Electrical Power and Energy Systems 64 (2015) 328–339

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

A novel control method for series hybrid active power filter workingunder unbalanced supply conditions

http://dx.doi.org/10.1016/j.ijepes.2014.07.0220142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: mam@eed.svnit.ac.in (M.A. Mulla), rc@eed.svnit.ac.in

(R. Chudamani), ac@eed.svnit.ac.in (A. Chowdhury).

Mahmadasraf Abdulhamid Mulla ⇑, Chudamani Rajagopalan, Anandita ChowdhuryDepartment of Electrical Engineering, S. V. National Institute of Technology, Ichchhanath, Surat, Gujarat 395007, India

a r t i c l e i n f o

Article history:Received 23 November 2013Received in revised form 30 May 2014Accepted 6 July 2014

Keywords:Active power filterGeneralised instantaneous power theoryPassive filterPower multi-vectorReference voltage

a b s t r a c t

In this paper a new control algorithm for a Series Hybrid Active Power Filter (SHAPF) is proposed. Withthe proposed control algorithm, the series active power filter simultaneously compensates for sourcevoltage unbalance and source current harmonics generated by non-linear loads. The proposed controlalgorithm is based on the generalised instantaneous power theory where the instantaneous inactivepower is represented as a second order tensor. The reference voltage is directly associated with three-phase instantaneous voltages and currents and are separated in three-phase co-ordinate systems.Therefore, the calculation of the compensation reference voltage is much simpler than the other availablecontrol algorithms. It can be applied for both voltage and current harmonic generating loads connectedacross balanced and unbalanced source voltages. The mathematical formulation of the proposed controlalgorithm with its applications to SHAPF is presented. The validity of the proposed control algorithm isverified with extensive experimental study and results are reported.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

With the increased use of power electronic converters in thepower system, there has been increased concern for power qualityand voltage stability. Power quality degradation generally resultsfrom non-linear loads and more complex steps are required toovercome these power quality problems. In addition to the com-pensation of harmonics produced by non-linear loads, the unbal-ance existing in electrical networks should also be corrected. Theunbalance in current is several times because of the unbalance inthe source voltage which results into the three-phase currents dif-fer considerably and leads to single phasing.

Traditionally shunt passive power filters (PPFs) have been usedto eliminate harmonic currents but many shunt PPFs would berequired to eliminate wide range of harmonics. The filtering char-acteristic of the shunt PPF is strongly influenced by the sourceimpedance and in addition, the hazards of series and parallel reso-nance become quite difficult to avoid [1]. Active power filters (APF)emerged as an alternate solution to the conventional PPFs; this ismore expensive but has an advantage that it can eliminate widerange of frequency components. The required power rating ofpower converter in APF is comparable as compared to the loadrating. This limits the applications of active filters in the power

system. Hybrid active filter topologies have been developed toeffectively solve the problems of harmonic currents and reactivepower [2,3]. Using low cost passive filters in the hybrid active filter,the power rating of active converter is reduced compared with thatof pure active filters. Hybrid active filters retain the advantages ofboth series and shunt APF and overcome the limitations of stand-alone passive and active filters. The hybrid active filters are costeffective and have become more practical in industry applications.

In an alternative approach, power factor correction (PFC) cir-cuits integrated in the converter configuration are proposed forthe compensation of harmonic current. Diode rectifier with thecontinuous-conduction mode (CCM) boost converter [4–7], pulsewidth modulated (PWM) rectifier [8], PWM AC choppers [9] arefew topologies for implementing PFC. The closed loop operationof the static power converter with PFC assures satisfactory perfor-mance to achieve a high input power factor and regulate converteroutput voltage over a wide operating range. Increased complexity,conducted electromagnetic interference (EMI) and reduced robust-ness are distinct characteristics of these approaches [10]. Thesesolutions address the compensation of source current harmonicsbut they do not compensate for source voltage unbalance. Theapplication of these configurations is limited to low power leveldue to rating constraints of semiconductor switches and efficiencyissues at high power levels.

Out of many APF configurations, the popularly used activepower filter configurations are: shunt active power filter, whichinjects compensation currents [11–18]; series active power filter,

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 329

which injects compensation voltages through a transformer[19–23]; and the hybrid active power filter, which is a combinedsystem of APF and PPF [24–37]. Two configurations of hybrid activepower filter have become very popular: active filter connected inseries with a shunt passive filter (injection type hybrid activepower filter (IHAPF)) and series active filter combined with shuntpassive filter (Series Hybrid Active Power Filter (SHAPF)) [32–36].Both topologies are useful to compensate current harmonics gener-ating load. However, when the load also generates voltage har-monics, the second topology is more appropriate [2,38].

The SHAPF works as a kind of harmonic isolator rather than aharmonic compensator and force the harmonic current to flowthrough the shunt passive filters. In addition, the SHAPF can regu-late the voltage at the point of common coupling at a desired valueby controlling the inverter output so as to compensate for abnor-mal utility voltage. The required rating of the series active filterin SHAPF configuration is much smaller than that of a conventionalshunt active filter [24,25]. SHAPF configuration is preferred forsimultaneous compensation of current harmonics and source volt-age unbalances [22,32,39–43]. SHAPF has very good potential athigh power levels, since it needs a very low rating voltage sourceinverter and this configuration overcomes all the problems of PPFs.This motivated the researcher to explore the application of activefilters at very high power level which is otherwise restricted dueto non-availability of high speed high power semiconductorswitches. Due to these multi-functionalities and advantages, theSHAPF and its controlling methods are studied more in recenttimes [31–37,44–46].

The SHAPF filtering characteristics and efficiency of harmoniccompensation depend on the control algorithm applied to calculatethe reference voltage. Several direct and indirect control methodsare proposed for generating reference signals. The direct methodincludes low-pass to band-pass transformation, indirect currentcontrol scheme, PI control strategy, S-transform to extract the fun-damental component, etc. [31,32,36,44–48]. In indirect approaches,instantaneous power theory has been used for generating referenceof the hybrid active power filters. Several publications appeared inthe literature suggests different definitions of instantaneous powertheories for deriving reference quantities. Instantaneous p–q the-ory, dual p–q theory, synchronous reference frame theory, vectorialtheory, generalised a–b–c reference frame theory, etc. are fewwidely used definitions used by researchers for separating refer-ence [28,29,34,46,48–50].

SHAPF configuration is suitable for simultaneous compensationof source current harmonics and source voltage unbalance and sev-eral control methods are also proposed to achieve this objective[22,32,39–43]. Most of these approaches use Fortescue sequencecomponents, instantaneous power theories, PLL and numbers oflow-pass filters in control circuit to extract final reference voltage.For separating reference voltage corresponding to source currentharmonics, instantaneous power definitions are generally used.The end expression of existing control algorithms reported in theliterature is generally complex, computationally intensive andrequires selection of different gain factors for proper compensation[22,32,39–43]. A need have been felt therefore to have a simple anddirect expression of reference voltage for SHAPF which simulta-neously compensate for source voltage unbalance and source cur-rent harmonics.

In this paper, a novel control scheme for SHAPF is proposedwhich simultaneously compensates the source voltage unbalancesand source current harmonics. In proposed method the referencevoltage is derived in two parts viz., reference voltage for sourceunbalance and reference voltage for source current harmonics.The first part compensates for abnormal utility voltage and isderived using the instantaneous sequence component of theunbalance source voltages. For deriving the second component,

the positive sequence component of source voltage is consideredas the fundamental voltage applied to the nonlinear load. The ref-erence voltage for SHAPF that compensates source current har-monics is derived using the generalised instantaneous powertheory. It is proposed to decompose multiphase voltage vector intoquantities that represent different components of power. Usingvector algebra, it is possible to obtain the voltage vectors corre-sponding to these components of the power multivector [51–53].The separated components of voltage vectors corresponding tounwanted components of instantaneous powers are used for gen-erating a reference voltage of SHAPF which compensates sourcecurrent harmonics. The addition of these two components gives asimplified direct formula for SHAPF reference voltage.

For experimental verification of proposed control algorithm, aprototype of SHAPF is developed and tested for compensating cur-rent harmonic generating load as well as voltage harmonic gener-ating load working under balanced as well as unbalanced sourceconditions. An extensive experimental study is done to verify theeffectiveness of proposed control algorithm and the results showthat SHAPF adopting proposed control algorithm effectively com-pensate source voltage unbalance and source current harmonics.The performance of proposed control algorithm is also comparedwith other normally used algorithms. Since the numbers of calcu-lation steps required to separate reference voltage are considerablyless in proposed reference voltage expression its implementation issimpler and fast as compared to other expressions.

This paper is organised as follows: The detail of SHAPF systemconfiguration is described in Section ‘System configuration’. Sec-tion ‘Proposed control algorithm’ presents the proposed controlscheme in different parts viz., finding fundamental unbalancedvoltage, the formulation of generalised instantaneous powertheory, decomposition of voltage vector and selection of propervoltage components for reference generation. The details of exper-imental model along with results obtained while compensatingcurrent and voltage harmonic generating load are presented in Sec-tion ‘Experimental results and discussion’.

System configuration

SHAPF is a combination of shunt passive filter and series activefilter. The series active filter improves the performance of the pas-sive power filter (PPF) by providing a high impedance path to theharmonic components present in the load current. Fig. 1 showsthe power circuit configuration of SHAPF, which has a series activepower filter and a bank of shunt PPF. This configuration reducesthe need for precise tuning of the PPF banks and eliminates thepossibility of series and parallel resonance. The shunt PPF bankused in this study is made up of a 5th harmonic tuned filter, a7th harmonic tuned filter and a high-pass filter which work as aharmonic current sink path. Since, dominating lower orderharmonics have been eliminated by passive filters, the series activefilter has to compensate only higher order harmonics and as aresult the rating of the active filter needed will be less comparedto conventional active filters [1].

The power circuit of the series active power filter is made up ofthe three-phase pulse width modulated voltage source inverter,the coupling transformers, and the ripple filter. The turns ratio ofthe series transformer connecting the active power filter to thepower line is chosen as unity in this study. However, in the highpower system, it is chosen to match the low power inverter ratingwith the system voltage and current. The ripple filter is used tosuppress the switching ripples generated due to the high frequencyswitching of the PWM inverter.

The supply voltage is stepped down to 110 V using an autotransformer. The unbalance in the magnitude and phase is

~ iLaZsa

Currentor

Voltage HarmonicproducingNon-linear

Load

iLb

iLc

vLa

vLb

vLc

~~

va

vb

vc

vcai

vcbi

vcci

Vdc

Zsb

Zsc

Passive Filter Bank

ia

ib

ic

5th 7th HPF

Cd1

Cd2

Voltage Source InverterRipple Filter

G1 G3 G5

G2G6G4

vscvsbvsa

Fig. 1. Diagram of SHAPF experimental setup.

330 M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339

introduced by connections of zig–zag transformer. Two types ofloading arrangement having characteristics of current harmonicand voltage harmonic generating load are created. For current har-monic generating load, three-phase diode rectifier with resistiveload is considered whereas for voltage harmonic generating load,a large capacitor is connected across the resistive load of three-phase diode rectifier. The inverter in the power circuit is controlledby the control circuit which generates gate pulses for series activepower as shown in Fig. 2. The point of common coupling voltagesand currents are acquired and connected as input to the controlcircuit. The detail of proposed control scheme for SHAPF isexplained in the following section.

Proposed control algorithm

The reference signal to compensate source voltage unbalanceand source current harmonics is calculated in two steps. First ofall, the unbalance fundamental component of the source voltageis derived using Fortescue sequence analysis. The positivesequence component of source voltage derived using sequenceanalysis is regarded as the fundamental voltage applied to thenon-linear load. In the second step, the reference voltage to com-pensate supply current harmonics is derived by decomposing thevoltage vector into components that represent different powerquantities. Generalised instantaneous power theory is used todefine instantaneous active and inactive power and then theappropriate voltage component is chosen as the reference voltageto compensate source current harmonics. These two referencevoltage components are added together in order to get resultant

Sequence Analysis

+-

+-

+-

+ +

+ ++ +

p

q

pc

Selection of appropriate

Power Components

Calculation of Voltage

Component ivq

ivp

×=

⋅=

qc

-+

vca

vcbvcc

-+

-+

G1

G4

G3

G6

G5

G2

vsbubvscub

vha vhb vhc

vsavsbvsc

iaibic

Separation of ‘p’ & ‘q’ into different power

components

Carrier Wave

vsaubvsa+

vsb+

vsc+

Fig. 2. Block diagram of the proposed control algorithm for SHAPF.

reference voltage for SHAPF. The reference voltages are comparedwith high frequency carrier wave in order to generate gate pulsesfor VSI. Fig. 2 shows the overall block diagram of the control circuitand following subsection explains the mathematical formulation ofoverall control circuit calculations.

Compensation of source voltage unbalance

For generating the reference for compensating the source volt-age unbalance, first of all the positive sequence components of thesource voltage is derived using sequence analysis of unbalancedsource voltage as following.

vþsa

vþsb

vþsc

264

375 ¼ 1

3

1 a a2

a2 1 a

a a2 1

264

375

v sa

v sb

v sc

264

375 ð1Þ

where operator a � ej2p3 .

The unbalance fundamental component of the source voltage isthen calculated as,

vsaub

v sbub

vscub

264

375 ¼

vþsa � v sa

vþsb � v sb

vþsc � v sc

264

375 ð2Þ

This is the first part of reference voltage which compensatessource voltage unbalance. The positive sequence component ofsource voltage is considered as the fundamental voltage appliedto the non-linear load.

Reference signal generation for harmonic elimination

The generation of the reference voltage signal for compensatingthe source current harmonics is explained in different parts viz.,the formulation of generalised instantaneous power theory,decomposition of voltage vector and selection of proper voltagecomponents for reference generation.

Generalised instantaneous power theoryFor a three-phase system the instantaneous quantities of source

voltage and currents are expressed as ~v ¼ ½vsa;v sb;v sc�T and~i ¼ ½ia; ib; ic�T . The instantaneous power multi-vector is defined asthe geometric product of voltage and current vectors:

~sðtÞ ¼ vðtÞiðtÞ ¼ vðtÞ � iðtÞ þ vðtÞ � iðtÞ ð3Þ

Instantaneous active power ‘p’ is defined as the inner product ofvoltage and current vectors.

pðtÞ ¼ ~vðtÞ �~iðtÞ ¼ vT i ¼ v saia þ vsbib þ v scic ð4Þ

Instantaneous inactive power~qðtÞ is defined as the outer product

of voltage and current vectors,~qðtÞ ¼ ~vðtÞ �~iðtÞ. The outer product

is defined by means of the tensor product ~vðtÞ �~iðtÞ ¼~iðtÞ �~vðtÞ�~vðtÞ �~iðtÞ.

The tensor product of current vector over voltage vector is:

~iðtÞ �~vðtÞ ¼ia

ib

ic

264

375 vsa v sb v sc½ � ¼

iav sa iav sb iav sc

ibv sa ibv sb ibv sc

icv sa icv sb icv sc

264

375 ð5Þ

The tensor product of voltage vector over current vector is:

~vðtÞ �~iðtÞ ¼v sa

vsb

v sc

264

375 ia ib ic½ � ¼

vsaia vsaib vsaic

v sbia v sbib v sbic

vscia vscib v scic

264

375 ð6Þ

Subtracting (6) from (5) formula for instantaneous inactivepower is expressed as

Table 1System parameters considered for experimental study.

Sr.no.

Parameters of thesystem

Value

1 Source voltage 110 V, 50 Hz (line-line)2 Source impedance Rs = 0.5 X, Ls = 0.1 mH3 Tuned PPF

(250 Hz)L5 = 12.32 mH, C5 = 32.88 lF

4 Tuned PPF(350 Hz)

L7 = 6.29 mH, C7 = 32.88 lF

5 High-pass PPF L = 2.36 mH, C = 29.88 lF, R = 17.75 X6 Series transformer 1:17 Ripple filter Lf = 1.35 mH, Cf = 50 lF8 VSI DC link voltage 100 V9 Switching

frequency20 kHz

10 Load-I Diode rectifier with R load (265 X)11 Load-II Diode rectifier with R-C load (1000 lF, 265 X

connected parallel)

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 331

~qðtÞ ¼0 �ðv saib � vsbiaÞ vscia � v saic

v saib � v sbia 0 �ðv sbic � v scibÞ�ðv scia � vsaicÞ vsbic � v scib 0

264

375 ð7Þ

This can further be expressed as

~qðtÞ ¼ ~vðtÞ �~iðtÞ ¼0 �qab qca

qab 0 �qbc

�qca qbc 0

264

375 ð8Þ

where qab = vsaib � vsbia; qbc = vsbic � vscib; qca = vscia � vsaic.This second-order tensor is a direct and simple expression of

instantaneous inactive quantities and can be applied to three-phase three-wire and three-phase four-wire power systems. Thepower quantities defined in this section are further used to derivethe reference voltage for compensating the source currentharmonics.

Decomposition of voltage vectorThe applied voltage vector ~vðtÞ can be decomposed into two

components, ~vpðtÞ that correspond to active power and ~vqðtÞ thatcorresponds to inactive power. Substituting ~vðtÞ ¼ ~vpðtÞ þ~vqðtÞ in

(3) we get~sðtÞ ¼ ½~vpðtÞ þ~vqðtÞ� �~iðtÞ þ ½~vpðtÞ þ~vqðtÞ� �~iðtÞ which isfurther simplified as,

~sðtÞ ¼ ~vpðtÞ �~iðtÞ þ~vqðtÞ �~iðtÞ ð9Þ

The two terms of (9) can be recognised as p(t) and ~qðtÞ respec-tively. Using the first term of (9) the component of instantaneousvoltage vector ‘~vp’, can be expressed as,

~vpðtÞ ¼ ½vpa;vpb;vpc�T ¼~i�1ðtÞpðtÞ ¼~iðtÞk~ik2

pðtÞ ð10Þ

where the vector ‘~vp’ is denoted as instantaneous active voltagetensor.

The second term of (9) can be used to obtain the component ofinstantaneous voltage vector ‘~vq’ as follows.

~qðtÞ ¼ ~vqðtÞ �~iðtÞ ð11aÞ

Multiplying both sides by current vector ~iðtÞ and expandingcross product of three vectors we get

~iðtÞ �~qðtÞ ¼~iðtÞ �~vqðtÞ �~iðtÞ ð11bÞ~iðtÞ �~qðtÞ ¼ ð~iðtÞ �~iðtÞÞ~vqðtÞ � ð~vqðtÞ �~iðtÞÞ~iðtÞ ð11cÞ~iðtÞ �~qðtÞ ¼ k~ik2~vqðtÞ � 0 ð11dÞ

~vqðtÞ ¼ ½vqa;vqb;vqc�T ¼~iðtÞ �~qðtÞk~ik2

ð11eÞ

In the geometric algebra framework, the conversion of thisouter product multiplication to matrix multiplication is done using

relations,~i�~q ¼ ½~i�x~q ¼ ½~q�Tx~i where ½~q�x ¼ ðv

*~iTÞT� v

*~iT and~q ¼ v*�~i.

Using this, ~vqðtÞ is expressed as,

~vqðtÞ ¼1

k i*

k2

0 qab �qca

�qab 0 qbc

qca �qbc 0

264

375

ia

ib

ic

264

375 ð12Þ

The vector ‘~vq’ is denoted as instantaneous inactive voltagetensor. The quantities defined by ‘~vp’ and ‘~vq’ as per (10) and (12)represent components of instantaneous voltages that correspondto active power and inactive power drawn by the load. These com-ponents are directly associated with three-phase instantaneousvoltages and currents and are separated directly in three-phasecoordinate system.

Reference signal generation for harmonic eliminationThe quantity p(t) that appears in (4) can be further divided into

two components, namely, average active power �pðtÞ and oscillatingactive power ~pðtÞ. Voltages corresponding to these two compo-nents of active powers are,

~vp ¼~i

k i*

k2½�pþ ~p� ¼ ~v �p þ~v ~p ð13Þ

Similarly, the total inactive power calculated using (8) is alsodivided into average inactive power �qðtÞ and oscillating inactivepower ~qðtÞ. Voltages corresponding to these two components ofinactive powers are,

~vqðtÞ ¼ ~v�qðtÞ þ~v~qðtÞ ð14Þ

The required components of active and inactive power thatneed to be considered for harmonic compensation arephðtÞ ¼ ~pðtÞ, qhðtÞ ¼ ~qðtÞ. The corresponding reference voltage forharmonic compensation is ~vhðtÞ ¼ ~v ~pðtÞ þ~v~qðtÞ.

~vha

~vhb

~vhc

264

375 ¼

~va~p þ~va~q

~vb~p þ~vb~q

~vc~p þ~vc~q

264

375 ð15Þ

The overall resultant reference voltage for SHAPF is calculatingby adding (2) and (15) as,

~vca

~vcb

~vcc

264

375 ¼

~v saub þ~vha

~v sbub þ~vhb

~v scub þ~vhc

264

375 ð16Þ

SHAPF injecting voltages corresponding to (16) can compensatefor the source voltage unbalances and source current harmonicssimultaneously. The implementation of SHAPF adopting this refer-ence voltage algorithm is discussed in further section.

Experimental results and discussion

For verification of proposed control method, an experimentalprototype of SHAPF is developed. The control circuit is realisedwith STM32F407VGT6, which is ARM Cortex-M4 based 32-bitmicrocontroller. The prototype is designed for 110 V, 50 Hz,three-phase system. Table 1 shows the system parameters of theexperimental setup and Fig. 3 shows the photograph of experimen-tal setup mentioning different components. The voltages andsource currents at the point of common coupling are acquiredand interfaced with analogue to digital converter (ADC) of thecontroller. Calculation of reference voltage signal and its

Fig. 3. Photograph of experimental setup.

332 M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339

comparison with carrier wave to generate gate pulses are part ofthe controller program.

STM32F407VGT6 is a high-performance ARM Cortex-M4 based32-bit microcontroller operating at a frequency of 168 MHz. TheCortex-M4 core features a floating point unit which supports

vsa vsb vsc

(a) Balanced source voltage

(e) Reference voltage calculated using proposed algorithm

vca

vcb

vcc

(c) Source current after connecting PPF

ia ib ic

(

Fig. 4. Performance of the system when Loa

single-precision data-processing instructions, data types and a fullset of DSP instructions. Six numbers of 12-bit, 2.4 mega samplesper cycle (MSPS) ADC channels are configured to acquire threevoltages and three currents. The ADC channel conversion time iscalculated as 5 ls considering channel changeover delay.Mathematical calculations on sampled data are performed toderive reference signals as per the proposed control strategy. Thecomparison of this calculated reference signal and carrier wave isperformed using a fast time-base timer in order to generate sixgate pulses for pulse width modulated voltage source inverter.

The PWM VSI is implemented using six STGW30NC120HDIGBTs from ST Microelectronics and three-phase bridge driverIR2130 from International Rectifier. Six gate pulses generated bythe controller are optically isolated before it is connected toIR2130. The turns ratio of three single phase matching transform-ers used is 1:1. A reasonably high switching frequency of 20 kHz isconsidered for implementation and the kVA rating of the VSI usedis 2 kVA. The SHAPF experimental setup with the proposed controlscheme is tested for compensating both current harmonics gener-ating load (Load-I) as well as voltage harmonics generating load(Load-II). The performance of the system is first tested withbalanced source voltages and then with unbalanced source

(b) Source current without any filter

(f) Series injected voltage

ia

ib

ic

vcai

vcbi

vcci

d) Source current after connecting SHAPF

ia ib ic

d-I is connected across balanced source.

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 333

voltages. The performance results are discussed in followingsubsections.

Performance with balanced source voltage

Compensation of current harmonic generating loadFor testing the performance of proposed control algorithm with

current harmonic generating load, Load-I is connected in the sys-tem. First the system performance is observed by connecting onlyPPF bank in the system. It is observed that the distortion in thesource current is reduced after connecting PPF bank as the domi-nant lower order harmonics are eliminated by providing a lowimpedance path through the PPF bank. In the next step the systemperformance is observed by connecting SHAPF in the system. It isobserved that all the harmonics are considerably removed whencompensation is done with SHAPF.

vsa vsb vsc

(a) Source voltage

(b)Source current without filter

(c)Source current with PPF

(d)Source current with SHAPF

ia

ia

ia

ib

ib

ib

Fig. 5. Performance of the system recorded with power ana

Table 2Performance of the system with balanced source.

Type of load Type of compensator

Isa

Load-I Without compensation 26.40With PPF bank 8.00With SHAPF 4.20

Load-II Without compensation 70.30With PPF bank 13.30With SHAPF 4.50

Fig. 4(a)–(d) shows the waveforms of the source voltages,source current without any filter connected in the system, sourcecurrent when PPF bank is connected and source current when com-pensation is done with SHAPF respectively. Fig. 4(e) and (f) showsthe reference voltage calculated by the control circuit and corre-sponding series injected voltage respectively. The magnitude ofindividual harmonics and percentage THD are measured usingthe harmonic spectra of these waveforms observed on MECO makepower and harmonic analyzer (Model PHA 5850). Fig. 5 shows therecorded harmonic spectrum and Table 2 shows the overall perfor-mance of the system when Load-I is compensated.

The value in bold is to highlight the reader reduction in totalharmonic distortion (THD) achieved. The average percentage THDof source current is 26.77% without compensation, which reducesto 7.97% after connecting PPF bank and which further reduces to3.57% after connecting SHAPF. The appreciable reduction in THDdue to PPF shows that dominant harmonics are considerably

vsa

ic

ic

ic

lyser when Load-I is connected across balanced source.

% THD in source current

Isb Isc %THD

27.00 26.90 26.777.40 8.50 7.973.60 2.90 3.57

72.00 73.20 71.8313.40 13.60 13.43

3.70 3.90 4.03

334 M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339

eliminated, reducing burden on the SHAPF. The reduced THD of3.57% after connecting SHAPF implies nearly sinusoidal current isdrawn from the source and thus ensuring nearly sinusoidal voltageat the PCC.

Compensation of voltage harmonic generating loadThe series active filter is more suitable for voltage harmonic

generating load like switch mode power supply (SMPS). Load-II isconsidered as a representative load of such load. In order to showthe efficacy of the SHAPF when compensation is required for suchhighly nonlinear load, Load-II is connected in the system.

Fig. 6(a)–(d) shows the waveforms of the balanced source volt-ages, source current without any filter connected in the system,source current when PPF bank is connected and source currentwhen compensation is done with SHAPF respectively. Fig. 6(e)and (f) shows the reference voltage calculated using proposedalgorithm and corresponding series injected voltage respectively.It is observed that all the harmonics are considerably removedand the THD of source current is reduced to 4.03% after connectingSHAPF. Table 2 shows the performance of the system when Load-IIis compensated. The average THD of source current is 71.83%

vsa vsb vsc

(a) Balanced source voltage

vca

vcb

vcc

(c) Source current after connecting PPF

ia ib ic

(

(e) Reference voltage calculated using proposed algorithm

Fig. 6. Performance of the system when Load

without compensation, which reduces to 13.43% after connectingPPF and which further reduces to 4.03% after connecting SHAPF.

The performance of the proposed control algorithm is comparedwith two other control algorithms used for SHAPF referencevoltage generation. First two control algorithms of Ref. [28] arecompared with the proposed algorithm. Three control algorithms(CA) compared here are as follows:

1. Control Algorithm-I (CA-I): This control technique derives refer-ence voltage proportional to the source current harmonics.The source current harmonics are separated using instanta-neous p–q theory.

2. Control Algorithm-II (CA-II): This control technique derives refer-ence voltage from voltage harmonics derived using the dual ofinstantaneous power theory.

3. Control Algorithm-III (CA-III): This control technique derives ref-erence voltage using the proposed control algorithm.

A comparison of three control technique is presented in Table 3.Control technique based on the instantaneous p–q theory requiresapproximately 39 multiplications to decide the reference voltage,

(b) Source current without any filter

(f) Series injected voltage

vcai

vcbi

vcci

d) Source current after connecting SHAPF

ia ib ic

ia

ib

ic

-II is connected across balanced source.

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 335

whereas the control technique based on voltage decompositionrequires approximately 21 multiplications to decide the referencevoltage. The time taken in calculating reference voltage by CA-IIIis quite small as compared to CA-I and CA-II. This study proves that,the proposed control algorithm (CA-III) is computationally lessintensive, fast and more effective in extracting reference voltageof SHAPF.

These experimental results confirm the filtering capabilities ofSHAPF and effectiveness of proposed control scheme in compen-sating both current and voltage harmonic generating loads underbalanced source conditions.

Performance with unbalanced source voltage

For testing the performance of proposed SHAPF configurationunder unbalanced source voltages, the system is supplied withvoltages having a phase and line values as follows:

Van ¼ 57 sinðxtÞ Vab ¼ 84 sinðxt þ 34:20ÞVbn ¼ 49 sinðxt � 1050Þ Vbc ¼ 99 sinðxt � 720ÞVcn ¼ 64 sinðxt þ 1330Þ Vca ¼ 110 sinðxt þ 1550Þ

ð17Þ

These voltages are generated by using zig–zag transformersacross three-phase balanced AC source voltages. In order to createmagnitude and phase unbalance, these zig–zag transformers areconnected having unequal turns in extended delta portion of dif-ferent phases. The SHAPF configuration is tested with both Load-Iand Load-II connected across unbalanced source and the resultsare presented in following sub sections.

Compensation of current harmonic generating loadFor testing the performance of SHAPF in compensating current

harmonics generated load, Load-I is connected in the system.Fig. 7 shows the control circuit waveform while compensatingLoad-I. Fig. 7(a) and (b) shows the captured source voltage andsource current respectively. After performing sequence analysis,

Table 3Comparison of the proposed algorithm with other control algorithms.

Sr.no.

Parameter ofcomparison

CA-I

1 Reference voltageformula

vca

vcbvcc

24

35 ¼ K

ica

icbicc

24

35 vca

vcbvcc

24

35 ¼

where whereica

icbicc

24

35 ¼ ffiffiffiffiffiffiffiffi

2=3p 1=

ffiffiffi2p

1 01=

ffiffiffi2p

�1=2ffiffiffi3p

=21=

ffiffiffi2p

�1=2 �ffiffiffi3p

=2

24

35 ic0

icaicb

24

35 vLa

vLbvLc

24

35 ¼

ico

icaicb

24

35 ¼ v0 0 0

0 va vb

0 vb �va

24

35�1 p0

~p~q

24

35 vc0

vcavcb

24

35 ¼

2 Instantaneouspower formula

p0pq

24

35 ¼ v0 0 0

0 va vb

0 vb �va

24

35 i0

iaib

24

35 ¼ p0

�pþ ~p�qþ ~q

24

35 p0

pq

24

35 ¼

3 Power calculationsteps (no. ofmultiplications)

23 23

4 Reference voltagecalculationsteps (no. ofmultiplications)

39 39

5 Time taken by incalculation ofalgorithm(measured values)

98 ls 96 ls

the calculated positive sequence voltages and fundamental unbal-ance voltages are as presented in Fig. 7(c) and (d) respectively.Considering positive sequence voltages as applied voltages, theinstantaneous active and inactive powers are calculated and it isas shown in Fig. 7(e). Using the proposed voltage decompositionmethod, the calculated voltages corresponding to instantaneousacting and inactive power are as shown in Fig. 7(f) and (g) respec-tively. The overall reference voltage is calculated by adding thefundamental unbalance voltage and voltage corresponding toharmonics, and it is as shown in Fig. 7(h). SHAPF injectingvoltage corresponding to this reference voltage will compensatesource voltage unbalance and source current harmonicssimultaneously.

The performance of SHAPF is observed with calculated refer-ence voltages. Fig. 8(a) and (b) shows the waveform of load voltageand source current without any filter connected in the circuit. Inthe next step PPF bank is connected in the system. The waveformof load voltage and source current after connecting PPF bank forcompensation are shown in Fig. 8(c) and (d) respectively. It isobserved that due to the source unbalance, the source currentsare not compensated satisfactorily by the PPF bank.

The system performance is further tested with SHAPF con-nected in the system. Fig. 8(e) and (f) shows the waveform of loadvoltage and source current after compensation. It is observed that,after compensation the source current becomes sinusoidal and theload voltage is restored to the balanced set of sinusoidal voltages.As a performance parameter, the percentage unbalance in the loadvoltage and the percentage THD in the source current arerecorded at different stages of compensation. The recorded perfor-mance of the system is tabulated in Table 4. From Table 4, it isseen that the THD in the source current is 27.63% before compen-sation and is reduced to 4.12% when SHAPF is connected forcompensation.

The percentage voltage unbalance is calculated using followingapproximate formula suggested in EN 50160 standard [54], whichtakes care of both magnitude and phase unbalance.

CA-II CA-III

�vLavLbvLc

24

35 vca

vcbvcc

24

35 ¼ va~p þ va~q

vb~p þ vb~qvc~p þ vc~q

24

35

where

ffiffiffiffiffiffiffiffi2=3

p 1=ffiffiffi2p

1 01=

ffiffiffi2p

�1=2ffiffiffi3p

=21=

ffiffiffi2p

�1=2 �ffiffiffi3p

=2

24

35 vc0

vcavcb

24

35 ~vpðtÞ ¼ ~pðtÞ

jj~ijj2

iaibic

24

35

i0 0 00 ia ib0 �ib ia

24

35�1 p0

~p~q

24

35 ~vqðtÞ ¼ 1

jj~ijj2

0 qab �qca�qab 0 qbcqca �qbc 0

24

35 ia

ibic

24

35

qab ¼ vsaib � vsbia; qbc ¼ vsbic � vscib;

qca ¼ vsc ia � vsaic

i0 0 00 ia ib0 �ib ia

24

35 v0

vavb

24

35 ¼ p0

�pþ ~p�qþ ~q

24

35 pðtÞ ¼ vsaia þ vsbib þ vscic

~qðtÞ ¼0 �qab qca

qab 0 �qbc�qca qbc 0

24

35

9

21

58 ls

vsa vsb vsc

tnerrucecruoS)b(egatlovecruoS)a(

(f) Voltage corresponding to oscillating active power

isa isb isc

(e) Instantaneous active powers

(d) Fundamental unbalance voltage

p pavg

posc

vsaub

(h) Overall reference voltage

vpac

vpbc

vpcc

vca

vcb

vcc

(g) Voltage corresponding to oscillating inactive power

vqac

vqbc

vqcc

vsa+ vsb

+ vsc+

vsbub

vscub

(c) Positive sequence voltage

Fig. 7. Control circuit waveforms while compensating Load-I under unbalanced source.

336 M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339

% Voltage Unbalance Factor ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3� 6b

p1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3� 6b

ps

� 100 ð18Þ

where

b ¼ V4ab þ V4

bc þ V4ca

ðV2ab þ V2

bc þ V2caÞ

2

The percentage unbalance observed in the load voltage is15.42% without compensation, which reduces to 1.13% when

SHAPF is compensating the system. This implies that the load volt-age is restored to the balanced set of sinusoidal voltages aftercompensation.

Compensation of voltage harmonic generating loadWhen the SHAPF is compensating Load-II, it compensates for

voltage harmonics produced by this load. The oscilloscope viewof unbalanced load voltages and source currents without compen-sation are as shown in Fig. 9(a) and (b). It is observed that the

vla vlb vlc

(a) Load voltage without any filter (b) Source current without any filter

(e) Load voltage after connecting SHAPF (f) Source current after connecting SHAPF

ia ib ic

(c) Load voltage after connecting PPF (d) Source current after connecting PPF

ia ib icvla vlb vlc

vla vlb vlcia ib ic

Fig. 8. Performance of the system when Load-I is connected across unbalanced source.

Table 4Performance of the system with unbalanced source.

Type of load Type of compensator Magnitude of load voltages % THD in source current

Vla Vlb Vlc %Unbalance Isa Isb Isc %THD

Load-I Without compensation 57.0 49.0 64.0 15.42 25.80 35.20 21.90 27.63With PPF bank 57.0 49.0 64.2 15.62 11.70 16.30 11.30 13.10With SHAPF 61.3 60.7 61.9 1.13 4.09 4.37 3.90 4.12

Load-II Without compensation 57.0 50.7 64.1 13.70 86.40 117.30 71.50 91.73With PPF bank 57.0 50.4 64.3 14.22 119.40 50.90 45.10 71.80With SHAPF 62.1 64.0 63.0 1.74 4.09 4.28 4.47 4.28

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 337

source current in this situation is highly nonlinear. Fig. 9(c) and (d)show the oscilloscope view of the load voltage and source currents,when compensation is done by the only PPF bank. In the next stepthe load is compensated by the SHAPF adopting the proposed con-trol scheme, the load voltage and source currents aftercompensation are as shown in Fig. 9(e) and (f) respectively. It isobserved that after compensation the load voltage becomes a bal-anced set of sinusoidal voltages and the source current approxi-mates to a balance sinusoidal wave.

For comparison, the harmonic contents of the source currentsand unbalance in a load voltage without any filter, with PPF and

with SHAPF are tabulated in Table 4. The THD of source currentis 91.73% without compensation, which reduces to 71.80% afterconnecting PPF and which further reduces to 4.28% after connect-ing SHAPF in the system. The percentage unbalance observed inload voltage is 13.70% before compensation which is reduced to1.74% after compensation. The reduced THD of source currentand percentage unbalance in load voltages mean the balancedsinusoidal current is drawn from the source and the unbalancesource voltage is compensated across the load terminals. Besidesthe reduced percentage of unbalance in a load voltage ensures thatload always gets balanced set of sinusoidal voltages after compen-

vla vlb vlc

(a) Load voltage without any filter (b) Source current without any filter

(e) Load voltage after connecting SHAPF (f) Source current after connecting SHAPF

ia

ib

ic

(c) Load voltage after connecting PPF (d) Source current after connecting PPF

vla vlb vlc

vla vlb vlcia ib ic

ia

ib

ic

Fig. 9. Performance of the system when Load-II is connected across unbalanced source.

338 M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339

sating with the SHAPF. These experimental results confirm theeffectiveness of proposed control algorithm for simultaneous com-pensation of source current harmonics and voltage unbalances.

These experimental results show that SHAPF effectively com-pensates both current harmonics generating load as well as voltageharmonics generating load working under balanced and unbalanceutility conditions. The reduced THD and reduced voltage unbalanceimplies nearly sinusoidal current is drawn from the source andnearly sinusoidal voltage at the PCC.

Conclusions

In the area of active filters, SHAPF configuration is finding moreapplications because of the multiple functionalities it offers andreduced rating voltage source inverter requirements. In this papera new control algorithm for SHAPF which simultaneously compen-sates source voltage unbalance and source current harmonics hasbeen proposed, developed and tested. The control algorithmderives reference voltage for unbalance supply from the sequencecomponents and reference voltage for harmonic compensation bydecomposing voltage vector into quantities that represent differentcomponents of power. The generalised instantaneous power

theory, where the instantaneous inactive power is defined as sec-ond-order tensor is used to define instantaneous power. Thisapproach presents the following advantages as compared to exist-ing state of the art:

� This reference voltage is directly associated with three-phaseinstantaneous voltages and currents.� This reference voltage is separated without co-ordinate trans-

formation as required in other methods.� Numbers of calculation steps required to calculate power and

reference voltage are considerably less in this method, thereforethe digital implementation of this reference voltage expressionis simpler and fast as compared to other methods.� This reference voltage does not require selection of gain factors

with different components of reference voltage components forproper compensation of the system.

The validity of the proposed control scheme has been verifiedby the experimental results of SHAPF prototype. Digital implemen-tation of proposed control scheme is done using ARM Cortex-M4microcontroller STM32F407VGT6. Experiments on compensatingthe current harmonics generating load and the voltage harmonicsgenerating load have been carried out under balanced and unbal-

M.A. Mulla et al. / Electrical Power and Energy Systems 64 (2015) 328–339 339

anced utility conditions. It has been observed that in all the cases oftesting the THD of source currents is less than 5%, which meets theregulations of IEEE 519 standard and simultaneously voltageunbalance is less than 2%, which meets the guidelines of EN50160 standard. These experimental results confirm the effective-ness of the proposed control algorithm in simultaneously compen-sating source voltage unbalance and source current harmonics.

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