Improvement of the Electric Power Quality Using Series Active and

1058 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010

Improvement of the Electric Power Quality UsingSeries Active and Shunt Passive Filters

P. Salmerón and S. P. Litrán

Abstract—A control algorithm for a three-phase hybrid powerfilter is proposed. It is constituted by a series active filter and a pas-sive filter connected in parallel with the load. The control strategyis based on the vectorial theory dual formulation of instantaneousreactive power, so that the voltage waveform injected by the activefilter is able to compensate the reactive power and the load cur-rent harmonics and to balance asymmetrical loads. The proposedalgorithm also improves the behavior of the passive filter. Simu-lations have been carried out on the MATLAB-Simulink platformwith different loads and with variation in the source impedance.This analysis allowed an experimental prototype to be developed.Experimental and simulation results are presented.

Index Terms—Active power filters, harmonics, hybrid filters, in-stantaneous reactive power, power quality.

I. INTRODUCTION

T HE increase of nonlinear loads due to the proliferation ofelectronic equipment causes power quality in the power

system to deteriorate. Harmonic current drawn from a supply bythe nonlinear load results in the distortion of the supply voltagewaveform at the point of common coupling (PCC) due to thesource impedance. Both distorted current and voltage may causeend-user equipment to malfunction, conductors to overheat andmay reduce the efficiency and life expectancy of the equipmentconnected at the PCC.

Traditionally, a passive LC power filter is used to eliminatecurrent harmonics when it is connected in parallel with the load[1]. This compensation equipment has some drawbacks [2]–[4],due to which the passive filter cannot provide a complete solu-tion. These disadvantages are mainly the following.

— The compensation characteristics heavily depend on thesystem impedance because the filter impedance has to besmaller than the source impedance in order to eliminatesource current harmonics.

— Overloads can happen in the passive filter due to the cir-culation of harmonics coming from nonlinear loads con-nected near the connection point of the passive filter.

— They are not suitable for variable loads, since, on one hand,they are designed for a specific reactive power, and on theother hand, the variation of the load impedance can detunethe filter.

Manuscript received October 24, 2008; revised May 07, 2009. First pub-lished December 28, 2009; current version published March 24, 2010. Paperno. TPWRD-00781-2008.

The authors are with the Electrical Engineering Department, Huelva Univer-sity, Huelva, Spain (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2009.2034902

Fig. 1. Series active filter and parallel passive filter.

— Series and/or parallel resonances with the rest of thesystem can appear.

An active power filter, APF, typically consists of a three-phase pulsewidth modulation (PWM) voltage source inverter[5]. When this equipment is connected in series to the ac sourceimpedance it is possible to improve the compensation charac-teristics of the passive filters in parallel connection [6], [7]. Thistopology is shown in Fig. 1, where the active filter is representedby a controlled source, where is the voltage that the invertershould generate to achieve the objective of the proposed controlalgorithm.

Different techniques have been applied to obtain a controlsignal for the active filter [8]–[10]. One such is the genera-tion of a voltage proportional to the source current harmonics[11], [12]. With this control algorithm, the elimination of seriesand/or parallel resonances with the rest of the system is pos-sible. The active filter can prevent the passive filter becoming aharmonics drain on the close loads. Additionally, it can preventthe compensation features depending on the system impedance.From the theoretical point of view, the ideal situation wouldbe that the proportionality constant, k, between the active filteroutput voltage and source current harmonics, had a high value.However, at the limit this would be an infinite value and wouldmean that the control objective was impossible to achieve. Thechosen k value is usually small so as to avoid high power activefilters and instabilities in the system. However, the choice of theappropriate k value is an unsolved question since it is related tothe passive filter and the source impedance values. Besides, thisstrategy is not suitable for use in systems with variable loads be-cause the passive filter reactive power is constant, and therefore,the set compensation equipment and load has a variable powerfactor.

In another proposed control technique, the APF generates avoltage waveform similar to the voltage harmonics at the loadside but in opposition [13]. This strategy only prevents the par-allel passive filter depending on the source impedance; the otherlimitations of the passive filter nevertheless remain.

0885-8977/$26.00 © 2010 IEEE

SALMERÓN AND LITRÁN: IMPROVEMENT OF THE ELECTRIC POWER QUALITY USING SERIES ACTIVE AND SHUNT PASSIVE FILTERS 1059

Fig. 2. Transformation from the phase reference system (abc) to the ��

system.

Other control strategies combining both the above have beenproposed to improve the parallel passive filter compensationcharacteristics [14], [15], but they continue to suffer from thedifficulty of finding an appropriate value for the APF gain k.

Finally, another approach has recently been proposed [16]. Itsuggests that the active filter generates a voltage which compen-sates the passive filter and load reactive power, so it allows thecurrent harmonics to be eliminated. The calculation algorithmis based on the instantaneous reactive power theory [17]. There,the control target is to achieve constant power in the source side.

In this paper a new control strategy based on the dual formula-tion of the electric power vectorial theory [18], [19] is proposed.For this, a balanced and resistive load is considered as referenceload. The strategy obtains the voltage that the active filter hasto generate to attain the objective of achieving ideal behaviorfor the set hybrid filter-load. When the source voltages are si-nusoidal and balanced the power factor is unity, in other words,the load reactive power is compensated and the source currentharmonics are eliminated. By this means, it is possible to im-prove the passive filter compensation characteristics without de-pending on the system impedance, since the set load-filter wouldpresent resistive behavior. It also avoids the danger that the pas-sive filter behaves as a harmonic drain of close loads and like-wise the risk of possible series and/or parallel resonances withthe rest of the system. In addition, the compensation is also pos-sible with variable loads, not affecting the possible the passivefilter detuning.

Although the APF series control based on the instantaneousreactive power theory is not new, in this paper the authors pro-pose a new formulation that has consequences in the controlloop design. In fact, the instantaneous reactive power here isdefined from a dot product whereas in [16], [17] it is defined asa cross product; this results in a remarkable simplification in theimplementation of the reference generation method. The finaldevelopment allows any compensation strategy to be obtained,among them, unit power factor.

The compensated electric system was simulated inMATLAB-Simulink, and the strategy was applied to athree-phase system with balanced and unbalanced loads.The simulation results used to verify the theoretical behaviorare presented. Finally, an experimental prototype was manufac-tured and its behavior checked. Experimental results are alsopresented.

II. THE DUAL INSTANTANEOUS REACTIVE POWER THEORY

The instantaneous reactive power theory is the most widelyused as a control strategy for the APF. It is mainly applied to

Fig. 3. Three-phase system.

compensation equipment in parallel connection. This theory isbased on a Clarke coordinate transformation from the phase co-ordinates (see Fig. 2).

In a three-phase system such as that presented in Fig. 3,voltage and current vectors can be defined by

(1)

The vector transformations from the phase reference systema-b-c to coordinates can be obtained, thus

(2)

(3)

The instantaneous real power in the frame is cal-culated as follows:

(4)

This power can be written as

(5)

where is the instantaneous real power without zero sequencecomponent and given by

(6)

It can be written in vectorial form by means of dot product

(7)

where is the transposed current vector in coordinates

(8)

In the same way, is the voltage vector in the same coor-dinates

(9)

In (5), is the zero sequence instantaneous power, calculatedas follows:

(10)

In a three-wire system there are no zero-sequence currentcomponents, that is, . In this case, only the instantaneous


Fig. 4. Decomposition of the voltage vector.

power defined on the axes exists, because the productis always zero.

The imaginary instantaneous power is defined by the equation

(11)

In accordance with (7), this can be expressed by means of thedot product

(12)

where is the transposed current vector perpendicular toand it can be defined as follows:

(13)

Both power variables previously defined can be expressed as

(14)

In the plane, and vectors establish two coordi-nates axes. The voltage vector can be decomposed in its or-thogonal projection on the axis defined by the currents vectors,Fig. 4. By means of the current vectors and the real and imagi-nary instantaneous power, the voltage vector can be calculated

(15)

In a four-wire system, the zero sequence instantaneous power,, is not null. In this case, (15) would have to include an ad-

ditional term with the form , where is the zero se-quence current vector.

III. COMPENSATION STRATEGY

Electric companies try to generate electrical power as sinu-soidal and balanced voltages so it has been obtained as a refer-ence condition in the supply. Due to this fact, the compensationtarget is based on an ideal reference load which must be resis-tive, balanced and linear. It means that the source currents arecollinear to the supply voltages and the system will have unitypower factor. If, in Fig. 3, voltages are considered as balancedand sinusoidal, ideal currents will be proportional to the supplyvoltages

(16)

is the equivalent resistance, the load voltage vector andthe load current vector.

Fig. 5. System with compensation equipment.

The average power supplied by the source will be

(17)

In this equation, is the square rms value of the fundamentalharmonics of the source current vector. It must be supposed thatwhen voltage is sinusoidal and balanced, only the current funda-mental component transports the power consumed by the load.

Compensator instantaneous power is the difference betweenthe total real instantaneous power required by the load and theinstantaneous power supplied by the source

(18)

In this equation, the average power exchanged by the com-pensator has to be null, that is

(19)

When average values are calculated in (18), and (17) and (19)are taken into account

(20)

Therefore, the equivalent resistance can be calculated as

(21)

where is the load average power, defined as

(22)

Fig. 5 shows the system with series active filter, parallel pas-sive filter and unbalanced and nonsinusoidal load. The aim isthat the set compensation equipment and load has an ideal be-havior from the PCC. The voltage at the active filter connectionpoint in coordinates can be calculated as follows:

(23)

is the source current in coordinates. In this equation,the restriction of null average power exchanged by the activefilter is imposed.


The load voltage is given according to (15) by

(24)

where is the real instantaneous power and is the loadimaginary instantaneous power.

The reference signal for the output voltage of the active filteris

(25)

Considering (23) and (24), the compensation voltage is

(26)

When the active filter supplies this compensation voltage, theset load and compensation equipment behaves as a resistor .

Finally, if currents are unbalanced and nonsinusoidal, a bal-anced resistive load is considered as ideal reference load. There-fore, the equivalent resistance must be defined by the equation

(27)

Here, is the square rms value of the positive sequencefundamental component. In this case, (26) is modified, where

is replaced by , that is

(28)

Reference signals are obtained by means of the reference cal-culator shown in Fig. 9 and Fig. 10. In the case of unbalancedloads, the block “fundamental component calculation” in Fig. 9is replaced by the scheme shown in Fig. 17, which calculatesthe current positive sequence fundamental component.

The compensation target imposed on a four-wire system isthe one presented in (16). However, a modification in the con-trol scheme of Fig. 9 is necessary. This consists in including athird input signal from the zero sequence power in the con-trol block where is generated.

The proposed control strategy may be suitable in a stiff feeder,where voltage could be considered undistorted.

IV. SIMULATION RESULTS

The system shown in Fig. 6 has been simulated in the Matlab-Simulink platform to verify the proposed control. Each powerdevice has been modeled using the SimPowerSystem toolboxlibrary. The power circuit is a three-phase system supplied bya sinusoidal balanced three-phase 100-V source with a sourceinductance of 5.8 mH and a source resistance of 3.6 . Theinverter consists of an Insulated Gate Bipolar Transistor (IGBT)bridge. On the dc side, two 100-V dc sources are connected.An LC filter has been included to eliminate the high frequencycomponents at the output of the inverter. This set is connected tothe power system by means of three single-phase transformerswith a turn ratio of 1:1.

Fig. 6. Series active power and passive filter topology.

TABLE IPASSIVE ELEMENT VALUES

The passive filter is constituted by two LC branches tuned tothe fifth and seventh harmonics. Each element value is includedin Table I.

The selection criteria to fix the ripple filter were, in the caseof low frequency components, that the inverter output voltagebe almost equal to voltage across . However, in the case ofhigh-frequency components, the reduced voltage in must behigher than in the capacitor . Furthermore, and valuesmust be selected so as not to exceed the transformer burden.Therefore, the following design criteria must be satisfied.

— , to ensure that inverter output voltage dropsacross at the switching frequency;

— , to ensure that voltage divider is betweenand , where is the source impedance, the

shunt passive filter, reflected by the secondary winding.At 20-kHz switching frequency, , ,

, .Two load types were simulated:— nonlinear balanced load;— nonlinear unbalanced load.

A. Case 1: Nonlinear Balanced Load

In this case, the nonlinear load consists of an uncontrolledthree-phase rectifier with an inductance of 55 mH and a 25resistor connected in series on the dc side.

Fig. 7 shows the phase “a” load current. The load currenttotal harmonics distortion (THD) is 18.6% and the power factor0.947, when the system is not compensated.

The 5th and 7th harmonics are the most important in the cur-rent waveform. They are 16.3% and 8.4% of the fundamentalharmonic, respectively.

Two LC branches were connected to mitigate the fifth andseventh harmonics. The source current waveform with the pas-sive filter connected is shown in Fig. 8. The THD falls to 4.7%.The 5th and 7th harmonics decrease to 3.6% and 0.9%, respec-tively. The passive filter was designed only to compensate the


Fig. 7. Load current of the phase “a”.

Fig. 8. Source current when the passive filter is connected.

Fig. 9. Control scheme.

source current harmonics; the reactive power was not consid-ered. The power factor of the set load and passive filter is 0.97.

To simulate the active filter series connection with a passivefilter, Fig. 6, it is necessary to determine the APF referencesignal. The control scheme used to calculate the active filtercompensation voltage is shown in Fig. 9. The voltage vector onthe load side and the source current vectors are the input sig-nals. By means of a calculation block, e vectors incoordinates can be determined. The product of these vectors al-lows the instantaneous real power to be calculated, obtaining its

Fig. 10. Calculation fundamental component.

Fig. 11. Source current when the active filter is connected.

average value with a low-pass filter (LPF). This is the power re-quired by the set passive filter and load. The average power isdivided by the average value of the sum of the square of the in-stantaneous values of the current fundamental component.

The fundamental component is obtained by means of a blockwith the scheme shown in Fig. 10. Each component of the sourcecurrent vector is multiplied by and where is thefundamental frequency in rad/s. The average values of the re-sults are obtained using two low-pass filters. They are multipliedby and again and then by 2. This allows the currentvector fundamental component to be obtained; conversely, thereal instantaneous power is divided by . The result is mul-tiplied by the current vector , which allows the first term inthe compensation voltage in (26) to be determined.

On the other hand, the imaginary instantaneous power is ob-tained and divided by and finally multiplied by the currentvector . This determines the second term in the compensa-tion voltage (26).

When the active filter is connected, the source current THDfalls to 1.30%. The waveform is shown in Fig. 11. Now, thepower factor rises to 0.99. This allows the proposed control tobe verified, the passive filter compensation characteristic to beimproved and unity power factor is practically achieved.

The passive filter impedance has to be lower than the systemimpedance in order to be effective. When the branch LC orimpedance source quality factor is low, the harmonics filteringdeteriorates. To verify the behavior of the compensation equip-ment in this situation, the source impedance is modified. It ischanged from 3.6 and 5.8 mH to 1.3 and 2.34 mH. Thesource current has a THD of 10.1%, when the active filter is notconnected and the compensation equipment is only the passivefilter. The source current waveform is shown in Fig. 12. The 5thand 7th harmonics are 8.2% and 2.5% of the fundamental har-monic and the power factor is 0.97.


Fig. 12. Source current when passive filter is only connected. Sourceimpedance, 1.3 � and 2.34 mH.

Fig. 13. Source current when the active filter is connected. Source impedance,1.3 � and 2.34 mH.

Fig. 14. Source current when only the passive filter is connected and the resistoron the dc side is 50 �.

When the active filter is working with the proposed controlalgorithm, the THD of the source current improves to 1.6% andthe power factor is 0.99. This current waveform is shown inFig. 13.

In a distribution system, variations may appear in the loadpower. To verify the behavior of the proposed control algorithm,the resistor value connected at the dc side of the uncontrolledthree-phase rectifier was changed from 25 to 50 . The sourceimpedance is 3.6 and 5.8 mH. When the passive filter is con-nected, the source current waveform is shown in the Fig. 14,which has a THD of 4.9%. In this case, the power factor is 0.91.

With the active filter connected the source current has thewaveform shown in Fig. 15. The THD falls from 4.9 to 1.8%and the power factor rises to 0.99

Therefore, with the proposed control algorithm, the set activefilter and passive filter allow the compensation of variable loads.

Fig. 15. Source current when the active filter is connected and the resistor onthe dc side is 50 �.

TABLE IIPASSIVE ELEMENT VALUES OF THE LOAD

Fig. 16. Source current without filters. Unbalanced load.

This control algorithm can compensate reactive power and canimprove the behavior of the passive filter.

B. Case 2: Non-Linear Unbalanced Load

In this case, the three-phase load is built with three single-phase uncontrolled rectifiers with capacitors and resistors con-nected in parallel at the dc side with the values shown in Table II.

Fig. 16 shows the source currents in the uncompensatedsystem. Current THDs of “a”, “b”, and “c” phase are 18.8%,35.0%, and 37.6%, respectively.

The control scheme for the active filter shown in Fig. 9, ismodified for unbalanced loads. The block “fundamental com-ponent calculation” in Fig. 9 is replaced by the scheme shownin Fig. 17. Now the average power P is divided by the squarerms value of positive sequence fundamental component. In thiscase, the positive sequence component is calculated by meansof the block “positive sequence component”, where the oper-ator necessary to implement the Fortescue trans-formation is obtained with an all pass filter. Subsequently, itsfundamental value is calculated and the Fortescue inverse trans-formation applied.

Fig. 18 shows the three source currents when this control isapplied to the active filter. The system presents a behavior sim-ilar to a resistive and balanced load. The source currents THDare 1.4%, 0.85%, and 1.3% in phases “a”, “b”, and “c”.


Fig. 17. Modification in the control scheme for unbalanced load.

Fig. 18. Source current with active filters and unbalanced load.

Fig. 19. Experimental prototype.

In (16), the compensation aim is to obtain unity power factor.When the voltage is sinusoidal and balanced, a sinusoidal andbalanced source current is obtained. When the voltage is dis-torted, unity power factor is achieved, although the source cur-rent is distorted.

V. EXPERIMENTAL RESULTS

The experimental prototype which has been developed isshown in Fig. 19. It is a three-phase system supplied by a si-nusoidal balanced three-phase 100-V rms source. Fig. 5 showsthe power circuit scheme.

The converter is a Semikron SKM50GB123-type IGBTbridge at the dc side, two 100-V capacitors are connected. Atthe ac side, an LC filter has been included to eliminate highswitching frequency. This set is matched to the power systemby means of three single-phase transformers with a turn ratioof 1:1 to ensure galvanic isolation.

Two dc sources in the APF simulation model were consid-ered. It simplifies the control scheme and makes the simulationeasier. The prototype also includes two capacitors. The controlscheme includes a loop with PI controller to ensure the capac-itor voltages remain constant [11].

Fig. 20. Source voltage and current, phase “a”, uncompensated system. Voltage48 V/div and current 4 A/div.

The passive power filter compensation is formed by two LCbranches tuned to the fifth and seventh harmonics. Each passiveelement values are included in Table I.

The control strategy was implemented in a control and gen-eral application data acquisition cards compatible with Matlab-Simulink and developed by dSPACE were used.

dSPACE Real-Time Interface (RTI) together with MathworksReal Time Workshop (RTW) automatically generate real timecode in dSPACE. This allows the processor board to be pro-grammed and I/O boards to be selected. It is based on the DS1005 PPC placed in a dSPACE expansion box. The input boardwas the dSPACE DS 2004 A/D and the output board the DS51001 DWO.

The control board has a PowerPC 750GX processor runningat 1 GHz. For the experimental prototype the sampling rate waslimited to 50 in order to avoid overrun errors.

A hysteresis band control was developed. The IGBT gatingsignals were generated comparing the reference signal withthe inverter output voltage considering a hysteresis band.This method switches the transistor when the error exceeds afixed magnitude: the hysteresis band. Therefore, the switchingfrequency is variable, although in our design this frequencyis limited to 20 kHz so as not to reach the IGBTs maximumswitching frequency.

The prototype was verified using two different loads: a non-linear balanced load and a nonlinear unbalanced load.

A. Case 1. Nonlinear Balanced Load

In the first experiment the source impedance has a induc-tance of 5.8 mH and resistance of 3.6 . The nonlinear loadconsists of an uncontrolled three-phase rectifier with an induc-tance of 55 mH and a 25 resistor connected on the dc side.Fig. 20 shows the phase “a” load current and voltage, mea-sured without compensation. This waveform is obtained using aLECROY Wavesurfer 424- type oscilloscope. The current THDmeasured using the Fluke 43 power quality analyzer is 21.5%and the voltage THD 11.2%. The measured power factor is 0.96.

Fig. 21 shows source current and voltage at the connectionpoint when the shunt passive filter is connected. This currentand voltage have a THD of 5.1% and 4.3% respectively. Thepassive power filter was designed to eliminate source currentharmonics; the reactive power was not taken into account. The


Fig. 21. Source voltage and current, phase “a”, in the system with passive filter.Voltage 48 V/div and current 4 A/div.

Fig. 22. Source voltage and current, phase “a”, system with active filter.Voltage 48 V/div and current 4 A/div.

power factor corresponding to the set load and passive filter is0.86.

When the series active filter is connected, the source currentTHD falls to 1.0%. This current waveform is shown in Fig. 22.Now, the power factor rises to 0.99, practically achieving unitypower factor. The voltage THD in the PCC is 1.3%. Its wave-form is shown in Fig. 22 with the phase “a” current. These re-sults verify the resistive behavior of the system; voltage and cur-rent are sinusoidal and they are in phase.

Another experiment to verify the behavior of the system wasto modify the source impedance. This was changed from 3.6and 5.8 mH to 1.3 and 2.34 mH. Fig. 23 shows the voltageand source current waveforms at the point of common couplingwhen the load is compensated with only a passive filter. Thewaveforms are worse than the previous experiment. The voltageand current THD are 5.5% and 10.8% , respectively. The powerfactor is 0.95.

When the active filter is connected, the voltage THD at thepoint of common coupling is 0.8% and the source current THDis 0.9%. The power factor rises to 0.99. This waveform is shownin Fig. 24.

Another typical situation in a power system is that corre-sponding to variable load. To verify hybrid filter behavior, theresistance at the dc side is changed from 25 to 50 . Fig. 25shows the voltage and current waveforms with the passive filterconnected. When the active filter is connected, the voltage THD

Fig. 23. Source voltage and current, phase “a”, system with passive filter andsource impedance modified. Voltage 48 V/div and current 10 A/div.

Fig. 24. Source voltage and current, phase “a”. System with active and passivefilter and variation in source impedance. Voltage 48 V/div and current 4 A/div.

Fig. 25. Source voltage and current, phase “a”, system with passive filter andvariation in load. Voltage 48 V/div and current 10 A/div.

falls from 7% to 1.5% and the current THD changes from 5.7%to 0.5%. Fig. 26 shows the waveforms.

Finally, to verify the system dynamic response experimen-tally, load impedance was changed and current waveform wasrecorded. The APF transient performance was mainly deter-mined by the dynamic response of the low-pass filters in thecontrol scheme. The control circuit was automatically imple-mented with MATLAB-Simulink and the toolbox Real TimeWorkshop (RTW) together with the Real Time Interface (RTI)from dSpace, which generated the code to program the controlboard. Therefore, the low-pass filters were implemented within


Fig. 26. Source voltage and current, phase “a”. System with active filter andvariation in load. Voltage 48 V/div and current 10 A/div.

Fig. 27. Dynamic response of the compensated system. Current 4 A/div.

a Simulink block. This block was modeled as a second orderfilter with a cut-off frequency fixed to 100 Hz and the dampingfactor to 0.707. It allowed a settling time of 8 ms to be achieved.

Fig. 27 shows the dynamic response of the source currentwhen a sudden change of load happens. The resistance at thedc side of the three-phase rectifier changes from 50 to 25 .The response time is about 4 cycles.

B. Case 2. Nonlinear Unbalanced Load

The nonlinear unbalanced load consisted of threesingle-phase uncontrolled rectifiers with a capacitor and aresistor connected in parallel at the dc side. The capacitor wasthe same in the three phases, 2200 , however, the resistorwas different for each one. It was 16.7 for phase “a”, 25for phase “b” and 50 for phase “c”. Fig. 28 shows the threesource currents. The THD measured was 15.6%, 38.7%, and42.2% in each phase.

When the active filter was connected using the proposed con-trol strategy for unbalanced loads, the source currents wave-forms were almost sinusoidal and balanced, which is the aimof the control strategy. Fig. 29 shows these currents. The THDvalues are 1.8%, 1.0%, and 1.7% in each phase.

Fig. 30 shows the common connection point voltage andsource current in phase “a”. Both signals are almost sinusoidaland in phase. When only phase “a” is considered the powerfactor measured is 0.99.

Fig. 28. Source currents, system without compensating, unbalanced load.4 A/div.

Fig. 29. Source currents, system with active filter, unbalanced load. 4 A/div.

Fig. 30. Common coupling connection voltage and source current in phase“a”. system with active filter. Unbalanced load. Voltage 48 V/div and current10 A/div.

VI. CONCLUSIONS

A control algorithm for a hybrid power filter constituted by aseries active filter and a passive filter connected in parallel withthe load is proposed. The control strategy is based on the dualvectorial theory of electric power. The new control approachachieves the following targets.

— The compensation characteristics of the hybrid compen-sator do not depend on the system impedance.

— The set hybrid filter and load presents a resistive behavior.This fact eliminates the risk of overload due to the cur-rent harmonics of nonlinear loads close to the compensatedsystem.


— This compensator can be applied to loads with randompower variation as it is not affected by changes in thetuning frequency of the passive filter. Furthermore, the re-active power variation is compensated by the active filter.

— Series and/or parallel resonances with the rest of thesystem are avoided because compensation equipment andload presents resistive behavior.

Therefore, with the proposed control algorithm, the activefilter improves the harmonic compensation features of the pas-sive filter and the power factor of the load.

Simulations with the MATLAB-Simulink platform were per-formed with different loads and with variation in the sourceimpedance. This fact allowed an experimental prototype to bedeveloped. Experimental and simulation results are presented.They allow the verification of the developed theoretical analysis.

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[19] P. Salmerón, R. S. Herrera, and J. R. Vázquez, “Mapping matricesagainst vectorial frame in the instantaneous reactive power compensa-tion,” IET Elect. Power Applic., vol. 1, no. 5, pp. 727–736, Sep. 2007.

P. Salmerón was born in Huelva, Spain. He receivedthe Ph.D. degree from the Electrical EngineeringDepartment, University of Seville, Seville, Spain, in1993.

In 1983, he joined the University of Seville as anAssistant and then Associate Professor in the Depart-ment of Electrical Engineering. Since 1993, he hasbeen a Professor, and is currently Dean, at EscuelaPolitécnica Superior, University of Huelva, Huelva,Spain. He has joined various projects in connectionwith research in power theory of nonsinusoidal sys-

tems and power control in electrical systems. His research interests include elec-trical power theory, electrical power systems, active power filters, and powerconversion systems.

S. P. Litrán was born in Sanlúcar de Barrameda,Spain. He received the B.Sc. degree in automationand industrial electronics engineering from theUniversity of Seville, Seville, Spain, in 2002.

Since 1989, he has been teaching circuit theoryand power electric systems with the Escuela Politéc-nica Superior, Department of Electrical Engineering,University of Huelva, Huelva, Spain. His currentresearch includes power quality, electrical powertheory, and active power filters.

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Improvement of the Electric Power Quality Using Series Active and