a unified power quality conditioner (upqc) for simultaneous voltage and current compensation

Electric Power Systems Research 59 (2001) 55–63

A unified power quality conditioner (UPQC) for simultaneousvoltage and current compensation

Arindam Ghosh 1, Gerard Ledwich *School of Electrical & Electronic Systems Engineering, Queensland Uni�ersity of Technology, Brisbane, Qld, Australia

Received 8 August 2000; received in revised form 9 April 2001; accepted 7 June 2001

Abstract

The paper discusses the topology and control of a unified power quality conditioner (UPQC) that can be used simultaneouslyin voltage or current control mode in a power distribution system. In the voltage control mode, the UPQC can force the voltageof a distribution bus to be balanced sinusoids. At the same time it can also perform load compensation resulting in the drawingof balanced sinusoidal currents from the distribution system bus in the current control mode. Both these objectives are achievedirrespective of unbalance and harmonic distortions in load currents or source voltages. We shall discuss a suitable UPQC structurethat allows the tracking of reference current and voltage generated to meet the objective stated above. The reference generationscheme along with the switching control scheme is presented in detail. Extensive results of digital computer simulation studies arepresented to validate the proposed structure and control. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: UPQC; Voltage control mode; Current control mode; Switching control

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1. Introduction

A unified power quality conditioner (UPQC) is adevice that is similar in construction to a unified powerflow conditioner (UPFC) [1]. The UPQC, just as in aUPFC, employs two voltage source inverters (VSIs)that connected to a d.c. energy storage capacitor. Oneof these two VSIs is connected in series with a.c. linewhile the other is connected in shunt with the a.c.system. A UPFC is employed in a power transmissionsystem to perform shunt and series compensation at thesame time. Similarly a UPQC also performs shunt andseries compensation in a power distribution system.However, at this point the similarities in the operatingprinciples of these two devices end. Since a powertransmission line generally operates in a balanced, dis-tortion (harmonic) free environment, a UPFC mustonly provide balanced shunt or series compensation. Apower distribution system, on the other hand, may

contain unbalance, distortion and even d.c. compo-nents. Therefore a UPQC must operate with all theseaspects in order to provide shunt or seriescompensation.

Power quality issues are gaining significant attentionthese days as an increasing range of equipment that aresensitive to distortions or dips in supply voltages areused [2]. At the same time an increasing number ofpower electronic units such as adjustable speed drives(ASD), uninterruptible power supplies (UPS) etc arebeing used causing rising harmonic pollution in distri-bution networks. To curb this, regulations apply inmany places that limit the distortion and unbalancethat a customer can inject to a distribution system.These regulations may require the installation of com-pensators (filters) on customer premises. At the sametime, it is the duty of any utility to supply a neardistortion-free balanced voltage to its customers, espe-cially those sensitive ones. In this paper we utilize theUPQC to perform both these tasks simultaneously.

The UPQC is a relatively new device and not muchwork has yet been reported on it. It has been viewed ascombination series and shunt active filters in [3]. In thatpaper it has been shown that it can be used to attenuate

* Corresponding author. Tel.: +61-7-3664-2864; fax: +61-7-3864-1516.

E-mail address: [email protected] (G. Ledwich).1 On a leave of absence from Indian Institute of Technology,

Kanpur, India.

0378-7796/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S 0 3 7 8 -7796 (01 )00141 -9

A. Ghosh, G. Ledwich / Electric Power Systems Research 59 (2001) 55–6356

current harmonics by inserting a series voltage propor-tional to the line current. Alternatively, the insertedseries voltage is added to the voltage at the point ofcommon coupling such that the device can provide abuffer to eliminate any voltage dip or flicker. It is alsopossible to operate it as a combination of these twomodes. In either case the shunt device is used forproviding a path for the real power to flow to aid theoperation of the series connected VSI. Also included inthis structure is a shunt passive filter to which all therelatively low frequency harmonics are directed. Experi-mental results with a relatively stiff voltage source arealso provided in [3].

In this paper we propose the operation of a UPQCthat combines the operations of a distribution staticcompensator (DSTATCOM) and dynamic voltage re-storer (DVR) together. The series component of theUPQC inserts voltage so as to maintain the voltage atthe load terminals balanced and free of distortion.Simultaneously, the shunt component of the UPQCinjects current in the a.c. system such that the currentsentering the bus to which the UPQC is connected arebalanced sinusoids. Both these objectives must be metirrespective of unbalance or distortion in either sourceor load sides. To achieve this, we examine one suitablestructure of the UPQC in which six single-phase H-bridge inverters are connected to a common d.c. stor-age capacitor. Of these six inverters three are used forseries voltage insertion and the other three are used forshunt current injection. The UPQC current and voltagereferences are generated based on Fourier series extrac-tion of fundamental sequence components using halfcycle running (moving) averaging. We also propose alinear quadratic regulator (LQR) based switching con-troller scheme that tracks a reference using the pro-posed compensator. Extensive simulation results areprovided to validate the operation of the UPQC.

2. UPQC in power distribution systems

A UPQC compensated distribution system is shownin Fig. 1. It consists of load that supplied by a sourcethrough a feeder. We denote the load voltage by �l andthe source voltage by �s. The resistance R and induc-tance L denote the feeder impedance. It is to be notedthat this impedance can also be the Thevenin’s

Fig. 2. The schematic diagram of the proposed UPQC.

impedance looking into the network from the point ofcommon coupling (PCC). In that event �s would be theThevenin’s voltage. We further denote the voltage atthe point of common coupling by the terminal voltage�t.

The idealized UPQC combines the current source ifand the voltage source �d. The purpose of the seriesvoltage source of the UPQC is to insert voltage �d suchthat the load voltage �t is a balanced sinusoid irrespec-tive of unbalance or distortion in the terminal voltage�t. On the other hand, the purpose of the shunt currentsource is to inject current if such that the source currentis is balanced and distortion free irrespective of theshape of the load current il. The UPQC must thereforeprovide a steady voltage to the load terminal and at thesame time draw pure sinewave current from the sourceirrespective unbalance or distortion in the system quan-tities. Furthermore, we stipulate that the UPQC mustbe controlled using the local variables only, which inthis case are the terminal voltage, load and sourcecurrents.

A three-phase, four-wire distribution system shuntcompensator usually deals with unbalanced and dis-torted currents and voltages. It is imperative that threeindependent currents must flow through the threephases of the compensator in order to compensate forthe unbalance or distortion. As a result of this, athree-phase bridge inverter cannot be used directly, as itdoes not provide for the neutral current to flow. It ishowever possible to use such an inverter provided thatit is supplied by two d.c. storage capacitors separatedby a center point that is connected to the load neutral[4]. The center point then allows the neutral current toflow. A similar observation can also be made for theseries compensator.Fig. 1. A UPQC compensated distribution system.

A. Ghosh, G. Ledwich / Electric Power Systems Research 59 (2001) 55–63 57

Fig. 4. Equivalent circuit of the UPQC compensated system

Fig. 3. Equivalent circuit of UPQC.

In this paper three single-phase H-bridge invertersrealize each three-phase VSI as shown in Fig. 2. TheseVSIs are connected to a common d.c. storage capacitor,denoted by Cd.c.. This topology allows three indepen-dent shunt current injections through the three separateH-bridge inverters connected in shunt. Similarly, threeH-bridge inverters connected in series can also injectthree independent series voltages. The transformersconnected at the output of each H-bridge inverterprovide isolation and also prevent the d.c. capacitorbeing shorted due to the operation of various switches.The a.c. capacitors connected at the output of eachH-bridge inverter, transformer combination provide apath for the switch frequency harmonic components.Therefore, the capacitors are referred to as the filtercapacitors. The topology of the shunt VSI is the sameas given in [5].

The equivalent circuit of the UPQC is shown in Fig.3. It denotes the shunt and series voltage source invert-ers VSI No.1 and VSI No.2, respectively. These VSIsare driven by a common d.c. energy storage capacitorCd.c.. The two VSIs are connected to two transformersT1 and T2. While the output of the transformer T1 isconnected in shunt with the feeder, the output oftransformer T2 is connected in parallel with the capaci-tor C2 and the capacitor is connected in series with thefeeder and the load. Also connected in shunt is afilter-capacitor C1 that absorbs the high frequency com-ponent of current. The voltage across the filter-capaci-tor is the terminal voltage �t.

3. UPQC control

In this section we present the control design for thesystem shown in Fig. 1. The equivalent circuit of thecompensated system is shown in Fig. 4. The inductanceLf in this figure represents the leakage inductance of theshunt transformer and additional external inductance,if any. Similarly the inductance Ld is the leakage induc-tance of the series transformer. The switching losses ofan inverter and the copper loss of the connectingtransformer are represented by a resistance Rf and Rd.The iron losses of the transformer are neglected. Theload is assumed to be an RL load characterized by Rl

and Ll. The voltage sources Vd.c.1 and Vd.c.2 are thevoltage Vd.c. across the d.c. storage capacitor multipliedby the switch function of the shunt and series invertersrespectively. The purpose of UPQC control is to deter-mine these switch functions.

Let us define the following state vector

xT= [i1 i2 i3 i4 �t �d].

The state-space equation of the circuit then can bewritten as

x� =Ax+B1�s+B2u (1)where

A=

��

−R/L 0 0 0 −1/L 0

0 −Rf/Lf 0 0 1/Lf 0

0 0 −Rl/Ll 0 1/Ll 0

0 0 0 −Rd/Ld 0 −1/Ld

1/C1 −1/C1 −1/C1 0 0 0

0 0 −1/C2 1/C2 0 0

��

,

B1=

��

1/L

0

0

0

0

0

��

, B2=

��

0 0

−Vd.c./Lf 0

0 0

0 Vd.c./Ld

0 0

0 0

��

and u=�u1

u2

n=

1

Vd.c.

�Vd.c.1

Vd.c.2

n


The state variables that are defined may not be thebest control variables. In general the control variablesare injected current if, inserted voltage �d, the termi-nal voltage �t along with the two capacitor currents.Furthermore, the presence of the load current in thestate variable feedback is undesirable as the load maychange at any time. We must therefore perform asuitable state transformation such that all the perti-nent signals appear as state variables. One suitabletransformation is given by

z=

��

ific1

�t

isic2

�d

��

=

��

−1 0 1 0 0 0

1 −1 −1 0 0 0

0 0 0 0 1 0

1 0 0 0 0 0

0 0 −1 1 0 0

0 0 0 0 0 1

��

x=Px.

(2)

The state Eq. (1) then can be transformed into

z� =PAP−1z+PB1�s+PB2u=�z+�1�s+�2u (3)

Assuming we have full control over u, an infinitetime linear quadratic regulator (LQR) can be de-signed for this problem. The control is of the form

u= −K(z−zref) (4)

where zref is the desired state vector. In an LQRproblem a performance index is chosen in the form

J=��

0

{(z−zref)TQ(z−zref)+uTRu}dt (5)

and it is minimized to obtain u thorough the solutionof steady state Ricaati equation [6].

The control signal computed so far using the LQRis a continuous signal. In practice the control signal uis the switching decision of the VSIs of the UPQCand is thus constrained to be either +1 or −1. Theapproach taken here is to design a switching con-troller based on the LQR gain [7]. The switching isthen based on

u= −hys{K(z−zref)} (6)

where the hys function is defined by

if w� lim then hys(w)=1 else if w

� − lim then hys(w)= −1 (7)

The selection of lim determines the switching fre-quency while tracking the reference. This applicationof LQR design to switching control gives good con-vergence to the tracking band as well as good stabil-ity of tracking provided that 1/2�K(z−zref)�2. Inthis control law the switching decision is based on alinear combination of multiple states. Hence we call

this control a switching band tracking control. Theproof of stability of this control scheme is given inAppendix A.

4. Reference generation and tracking using UPQC

The closed loop inverter control technique pre-sented in Section 3 will now be used in tracking thereference current and voltage generated. These refer-ence voltage and current are so generated that thevoltage at the load terminal is sinusoidal and so thesource current. The reference generation in the paperis based on half cycle averaging of the current andvoltage waveform. To extract the sinusoidal steadystate quantities, we use the instantaneous symmetricalcomponents. The power invariant instantaneous sym-metrical components are then defined by [8]

ia012=

��

ia0

ia1

ia2

��

=1

�3

��

1 1 11 a a2

1 a2 a

��

��

iaibic

��

(8)

where a=e j 120�. Similar expression can also be writ-

ten for voltages.Let us now denote the zero, positive and negative

sequence phasors as Ia0, Ia1 and Ia2 respectively.Defining a vector as Ia012

T = [Ia0 Ia1 Ia2], we use thefollowing to obtain the symmetrical componentphasors

Ia012=�2T

� t1+T

t 1

ia012e− j(�t−90�)dt (9)

that do not contain any harmonics even if the origi-nal signal contains harmonics. We choose the timeinterval T as half a cycle to provide a low delayrejection of harmonics. It is to be noted that theabove equation signifies the average over half a cycle.This averaging can be between any two points thatare half a cycle apart and need not be synchronizedwith the zero crossing of the current (or voltage)waveform. We have therefore used a moving averageprocess such that the variables are obtained continu-ously. It is to be note that the averaging period ofhalf a cycle is sufficient when the signal does notcontain any even harmonics.

4.1. Obtaining �oltage reference

Since the inverter operation is continuous, the ref-erence voltage and current that are generated must beinstantaneous. Generating reference for the series in-verter is a trivial problem. Let us assume that the


desired load voltage has a magnitude of 1.0 per unitsuch that

�labc–ref=

��

�la

�lb

�lc

��

=

��

sin(�t+�)sin(�t+�−120°)sin(�t+�+120°)

��

(10)

where subscripts a, b and c indicate the three phases,the subscript abc denote a vector that contains thesethree phases and � is an offset angle. From Fig. 1 wethen get the reference voltage for the series inverter as

�tabc–ref=�labc–ref−�tabc (11)

It is possible to choose any arbitrary value for theangle �. However, in order to restrict the peak of theseries voltage to be inserted, this angle is chosen equalto the fundamental positive sequence of the terminalvoltage �t.

The current generation scheme varies depending onthe compensation requirement and can be classified intothe following three different categories:1. When both source and load are unbalanced.2. When both source and load are unbalanced and the

load is distorted.3. When both source and load are unbalanced as well

as distorted.

4.2. Case 1: both load and source unbalanced

To extract a reference for the injected shunt currentwe note that since the source current must be funda-mental positive sequence, the compensator must supplythe negative and zero sequence required by the loadcurrent. We can then write

if0–ref= il0if2–ref= il2if1–ref=0

��

(12)

where the subscripts 0, 1 and 2 indicate zero, positiveand negative sequences. The algorithm for the extract-ing the sequence components from their samples isdiscussed before.

Example 1—Let us consider the system shown inFig. 1 with a fundamental frequency of 50 Hz. It isassumed that the source (or Thevenin’s equivalent)voltages are unbalanced and are given by

�sa=sin(100�t) per unit, �sb

=1.25 sin (100�t−120�) per unit, �sc

=0.85 sin(100�t+120�) per unit.

The feeder impedance is given in per unit by

R=0.05 and X=�L=0.3.

It is assumed that the load buses to the right of the

PCC contain passive RL loads. The load impedancesare unbalanced and are given in per unit by

Zla=Rla+ jXla=2.0+ j 1.5, Zlb=Rlb+ jXlb

=2.55+ j 1.25, and Zlc=Rlc+ jXlc=1.0+ j 2.3

It is assumed that the VSIs are lossless and suppliedby a fixed d.c. storage instead of the dc storage capaci-tor. The UPQC parameters are given in per unit are

Vdc=1.5, Rf=0, Xf=�Lf=0.2, X1=1

�C1

=7.02,

Rd=0, Xd=�Ld=0.025 and X2=1

�C2

=4.0

The control is designed with

Q=diag(20 1 1 0 0 10) R=0.05.

where diag is a diagonal matrix. The maximum weightis given to the injected current if followed by theinserted voltage �d, see Eq. (2). The terminal voltageand current through the filter capacitor are given verylittle weightage, while the source current and the cur-rent ic2 have not been given any weight. This weightingmatrix Q reflects the importance of these states. Forthis set of parameters, the gain matrix for phase-a isthen given by

K=�16.09 7.25 11.58 −3.24 0.01 0.22

2.11 0.12 0.75 −0.22 1.62 13.20n

To avoid the complexities involved with a full statefeedback, we use instead the gain matrix that isolatesthe shunt controller from the series as

K=�16.09 7.25 11.58 0 0 0

0 0 0 0 1.62 13.20n

.

This choice however results in a minimal shift in theclosed-loop eigenvalues. In fact it is observed that thedamping of the two pairs of complex conjugate eigen-values are marginally increased while the two real ei-genvalues have slightly shifted right towards theimaginary axis in the complex plane. Thus stability isnot at all endangered by the reduced feedback, but thecomputation is reduced considerably. Furthermore, thesame feedback matrix that is designed for phase-a onlyis used for the other two phases as well. For loadimpedance changing from 10 to 1000% of nominal, theworst damped oscillatory eigenvalues of the closed loopsystem deteriorated by 2.5% using the reduced matrixand 7% with the full state feedback.

A successful implementation of the control schemerequires a set of consistent reference signals that are tobe tracked. The references for the shunt current and theseries voltage are obtained through Eqs. (12) and (11)respectively. We further require the references for the


terminal voltage �t and the two capacitor currents ic1 andic2. Of these, the reference for the terminal voltage ischosen to be the fundamental of this voltage in theprevious half cycle, ie, �t–ref=�t– fund. The offset angle �

given in Eq. (10) is chosen equal to the angle of theterminal voltage such that fundamental of the insertedseries voltage be in phase with the load voltage, requiringa minimum voltage injection. Once this reference ischosen the reference for ic1 is chosen from the differentialrelation as follows. Let the reference voltage for phase-ais given by sin(�t+�a). The reference current for thisphase is then given by �C1 cos(�t+�a). It is howeverrather difficult to obtain a reference for ic2. We eitherassume that it is zero or extract the fundamental of thisquantity over the previous half cycle. This will result inslight degradation in tracking performance that cannotbe avoided.

The system response for this case is shown in Fig. 5.It is assumed that the UPQC is connected to the systemat the end of first half cycle (0.01 s) when the first set ofaverage values are available. It is obvious that the UPQCperforms its job satisfactorily.

4.3. Case 2—both load and source unbalanced andload contains harmonics

To extract a reference for the injected current we mustremember that the compensator should not only supplythe sequence currents given in Eq. (12), but should alsosupply the harmonic contents of the load. To facilitatethis, let us assume that we have obtained i �f–ref from theinverse transformation of if0–ref, if1–ref and if2–ref given inEq. (12). We then use the following relation generate areference current if–ref that cancels the effects of loadcurrent harmonics

if–ref= i �f–ref+ il− il– fund (13)

Example 2—Let us consider the same system as givenin Example 1. We further add a balanced rectifier type

Fig. 6. Performance of UPQC compensated system when both sourceand load are unbalanced and the load contains harmonics.

load that draws a peak current with the unbalanced RLloads. The load currents are given in Fig. 6(a). TheUPQC is connected to the system at the end of the firsthalf cycle and the results are shown in Fig. 6. It is obviousthat the UPQC forces the load voltages and sourcecurrents to be balanced sinusoids. From the injectedcurrent tracking error for phase-a is shown in Fig. 6(d)it can be surmised that the tracking system convergeswithin about half a cycle.4.4. Case 3—both load and source unbalanced anddistorted

This is the case in which we assume that both thesource voltages and load currents are distorted byharmonics. This case has to be treated differently thanthe previous two cases as the generation of references isof a completely different nature. Consider the equivalentcircuit of Fig. 4. If we want the source current to bebalanced and harmonic free, then the terminal voltagemust contain exactly the same amount of harmonics asthe source. We still use Eqs. (11)– (13) to obtain thereference for the series voltage and shunt current. How-ever, the reference for terminal voltage must be

�t–ref=�t– fund+�s–harm (14)

where �s–harm is the harmonic content of the source.Typically, the source does not contain any even harmon-ics and for phase-a is

�s–harm= �n=3,5,7,···

Vsan sin(n� t). (15)

The above equation assumes that the measurement ofthe source voltage is completely available to us. This isnot a valid assumption as the source may be remotelylocated and most likely the source is a Thevenin’s voltagesource in a radially connected distribution system. Wemust therefore estimate the harmonic content of the

Fig. 5. Performance of UPQC compensated system when both sourceand load are unbalanced.


source voltage from the measured data. This can beeasily done when the feeder impedance is completelyknown. Referring to Fig. 3, we can determine the 5thharmonic component of the source voltage through themeasurement of 5th harmonic component of terminalvoltage and source current as

Vb s5=Vb t5+ (R+ j 5�X)Ib s5

where the arrow indicates phasor quantity. Similaroperation must also be performed for all odd harmoniccomponents up to a defined order.

It is further unrealistic to expect that the feederimpedance be completely known as it may also be aThevenin’s impedance. Fortunately however, estimationof the entire feeder impedance is not necessary for theextraction of terminal voltage reference. The circuit tothe point of common coupling can be viewed as auniformly distributed feeder that is supplied by a stiffsource. We thus need the voltage at any point on thisfeeder and the corresponding impedance. We shall callthe procedure of estimating the voltage using a frac-tional value of the Thevenin’s impedance as partialback projection. For example a 50% back projectionwill mean using 0.5(R+ jn�X) in computing the sourcevoltage of nth harmonic. Let us illustrate the idea withthe help of the following example.

Example 3—Let us consider the same system asExample 2. We further assume that the source is dis-torted with 5th and 7th harmonics with the sourcevoltage being the same as given in Example 1. Theamplitudes of the harmonic voltages are inversely pro-portional to their harmonic number. Fig. 7 shows thecompensated source currents for four different valuesof back projection. It can be seen that these currents getbalanced within two cycles for 75 and 125% backprojection, but takes a longer time to settle for theother two cases. The system will however diverge forback projection less than 50% or greater than 150%.We can thus conclude that even if the estimate of the

Fig. 8. Performance of UPQC source contains voltage flicker.

feeder impedance is erroneous by about 50%, the sys-tem performance will still be acceptable.

Let us now consider the case when there are randomvariations in the source voltage. We assume that thesource is unbalanced and load is both unbalanced anddistorted. The source voltage, as shown Fig. 7(a), con-tains spikes of irregular height that appear randomly.The UPQC is connected at the end of the first halfcycle. The terminal voltages are shown in Fig. 8(b),while the load voltages and source currents are shownin Fig. 8(c) and (d) respectively. It can be seen that allthese quantities are severely distorted prior to the con-nection of the UPQC. However, the load voltage getsalmost balanced after the UPQC is connected, while theshape of both the terminal voltage and source currentbecome significantly better after the UPQC connection.It is to be noted that since the variations in the sourcevoltage are random in nature, it will not be possible tomake the source current sinusoidal through back pro-jection in this case.

5. D.C. capacitor control

So far in the discussion we have assumed that a d.c.source, rather than a d.c. capacitor supply the VSIs ofthe DSTATCOM. We have assumed further that thecompensator is lossless (Rf=0 and Rd=0). This isagain an invalid assumption as there always are switch-ing losses and losses in the connecting transformer.These losses will force the d.c. capacitor to dischargeresulting in loss of tracking. It is therefore imperativethat the d.c. voltage stored (Vd.c.) in the storage capaci-tor Cd.c. is maintained around a respecified set value.This is only possible by drawing additional power toovercome the losses due Rf and Rd.

Refer to Eq. (12), which gives the relation for refer-ence shunt currents. The equation is derived assumingthat the fundamental positive sequence of the sourceFig. 7. Source current for different amount of back projection.


current is equal to that of the load current. Thisassumption will no longer be correct, as the positivesequence of the source current must be higher than itsload current counterpart in order to supply the realpower requirement of the d.c. capacitor. The differencein two currents will be forced through the shunt path.We can then modify Eq. (12) as

if0–ref= il0if2–ref= il2if1–ref= idc

��

(16)

where id.c. is the current required by the d.c. capacitorto maintain its charge and it must be obtained from thed.c. capacitor feedback loop.

The feedback should be able to correct the deviationof the average value of Vd.c. from a reference value Vref.Let us define the following error signal

e=Vref−Vd.c.cyl (17)

where Vd.c.cyl is either the average value of the d.c.

capacitor voltage, measured at the end of a cycle. In thesimplest form of feedback, we have used a propor-tional-plus-integral (PI) controller to correct for anydischarge in the capacitor voltage. The controller isthen given by

uc=KPe+KI�

e d t. (18)

The amount of uc required to sustain the d.c. capaci-tor voltage must then be drawn equally from the threephases. As a result of which we can substitute in Eq.(16)

id.c.= −uc/3. (19)

Example 4—Let us consider the same system asdiscussed before. We have assumed that the load side isharmonically distorted, while the source side is free ofharmonics. We have removed the assumption that thecompensator is lossless and have chosen the followingper unit quantities

Rf=Rd=0.1 and Xd.c.=1

�Cd.c.

=0.106

The PI controller parameters chosen are

KP=5 and KI=30.

The system is started from rest, ie the compensator isconnected at the end of first half cycle after the averageload power is obtained. The capacitor is assumed to beprecharged to 1.5 per unit and this value is also chosenas the set point of this voltage. The controller is startedfrom zero initial condition. The results are shown inFig. 9. It can be seen that both the control signal andd.c. capacitor voltage settle within about 0.4 s. Thesteady state waveforms of the load voltage and source

current are also plotted in this figure. It can be seenthat these are balanced without any distortion.

6. Conclusions

The paper discusses the topology and control tech-nique of a UPQC that operates in simultaneous voltageand current control modes. In the voltage control modeit can make bus voltage at a load terminal sinusoidalagainst any unbalance, harmonic or flicker in thesource voltage or unbalance or harmonic in the loadcurrent. In the current control mode, it draws a bal-anced sinusoidal current from the utility bus irrespec-tive unbalance and harmonic in either source voltage orload current.

The operation of UPQC presented in this paper issuitable for both utilities and customers having sensitiveloads. From the utility standpoint, it can make thecurrent drawn balanced sinusoidal. To accomplish this,the voltage at the point of common coupling must be ofsimilar nature and also must contain the same amountof harmonics as the source. From the point of view ofa customer, the UPQC can provide balanced voltagesto their equipment that are sensitive to voltage dips. Atthe same time, the UPQC also filters out the currentharmonics of the load. Therefore, the operation ofUPQC is ideal from both viewpoints. It is however tobe mentioned that a UPQC is a very powerful deviceand can be operated in various other modes dependingits ownership. We have presented a method of controlthat is beneficial to both utility and customer.

Appendix A. Proof of tracking controller convergence

The system state space description is given in Eq. (3)as

Fig. 9. Performance of UPQC with d.c. capacitor control system.


z� =�z+�1�s+�2u. (A1)

Let us form a reference that is defined by

z� ref=�zref+�1�s+�2u*. (A2)

Defining an error vector as e=z−zref, we can writefrom the above two equations

e� =�e+�2(u−u*). (A3)

From the control law given in Eq. (5), if we remain onthe switching surface [6]

K(z−zref)=0 Ke=0.

We can then write

Ke� =0 K�e+K�2(u−u*)=0.

From the above equation we get

(u−u*)= −K�K�2

e. (A4)

Substituting Eq. (A4) in Eq. (A3) the error equationbecomes

e� =�I−

�2KK�2

��e. (A5)

Hence the tracking error will converge to zero for anyinitial condition provided that:

1. all the eigenvalues of the matrix�

I−�2KK�2

�� have

negative real parts,2. the reference signal can be generated by an equation

in the form of Eq. (A2) and3. since u is bounded between +1 and −1, Eq. (A4)

requires that −1�u*−K�K�2

e� +1.

It is a property of switching law based on LQR designthat condition Eq. (1) above is satisfied. Most trackingproblems are posed as the output of the plant followingsome reference yref. Our task is to define a state refer-ence satisfying yref=Hzref. In frequency domain theoutput equation can be given as

Yref(s)=H(sI−�)−1[�1Vs(s)+�2U*(s)]. (A6)

Assuming that we are tracking a single output and since

the plant in Eq. (A1) is single input, we can write fromEq. (A6)

U*(s)=1

H(sI−�)−1�2

[Yref(s)−H(sI−�)−1�1Vs(s)].

(A7)

Thus the corresponding reference state can be formedfrom

Zref(s)= (sI−�)−1[�1Vs(s)+�2U*(s)]. (A8)

Hence any single output-tracking problem can betranslated into a state tracking problem and expressedin the form of Eq. (A2). In practice, the circuit analysiswould be easiest method to form zref from yref, particu-larly for sinusoidal tracking. This will satisfy condition(2).

Condition (3) cannot be satisfied for arbitrary refer-ences. Since the source �s is always bounded, from Eq.(A7) we can see that a bounded yref implies a boundedu*. The system states are not necessarily bounded. Butif yref and the system states are sufficiently small, thenthe condition (3) can be satisfied and perfect trackingcan occur.

References

[1] L. Gyugyi, Unified power flow control concept for flexible actransmission systems, Proc. IEE 139(C) (1992) 323–331.

[2] R.C. Dugan, M.F. McGranaghan, H.W. Beaty, Electrical PowerSystems Quality, McGraw Hill, New York, 1996.

[3] H. Fujita, H. Akagi, The unified power quality conditioner: theintegration of series- and shunt-active filters, IEEE Trans. PowerElect. 13 (2) (1998) 315–322.

[4] M.K. Mishra, A. Ghosh, A. Joshi, A new STATCOM topologyto compensate loads containing a.c. and d.c. components, Pro-ceedings of IEEE-PES Winter Meeting, Singapore, 2000.

[5] A. Ghosh, A. Joshi, Use of instantaneous symmetrical compo-nents for balancing a delta connected load and power factorcorrection, Elect. Power Syst. Res. 54 (1) (2000) 67–74.

[6] B.D.O. Anderson, J.B. Moore, Linear Optimal Control, Prentice-Hall, Englewood Cliffs, 1971.

[7] G. Ledwich, Linear switching controller convergence, Proc. IEECont. Theory Applic. 142 (4) (1995) 329–334.

[8] W.A. Lyon, Transient Analysis of Alternating-Current Machin-ery, Wiley, New York, 1954 Chapter 2.

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a unified power quality conditioner (upqc) for simultaneous voltage and current compensation

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