model-based h∞ control of a upqc

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009 2493

Model-Based H Control of a UnifiedPower Quality Conditioner

Kian Hoong Kwan, Member, IEEE, Yun Chung Chu, Senior Member, IEEE, andPing Lam So, Senior Member, IEEE

AbstractThis paper presents a solution to the control of a uni-fied power quality (PQ) conditioner (UPQC) for PQ improvementin power distribution systems. The problem formulation allowsnot only harmonic compensation but also voltage sags/swells,load demand changes, and power factor correction to be tackledin a unified framework. The proposed controller combines themultivariable regulator theory with H loop shaping, so thatzero steady-state error, robustness to modeling uncertainties, andinsensitivity to supply frequency variations can be accomplishedsimultaneously, thus providing a complete theoretical solution toall the aforementioned PQ problems. The effectiveness of theproposed controller is, in practice, verified by experimental studieson a single-phase power distribution system.

Index TermsActive filter, harmonic compensation, H-infinityloop shaping, Kalman filters, multivariable regulator, power qual-ity (PQ), unified PQ conditioners (UPQCs).

I. INTRODUCTION

IN RECENT years, the increasing use of power electronicdevices has led to the deterioration of power quality (PQ)due to harmonic generations [1][3]. On the other hand, a stablesupply voltage has always been desired for smooth operationsof many industrial power plants. Therefore, compensating de-vices such as dynamic voltage restorers [4][7], uninterrupt-ible power supplies [8][10], and active filters [11][17] areproposed to ensure PQ. However, their capabilities are usuallylimited as they can only solve one or two PQ problems. Recentresearch has shown that the unified power quality conditioners(UPQCs) [18][27], an integration of series and shunt active fil-ters, can be utilized to solve most PQ problems simultaneously.This motivates us to develop comprehensive and cost-effectivecontrollers that cannot only be implemented easily but also fullyutilize the UPQC to solve a wide range of PQ problems.

Different control approaches for the UPQC have been pro-posed. The most common approach focuses on extracting and

Manuscript received July 16, 2008; revised November 18, 2008 andFebruary 18, 2009. First published April 21, 2009; current version publishedJuly 1, 2009. This work was supported by the School of Electrical andElectronic Engineering, Nanyang Technological University, Singapore.

K. H. Kwan is with the Laboratory for Clean Energy Research, Schoolof Electrical and Electronic Engineering, Nanyang Technological University,Singapore 639798, and also with Temasek Polytechnic, Singapore 529757(e-mail: [email protected]).

Y. C. Chu is with the Division of Control and Instrumentation, Schoolof Electrical and Electronic Engineering, Nanyang Technological University,Singapore 639798.

P. L. So is with the Laboratory for Clean Energy Research, School of Electri-cal and Electronic Engineering, Nanyang Technological University, Singapore639798.

Digital Object Identifier 10.1109/TIE.2009.2020705

injecting distorted components, e.g., harmonics (from sam-pled supply voltage and load current), into the network [20][24]. This aims to make the load voltage and supply currentundistorted. However, there is no feedback (FB) of the loadvoltage and supply current in these designs to show that theyare undistorted. From this point of view, these designs areopen-loop control. Also, the shunt and series filters of theseapproaches are usually controlled independently, despite theexistence of a coupling effect between the series and shuntfilters [25]. Furthermore, if there is a drift in the operatingfrequency, the extraction of harmonic components can becomeinaccurate. For these reasons, this type of control approachmight not result in the best performance of the UPQC.

Another approach is the model-based control [26], [27].Here, the UPQC is modeled with a coordinated control scheme.The coupling effect is considered in the UPQC model. How-ever, the cost and complexity of the UPQC will increase dueto the additional sensors or high-speed DSP needed. Moreover,any modeling error can be detrimental to its performance.

The proposed approach in this paper is a model-based feed-forward (FF)/FB control. First, a UPQC model is formulated.Then, the FF control is applied to make the model outputs, i.e.,the load voltage and the supply current, track certain desiredwaveforms. It can ensure zero steady-state tracking error ifthere is no modeling error. Otherwise, the negative effectsintroduced by any modeling error can be mitigated by theFB control simultaneously. This approach provides direct FBto the controller and shows how well the PQ of the outputscan be improved. The coupling effect between the series andshunt filters is also taken care of. To minimize the cost, digitalKalman filters are implemented in place of hardware sensors.To minimize the complexity of the UPQC, the gains of thecontroller and the Kalman filters are calculated offline andthen implemented as constant gains online. Also, the proposedcontrol approach ensures that the UPQC can still operate underslight frequency variations in the supply voltage.

In what follows, this paper provides a complete solution forthe operation of a UPQC from the control theoretic point ofview, based on a multi-inputmulti-output (MIMO) state-spacemodel that is to be presented in Section III. The following fourtasks will be accomplished simultaneously by the UPQC:

1) compensating the harmonics in the supply voltage andload current;

2) eliminating the disturbances due to voltage sags/swells atthe supply side or changes in the load demand;

3) correcting the power factor at the supply side;0278-0046/$25.00 2009 IEEE

2494 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009

Fig. 1. Classical control approach for the series active filter of the UPQC.

4) maintaining the power quality despite slight frequencyvariations in the supply voltage.

In Sections IV and V, the technical details of the afore-mentioned tasks are given. In Section VI, the experimentalresults of the proposed control scheme are presented. Finally,in Section VII, the results of this paper are summarized.

II. STUDIES OF PRESENT CONTROL APPROACHES

Generally, the control of the UPQC can be classified into twotypes. They are as follows.

A. Type 1Extraction and Injection of Distorted ComponentsThe distorted components of the supply voltage and load

current, e.g., harmonics, are extracted. These form referencesto be injected into the network to make the load voltage andsupply current undistorted [20][24].

For example, in Fig. 1, to achieve voltage harmonic compen-sation in the distorted supply voltage vS , vS is passed into anextraction circuit to extract the fundamental component vf . vfis then subtracted from vS to obtain the harmonic componentsvh. vh forms the reference to be injected into the network viaa controller and the series active filter. The same approach isapplied independently for current harmonic compensation.

This approach is simple and can easily be implemented.However, the controls of the series and shunt filters are indepen-dent, so their coupling effect is neglected. Moreover, the voltagedrop across the line impedance and the voltage source inverters(VSIs) are also neglected. Obviously, all these will affect theperformance of the UPQC.

B. Type 2Model-Based Control

A model-based coordinated control determines the switchingsignals for the VSIs of the series and shunt filters of the UPQC[26], [27]. Here, the power distribution network is modeledwith the UQPC into a multi-inputmulti-output state-spacemodel. The impedances present in the different components andin the line can be included in the model. Then, a coordinatedcontrol scheme is applied to the model. It will generate theswitching sequences for the VSIs of the series and shunt filtersof the UPQC. In this way, it calculates what is to be injectedinto the system while taking into account the coupling effectand the voltage drop across different impedances. Hence, theperformance of the UPQC is optimized as far as possible.

However, one drawback of such an approach is that anymodeling error can be detrimental to the performance. Also,it may require a high-speed DSP and additional sensors for the

sampling of the states of the state-space model. Consequently,the cost and complexity of the UPQC will increase.

C. Proposed MethodModel-Based With FF and FB Control

In this paper, a model-based coordinated control is proposedfor the UPQC. It is an FF/FB control that aims to regulate theload voltage and supply current to the desired waveforms di-rectly so that they are undistorted. The coupling effect betweenthe series and shunt filters is also accounted for. In the absenceof any modeling error, zero steady-state error can be achievedby the FF control in principle. Otherwise, the negative effects ofany modeling errors introduced are mitigated by the FB control.

In general, the proposed control approach combines thefollowing.

1) An FF control that makes use of the linear regulatortheory [28], [29] to eliminate the tracking error betweenthe model outputs and their desired references in thesteady state if there is no modeling error.

2) An FB control to eliminate the effects of any modelingerrors and maintain a satisfactory performance underslight frequency variations in the supply voltage. A loop-shaping approach that effectively extends the idea ofrepetitive control [11], [30], [31] to tolerate small fre-quency variations is adopted. To provide an overall robuststabilization, H optimization [32][34] is applied tomaximize the stability margin of the system.

Furthermore, the control gains can be calculated offline andimplemented as constants. This control approach incorporatesKalman filters as extraction circuits to extract the harmonicspectra of the supply voltage and load current. All these canreduce the implementation complexity and cost significantly.

The following section details the modeling of the UPQC,followed by the construction of the proposed controller.

III. UPQC MODELFig. 2 shows a single-phase representation of the UPQC [35].

vS models the supply voltage at the point of common coupling(PCC), and iL models the current drawn by the load. Due tothe use of advanced power electronic equipment nowadays, theload could be nonlinear. Therefore, iL consists of both thefundamental if and the harmonic ih. If the harmonics aretransmitted via the source impedance to the supply network,vS , being the difference between the source voltage and thevoltage across the source impedance, will also be distorted. Asa result, other customers at the PCC will receive this distortedvS that consists of both the fundamental vf and the harmonicvh, which is highly undesirable. A purpose of the UPQC is toensure that the supply current iS remains harmonics free despitethe harmonics in iL (caused by the customers own nonlinearload), and the load voltage vL remains sinusoidal despite thepossibly distorted vS (caused by other customers nonlinearload currents transmitted to the supply network).

In Fig. 2, u1(Vdc/2) and u2(Vdc/2) represent the switchedvoltages across the series and shunt VSIs of the UPQC, respec-tively. Rse and Rsh are the losses of the respective series andshunt VSIs, respectively. Lse, Cse, Lsh, and Csh represent two

KWAN et al.: MODEL-BASED H CONTROL OF A UNIFIED POWER QUALITY CONDITIONER 2495

Fig. 2. Single-phase representation of the UPQC.

second-order low-pass interfacing filters designed to removethe high-frequency components generated by the VSIs. vinjdenotes the injected voltage of the series active filter, while iinjdenotes the injected current of the shunt active filter. Finally,the line impedance is represented by Rl and Ll.

With the details given in the Appendix, a state-space modelof the UPQC in Fig. 2 can be derived as follows:

x =Ax + B1

[vSiL

]+ B2u (1)

y =Cx + D1

[vSiL

]+ D2u (2)

where

A =

RlLl 0 0 1Ll 1Ll0 RseLse 0 1Lse 00 0 RshLsh 0 1Lsh1

Cse1

Cse0 0 0

1Csh

0 1Csh 0 0

B1 =

1Ll

00 00 00 00 1Csh

B2 =

0 0Vdc2Lse

00 Vdc2Lsh0 00 0

C =[0 0 0 0 11 0 0 0 0

]

D1 =[0 00 0

]D2 =

[0 00 0

]

x = [iS ise iinj vinj vCsh]T is the state vector; u =[u1 u2]T is the control input, with 1 uk 1, k = 1, 2;and y = [vL iS ]T is the output, which will be regulated totrack the desired sinusoidal waveforms.

In some previous approaches [25], [35], [36], state-FB con-trol designs were adopted such that additional sensory circuitsmay be required. However, in this paper, a direct output-FBapproach, which is to be explained in Section IV, is adopted.Furthermore, the plant model is combined with an exosystemobserver for the control design. This not only replaces sensory

circuits but also allows us to obtain a complete discrete-timesolution for the original continuous-time UPQC model andexosystem, which is to be explained in Section V.

IV. CONTROL DESIGN

Using the UPQC model discussed in Section III, the pro-posed control law (that consists of the FF and FB controls) forthe UPQC is given by

u = u + ufb (3)

where u refers to the FF control law and ufb refers to the FBcontrol law.

Ideally, u is the FF control law that guarantees zero trackingerror between the plant outputs in (2) and their desired refer-ences in the steady state if there is no modeling error and ufb isa stabilizing FB control law.

Generally, the tracking error might tend to a small butnonzero value due to the truncation of the Fourier series (to beexplained hereinafter), and it might also have a large transientenergy due to voltage sags/swells or load demand changes. Theformer may be regarded as a modeling error, and the latter maybe considered as a disturbance. Therefore, a task of the FBcontroller ufb is to minimize the effects of such modeling errorand disturbance on the tracking error. The following sectionwill first discuss how to formulate the FF control law basedon the linear regulator theory and then how to formulate the FBcontrol law based on the idea of repetitive control theory andH loop shaping to provide an overall system stabilization.

A. Design of FF ControlThe first step of our control design is to represent the pe-

riodic disturbance of the model [vS iL]T by another state-space model known as the exosystem. The basic idea is thatany periodic signal v(t) that consists of a finite number ofharmonics, i.e., v(t) =

i i sin(it + i), can be represented

by this state-space model (or the exosystem)

=A (4)v =C (5)


where A is a block-diagonal matrix, with the blocks given by[0 ii 0

], and C = [1 0 1 0 1 0]. A differ-

ent initial condition (0) then corresponds to a different setof Fourier coefficients. Conversely, for a measurable periodicsignal v(t), its state can be estimated using an observer asfollows:

=A + Lw (6)v =C . (7)

The observer gain L can be designed from a steady-stateKalman filter, and w = v v is called innovation, which isessentially the difference between the target signal v(t) andthe estimate v(t), generated from the Kalman filter, such thatw(t) should tend to zero as t , provided that the model(4) and (5) is exact and the matrix A LC is stable.Since is actually a Fourier decomposition of the periodicsignal v(t), this Kalman filter (6) and (7) functions like a har-monic extraction circuit from the power system point of view[37][39].

Next, we let the desired sinusoidal waveforms that vL and iSare to track be represented by d = [dvL diS ]T. If harmoniccompensation is the only task [27], then we simply need toapply the aforesaid Kalman filter to vS and iL to extract theirfundamentals vf and if (which are given by the first compo-nents of the states s of the two Kalman filters) and let dvLand diS be equated to them, respectively. Unfortunately, thissimple mechanism does not extend to handle voltage sag/swellcompensation and power factor correction easily. In this paper,we propose to use two Kalman filters similar to (6) and (7)to generate d = [dvL diS ]T, an estimate of d. Of course, theassociated A matrices are only 2 2 since both dvL and diSare purely sinusoidal, but the corresponding innovations w mustbe designed carefully, as detailed in the following.

1) Normally, dvL is supposed to be vf , the first state com-ponent of the Kalman filter for vS . However, if anyvoltage sag/swell occurs in vS , the reference dvL shouldbe decoupled from vf so that it will not be affected. Inother words, the control system is designed to maintainthe magnitude of vL even when the voltage sag/swelloccurs. Therefore, we may let the innovation for dvL be

w ={

vf dvL , if no voltage sag/swell0, if voltage sag/swell.

(8)

In practice, voltage sag/swell might occur anytime, anddvL can be decoupled from vf once it settles down afteran initialization period.

2) For the current, instead of synchronizing diS with if , thefirst state component of the Kalman filter for iL, we mayalter the phase of diS to make it in phase with vf . This isbasically the power factor correction desired. Hence, theinnovation for diS is given by

w = vf diS (9)

with the scaling factor designed such that when theinnovation (9) vanishes, the conservation of energy willbe followed

|vf ||diS | = |dvL ||if | cos (10)where | | denotes the magnitude of a sine wave and isthe phase angle between dvL and if . Note that (10) doesnot assume that the frequencies at the supply side and theload side must equal each other, thus remaining valid evenunder frequency variations at the supply side.

The four Kalman filters for vS , iL, dvL , and diS can becombined into a more compact representation

=A + Lw (11)[

vSiL

]=C1 (12)

d =C2 (13)where w is the vector of innovations. An FF controller can thenbe designed by solving a pair of matrix equations known as theregulator equations

XA =AX + B0 + B2U (14)C2 =CX + B0 + D2U (15)

for the matrices X and U , where

B0 = B1C1 D0 = D1C1.

Let the control u be decomposed into

u = u + ufb. (16)The FF control law is given by

u = U. (17)In effect, the regulator equations transform the original plantmodel (1) and (2) into the following open-loop system:

d

dt(xX) =A(xX) + BXw + B2(u U) (18)

e =C(xX) + D1w + D2(u U) (19)where

BX = B1 XL, B1 = [B1 0], D1 = [D1 0]and e is the estimated tracking error defined by

e = y d. (20)The FF control can be represented by Fig. 3.

The FF control law (17) can guarantee zero tracking errorin the steady state, provided that no modeling error is presentand the innovation w(t) 0. However, in reality, there willbe certain modeling errors, e.g., the variations of the variousimpedance values of the plant or the truncation of the Fourier


Fig. 3. FF control for the UPQC, with K/F denoting the Kalman filter.

Fig. 4. Combining the precompensator W1(s), the postcompensator W2(s),and the stabilizing controller K(s) into an overall FB controller.

series in the formulation of the exosystem. Therefore, a com-plimentary FB control, which can be implemented easily, isdesigned to mitigate the negative effects of any modeling errorsand to ensure satisfactory performance of the UPQC underslight drift of the fundamental frequency.

B. Design of FB ControlIn this paper, the FB control law is designed based on the H

loop shaping.For a given linear time-invariant MIMO plant G(s), the idea

of H loop shaping [32][34] is to employ a precompensatorW1(s) and a postcompensator W2(s) to modify the open-loopgain to a desired one and then close the loop with a stabilizingcontroller K(s) that is computed by some H optimizationsto maximize the stability margin. Thus, the overall FB con-troller is given by W1(s)K(s)W2(s), as shown in Fig. 4.

Although the synthesis of the stabilizing controller K(s)is pretty systematic, the design of the precompensator W1(s)and the postcompensator W2(s) is problem dependent andrequires some engineering skills. Several case studies of Hloop shaping in power system applications can be found in[40][42]. In [40], where H loop shaping was applied tothe steam-generator-level control in EDF nuclear power plants,the precompensator W1(s) was chosen as a second-order low-pass filter to increase the roll-off rate at high frequencies forbetter noise attenuation, whereas the postcompensator W2(s)was chosen as a PI controller for zero steady-state error. On theother hand, for the power system stabilizers in [42], W1(s) wassimply set to one, whereas W2(s) was designed to increase theloop gain in the frequency range of the interarea mode but notat other frequencies.

Our H loop-shaping approach to the UPQC is motivatedby the idea that slight frequency variations can be tackled byproperly designing W1(s) and W2(s), while the impedancevariations in the system can be handled by the robust stabilizingcontroller K(s). Note that the values of the line impedanceand VSI impedances are not exactly known in practice. There-fore, the robustness offered by K(s) is an effective meansto maintain a desirable performance under such modelinguncertainties.

To design W1(s) and W2(s), we note that the signals con-sidered here are periodic. Therefore, the desired open-loop

Fig. 5. Magnitude plot of W2(s) with three peaks at 50, 150, and 250 Hz.

shape should have a high gain at the fundamental frequency,denoted by 1, and its integral multiples. Indeed, the conceptof repetitive control in the literature [11], [30], [31] is to createan infinite gain at all such frequencies by placing open-looppoles on the imaginary axis, but how to robustly stabilizesuch a system when the loop is closed remains a tricky issue.The proposal of this paper is that, since an FF controller wasalready employed in Section IV, we shall only focus on a fewimportant frequencies (typically the principal odd harmonicsinherent in a power system) rather than all integral multiplesof 1. Hence, the closed-loop system can be robustly stabi-lized via H optimizations. Another important concern in thispaper is that the proposed control approach should be able tomaintain power quality even when there is a slight drift ofthe fundamental frequency, which is not handled by the FFcontroller in the previous section. To address this issue, thehigh-gain region around 1 and its integral multiples should bein the logarithmic scale of the frequency, instead of the linearscale used in the repetitive control, since all harmonics areshifted by the same ratio when the signal frequency deviatesfrom the nominal value. Based on these considerations, theprecompensator W1(s) and the postcompensator W2(s) for theH loop-shaping design are selected as follows. First,

W2(s) =n

i=1

(s + i)2

s2 + 2is + 2i(21)

with > 0 but very close to zero. In the experimental studiesin Section VI, W2(s) consists of three peaks at 50-, 150-, and250-Hz frequencies, i.e., the fundamental, third, and fifth har-monics, with the damping ratio

=

(co/1)2 + (co/1)2 22(co/1)2 + 2(co/1)2

(22)

and the 3-dB cutoff frequency co chosen as 1.05 1. SeeFig. 5 for its magnitude plot. Note also that the loop gainremains reasonably high even between integral multiplies of 1,implying that not only integral harmonics but also any possibleinterharmonics caused by the frequency drifts will be removedeffectively. Second, W1(s) is chosen to be

W1(s) =s + 10110s + 1

(23)


Fig. 6. FB control for the UPQC, with FB/C denoting the FB controller.

Fig. 7. Overall FF/FB control for the UPQC.

which gives a typical loop shape of high gain at low frequenciesand low gain at high frequencies. This choice of W1(s) mayalso be interpreted as penalizing the high-frequency variationsof ufb.

Finally, the stabilizing controller K(s) that maximizes thestability margin can be computed using tools available in theMatlab Robust Control Toolbox. The overall FB control law isthen given by

ufb = W1(s)K(s)W2(s)e. (24)

The FB control can be represented by Fig. 6.In other words, if there is no modeling error and w(t) 0,

then e(t) 0 and, hence, ufb 0 as t . Otherwise, thecomplimentary ufb will seek to mitigate the negative effects ofany modeling error simultaneously.

By combining the FF and FB controls, the overall FF/FBcontrol in Fig. 7 is proposed. As can be seen, although thiscontrol is model based, there is no need to have additionalsensors for the sampling of the states of the UPQC model (1)and (2). Only four sensory circuits are needed for vS , vL, iS ,and iL.

V. DISCRETE-TIME CASE

As the combined control law (3) given by

u =u + ufb

=U + W1(s)K(s)W2(s)e (25)

and the Kalman filter will both be implemented in discrete timefor experimental studies, this section describes the key elementsrequired for discretization.

First and the most important of all is to obtain a discretizedversion of the plant model, based on which the discrete-timecontroller will be designed. Note that it is not preferable todirectly apply zero-order hold (ZOH) to the UPQC model (1)and (2) because the signals vS and iL are not piecewise constantin the steady state. A way to overcome this is to combine theexosystem observer (11)(13) with the UPQC model (1) and

(2) to become[

x

]=[A 0B0 A

] [

x

]+[L

B1

]w +

[0B2

]u (26)[

d

y

]=[C2 0D0 C

] [

x

]+[

0D1

]w +

[0D2

]u (27)

and then apply ZOH to this combined system. The A matrixafter discretization will remain in a triangular form, implyingthat the system can be decomposed back into a discrete-timeexosystem observer, followed by a discrete-time UPQC model.The only point to note is that this discrete-time UPQC modeldoes not take [vS iL]T as input but instead the estimatedexosystem state and the innovation vector w directly.

Hence, the regulator equations (14) and (15) are still theequations to solve but are applied to the discrete-time modeldata instead of the continuous-time ones. The solution matrix Uwill be the FF gain. Putting the disturbance w and the modelingerrors aside, the FF control law guarantees zero steady-statetracking error as in the continuous-time case but only at thesampling moments since the problem formulation is now dis-crete. It is also worth mentioning that the observer gain L canbe designed from a discrete-time Kalman filter directly, ratherthan the discretization of a continuous-time Kalman filter.

As for the FB part of the control law, the compensatorsW1(s) in (23) and W2(s) in (21) can be converted into discretetime using the matched pole-zero method, and the H synthesiswill be carried out in the discrete domain.

In this way, we have obtained a complete discrete-timesolution for the original continuous-time UPQC model andexosystem.

One important point to note is that, although the formula-tion and the discretization of the control law (25) may seemcomplex, its control gains, i.e., U and W1(s)K(s)W2(s),are computed offline. This eliminates the need for real-timecomputation of any control gains and hence reduces the im-plementation complexity. On the other hand, despite the ro-bustness of our control design, it is only meant to deal withsmall variations of circuit parameters or supply frequency, andperformance may deteriorate significantly when such variationsbecome large. This limitation should be taken into account forreal applications.

VI. EXPERIMENTAL RESULTS

Both computer simulation and experiment have been con-ducted to verify the control performance of the UPQC, butonly the experimental results are reported in this paper forbrevity. A single-phase power distribution system supplied bya programmable voltage source, rated at 100 VRMS50 Hz, isconstructed. Several light dimmers are used as the nonlinearload. By adjusting the light intensity of the dimmers, thedemand and the harmonic content of the load current iL canbe varied. The supply voltage vS at the PCC can also bedistorted to a variable degree by paralleling additional lightdimmers. Note that a single-phase system is used merely forsimplicity. Our control methodology can easily be extended to a


Fig. 8. Overall configuration of the UPQC, with K/F denoting the Kalman filter and FB/C denoting the FB controller.

TABLE IVALUES OF THE COMPONENTS OF THE UPQC

TABLE IILINE IMPEDANCE AND VSI IMPEDANCES OF THE UPQC

three-phase UPQC topology [35] by adopting three sets ofcontroller, each working independently on each phase.

The control design of the UPQC is implemented usingdSPACE 1103. Data collection of the experimental results isperformed by Tektronix TPS2024 for graphical representations.Note that dSPACE 1103 is chosen here mainly for fast prototyp-ing. A more cost-effective implementation may be achieved by,for example, Texas Instruments TMS320F2808.

The control law and the Kalman filter are computed in dis-crete time (see Section V) with a sampling frequency of 20 kHz.The exosystem state consists of odd harmonics up to the 29thorder, which is expected to be high enough for the innovation wto be negligible in the steady state. The decoupling of dvL fromvf , as described in Section IV, is done after 10 cycles (0.2 s)upon the installation of the UPQC.

The overall configuration of the UPQC is shown in Fig. 8.The physical design parameters of the UPQC are summarizedin Table I. The control design also requires the values of the lineimpedance and VSI impedances, which are not precisely knownin practice and become a source of modeling uncertainties. Theimpedance values are coarsely estimated and listed in Table II.Another point to note is that the control u is converted intothe switching signals for the VSIs by means of pulsewidthmodulation (PWM). The switching frequency must be highenough for the harmonics to be tackled (up to the 29th orderhere) and is chosen as 7 kHz in the experiment. The PWMalso introduces nonlinear effects that are not represented bythe simple model in Fig. 2. The robustness of our control de-sign to the aforementioned impedance uncertainties and PWMnonlinearities will then be examined in the experiment. In

what follows, four test cases are carried out to investigate theperformance of the UPQC.

A. Test Case 1: Steady-State PerformanceThe first test case demonstrates the steady-state performance

of the UPQC in harmonic compensation and power factorcorrection. The voltage and current waveforms under this testcase are shown in Fig. 9, where the total harmonic distortion(THD) values of vS and iL are 10.0% and 26.4%, respectively,but the UPQC manages to give a clean vL of 2.9% THD and aclean iS of 3.5% THD. Note that they are not totally zero due tothe nonlinear effects of the PWM mentioned earlier but remainsatisfactorily small. On the other hand, the waveform of iS isin phase with that of vS despite the fact that the waveform ofiL lags that of vL by around 30. This confirms that the powerfactor at the supply side has been corrected near to unity. Asa result of the power factor correction, the root-mean-square(rms) value of the supply current iS (which consists primarilyof the load fundamental component that is in phase with vS) islower than that of the load current iL, which will also be truein all other test cases in this paper (see, for example, Fig. 11 intest case 2).

B. Test Case 2: Sags and Swells in the Supply Voltage

The second test case shows how the UPQC copes with sagsand swells in the supply voltage. The voltage and currentwaveforms are shown in Fig. 10. A programmable voltagesource simulates a voltage sag of 30% for 0.2 < t < 0.3 s anda voltage swell of 30% for 0.4 < t < 0.5 s, while the loaddemand is kept constant throughout the entire interval. It canbe seen that vL is hardly distorted, which is also confirmed bythe rms value measured and shown in Fig. 11. However, the sag(swell) in vS instantaneously decreases (increases) the supplypower (see the real power measured and shown in Fig. 12). TheVdc of the UPQC temporarily provides for this power differenceto maintain a pretty steady power consumed by the load (thedashed lines in Fig. 12). If the sag (swell) is going to last, the


Fig. 9. Experimental test case 1: voltage and current waveforms.

UPQC will demand a larger (smaller) iS , resulting in the rise(drop) of iS in Fig. 11. For 0.2 t < 0.3 s, during the sag invS , as seen in Fig. 12, the supply power (the real power) drops.The controller will automatically adjust the supply current torise [based on (10)] so that the supply power can recoverback to its original level for the conservation of energy to beachieved during the sag period. When the sag in vS recovers att = 0.3 s, the supply power rises. Once again, the supply currentis adjusted to drop [again according to (10)] so that the supplypower can recover back to its original level for the conservationof energy to be maintained when the sag is cleared. Then, for0.4 t < 0.5 s, during the swell in vS , the supply power (thereal power) rises. The supply current is automatically adjustedto drop so that the supply power recovers back to its originallevel. This is done so that the conservation of energy can still bemaintained during this swell period. Finally, when the swell iscleared at t = 0.5 s, the supply power drops. The supply currentis once again adjusted to rise to its predisturbance level, suchthat the drop of the supply power is able to recover back to itsoriginal level for the conservation of energy to be achieved onceagain.

Furthermore, the reactive power delivered by the supply(the solid lines) in Fig. 12 remains significantly close to zeroduring the entire test period, confirming that the power factorcorrection can be achieved at the supply side concurrently.

C. Test Case 3: Changes in the Load Demand

The third test case demonstrates how the UPQC adapts tochanges in the load demand. vS is basically the same as inthe first test case, with a THD value of about 10.0%. Theload current and its harmonic content are varied by adjustingthe light intensity of the dimmers. Three waveforms of thedistorted iL, from (I) having the highest light intensity but thelowest distortion to (III) having the lowest light intensity butthe highest distortion, are shown in Fig. 13. The waveformsof the corresponding compensated supply current iS , whichshow a low THD value of below 4%, are shown in the samefigure. The THD value of vL also measures 3% or below in all

cases, confirming that both voltage and current are compensateddespite the load variations.

D. Test Case 4: Slight and Unknown Frequency Variations inthe Supply Voltage

The fourth test case explores the capabilities of the UPQCto maintain the power quality under slight frequency variationsin the supply voltage, which may be regarded as a modelingerror in the exosystem. The voltage and current waveforms areshown in Fig. 14. The programmable voltage source simulates3 cycles of vS at 50 Hz, followed by 3 cycles of vS at 53 Hzand followed by 3 cycles of vS at 47 Hz, while the load currentiL is always at 50 Hz. Note that the UPQC would attempt tomaintain vL at 50 Hz (the reference dvL has been decoupledfrom vf since t = 0.2 s). On the other hand, even though itdoes not know the drift of the supply frequency explicitly, theUPQC automatically tries to match the frequency of iS to thechanging frequency of vS based on the innovation (9), as shownin the waveforms in Fig. 14. Therefore, the task of maintaininga clean iS is much more challenging than that of maintaining aclean vL. As a result, the distortion of vL is very mild, but thedistortion of iS is more noticeable in Fig. 14.

It is important to examine the effectiveness of the Hloop-shaping approach in dealing with the unknown frequencyvariations. Fig. 15 shows the contents of the signals fromthe second harmonic up to the 29th harmonic, relative to thefundamental one, measured when vS is at the third cycle of47 Hz. A breakdown of THD values (in percent) into the oddharmonics of the voltages and currents is given in Table III.As our W2(s) in (21) contains peaks at 50, 150, and 250 Hz,the corresponding third and fifth harmonics in vL and iSshould be low, which is confirmed by the figures in Table III.The residual harmonics in iS are mainly due to the 13th and17th harmonics of vS (note that the 13th/17th harmonic of iLactually has a different frequency from the 13th/17th harmonicof iS). On the other hand, the strong third and fifth harmonicsof vS and iL are mostly suppressed in vL and iS . This confirmsthat the H loop-shaping approach is effective in handling



Fig. 11. Experimental test case 2: rms value of voltages and currents.

Fig. 12. Experimental test case 2: power delivered by (solid lines) the supply and consumed by (dashed lines) the load.

unknown frequency variations, a source of modeling error inthe exosystem, at the supply side.

Table IV summarizes the advantages of using the proposedcontroller over a conventional PI-controlled UPQC [43]. ThePI parameters have properly been tuned to optimize the perfor-mance at 50 Hz. However, during the 6 cycles of frequency vari-ations at 53/47 Hz, the power quality fluctuates significantly,with a serious dip in vL and a big drop in the power factor. Thecontrol signal u2 also saturates at1, which partly accounts forthe performance degradation. On the other hand, our controllercan maintain the power quality more steadily over the 6 cycles

of frequency variations, and it is observed that saturations occuronly when the frequency variations last 10 cycles or longer.

VII. CONCLUSION

In this paper, a model-based solution via H loop shapinghas been presented for the control of a UPQC as a multi-inputmulti-output system. This will handle the coupling effectbetween the series and shunt filters. The proposed solutionintegrates Kalman filters to extract the harmonics of the signals,linear regulator theory to design an FF controller for zero


Fig. 13. Experimental test case 3: (top) load current waveforms and (bottom) supply current waveforms after compensation.


Fig. 15. Experimental test case 4: harmonic spectrum of voltages and currents when vS is at 47 Hz.

TABLE IIIBREAKDOWN OF THD VALUES (IN PERCENT) OF VOLTAGES AND

CURRENTS UP TO THE 17TH ORDER

TABLE IV

POWER QUALITY FLUCTUATIONS DURING FREQUENCY VARIATIONS


steady-state error in principle, and H loop shaping to syn-thesize an FB controller that robustly stabilizes the closed-loopsystem. By properly choosing the innovations of the Kalmanfilters and the loop shape, a wide range of power quality issueshave been put into the same methodological framework andtackled simultaneously. Experimental studies have confirmedthat the H loop-shaping design is robust to modeling errors,including the nonlinear effects introduced by the PWM andthe uncertain values of the impedance in the line and VSIs.Furthermore, the proposed loop shape is an effective meansto maintain a good control performance when slight frequencyvariations occur in the supply voltage. It is concluded that thispaper has demonstrated a systematic approach to the controldesign of UPQC, providing an overall solution to a variety ofpower quality problems encountered in a power distributionsystem.

APPENDIX

To derive a state-space model for the UPQC in Section III,Kirchhoffs voltage and current laws are applied to the threecurrent loops shown in Fig. 2.

From loop iS , we obtain

vS = iSRl + LldiSdt

+ vinj + vL. (28)

From loop ise, we obtain

u1Vdc2

=Rseise + Lsedisedt

+ vinj (29)

vinj =1

Cse

(iS + ise)dt. (30)

From loop iCsh , we obtain

u2Vdc2 iinjRsh Lsh diinj

dt= vL (31)

vCsh = (1/Csh)

iCshdt = vL (32)

iS + iinj iCsh = iL. (33)

Rearranging (28)(33), we obtain the state-space representationof the UPQC model in (1) and (2).

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Kian Hoong Kwan (S06M08) received theB.Eng. degree (first-class honors) in electrical andelectronic engineering from Nanyang TechnologicalUniversity, Singapore, in 2004, where he is currentlyworking toward the Ph.D. degree in the Laboratoryfor Clean Energy Research, School of Electrical andElectronic Engineering.

He is currently a Lecturer with Temasek Polytech-nic, Singapore. His interests include active filters,power electronics, power quality, control theory, andsustainable energy.

Mr. Kwan is currently a Committee Member of the Power EngineeringChapter, IEEE Singapore Section. He received the IEEE Singapore PowerEngineering Chapter Gold Medal and Book Prize Awards and the SingaporePower Ltd. Book Prize Award during his undergraduate studies.

Yun Chung Chu (S88M97SM06) received theB.Sc. degree in electronics and the M.Phil. degree ininformation engineering from The Chinese Univer-sity of Hong Kong, Hong Kong, in 1990 and 1992,respectively, and the Ph.D. degree in control from theUniversity of Cambridge, Cambridge, U.K., in 1996.

He was a Postdoctoral Fellow with the ChineseUniversity of Hong Kong in 19961997, was a Re-search Associate with the University of Cambridgein 19981999, and is currently an Associate Profes-sor with the Division of Control and Instrumentation,

School of Electrical and Electronic Engineering, Nanyang Technological Uni-versity, Singapore. His research interests include control theory and artificialneural networks, with applications to spacecraft, underwater vehicles, combus-tion oscillations, and power systems.

Dr. Chu was a Croucher Scholar in 19931995 and has been a Fellow of theCambridge Philosophical Society since 1993.

Ping Lam So (M98SM03) received the B.Eng.degree (first-class honors) in electrical engineeringfrom the University of Warwick, Coventry, U.K., in1993, and the Ph.D. degree in electrical power sys-tems from Imperial College, University of London,London, U.K., in 1997.

He is currently an Associate Professor withthe Laboratory for Clean Energy Research, Schoolof Electrical and Electronic Engineering, NanyangTechnological University, Singapore. Prior to hisacademic career, he worked for 11 years as a Second

Engineer with China Light and Power Company Ltd., Hong Kong, in the field ofpower system protection. His research interests include power system stabilityand control, flexible ac transmission systems, power quality, and power linecommunications.

Dr. So is currently the Chairman of the IEEE Singapore Section.

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