Optimal Multiobjective Design of Hybrid Active Power Filters Considering a Distorted Environment

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1 Optimal Multiobjective Design of Hybrid Active Power Filters Considering a Distorted Environment Abstract Te development of new passive, active and ybrid filtering tecniques is important, and te issues of iger quality, reduced complexity, iger efficiency, and lower cost are important conditions tat need to be addressed wit regard to te expected stringent trends in power quality obligations. Tis paper suggests a new approac for te optimal sizing of ybrid active power filter (HAPF) parameters, presented for tree-pase industrial power systems. Hybrid filter topology can be used to compensate armonic currents as well as for power factor corrections, witout concern for importing and exporting armonics, or simply te series and parallel resonance tat may occur. Te new trend in armonic power filter design is not to obtain te best solution from a single objective optimization, but to obtain a good compromise solution accomplised under oter conflicting objectives. FORTRAN Feasible Sequential Quadratic Programming (FFSQP) is used to determine te proposed filter optimal sizing to minimize te total voltage armonic distortion as te main objective function, were maintaining te load power factor at an acceptable limit is desired. If te total armonic voltage distortion acieves te specified goal, ten te objective is redirected into minimizing te resultant voltage and current total armonic distortions. Te optimal design of te HAPF is analyzed by means of tree case studies. Index Terms Hybrid power filters, Optimization, Power quality, Power system armonics. I. NOMENCLATURE R LH, X LH Load resistance and reactance in oms at armonic number G LH, B LH Load conductance and susceptance in mo at armonic number R SH, X SH Transmission system resistance and reactance in oms at armonic number G Controllable gain of te dependent source in oms V H Average value of te controlled voltage source in volts representing te active filter at armonic number X L, X C Magnitude of te fundamental inductive and capacitive reactance in oms of te single tuned passive filter I SH Supply current in amperes at armonic number I S Root-mean-square (RMS) value of supply current in amperes I LH Average value of load armonic current in amperes I L RMS value of rated load current in amperes V LH Average value of load voltage in volts at armonic number V SH Average value of te supply voltage in volts at armonic number V L V S P L P S RMS value of te load voltage (line-toneutral) in volts RMS value of te supply voltage (line-toneutral) in volts Load active power per pase in watts Supply active power per pase in watts II. INTRODUCTION Te exponential growt of armonic pollution as become more serious recently due to te wide use of nonlinear loads, wic result in an obvious degradation of power quality. Tese problems ave different effects on all electrical sectors, ranging from minor variations in power up to bringing wole factories to a standstill [1] [3]. Proposed early stage armonic compensation tecniques provide different solutions for te proper limitation of armonic disturbance levels, and among te various tecniques used to reduce tese armonic disturbances, te most employed are tuned passive filters, due to teir simplicity and different frequency response caracteristics tat can be accomplised wit a certain armonic filtering objective, in addition to teir economic cost. Accordingly, te actual tecnical and economic approac for armonic suppression is troug te use of passive filters [4] [6]. However, te latent danger in teir practical operation is very serious. Te filtering effectiveness of conventional passive filters depends on te source impedance, wic as previously not been determined accurately. Furter problems include importing armonics by te series resonance wit source impedance, or te possibility of idden risks due to parallel resonance between te source impedance and te passive filter at a specific frequency; tus, exporting azards to te entire system, and causing distortion in te voltage at te point of common coupling (PCC). In addition, te configured passive filter components, suc as te inductance and/or te capacitance, are not durable against tuning frequency variations. Terefore, tere is great concern about teir manufacturing tolerance [7]. On te oter and, active filters are more reliable tan passive filters, exibiting better performance wilst at te same time avoiding most of te problems tat occur in passive facilities [8]. Unfortunately, complexity, difficult maintenance, and te iger cost of active facilities compared wit traditional passive facilities ave been sensed in te power quality markets, delaying teir widespread deployment in a broad sense. Tus, te ceapest facility for power factor correction and armonic mitigation is still te passive facility [9]. Consequently, in te last twenty years, since te early 1

2 1990s, topology combining passive and active facilities as been developed. Tis combination partially solves te problem of ig cost associated wit te active power filter, because te size or te rating of te active filter used in te ybrid power filter is muc smaller tan tat used wit pure active filter tecniques, wilst maintaining te properties necessary to solve te problems caused by passive filters, and removing te resonance tat may occur. Despite te beneficial development added by ybrid power filter tecnology, te most managed solution for power factor correction is still te passive facility, because of te complex design of te ybrid topology compared wit te passive facility. For example, te selection of te gain value of te ybrid active filter is usually a matter of trial and error. Some begin wit te power converter gain equaling one or any oter value according to te filter type, but it will be commonly noted tat better performance is obtained wit oter gain values, especially wen considering source and load nonlinearities, making active or ybrid filter design difficult wen guessing te initial feasible values for its parameters. In oter words, acieving ybrid filter parameters, performance, and interaction wit te utility grid at a programmable optimization level is not as simple as wit passive filters [10] [13]. Any armonic filter design must acieve te optimal solution wilst satisfying many objectives; generally, tese objectives migt conflict wit eac oter. An important substitute for multiobjective optimization is not to obtain te best solution, but to obtain a good compromise solution [14]. In tis paper, a suggested ybrid power filter design is investigated, using te FFSQP optimization package to determine te optimum values for te filter parameters represented in its inductance, capacitance (elements of its tuned passive portion), and gain, in order to reduce total armonic voltage distortion (VTHD) at te PCC in te power system to an acceptable level, regardless of te source impedance, and also to improve te load power factor to a desired value (90% PF 95%). If te VTHD acieves te specified value, wile complying wit te oter constraints, ten te objective becomes te minimization of bot te resultant voltage and current total armonic distortion. Te tecnical merits of te proposed ybrid active filter (HAPF) are discussed and analyzed in various case studies, considering source and load nonlinearities. In tis paper, a series-type ybrid filter is introduced as a series combination of passive filters and an active filter (witout introducing a matcing transformer). As te series capacitor sustains te fundamental component of te grid voltage, te active filter can be operated wit a very low DC bus voltage, wic is te significant advantage of reducing bot te rated kva capacity and te switcing ripples. Additionally, to reduce te oversoot current in te capacitor, a small inductance sould be in series wit te capacitor. Te compensation performances are greatly affected by te gain value (G) and oter passive filter parameters (L and C); if te gain is small, te passive filtering will be dominant and te conventional problems of passive filters will appear because of te decrease in te ybrid filter bandwidt. Tis leads some to say tat te total current armonic distortion (ITHD) decreases if te gain increases and larger gains improve te ybrid filter compensation performance. Finally, if te passive elements are not properly selected, te active filter gain must be substantially increased to maintain te same compensation performance. Tus, te optimal coice of te tree variables (C, L and G) is treated as a nonlinear programming problem. Terefore, te main contribution of tis paper can be summarized as using an optimization metod to ascertain te optimal ybrid active filter gain value and oter passive parameters, in order to overcome te observed difficulties in te ybrid filter design wen guessing te initial feasible values of te parameters. Te optimization package FFSQP is cosen from among te many sequential quadratic programming packages for te proposed optimal design because of its advantages. It as te ability to acieve an improvement in solution accuracy, provides convergence to te global solution, and is considered to be a well-built and rapid metod for solving minimization or maximization of nonlinear optimization problems, subject to general constraints [6], [15] [16]. III. HYBRID POWER FILTERS FOR HARMONIC COMPENSATION Figure 1 sows te system configuration of te ybrid compensation required for armonic suppression and reactive power compensation for an industrial power system. Te ybrid active power filter is based on a tree-pase voltagesource power converter, using IGBT switces connected in parallel wit te utility grid, and a set of tuned filters or simply a single tuned filter according to te system requirements [17]. Te tuned filter is used to decrease te capacity of te power converter, wic enables te active power filter to be used in a ig-power situation [18]. Te voltage-source converter is usually used rater tan te current-source converter because it as iger efficiency, lower cost, and is smaller in size tan te current converter. Moreover, reference [8] clarifies tat te IGBT module is more suitable for te voltage-source converter because a freeweeling diode is connected in antiparallel wit eac IGBT. Tis means tat te IGBT does not need to provide te capability of reverse blocking in itself; tus, bringing more flexibility to te device design wit a compromise among conducting and switcing losses and sort-circuit capability, tan wit reverse-blocking IGBT. Te power converter of te ybrid power filter is establised to mitigate te flowing armonic current. It improves te filtering caracteristic of its tuned filter by injecting a voltage armonic waveform at its terminals proportional to te armonic component of te supply current wit amplitude equal to VH G*ISH Te active power filter is considered to be a controlled voltage source V H, were (G) is te controlled gain of te dependent source, and it is designed to equal zero at te fundamental frequency; in oter words, it acts as a virtual armonic resistor in series wit te mains impedance at te armonic frequency causing enlargement in te impedance,

3 3 and ence, te power converter can suppress te armonic current due to te virtual armonic resistor inserted [17] [18]. Tis means tat te ybrid power filter performance can be controlled by adjusting te gain value, causing a notable reduction in te total armonic distortion (ITHD) of te source current. Because of te series combination of passive and active filters, a considerable reduction of inverter power rating is acieved by decreasing bot te line current and line-to-line voltage. In tis topology, te fundamental frequency component voltage drops on te capacitor of te passive filter as it presents ig reactance for low frequencies. At iger frequencies, te voltage drop on te capacitor is low. As te fundamental component voltage drops on te capacitor, te inverter as to work against a lower line voltage (dominant fundamental frequency component). Tis means tat te required voltage rating of te inverter is significantly reduced. Fig.. Single pase equivalent circuit for te proposed HAPF for armonic current source Recalling reference [6], te Tevenin voltage source representing te utility supply voltage and te armonic current source representing te nonlinear load are: v S(t) v SH(t) (1) i L(t) i LH(t) () Te t armonic Tevenin source impedance is: ZSH RSH jx SH (3) and te t armonic load impedance is: ZLH RLH jx LH (4) or by admittance: Y G jb (5) LH LH LH Te model sown is satisfactory were te VTHD is less tan ten percent [19]. After some derivations for te studied system sown in Figure, te main compensated system indices analyzing te system performance would be as follows. Te compensated utility supply current (I SH ) is given as: VSnRLn ILnRC jvsn XLn XFn ILnXC ISn R GR R X X j X GX X R X TLn Ln C Sn Fn TLn Ln C Sn Fn Fig.1. System configuration of te proposed ybrid compensation Tis topology performs well, wile considering load nonlinearity. However, a more complicated situation occurs wen considering bot source and load nonlinearities, because tis often involves various conflicting objectives and constraints; terefore, sequential quadratic programming is used. IV. COMPENSATED SYSTEM CONFIGURATION In te proposed system, a controlled voltage source, representing a conventional active power filter, is connected in series wit a single tuned passive filter, as in Figure, for a power system feeding a armonic-current type nonlinear load. Te compensated load voltage (V LH ) is given as: E jf V LH C jd (7) were: AV R I X X, SH LH LH LH FH BVSH XLH XFH ILHRLHX FH, C RTLH GR LH (XLH X SH )X FH, D X GX R R X, TLH LH LH SH FH X X C C E VSH GRLH XLH XL ILHXTLH X L, X X so tat: R R R X X, C C FVSH RLH XL GXLH ILHRTLH X L. TLH SH LH LH SH X R X R X. TLH LH SH SH LH Because of te inverse proportionality between te gain (G)

4 4 and te compensated utility supply current (I SH ), as sown in (6), increasing te gain G to muc larger values results in a reduction in te source impedance effect on te filtering caracteristics of te passive filter; tus, reducing te source armonic current to its minimum value. Additionally, no amplification occurs in te armonic current at te different resonant frequencies because te active filter acts as a damping resistance [18]. On te oter and, tis situation does not agree wit te compensated load voltage, as sown in (7). Oter system performance indices can be given by: Te compensated load power factor (PF): GLHVLH P L PF (8) VI I V L S SH LH Also, te compensated load displacement power factor (Dpf): PL1 Dpf (9) VL1IS1 were subscript 1 represents te fundamental component. Te transmission losses (P LOSS ): P I R (10) LOSS SH SH Te transmission efficiency (η): GLHVLH P L P I R G V S SH SH LH LH (11) Te compensated VTHD at te load terminals: VLH 1 VTHD (1) VL1 Similarly, te ITHD for te utility supply current is given as: ISH 1 ITHD (13) IS1 Usually, current distortion is muc iger tan te voltage distortion. Tis mirrors te basic concern of IEEE , in wic te iger ITHD reflects te VTHD, leading to its increase [6]. Tis idea leads some to define armonic pollution as a function of ITHD; owever, according to [0], te armonic pollution formula (HP) can be approximated and given by: (14) Te fitness of te power armonic filters for bot armonic currents and voltages can be evaluated from suc a measurement. V. CONSTRAINTS AND OBJECTIVE FUNCTION FORMULATION Most researc papers introduce a predetermined filter feedback gain and ten build all te system performance on it. Additionally, te effect of increasing gain on te utility armonic current distortion and on te resonance, wic may occur between te supply and te passive elements, are usually discussed under te condition of sinusoidal supply voltage. Reference [1] presented a new metod based on te limitation of te gain value to certain values due to te stability problems of te system. Tis paper introduces a different topology in wic tere is no pre-determination of te filter feedback gain, but a searc for te optimum, wic leads to te optimum results required, wilst taking into account compliance wit IEEE Standard for armonic currents. Te constraints may be detailed as follows []: A) Source nonlinearity Represented in te source armonic currents as (I SH ) and voltages as (V SH ). B) Load nonlinearity Represented in armonic load currents as (I LH ) and voltages as (V LH ). C) IEEE Standard According to IEEE , VTHD for voltage level up to 69 kv is less tan or equal to 5.0%. Also, ITHD sould be limited to a standard percent according to te system (I SC /I L ) ratio. D) Load power factor Maintaining a given load power factor at a specified range is desired, 90% PF 95%. E) Parameter constraints Te ybrid active power filter (HAPF) compensator parameters (X C, X L, and G) are manipulated as continuously constrained to lie between specified bounds. Te selected numerical value ranges are given in oms as: 0.00 G 0.00, 0.00 X C 10.00, 0.00 X L Tus, te object functions considered in te optimal design of te HAPF complying wit te former constraints are presented as follows: Minimize VTHD (X C, X L, G) subject to: VTHD (X C, X L, G) 5%. 90% PF (X C, X L, G) 95%. If te VTHD acieves te specified value wilst complying wit te oter constraints, te objective function is redirected into minimizing bot te resultant voltage and current total armonic distortion wit parameter values (X C *, X L *, G * ) imported from te VTHD local minimum parameters as follows: Minimize HP (X C, X L, G) subject to: (X C, X L, G) (X C *, X L *, G * ) VI. OPTIMIZATION TECHNIQUE AND THE SEARCH ALGORITHM Recently, references [6] and [16] examined FFSQP searc codes in te field of armonic power filters, and te general searc formulation was attractive because of te simplicity of te sequential approximation in replacing te given nonlinear problem by a sequence of sub problems tat are more easily

5 5 solved. Te most important property of te FFSQP metod is te reduced computation time needed to guarantee convergence to te global solution, even if te initial guess proposed by te user is infeasible for some inequality and/or equality constraint [15]. Te summary of te proposed searc algoritm is demonstrated below: 1. Determine te specifications of te FFSQP subroutine and construct te necessary subroutines to develop te FFSQP [15]; specify te lower and upper bounds for eac parameter in te ranges previously demonstrated.. Substitute te values of X C, X L and G into te objective function, and calculate te minimum VTHD, wilst complying wit te constraints. 3. Run te searc algoritm considering te last values of filter parameters to be te initial values tested at te beginning of eac searc. 4. Te algoritm will stop wen a feasible point is reaced or wen te stop criterion is acieved; tis criterion is te relative variation ( ) in te objective function, and it is defined in te searc algoritm as: After stopping, scan troug te local minimums satisfying te constraints. 6. Calculate te local minimums of te HP corresponding to te predetermined local minimums of VTHD. 7. Scan troug tem in order to ascertain te global solution. 8. Determine te compensator parameter values corresponding to te global solution. Use te obtained optimum values to evaluate some oter functions tat explain te system performance wen installing te proposed filter. VII. CASE STUDIES AND RESULTS Tree case studies of an industrial plant (Table I) were simulated using te FFSQP optimization metod. Te numerical data were taken from an example in IEEE publications [], were te inductive tree-pase loads are 5100 kw and 4965 kvar wit a displacement load power factor of 71.65%. Te 60-cycle supply bus voltage is 4.16 kv (400 volt line-to-neutral). Te sort-circuit capacity is 80 MVA. Te source and load armonics were assumed to be time-invariant quantities and were cosen arbitrarily to ave more armonic content tan present in many previous publications [6], [19]. Also, te load and source resistances are assumed to be frequency independent, suc tat (R LH = R L and R SH = R S ) [6]. Table II sows te uncompensated system results to be defined and compared wit te HAPF compensation results. For te uncompensated system, te existence of a small armonic current can cause very ig voltage distortion, as sown in Case 1 for te clean utility voltage source. Te system under study as been analyzed for different configurations tat sow te system performance wit te HAPF installed. Table III sows te proposed tecnique providing an efficient system performance, resulting in: a reduction of te utility supply current, a lower transmission loss, iger transmission efficiency, iger displacement power factor, and iger load power factor tan in te uncompensated system cases sown in Table II. Furtermore, Table IV summarizes te results indicating te percentage of improvement in te main indices wit reference to te uncompensated system results, illustrating system performance wit te HAPF installed. Additionally, Table V sows te system beavior wen a random guess of te variables under consideration is implemented for Case 3. TABLE I THREE CASE STUDIES OF AN INDUSTRIAL PLANT [6] Parameters and cases Case 1 Case Case 3 R S1 (Ω) X S1 (Ω) R L1 (Ω) X L1 (Ω) V S1 (kv) V S5 (%V S1 ) V S7 (%V S1) V S11 (%V S1 ) V S13 (%V S1 ) I L5 (%I L) I L7 (%I L ) I L11 (%I L) I L13 (%I L ) TABLE II UNCOMPENSATED SYSTEM RESULTS IN THE THREE CASES Parameters and cases Case 1 Case Case 3 PF (%) I S (A) Dpf (%) V L(V) η (%) P LOSS (kw) ITHD (%) VTHD (%) HP (%) TABLE III RESULTS IN THE THREE CASES FOR THE OPTIMIZATION PROCESS FOR THE HAPF Parameters and cases Case 1 Case Case 3 X C (Ω) X L (mω) *10-6 G (Ω) PF (%) Dpf (%) I S (A) V L (V) η (%) P LOSS (kw) ITHD (%) VTHD (%) HP (%) TABLE IV PERCENTAGE OF IMPROVEMENT REFERRED TO THE UNCOMPENSATED SYSTEM IN THE THREE CASES Parameters and cases Status Case 1 Case Case 3

6 6 PF (%) Increases by Dpf (%) Increases by η (%) Increases by P LOSS (kw) Decreases by ITHD (%) Decreases by VTHD (%) Decreases by HP (%) Decreases by TABLE V RANDOM GUESSES OF VARIABLES UNDER STUDY: CASE 3 Parameters Guess 1 Guess Guess 3 X C (Ω) X L (mω) G (Ω) PF (%) Dpf (%) η (%) P LOSS (kw) ITHD (%) VTHD (%) HP (%) It is clear tat te fitted filter causes a significant reduction in te HP percent. Tis can be considered a good sign for te capability of te proposed ybrid power filter in armonic mitigation. Tus, te quality of te electrical system can be improved considerably. Te HAPF as a compromise capability in suppression of te armonic voltage distortion below te standard limits in all cases, as sown in Table III, for te VTHD percent of te compensated load voltage. Additionally, Figures 3 and 4 sow te values of te load armonic voltage components before and after compensation in Cases 1 and 3, respectively. It is obvious tat te resultant values are all well witin standard limits. Fig.4. Harmonic content of te load voltage before and after compensation: Case 3 Moreover, te demonstrated metod comprises less HP of te supply current, compared wit te conventional power filters, wilst maintaining te quality of voltage in its acceptable limits wen considering supply nonlinearities. Te total armonic current distortion value of te compensated supply current is dramatically reduced to a very reasonable limit. Figures 5 and 6 sow te values of te supply current armonic content before and after compensation in Cases 1 and 3, respectively. Fig.5. Harmonic content of te supply current before and after compensation: Case 1 Fig.6. Harmonic content of te supply current before and after compensation: Case 3 Fig.3. Harmonic content of te load voltage before and after compensation: Case 1 Comparing Tables III and V, it is evident tat a random guess of te variables can converge to te optimal solution, as sown in Guess 1, and only a cange in te gain will be required. Also, it can diverge from te optimal solution, or fall in te resonance region, as sown in Guess 3. As sown in Table III, it is obvious for equal sort-circuit capacity systems wit additional utility voltage armonic content, tat a iger HP ratio will be observed at te PCC. Tus, tere are iger transmission losses, iger RMS load voltages, and iger load VTHD levels because of te increase in te armonic content wit respect to te fundamental component. Also, iger transmission voltage drop and increase in te active load power consumption will be noted, wic represents additional loading for te network. As a normal reaction, overall transmission efficiency will decrease. Additionally, because te proposed system consists of a small rated voltage-source active power filter in series wit a passive filter connected to eac pase, no additional switcing filter is required for te current ripples.

7 7 Te ybrid filter bandwidt can be modified by canging te active power filter gain, and larger values of gain (G>1) improve te ybrid filter compensation performance [3], [4]. Figure 7 sows te effect of increasing te active power filter gain on VTHD, ITHD, and HP in te nonlinear problem in Case 3, complying wit te pre-specified constraints, all at a load power factor approximately equal to 95%. It is observed tat iger values of gain improve te ybrid filter compensation capability, especially for te mitigation of current distortion percentage, validating tat te ITHD of te supply current decreases if te gain increases [5], [6]. However, Figure 7 indicates tat no significant improvement is obtained for greater values of gain if it is not related to te VTHD variation. Fig.7. VTHD, ITHD, and HP versus active power filter gain: Case 3 Finally, if te passive elements are not properly selected, te active filter gain must be substantially increased to maintain te same compensation performance. Also, if te active power filter gain is not properly cosen, poorer system performance migt occur, especially wen considering ig supply voltage distortion. To avoid tis difficulty, it is necessary to report te cange in te active power filter gain wit VTHD and ITHD to guarantee better system performance. VIII. CONCLUSION In recent years, muc attention as focused on simplifying te frequently used solutions concerning armonic contamination associated wit low load power factors in power networks supplying nonlinear loads. Different solutions ave been proposed to improve and synopsize te practical utilization of armonic filters. Selection of an adequate solution requires some knowledge of te different topologies to ensure tat it is te appropriate solution for te specified goal, bot tecnically and economically. In tis paper, te proposed power filter mitigates bot current and voltage HP more effectively tan oter metods. 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