t. suneel 32 space vector modulation controlled hybrid ... 1/issue4/4. space vector... · space...

T. Suneel 32

International Journal of Emerging Trends in Electrical and Electronics (IJETEE) Vol. 1, Issue. 4, March-2013.

Space Vector Modulation Controlled HybridActive Power Filter for Power Conditioning

T. Suneel

Abstract: Active power filters are widely used in powersystems due to their advantages to maintain power quality. Inthis paper, presents a control method for hybrid active powerfilter using Space Vector Pulse Width Modulation (SVPWM).In the proposed control method, the Active Power Filter (APF)reference voltage vector is generated instead of the referencecurrent, and the desired APF output voltage is generated bySVPWM. Proper controller is developed to maintain powerquality with APF. The entire power system block set model ofthe proposed scheme has been developed in MATLABenvironment. The APF based on the proposed method caneliminate harmonics, compensate reactive power and balanceload asymmetry. Extensive simulation results are presentedwith case studies.

Key Words: Active power filters, Non-linear loads,Space Vector Modulation

1.1 Introduction

The growing use of power system, non-linear and time-varying loads has led to distortion of voltage and currentwaveforms and increased reactive power demand in acmains. In this process, harmonics are induced and affectedon input side of the supply as well as load side. Harmonicdistortion is known to be source of several problems, suchas increased power losses, excessive heating in rotatingmachinery, and harmonic resonances in the utility,significant interference with communication circuits, flickerand audible noise, incorrect operation of sensitive loads [1,2]. Traditionally, LC tuned passive filters have been used toabsorb harmonic currents generated by nonlinear loads.Their main advantage is high reliability and low cost.However, passive filters have several drawbacks, whichmay cause harmonic interaction with the utility problemswith the utility system, in the presence of stiff utility sharptuning of the LC filter is required and may not meet thespecified harmonic current limits [3, 4]. This provides themotivation for investigation of an active filter topology,which is practically viable, cost effective and can meet therecommended standard for high power nonlinear loads. Forhigh-power applications, the active filters are not costeffective due to their large rating and high switching-frequency requirement of the Pulse Width Modulation(PWM) inverter.

T.Suneel is currently working as an Assistant Professor in Electrical andElectronics Engineering Department at V.R.Siddhartha EngineeringCollege Vijayawada, (INDIA).

1.2 PROPOSED WORK

In this paper, a new controller is proposed to maintain goodpower quality. Among the various topologies the shuntactive filter based on Voltage Source Inverter (VSI) is themost common one because of its efficiency [5]. Proposedcontroller is tested by Matlab simulation. The performanceof active filter depends on the adoptive control approaches.There are two major parts of an active power filtercontroller. The first is that determines the reference currentof APF and maintains a stable DC bus voltage. Variouscurrent detection methods, such as instantaneous reactivepower theory, synchronous reference frame method,supplying current regulation and etc., are presented. Thecommonness of these methods is the request for generatingreference current of Active Power Filter (APF), either withthe load current or the mains current. The second is thatcontrols the VSI to inject the compensating current into acmains. The commonness of these methods is to control VSIwith the difference between real current and referencecurrent.

An alternative control method for shunt APF’s isproposed in this project [6]. The proposed method differsfrom previously discussed approaches in the followingways: a) To generate APF reference voltage vector insteadof reference current; b) to generate desired APF outputvoltage by Space Vector Pulse Width Modulation(SVPWM) [7, 8] based on generated reference voltage.Therefore, the proposed method is simple and easy tocarryout. This project discussed the basic principle of thismethod in detail and proved its validity by simulationresults.

In order to maintain good power quality, variousinternational agencies recommended limits of harmoniccurrent injecting into the utility according to IEEE-519standards the limits on the magnitude of harmonic currentsand harmonic voltage distortion at various frequency arespecified given in Tables 2.1 and 2.2.

The amount of distortion in the voltage or currentwaveform is quantified by means of an index called THD,the THD in current is defined as

% THD =100× 1 Isn/Is1 2

n

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Table 2.1:Isc/I1 h<11 11≤h≤17 17<h<23 23≤h<35 THD

<20 4 2 1.5 0.6 5

20-50 7 3.5 2.5 1 8

50-100 10 4.5 4 1.5 12

100-1000

12 5.5 5 2 15

Where Isc is the main short circuit current atthe point of common coupling. I1 is the maximumfundamental frequency load current.Table 2.2HARMONIC VOLTAGE LIMITS FOR POWERPRODUCERS:

2.3-69 kv 69-138 kvMax.forinducedharmonics

3.0 1.5

THD 5.0 2.5

The table 2.2 lists the quality of the voltage thatpower producer is required to furnish a user. It is based onthe voltage level at which the user is supplied.

2.4 HOW NON-LINEAR LOADS CREATE VOLAGEDISTORTION

The majority of voltage producers distortionfound in today’s distribution system by the loadsthemselves, not the supply. Since heavy non linear loads arepresent they take currents in a non-sinusoidal manner. Bydefinition a non sinusoidal waveform is composed ofharmonic current sources, which circulate through thesystem. The voltage drop due to these harmonic currentsresults in the voltage distortion.

By ohm’s law vh= (Ih×zh)The voltage drop appears as a harmonic voltage and theaccumulates of these voltages at the harmonic frequenciesproduces the voltage distortion.

Vth = 2

(Vh)2h

n

n is any integer greater than are notequal to 1.

Vth is the total harmonic distortion ofvoltage.

Vh is voltage at harmonic ‘h’.V1 is the fundamental voltage.

Distortion level can be quite high when the sourceimpedance is high.

2.5 CLASSIFICATION OF HARMONIC PRODUCINGLOADS

1. HARMONIC PRODUCING LOADS

Nonlinear loads drawing non sinusoidal currents fromutilities are classified into identified and unidentified loads.High-power diode/thyristor rectifiers, cycloconverters, andarc furnaces are typically characterized as identifiedharmonic producing loads because utilities identify theindividual non-linear loads installed by high-powerconsumers on power distribution systems in many cases.The utilities determine the point of common coupling withhigh-power consumers who install their own harmonic-producing loads on power distribution systems, and also candetermine the amount of harmonic current injected from anindividual consumer. A “single” low-power diode rectifierproduces a negligible amount of harmonic current.However, multiple low-power diode rectifiers can inject alarge amount of harmonics into power distribution systems.A low-power diode rectifier used as a utility interface in anelectric appliance is typically considered an unidentifiedharmonic-producing load.

Fig 2.1(a)-2.1(d) show various utility interfacefront-ends for industrial loads. Figs. 2.1(a)-2.1(b) are themost commonly used front-ends for diode and thyristorrectifiers respectively. The utility interface characteristicsand impact on active filtering requirements depends on thefiltering elements used, as given by typical supply currentTHD and displacement power factor (DPF) values.

Current THD=60%-130%DPF=0.98

Fig 2.1(a) Dilde Rectifier With dc side capacitor

Current THD=25%-40%DPF>0.7/0.98Fig 2.1(b) Thyristor/diode rectifier with dc inductor andcapacitor

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Current THD=30%-40% DPF>0.95Fig 2.1(c) Diode Rectifier With ac line reactors

and dc capacitor

Current THD=25%-30%DPF>0.7/0.95

Fig 2.1(d)Thyristor/Diode Rectifier With ac linereactors , dc side inductor

and dc capacitor-/Optimal utility interfacefront- end

2.6 HARMONIC MITIGATION TECHNIQUES2.6.1 PASSIVE FILTERS

One of the most popular methods of harmonicreduction involves the use of passive harmonic filters. Thesefilters use inductors and capacitors, which are tuned to blockor absorb particular harmonic content. These passive filterstend to be relatively large and expensive and they cannotprovide optimal harmonic reduction without unwanted sideeffects such as ringing transient response, unwantedresonance.2.6.2 ACTIVE HARMONIC FILTER

Active harmonic filters are commerciallyavailable. In principle, with sophisticated power electronicdevices, it is possible to produce a device that eitherprovides variable harmonic impedance to absorb some or allof the harmonic currents generated by the non-linear loadsor else provides harmonic currents of opposite polarity tocancel the non-linear load’s harmonic currents. These activefilters are very expensive and are not widely available.

Other harmonic reduction techniques appliedinvolves the use of transformer to cancel certain harmoniccurrents. The triplen harmonics (viz 3rd, 9th, 15th) circulatein the delta of the transformer with the unbalanced portionpresent in the transformer input line currents, cancels the 3rd,9th, 15th harmonics.Other way to cancel some harmonics is to connect the zig-zag grounding transformer that employs a 3-phase autotransformer to cancel third and triplen harmonics.

2.7 MERITS OF ACTIVE FILTERS OVER PASSIVEFILTERS AND OTHER FILTERING TECHNIQUES

Traditionally, LC tuned passive filters have beenused to absorb harmonic currents generated by nonlinearloads. Their main advantage is high reliability and low cost.However they have several drawbacks:

The numbers of passive filters installed would depend onthe number of harmonic component to be compensated, thisdemands for the information of harmonic content to beknown in advance. At some frequencies the passive filters may lead toresonance in the system. Passive filters cannot function under the saturatedcondition. Passive filters once designed have to be changedeven for the slightest changes in the system rating. Passive filters do not adjust to the variation in thesystem impedance. Other filtering techniques mentioned above requiremulti-winding transformer to be connected, which are bulkyand are costly. The LC tuned filter may also attract harmoniccurrents from ambient harmonic loads that may causeoverloading. Mistuning occurs due to component tolerances ofthe inductors and capacitors, typically ±10% from thenominal values.

All above demerits of the filters are overcome bythe use of active filter, which of great advantage. Theincreased severity of harmonic pollution in power networkshas attracted the attention of power electronic and powersystems engineers to develop dynamic and adjustablesolutions to the power quality problems, such equipment,generally known as Active filters.

3.2 Theory of Active Power Filter (APF)In a modern power system, the growing use of non-

linear loads and time-varying loads are increasing. Thesenonlinear loads may cause poor power factor, high degree ofharmonics and distortion of current and voltage waveforms.These problems are solved by using APF’s. Byimplementing these for power conditioning, it providesfunctions such as reactive power compensations, harmoniccompensations, negative-sequence current or voltagecompensation and voltage regulation. The main purpose ofthe APF installation by individual consumers is tocompensate current harmonics or current imbalance of theirown harmonic-producing loads. Besides that, the purpose ofthe APF installation by the utilities is to compensate forvoltage imbalance or provide harmonic damping factor to

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the power distribution systems. Fig.3.1 shows the basic APFblock diagram including non-linear load on three-phasesupply conditions.APF consisting of VSI and a dc capacitor have beenresearched and developed for improving the power factorand stability of transmission systems. APF have the abilityto adjust the amplitude of the synthesized ac voltage orcurrent of the inverter by means of pulse width modulationor by control of dc-link voltage, thus by drawing eitherleading or lagging reactive power from the supply. APF isan up-to-date solution to power quality problems. Normally,APF can be classified into shunt and series. Both aredesigned to compensate for reactive power or harmonics.APF consists of an inverter with switching control circuit.The inverter of the APF will generate the desiredcompensating harmonics based on the switching gatesprovided by the controller. The APF injects an equal-but-opposite distortion harmonics back into the power line andcancel with the original distorted harmonics on the line.Fig.3.1 shows the basic idea for the compensation principleof an APF, and Fig 3.2 shows the basic idea of operation ofAPF for a diode rectifier.

Fig 3.2 Principle of operation of a APF compensating adiode rectifier

The harmonic current compensation by the APF iscontrolled in a closed loop manner. The APF will draw andinject the compensating current, if to the line based on thechanges of the load in the power supply system. The supplyline current, is is described by the following equation (3.1).

lfs iii (3.1)

The line current, is is shaped to be sinusoidal byadding the compensating current, if into the distorted loadcurrent, il. The problem of this APF is the suitable design forthe controller and the filter configuration. Traditionally, itscontrol techniques were mostly using Pulse WidthModulation (PWM) technique. However, before developing

the controller, the configuration of the APF used in thedesign has to be defined.

3.3 INVERTERS AS SHUNT ACTIVE POWERFILTERS

The principal parts of an inverter based shunt APFare discussed below, the first part is a smoothing couplinglow pass filter which can be a first order (inductor) or a thirdorder filter in case of a voltage source inverter (VSI)otherwise a second order filter (an inductor and a capacitor)in case of a current source inverter (CSI). This filter allowsthe connection between the converter and the network. Thesecond part is the converter, the third part represent the DCenergy storage element, which can be either a capacitor forthe VSI or an inductor for the CSI. Finally, the last partrepresents the control system of the APF, the role of whichis to extract and control compensating current and regulatethe current or voltage of the DC energy storage element.

In fact the VSI and CSI are similar in behavior, thechoice between the two configurations depends on severalcriterion namely the semiconductors used, the DC energystorage element, power ratings, control complexity, etc...Thecomparison between the two configurations is presented intable 3.1, show a significant advantageous aspect of theVSI’s compared to the CSI’s as shunt APFs this can explainthe dominance of the VSI based APFs.

The performances of a VSI based shunt APF tocancel harmonic distortion depend on several parametersnamely the dimension of the smoothing and couplingelement (Lf), the energy storage element dimension (Cdc),the methods adopted to extract compensation references andthe control techniques used to regulate the filter currents andthe DC bus voltage ( VdC ).

Active power filter type

System Current sourceinverter (CSI)

Voltage sourceinverter (VSI)

Action Injects currents atPCC to cancelcurrent harmonics

Acts with currentcontrol loop togenerate thecompensatingwaveform

Power rating Medium powerapplications

Low/medium powerapplications, highpower for multilevelversion

Dc energy storageelements

Large DC inductor Large DC capacitor

Switchingfrequency(KHZ)

2-5 20-30

Response speed Medium (-1) Fast

Controlcomplexity

Complex (keepinductor currentconstant)

Simple (keepcapacitor voltageconstant)

Expandable No Yes (Multilevelversions)

Losses High Low

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Cost Heavy / Expensive Lighter / Cheaper

TABLE 3.1 COMPARISON OF CSI AND VSI AS APF’S

3.4 CLASSIFICATION OF APFAF’s can be classified based on converter type,

topology, and the number of phases. The converter type canbe either CSI or VSI bridge structure. The topology can beshunt, series, or a combination of both. The thirdclassification is based on the number of phases, such as two-wire (single phase) and three- or four-wire three-phasesystems.APF’s are divided into dc and ac filters. The dc filters aredesigned to compensate for current or voltage harmonics onthe dc side of thyristor converters for HVDC systems andthe dc link rectifier or inverter for traction systems. The acfilters are normally designed for the ac power systemharmonic compensations. However, the APF is usuallyreferred to the active ac power systems.

Hybrid Active-Passive Filters (HAPF) consists of thecombination of the active and passive filter in order toperform better. Hybrid active filters inherit the efficiency ofpassive filters and theimproved performance of active filters, and thus constitute aviable improved approach for harmonic compensation. Thecombination can be in different ways such as thecombination of shunt active filter and shunt passive filter, orcombination of series active filter and shunt passive filter, orcombination of active filter connected in series with shuntpassive filter and many more. Each of these combinationswill have different performance. However, the combinationof shunt active and shunt passive filter is morecommercialized and more commonly used. The series activefilter with shunt passive filter is usually used in testingField.

In this project, the HAPF is formed by a singletuned LC filter per phase and a three phase active filter,which are directly connected in series without any matchingtransformer. Thus, no additional switching-ripple filter isrequired for the active filter because the LC filter functionsnot only as a harmonic filter but also as a switching-ripplefilter.

Variable voltage and frequency supply to ac drives isinvariably obtained from a three-phase voltage sourceinverter (VSI). A number of Pulse widthmodulation(PWM) scheme is used to obtain variable voltage andfrequency supply. The most widely used PWM schemes forthree-phase VSI are carrier-based sinusoidal PWM andspace vector PWM (SVPWM). There is an increasing trendof using space vector PWM (SVPWM) because of theireasier digital realization and better dc bus utilization.

4.2 TWO-LEVEL INVERTERS AND MODULATIONSCHEMES

Inverters built with aforementioned devices have becomevery popular and were accepted by the industry owing to

their simplicity and ruggedness. With the advancements inthe Pulse Width Modulated (PWM) control schemes, theharmonic spectrum of the output voltage can be maneuveredto contain a pronounced fundamental component and totransfer the harmonic energy to the components of higherfrequency. This is desirable, as it is relatively easier to filterout the components of higher frequency compared to thecomponents of the lower frequency. A typical two-levelinverter is shown in Fig.4.1.

Fig.4.1 A Conventional Induction motor drive using a two-level inverter

Sinusoidal Pulse Width Modulation (SPWM) is one of themost popular schemes devised for the control of a two-levelinverter. In SPWM, a modulating sine wave correspondingto the fundamental frequency of the output voltage iscompared with a triangular carrier wave of high frequency,which corresponds to the switching frequency of thedevices. Each leg of the two-level inverter is controlled bythe corresponding modulating wave. The modulating wavesfor the individual legs are displaced by 1200 with respect toeach other as shown in the top trace of Fig.4.2.

Fig4.2 Modulating and carrier signals in SPWM for a two-level inverter (Top)and pole voltage AOv (bottom) showing two levelsThus, the inverter employed in the system shown in Fig.4.1is a two-level inverter because any pole voltage e.g. AOv

T. Suneel 37


assumes one of the two possible values namely 0 (when S4is turned on) or dcV (when S1 is turned on) as shown inFig4.2.The ratio of the peak value of the modulating signal and thepeak value of the carrier signal is defined as the amplitudemodulation ratio (also called modulation index) and isdenoted as am . The ratio of the frequencies of the carrierwave and the modulating wave is defined as the frequencymodulation ratio and is denoted as fm . In the range oflinear modulation,

0 < am <1. For the situation

depicted in Fig.1.2, am = 0.8 and

fm = 15.The pole voltage waveform contains significant amount ofcommon mode voltage. The common mode voltages, alsocalled the zero-sequence voltage, are comprised of thetriplen harmonic components in the pole voltages. In thecircuit depicted in Fig.4.1, these are dropped between thepoints ‘O’ and ‘N’. Consequently the load phase voltages donot possess the zero sequence voltage.

Fig.4.3 Typical waveforms of phase voltage (Top) andphase current (Bottom) of a two-level inverter in the rangeof linear modulation

The waveform of output voltage (the motor phasevoltage waveform ANv ) and the motor phase current whenthe inverter is operated in the range of linear-modulation areshown in Fig.4.3.A two-level inverter is capable of being operated in the six-step mode in which the inverter displays the maximumvoltage capability. Typical phase voltage and phase currentwhen a two-level inverter is operated in this mode is shownin Fig.9.4. The typical harmonic spectra of the phase voltagewhen the inverter is operated in the range of linearmodulation and in the six-step mode are shown in Fig.4.5.

Fig 4.4 Typical waveforms of phase voltage (Top) andphase current(Bottom) of a two-level inverter in the six-step mode ofoperation

Fig.4.5 Typical normalized harmonic spectra of the phasevoltage when the inverter is operated in the range of linearmodulation with am = 0.8 and fm = 15 (Top) and in thesix-step mode (Bottom)From the harmonic spectra presented in Fig.4.5, it is evidentthat in the range of linearmodulation, the predominantharmonics are pushed to the order of the switchingfrequency. In the six-step mode of operation, the harmonicorder is given by 16 n (n = 1,2,3…).

These spectra explain as to why SPWM control fortwo-level inverters has become popular. In the range oflinear-modulation, not only a smooth control over thefundamental component of the output voltage is obtained,but also the harmonic spectrum is acceptable. By increasingthe switching frequency, one may push significantharmonics further up. However, for high power applications,this is not attempted as the switching losses in the powersemiconductor devices also increase.Another possibility of reducing harmonic distortion is toeliminate certain specific harmonics. This modulationscheme is known as the Selective Harmonic Elimination(SHE). It is possible to suppress one harmonic component

T. Suneel 38


by each commutation per quarter period. Each commutationnotch per quarter period provides one degree of freedom.With an appropriate selection of the m degrees of freedom,it is possible to control the fundamental component and toeliminate )1( m harmonics. The advantage with thisscheme is that, it allows the undesirable lower orderharmonics to be eliminated, without making the switchingfrequency very high. However, this scheme involves thenumerical solution of nonlinear equations and is difficult toimplement for a large value of m .4.3 THEORY OF SVPWM TECHNIQUESVPWM technique was originally developed as a vectorapproach to pulse–width modulation for three-phaseinverters. The SVPWM method is frequently used in vectorcontrolled applications. In vector controlled applications thistechnique is used for reference voltage generation whencurrent control is exercised. It is a more sophisticated,advanced, computation intensive technique for generatingsine wave that provides a

higher voltage with lower total harmonic distortion and ispossibly the best among all the pulse width modulationtechniques. It confines space vectors to be applied accordingto the region where the output voltage vector is located.Because of its superior performance characteristics, it isbeen finding wide spread applications in recent years. Themain aim of any modulation technique is to obtain variableoutput voltage having a maximum fundamental componentwith minimum harmonics. Many PWM techniques havebeen developed for letting the inverters to posses variousdesired output characteristics to achieve the wide linearmodulation range, less switching losses, lower harmonicdistortion. The SVPWM technique is more popular thanconventional technique because of its excellent features.

More efficient use of DC supply voltage. 15% more output voltage thenconventional modulation. Lower total Harmonic distortion Prevent un-necessary switching henceless commutation losses

4.4 PRINCIPLE OF SVPWMFirstly model of a three-phase inverter is presented on thebasis of space vector representation. The three-phase VSI isreproduced in Fig.3.1. S1to S6 are the six power switchesthat shape the output, which are controlled by the switchingvariables a, a’, b, b’, c and c’. When an upper transistor isswitched on, i.e., the corresponding a’, b’, or c’ is 0.Therefore, the on and off states of the upper switches S1, S3,S5 can be used to determine the output voltage.

Fig 4.6 Power circuit of a three-phase VSI

The relationship between the switching variable vector [a, b,c]t and line-to-line voltage vector [Vab Vbc Vca] is given by(4.1) in the following:

cba

VVVV

dc

ca

bc

ab

101110

011(4.1)

Also, the relationship between the switching variable vector[a, b, c]t and the phase voltage vector [Va Vb Vc]t can beexpressed below.

cba

V

VVV

dc

cn

bn

an

211121112

3

(4.2)As illustrated in Fig.4.6, there are eight possiblecombinations of on and off patterns for the three upperpower switches. The on and off states of the lower powerdevices are opposite to the upper one and so are easilydetermined once the states of the upper power transistors aredetermined. According to equations (4.1) and (4.2), the eightswitching vectors, output line to neutral voltage (phasevoltage), and output line-to-line voltages in terms of DC-link Vdc, are given in Table 4.1 and Fig.4.2 shows the eightinverter voltage vectors (V0 to V7).

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Table 4.1 Switching vectors, phase voltages and output lineto line voltages

SVPWM refers to a special switching sequence of the upperpower switches of a three-phase power inverter. It has beenshown to generate less harmonic distortion in the outputvoltages and/or currents applied to the phases of a powersystem and to provide more efficient use of supply voltagecompared with other modulation technique.

Fig.4.7 Eight inverter voltages vectors (V0 to V7)

To implement SVPWM, the voltage equations in the abcreference frame can be transformed into the stationary d-qreference frame that consists of the horizontal (d) andvertical (q) axes as depicted in Fig.4.8.

Fig.4.8 The relationship of abc reference frame andstationary d-q reference frame

From this figure, the relation between these two referenceframes is given as

fdq0 = Ks fabc(4.3)

where, ks =

21212123230

21211

32

, fdq0 =

[ 0fff qd ]T, fabc = [ cba fff ]T, and f denotes either avoltage or a current variable.As described in Fig.4.8, this transformation is equivalent toan orthogonal projection of [a, b, c]t onto the two-dimensional perpendicular to the vector [1, 1, 1]t (theequivalent d-q plane) in a three-dimensional coordinatesystem. As a result, six non-zero (active) vectors and twozero vectors are possible. Six non-zero vectors (V1 - V6)shape the axes of a hexagonal as depicted in Fig.4.9, andfeed electric power to the system. The angle between anyadjacent two non-zero vectors is 60 degrees. Meanwhile,two zero vectors (V0 and V7) are at the origin and apply zerovoltage to the load. The eight vectors are called the basicspace vectors and are denoted by V0(000), V1(100), V2(110),V3(010), V4(011), V5(001), V6(101), V7(111). The binarynumbers indicate the switch state of inverter legs. Here 1implies upper switch being on and 0 refers to the lowerswitch of the leg being on. The same transformation can beapplied to the desired output voltage to get the desiredreference voltage vector Vref in the d-q plane.The objective of SVPWM technique is to approximate thereference voltage vector Vref using the eight switchingpatterns. One simple method of approximation is to

qaxis

daxis

a

b

c

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generate the average output of the inverter in a small period,

T to be the same as that of Vref in the same period.

Fig.4.9 Basic switching vectors and sectors

Therefore, space vector PWM can be implemented by thefollowing steps: Step 1. Determination of Vd. Vq, Vref andangle(α) Step 2. Determination of time duration T1,T2, T0 Step 3. Determination of the switchingtime of each switch (S1 to S6)

4.4.1 Step 1: Determination of Vd, Vq, Vref, and angle (α)

60cos60cos cnbnand VVVV

= cnbnan VVV21

21

30cos30cos0 cnbnq VVV

= cnbnan VVV23

23

cn

bn

an

q

d

VVV

VV

23

230

21

211

32

22qdref VVV

fttVV

d

q 2tan 1

, where f

=fundamental frequency.

Fig.4.10 Voltage Space Vector and its components in (d, q)

4.4.2 Step 2: Determination of time duration T1, T2, T0From Fig.3.6, the switching time duration can be calculatedas follows: Switching time duration at Sector 1

1 21

1 210021

0

T TT

T

T

TT

T

ref

zz

VdtVdtVV

)..( 2211 VTVTVT refz

3sin3cos

32

01

.32

sincos

21

dcdcrefz VTVTVT

(where, 0 ≤ α ≤ 60°) 3sin3sin

1

aTT z

3sin

sin2

aTT z

dc

ref

zzz

V

Vaand

fTwhereTTTT

32

1210

4.4.3 Step 3: Determination of the switching time of eachswitch (S1 to S6)

In Fig 4.12 Switching pulses of the upper switches areshown.

Fig.4.12 SVPWM switching patterns of upper switches ateach sector

α

sector5

sector6

sector1

sector2sector

3

sector4

d axis

qaxis

V1(100)

V2(110)

V3(010)

V4(011)

V5(001)

V6(101)

refV

q axis

d axisa

b

c

α

refV

Vd

Vq

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Switching Time Table at EachSector

Table 4.2: Switching SequenceTable

Sector number On-sequence Off-sequence

1 0-1-2-7 7-2-1-0

2 0-3-2-7 7-2-3-0

3 0-3-4-7 7-4-3-0

4 0-5-4-7 7-4-5-0

5 0-5-6-7 7-6-5-0

6 0-1-6-7 7-6-1-0

Table 4.3 Switching sequences for two-level inverter in allthe sectors for Space Vector ModulationThe waveforms considered here are the switching pulses ofthe upper switches and mirror images represent the pulses oflower switches. Based on Fig.3.7, the switching time at eachsector a MATLAB code is developed for generating theSVPWM pattern pulses. The code requires magnitude of thereference, the angle of the reference and the timer signal forcomparison. The magnitude of the voltage reference as thefirst output and the angle of the reference as the secondoutput from the control block are given to the developedcode. The angle of the reference voltage is hold for eachswitching period so that its value does not change duringtime calculation. A ramping time signal is generated usingrepeating sequence block, and the simple matlab/simulinkmodel of svpwm is shown in Fig 4.13.The code firstly identifies the sector of the referencevoltage. The time of application of active and zero vectorsare then calculated based on the equations from step 2. The

times are then arranged according to Fig.3.7. This time isthen compared with the ramp timer signal. Depending uponthe location of the time signal, the switch state is defined.This switch states are then passed on to the inverter.

Fig 4.13 Matlab/Simulink model ofSVPWM

4.5 DC bus utilization with SVPWM:The principal advantage of the SVPWM over SPWM is thatit enhances the DC bus utilization by about 15%. It isinstructive to evaluate the sample-averaged pole voltage of aphase, AOV for instance, to understand this fact.

Fig.4.14 Determination of the sample-averaged polevoltage

)3/sin()3/sin(||

1

dc

s

VTT

srv (4.4a)

)3/sin(sin||

2

dc

s

VTT srv (4.4b)

Which are calculated already.

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In eqn.4.4, || srv denotes the amplitude of the referencevector and ‘ ’ represents the position of the referencevector with respect to the beginning of the sector in whichthe tip of the reference vector is situated.

During 00 300 t

)7.4(22

2/

)6.4(22

2/

)5.4(22

2/

021

0,

021

0,

021

0,

TTTTT

VV

TTTTT

VV

TTTTT

VV

s

dcavgCO

s

dcavgBO

s

dcavgAO

During 00 9030 t

)10.4(22

2/

)9.4(22

2/

)8.4(22

2/

021

0,

021

0,

021

0,

TTTTT

VV

TTTTT

VV

TTTTT

VV

s

dcavgCO

s

dcavgBO

s

dcavgAO

Substituting eqn.4.4 in eqn. 4.5 one obtains:

)11.4(sin)60sin(60sin

**2/ 0

0, s

dc

sr

s

dcavgAO

TVV

TVV

Noting that 030 t , when 030t andsimplifying,

)12.4(, tSinVsrV avgAO

Substituting eqn.4.4 in eqn. 4.8 one obtains:

)13.4(sin)60sin(60sin

**2/ 0

0, s

dc

sr

s

dcavgAO

TVV

TVV

Noting that 030 t , when 00 9030 t andsimplifying,

)14.4()30(3

0, tSin

VsrV avgAO

The average pole voltage variation is plotted in Fig.4.15.The waveform of the average pole voltage consists of afundamental component and components of the triplenorder.

Fig 4.15 Waveforms of averaged pole voltage, phase voltageand line-line voltage

The waveform of the averaged line-line voltage is sinusoidalas the triplen voltage components of the pole voltagescancel out each other, being cophasal. The averaged phasevoltage also remains sinusoidal with a peak value, which is

31

times that of the peak value of the line-line voltage.

The peak value of the A-phase voltage, while the inverter isoperated in the range of linear modulation is given by:

srpeakph VV *)3/2(, (4.15)maximum magnitude of the reference voltage space

vector corresponds to the radius of the biggest circle that canbe inscribed in the hexagon as shown in figure 4.14, and is

equal to dcV23

, where dcV is the input DC voltage. Thus,

the maximum value of the peak-phase voltage is given by

dcdc

dcpeakph VVVV *577.03

*23*

32

max,, (4.16)

It is known that the maximum value of the peak-phasevoltage that can be obtained from a 3-Ph inverter withSinusoidal Pulse Width Modulation (SPWM) technique isequal to dcV*5.0 . It is therefore evident that SVPWMachieves a better DC bus utilization compared to SPWM (byabout 15.4%).

5.2 BLOCK DIAGRAM OF CONTROL SYSTEMThe main section of the APF shown in Fig.5.1 is a forced-commutated VSI connected to dc capacitor.Fig.5.1 Configuration of an APF using SVPWM

Considering that the distortion of the voltage in publicpower network is usually very low, it can be assumed thatthe supply voltage is ideal sinusoidal and three-phasebalanced as shown below:

T. Suneel 43


32sin32sin

sin

tVvtVvtVv

ssc

ssb

ssa

(5.1)

Where Vs the supply voltage amplitude

It is known that the three-phase voltages [vsa vsb vsc] in a-b-ccan be expressed as two-phase representation in d-q frameby Clark’s transformation and it is given by

sV

=

sc

sb

sa

q

d

VVV

VV

23

230

21

211

32

(5.2)

It is possible to write equation (5.2) more compactly as

sssqsdscsbsas VjVVavavavV 210

32

where

32j

ea , so balanced three-phase set of voltages isrepresented in the stationary reference frame by a spacevector of constant magnitude, equal to the amplitude of thevoltages, and rotating with angular speed f 2 .As shown in Fig.5.1, the shunt APF takes a three-phasevoltage source inverter as the main circuit and usescapacitor as the energy storage element on the dc side tomaintain the dc bus voltage Vdc constant. Fig.5.2 shows the

per-

phase (Phase A) equivalent circuit of the system describedin Fig.5.1.

Fig.5.2 Equivalent circuit of a simple power system togetherwith the APF5.3 COMPENSATION PRINCIPLE

In the Fig.5.2, vfa,1 and vfa,h denote the output fundamentaland harmonic voltages of the inverter, respectively. Thesevoltage sources are connected to a supply source ( vsa ) inparallel via a link inductor Lf and capacitor Cf .The supplycurrent isa is forced to be free of harmonics by appropriatevoltages from the APF and the harmonic current emittedfrom the load is then automatically compensated.It is known from Fig.5.2, that only fundamental component

is taken into account, the voltages of the ac supply and theAPF exist the following relationship in the steady state

111 1

ff

f

ffs VdtI

CdtIdLV (5.3)

where sV is the supply voltage, 1fI is the fundamental

current of APF, 1fV is the fundamental voltage of APF,and above variables are expressed in form of space vector.The APF is joined into the network through the inductor Lfand Cf. The function of these is to filter higher harmonicsnearly switching frequency in the current and to link two acvoltage sources of the inverter and the network. So therequired inductance and capacitance can just adopt a smallvalue. Then the total reactance caused by inductor andcapacitor for the frequency of 50Hz, and the fundamentalvoltages across the link inductors and capacitors are alsovery small, especially compared with the mains voltages.Thus the effect of the voltage of the link inductor andcapacitor is neglected. So the following simplified voltagebalanced equation can be obtained from equation (5.3).

1fs VV (5.4)The control object of APF is to make the supply currentsinusoidal and in phase with the supply voltage. Thus thenonlinear load and the active power filter equals to a pureresistance load Rs, and the supply voltage and the supplycurrent satisfy the following equation:

sss IRV (5.5)where

issqsdscsbsas IjIIaiaiaiI 210

32

.

Then the relationship between Is and the supply voltageamplitude Vs is

sss IRV (5.6)Substituting (5.5), (5.6) into (5.4) results in

s

s

sf I

IVV 1 (5.7)

Equation (5.7) describes the relationship between the outputfundamental voltage of APF, the supply voltage and thesupply current, which ensure that the APF operate normally.However, for making the APF normally achieving therequired effect, the dc bus voltage Vdc has to be high enough

T. Suneel 44


and stable. In the steady state, the power supplied from thesupply must be equal to the real power demanded by theload, and no real power passes through the power converterfor a lossless APF system. Hence, the average voltage of dccapacitor can be maintained at a constant value. If a powerimbalance, such as the transient caused by load change,occurs, the dc capacitor must supply the power differencebetween the supply and the load, the average voltage of thedc capacitor is reduced. At this moment, the magnitude ofthe supply current must be enlarged to increase the realpower delivered by the supply. On the contrary, the averagevoltage of the dc capacitor rises, and the supply current mustbe decreased. Therefore, the average voltage of the dccapacitor can reflect the real power flow information. Inorder to maintain the dc bus voltage as constant, thedetected dc bus voltage is compared with a setting voltage.The compared results is fed to a PI controller, and amplitudecontrol of the supply current Is can be obtained by output ofPI controller.

Fig.5.3 Control block diagram of proposed algorithm

The Fig.5.3 shows the block diagram of active filtercontroller implemented for reducing the harmonics withhybrid active filter system. In each switching cycle, thecontroller samples the supply currents isa ,isc and the supplycurrent isc is calculated with the equation of -(isa+isc), as thesummation of three supply current is equal to zero. Thesethree-phase supply currents are measured and transformedinto synchronous reference frame (d-q axis). Thefundamental component of the supply current is transformedinto dc quantities in the (d-q) axis and the supply current

amplitude Is generated by the PI controller with Vdc and Vref,the reference value of the dc bus voltage. The obtained d-qaxis components generate voltage command signal. Byusing Fourier magnitude block, voltage magnitude and angleis calculated from the obtained signal. These values are fedto the developed code and compared with the repeatingsequence. Then the time durations T1, T2 and T0, the on-timeof V1, V2 and V0 are calculated as already explained inchapter 3. The generated switching actions are applied to theAPF and power balancing of the filter takes place.

6.1 INTRODUCTIONThe developed control method for three-phase shunt APF issimulated in MATLAB/Simulink. Firstly, the three-phasesupply currents are sensed and transformed intosynchronous reference frame (d-q) axis. The fundamentalcomponent of the supply current is transformed into dcquantities in the (d-q) axis and the supply current amplitudeIs generated by the PI controller. The obtained d-q axiscomponents generate voltage command signal. By usingFourier magnitude block, voltage magnitude and angle is

calculated from the obtained signal. These values are fed tothe developed code and generated switching actions areapplied to the APF. Thus, power balancing of the filter takesplace. Further, the performance with different type of loadsis presented.

The complete simulation model of APF with different typeof loads is shown in Fig.6.1 and Fig.6.2. For an input supplyvoltage of 230V (rms) and switching frequency of 5kHz, thesimulation results before and after power balancing areshown.

Table 6.1 parameter values

System parameters Values of parametersSupply system 230 V (rms), 50 Hz, three-phase supplyBalanced linear load Zl = 75 + j 62.83 Ω

Unbalanced linearload

Zla = 75 + j 31.42 Ω, Zlb = 100 + j 23.56Ω,Zlc =85+ j 31.42 Ω

Non-linear load withresistance

R=1000 Ω

APF Cdc=1000µf, Vref = 750V, Cf = 24µf,Lf = 30 mH

T. Suneel 45


Fig.6.1 Simulation model of APF with linear load

6.2.1 For balanced linear loadSource current and load current are scaled by factor 25 for comparison purpose.

(a)

T. Suneel 46


(b)

Fig.6.2 Simulation results of balanced linear load(a) The phase-A supply voltage and load current waveforms(b) The phase-A supply voltage and supply current waveforms

The Fig.6.2 shows the simulation results of the APF when load is three-phase balanced RL load. Fig.6.2 (a) is thewaveforms of the phase-A supply voltage and the load current before compensation. Fig.6.2 (b) is the waveforms of thephase-A supply voltage and the supply current after compensation.

6.2.2 For unbalanced linear load

(a)

(b)

Fig.6.3 Simulation results of unbalanced linear load(a) Three-phase load current waveforms

(b) Three-phase supply current waveforms

T. Suneel 47


The Fig.6.3 shows the simulation results of APF when three-phase unbalanced RL load is considered. Fig.6.3 (a) isthe waveforms of the three-phase load current before compensation. Fig.6.3 (b) is the waveforms of the three-phase mainscurrent after compensation. From the figures, it can be seen that APF controller can remedy the system unbalance.

Fig.6.4 Simulation model of APF with non-linear load

6.2.3 For non-linear load with resistance

T. Suneel 48


Fig.6.5 Simulation results of non-linear load(a) The three-phase source voltage waveforms

(b) The three-phase load current waveforms(c) The three-phase source current waveforms

The Fig.6.5 shows the behavior of the APF when the non-linear load is a three-phase diode bridge rectifier withresistance load. Fig.6.5 (a) is the waveforms of the source phase voltage. Fig.65.5 (b) is the wave forms of the load currentbefore compensation. Fig.6.5 (c) is the waveforms of the supply current after compensation.

(a)

T. Suneel 49


(b)Fig.6.6 Harmonic spectrum of non-linear load

(a) The phase-A load current harmonic spectrum(b) The phase-A source current harmonic spectrum

The Fig.6.6 shows the simulation of harmonic spectrum ofAPF when the non-linear is a three-phase diode bridgerectifier with resistance load. Fig.6.6 (a) is the harmonicspectrum of the current before compensation on the loadside. Fig.6.6 (b) is the harmonic spectrum of the currentafter compensation on the source side. The harmonicspectrum of the load current shows that magnitude of the 5th,7th, 11th and 13th harmonics is very large. The harmonicspectrum of the source current shows that magnitude of the5th, 7th, 11th and 13th harmonics are evidently reduced aftercompensation. The load current Total Harmonic Distortion(THD) is 27.98%, while the supply current THD is 6.32%. Itshould be noted that the higher frequency harmonics causedby APF in mains current can be canceled easily by a smallpassive filter, and there are pulses in main current at the

points, where dtdi of load current is large, because fixed

switching frequency restrict the tracking capability of APF.

6.3 CONCLUSIONFrom the above results the performance of balanced linearload, unbalanced linear load and non linear load with theproposed control algorithm is observed. The three-phasesource voltage is made in phase with source current forbalanced linear load. The three-phase source current is madeequal in magnitude when an unbalanced linear load issimulated. The harmonic spectrum shows that reduction ofhigher order harmonics in three-phase source current when

non-linear load is simulated. The hybrid filter, draw theharmonic currents coming from the nonlinear load, so theharmonics are not flowing into the grid. Though the loaddraws non-sinusoidal current and supply current remainssinusoidal this means that the hybrid filter is achieving aseparation between load and supply, regarding the harmoniccurrents.

In this project, a control methodology for the APF usingSVPWM is proposed. This method requires few sensors,simple in algorithm and able to compensate harmonics andunbalanced loads. The performance of APF with thismethod is done in MATLAB/Simulink. The algorithm willbe able to reduce the complexity of the control circuitry.The harmonic spectrum under non-linear load conditionsshows that reduction of harmonics is better. Underunbalanced linear load, the magnitude of three-phase sourcecurrents are made equal and also with balanced linear loadthe voltage and current are made in phase with each other.The simulation study of two level inverter is carried outusing SVPWM because of its better utilization of dc busvoltage more efficiently and generates less harmonicdistortion in three-phase voltage source inverter. ThisSVPWM control methodology can be used with series APFto compensate power quality distortions.

REFERENCES:

T. Suneel 50


[1] EI-Habrouk. M, Darwish. M. K, Mehta. P, “Active powerfilters-A review,” Proc. IEE-Elec. Power Applicat., vol. 147,no. 5, Sept. 2000, pp. 403-413.

[2] Akagi, H., “New trends in active filters for powerconditioning,” IEEE Trans. on Industry applications, vol. 32,No. 6, Nov-Dec, 1996, pp. 1312-1322.

[3] Singh.B, Al-Haddad.K, Chandra.A, “Review of active filtersfor power quality improvement,” IEEE Trans. Ind. Electron.,vol. 46, No. 5, Oct, 1999, pp. 960-971.

[4] Ozdemir.E, Murat Kale, Sule Ozdemir, “Active power filtersfor power compensation under non-ideal mains voltages,”IEEE Trans. on Industry applications, vol.12, 20-24 Aug, 2003,pp.112-118.

[5] Dan.S.G, Benjamin.D.D, Magureanu.R, Asimionoaei.L,Teodorescu.R, Blaabjerg.F, “Control strategies of active filtersin the context of power conditioning,” IEEE Trans. on Ind.applications,vol.25,11-14 Sept-2005, pp.10-20

[6] Wang Jianze, Peng Fenghua, Wu Quitao, Ji Yanchao, “A novelcontrol method for shunt active power filters using svpwm,”IEEE Trans. on Industry applications, vol.1, 3-7 Oct, 2004,pp.134-139.

[7] Atif Iqbal, Lamine.A, Imtiaz.Ashraf, Mohibullah, “Matlabmodel of space vector pwm for three-phase voltage sourceinverter,” universities power engineering conference, 2006,UPEC’06, proceedings of the 41st international volume 3, 6-8Sept. 2006, pages:1096-1100.

[8] Rathnakumar.D, LakshmanaPerumal, Srinivasan.T, “A newsoftware implementation of space vector pwm,” IEEE Trans.Power Electron., vol.14,8-10 April 2005, pp.131-136.

[9] http://www.mathworks.com

T.Suneel received his Bachelor degree inElectrical and Electronics Engineeringfrom Gudlavalleru Engineering College,Gudlavalleru (INDIA) in 2007 andM.Tech in Power Electronics and Drivesfrom VIGNAN Engineering College,JNTU University Kakinada, (INDIA) in2009. He is currently working as anAssistant Professor in Electrical andElectronics Engineering Department atV.R.Siddhartha Engineering College

Vijayawada, (INDIA). Her research interests includes PowerElectronics, Power Electronics Drives and Power Systems.

t. suneel 32 space vector modulation controlled hybrid ... 1/issue4/4. space vector... · space...

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