Electrical Power and Energy Systems 33 (2011) 1092–1100

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Electrical Power and Energy Systems

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Robust control of an isolated hybrid wind–diesel power system using LinearQuadratic Gaussian approach

Ahmed M. Kassem a,⇑, Ali M. Yousef b

a Control Technology Dep., Beni-Suef University, Egyptb Electrical Eng. Dep., Assiut University, Egypt

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 October 2008Accepted 1 January 2011Available online 19 February 2011

Keywords:Wind turbineInduction generatorSynchronous generatorRobust control and LQG control

0142-0615/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijepes.2011.01.028

⇑ Corresponding author.E-mail address: Kassem_ahmed53@hotmail.com (A

This paper presents the application of the Linear Quadratic Gaussian (LQG) controller for voltage and fre-quency regulation of an isolated hybrid wind–diesel scheme. The scheme essentially consists of a verticalaxis wind turbine driving a self-excited induction generator connected via an asynchronous (AC–DC–AC)link to a synchronous generator driven by a diesel engine. The synchronous generator is equipped with avoltage regulator and a static exciter. The wind generator and the synchronous generator together caterfor the local load and power requirement. However, the load bus voltage and frequency are governed bythe synchronous generator. The control objective aims to regulate the load voltage and frequency. This isaccomplished via controlling the field voltage and rotational speed of the synchronous generator. Thecomplete nonlinear dynamic model of the system has been described and linearized around an operatingpoint. The standard Kalman filter technique has been employed to estimate the full states of the system.The computational burden has been minimized to a great extent by computing the optimal state feed-back gains and the Kalman state space model off-line. The proposed controller has the advantages ofrobustness, fast response and good performance. The hybrid wind diesel energy scheme with the pro-posed controller has been tested through a step change in both wind speed and load impedance. Simu-lation results show that accurate tracking performance of the proposed hybrid wind diesel energy systemhas been achieved.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

During last three decades, the assessment of potential of thesustainable eco-friendly alternative sources and refinement intechnology has taken place to a stage so that economical and reli-able power can be produced. Different renewable sources are avail-able at different geographical locations close to loads, therefore,the latest trend is to have distributed or dispersed power system.Example of such systems is wind–diesel. This system is known ashybrid power systems.

The advantage of hybrid power systems is the combination ofthe continuously available diesel power and locally available, pol-lution-free wind energy. With the hybrid power system, the annualdiesel fuel consumption can be reduced and, at the same time, thelevel of pollution can be minimized. A proper control strategy hasto be developed to take full advantage of the wind energy duringthe periods of time it is available and to minimize diesel fuel con-sumption. Therefore, a proper control system has to be designed,subject to the specific constraints for a particular application. Ithas to maintain power quality, measured by the quality of

ll rights reserved.

.M. Kassem).

electrical performance, i.e., both the voltage and the frequencyhave to be properly controlled [1]. These results in a need for a sim-ulation study of each new system to confirm that a control strategyresults in desired system performance.

The wind–diesel systems are normally equipped with a controlsystem, which functions to reduce the system frequency oscilla-tions, when the system is subjected to wind/load disturbances [2].

Various control strategies have concerned with the voltage and/or frequency control of the hybrid wind–diesel power system andachieving optimal out of the turbine. In some schemes, the hybridwind–diesel power system uses compressed air energy storagewith the wind–diesel hybrid system [3]. Other control schemesuse static VAR compensators for reactive power control [4]. Math-ematical modeling of a typical hybrid system with PI controllersand system dynamic studies on it has been reported by Scott [5].However, it is well known that the performance of the systemswith fixed gain controllers designed on the fixed parameter modelof the system does not stay optimal as the system parameters un-dergo a change.

Recently, advanced control techniques, which were applied suc-cessfully on the machine drives, have been proposed for regulatingthe wind power in a grid connected wind energy conversionscheme. They include Artificial neural networks [6–8], fuzzy

Nomenclature

vds, vqs d–q stator voltages of induction generatorids, iqs d–q stator currents of induction generatoridr, iqr d–q rotor currents of induction generatorRs, Rr stator and rotor resistances per phase of induction gen-

eratorLs, Lr, Lm stator, rotor and magnetizing inductances of induction

generatorC0 self excitation capacitance per phase of induction gener-

atorxs angular stator frequency of the induction generatorxm angular rotor speed (electrical rads/s) of the induction

generatorJ moment of inertiaf friction coefficientp differential operator d/dtLDC DC-link inductanceRDC DC-link resistanceaR, aI firing angles of the converter and invertervdcon, vqcon d–q input voltage of the converter

idcon, iqcon d–q input current of the converterIDC DC-link currentvinv inverter output voltagevr

q;v rd d–q stator voltages of synchronous generator

vrkd;v

rkq d–q damper winding voltages of synchronous generator

vrf field winding voltage of synchronous generator

ird; irq d–q stator currents of synchronous generator

irkd; irkq d–q damper winding currents of synchronous generator

irf field winding current of synchronous generatorRs stator resistance of synchronous generatorRkd, Rkq d and q damper winding resistancesLmd, Lmq d and q mutual inductancesLd, Lq d and q self inductancesxsg rotor speed (electrical rads/s) of the synchronous gener-

atorTmd torque input from diesel engineur, uf applied and actual fuel flow rate of diesel engines1 combustion delay time constants2, K2 time constant and gain of fuel rack position actuator

A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100 1093

control [7–9] and vector control [10]. In these methods, the speedfeedback may be necessary to avoid instability. Moreover, windvelocity information may be needed as well. Also, the key pointof direct power schemes is a correct and fast estimation of the ac-tive and reactive power as well as fast PI controllers.

In This paper, A controller design and simulations of awind–diesel generation plant based on LQG approach is pre-sented. This generation plant is conceived to supply electricpower to an isolated load not connected to the electrical net-work. The main power generation system consists of a windturbine driving a self-excited induction generator connectedvia an asynchronous DC-link to a synchronous generator drivenby a diesel engine. The synchronous generator is equippedwith a voltage regulator and a static exciter. The wind gener-ator and the synchronous generator together feed the localload.

The proposed hybrid wind diesel energy scheme with the pro-posed controller has been tested through a step change in bothwind speed and load impedance. Simulation results show that

Fig. 1. Block schematic diagram of the propose

accurate tracking performance of the proposed hybrid wind dieselenergy system.

2. System description

Fig. 1 shows a hybrid wind–diesel interface scheme, to supply alocal isolated load. The scheme essentially consists of a vertical axiswind turbine driving a self-excited induction generator (SEIG) con-nected via an asynchronous (AC–DC–AC) link to a synchronousgenerator driven by a diesel engine. The synchronous generatoris equipped with a voltage regulator and a static exciter. The windgenerator and the synchronous generator together feed the localload power requirement.

3. System dynamic model

The dynamic models of the different parts of the system can bedescribed as follows.

d hybrid wind–diesel generation system.

1094 A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100

3.1. Wind side dynamic model

The wind side system is consists of wind turbine, induction gen-erator and DC-link which can model as following.

3.2. Wind turbine dynamic model

The wind turbine is characterized by no dimensional curves ofthe power coefficient Cp as a function of both the tip speed ratio,k and the blade pitch angle, b. In order to fully utilize the availablewind energy, the value of k should be maintained at its optimumvalue. Hence, the power coefficient corresponding to that valuewill become maximum also.

The tip speed ratio k can be defined as the ratio of the angularrotor speed of the wind turbine to the linear wind speed at thetip of the blades. It can be expressed as follows:

k ¼ xtR=Vw ð1Þ

where R is the wind turbine rotor radius, Vw is the wind speed andxt is the mechanical angular rotor speed of the wind turbine.

The torque available from the wind turbine can be expressed as[11]:

Tm ¼ 0:5qAR ð0:44� 0:0167Þb sinxt RVw� 3

15� 0:3b

!"

�0:00184xtRVw� 3

� �b

#V3

w=xt: ð2Þ

where q is the air density, and A is the swept area by the blades.

3.3. Induction generator dynamic model

The dynamic behavior of the induction generator in the dr�qr

axis synchronously rotating reference frame is given by [12]:

piqs ¼ �RsA1iqs � ðxs þ A2xmLmÞids þ RrA2iqr � A1xmLridr ð5Þpids ¼ ðxs þ A2xmLmÞiqs � RsA1ids þ RrA2idr þ A1xmLmiqr � A1vds ð6Þpiqr ¼ RsA2iqs þ A2xmLsids � A3iqr þ ð�xs þ A1xmLsÞidr ð7Þpidr ¼ �A2xmLsiqs þ RsA2ids þ ðxs � A1xmLsÞiqr � A3idr þ A2vds ð8Þ

where vqs = 0, due to the choice of axis alignment, and

A1 ¼ Lr=ðLsLr � L2mÞ; A2 ¼ Lm=ðLsLr � L2

mÞ; and

A3 ¼ Rrð1þ A2LmÞ=Lr

The rotor speed xm is governed by the following differentialequation:

Tm þ Te ¼ ðJpþ f Þxm=P ð9Þ

where P is number of poles of the induction generator, Tm is the in-put torque from the prim-mover, and Te is the electromagnetic tor-que representing the load on the induction generator (Te is negativefor generator action ) which is given by:

Te ¼ 1:5PLmðiqsidr � idsiqrÞ ð10Þ

Eqs. (9) and (10) are combined as

pxm ¼ ð�fxm þ PTm þ 1:5P2Lmðiqsidr � idsiqrÞÞ=J ð11Þ

dsvqsv

dsi

dci qci

qlidli qsi

0C0C

Fig. 2. d–q Equivalent circuit of the self excitation capacitor.

3.4. Asynchronous DC-link model

The asynchronous DC-link (used to interface the wind energysystem to the utility) consists of a six pulse line commutated con-verter, a smoothing reactor, and a six pulse line commutated inver-ter. An isolating transformer of turns ratio 1:n interconnects theinduction generator to the converter. Neglecting the resistance

and leakage reactance of the isolating transformer, the various acquantities on the primary and secondary sides can be related by:

vdcon ¼ nvds; vqcon ¼ nvqs; iqcon ¼ iql=n; idcon ¼ idl=n ð12Þ

Assuming the converter is lossless, the instantaneous power bal-ance equation (vqcon = 0, due to the choice of axis alignment):

32

vdconidcon ¼ VRIDC ð13Þ

where VR is the DC voltage at the converter output terminals whichcan be written as:

VR ¼3ffiffiffi3p

pnvds cos aR ð14Þ

The ac and dc currents of the converter are related by:

icon ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiði2

qcon þ i2dconÞ

q¼ 2

ffiffiffi3p

pIDC ð15Þ

Neglecting the commutation overlap, the d–q converter currentscan be deduced using Eqs. (13)–(15) as:

idcon ¼ icon cos aR ¼2ffiffiffi3p

pIDC cos aR ð16Þ

iqcon ¼ �icon sin aR ¼ �2ffiffiffi3p

pIDC sin aR ð17Þ

Referring to Fig. 1, the dynamics introduced by the DC-link is givenby:

LDCpIDC þ RDCIDC ¼ VR � VI ð18Þ

where VI is the DC voltage at the inverter input terminals which canbe expressed as:

VI ¼ �3ffiffiffi3p

pv inv cos aI þ

3xci

pIDC ð19Þ

where xci is the commutating reactance.Combining Eqs. (12), (17) and (18) the following equation can

be obtained:

pIDC ¼ �RDCIDC þ3ffiffiffi3p

pnvds cos aR þ

3ffiffiffi3p

pv inv cos aI �

3xci

pIDC

!,LDC

pIDC ¼�RDC � 3xci

p �18RLp2 cos aIð Þ2 � 18xeLL

p2 sin aIð Þ2� �

IDC

þ 3ffiffi3p

p n cos aRvds þ 3ffiffi3p

nop cos aI

irq cosðdÞ þ ir

d sinðdÞ�ir

q sinðdÞ þ ird cosðdÞ

!0BBB@

1CCCA,

LDC

ð20Þ

3.5. Self excitation capacitor model

Referring to the d–q equivalent circuit of the self excitationcapacitor shown in Fig. 2, the following differential equations canbe written:

A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100 1095

pvqs ¼iqc

C0�xsvds ð21Þ

pvds ¼idc

C0þxsvqs ð22Þ

Since, vqs = 0, due to the choice of axis alignment, Eqs. (21), (22) canbe rewritten as:

xs ¼iqc

C0vdsð23Þ

pvds ¼idc

C0ð24Þ

Referring to Fig. 2, the values of iqc and idc can be written as:

iqc ¼ iqs � iql; idc ¼ ids � idl ð25Þ

Eqs. (12), (15) and (16) are combined with Eq. (25) as:

iqc ¼ iqs þ2ffiffiffi3p

pnIDC sin aR; idc ¼ ids �

2ffiffiffi3p

pnIDC cos aR ð26Þ

Substituting the values of iqc and idc from Eq. (26) into Eqs. (23) and(24) would give:

xs ¼iqs þ 2

ffiffi3p

p nIDC sinaR

C0vdsð27Þ

pvds ¼ids � 2

ffiffi3p

p nIDC cos aR

C0ð28Þ

Eq. (27) can be used to determine the electrical frequency of thevoltage generated by the induction generator.

3.6. Diesel side dynamic model

Diesel side system consists of diesel engine, synchronous gener-ator and the load which can modeled as following

3.7. Synchronous generator dynamic modeling

The dynamic behavior of the synchronous generator in the dr–qr

axis synchronously rotating reference frame fixed in the rotor (i.e.,dr–qr reference frame rotating at the rotor speed xsg) is given by[12]:

pirq ¼

L0kq

L0kq � L2mq

� � �Rsirq �

L0kqL0mq

L0kq

ir0

kq

"

�xsgird þxsgLmdir0

kd þxsgLmdir0

f � Vrq

#: ð29Þ

pird ¼

1K11

xsgLqirq � Rsi

rd �xsgLmqir0

kq

þ K22R0kdL0f þ K33R0kdLmd

� �ir0

kd

� K22Lmd þ K33L0kd

� �R0f ir0

f

þ K22Lmd þ K33L0kd

� �v r0

f � v rd

26666664

37777775 ð30Þ

pir0

kq ¼ �R0kq

L0kq

ir0

kq þ K44

�Rsirq �

R0kqLmq

L0kqir0

kq �xsgLdird

þxsgLmdir0

kd þxsgLmdir0

f � v rq

24 35 ð31Þ

pir0

kd ¼ K22

v r0f þ

Lmd�L0fð ÞK11

xsgLqirq � Rsi

rd �xsgLmqir0

kq

þðK22L0f R0kd þ K33LmdR0kdÞir0

kd

�ðK22LmdR0kd þ K33L0kdÞR0f i

r0

f

þðK22LmdR0kd þ K33L0kdÞv r0f � v r

d

0BBBBB@

1CCCCCAþ R0kdL0f

Lmdir0

kd � R0f ir0

f

26666666664

37777777775ð32Þ

pir0

f ¼L0kd

LmdK33

v r0f þ 1

K11K55

xsgLqirq � Rsi

rd �xsgLmqir0

kq

þðK22L0f R0kd þ K33LmdR0kdÞir0

kd

�ðK22Lmd þ K33L0kdÞR0f i

r0

f

þðK22L0f R0kd þ K33LmdR0kdÞv r0f � v r

d

0BBBBB@

1CCCCCAþ R0kdLmd

L0kdir0

kd � R0f ir0

f

26666666664

37777777775:

ð33Þ

where

K11 ¼ Ld �L2

md Lmd � L0f� �

L2md � L0f L

0kd

� � � Lmd LmdL0kd � L2md

� �L0f L0kd � L2

md

� �K22 ¼

Lmd

L2md � L0f L0kd

� � ; K33 ¼Lmd

L0f L0kd � L2md

� � ;K44 ¼

Lmq

LqL0kq � L2mq

� � ; K55 ¼L0kd

LmdL0kd � L2md

� � ;The qr and dr stator voltages in the reference frame fixed in the rotorare given by:

v rq ¼ �ir

qRs �xsgLdird þxsgLmdir0

kd þxsgLmdir0

f ð34Þ

v rd ¼ �ir

dRs þxsgLqirq �xsgLmqir0

kq ð35Þ

The rotor speed wsg is governed by the following differentialequation:

2po

Jpxsg þ fxsg� �

¼ Tmd � Te ð36Þ

where Po is the number of poles of synchronous generator, Tmd is theinput torque from the prime mover (diesel engine) and Te is theelectromagnetic torque representing the electrical load on the syn-chronous generator and is given by:

Te ¼32

� �po

2

� �Lmd �ir

d þ ir0

f þ ir0

kd

� �irq � Lmq �ir

q þ ir0

kq

� �ird

h ið37Þ

Lastly, the torque angle representing the electrical load on the syn-chronous generator is given by:

pd ¼ 2po

xsg �xe� �

þ do ð38Þ

where wsg and we are the synchronous generator’s rotor speed andelectrical frequency respectively and do is the initial torque angle. Insteady state, wsg and we are the same, but during transient wsg

changes and ultimately settles down to the value we. The veq and

ved stator voltages in the reference frame fixed with the synchro-

nously rotating frame MMF vector rotating at an angular velocityxe are given by:

veq ¼ v r

q cosðdÞ þ v rd sinðdÞ ð39Þ

ved ¼ �v r

q sinðdÞ þ v rd cosðdÞ ¼ 0 ð40Þ

vL ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffive

q

� �2þ ve

d

� �2

r¼ ve

q ð41Þ

The initial orientation of q and d reference frame is chosen such thatve

d is initially zero and the load voltage VL ¼ veq.

3.8. Voltage regulator and static exciter model

The voltage and frequency at the local load bus are set by thesynchronous generator. Under load excursion, the load voltagetends to vary. In order to regulate the bus voltage, the synchronousgenerator is equipped with an automatic voltage regulator (AVR)and a static exciter [12]. The static exciter is an ‘‘inverted’’ three

s

1e

e

s

K

τ+1

Lrefv fv′cv

Lv

Fig. 3. Static voltage regulator loop.

1096 A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100

phase generator, with the automatic windings on the rotor and thefield windings on the stator. The AC armature voltage is rectifiedusing diodes mounted on the rotating shaft, and the rectified volt-age is applied to the synchronous generator field as shown in Fig. 3.The differential equations describing the excitation system for thesynchronous generator are as follows:

pvc ¼ðVLref � VLÞ ¼ Vref

�RL ir

q cosðdÞ þ ird sinðdÞ � 2

ffiffi3p

pnoIDC cosðaiÞ

� �þxeLL �ir

q sinðdÞ þ ird cosðdÞ � 2

ffiffi3p

pnoIDC sinðaiÞ

� �8><>:

9>=>; ð42Þ

pv 0f ¼Kevc � v 0f

seð43Þ

where Ke is the gain of the exciter and se is the time constant of theexciter.

3.9. Speed regulator and diesel engine model

The synchronous generator is driven by a diesel engine whichcontrols the mechanical power input to the generator to balancethe electrical load on the machine. If the electrical load on the gen-erator changes due to change in power drawn by the local load, therotor speed and hence the electrical frequency tend to change. Insuch a situation the mechanical power (or torque) input to the syn-chronous generator is controlled to regulate the system electricalfrequency. The block diagram of the diesel engine is shown inFig. 4 [12]. The input signal is the speed (frequency) error and isused to determine the applied fuel flow rate ur depends on the po-sition of the fuel rack which is controlled by the fuel actuator, char-acterized by a gain k2 and a time constant s2. the torque output Tmd

of the diesel engine is proportional to the actual fuel flow rate uf,but is delayed by the fuel combustion process time delay s1. Thetorque output of the diesel engine is:

Tmd ¼ K1/f e�s1s ð44Þ

where K1 is constant relating the torque output to the fuel flow rate.The combustion process delay can be approximated using first or-der Pad’s approximation as follows:

Fig. 4. state space representation of dies

e�s1s ¼2s1� s

� �2s1þ s

� � ð45Þ

The actual fuel flow rate uf is dependent on the applied fuel flowrate ur and is given by:

uf ¼K2

1þ s2sð Þur ð46Þ

where K2 and s2are gain and time constant of the fuel actuator. Thedifferential equations describing the diesel engine and its speedgovernor are given by [12]:

pur ¼ xsgref �xsg ð47Þ

puf ¼K2ur �uf

s2ð48Þ

px1 ¼4uf � 2x1

s1ð49Þ

Tmd ¼ K1ðx1 �uf Þ ð50Þ

4. Small signal linearized model

The subsystem models can be interfaced to form the unifiednonlinear model.

The nonlinear model of the hybrid wind–diesel generation sys-tem are linearized around an operating point as following:

px ¼ Axþ Blþ vd ð51Þ

where

x ¼ X1 X2½ �

and

X1 ¼ Diqs Dids Diqr Didr Dxm Dvds DIDC Dirq Dir

d Dirkq

h i

X2 ¼ Dirkd Dir

f Dxsg Dd DVc DV 0f Dur Duf Dx1

h il ¼ VLref xsgref½ �t

d ¼ DZL Vw½ �

A ¼ ½aij� is a 19� 19 matrix:

5. Control strategy

In this paper, the LQG controller has been employed to controlthe terminal voltage and frequency of an isolated hybrid wind–

el engine and speed regulator loop.

A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100 1097

diesel generation unit. The LQG is a modern state space techniquefor designing optimal dynamic regulators. It has the followingadvantages:

(1) It enables to trade off regulation performance and controleffort.

(2) It takes into account the process disturbance and measure-ment noise.

The LQG controller consists of an optimal state feedback gain‘‘k ’’ and a Kalman state estimator. The optimal feedback gain is cal-culated such that the feedback control law

u ¼ �kx

minimizes the performance index:

H ¼Z /

0xT Qxþ uT Ru� �

dt

where Q and R are positive definite or semi definite Hermittian orreal symmetric matrices. The optimal state feedback u =�kx is notimplemental without full state measurement. In our case, the loadcurrent only is chosen to be the output measured signal. The Kal-man filter estimator is used to drive the state estimation:

x ¼ bX1bX2

h iandbX1 ¼ Diqs Dids Diqr Didr Dxm Dvds DbIDC Dir

q Dird Dir

kq

h ibX2 ¼ Dir

kd Dirf Dxsg Dd DbV c DcV 0 f Dur Duf Dx1

h i

Fig. 5. Block diagram of the hybrid wind–diesel generati

such that

u ¼ �kx

remains optimal for the output feedback problem. The state estima-tion is generated from [16]:

P ¼ ðA� Bk� LCÞxþ Ly

where L is the Kalman gain which is determined by knowing thesystem noise and measurement covariance Qn and Rn. However,the accuracy of the filter’s performance depends heavily upon theaccuracy of these covariance. On the other hand the matrices Aand B containing the hybrid wind–diesel generation system param-eters are not required to be very accurate due to the inherent feed-back nature of the system. The Kalman filter performs best for linearsystems. Therefore, The nonlinear model of the complete systemhas been linearized around an operating point. The optimal statefeedback gains and the Kalman state space model have been calcu-lated off-line which results in great saving in computational burden.On this basis, the implementation of the proposed controller be-comes easier and the hardware will be reduced to minimum.

6. System configuration

The block diagram of the isolated hybrid wind–diesel genera-tion system with the proposed LQG controller is shown in Fig. 5.All the commanded values are superscripted with asterisk in thediagram. The LQG controller contains the Kalman state estimatorin addition to optimal state feedback gains. The Kalman estimatoruses both the measured d–q stator current components of induc-tion generator and synchronous generator in order to estimateall the states including the d–q rotor current components of

on power system with the proposed LQG controller.

Fig. 6. Dynamic response of the proposed system with a step change in load impedance.

1098 A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100

synchronous generator, generator speed of induction and synchro-nous machines, d-axis generated voltage at induction generator,DC-link current, damper and field currents of synchronous genera-tor, fuel flow rate of diesel engine. These states are multiplied bythe corresponding optimal gains and summed to produce the con-trol signals necessary to regulate the field voltage and the shaftrotational speed of the synchronous generator.

The entire system has been simulated on the digital computerusing the Matlab/Simulink software package. The specificationsof the system used in the simulation procedure are listed in appen-dix [12].

The noise and measurement covariance are set as:

Q n ¼ diagð10;10Þ; Rn ¼ diagð1;1Þ

Also, the values of Q and R matrices which are necessary to calculatethe optimal feedback gains are set as:

Q ¼ diagð200 10 10 10 100 10 10 10 10 100 10 10

R ¼ diagð2:05 2:05 Þ:

7. Simulation results

Digital simulations have been carried out to validate the effec-tiveness of the proposed system under wind speed and load varia-tions. The performance of the proposed scheme has been testedwith a step changes in both wind speed and load impedance.

The simulation results depicting the variations in various vari-ables with a step change in local load impedance is shown inFig. 6. It is seen that as the local load impedance increases (the lo-cal current decrease), with wind velocity remaining constant, sothe rotor speed of the synchronous generator tried to increase.The control action comes in operation and decrease the power out-put of the synchronous generator to meet the decreased power de-mand of the load. This is achieved by decreasing the diesel fuel rate/f which in turn decreases the torque (mechanical power) to thesynchronous generator. Also, the field current is decreased to

10 10 10 10 10 10 1000 Þ;

Fig. 7. Dynamic response of the proposed system with a step change in wind speed.

A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100 1099

regulate the local bus voltage. And the opposed will happen whenthe local impedance decreases.

The effect of variations in wind velocity on the various systemvariables are shown in Fig. 7. It seen that with increase in windvelocity (that’s mean the power contributed by the inverter in-creases) and hence the load voltage and current increase. So thesame as the case of load impedance reduction, the controller comein operation and reduce the diesel fuel rate /f which in turn de-creases the torque (mechanical power) to the synchronous gener-ator. Also the field current of the synchronous generator decreases.That’s leads to adjusting the load voltage and frequency and viceversa if the wind speed decreases. It is also seen that the damperwinding current only come into play during the initial transients,and reduce to zero subsequently.

Simulation results indicate that a hybrid wind–diesel schemecan be adequately controlled and the local bus voltage andfrequency can be regulated by the use of AVR and a diesel enginewith robust LQG control.

8. Conclusions

This paper investigates the robust control of an isolatedwind–diesel generation system based on the LQG approach. Thecontrolled system consists of a diesel turbine that drives a synchro-nous generator connected to an isolated load and the synchronousgenerator is equipped with an automatic voltage regulator (AVR)and a static exciter and also wind turbine driven SEIG, which inter-faced to the load bus through DC-link. A complete model, controldesign and simulations of this scheme have been developed show-ing the ability of the controller to compensate both the wind poweroscillations and load disturbances. The local load bus voltage andfrequency are governed by the synchronous machine. The loadbus voltage is regulated via controlling the field current of the syn-chronous generator. Also, the load bus frequency is adjusted bycontrolling the rotor speed of the synchronous generator whichis adjusted by controlling the diesel fuel flow rate ur which in turnaffects the torque (mechanical power) input to the synchronous

1100 A.M. Kassem, A.M. Yousef / Electrical Power and Energy Systems 33 (2011) 1092–1100

generator and hence its rotation speed. The standard Kalman filtertechnique has been used to estimate the full states of the systemby measuring only the currents of both induction and synchronousgenerators. The proposed controller has the advantages of robust-ness, easy implementation and adequate performance in face ofuncertainties.

Digital simulations have been carried out in order to evaluatethe effectiveness of the proposed scheme. The wind–diesel energysystem with the proposed controller has been tested through stepchanges in wind speed and load impedance. The results prove thatthe proposed controller is successful in regulating the terminalvoltage and frequency of a stand alone wind–diesel energy conver-sion system under wind and/or load execursion.

Appendix A

A.1. Synchronous machine parameters

Rating: 2 kw, 208 V (line), 9 A, 4 pole, unity power factor.Constants: Rs = 0.88 X, Rf = 67.0 X, Lmd = 58 mH, Lmq = 24.9 mH,Llsd = Llsq = 2.92 mH, Llfd = 2.92 mH

Nse : Nfd ¼ 0:047 : 1Nse : Nkd ¼ 2:95 : 1Nse : Nkq ¼ 2:95 : 1

A.2. Wind turbine

Rating: 1 kw, 450 rpm (low speed side) at Vw = 12 m/s.Size: height = 4 m, equator radius = 1 m, swept area = 4 m2,q = 1.25 kg/m2.

A.3. Induction machine

Rating: 3-phase, 2 kw, 120 V, 10 A, 4-pole, 1740 rpm.Parameters: Rs = 0.62 X, Rr = 0.566 X, Ls = Lr = 0.058174 H.,Lm = 0.054H, J = 0.0622 kg m2, f = 0.00366 N m/rad/s.

A.4. DC-link

RDC = 1.7 X, LDC = 0.15 H.

A.5. Self excitation capacitor

Rating: 176 lf/phase, 350 V, 8 A.

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