Static Var Compensator and Active Power Filter With …hrudnick.sitios.ing.uc.cl/paperspdf/dixon/39.pdfAbstract—An active power ﬁlter and static var compensator with active power

130 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 1, JANUARY 2009

Static Var Compensator and Active Power Filter WithPower Injection Capability, Using 27-Level

Inverters and Photovoltaic CellsPatricio Flores, Juan Dixon, Senior Member, IEEE, Micah Ortúzar,

Rodrigo Carmi, Pablo Barriuso, and Luis Morán, Fellow, IEEE

Abstract—An active power filter and static var compensatorwith active power generation capability has been implementedusing a 27-level inverter. Each phase of this inverter is composedof three “H” bridges, all of them connected to the same dc linkand their outputs connected through output transformers scaledin the power of three. The filter can compensate load currentswith a high harmonic content and a low power factor, resultingin sinusoidal currents from the source. To take advantage of thiscompensator, the dc link, instead of a capacitor, uses a batterypack, which is charged from a photovoltaic array connected to thebatteries through a maximum power point tracker. This combinedtopology make it possible to produce active power and even to feedthe loads during prolonged voltage outages. Simulation results forthis application are shown, and some experiments with a 3-kVAdevice are displayed.

Index Terms—Active filters, multilevel systems, solar powergeneration, static var compensators (SVCs).

I. INTRODUCTION

POWER electronic devices contribute an important part ofharmonics in all kinds of applications such as power recti-

fiers, thyristor converters, and static var compensators (SVCs).On the other hand, the pulsewidth modulation (PWM) tech-niques used today to control modern static converters such asmachine drives, power factor compensators, and active powerfilters do not give perfect waveforms, which strongly dependon the switching frequency of the power semiconductors. Nor-mally, voltage (or current in dual devices) moves to discretevalues, forcing the design of machines with good isolationand, sometimes, loads with inductances in excess of the re-quired value. In other words, neither voltage nor current areas expected. This also means that harmonic contamination,

Manuscript received January 11, 2007; revised May 28, 2008. First publishedNovember 18, 2008; current version published December 30, 2008. Thiswork was supported by the Comisión Nacional de Investigación Cientifica yTecnológica (CONICYT) through Project Fondecyt 1080237 and MilleniumProject P-04-048-F.

P. Flores and J. Dixon are with the Department of Electrical Engineering,Pontificia Universidad Católica de Chile, 6904411 Santiago, Chile (e-mail:[email protected]; [email protected]).

M. Ortúzar is with the Compania Americana de Multiservicios Ltda. (CAM),Endesa, 8330287 Santiago, Chile (e-mail: [email protected]).

R. Carmi is with the National Transmission Electrical Utility Company,8340434 Santiago, Chile (e-mail: [email protected]).

P. Barriuso is with CDEC-SIC, 8330287 Santiago, Chile (e-mail: [email protected]).

L. Morán is with the Department of Electrical Engineering, Universidad deConcepción, 160 Concepción, Chile (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2008.927229

additional power losses, and high-frequency noise can affect thecontrollers. All these reasons have generated, for many years, alarge amount of research works on the topic of PWM [1]–[3].

Today, research is focused on multilevel converters, becausethey are able to generate voltage waveforms with less distor-tion than conventional inverters based on two-level topologies[4]–[6]. However, one step ahead has been the new multistageconverter technology, which allows us to generate [7], [9] manymore levels of voltage with fewer power semiconductors. Whenthe number of levels is high enough (more than 20), multilevelinverters are able to produce current waveforms with negligibletotal harmonic distortion. Furthermore, they can work usingboth amplitude modulation and PWM strategies.

One of the multistage technologies that allows producingmany levels of voltage with a few number of transistors isthe one based on “H” bridges scaled in the power of three[10]–[12]. This topology uses relatively few power devices,and each one of the “H” bridges work at a very low switchingfrequency, which gives the possibility of working in high powerwith low-speed semiconductors and generating low-switching-frequency losses, which makes them very suitable for machinedrive [13] or power grid improvement applications.

The objective of this paper is to show the advantages of a27-level active power filter and var compensator, which is alsoused as an active power generator. Compared to conventionalPWM techniques, this converter, in any of its functionalities, isable to produce current waveforms with negligible harmoniccontent. To produce active power, the system uses a batterypack kept charged using photovoltaic arrays. Furthermore, thebatteries can also be charged from the mains when required.

The paper describes the topology of the system and showssimulations and experiments with a small 3-kVA prototype. Insummary, the final objective of this line of research is to takeadvantage of active filters and var compensators, which canalso be used for power generation, and achieve a reliable andeconomic device for distributed generation, using renewableenergy such as solar sources to support the grid in high-demandhours.

II. OPERATION CHARACTERISTICS

A. Basic Principle

The circuit in Fig. 1 shows the basic topology of one con-verter used for the implementation of the multistage 27-level

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FLORES et al.: STATIC VAR COMPENSATOR AND ACTIVE POWER FILTER WITH POWER INJECTION CAPABILITY 131

Fig. 1. Three-level module for building multistage converters.

inverter. It is based on the simple four-switch device (“H”converter) used for single-phase inverters. These converters areable to produce three levels of voltage at the ac side: 1) +Vdc;2) −Vdc; and 3) zero.

Reference [14] has proposed a per-phase power conversionscheme for synthesizing multilevel waveforms, linking manyconverters in a series connection, like the system shown inFig. 1, but with all the dc voltages equal to “Vdc.” Sucha multilevel inverter with “n” equal dc voltage levels canoffer only 2n + 1 different voltage levels at the phase output.Reference [15] goes one step ahead with dc voltages varyingin a binary fashion, which gives an exponential increase in thenumber of levels. For “n” such cascaded inverters, 2n+1 − 1distinct voltage levels may be achieved.

In this paper, the outputs of the modules are connectedthorough transformers whose voltage ratios are scaled in thepower of three, allowing 3n levels of voltage [16]. Then, withonly three converters (n = 3), 27 different levels of voltageare obtained: 13 levels of positive values, 13 levels of negativevalues, and zero. As a comparison, the first topology with equaldc voltages only achieves seven levels with three converters,and the second topology, scaled in power of two, achievesjust 15 levels. This strategy represents an optimization of thenumber of levels, and their drawback is that there are noredundant levels, which are necessary to avoid negative powerback to the dc link. However, in this particular application,redundant levels are unnecessary because the topology usesoutput transformers and a battery pack at the dc link that allowsbidirectional power flow.

B. System Components

Fig. 2 displays the main components of the three-stage27-level converter that is being used in this work. The figureonly shows one of the three phases of the complete system. Ascan be seen, a battery pack, which is being charged through amaximum power point tracker (MPPT), is used in the dc link.MPPT [17] is a special dc–dc converter, able to maximize thelevel of power transfer from the photovoltaic array to the batterypack, with a very high efficiency (normally around 99% at80 Vdc). The solar array consists of two parallel groups of threeserial connected panels, each one composed of 50 photovoltaiccells, producing, at peak sunlight, 370 W of power. During 8 hof charging, the photovoltaic array is able to deliver 2 kWh ofenergy to the battery pack, accounting for approximately 43%of the battery’s energy. The solar panels were handmade at thePontificia Universidad Católica de Chile, Santiago, Chile, using300 cells, type MAIN-1530, which are produced by SchottSolar. They have an efficiency higher than 15%, and their sizeis 15 cm × 10 cm.

Fig. 2. Main components of the system (one phase).

The transformer located at the bottom of the figure has thehighest voltage ratio and will be called the main converter.The rest of the modules will be the auxiliary converters (Aux).The main converter manages most of the power (80%) [18],[19] but works at the lowest switching frequency, which is anadditional advantage of this topology. P and Q are indepen-dently controlled. The reference for P depends on the state ofcharge (SOC) of the battery pack and thus can be controlledusing the SOC information. On the other hand, Q can becontrolled by keeping a unity power factor (for example) at theconverter connection point. The load harmonics are filtered byforcing the current from the mains (IMAINS) to be sinusoidal.

The utilization of transformers make the system less efficient,but most of the time, active filters and var compensators usethem when the voltage between the source and the line doesnot match. Furthermore, these transformers are fed with squarevoltages, which reduces even more the efficiency of the system.However, as the winding currents are sinusoidal, the extraloss of efficiency is only because of core losses, which donot drastically increase. For example, for a 100-kVA system(33.3 kVA/phase), each main transformer has to be 27 kVA. Ifthis is a normal transformer, with 96% efficiency, this efficiencywill be reduced, due to extra core losses, to 95.7%. If atransformerless topology is an option, then the topology shownin Fig. 3 is feasible, with the advantage of being much moreefficient and cheaper. However, because of matching voltagesand isolation problems, this is not always a viable solution.Moreover, with transformerless topologies, nine independentand isolated solar panels are required for the three phases,and additional control strategies to separately manage each ofthem must be implemented. For these reasons and mainly forthe aforementioned matching problems, this paper has beenfocused on a system with output transformers, which is typicalin most of the active filters and var compensators connectedto the grid today. It should be noted that the main idea here



Fig. 3. Transformerless option (one phase).

Fig. 4. (a) Switching frequency and voltage amplitude in each “H” converter.(b) Voltage waveforms for 27 levels.

is to make active filters and var compensators more useful byadding active power sources at the dc link instead of a typicalcapacitor.

C. Multiconverter Operation

Fig. 4(a) shows the switching frequency in each one of thethree “H” converters of the multistage converter implemented.It can be noted that the switching frequency of the mainconverter, which manages more than 80% of the total power, isthe same frequency of the system, in this case, only 50 Hz. Thefrequency of the auxiliary converters is also low but increasesas the voltage level of the converter becomes lower in the chain,as seen in Fig. 4(a). The modulation algorithm to synthesize thewaveforms shown in Fig. 4 is described as follows: There isa three-digit trinary number associated with the instantaneousamplitude of the voltage. The three-digit number could be +1,

Fig. 5. Main components of the control scheme.

0, or −1 (positive, zero, or negative output at the corresponding“H” bridge). Each one of the three digits of the trinary numberis applied to each one of the three “H” bridges of the converter,which defines the output of the 27-level converter. For example,level 8 is obtained with the three-digit number {1, 0,−1} or 9 ·1 + 3 · 0 + 1 · −1 = 8. The maximum positive level is {1, 1, 1}or 13, and the minimum level (or maximum negative level) is{−1,−1,−1} or −13. It is important to mention that morecomplicated PWM strategies can also be applied in this kindof converters [20]–[22].

III. CONTROL SCHEME

Fig. 5 shows the block diagram of the control scheme, whereP and Q are independently controlled through IP and IQ,respectively. Overall, the control system has been programmedusing the DSP TMS-320 F241. The utilization of a DSP givesflexibility when changes in parameters, modifications, or im-provements need to be included in the control scheme [23].

A. Active Power Control

The control of the active power generated (P ) is through theSOC of the battery pack and is shown in Fig. 6. If SOC > 70%,then the battery pack can inject power to the mains (IREF > 0in Fig. 6). When SOC is between 70% and 60%, then no poweris injected to the mains, and IREF will be set to zero. Now, whenSOC is lower than 60% because solar panels are not givingenough energy to the battery pack, then IREF < 0, which meansthat the mains can charge and recover the battery pack. TheseSOC limits have been arbitrarily selected and are restrainedby the physical limitations of the battery pack. For powerinjection, it could be the maximum current that the photovoltaicarray can provide or the maximum discharge current of thepack. For a battery charge, the current is limited by the packmaximum charging current. The charging of the battery throughthe solar array is independent of the operation of the multilevelsystem and gives energy to the batteries whenever the sun isradiating. MPPT always delivers the optimum amount of energyfrom the solar panel, and the multilevel system will only take



Fig. 6. Active component generation.

power from the batteries when SOC information allows thisoperation.

It is important to mention that IP (ref) will be set automati-cally to a given value from the proportional–integral (PI) block,even when IREF is set to zero. This is because IP (ref) hasto satisfy the active power requirements of the contaminatingloads, which will come from the mains’ supply.

Looking at the connection between the VMAINS and themultilevel converter in Fig. 5, it can be seen that under a no-loadscenario, IMAINS = −IFILTER. If IREF is set to zero (Fig. 6),then IBAT will be zero, and hence, automatically IP (ref) willbe set to zero (no active power to or from the converter becauseIBAT = 0), and there will be no current ILOAD because this isa no-load condition.

When a load is connected to the system and IREF is still setto zero, then IBAT = 0, but IP (ref) is automatically set by thePI control in Fig. 6 at a value required for the active load thathas been connected.

When IREF is set positive because the battery has SOC >70%, then IBAT will follow IREF to give active power to thesystem, helping the mains to feed the load. Under a no-loadcondition, the battery energy will go directly to the mains’supply. The opposite situation will be observed when IREF isset to a negative value (SOC < 60%). In both cases, the valueof IREF will depend on the size of the battery pack and thepower capability of the multilevel converter.

Fig. 7 shows the complete control topology for the system,including the two PI blocks. Both PI blocks are configuredusing MATLAB’s sisotool, which is a way to graphicallyconfigure a compensator for a transfer function based on theroot locus method. The transfer functions, one for each block,are given in (1) and (2), shown at the bottom of the page.In both transfer functions, KINV represents the inverter gain,

RLIN and LLIN are the parameters of the line that connectsthe mains to the charge, and cos(ϕ) is the power factor of theinverter. Finally, KPMAINS and KIMAINS are the parametersof the PI block that controls the mains’ current. Obviously, itis necessary to configure the PI block for the mains’ currentcontrol before configuring the PI block for battery currentcontrol. The Appendix contains the set of equations used toobtain the transfer functions.

B. Reactive Power Control

The injection of reactive power (Q) is only necessary whenfor some reason the system requires reactive power assistance.When Q is set to zero (IQ(ref) = 0), the compensating systemautomatically generates the Q required for all loads connectedafter the multilevel converter. In other words, when Q is set tozero, the mains always see a unity power factor, independentof the type of contaminating load being compensated. If Q isset to a positive value, then the multilevel converter can assistthe mains, injecting additional reactive power to the grid. Q canalso be set to negative values, but this operation is normally notrequired. According to this explanation, the system works likea synchronous machine, where the reactive power is controlledthrough the excitation coil. In this case, it is controlled throughIQ(ref).

IV. SIMULATIONS

Simulations were performed using the software PSIM [24].Fig. 8 shows a typical battery charge–discharge operation, whenILOAD = 0 and IQ(ref) = 0 (see Fig. 7). As can be observed,the quality of currents is quite good. As IQ(ref) has been set tozero, no reactive power comes from the mains, which meansthat IMAINS is in phase with the voltage VMAINS, as shown inthe figure.

Fig. 9 shows a reactive power reference change from zero toa positive and then to a negative number when ILOAD = 0. Itcan be appreciated that the current IMAINS changes from zeroto leading and then to lagging. In this simulation, IREF has beenset to zero. Moreover, the current waveform is quite good.

Fig. 9 shows the filter operation when a power rectifier isconnected as contaminated load. The current of the rectifier isshown as ILOAD and changes from zero (no load) to 20 A dcand then to almost 40 A. In this case, IQ(ref) has been set tozero, and the battery current is also zero. As a result, the sourcecurrent IMAINS remains in phase with the voltage VMAINS,and IFILTER (from the multilevel converter), generates all theharmonics required by the load. In this case, only the 27-leveloperation is displayed.

IMAINS

VMOD= − KINV

LLIN · s + RLIN(1)

IBAT

IMAINSREF

=3 · KINV · cos(φ) · (KPMAINS · s + KIMAINS) · VMAINS

VBAT · s · (LINV · s + RINV)(2)



Fig. 7. Complete control topology.

Fig. 8. Step battery charge–discharge.

Fig. 9. Step reactive power change.

In Fig. 10, the oscillogram located at the bottom shows thesmall phase displacement between the mains’ voltage VMAINS

and the inverter voltage VMULTILEVEL. It can be noted that theyare in phase when ILOAD = 0, and then, they begin to shift, asexpected, when the active load appears.

Fig. 11 shows a combined operation of the multilevel con-verter. In the first 5 ms, the converter is injecting Q to thepower systems (IMAINS leads VMAINS, as shown in the lastoscillogram). Then, the battery begins to be charged fromthe mains, and IMAINS becomes more in-phase with VMAINS.Around t = 8 ms, the power rectifier is connected. Later on,at t = 10 ms, an inductive load (in parallel with the rectifier)

is connected. This inductive load is again disconnected at t =30 ms. In the simulation, the current IREF is changing frompositive to negative values every 10 ms.

As can be seen in Fig. 11(a), the filter current is compensatingthe harmonics of the rectifier to keep the source current IMAINS

sinusoidal [Fig. 11(c)]. On the other hand, Fig. 11(b) is showingIREF, IBAT, and IP (ref). It can be noted that the batterycurrent IBAT oscillates when the rectifier is connected to thesystem. This is due to the harmonics generated by the multilevelconverter to compensate the load.

V. EXPERIMENTAL RESULTS

The prototype used for the experiments is shown in Fig. 12.It is a four-stage 81-level converter, able to operate as a three-stage 27-level converter as well as a two-stage nine-level con-verter. The power connections are like the drawing showed inFig. 2. All the control tasks are executed by a DSP, which allowsthe programming of the algorithms related with this system.

Fig. 13 clearly shows the 27 levels of the power converter.On other hand, Fig. 14 shows the phase voltage and currents inone of the three phases of the multiconverter when it feeds aGraetz bridge rectifier. Finally, in Fig. 15, a transient responseunder rectifier connection is showed. In this case, the controlkeeps active power from the mains constant, and reactive powerQ = 0 (changes in reference Q were not experimentally imple-mented). Finally, the last oscillogram shows the battery current,which is being charged from the mains, from large to smallcurrent. This oscillogram also shows perturbations producedby harmonic voltage in the waveform obtained with the 3-kVAprototype in Fig. 12.

VI. CONCLUSION

A 27-level active power filter and SVC, with active powergeneration capability, has been implemented simulated andtested. Each phase of the filter is composed of three “H”converters per phase, all of them connected to a battery pack.The filter can compensate load currents with a high harmonic



Fig. 10. Step rectifier load.

Fig. 11. Combined operation of the multilevel converter (phase a). (a) IFILTER, IREACTOR, ILOAD, and IRECT. (b) IBAT, IP (ref), and IREF. (c) IMAINS,VMAINS, and ILOAD.

Fig. 12. Twenty-seven-level cascade H-bridge prototype.

distortion and a low power factor, resulting in sinusoidal cur-rents from the source. The battery pack can be charged fromeither the ac mains’ supply during nights or a photovoltaicarray during sunny days. This solar panel is connected tothe batteries through MPPT, which is able to maximize thepower conversion from the sun. These characteristics makes it

possible to deliver active power to the net when the SOC of thebatteries is higher than 70%, allowing feeding the contaminat-ing load during prolonged voltage outages. Simulation resultsfor this application are shown, and some experiments with a3-kVA device allow us to verify the operation of the proposedsystem. Future work will focus on the efficiency and losses oftransformers.

APPENDIX

The basic equations for the converter control are the voltagedrop between the mains (VMAINS) and the inverter (VMOD)

VMAINS − VMOD = ZLIN · IMAINS − ZINV · IFILTER (3)

where ZLIN and ZINV are the line impedance and the trans-former series impedance, respectively. The inverter is assumedto be an amplifier with a gain KINV (inverter’s simplifiedmodel)

VMOD = KINV · VREF. (4)

The mains’ line impedance is given as follows:

ZLIN = RLIN + LLIN · d/dt. (5)



Fig. 13. (Bottom) Voltage step waveforms in the 27-level converter (scale: 100 V/div).

Fig. 14. Unity power factor operation with contaminating load (rectifier). (Top) Rectifier current IRECT. (Middle) Filter current IFILTER. (Bottom) Mains’current IMAINS and mains’ voltage VMAINS (in phase). (scale: 10 A/div and 100 V/div).

Fig. 15. Transient response under rectifier connection. (Top to bottom) Rectifier current IRECT, filter current IFILTER, mains’ current IMAINS, and batterycurrent IBAT, which changes from heavy to light load (scale: 10 A/div).

The inverter’s connection line impedance is given as follows:

ZINV = RINV + LINV · d/dt. (6)

Replacing (4), (5), and (6) into (3), we obtain

VMAINS−KINV · VREF =RLIN · IMAINS+LLIN

·dIMAINS/dt−RINV · IFILTER−LINV · dIFILTER/dt. (7)

Linearization is possible where the inverter’s output currentis considered to be constant, given that it derives from thereference signal imposed to the inverter. The mains’ voltage isassumed to be constant. The linearization around an operationpoint for VMOD, IMAINS, and dIMAINS/dt is

−KINV · ΔVREF =RLIN · ΔIMAINS+LLIN · ΔdIMAINS/dt.(8)



VMAINS − KINV ·(

KPMAINS ·(IMAINS − IMAINS

REF

)+KIMAINS ·

∫ (IMAINS − IMAINS

REF

)dt

)

= RLIN · IMAINS − VBAT · (RINV · IBAT + LINV · dIBAT/dt)

3 · KINV ·(

KPMAINS ·(IMAINS − IMAINS

REF

)+KIMAINS ·

∫ (IMAINS − IMAINS

REF

)dt

)· cos(φ)

(14)

In the Laplace domain, we have

−KINV · VREF(s)=RLIN · IMAINS(s)+LLIN · s · IMAINS(s).(9)

The transfer function is [the same as (1)]

IMAINS(s)VREF(s)

=−KINV

LLIN · s + RLIN(10)

Now, the transfer function between IBAT and IMAINSREF (see

Fig. 7) will be obtained. Starting from (6), the transfer functionfor the battery current has to include the already configured PIblock for the mains’ current control. The input signal of theinverter is the output of the previous PI block:

VREF =(

KPMAINS + KIMAINS ·∫

dt

)

·(IMAINS − IMAINS

REF

). (11)

The inverter current can be deducted from the active power flowequation of the inverter (balance of the active power betweenthe ac and the dc sides plus the losses)

VBAT · IBAT = 3 · VMOD · IFILTER · cos(φ) + PL

→ IFILTER = (VBAT · IBAT − PL)/ (3 · VMOD · cos(φ)) .

(12)

Replacing (12) into (7), we obtain

VMAINS − KINV · VMOD

= RLIN · IMAINS − RINV

· (VBAT · IBAT − PL)/ (3 · VMOD · cos(φ))

− LINV · d(

VBAT · IBAT − PL

3 · VMOD · cos(φ)

)/dt

→ VMAINS − KINV · VREF

= RLIN · IMAINS − RINV · VBAT · IBAT − PL

3 · VMOD · cos(φ)

− LINV · VBAT

3 · VMOD · cos(φ)· dIBAT

dt. (13)

It can be seen that VMOD has been left out of the differentiationcaused by LINV. The reason for this is that VMOD is the resultof the control block for the ac sinusoidal mains’ current, whichhas a considerably faster time constant than the control blockfor the dc battery current in the tuning process. Hence, fordifferentiation purposes, the sinusoidal parameters can be con-sidered as constants, which means that their differentiations arezero (the same applies for the differentiation of IMAINS causedby LLIN). Replacing (4) and (11) into (13), we obtain (14),shown at the top of the page. The expansion of the equationwill introduce quadratic expressions for the state variables and

again linearization comes in handy. For space considerations,the steps of linearization and replacement of IREF0 = IMAINS

REF0

will not be displayed. In the Laplace domain, we have

− 3 · s · IMAINSREF (s) · KINV · cos(φ) · VMAINS · KPMAINS

+ 3 · s · IMAINSREF (s) · RLIN · IMAINS0 · KINV · cos(φ)

· KPMAINS − 3 · IMAINSREF (s) · KINV · cos(φ) · VMAINS

· KIMAINS + 3 · IMAINSREF (s) · RLIN · IMAINS0 · KINV

· cos(φ) · KIMAINS + 3 · s · IMAINS(s) · KINV · cos(φ)

· VMAINS · KPMAINS − 3 · s · IMAINS(s) · RLIN

· IMAINS0 · KINV · cos(φ) · KPMAINS + 3 · IMAINS(s)

· KINV · cos(φ) · VMAINS · KIMAINS − 3 · IMAINS(s)

· RLIN · IMAINS0 · KINV · cos(φ) · KIMAINS + VBAT

· LINV · s2 · IBAT(s) + VBAT · RINV · s · IBAT(s) = 0.

(15)

Given that the only interest is on the transfer function betweenIBAT(s) and IMAINS

REF (s), IMAINS(s) is set to zero, and thetransfer function (2) is obtained

IBAT(s)IMAINSREF (s)

=3·KINV ·cos(φ)·VMAINS(KPMAINS ·s+KIMAINS)

VBAT ·s·(LINV ·s+RINV). (16)

Since the resistive component of the mains’ line impedance isexpected to be low, the mains’ current equilibrium value canbe neglected from the final transfer function, which is alsoevaluated for a unity power factor.

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Patricio Flores was born in Santiago, Chile. Hereceived the B.S. degree from the Pontificia Uni-versidad Católica de Chile, Santiago, in 2006. Heis currently working toward the M.S. degree inthe Department of Electrical Engineering, PontificiaUniversidad Católica de Chile.

Since 2005, he has been working on active powerfilter projects.

Juan Dixon (M’90–SM’95) was born in Santiago,Chile. He received the professional degree in elec-trical engineering from the Universidad de Chile,Santiago, in 1977, and the M.Eng. and Ph.D. degreesfrom McGill University, Montreal, QC, Canada, in1986 and 1988, respectively.

Since 1979, he has been with the Departmentof Electrical Engineering, Pontificia UniversidadCatólica de Chile, Santiago, where he is currently aProfessor. He has presented more than 70 works atinternational conferences. He is the author of more

than 30 papers related to power electronics in international journals. His mainareas of interest are in electric traction, PWM rectifiers, active filters, powerfactor compensators, and multilevel converters. He has created an electricvehicle laboratory, where state-of-the-art vehicles are investigated.

Micah Ortúzar received the professional degree inelectrical engineering and the Ph.D. degree in 2005from the Pontificia Universidad Católica de Chile,Santiago, Chile.

He worked in the areas of power active filters,power electronics, and electric vehicles researchprojects while working toward his Ph.D. degree.He continued working on power-electronics-relatedresearch projects at the same university from 2005 to2007. He is currently with the Compania Americanade Multiservicios Ltda. (CAM), Endesa, Santiago, in

the energy distribution industry.

Rodrigo Carmi was born in Santiago, Chile. Hereceived the professional degree in electrical engi-neering from the Pontificia Universidad Católica deChile, Santiago, in 2005.

Between 2003 and 2005, he worked on ac-tive power filter projects. He is currently with theNational Transmission Electrical Utility Company,Santiago.

Mr. Carmi is a coauthor of two papers publishedin IEEE conference proceedings.

Pablo Barriuso received the electrical engineeringand M.Sc. degrees from the Pontificia UniversidadCatólica de Chile, Santiago, Chile, in 2008.

Currently, he is an Engineer with CDEC-SIC,Santiago, Chile, the ISO of the Chilean electricalinterconnected system. During his M.Sc. prepara-tion, he was involved with the design and applicationof power electronics devices and studied the fieldsof photovoltaic generation, harmonic filtering, andfault-tolerant control.

Luis Morán (S’79–M’81–SM’94–F’05) was born inConcepción, Chile. He received the B.Eng. degreein electrical engineering from the Universidad deConcepción, Concepción, in 1982, and the Ph.D.degree from Concordia University, Montreal, QC,Canada, in 1990.

Since 1990, he has been with the Department ofElectrical Engineering, Universidad de Concepción,where he is a Professor. His main areas of interestsare in ac drives, power quality, active power filters,FACTS, and power protection systems.

Dr. Morán is the author of more than 30 papers on active power filters andstatic var compensators published in IEEE TRANSACTIONS. He is the principalauthor of the paper that received the IEEE Outstanding Paper Award from theIEEE Industrial Electronics Society for the best paper published in the IEEETRANSACTIONS ON INDUSTRIAL ELECTRONICS in 1995 and is the coauthorof the paper that was awarded in 2002 by the IEEE Industry ApplicationsSociety Static Power Converter Committee.


Documents

Static Var Compensator and Active Power Filter With …hrudnick.sitios.ing.uc.cl/paperspdf/dixon/39.pdfAbstract—An active power ﬁlter and static var compensator with active power