Research Article Evaluation of a Trapezoidal Predictive ...
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Research ArticleEvaluation of a Trapezoidal Predictive Controller fora Four-Wire Active Power Filter for Utility Equipment ofMetro Railway Power-Land Substations
Sergio Salas-Duarte1 Ismael Araujo-Vargas1
Jazmin Ramirez-Hernandez1 and Marco Rivera2
1Escuela Superior de IngenierıaMecanica y Electrica Unidad Culhuacan Instituto Politecnico Nacional Avenida Santa AnaNo 1000Col San Francisco Culhuacan 04430 Mexico DF Mexico2Universidad de Talca 2 Norte 685 Talca Chile
Correspondence should be addressed to Ismael Araujo-Vargas iaraujoipnmx
Received 14 August 2015 Accepted 20 December 2015
Academic Editor Shengbo Eben Li
Copyright copy 2016 Sergio Salas-Duarte et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The realization of an improved predictive current controller based on a trapezoidal model is described and the impact of thistechnique is assessed on the performance of a 2 kW 216 kHz four-wire Active Power Filter for utility equipment of Metro RailwayPower-Land SubstationsThe operation of the trapezoidal predictive current controller is contrasted with that of a typical predictivecontrol technique based on a single Euler approximation which has demonstrated generation of high-quality line currents eachusing a 400V DC link to improve the power quality of an unbalanced nonlinear load of Metro Railway The results show that thesupply current waveforms become virtually sinusoidal waves reducing the current ripple by 50 and improving its power factorfrom 08 to 0989 when the active filter is operated with a 16 kW load The principle of operation of the trapezoidal predictivecontroller is analysed together with a description of its practical development showing experimental results obtained with a 2 kWprototype
1 Introduction
The use of Active Power Filters (APFs) in the electrical gridis critical for on-land transportation applications such asMetropolitan Railway Substations which reduce the flowingof current harmonics caused by the increased utilizationof nonlinear loads whilst improving the power quality ofthe supply APFs are an attractive solution to comply withthe national and international power quality standards atevery level of the network infrastructure [1ndash3] since high-performance switching devices appear available in themarketto develop power converters [4] In addition the develop-ment of fast and versatile microprocessors has facilitated theimplementation of nonlinear control techniques and therebyAPFs are becoming accurate power processors that reshapeclean sinusoidal supply currents [5ndash9]
Four-wire shunt APFs are a commonplace strategythat exhibit attractive characteristics to inject currents andreshape the line currents drawn by unbalanced nonlinearloads whilst providing a path to cancel the neutral currentby using either an additional switching limb or a split DC link[10 11]These circuits typically incur in the use of a power the-ory to calculate the reference currents [12] such that the filtermay operate as a current amplifier that injects compensatingcurrents to the grid causing a complex transistor switchingscheme since the generated filter currents must track thereferences Predictive control is an attractive method for con-trolling current waveforms in three-phase converters [6 713ndash20] since a piecewise linearmodel of the converter is usedtogether with a cost function to determine an appropriateconverter switching
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 2712976 11 pageshttpdxdoiorg10115520162712976
2 Mathematical Problems in Engineering
997888997888rarri1205721205730
997888997888rarri1205721205730
N
997888rarris
997888rarriL
997888rarriL
997888997888997888rarriLoad
997888997888997888rarriL1205721205730
997888997888997888rarriL1205721205730
997888997888997888rarrs1205721205730997888997888997888rarrs1205721205730
997888997888997888rarrs1205721205730
997888997888997888rarrs1205721205730 997888rarrs
q120572
q120573
q0
pT
plossminus
minus
minus
minus
HE(s)Eref
400V
i120572lowast
i120573lowast
i0lowast
+
+
+
+
+
+
Hbal(s)
P-Q theory InverseP-Q theory
Predictivecurrent
controller
Clarktransform
PLL and clarktransform
Clarktransform
IGBTdrivers
Unbalancednonlinear load
Active powerfilter
NDCreject
pT
i0bal E
vge1lowast
vge2lowast
vge6lowast
E
vge1
vge2
vge6
E1 E2
C1 C2
Q1 Q4
Q5 Q2
Q3 Q6
D1
D5 D2
D3 D6
D4
vTC
vSC
vRC
Lf
vdiff
sum
sumsum
sum
sum
Figure 1 Four-wire shunt active filter and its corresponding control block diagram
This paper presents the realization and experimentalverification of a trapezoidal predictive current controller fora four-wire shunt APF that improves the power quality ofunbalanced AC loads in contrast to the typical predictiveEuler control strategy The trapezoidal strategy relies itsoperation on a discrete trapezoidal linear approximation thatmore accurately determines the switching of the active filterfor the one-step ahead current sample such that three signifi-cant advantages are potentially exhibited first the trapezoidalpredictive controller slightly increments the processing timewithout affecting the switching of the power convertersecond in contrast to the typical Euler approximation usedin other works [6 7 13ndash20] the trapezoidalmethod generateslower AC current ripple and third the convergence time andload operating performance are wider than those obtainedusing the typical predictive control strategy which improvesthe reference current tracking and therefore the powerquality Experimental results obtainedwith a 2 kVAprototypeare presented demonstrating that the trapezoidal predictivecontrol may accurately compensate the currents drawn byan unbalanced nonlinear load under static and dynamicconditions
2 Four-Wire Shunt Active Filter
21 Circuit Description The four-wire shunt APF is con-nected in parallel to the unbalanced nonlinear load as shownat the right-hand side of Figure 1 which consists of a splitDC link formed by 119862
1and 119862
2which refer to the AC supply
neutral node119873 to provide a path tomitigate a commonmodecurrent a typical three-phase current-feed active converterformed by transistors 119876
1to 1198766and diodes 119863
1ndash1198636 and three
line filter inductors 119871119891used to generate the filter current
vector 997888rarr119894119871
= [119894119871119877 119894119871119878
119894119871119879]119879 by the difference between the
supply and converter voltage vectors 997888rarrV119904= [V119877119873 V
119878119873V119879119873]119879
and 997888rarrV119862
= [V119877119862119873 V119878119862119873
V119879119862119873]119879 thereby obtaining virtual
sinusoidal supply currents 997888rarr119894119904= [119894119878119877 119894
119878119878119894119878119879]119879
22 Principle of Operation of the Active Filter The principleof operation of the APF of Figure 1 may be described usingthe control block diagram presented at the left-hand side ofFigure 1 An instantaneous active and reactive power theoryP-Q theory block in Figure 1 [12] is used to obtain an effectivecalculation of the reference currents that the APF may injectto the supply to instantaneously mitigate the reactive anddistorted power components drawn by the nonlinear loadand balance the active power per phase The P-Q theory usesthe Clarke transformation of the supply voltage and loadcurrent as shown in
V120572120573120579
=[[[
[
V0
V120572
V120573
]]]
]
= radic2
3
[[[[[[[[
[
1
radic2
1
radic2
1
radic2
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]]]]]]
]
[[
[
V119877119873
V119878119873
V119879119873
]]
]
Mathematical Problems in Engineering 3
119894120572120573120579
=[[[
[
1198940
119894120572
119894120573
]]]
]
= radic2
3
[[[[[[[[
[
1
radic2
1
radic2
1
radic2
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]]]]]]
]
[[
[
119894Load119877
119894Load119878
119894Load119879
]]
]
(1)
such that the calculation of the active and reactive instanta-neous powers in the 1205721205730 coordinate system is obtained asrespectively shown in
119901119879
=997888997888rarrV1205721205730
sdot997888997888rarr1198941205721205730
= V120572119894120572+ V120573119894120573+ V01198940 (2)
119902 =997888997888rarrV1205721205730
times997888997888rarr1198941205721205730
=[[
[
119902120572
119902120573
119902120579
]]
]
=
[[[[[[[[[[[
[
[
V120573
V0
119894120573
1198940
]
[V120579
V120572
1198940
119894120572
]
[
V120572
V120573
119894120572
119894120573
]
]]]]]]]]]]]
]
(3)
where 119901119879is the real power or internal product of the voltage
and current vectors and 119902 is the imaginary vector power orexternal product of the voltage and current vectors whichis composed of 119902
120572 119902120573 and 119902
0 Since the load uses a fourth
conductor namely the neutral which is very common in low-voltage distribution system the P-Q calculation may includeboth zero-sequence voltage and current as shown in (2) and(3) Therefore the instantaneous powers defined above maybe combined in a single matrix transformation as shown asfollows
[[[[[
[
119901119879
119902120572
119902120573
1199020
]]]]]
]
=
[[[[[
[
V120572
V120573
V0
0 minusV0
V120573
V0
0 minusV120572
minusV120573
V120572
0
]]]]]
]
[[
[
119894120572
119894120573
1198940
]]
]
(4)
which is defined on the 1205721205730 reference frame 119901119879and 119902 are
instantaneous power signals that have averaged and oscilla-tory components that may be used to calculate a referencecurrent vector for the APF control systemThe average of 119901
119879
119901 corresponds to the energy per time unity that is transferredfrom the supply to the load and becomes the power that thesystem truly uses [8] In this way the ideal condition wouldbe to remove the oscillatory portion of the real power 119901 andthe imaginary power 119902 of power drawn by the load such thatthe calculation of the reference currents for compensatingthe currents drawn by the load may be given with
[[
[
119894120572reflowast
119894120573reflowast
1198940reflowast
]]
]
=1
V2120572120573120579
[[[
[
V120572
0 V120579
minusV120573
V120573
minusV120579
0 V120572
V120579
V120573
minusV120572
0
]]]
]
[[[[[
[
119902120572
lowast
119902120573
lowast
1199020
lowast
]]]]]
]
(5)
which is represented in Figure 1 as the inverse P-Q theoryblock which subtracts 119901 from 119901 to obtain the oscillatorycomponent of 119901 In this fashion the reference currents of(5) are used to operate the three-phase converter of Figure 1as a current amplifier driven by the trapezoidal predictivecurrent controller block shown at the centre of Figure 1
23 DC-Link Voltage Controller The APF requires a fixedDC-link capacitor voltage 119864 greater than the peak value ofthe line-to-line supply voltage for instance 119864 = 400V whena 220V 60Hz supply is being used Since the shunt APFtopology is identical to that of an active three-phase rectifier[14] the circuit boosts the DC-link voltage using an externalvoltage control loop that generates a loss power control signal119901loss which is added to to supply energy for the DC-linkcapacitor and compensate the power losses of theAPF circuitThis is shown in the left bottom side of Figure 1 where a linearcontrol loop calculates 119901loss using the error between the 119864
reference 119864ref and the DC-link voltage 119864 which is obtainedadding the measured DC-link capacitor voltages and com-pensating this error with 119867
119864(119904)
24 DC-Link Capacitor Voltage Balancing Controller Sincethe split DC-link node 119873 is used to draw a compensatingcurrent for the neutral wire of the supply the DC-linkcapacitor voltages may become unbalanced due to the flow ofa small DC current An additional zero-sequence balancingcurrent 119894
0bal is used after the zero-sequence reference currentcalculation to overcome a voltage unbalance between thecapacitors of the split DC link [21] This is shown at the bot-tom of Figure 1 where again a linear control loop calculates1198940bal by compensating the error between the DC-link capaci-tor voltages Vdif with 119867bal(119904)
3 Trapezoidal Predictive Current Controller
31 Discrete Linear Model of the APF Converter A spacevector AC-side model of the APF three-phase converter isderived calculating the filter inductor voltage vector as shownin
997888997888997888rarrV1198711205721205730
= 119871119889997888997888997888rarr1198941198711205721205730
119889119905
=997888997888997888rarrV1199041205721205730
minus997888997888997888rarrV1198881205721205730
(6)
which may be solved to calculate the line current vector 997888rarr119894119871as
shown as follows
997888997888997888rarr1198941198711205721205730
(1199051) =
997888997888997888rarr1198941198711205721205730
(1199051+ 119896119879) + int
1199051+(119896+1)119879
1199051+119896119879
997888997888997888rarrV1198711205721205730
(119905) 119889119905 (7)
A discrete time model of (7) may be obtained by usingthe trapezoidal approximation shown in Figure 2 such that(7) becomes
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
+997888997888997888rarrV1199041205721205730119896+1
minus997888997888997888rarrV1198881205721205730119896+1
]
(8)
4 Mathematical Problems in Engineering
tt
1 + kT t1 + (k + 1)T
997888997888997888997888rarrL1205721205730(t1 + kT)
997888997888997888997888rarrL1205721205730(t1 + (k + 1)T)
997888997888997888997888rarrL1205721205730(t) =997888997888997888rarrs1205721205730(t) minus
997888997888997888rarrc1205721205730(t)
Figure 2 Trapezoidal approximation of the volt-seconds integral of(9)
where119879 is the sampling period thatmust be small to obtain anaccurate model approximation of the system Since 997888997888997888rarrV
1199041205721205730119896asymp
997888997888997888rarrV1199041205721205730119896+1
(8) is rewritten as follows
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[2
997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (9)
which may produce eight one-step ahead current vectors997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 since 997888997888997888rarrV
1198881205721205730119896+1has six active 997888997888997888rarrV
1198881205721205730
1 to997888997888997888rarrV1198881205721205730
6 and two neutral vectors 997888997888997888rarrV1198881205721205730
0 and 997888997888997888rarrV1198881205721205730
7 that arelisted in Table 1 with respect to their transistor switchingstates assuming the common mode voltage due to the ACneutral node connection to the DC link [15] 997888997888997888rarr
1198941198711205721205730
0
119896+1to
997888997888997888rarr1198941198711205721205730
7
119896+1are dispersed around the 119896th current sample 997888997888997888rarr119894
1198711205721205730119896
as shown in 1205721205730 frame of Figure 3 such that one of thesemaybecome near to the reference current sample 997888997888997888rarr
1198941198711205721205730
lowast
119896
32 Cost Function of the Current Controller An error currentvector 997888997888997888997888rarr
1198941198711198901205721205730119896
may be used as a cost function to evaluatewhich of the transistor switching states causes the nearestone-step ahead current sample to997888997888997888rarr
1198941198711205721205730
lowast
119896 such that997888997888997888997888rarr119894
1198711198901205721205730119896may
be expressed as shown as follows [16]
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896=
997888997888997888rarr1198941198711205721205730
lowast
119896minus
997888997888997888rarr1198941198711205721205730
0minus7
119896+1 (10)
The size of (10) may be evaluated using the Euclidean normof 997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 which is equal to
1003817100381710038171003817100381710038171003817
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896
1003817100381710038171003817100381710038171003817
2
=10038161003816100381610038161003816119894lowast
119871120572119896minus 1198940minus7
119871120572 119896+1
10038161003816100381610038161003816
2
+100381610038161003816100381610038161003816119894lowast
119871120573119896minus 1198940minus7
119871120573 119896+1
100381610038161003816100381610038161003816
2
+10038161003816100381610038161003816119894lowast
1198710119896minus 1198940minus7
1198710 119896+1
10038161003816100381610038161003816
2
(11)
such that theminimum 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 determines the transistor
switching state that may be used at the 119896th instant toproduce an appropriate three-phase filter current trackingwith respect to the current reference vector [17]
33 Control Algorithm of the Four-Wire APF Following thedescription given above a flow diagram of the APF controlalgorithmof Figure 1 is shown in Figure 4This diagram startswith the parameters initialization of the microcontroller andthen enters to an iterative loop control cycle In this cycle allthe voltage and currents variables are sensed such as the sup-ply voltage997888rarrV
119904 the filter current997888rarr119894
119871 the load current 119894Load and
the DC-link voltage 119864 where the AC inputs are converted to1205721205730 plane using (1) Since the APF may operate with a dis-torted voltage or high source impedance [22]997888rarrV
119904is processed
with a Phase Locked Loop (PLL) to obtain a clean three-phasesupply and phase referenceThe next process in the algorithmis the calculation of the two external voltage controllers usedto maintain charged and balanced DC-link capacitors at afixed voltage level which contribute to calculate the referencecurrents through the inverse P-Q theory (4) and (5)Once thereference currents are calculated an ldquoelse-ifrdquo tree is startedto process the trapezoidal predictive current controller withthe eight possible transistor state combinations of the APFconverter which uses the discrete current model of (7) andthe cost function of (10) such that eight one-step aheadcurrent values are evaluated and then weighted against thecurrent reference vector using (10) Finally the converter statevector that minimizes the cost function is determined andthereby the algorithm applies the selected state vector to theAPF converter
4 Experimental Verification
41 Prototype Description A 2 kVA four-wire shunt APFprototype rig was built to evaluate the operation of theAPF of Figure 1 Table 2 lists the operating parameters andcomponents of the rig
A 150MHz TMS320F28335 Digital Signal Processor(DSP) was used to implement the control strategy of Figures 1and 4 using a 32-bit data word length for floating point oper-ations ensuring numerical stability Additional hardware wasutilized to interface the DSP with the power converter suchas voltage and current sensors signal conditioners IGBTdrivers and fiber optic links The APF was operated withthe aid of a PLL [22] and driven with either the trapezoidalpredictive controller (9) or a typical predictive controller thatuses the Euler approximation of
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (12)
to experimentally compare the performance
42 Experimental Results The 2 kVA APF prototype wasverified with the Euler and trapezoidal predictive currentcontrollers and a 127V 60Hz line-to-neutral supply voltageand under three nonlinear load conditions a 16 kW naturallycontrolled three-phase rectifier with a 119871119862 filter Figure 5(a)a 09 kW four-wire unbalanced load Figure 5(b) that con-sisted of two naturally controlled single-phase rectifiers bothwith a 119871119862 output filter and each supplied with different singlephases and a resistive load supplied with a single phase and a1 kW unbalanced load condition Figure 5(c) similar to
Mathematical Problems in Engineering 5
Table 1 Normalized converter voltage space vectors with respect to the transistor switching states
Transistor state combination 997888997888997888rarrV1198881205721205730
Normalized converter voltages1198761
1198762
1198763
1198764
1198765
1198766
119881120572E 119881
120573E 119881
0E
0 1 0 1 0 1 997888997888997888rarrV1198881205721205730
0
0 0 minus1
2
1 1 0 0 0 1 997888997888997888rarrV1198881205721205730
1
radic2
30 minus
1
6
1 1 1 0 0 0 997888997888997888rarrV1198881205721205730
2 radic6
6
1
radic2
1
6
0 1 1 1 0 0 997888997888997888rarrV1198881205721205730
3
minusradic6
6
1
radic2minus1
6
0 0 1 1 1 0 997888997888997888rarrV1198881205721205730
4
minusradic2
30
1
6
0 0 0 1 1 1 997888997888997888rarrV1198881205721205730
5
minusradic6
6
minus1
radic2minus1
6
1 0 0 0 1 1 997888997888997888rarrV1198881205721205730
6 radic6
6
minus1
radic2
1
6
1 0 1 0 1 0 997888997888997888rarrV1198881205721205730
7
0 01
2
Table 2 Operating parameters and components of the four-wire APF prototype
Electrical parametersVariable Value
Prototype power rating (laboratory design) 2 kWThree-phase supply 119881
119878119873127V 60Hz
DC-link voltage reference 119864 400VSampling frequency 119891
119878216 kHz
ADC resolution 12 bitsPrototype components
Line filters inductors 119871119891
10mHDC-link capacitors 119862 10mFPower IGBTs BSM100GD60DLC 1200V 30AIGBT drivers Infineon 2ED300CL7-sACDC voltage sensors LEM LV 25-PACDC current sensors Honeywell CSNA111DC-link voltage controller 119867
119864(119904) 3000119904 + 45e4
1199042 + 1000 minus 671e minus 8
DC-link voltage balance controller 119867bal(119904)400119904 + 10
119904
the one used at a power substation of Line B MetropolitanRailway ofMexico City for powering electronic utility equip-ment
Figure 6(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and one supply phase voltage V
119877119873 obtained
with the load condition of Figure 6(a) The experimental linecurrent waveforms were typical of a three-phase 6-pulserectifier without the operation of the APF but when theAPF was turned on using the Euler predictive controller thesupply currents became virtually sinusoidal waveforms withthe supply currents Total Harmonic Distortion (THD) andthe total power factor being improved from 29 to 15 andfrom 095 to 098 respectively which confirmed that the APFwas properly operating Twomain characteristics were foundin the experimental supply current waveforms of Figure 6(a)a 42 kHz high-frequency ripple and a small glitch occurringat every rising and falling slope of the load current waveform
The first was attributed to the Euler approximation used withthe predictive control switching that continuously tracks thereference currents [23] which was confirmed with a dynamiccondition of stepping the output filter inductance from50mH to 100mH Figure 6(b) shows that the operation ofthe APF with the Euler predictive current control and the P-Q theory is maintained throughout the filter inductance stepsince the sinusoidal waveformquality of the supply currents isstable as shown in Figure 6(b) ensuring reliable operation ofthe APF and therefore the predictive controller is likely to becompliant under dynamic conditions a typical requirementfor control techniques however the amplitude of the filtercurrent waveforms slightly fell from 2A to 15 A duringthe transient response with the supply current THD beingbarely degraded around 24 The second characteristic wasconfirmed by contrasting the measured filter current 119894
119871119877
with its digital reference 119894119871119877
lowast as shown in the left-hand side
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
997888997888rarri1205721205730
997888997888rarri1205721205730
N
997888rarris
997888rarriL
997888rarriL
997888997888997888rarriLoad
997888997888997888rarriL1205721205730
997888997888997888rarriL1205721205730
997888997888997888rarrs1205721205730997888997888997888rarrs1205721205730
997888997888997888rarrs1205721205730
997888997888997888rarrs1205721205730 997888rarrs
q120572
q120573
q0
pT
plossminus
minus
minus
minus
HE(s)Eref
400V
i120572lowast
i120573lowast
i0lowast
+
+
+
+
+
+
Hbal(s)
P-Q theory InverseP-Q theory
Predictivecurrent
controller
Clarktransform
PLL and clarktransform
Clarktransform
IGBTdrivers
Unbalancednonlinear load
Active powerfilter
NDCreject
pT
i0bal E
vge1lowast
vge2lowast
vge6lowast
E
vge1
vge2
vge6
E1 E2
C1 C2
Q1 Q4
Q5 Q2
Q3 Q6
D1
D5 D2
D3 D6
D4
vTC
vSC
vRC
Lf
vdiff
sum
sumsum
sum
sum
Figure 1 Four-wire shunt active filter and its corresponding control block diagram
This paper presents the realization and experimentalverification of a trapezoidal predictive current controller fora four-wire shunt APF that improves the power quality ofunbalanced AC loads in contrast to the typical predictiveEuler control strategy The trapezoidal strategy relies itsoperation on a discrete trapezoidal linear approximation thatmore accurately determines the switching of the active filterfor the one-step ahead current sample such that three signifi-cant advantages are potentially exhibited first the trapezoidalpredictive controller slightly increments the processing timewithout affecting the switching of the power convertersecond in contrast to the typical Euler approximation usedin other works [6 7 13ndash20] the trapezoidalmethod generateslower AC current ripple and third the convergence time andload operating performance are wider than those obtainedusing the typical predictive control strategy which improvesthe reference current tracking and therefore the powerquality Experimental results obtainedwith a 2 kVAprototypeare presented demonstrating that the trapezoidal predictivecontrol may accurately compensate the currents drawn byan unbalanced nonlinear load under static and dynamicconditions
2 Four-Wire Shunt Active Filter
21 Circuit Description The four-wire shunt APF is con-nected in parallel to the unbalanced nonlinear load as shownat the right-hand side of Figure 1 which consists of a splitDC link formed by 119862
1and 119862
2which refer to the AC supply
neutral node119873 to provide a path tomitigate a commonmodecurrent a typical three-phase current-feed active converterformed by transistors 119876
1to 1198766and diodes 119863
1ndash1198636 and three
line filter inductors 119871119891used to generate the filter current
vector 997888rarr119894119871
= [119894119871119877 119894119871119878
119894119871119879]119879 by the difference between the
supply and converter voltage vectors 997888rarrV119904= [V119877119873 V
119878119873V119879119873]119879
and 997888rarrV119862
= [V119877119862119873 V119878119862119873
V119879119862119873]119879 thereby obtaining virtual
sinusoidal supply currents 997888rarr119894119904= [119894119878119877 119894
119878119878119894119878119879]119879
22 Principle of Operation of the Active Filter The principleof operation of the APF of Figure 1 may be described usingthe control block diagram presented at the left-hand side ofFigure 1 An instantaneous active and reactive power theoryP-Q theory block in Figure 1 [12] is used to obtain an effectivecalculation of the reference currents that the APF may injectto the supply to instantaneously mitigate the reactive anddistorted power components drawn by the nonlinear loadand balance the active power per phase The P-Q theory usesthe Clarke transformation of the supply voltage and loadcurrent as shown in
V120572120573120579
=[[[
[
V0
V120572
V120573
]]]
]
= radic2
3
[[[[[[[[
[
1
radic2
1
radic2
1
radic2
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]]]]]]
]
[[
[
V119877119873
V119878119873
V119879119873
]]
]
Mathematical Problems in Engineering 3
119894120572120573120579
=[[[
[
1198940
119894120572
119894120573
]]]
]
= radic2
3
[[[[[[[[
[
1
radic2
1
radic2
1
radic2
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]]]]]]
]
[[
[
119894Load119877
119894Load119878
119894Load119879
]]
]
(1)
such that the calculation of the active and reactive instanta-neous powers in the 1205721205730 coordinate system is obtained asrespectively shown in
119901119879
=997888997888rarrV1205721205730
sdot997888997888rarr1198941205721205730
= V120572119894120572+ V120573119894120573+ V01198940 (2)
119902 =997888997888rarrV1205721205730
times997888997888rarr1198941205721205730
=[[
[
119902120572
119902120573
119902120579
]]
]
=
[[[[[[[[[[[
[
[
V120573
V0
119894120573
1198940
]
[V120579
V120572
1198940
119894120572
]
[
V120572
V120573
119894120572
119894120573
]
]]]]]]]]]]]
]
(3)
where 119901119879is the real power or internal product of the voltage
and current vectors and 119902 is the imaginary vector power orexternal product of the voltage and current vectors whichis composed of 119902
120572 119902120573 and 119902
0 Since the load uses a fourth
conductor namely the neutral which is very common in low-voltage distribution system the P-Q calculation may includeboth zero-sequence voltage and current as shown in (2) and(3) Therefore the instantaneous powers defined above maybe combined in a single matrix transformation as shown asfollows
[[[[[
[
119901119879
119902120572
119902120573
1199020
]]]]]
]
=
[[[[[
[
V120572
V120573
V0
0 minusV0
V120573
V0
0 minusV120572
minusV120573
V120572
0
]]]]]
]
[[
[
119894120572
119894120573
1198940
]]
]
(4)
which is defined on the 1205721205730 reference frame 119901119879and 119902 are
instantaneous power signals that have averaged and oscilla-tory components that may be used to calculate a referencecurrent vector for the APF control systemThe average of 119901
119879
119901 corresponds to the energy per time unity that is transferredfrom the supply to the load and becomes the power that thesystem truly uses [8] In this way the ideal condition wouldbe to remove the oscillatory portion of the real power 119901 andthe imaginary power 119902 of power drawn by the load such thatthe calculation of the reference currents for compensatingthe currents drawn by the load may be given with
[[
[
119894120572reflowast
119894120573reflowast
1198940reflowast
]]
]
=1
V2120572120573120579
[[[
[
V120572
0 V120579
minusV120573
V120573
minusV120579
0 V120572
V120579
V120573
minusV120572
0
]]]
]
[[[[[
[
119902120572
lowast
119902120573
lowast
1199020
lowast
]]]]]
]
(5)
which is represented in Figure 1 as the inverse P-Q theoryblock which subtracts 119901 from 119901 to obtain the oscillatorycomponent of 119901 In this fashion the reference currents of(5) are used to operate the three-phase converter of Figure 1as a current amplifier driven by the trapezoidal predictivecurrent controller block shown at the centre of Figure 1
23 DC-Link Voltage Controller The APF requires a fixedDC-link capacitor voltage 119864 greater than the peak value ofthe line-to-line supply voltage for instance 119864 = 400V whena 220V 60Hz supply is being used Since the shunt APFtopology is identical to that of an active three-phase rectifier[14] the circuit boosts the DC-link voltage using an externalvoltage control loop that generates a loss power control signal119901loss which is added to to supply energy for the DC-linkcapacitor and compensate the power losses of theAPF circuitThis is shown in the left bottom side of Figure 1 where a linearcontrol loop calculates 119901loss using the error between the 119864
reference 119864ref and the DC-link voltage 119864 which is obtainedadding the measured DC-link capacitor voltages and com-pensating this error with 119867
119864(119904)
24 DC-Link Capacitor Voltage Balancing Controller Sincethe split DC-link node 119873 is used to draw a compensatingcurrent for the neutral wire of the supply the DC-linkcapacitor voltages may become unbalanced due to the flow ofa small DC current An additional zero-sequence balancingcurrent 119894
0bal is used after the zero-sequence reference currentcalculation to overcome a voltage unbalance between thecapacitors of the split DC link [21] This is shown at the bot-tom of Figure 1 where again a linear control loop calculates1198940bal by compensating the error between the DC-link capaci-tor voltages Vdif with 119867bal(119904)
3 Trapezoidal Predictive Current Controller
31 Discrete Linear Model of the APF Converter A spacevector AC-side model of the APF three-phase converter isderived calculating the filter inductor voltage vector as shownin
997888997888997888rarrV1198711205721205730
= 119871119889997888997888997888rarr1198941198711205721205730
119889119905
=997888997888997888rarrV1199041205721205730
minus997888997888997888rarrV1198881205721205730
(6)
which may be solved to calculate the line current vector 997888rarr119894119871as
shown as follows
997888997888997888rarr1198941198711205721205730
(1199051) =
997888997888997888rarr1198941198711205721205730
(1199051+ 119896119879) + int
1199051+(119896+1)119879
1199051+119896119879
997888997888997888rarrV1198711205721205730
(119905) 119889119905 (7)
A discrete time model of (7) may be obtained by usingthe trapezoidal approximation shown in Figure 2 such that(7) becomes
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
+997888997888997888rarrV1199041205721205730119896+1
minus997888997888997888rarrV1198881205721205730119896+1
]
(8)
4 Mathematical Problems in Engineering
tt
1 + kT t1 + (k + 1)T
997888997888997888997888rarrL1205721205730(t1 + kT)
997888997888997888997888rarrL1205721205730(t1 + (k + 1)T)
997888997888997888997888rarrL1205721205730(t) =997888997888997888rarrs1205721205730(t) minus
997888997888997888rarrc1205721205730(t)
Figure 2 Trapezoidal approximation of the volt-seconds integral of(9)
where119879 is the sampling period thatmust be small to obtain anaccurate model approximation of the system Since 997888997888997888rarrV
1199041205721205730119896asymp
997888997888997888rarrV1199041205721205730119896+1
(8) is rewritten as follows
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[2
997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (9)
which may produce eight one-step ahead current vectors997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 since 997888997888997888rarrV
1198881205721205730119896+1has six active 997888997888997888rarrV
1198881205721205730
1 to997888997888997888rarrV1198881205721205730
6 and two neutral vectors 997888997888997888rarrV1198881205721205730
0 and 997888997888997888rarrV1198881205721205730
7 that arelisted in Table 1 with respect to their transistor switchingstates assuming the common mode voltage due to the ACneutral node connection to the DC link [15] 997888997888997888rarr
1198941198711205721205730
0
119896+1to
997888997888997888rarr1198941198711205721205730
7
119896+1are dispersed around the 119896th current sample 997888997888997888rarr119894
1198711205721205730119896
as shown in 1205721205730 frame of Figure 3 such that one of thesemaybecome near to the reference current sample 997888997888997888rarr
1198941198711205721205730
lowast
119896
32 Cost Function of the Current Controller An error currentvector 997888997888997888997888rarr
1198941198711198901205721205730119896
may be used as a cost function to evaluatewhich of the transistor switching states causes the nearestone-step ahead current sample to997888997888997888rarr
1198941198711205721205730
lowast
119896 such that997888997888997888997888rarr119894
1198711198901205721205730119896may
be expressed as shown as follows [16]
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896=
997888997888997888rarr1198941198711205721205730
lowast
119896minus
997888997888997888rarr1198941198711205721205730
0minus7
119896+1 (10)
The size of (10) may be evaluated using the Euclidean normof 997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 which is equal to
1003817100381710038171003817100381710038171003817
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896
1003817100381710038171003817100381710038171003817
2
=10038161003816100381610038161003816119894lowast
119871120572119896minus 1198940minus7
119871120572 119896+1
10038161003816100381610038161003816
2
+100381610038161003816100381610038161003816119894lowast
119871120573119896minus 1198940minus7
119871120573 119896+1
100381610038161003816100381610038161003816
2
+10038161003816100381610038161003816119894lowast
1198710119896minus 1198940minus7
1198710 119896+1
10038161003816100381610038161003816
2
(11)
such that theminimum 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 determines the transistor
switching state that may be used at the 119896th instant toproduce an appropriate three-phase filter current trackingwith respect to the current reference vector [17]
33 Control Algorithm of the Four-Wire APF Following thedescription given above a flow diagram of the APF controlalgorithmof Figure 1 is shown in Figure 4This diagram startswith the parameters initialization of the microcontroller andthen enters to an iterative loop control cycle In this cycle allthe voltage and currents variables are sensed such as the sup-ply voltage997888rarrV
119904 the filter current997888rarr119894
119871 the load current 119894Load and
the DC-link voltage 119864 where the AC inputs are converted to1205721205730 plane using (1) Since the APF may operate with a dis-torted voltage or high source impedance [22]997888rarrV
119904is processed
with a Phase Locked Loop (PLL) to obtain a clean three-phasesupply and phase referenceThe next process in the algorithmis the calculation of the two external voltage controllers usedto maintain charged and balanced DC-link capacitors at afixed voltage level which contribute to calculate the referencecurrents through the inverse P-Q theory (4) and (5)Once thereference currents are calculated an ldquoelse-ifrdquo tree is startedto process the trapezoidal predictive current controller withthe eight possible transistor state combinations of the APFconverter which uses the discrete current model of (7) andthe cost function of (10) such that eight one-step aheadcurrent values are evaluated and then weighted against thecurrent reference vector using (10) Finally the converter statevector that minimizes the cost function is determined andthereby the algorithm applies the selected state vector to theAPF converter
4 Experimental Verification
41 Prototype Description A 2 kVA four-wire shunt APFprototype rig was built to evaluate the operation of theAPF of Figure 1 Table 2 lists the operating parameters andcomponents of the rig
A 150MHz TMS320F28335 Digital Signal Processor(DSP) was used to implement the control strategy of Figures 1and 4 using a 32-bit data word length for floating point oper-ations ensuring numerical stability Additional hardware wasutilized to interface the DSP with the power converter suchas voltage and current sensors signal conditioners IGBTdrivers and fiber optic links The APF was operated withthe aid of a PLL [22] and driven with either the trapezoidalpredictive controller (9) or a typical predictive controller thatuses the Euler approximation of
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (12)
to experimentally compare the performance
42 Experimental Results The 2 kVA APF prototype wasverified with the Euler and trapezoidal predictive currentcontrollers and a 127V 60Hz line-to-neutral supply voltageand under three nonlinear load conditions a 16 kW naturallycontrolled three-phase rectifier with a 119871119862 filter Figure 5(a)a 09 kW four-wire unbalanced load Figure 5(b) that con-sisted of two naturally controlled single-phase rectifiers bothwith a 119871119862 output filter and each supplied with different singlephases and a resistive load supplied with a single phase and a1 kW unbalanced load condition Figure 5(c) similar to
Mathematical Problems in Engineering 5
Table 1 Normalized converter voltage space vectors with respect to the transistor switching states
Transistor state combination 997888997888997888rarrV1198881205721205730
Normalized converter voltages1198761
1198762
1198763
1198764
1198765
1198766
119881120572E 119881
120573E 119881
0E
0 1 0 1 0 1 997888997888997888rarrV1198881205721205730
0
0 0 minus1
2
1 1 0 0 0 1 997888997888997888rarrV1198881205721205730
1
radic2
30 minus
1
6
1 1 1 0 0 0 997888997888997888rarrV1198881205721205730
2 radic6
6
1
radic2
1
6
0 1 1 1 0 0 997888997888997888rarrV1198881205721205730
3
minusradic6
6
1
radic2minus1
6
0 0 1 1 1 0 997888997888997888rarrV1198881205721205730
4
minusradic2
30
1
6
0 0 0 1 1 1 997888997888997888rarrV1198881205721205730
5
minusradic6
6
minus1
radic2minus1
6
1 0 0 0 1 1 997888997888997888rarrV1198881205721205730
6 radic6
6
minus1
radic2
1
6
1 0 1 0 1 0 997888997888997888rarrV1198881205721205730
7
0 01
2
Table 2 Operating parameters and components of the four-wire APF prototype
Electrical parametersVariable Value
Prototype power rating (laboratory design) 2 kWThree-phase supply 119881
119878119873127V 60Hz
DC-link voltage reference 119864 400VSampling frequency 119891
119878216 kHz
ADC resolution 12 bitsPrototype components
Line filters inductors 119871119891
10mHDC-link capacitors 119862 10mFPower IGBTs BSM100GD60DLC 1200V 30AIGBT drivers Infineon 2ED300CL7-sACDC voltage sensors LEM LV 25-PACDC current sensors Honeywell CSNA111DC-link voltage controller 119867
119864(119904) 3000119904 + 45e4
1199042 + 1000 minus 671e minus 8
DC-link voltage balance controller 119867bal(119904)400119904 + 10
119904
the one used at a power substation of Line B MetropolitanRailway ofMexico City for powering electronic utility equip-ment
Figure 6(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and one supply phase voltage V
119877119873 obtained
with the load condition of Figure 6(a) The experimental linecurrent waveforms were typical of a three-phase 6-pulserectifier without the operation of the APF but when theAPF was turned on using the Euler predictive controller thesupply currents became virtually sinusoidal waveforms withthe supply currents Total Harmonic Distortion (THD) andthe total power factor being improved from 29 to 15 andfrom 095 to 098 respectively which confirmed that the APFwas properly operating Twomain characteristics were foundin the experimental supply current waveforms of Figure 6(a)a 42 kHz high-frequency ripple and a small glitch occurringat every rising and falling slope of the load current waveform
The first was attributed to the Euler approximation used withthe predictive control switching that continuously tracks thereference currents [23] which was confirmed with a dynamiccondition of stepping the output filter inductance from50mH to 100mH Figure 6(b) shows that the operation ofthe APF with the Euler predictive current control and the P-Q theory is maintained throughout the filter inductance stepsince the sinusoidal waveformquality of the supply currents isstable as shown in Figure 6(b) ensuring reliable operation ofthe APF and therefore the predictive controller is likely to becompliant under dynamic conditions a typical requirementfor control techniques however the amplitude of the filtercurrent waveforms slightly fell from 2A to 15 A duringthe transient response with the supply current THD beingbarely degraded around 24 The second characteristic wasconfirmed by contrasting the measured filter current 119894
119871119877
with its digital reference 119894119871119877
lowast as shown in the left-hand side
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
119894120572120573120579
=[[[
[
1198940
119894120572
119894120573
]]]
]
= radic2
3
[[[[[[[[
[
1
radic2
1
radic2
1
radic2
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]]]]]]
]
[[
[
119894Load119877
119894Load119878
119894Load119879
]]
]
(1)
such that the calculation of the active and reactive instanta-neous powers in the 1205721205730 coordinate system is obtained asrespectively shown in
119901119879
=997888997888rarrV1205721205730
sdot997888997888rarr1198941205721205730
= V120572119894120572+ V120573119894120573+ V01198940 (2)
119902 =997888997888rarrV1205721205730
times997888997888rarr1198941205721205730
=[[
[
119902120572
119902120573
119902120579
]]
]
=
[[[[[[[[[[[
[
[
V120573
V0
119894120573
1198940
]
[V120579
V120572
1198940
119894120572
]
[
V120572
V120573
119894120572
119894120573
]
]]]]]]]]]]]
]
(3)
where 119901119879is the real power or internal product of the voltage
and current vectors and 119902 is the imaginary vector power orexternal product of the voltage and current vectors whichis composed of 119902
120572 119902120573 and 119902
0 Since the load uses a fourth
conductor namely the neutral which is very common in low-voltage distribution system the P-Q calculation may includeboth zero-sequence voltage and current as shown in (2) and(3) Therefore the instantaneous powers defined above maybe combined in a single matrix transformation as shown asfollows
[[[[[
[
119901119879
119902120572
119902120573
1199020
]]]]]
]
=
[[[[[
[
V120572
V120573
V0
0 minusV0
V120573
V0
0 minusV120572
minusV120573
V120572
0
]]]]]
]
[[
[
119894120572
119894120573
1198940
]]
]
(4)
which is defined on the 1205721205730 reference frame 119901119879and 119902 are
instantaneous power signals that have averaged and oscilla-tory components that may be used to calculate a referencecurrent vector for the APF control systemThe average of 119901
119879
119901 corresponds to the energy per time unity that is transferredfrom the supply to the load and becomes the power that thesystem truly uses [8] In this way the ideal condition wouldbe to remove the oscillatory portion of the real power 119901 andthe imaginary power 119902 of power drawn by the load such thatthe calculation of the reference currents for compensatingthe currents drawn by the load may be given with
[[
[
119894120572reflowast
119894120573reflowast
1198940reflowast
]]
]
=1
V2120572120573120579
[[[
[
V120572
0 V120579
minusV120573
V120573
minusV120579
0 V120572
V120579
V120573
minusV120572
0
]]]
]
[[[[[
[
119902120572
lowast
119902120573
lowast
1199020
lowast
]]]]]
]
(5)
which is represented in Figure 1 as the inverse P-Q theoryblock which subtracts 119901 from 119901 to obtain the oscillatorycomponent of 119901 In this fashion the reference currents of(5) are used to operate the three-phase converter of Figure 1as a current amplifier driven by the trapezoidal predictivecurrent controller block shown at the centre of Figure 1
23 DC-Link Voltage Controller The APF requires a fixedDC-link capacitor voltage 119864 greater than the peak value ofthe line-to-line supply voltage for instance 119864 = 400V whena 220V 60Hz supply is being used Since the shunt APFtopology is identical to that of an active three-phase rectifier[14] the circuit boosts the DC-link voltage using an externalvoltage control loop that generates a loss power control signal119901loss which is added to to supply energy for the DC-linkcapacitor and compensate the power losses of theAPF circuitThis is shown in the left bottom side of Figure 1 where a linearcontrol loop calculates 119901loss using the error between the 119864
reference 119864ref and the DC-link voltage 119864 which is obtainedadding the measured DC-link capacitor voltages and com-pensating this error with 119867
119864(119904)
24 DC-Link Capacitor Voltage Balancing Controller Sincethe split DC-link node 119873 is used to draw a compensatingcurrent for the neutral wire of the supply the DC-linkcapacitor voltages may become unbalanced due to the flow ofa small DC current An additional zero-sequence balancingcurrent 119894
0bal is used after the zero-sequence reference currentcalculation to overcome a voltage unbalance between thecapacitors of the split DC link [21] This is shown at the bot-tom of Figure 1 where again a linear control loop calculates1198940bal by compensating the error between the DC-link capaci-tor voltages Vdif with 119867bal(119904)
3 Trapezoidal Predictive Current Controller
31 Discrete Linear Model of the APF Converter A spacevector AC-side model of the APF three-phase converter isderived calculating the filter inductor voltage vector as shownin
997888997888997888rarrV1198711205721205730
= 119871119889997888997888997888rarr1198941198711205721205730
119889119905
=997888997888997888rarrV1199041205721205730
minus997888997888997888rarrV1198881205721205730
(6)
which may be solved to calculate the line current vector 997888rarr119894119871as
shown as follows
997888997888997888rarr1198941198711205721205730
(1199051) =
997888997888997888rarr1198941198711205721205730
(1199051+ 119896119879) + int
1199051+(119896+1)119879
1199051+119896119879
997888997888997888rarrV1198711205721205730
(119905) 119889119905 (7)
A discrete time model of (7) may be obtained by usingthe trapezoidal approximation shown in Figure 2 such that(7) becomes
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
+997888997888997888rarrV1199041205721205730119896+1
minus997888997888997888rarrV1198881205721205730119896+1
]
(8)
4 Mathematical Problems in Engineering
tt
1 + kT t1 + (k + 1)T
997888997888997888997888rarrL1205721205730(t1 + kT)
997888997888997888997888rarrL1205721205730(t1 + (k + 1)T)
997888997888997888997888rarrL1205721205730(t) =997888997888997888rarrs1205721205730(t) minus
997888997888997888rarrc1205721205730(t)
Figure 2 Trapezoidal approximation of the volt-seconds integral of(9)
where119879 is the sampling period thatmust be small to obtain anaccurate model approximation of the system Since 997888997888997888rarrV
1199041205721205730119896asymp
997888997888997888rarrV1199041205721205730119896+1
(8) is rewritten as follows
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[2
997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (9)
which may produce eight one-step ahead current vectors997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 since 997888997888997888rarrV
1198881205721205730119896+1has six active 997888997888997888rarrV
1198881205721205730
1 to997888997888997888rarrV1198881205721205730
6 and two neutral vectors 997888997888997888rarrV1198881205721205730
0 and 997888997888997888rarrV1198881205721205730
7 that arelisted in Table 1 with respect to their transistor switchingstates assuming the common mode voltage due to the ACneutral node connection to the DC link [15] 997888997888997888rarr
1198941198711205721205730
0
119896+1to
997888997888997888rarr1198941198711205721205730
7
119896+1are dispersed around the 119896th current sample 997888997888997888rarr119894
1198711205721205730119896
as shown in 1205721205730 frame of Figure 3 such that one of thesemaybecome near to the reference current sample 997888997888997888rarr
1198941198711205721205730
lowast
119896
32 Cost Function of the Current Controller An error currentvector 997888997888997888997888rarr
1198941198711198901205721205730119896
may be used as a cost function to evaluatewhich of the transistor switching states causes the nearestone-step ahead current sample to997888997888997888rarr
1198941198711205721205730
lowast
119896 such that997888997888997888997888rarr119894
1198711198901205721205730119896may
be expressed as shown as follows [16]
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896=
997888997888997888rarr1198941198711205721205730
lowast
119896minus
997888997888997888rarr1198941198711205721205730
0minus7
119896+1 (10)
The size of (10) may be evaluated using the Euclidean normof 997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 which is equal to
1003817100381710038171003817100381710038171003817
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896
1003817100381710038171003817100381710038171003817
2
=10038161003816100381610038161003816119894lowast
119871120572119896minus 1198940minus7
119871120572 119896+1
10038161003816100381610038161003816
2
+100381610038161003816100381610038161003816119894lowast
119871120573119896minus 1198940minus7
119871120573 119896+1
100381610038161003816100381610038161003816
2
+10038161003816100381610038161003816119894lowast
1198710119896minus 1198940minus7
1198710 119896+1
10038161003816100381610038161003816
2
(11)
such that theminimum 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 determines the transistor
switching state that may be used at the 119896th instant toproduce an appropriate three-phase filter current trackingwith respect to the current reference vector [17]
33 Control Algorithm of the Four-Wire APF Following thedescription given above a flow diagram of the APF controlalgorithmof Figure 1 is shown in Figure 4This diagram startswith the parameters initialization of the microcontroller andthen enters to an iterative loop control cycle In this cycle allthe voltage and currents variables are sensed such as the sup-ply voltage997888rarrV
119904 the filter current997888rarr119894
119871 the load current 119894Load and
the DC-link voltage 119864 where the AC inputs are converted to1205721205730 plane using (1) Since the APF may operate with a dis-torted voltage or high source impedance [22]997888rarrV
119904is processed
with a Phase Locked Loop (PLL) to obtain a clean three-phasesupply and phase referenceThe next process in the algorithmis the calculation of the two external voltage controllers usedto maintain charged and balanced DC-link capacitors at afixed voltage level which contribute to calculate the referencecurrents through the inverse P-Q theory (4) and (5)Once thereference currents are calculated an ldquoelse-ifrdquo tree is startedto process the trapezoidal predictive current controller withthe eight possible transistor state combinations of the APFconverter which uses the discrete current model of (7) andthe cost function of (10) such that eight one-step aheadcurrent values are evaluated and then weighted against thecurrent reference vector using (10) Finally the converter statevector that minimizes the cost function is determined andthereby the algorithm applies the selected state vector to theAPF converter
4 Experimental Verification
41 Prototype Description A 2 kVA four-wire shunt APFprototype rig was built to evaluate the operation of theAPF of Figure 1 Table 2 lists the operating parameters andcomponents of the rig
A 150MHz TMS320F28335 Digital Signal Processor(DSP) was used to implement the control strategy of Figures 1and 4 using a 32-bit data word length for floating point oper-ations ensuring numerical stability Additional hardware wasutilized to interface the DSP with the power converter suchas voltage and current sensors signal conditioners IGBTdrivers and fiber optic links The APF was operated withthe aid of a PLL [22] and driven with either the trapezoidalpredictive controller (9) or a typical predictive controller thatuses the Euler approximation of
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (12)
to experimentally compare the performance
42 Experimental Results The 2 kVA APF prototype wasverified with the Euler and trapezoidal predictive currentcontrollers and a 127V 60Hz line-to-neutral supply voltageand under three nonlinear load conditions a 16 kW naturallycontrolled three-phase rectifier with a 119871119862 filter Figure 5(a)a 09 kW four-wire unbalanced load Figure 5(b) that con-sisted of two naturally controlled single-phase rectifiers bothwith a 119871119862 output filter and each supplied with different singlephases and a resistive load supplied with a single phase and a1 kW unbalanced load condition Figure 5(c) similar to
Mathematical Problems in Engineering 5
Table 1 Normalized converter voltage space vectors with respect to the transistor switching states
Transistor state combination 997888997888997888rarrV1198881205721205730
Normalized converter voltages1198761
1198762
1198763
1198764
1198765
1198766
119881120572E 119881
120573E 119881
0E
0 1 0 1 0 1 997888997888997888rarrV1198881205721205730
0
0 0 minus1
2
1 1 0 0 0 1 997888997888997888rarrV1198881205721205730
1
radic2
30 minus
1
6
1 1 1 0 0 0 997888997888997888rarrV1198881205721205730
2 radic6
6
1
radic2
1
6
0 1 1 1 0 0 997888997888997888rarrV1198881205721205730
3
minusradic6
6
1
radic2minus1
6
0 0 1 1 1 0 997888997888997888rarrV1198881205721205730
4
minusradic2
30
1
6
0 0 0 1 1 1 997888997888997888rarrV1198881205721205730
5
minusradic6
6
minus1
radic2minus1
6
1 0 0 0 1 1 997888997888997888rarrV1198881205721205730
6 radic6
6
minus1
radic2
1
6
1 0 1 0 1 0 997888997888997888rarrV1198881205721205730
7
0 01
2
Table 2 Operating parameters and components of the four-wire APF prototype
Electrical parametersVariable Value
Prototype power rating (laboratory design) 2 kWThree-phase supply 119881
119878119873127V 60Hz
DC-link voltage reference 119864 400VSampling frequency 119891
119878216 kHz
ADC resolution 12 bitsPrototype components
Line filters inductors 119871119891
10mHDC-link capacitors 119862 10mFPower IGBTs BSM100GD60DLC 1200V 30AIGBT drivers Infineon 2ED300CL7-sACDC voltage sensors LEM LV 25-PACDC current sensors Honeywell CSNA111DC-link voltage controller 119867
119864(119904) 3000119904 + 45e4
1199042 + 1000 minus 671e minus 8
DC-link voltage balance controller 119867bal(119904)400119904 + 10
119904
the one used at a power substation of Line B MetropolitanRailway ofMexico City for powering electronic utility equip-ment
Figure 6(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and one supply phase voltage V
119877119873 obtained
with the load condition of Figure 6(a) The experimental linecurrent waveforms were typical of a three-phase 6-pulserectifier without the operation of the APF but when theAPF was turned on using the Euler predictive controller thesupply currents became virtually sinusoidal waveforms withthe supply currents Total Harmonic Distortion (THD) andthe total power factor being improved from 29 to 15 andfrom 095 to 098 respectively which confirmed that the APFwas properly operating Twomain characteristics were foundin the experimental supply current waveforms of Figure 6(a)a 42 kHz high-frequency ripple and a small glitch occurringat every rising and falling slope of the load current waveform
The first was attributed to the Euler approximation used withthe predictive control switching that continuously tracks thereference currents [23] which was confirmed with a dynamiccondition of stepping the output filter inductance from50mH to 100mH Figure 6(b) shows that the operation ofthe APF with the Euler predictive current control and the P-Q theory is maintained throughout the filter inductance stepsince the sinusoidal waveformquality of the supply currents isstable as shown in Figure 6(b) ensuring reliable operation ofthe APF and therefore the predictive controller is likely to becompliant under dynamic conditions a typical requirementfor control techniques however the amplitude of the filtercurrent waveforms slightly fell from 2A to 15 A duringthe transient response with the supply current THD beingbarely degraded around 24 The second characteristic wasconfirmed by contrasting the measured filter current 119894
119871119877
with its digital reference 119894119871119877
lowast as shown in the left-hand side
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
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MathematicsJournal of
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Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
tt
1 + kT t1 + (k + 1)T
997888997888997888997888rarrL1205721205730(t1 + kT)
997888997888997888997888rarrL1205721205730(t1 + (k + 1)T)
997888997888997888997888rarrL1205721205730(t) =997888997888997888rarrs1205721205730(t) minus
997888997888997888rarrc1205721205730(t)
Figure 2 Trapezoidal approximation of the volt-seconds integral of(9)
where119879 is the sampling period thatmust be small to obtain anaccurate model approximation of the system Since 997888997888997888rarrV
1199041205721205730119896asymp
997888997888997888rarrV1199041205721205730119896+1
(8) is rewritten as follows
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
2119871[2
997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (9)
which may produce eight one-step ahead current vectors997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 since 997888997888997888rarrV
1198881205721205730119896+1has six active 997888997888997888rarrV
1198881205721205730
1 to997888997888997888rarrV1198881205721205730
6 and two neutral vectors 997888997888997888rarrV1198881205721205730
0 and 997888997888997888rarrV1198881205721205730
7 that arelisted in Table 1 with respect to their transistor switchingstates assuming the common mode voltage due to the ACneutral node connection to the DC link [15] 997888997888997888rarr
1198941198711205721205730
0
119896+1to
997888997888997888rarr1198941198711205721205730
7
119896+1are dispersed around the 119896th current sample 997888997888997888rarr119894
1198711205721205730119896
as shown in 1205721205730 frame of Figure 3 such that one of thesemaybecome near to the reference current sample 997888997888997888rarr
1198941198711205721205730
lowast
119896
32 Cost Function of the Current Controller An error currentvector 997888997888997888997888rarr
1198941198711198901205721205730119896
may be used as a cost function to evaluatewhich of the transistor switching states causes the nearestone-step ahead current sample to997888997888997888rarr
1198941198711205721205730
lowast
119896 such that997888997888997888997888rarr119894
1198711198901205721205730119896may
be expressed as shown as follows [16]
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896=
997888997888997888rarr1198941198711205721205730
lowast
119896minus
997888997888997888rarr1198941198711205721205730
0minus7
119896+1 (10)
The size of (10) may be evaluated using the Euclidean normof 997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 which is equal to
1003817100381710038171003817100381710038171003817
997888997888997888997888rarr1198941198711198901205721205730
0minus7
119896
1003817100381710038171003817100381710038171003817
2
=10038161003816100381610038161003816119894lowast
119871120572119896minus 1198940minus7
119871120572 119896+1
10038161003816100381610038161003816
2
+100381610038161003816100381610038161003816119894lowast
119871120573119896minus 1198940minus7
119871120573 119896+1
100381610038161003816100381610038161003816
2
+10038161003816100381610038161003816119894lowast
1198710119896minus 1198940minus7
1198710 119896+1
10038161003816100381610038161003816
2
(11)
such that theminimum 997888997888997888997888rarr1198941198711198901205721205730
0minus7
1198962 determines the transistor
switching state that may be used at the 119896th instant toproduce an appropriate three-phase filter current trackingwith respect to the current reference vector [17]
33 Control Algorithm of the Four-Wire APF Following thedescription given above a flow diagram of the APF controlalgorithmof Figure 1 is shown in Figure 4This diagram startswith the parameters initialization of the microcontroller andthen enters to an iterative loop control cycle In this cycle allthe voltage and currents variables are sensed such as the sup-ply voltage997888rarrV
119904 the filter current997888rarr119894
119871 the load current 119894Load and
the DC-link voltage 119864 where the AC inputs are converted to1205721205730 plane using (1) Since the APF may operate with a dis-torted voltage or high source impedance [22]997888rarrV
119904is processed
with a Phase Locked Loop (PLL) to obtain a clean three-phasesupply and phase referenceThe next process in the algorithmis the calculation of the two external voltage controllers usedto maintain charged and balanced DC-link capacitors at afixed voltage level which contribute to calculate the referencecurrents through the inverse P-Q theory (4) and (5)Once thereference currents are calculated an ldquoelse-ifrdquo tree is startedto process the trapezoidal predictive current controller withthe eight possible transistor state combinations of the APFconverter which uses the discrete current model of (7) andthe cost function of (10) such that eight one-step aheadcurrent values are evaluated and then weighted against thecurrent reference vector using (10) Finally the converter statevector that minimizes the cost function is determined andthereby the algorithm applies the selected state vector to theAPF converter
4 Experimental Verification
41 Prototype Description A 2 kVA four-wire shunt APFprototype rig was built to evaluate the operation of theAPF of Figure 1 Table 2 lists the operating parameters andcomponents of the rig
A 150MHz TMS320F28335 Digital Signal Processor(DSP) was used to implement the control strategy of Figures 1and 4 using a 32-bit data word length for floating point oper-ations ensuring numerical stability Additional hardware wasutilized to interface the DSP with the power converter suchas voltage and current sensors signal conditioners IGBTdrivers and fiber optic links The APF was operated withthe aid of a PLL [22] and driven with either the trapezoidalpredictive controller (9) or a typical predictive controller thatuses the Euler approximation of
997888997888997888rarr1198941198711205721205730119896+1
cong997888997888997888rarr1198941198711205721205730119896
+119879119904
119871[997888997888997888rarrV1199041205721205730119896
minus997888997888997888rarrV1198881205721205730119896+1
] (12)
to experimentally compare the performance
42 Experimental Results The 2 kVA APF prototype wasverified with the Euler and trapezoidal predictive currentcontrollers and a 127V 60Hz line-to-neutral supply voltageand under three nonlinear load conditions a 16 kW naturallycontrolled three-phase rectifier with a 119871119862 filter Figure 5(a)a 09 kW four-wire unbalanced load Figure 5(b) that con-sisted of two naturally controlled single-phase rectifiers bothwith a 119871119862 output filter and each supplied with different singlephases and a resistive load supplied with a single phase and a1 kW unbalanced load condition Figure 5(c) similar to
Mathematical Problems in Engineering 5
Table 1 Normalized converter voltage space vectors with respect to the transistor switching states
Transistor state combination 997888997888997888rarrV1198881205721205730
Normalized converter voltages1198761
1198762
1198763
1198764
1198765
1198766
119881120572E 119881
120573E 119881
0E
0 1 0 1 0 1 997888997888997888rarrV1198881205721205730
0
0 0 minus1
2
1 1 0 0 0 1 997888997888997888rarrV1198881205721205730
1
radic2
30 minus
1
6
1 1 1 0 0 0 997888997888997888rarrV1198881205721205730
2 radic6
6
1
radic2
1
6
0 1 1 1 0 0 997888997888997888rarrV1198881205721205730
3
minusradic6
6
1
radic2minus1
6
0 0 1 1 1 0 997888997888997888rarrV1198881205721205730
4
minusradic2
30
1
6
0 0 0 1 1 1 997888997888997888rarrV1198881205721205730
5
minusradic6
6
minus1
radic2minus1
6
1 0 0 0 1 1 997888997888997888rarrV1198881205721205730
6 radic6
6
minus1
radic2
1
6
1 0 1 0 1 0 997888997888997888rarrV1198881205721205730
7
0 01
2
Table 2 Operating parameters and components of the four-wire APF prototype
Electrical parametersVariable Value
Prototype power rating (laboratory design) 2 kWThree-phase supply 119881
119878119873127V 60Hz
DC-link voltage reference 119864 400VSampling frequency 119891
119878216 kHz
ADC resolution 12 bitsPrototype components
Line filters inductors 119871119891
10mHDC-link capacitors 119862 10mFPower IGBTs BSM100GD60DLC 1200V 30AIGBT drivers Infineon 2ED300CL7-sACDC voltage sensors LEM LV 25-PACDC current sensors Honeywell CSNA111DC-link voltage controller 119867
119864(119904) 3000119904 + 45e4
1199042 + 1000 minus 671e minus 8
DC-link voltage balance controller 119867bal(119904)400119904 + 10
119904
the one used at a power substation of Line B MetropolitanRailway ofMexico City for powering electronic utility equip-ment
Figure 6(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and one supply phase voltage V
119877119873 obtained
with the load condition of Figure 6(a) The experimental linecurrent waveforms were typical of a three-phase 6-pulserectifier without the operation of the APF but when theAPF was turned on using the Euler predictive controller thesupply currents became virtually sinusoidal waveforms withthe supply currents Total Harmonic Distortion (THD) andthe total power factor being improved from 29 to 15 andfrom 095 to 098 respectively which confirmed that the APFwas properly operating Twomain characteristics were foundin the experimental supply current waveforms of Figure 6(a)a 42 kHz high-frequency ripple and a small glitch occurringat every rising and falling slope of the load current waveform
The first was attributed to the Euler approximation used withthe predictive control switching that continuously tracks thereference currents [23] which was confirmed with a dynamiccondition of stepping the output filter inductance from50mH to 100mH Figure 6(b) shows that the operation ofthe APF with the Euler predictive current control and the P-Q theory is maintained throughout the filter inductance stepsince the sinusoidal waveformquality of the supply currents isstable as shown in Figure 6(b) ensuring reliable operation ofthe APF and therefore the predictive controller is likely to becompliant under dynamic conditions a typical requirementfor control techniques however the amplitude of the filtercurrent waveforms slightly fell from 2A to 15 A duringthe transient response with the supply current THD beingbarely degraded around 24 The second characteristic wasconfirmed by contrasting the measured filter current 119894
119871119877
with its digital reference 119894119871119877
lowast as shown in the left-hand side
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
Table 1 Normalized converter voltage space vectors with respect to the transistor switching states
Transistor state combination 997888997888997888rarrV1198881205721205730
Normalized converter voltages1198761
1198762
1198763
1198764
1198765
1198766
119881120572E 119881
120573E 119881
0E
0 1 0 1 0 1 997888997888997888rarrV1198881205721205730
0
0 0 minus1
2
1 1 0 0 0 1 997888997888997888rarrV1198881205721205730
1
radic2
30 minus
1
6
1 1 1 0 0 0 997888997888997888rarrV1198881205721205730
2 radic6
6
1
radic2
1
6
0 1 1 1 0 0 997888997888997888rarrV1198881205721205730
3
minusradic6
6
1
radic2minus1
6
0 0 1 1 1 0 997888997888997888rarrV1198881205721205730
4
minusradic2
30
1
6
0 0 0 1 1 1 997888997888997888rarrV1198881205721205730
5
minusradic6
6
minus1
radic2minus1
6
1 0 0 0 1 1 997888997888997888rarrV1198881205721205730
6 radic6
6
minus1
radic2
1
6
1 0 1 0 1 0 997888997888997888rarrV1198881205721205730
7
0 01
2
Table 2 Operating parameters and components of the four-wire APF prototype
Electrical parametersVariable Value
Prototype power rating (laboratory design) 2 kWThree-phase supply 119881
119878119873127V 60Hz
DC-link voltage reference 119864 400VSampling frequency 119891
119878216 kHz
ADC resolution 12 bitsPrototype components
Line filters inductors 119871119891
10mHDC-link capacitors 119862 10mFPower IGBTs BSM100GD60DLC 1200V 30AIGBT drivers Infineon 2ED300CL7-sACDC voltage sensors LEM LV 25-PACDC current sensors Honeywell CSNA111DC-link voltage controller 119867
119864(119904) 3000119904 + 45e4
1199042 + 1000 minus 671e minus 8
DC-link voltage balance controller 119867bal(119904)400119904 + 10
119904
the one used at a power substation of Line B MetropolitanRailway ofMexico City for powering electronic utility equip-ment
Figure 6(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and one supply phase voltage V
119877119873 obtained
with the load condition of Figure 6(a) The experimental linecurrent waveforms were typical of a three-phase 6-pulserectifier without the operation of the APF but when theAPF was turned on using the Euler predictive controller thesupply currents became virtually sinusoidal waveforms withthe supply currents Total Harmonic Distortion (THD) andthe total power factor being improved from 29 to 15 andfrom 095 to 098 respectively which confirmed that the APFwas properly operating Twomain characteristics were foundin the experimental supply current waveforms of Figure 6(a)a 42 kHz high-frequency ripple and a small glitch occurringat every rising and falling slope of the load current waveform
The first was attributed to the Euler approximation used withthe predictive control switching that continuously tracks thereference currents [23] which was confirmed with a dynamiccondition of stepping the output filter inductance from50mH to 100mH Figure 6(b) shows that the operation ofthe APF with the Euler predictive current control and the P-Q theory is maintained throughout the filter inductance stepsince the sinusoidal waveformquality of the supply currents isstable as shown in Figure 6(b) ensuring reliable operation ofthe APF and therefore the predictive controller is likely to becompliant under dynamic conditions a typical requirementfor control techniques however the amplitude of the filtercurrent waveforms slightly fell from 2A to 15 A duringthe transient response with the supply current THD beingbarely degraded around 24 The second characteristic wasconfirmed by contrasting the measured filter current 119894
119871119877
with its digital reference 119894119871119877
lowast as shown in the left-hand side
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
iL120573
997888997888997888rarriL1205721205730
3
k+1997888997888997888rarriL1205721205730
2
k+1
997888997888997888rarriL1205721205730
4
k+1
997888997888997888rarriL1205721205730
1
k+1
997888997888997888rarriL1205721205730
5
k+1
997888997888997888rarriL1205721205730
6
k+1
997888997888997888rarriL1205721205730kminus1997888997888997888rarr
iL1205721205730k
Path of 997888997888rarriLref (t)
997888997888997888rarriL1205721205730
07
k+1
997888997888997888rarriL1205721205730
lowast
k
iL120572
iL0
Figure 3 One-step ahead current samples 997888997888997888rarr1198941198711205721205730
0
119896+1to 997888997888997888rarr
1198941198711205721205730
7
119896+1 around 997888997888997888rarr
1198941198711205721205730119896
and 997888997888997888rarr1198941198711205721205730
lowast
119896in the 1205721205730 current frame
of Figure 6(c) revealing that the predictive current controlslightly follows the reference during the high 119889119894119889119905 periodsof the load current waveforms due to the simple Eulerapproximation used in the algorithm reducing the trackingaccuracy of the references and therefore introducing smallglitches to the supply current waveforms This undesiredphenomenon was improved by changing the Euler approx-imation of the predictive controller to the trapezoidal tech-nique as shown in the right-hand side of Figure 6(c) whichreveals in its amplification shown in Figure 6(d) that thetrapezoidal predictive controller reduces the current rippleamplitude by approximately 50 increasing its frequencyrate from 42 kHz to 95 kHz and producing a lower supplycurrent THD 102 and a power factor of 0989 in contrastto the Euler technique with the supply current waveformsbecoming virtually free of high-frequency glitches and ripple
Figure 7(a) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
unbalanced load condition of Figure 5(b) at 09 kW This fig-ure shows that the line currents are typical of an unbalancednonlinear load before the APF is activated and after the APFis on the supply currents become virtually balanced sinu-soidal waveforms of 24 A with the supply current THD andthe power factor being improved from an unbalanced 43 toa balanced 25 and from 093 to 0972 respectively revealingagain that the active filter prototype is correctly operatingwith a four-wire load In addition the same figure showsthat the power quality of the supply currents becomes muchmore improved when the predictive controller is changedfrom the Euler to the trapezoidal technique with the supplycurrent THD and the power factor becoming 15 and 098
respectively These experimental current waveforms haveagain a high-frequency ripple being 42 kHz when the APFis operated with the typical Euler technique and 95 kHz withthe proposed trapezoidal strategy In Figure 7(a) the neutralcurrent 119894
119873was virtuallymitigated after theAPFwas activated
becoming more reduced when the APF was driven with thetrapezoidal controllerThis experiment revealed the effective-ness of the 4-wire P-Q theory used in this work togetherwith the predictive current control switching
Figure 7(b) shows the experimental supply currents 119894119878119877
119894119878119878 and 119894
119878119879and the neutral current 119894
119873obtained with the
front-end controlled rectifier drive andmonophasic resistiveload of Figure 5(c) at 09 kW Before the APF is activated asshown in Figure 7(b) the experimental supply currents arecompletely unbalanced distorted and phase-displaced dueto the biphasic connection of the front-end rectifier of themotor drive and the resistive load connection however whenthe APF is on using firstly the Euler predictive techniqueand then the trapezoidal version the supply currents becomeagain balanced with virtual sinusoidal waveforms such thattheir THD was improved from an unbalanced 40 to abalanced 23 and 18 for the Euler and trapezoidalmethodsrespectively and the power factor from 08 to 097 and 098again for the Euler and trapezoidal methods respectively InFigure 7(b) the neutral current 119894
119873was again virtually miti-
gated after the APFwas activated becoming almost cancelledwhen the APF used the trapezoidal controller
A power analyser was used to measure the supply activepower 119875 the supply apparent power 119878 the per-phase supplycurrent THD 119868
119877119878THD 119868
119878119878THD and 119868
119879119878THD and the total
power factor during the experiments described above The
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
Start
Controller parameter initialization
Clark transform
PLL algorithm at kth instant
PQ theory calculation at kth instant
DC-link controller at kth instant
DC-link balance controller at kth instant
Combination = j
No
No
Yes
Yes
For j = 0 middot middot middot 7
Apply transistor state combination to APF
Measurement of 997888rarrsk997888rarriLk
997888997888997888997888rarriLoadk E1k E2k
Prediction of 997888997888997888rarriL1205721205730
0ndash7
k+1
997888997888997888997888rarriLe1205721205730
j
klt997888997888997888997888rarriLe1205721205730
jminus1
k
997888997888997888997888997888997888997888rarriLe1205721205730min
= 0 and combination = 0997888997888997888997888997888997888997888rarri Le1205721205730min
=997888997888997888997888rarriLe1205721205730
j
k
Saving 997888997888997888997888rarrc1205721205730Combinationk
for next sampling
j = 7
997888997888997888997888rarriLe1205721205730
j
kEvaluation of
Figure 4 Algorithm flow diagram of the predictive current controller
results are contrasted in the comparative bar plot of Figure 8calculated with a 2 kVA APF rating a 127V 60Hz line-to-neutral supply voltage and a 400V APF DC link Figure 8shows that 119875 slightly rise by approximately 5 100W whenthe APF prototype was used to improve and balance thesupply currents among the experiments the additional powerloss occurring in the transistors filter inductors and DC-linkcapacitors of the APF converter due to the high-frequencyoperation In comparison with the unbalanced load the cur-rent THD reduction is representative when the APF is usedtogether with the trapezoidal predictive controller to com-pensate the drawn currents of the balanced load as shown inFigure 8 whereas the current THD is slightly improved whenthe APF is used together with the Euler strategy and the loadcases of Figure 5 nevertheless the drawn current through theneutral wire is noticeably cancelled when the APF is usedto correct the power quality of the four-wire AC loads ofFigures 5(b) and 5(c) In contrast with the balanced load thedistribution between apparent and active power for the APF
with the unbalanced load becomes equilibrated due to cor-rection of current phase displacement
Closer inspection of the microprocessor operationrevealed that the total period to perform the algorithmof Figure 4 was around 29 120583s with the Euler predictivecontroller which is well below the sampling period to ensureminimal delay effects of the control system Unlike theexperimental verification of the Euler predictive controllerthe experimental verification of the APF with the trapezoidalpredictive controller resulted in a slight increment ofalgorithm processing time of Figure 4 from 29120583s to 30 120583swhich was imperceptible during the experimental verifica-tion of the APF
The presented trapezoidal predictive controller is slightlymore complex than the typical predictive strategy to per-form the current reference tracking and generates a slightincrease of power losses which could make it inadequatefor implementation in low-rated rigs nevertheless the ripplecurrent reduction closer current tracking and power quality
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadS
iLoadT
100mH
10mF
C R
50ohms
(a)
N
Active power filter
vRN vSN vTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
100mH
10mF
50mH
C R
50ohms
100 ohms
75ohms
D1
D2
D3
D1 D3
D4
D2D4
10mF
(b)
L
IM
N
Active power filter
vRN
VRN
vSN
VSN
vTN
VTN
iLR
iSR
iLS iLT
iSSiST
iLoadR
iLoadSiLoadT
CC
50ohms
D1Q1 Q3 Q5
Q2Q6Q4 D2
D3 D5
D4 D6
(c)
Figure 5 Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure 1 (a) Balanced three-wire load(b) unbalanced four-wire load and (c) unbalanced load used at a Metro Power Substation
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
C1 100Vdiv 2800V offsetC2 DC1M 100Adiv minus1150V offsetC3
C3
DC 100Adiv minus2820A offsetC4 BwL DC 100Adiv 730A offset
Tbase minus595ms
160msdiv160MS 100MSs
Trigger C1 DC
Stop 0VEdge Positive
BwL DC
APF on with the Euler controller
1M
APF on with the Euler controllerlA
C1
C2
C4
(a)
C3
C1 F B D1 100Vdiv minus29500VC2 DC 200Adiv 0mA offsetC3 INV DC1M 50Adiv minus14A offsetC4 BwL DC 200Adiv 4640A offset
Tbase minus9104ms160msdiv
160MS 100MSs
Trigger C1 DCStop minus68VEdge Positive
DC filter inductor step
C1
C2
C4
(b)
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Timebase 78ms
500msdiv500MS 100MSs
C2 HFR
158V
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF ith th t id l t llAPF on ithhhhhhhhh thehhhhhe Euler controllerl
C1
C2
C4
(c)
C1
C2
C4
Timebase 780ms
200msdiv500MS 250MSs
C2 HFR
158V
C1 F B D 500Adiv 480mA offsetC2 F B D1 500Vdiv 5080V offsetC3 F B D 500Adiv 5080A offsetC4 F B D1 500Adiv minus4820V offset
Trigger
StopEdge Positive
APF on with the trapezoidal controllerAPF on with the Euler controller APF on wwwwwwith the trapezoidal controllerlde nAPF on with the Euler controllerh
(d)
Figure 6 Experimental verification of the APF prototype with the 16 kW balanced load of (a) (a) Measured waveforms V119877119873
(yellow) 119894119878119877
(green) 119894119878119878(red) and 119894
119878119879(blue) before and after the activation of the APF (b) Measured response of V
119877119873(yellow) 119894
119871119877(red) 119894Load119877 (green)
and 119894119878119877
(yellow) to a filter inductance step from 50mH to 100mH (c) Measured response of 119894119871119877
(blue) and 119894119878119877
(green) to a predictive currentcontroller step from Euler to the trapezoidal approximation which is contrasted against the reference 119894
119871119877
lowast (red) and load current 119894Load119877 (d)Time amplification of (c) at the instant of the predictive controller step 127V 60Hz supply 400VAPFDC link and a 216 kHz APF samplingfrequency
improvement are important advantages to consider over thetraditional predictive controller technique Furthermore thedigital implementation is acceptable for fastmicrocontrollerssuch as a DSPs and hybrid digital controllers and will beused once the trapezoidal control strategy is implementedto control other power converter systems which would besuitable to obtain high power quality results
5 Conclusions
The utilization of a trapezoidal predictive technique to gen-erate the filter currents of a four-wire shunt APF allows the
power quality improvement of using unbalanced nonlinearloads for on-land utility applications such that the supplycurrents become virtual sinusoidal waves The latter makesthe current control strategy attractive for easy and straightimplementation on future power converters that requirehigh-performance power quality nevertheless the controltechnique is suitable for a wide range of power converterapplications In this work the trapezoidal predictive con-troller was experimentally verified and evaluated with thefour-wire APF under three load conditions in the first theload was set up with a three-wire balanced nonlinear circuitto preliminary check the basic operation of the control
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
C1 BwL DC1M 500Vdiv minus520V offsetC2 DC1M 500Vdiv 470V offsetC3 DC 500Adiv 1335A offsetC4 F B D 100Adiv minus29900A
minus15885 s Trigger C2 DC
100V
Tbase
160msdiv160MS 100MSs
StopEdge Positive
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4 APF PFAAAAAA F on with thhhhh thehhhhhhhhhhhhhhFFFtrapezoiooo dal controllerno
APF APFPFPFAPAPAAPFAAPAPFPFFAPAPFAPFPFPAPFFFFFPFFFAAPPFFFFFAA FFFFAPFFFFFFAAPFFA FA oon withhhhhhhhhhithithithththhhhhhhhhhhith iii hhhhhhhthhitiiithhhhhhithiitthhhhhhiiiiththhhhthhth thehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhA wwEuler controlleroon
(a)
minus1600ms200msdiv
500MS 25MSs
C3 HFR30V
TriggerTbase
StopEdge Positive
C1 BwL DC1M 500Vdiv minus570V offsetC2 DC1M 500Vdiv 1410V offsetC3 BwL DC1M 100Vdiv minus32400VC4 BwL DC 500Adiv 445A offset
APF on with thetrapezoidal controller
APF on with theEuler controller
C3
C1
C2
C4APF on withhhhh theAPF on with theF
trapezoie dal controllo ereeeapezoidal cont o eeeetzAPF on with theAPF on with thewwEuleulul r coontrorr llerrleEulll coontrolleooon
(b)
Figure 7 (a) Measured supply current waveforms 119894119878119877
(blue) 119894119878119878(yellow) 119894
119878119879(red) and 119894
119873(green) before and after the activation of the APF
with the Euler and Trapezoidal predictive controllers and the load condition of Figure 5(a) (b) Measured supply current waveforms 119894119878119877(red)
119894119878119878(yellow) 119894
119878119879(green) and 119894
119873(blue) before and after the activation of the APF with the Euler and trapezoidal predictive controllers and the
load condition of Figure 5(b) 127V 60Hz supply 400V APF DC link and 216 kHz APF sampling frequency
00102030405060708091
0102030405060708090
100
Bala
nced
load
of F
igur
e5(
a) w
ithou
t APF
Bala
nced
load
of F
igur
e5(
a) w
ith A
PF an
d th
eEu
ler m
etho
dBa
lanc
ed lo
ad o
f Fig
ure
5(a)
with
APF
and
the
trap
ezoi
dal m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
b) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Unb
alan
ced
load
of F
igur
e5(
c) w
ithou
t APF
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
eEu
ler m
etho
d
Unb
alan
ced
load
of F
igur
e5(
c) w
ith A
PF an
d th
etr
apez
oida
l met
hod
Supp
ly cu
rren
t TH
D (
)
Active power P (pu)Apparent power S (pu)
Power factoriSR THD
iSS THDiST THD
Figure 8 Bar plot of the power quality results for the AC loadcircuits of Figure 5 with the APF prototype operating with theEuler and trapezoidal predictive techniques 127V 60Hz supply and2 kVA APF rating
technique such that sinusoidal supply current waves weregenerated and the power quality was improved A currentTHD of 10 and a power factor of 0989 were measured inthe first experiment showing a noticeable improvement incontrast to the traditional predictive technique
In the second and third load conditions the load wasfour-wire unbalanced nonlinear load with the load currentsbeing much distorted and producing a neutral current pathin both load conditions The supply current waveforms wereall improved and balanced when the APF and the trapezoidal
predictive controller were activated with the neutral currentbeing mitigated the current THD was 15 and 18 respec-tively and the power factorwas 098 in both experiments witha 127V 60Hz three-phase supply voltage The shape of thesupply current waveforms and the power quality were signif-icantly improved in comparison with the original load cur-rents and power quality with the active power being slightlyincreased due to the high-frequency switching losses of theAPF power transistors
The practical realization of the presented trapezoidalpredictive controller could consider the use of an extendedsampled-data horizon either forward or backward to achievea faster convergence and reduce the current ripple amplitudeThis would be convenient for developing power converterswith new generation of switching power devices for otherapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors are grateful to the National Council of Sci-ence and Technology (CONACyT) the Instituto PolitecnicoNacional (IPN) of Mexico the Institute of Science andTechnology of Mexico City (ICyT) and the Universidad deTalca Chile for their encouragement and the realizationof the prototype Additionally the authors acknowledge theMetropolitan Railway Transportation System of Mexico City(SCT Metro) for the support offered to obtain power qualitymeasurements at Line B installations
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
References
[1] IEEEApplicationGuide for IEEE Standard 1547 ldquoIEEE standardfor interconnecting distributed resources with electric powersystemsrdquo IEEE Standard 15472-2008 2008
[2] S W Mohod andM V Aware ldquoA STATCOMmdashcontrol schemefor grid connected wind energy system for power qualityimprovementrdquo IEEE Systems Journal vol 4 no 3 pp 346ndash3522010
[3] IEEE ldquoIEEE recommended practices and requirements forharmonic control in electrical power systemsrdquo IEEE Standard519-1992 1992
[4] J D vanWyk and F C Lee ldquoOn a Future for Power ElectronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013
[5] P Kanjiya V Khadkikar and H H Zeineldin ldquoOptimal controlof shunt active power filter to meet IEEE Std 519 currentharmonic constraints under nonideal supply conditionrdquo IEEETransactions on Industrial Electronics vol 62 no 2 pp 724ndash734 2015
[6] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method for amultivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[7] P Acuna L Moran M Rivera R Aguilera R Burgos and VG Agelidis ldquoA single-objective predictive control method fora multivariable single-phase three-level NPC converter-basedactive power filterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 7 pp 4598ndash4607 2015
[8] P Jintakosonwit H Fujita and H Akagi ldquoControl and per-formance of a fully-digital-controlled shunt active filter forinstallation on a power distribution systemrdquo IEEE Transactionson Power Electronics vol 17 no 1 pp 132ndash140 2002
[9] Z Xiao X Deng R Yuan P Guo and Q Chen ldquoShunt activepower filter with enhanced dynamic performance using novelcontrol strategyrdquo IET Power Electronics vol 7 no 12 pp 3169ndash3181 2014
[10] P Acuna L Moran M Rivera J Rodriguez and J DixonldquoImproved active power filter performance for distributionsystems with renewable generationrdquo in Proceedings of the 38thAnnual Conference on IEEE Industrial Electronics Society(IECON rsquo12) pp 1344ndash1349 Montreal Canada October 2012
[11] P Acuna L Moran M Rivera J Dixon and J RodriguezldquoImproved active power filter performance for renewable powergeneration systemsrdquo IEEE Transactions on Power Electronicsvol 29 no 2 pp 687ndash694 2014
[12] H Akagi E H Watanabe and M Aredes Instantaneous PowerTheory and Applications to Power Conditioning IEEE PressSeries on Power Engineering Wiley-IEEE Press 2007
[13] R P Aguilera and D E Quevedo ldquoPredictive control of powerconverters designs with guaranteed performancerdquo IEEE Trans-actions on Industrial Informatics vol 11 no 1 pp 53ndash63 2015
[14] P Cortes J Rodrıguez P Antoniewicz andM KazmierkowskildquoDirect power control of an AFE using predictive controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2516ndash25232008
[15] J Scoltock T Geyer and U K Madawala ldquoModel predictivedirect power control for grid-connected NPC convertersrdquo IEEETransactions on Industrial Electronics vol 9 no 62 pp 5319ndash5328 2015
[16] M Lopez J Rodriguez C Silva and M Rivera ldquoPredictivetorque control of a multidrive system fed by a dual indirectmatrix converterrdquo IEEE Transactions on Industrial Electronicsvol 62 no 5 pp 2731ndash2741 2015
[17] A Bhattacharya and C Chakraborty ldquoA shunt active powerfilter with enhanced performance using ANN-based predictiveand adaptive controllersrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 2 pp 421ndash428 2011
[18] R Vargas U Ammann B Hudoffsky J Rodriguez and PWheeler ldquoPredictive torque control of an induction machinefed by a matrix converter with reactive input power controlrdquoIEEE Transactions on Power Electronics vol 25 no 6 pp 1426ndash1438 2010
[19] B S Riar T Geyer and U K Madawala ldquoModel predictivedirect current control of modular multilevel converters model-ing analysis and experimental evaluationrdquo IEEE Transactionson Power Electronics vol 30 no 1 pp 431ndash439 2015
[20] L Tarisciotti P Zanchetta A Watson J C Clare M Deganoand S Bifaretti ldquoModulated model predictive control for athree-phase active rectifierrdquo IEEE Transactions on IndustryApplications vol 51 no 2 pp 1610ndash1620 2015
[21] A Luo X Xu L Fang H Fang J Wu and C Wu ldquoFeedback-feedforward PI-type iterative learning control strategy forhybrid active power filter with injection circuitrdquo IEEE Trans-actions on Industrial Electronics vol 57 no 11 pp 3767ndash37792010
[22] Y F Wang and Y W Li ldquoThree-phase cascaded delayed signalcancellation PLL for fast selective harmonic detectionrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1452ndash1463 2013
[23] M Rivera C Rojas J Rodrıguez P Wheeler B Wu and JEspinoza ldquoPredictive current control with input filter resonancemitigation for a direct matrix converterrdquo IEEE Transactions onPower Electronics vol 26 no 10 pp 2794ndash2803 2011
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of