Description

We present a New Conjugate
Gradient Method for Solving Nonlinear
Unconstrained Optimization Problems
through a generalization of the
multivariable Taylor’s series as the model
of the objective function f. Numerical
results from this method produced the
global optimum of f

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A Novel Control Algorithm for Hybrid Power Filter to Compensate Three Phase Four-WireSystems
S. SURESH
1
Associate Professor/EEEKalaignar Karunanidhi Instituteof TechnologyCoimbatore, IndiaSuresh.seetharaman@ieee.org
1
M.GEETHA
2
Assistant Professor/ECEKalaignar Karunanidhi Instituteof TechnologyCoimbatore, Indiaengrsugeetha@gmail.com
2
Dr. N.DEVARAJAN
3
Professor/EEEGovernment College of TechnologyCoimbatore, India profdevarajan@ieee.org
3
A
bstract—
A control algorithm is proposed for a three-phase hybrid power ﬁlter constituted by a series activeﬁlter and a shunt passive ﬁlter. The control strategy isbased on the dual formulation of the compensation systemprinciples. It is applied by considering a balanced andresistive load as ideal load, so that the voltage waveforminjected by the active ﬁlter is able to compensate thereactive power, to eliminate harmonics of the load currentand to balance asymmetrical loads. This strategy improvesthe passive ﬁlter compensation characteristics withoutdepending on the system impedance, and avoiding theseries/shunt resonance problems, since the set load-ﬁlterwould present resistive behaviour. An experimentalprototype was developed and experimental results arepresented.
Index Terms—Active power ﬁlters (APFs), harmonics,hybridﬁlters, instantaneous reactive power, power quality.
I.
I
NTRODUCTION
M
any Social and economic activities depend onelectrical energy quality and efﬁciency. Both industrialand commercial users are interested in guaranteeing theelectrical waveform quality, which supplies their different systems. The nonlinear load can generatecurrent harmonics and/or voltage harmonics, whichmakes worse the power quality. Therefore, theseharmonics must be mitigating. In order to achieve this,series or parallel conﬁgurations or combinations of active and passive ﬁlters have been proposed dependingon the application type [1], [2].Traditionally, a passive LC power ﬁlter is used toeliminate current harmonics when it is connected in parallel with the load [3], [4]. This compensationequipment has some drawbacks [5] mainly related to theappearance of series or parallel resonances because of which the passive ﬁlter cannot provide a completesolution.Since the beginning of the 1980s, active power ﬁlters (APFs) have become one of the most habitualcompensation methods. A usual APF consists of a three- phase pulse width modulation (PWM) voltage sourceinverter. The APF can be connected either in parallel or in series with the load. The ﬁrst one is especiallyappropriate for the mitigation of harmonics of the loadscalled harmonic current source. In contrast, the seriesconﬁguration is suitable for the compensation of loadscalled harmonic voltage source. The shunt connectionAPF is the most studied topology [6]–[10]. However,the costs of shunt active ﬁlters are relatively high for large-scale system and are difﬁcult to use in high-voltage grids. In addition, their compensating performance is better in the harmonic current sourceload type than in the harmonic voltage source load type[10].Another solution for the harmonic problem is toadopt a hybrid APF [11]–[18]. The hybrid topologiesaim is to enhance the passive ﬁlter performance and power-rating reduction of the active ﬁlter. Twoconﬁgurations have been mainly proposed: active ﬁlter connected in series with a shunt passive ﬁlter and seriesactive ﬁlter combined with shunt passive ﬁlter. Bothtopologies are useful to compensate harmonic currentsource load type. However, when the load alsogenerates voltage harmonics, the second topology is themost appropriate. In this paper, the topology used isseries active ﬁlter combined with shunt passive ﬁlter.For this conﬁguration, different techniques have beenapplied to obtain the control signal for the APF [12]– [18]. The control target most used is that provides highimpedance for the harmonics while providing zeroimpedance for the fundamental harmonic. This strategyis achieved when the APF generates a voltage proportional to the source current harmonics [12], [13].With this control algorithm, the elimination of seriesand/or parallel resonances with the rest of the system is possible. The active ﬁlter can avoid that the passiveﬁlter becomes a harmonics drain of the close loads.Besides, it can prevent the compensation features fromits dependence on the system impedance. From thetheoretical point of view, the ideal situation would bethat the proportionality constant k between the activeﬁlter output voltage and source current harmonics had ahigh value, at the limit it would be an inﬁnite value.However, this would mean that the control objectivewas impossible to achieve. The chosen k value is
S. Suresh et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 3, Issue No. 1, 001 - 011ISSN: 2230-7818@ 2011 http://www.ijaest.iserp.org. All rights Reserved.Page 1
usually small. It avoids high power active ﬁlters.However, the choice of the appropriate k value is anunsolved question, since it is related to the passive ﬁlter and the source impedance values. Besides, this strategyis not suitable to be used in systems with variable loads because the passive ﬁlter reactive power is constant, andtherefore, the set compensation equipment and load hasa variable power factor.In another proposed control technique the APFgenerates a voltage waveform similar to the voltageharmonics at the load side, but in opposition [15]. Thisstrategy only prevents the parallel passive ﬁlter depending on the source impedance; the other limitations of the passive ﬁlter nevertheless remain.Other control strategies combining both theaforementioned have been proposed to improve the parallel passive ﬁlter compensation characteristics [11], but they go on suffering the difﬁculty of ﬁnding anappropriate value for the APF gain k.Finally, another approach has recently been proposed [16]. It suggests that the active ﬁlter generatesa voltage, which compensates the passive ﬁlter and loadreactive power, so it allows the current harmonics to beeliminated. The calculation algorithm is based on theinstantaneous reactive power theory [19], [22]. There,the control target is to achieve constant power in thesource side.All presented strategies are applied to a three-phasethree-wire system with balanced load.In this paper, a control strategy based on the dualapproach of the compensation principles is proposed,[21]. It is applied by considering a balanced andresistive load as ideal load. Thus, the determinedreference voltage is obtained to attain the objective of achieving ideal behaviour for the set hybrid ﬁlter load.With this strategy is possible to improve the passiveﬁlter compensation characteristics without depending onthe system impedance, since the set load ﬁlter would present resistive behaviour. It also avoids the danger that the passive ﬁlter behaves as a harmonic drain of close loads, and likewise, the risk of possible seriesand/or parallel resonances with the rest of the system. Inaddition, the compensation is also possible with variableloads, not affecting the possible the passive ﬁlter detuning. This strategy achieves unity power factor when the supply voltage is balanced sinusoidal. Thesystem compensation can be applied to nonlinear load, both harmonic current source loads and harmonicvoltage source loads. The control strategy was appliedto a three-phase four-wiresystem. An experimental prototype was manufactured and its behaviour checked.Experimental results are also presented.II.REFERENCE COMPENSATION VOLTAGE
A. Proposed Control Strategy
Electrical companies try to generate electrical power with sinusoidal and balanced voltages and it has beenobtained as areference condition in the supply. Due tothis fact, the compensation target is based on an idealreference load, which must beresistive, balanced, andlinear. It means that the source currentsare collinear tothe supply voltages and the system will haveunity power factor. Therefore, at the point of common coupling(PCC), the following expression will be satisﬁed:(1)Here, R
e
is the equivalent resistance, v is the voltagevectoron the connection point, and i is the supplycurrent vector.Fig. 1 shows the conﬁguration active ﬁlter connectedin serieswith passive ﬁlter connected in shunt with theload.In low voltage distribution systems, there is usuallythe presence of single-phase loads. That produces severeunbalance voltages and currents in the system. For thisreason, even if thevoltage source is balanced, the PCCvoltage cannot be balanceddue to the presence of unbalanced three-phase loads and/orsingle-phase loads.A compensating system will have to avoidthe propagation of the voltage imbalance from the PCC tootherconsumers.Fig. 1. Scheme of series active ﬁlter combined withshunt passive ﬁlter.Fig. 2.Three-phase four-wire system.
S. Suresh et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 3, Issue No. 1, 001 - 011ISSN: 2230-7818@ 2011 http://www.ijaest.iserp.org. All rights Reserved.Page 2
In a three-phase system as in Fig. 2, the voltage andcurrent vectors can be deﬁned by
(2)
When the load currents are unbalanced and non-sinusoidal, a balanced resistive load can be consideredthe ideal reference load. For the ideal load, the sourcecurrent vector will be balanced and sinusoidal. The balanced current from (2) can be obtained applying theFortescue transformation, deﬁned by the followingexpression:
(3)
where a = e
j120
and zero-, positive-, and negative-sequence components are denoted by superscripts 0, +,and –, respectively.The fundamental harmonic of the positive-sequencecomponent i
+
, can be calculated applying the followingrelations:
(4)(5)
Where I
+1
denote the rms value of the fundamentalharmonic of i
+
, ϕ is its initial phase, and ω is thefundamental frequency.The instantaneous value is given by the addition of (4) and (5), and multiplying (4) by sin ωt and (5) bycosωt, i.e.,
(6)
With the inverse transformation, the ideal sourcecurrent vector is obtained, which will be balanced andfree of harmonics(7)The active power supplied by the source will be
(8)
where I
1+2
is the norm of the positive-sequencefundamental component of the current vector [21], [22].This norm is deﬁned by(9)The compensator instantaneous power is difference between the total real instantaneous power required bythe load (p
L
) and the instantaneous power supplied bythe source (p
S
), i.e.,(10)When the average values are calculated in this equationand taking into account that the active power exchanged by the compensator has to be null, (10) can be rewrittenas follows:(11)Therefore, the equivalent resistance can be calculated by(12)P
L
is the load average power.The aim is that the compensation equipment andload have ideal behaviour from the PCC. The upstreamvoltage of the active ﬁlter can be calculated as follows:(13)where i is the source current vector. Thus, the referencesignal for the output voltage of the active ﬁlter is asfollows:(14)That is, when the active ﬁlter generates thiscompensation voltage, the set load and compensationequipment will behave as a resistor with a Re value.
B. Comparison between Resistive Load and Synchronous Reference Frame Methods
The synchronous reference frame (SRF) basedcontrol has been widely accepted by industrial sectors.Thus, some series active ﬁlter control schemes usetechniques based on the SRF to extract the fundamentalor harmonics component [24]. This method extracts thefundamental component without introducing any timedelay at the steady state.
However, this techniqueincluded generally a phase locked loop (PLL)in the detection system. It has good resultswhen the current supply is balancedandincludes low-order harmonics.
S. Suresh et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 3, Issue No. 1, 001 - 011ISSN: 2230-7818@ 2011 http://www.ijaest.iserp.org. All rights Reserved.Page 3
TABLE ICURRENT THD (%) FROM COMPARATIVE ANALYSIS OF THETWO CONTROL METHODS
Balanced Unbalanced
Without Comp50Hz 49Hz Without Comp50Hz 49Hz
SRF28.841.92 2.2427.209.30 9.22RL 1.31 2.20 2.26 3.07
Fig. 3.Reference voltage calculation.The PLL usually has small bandwidth to reduce theeffect of the high-frequency harmonics. This causes a poor dynamic response and an error in the detectedmagnitude. When the system is unbalanced, these errorsaffect to the fundamental component calculations.In this section, a comparative analysis between proposed RL method and the SRF-based control isrealized. The compensation system consists of combined ﬁlter constituted by an APF series and a parallel passive ﬁlter with two branch tuned to the ﬁfthand seventh harmonics. Two control voltages have beenimplemented. One has been obtained by means of the proposed method in this paper; the other one has beenobtained using the expression(15)where i
sh
is the source current harmonics drawn fromtheutility.The current harmonics has been extracted usingthe SRFmethod.Two nonlinear loads have been chosen: a balanced load and another unbalanced load. Supplyvoltages with different frequencies 50 and 49 Hz, wereapplied to the loads. It was simulated with MATLAB-Simulink and total harmonic distortion (THD) resultsare presented in Table I. The SRF use a PLL to obtainthe network frequency, however, the frequency in theRL method is ﬁxed to 50 Hz in both cases.The two techniques present a good behavior when achange in the frequency of the supply voltage takes place. When the load is balanced, the current THD aresimilar, however, when the load is unbalanced the SRFmethod present a current THD higher than the methodRL proposed in this paper.III. CONTROL SCHEME
A. Circuit Conﬁguration
The control scheme used to calculate the active ﬁlter compensation voltage is shown in Fig. 3. It wasimplemented in MATLAB-Simulink. The toolbox real-time workshop (RTW) together with the real-timeinterface (RTI) from dSPACEgenerates the code to program the control board.Fig. 4.Direct-sequence component calculation.Fig. 5.Fundamental component calculation.It let a rapid prototype of the control system presentedand explained in Section IV.The voltage vector at the load side and the sourcecurrent vectors are the input signals. Fig. 8 shows thelocation of measurement sensors. The product of thesevectors allows the instantaneous real power to becalculated, obtaining its average value with a low-passﬁlter (LPF). The LPFs are implemented with a Simulink block. This block is themodel of a second-order ﬁlter,where the cut-off frequency was ﬁxed to 100 Hz and thedamping factor to 0.707. It let to reach a settling time of 8ms.The load average power PL is divided by the normof the current-positive-sequence fundamentalcomponent. For this, the positive-sequence componentis calculated by means of the block “direct-sequencecomponent,” where the Fortescue instantaneoustransformation is applied. i.e.,( i
a
+ a i
b
+ a
2
i
c
) (16)Here, the a operator is deﬁned by
S. Suresh et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 3, Issue No. 1, 001 - 011ISSN: 2230-7818@ 2011 http://www.ijaest.iserp.org. All rights Reserved.Page 4

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