronics Engineering Division, School of Engineeringand Physics and Head of the Renewable EnergyGroup, The University of the South Pacific, Suva,Fiji. He was an Assistant Professor in the Department

of Electrical and Electronics Engineering, Birla Institute of Technology andScience, Pilani, India, from June 1999 to December 2005. He also worked fornine years with the Civil Construction Wing, All India Radio. He has publishedmore than 50 papers in national/international journals and conference proceed-ings. His research interests include reactive power control in renewable energysystems and conventional power systems, power system optimization, analysisof induction generators, and artificial intelligence techniques applications inpower systems.

Dr. Bansal is the Editor of the IEEE TRANSACTIONS ON ENERGY

CONVERSION and Power Engineering Letters. He is a member of the Institutionof Engineers (India) and a Life Member of the Indian Society of TechnicalEducation.

automatic reactive power control of isolated wind diesel hybrid power systems

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