Optimal C-type Filter for Harmonics Mitigation and Resonance Damping in Industrial Distribution Systems

Transcription

1 Optimal C-type Filter for Harmoics Mitigatio ad Resoace Dampig i Idustrial Distributio Systems Shady H. E. Abdel Aleem 1, Ahmed F. Zobaa th of May Higher Istitute of Egieerig, Mathematical, Physical, ad Egieerig Scieces, Helwa, Cairo, Egypt ( egyshady@ieee.org) 2 College of Egieerig, Desig & Physical Scieces, Bruel Uiversity Lodo, Uxbridge, Middlesex, UB8 3PH, Uited Kigdom ( azobaa@ieee.org) * Correspodig author: Tel.: Fax: egyshady@ieee.org 1

2 Optimal C-type Filter for Harmoics Mitigatio ad Resoace Dampig i Idustrial Distributio Systems Abstract: Sigle-tued passive filters offer reasoable mitigatio for harmoic distortio at a specific harmoic frequecy with a high filterig percetage, but resoace hazards exist. Traditioal damped filters offer high-pass filterig for the highfrequecy rage, but suffer from extra ohmic losses. C-type filters may operate i a maer similar to the tued filters with low dampig losses ad margial resoace dampig capabilities. Also, they ca be desiged as damped filters with icreased resoace dampig capability. I this paper, a methodology that facilitates sizig for the C-type damped filter parameters for harmoics mitigatio ad resoace dampig i balaced distributio system etworks, is preseted ad discussed usig the impedace-frequecy idex. This idex evaluates the resoace dampig capability provided by the damped filters aalytically rather tha the covetioal graphical method of impedace-frequecy scaig. It shows how to size shut passive filters, while makig a full use of their dampig capabilities. It ca disclose the parallel resoace frequecies of the equivalet system-filter impedace. A comparative study of the ew approach ad a covetioal filter desig approach, which aims to miimize total harmoic curret distortio, is preseted. Numerous simulatio results are provided to clarify the proposed methodology, advatages, ad disadvatages. Keywords: Damped filters, harmoic distortio, optimizatio, reactive power compesatio, resoace. 1. Itroductio Power system harmoics, a importat topic withi the quality of power domai, have bee a area of discussio for decades. Several solutios for mitigatig harmoic distortio i power systems have bee practiced. Ofte whe the subjects of power system harmoic suppressio ad reactive-power compesatio arise ad the ecoomical aspects are take ito accout, most idustrial firms routiely suppose the use of passive facilities. I geeral, passive filters are ot the best kid. They ca cause resoace with source impedace. Also, they are ot adaptable to the variatios i power system etworks. However, they are widely used ad represet the primary iterest of most users, especially for the existig idustrial firms for cotrollig harmoics ad correctio of power factors, because of their simplicity, low cost, ad easy cofiguratio ad maiteace [1 4]. Passive filters ca be classified ito two broad categories: (a) tued ad (b) high-pass filters. There are two mai kids of tued filters as sigle-tued ad double-tued filters [2, 5]. A sigle-tued (otch) filter has high atteuatio for harmoic orders close to its pre-determied tuig frequecy. But, it ca lead to resoace problems i the system [6]. Sice a doubletued filter behaves like two sigle-tued filters i parallel with each other [7], it iherits the same resoace problem, as the sigle-tued otch filter. Typically, high-pass passive filters are divided ito first order, secod order ad third order high-pass filters. Traditioal high-pass filter topologies guaratee high-pass filterig for the high-frequecy rage (basically, the 11th ad 13th harmoics, ad higher), but suffer from extra ohmic losses. Thus, they caot be ecoomically used at low order harmoics (the 5th ad 7th harmoics, ad lower). However, third order C-type damped filters may be applicable i such cases. A C-type passive filter (CTPF) is a alterative approach belogig to the high-pass filters family [5]. It ca atteuate a broad rage of harmoic frequecies geerated by oliear loads [7]. It has two distict advatages compared to tued ad high-pass damped filters. The first is the reduced fudametal frequecy loss compared to other cofiguratios of damped filters, ad the secod is its capability to dampe harmoic resoace that may occur, compared to the tued filters. Ref. [8] itroduced a optimal desig of the CTPF o the basis of miimizatio of the total harmoic voltage distortio (THDV), [9] used it for maximizatio of load power factor (PF), [10] used it to maximize trasformer's loadig capability uder o-siusoidal coditios. However, the itroduced filters were workig i a maer early idetical to the most traditioal series-tued filters, without cosiderig the additioal resoace dampig merits gaied by the C-type facility. The sizig of the parameters of the 2

3 CTPF determies how it operates. The CTPF ca act i a maer early idetical to the sigle-tued filter, the secod-order high-pass filter, or a resoace damper filter with adequate harmoics atteuatio capability. I this paper, a optimal sizig of the C damped filter parameters is itroduced. The proposed desig quatifies its resoace dampig capability aalytically rather tha the covetioal graphical method of impedace-frequecy scaig. For this aim, miimizatio of the frequecy respose idex, which is earlier defied i [5] to evaluate the performace of several passive filter combiatios, is chose as the objective of the proposed desig. The proposed desig decreases the chaces of series ad parallel resoace over a broad rage of harmoic frequecies, avoids overloadig of the passive filter, atteuates the harmoic distortio of the load voltage ad the lie curret waveforms accordig to the limitatios defied i IEEE Stadard 519. Additioally, it decreases the effect of variatios i system impedace (ulike sigle-tued filters), which represets a particular cocer i power system etworks usig passive filters [6]. A comparative study of the proposed desig ad a covetioal optimal filter desig approach, which aims to miimize total harmoic curret distortio (THDI), is preseted usig two study cases. It should be metioed that miimizig THDI is just a example of may covetioal filter desig approaches that exist i the literature, such as maximizatio of PF, miimizatio of THDV, filter loss, ad ivestmet cost [10]. Furthermore, a comparative study of the damped CTPF ad sigletued passive filter (STPF) desigs is preseted ad discussed to highlight the advatages ad disadvatages of the proposed methodology. By defiitio, a STPF is ot a damped filter, it ca offer low impedace oly the tued frequecy. However, it is oe of the most ecoomical types of passive filters that has a low filter loss, ad is frequetly used to provide power factor correctio i additio to harmoic mitigatio i distributio systems ad idustrial applicatios. The Fortra Feasible Sequetial Quadratic Programmig (FFSQP) algorithm has bee employed for the optimal desig of the proposed filters. It depeds o the approach of sequetial approximatio i reistatig the give oliear problem with a set of subproblems that are easier to solve. Additioally, depedig o the degree of compactess ad appropriate selectio of the costraits, trade-offs betwee desig alteratives will be expressively examied, ad the optimizatio process may be stopped after a few iteratios, yieldig a feasible poit. Hece, after determiatio of all feasible local poits, the localized global solutio will be selected. Fially, the most importat advatage of this algorithm is a reductio i the amout of computatio required i order to geerate a ew iterate with high computatioal speed [19]. Exact formulatios of the search algorithm of the FFSQP package are foud i [11]. Furthermore, FFSQP has bee used for damped ad sigle-tued shut passive filter desigs i [8, 12], respectively. 2. Theory of Operatio of the C-type Passive Filters Fig. 1(a) demostrates the equivalet circuit of the CTPF. Based o [7 10], the mai feature of this type of filter which distiguishes it from the secod-order high-pass filter is its auxiliary capacitive reactace X C2 i series with the iductive reactace X L. They resoate at the fudametal frequecy, X L =X C2 =X, bypassig the dampig resistor R d by the series-tued brach, which makes the filter equivalet to a capacitive reactace X C1 coected i parallel to the load, as show i Fig. 1(b), this is why it is commoly called a CTPF, hece, the fudametal power loss of the filter is miimized (theoretically eglected), allowig a CTPF to be tued to a low frequecy, this is the mai differece betwee a CTPF ad a secod order high-pass filter. The capacitive reactace X C1 is calculated from the values of reactive power Q C eeded for power factor correctio ad harmoic filterig, ad the load omial voltage V L [8, 10]. The th harmoic impedace of the CTPF (Z C ), where represets the harmoic umber, is give as 3

4 X jr X Z j R jx (1) C2 d L XC1 C F F XC2 R d j XL where 2 1 R d X R F R d X (2) 2 1 R d X XC1 X F R d X (3) 2 VL X C1 (4) Q C As frequecy icreases, the CTPF possesses a similar respose to the secod-order high-pass filter because of the low value of its auxiliary capacitive reactace X C2 ad the high value of the iductive reactace X L, as show i Fig. 1(c). Cosequetially, the iductive reactace of the filter resoates with its capacitive oe. I such a case, the CTPF is replaced by a resistace, R F, as show i Fig. 1(d). I other words, the th reactace X F of the filter at h equals zero, where h is the filter resoat-harmoic umber, X Fh =0. The value of R F is cosidered by determiatio of the maximum harmoic curret (ρ S ) that is allowed to flow through the supply reactace X S at h ad is a complex quatity [8]. Accordig to [2], covetioal shut passive filters may have a typical ρ S value of with a agle close to 2.6. Accordigly, [8] defied R F as follows: hx S R F (5) S(h) At high frequecies, the iductive reactace icreases rapidly ad most of the filter curret will pass through the resistive brach, which makes the filter behave as a first-order filter, as show i Fig. 1(e). Followig the previous coditios, the CTPF parameters, R d ad X ca be give as follows [9]: X 2 2 C1 hr F R d (6) 2 hrf 2 2 XC1 hr F X (7) 2 XC1 h 1 Also, the filterig percetage (FP) is defied as follows [13]: S FP 100* 1 (8) 4

5 A low ρ S meas a high filterig percetage, if ρ S is set as low as possible, the amout of harmoic curret flowig ito the filter will icrease, due to the small R F, but the filter will have less dampig compared to others with higher values of ρ S, because the dampig resistor R d will have a large value. Roughly speakig, the most advatageous filterig performace icreases the filter resistace R d i order to guaratee that a higher possible part of the elimiated harmoic curret will flow through the filter. Paradoxically, low values of R d will icrease the filter s ability to dampe resoace. Thus, the optimal value of R d should be a compromise betwee the resoace dampig eeded ad the required FP [14]. This leads [15] to defie R d directly as a fuctio of the mai capacitive reactace X C1 ad the filter resoat-harmoic umber h, as follows: X h C1 Rd m (9) where m is a factor that determies the filter parallel dampig resistace. Ref. [15] recommeds that values of m should be less tha 20 to achieve the highest performace of CTPFs. 3. The Cocept of the Impedace-Frequecy Idex Fig. 2 shows the Thevei equivalet circuit of a power system at the filter locatio ad the CTPF to be istalled. The source harmoic currets ad voltages are give as the poit of commo couplig (PCC) are give as the system. The oliear load o the load side is simplified as a curret source. I S ad V S respectively, while the load harmoic currets ad voltages at I L ad V L respectively, as show i the sigle-phase equivalet circuit of Z S (R S + jx S ), Z F (R F + jx F ), ad Z L (R Load, + jx Load, ) are the th Thevei, filter, ad load impedaces, respectively. The th harmoic mai curret I S ad load voltage V L are give respectively as; VS ZF ZL IL ZFZL I S (10) Z Z Z Z Z Z S F S L F L L S S S V V I Z (11) It should be oted that a dash above a respective variable deotes a complex value. Hece, the rms values of the load voltage (V L ), the supply curret (I S ), ad the expressios of THD V ad THD I measured at the PCC, ca be calculated. The true power factor (PF) measured at the PCC is give as P S V I cosφ L S PF= = (12) V I L S The trasmissio power loss (TL) is give as show i (13), where R S is give as a fuctio of the harmoic umber ad the fudametal value of the R S1. 2 TL ISR S (13) The equivalet impedace Z from the viewpoit of the harmoic curret-source o the load side is give as 5

6 Z Z Z S F L Z (14) ZSZF ZSZL ZFZL I I The harmoic curret feedback to the utility-side (assumig a ideal voltage source) is give as S L Z Z S (15) As parallel resoace occurs, Z will be amplified. Hece, the harmoic curret feedback to the utility-side will icrease as implied i (15). Dampig of parallel resoace meas that Z will get lower. Accordigly, the resoace dampig capability of the CTPF, or ay damped filter, ca be preseted usig the impedace-frequecy respose idex (FS) as follows: FS Z (16) 1 FS is calculated from the system frequecy-respose with the filter istalled. It is foud by summig ad groupig values of the impedace-frequecy sca at the th harmoics, as show i (16). Ref. [5] demostrates that the impedace magitudes may be weighted by a factor of (1/) for several filters combiatios as the ijected harmoic currets typically have a (1/) magitude relatioship. Referrig to Fig. 2, the total harmoic equivalet impedace Z T see from the sourceside is a combiatio of the system Thevei impedace F L Z Z, as follows: Z Z Z S F L ZT Z S (17) ZF ZL Cosiderig the load resistace ad reactace large eough [16]; (17) ca be simplified as follows: Z R R j X X (18) T S F S F ad the resultat parallel impedace of filter ad load Whe series resoace occurs, Z T will equal (R S + R F ). This meas that the combied system-filter resistace may preset sufficiet dampig for series resoace ad reduce the associated harmoic curret for high values of R F. Geerally speakig, a high value of FS idicates that the filter has little dampig capability. It may be a idicatio that we eed to fid a alterative approach, such as usig active ad/or hybrid filters. O the cotrary, a low value of FS implies that R d is small, ad thus a high value of R F is expected, providig adequate dampig for both series ad parallel resoaces. Thus, this idex ca be used to quatify the capability of dampig the resoace of the damped passive filters. 4. Formulatio of the Optimizatio Problems Miimizatio of the THD I, measured at the PCC, is selected to represet the covetioal approach for the optimal sizig of the CTPF. O the other had, miimizatio of the FS is used to represet the proposed approach for the sizig of the CTPF parameters as a damped filter with ehaced resoace dampig capability. Both of them are formulated as fuctios of the filter parameters. Hece, the oliear problem formulatios of the desig approaches are demostrated, respectively as follows. 6

7 X C1,X,Rd I C1 d Mi THD =f X, X, R (19) X C1,X,Rd C1 d Mi FS f X, X, R (20) Both the covetioal ad proposed objective fuctios give i (19) ad (20) are subjected to the followig costraits: C1 d 90% PF X, X, R 100% (21) max THDV X C1, X, R d THD (22) V IHD X, X, R IHD (23) max V C1 d V THD X, X, R THD (24) max I C1 d I IHD X, X, R IHD (25) max, I C1 d I max where THD is the maximum permissible THD limit for the cosidered voltage level. V max IHD is the maximum permissible idividual harmoic voltage distortio limit. They are cosidered to be equal 5% ad 3%, respectively, as defied i max IEEE for a voltage level less tha 69 kv [13]. THD is the maximum permissible curret THD limit, ad max, IHD is the maximum permissible idividual harmoic curret distortio limit. It depeds o the short-circuit stregth of I the system uder study as well as the harmoic umber [13]. Besides, for both approaches, compliace of the mai capacitor with the shut power capacitor duties defied i IEEE Stadard [17], is take ito accout. Readers may refer to [8, 12] for the formulatio of the search algorithms usig FFSQP. I V 5. Cases Uder Study ad their Simulated Results Two cases of a balaced idustrial distributio system are cosidered to examie the results of the proposed ad covetioal desig approaches. This typical system is origially take from [13]. Both system cases (Cases 1 ad 2) have: short circuit power capacity as 80 ad 150 MVA, respectively. The 60 Hz lie lie supply voltage is 4.16 kv. For cases 1 ad 2, the system s Thevei source impedace (Z S1 ) are j ad j0.1154, respectively. The cosumer sides of the cosidered system cases have a group of iductio motors, other differet loads, ad thyristor DC drive loads. For the cases without compesatio, the three-phase fudametal harmoic active ad three-phase fudametal harmoic reactive powers measured at the PCC are 5.1 MW ad Mvar. The short-circuit ratio (SCR) of the system uder study is give as ad for cases 1 ad 2, respectively. I both cases, the dpf measured at the same load bus is % laggig. For the sigle-phase equivalet of the exemplary system give i Fig. 2, harmoic compoets of the voltage ad curret sources are give i Table 1. For the ucompesated system, PF, THD V, THD I, ad TL (per-phase) are 71.27, 7.522, 5.776, ad kw for Case 1 ad 71.38, 5.01, 5.91, ad kw for Case 2, respectively. The compesated system simulatio results are give i Table 2. Table 3 shows the optimal size of the proposed filters parameters, specificatios, mai capacitors loadig duties, filterig percetages, ad the impedace-frequecy respose idices. Table 4 shows the performace of the STPF, for the two preseted approaches uder the same coditios i order to show the effectiveess of the proposed CTPF i harmoic mitigatio ad resoace dampe compared to the system usig STPF. Although STPF is ot a damped filter, its iteral resistace added to a optioal exteral resistace i series with the 7

8 iductor may provide margial resoace dampig ad reduce the harmoic curret [18]. Table 1 Harmoic compoets of the supply voltage ad the load curret V S (V) I L (A) , 19, 23, , 31, 35, , 43, 47, Table 2 The system results after compesatio for the CTPF Approach Covetioal Proposed Parameters Case 1 Case 2 Case 1 Case 2 PF (%) dpf (%) I S (A) V L (V) TL (kw) THD I (%) THD V (%) Table 3 The CTPF specificatios for both approaches Approach Covetioal Proposed Parameters Case 1 Case 2 Case 1 Case 2 X C1 (Ω) X (Ω) R d (Ω) Filter losses (kw) m h FP (%) FS (Ω) Mai capacitor duties with respect to omial values V C (%) V C, peak (%) I C (%) Q C (%)

9 Table 4 The system results after compesatio for the STPF Approach Covetioal Proposed Parameters Case 1 Case 2 Case 1 Case 2 X C (Ω) X L (Ω) R (Ω) PF (%) dpf (%) I S (A) V L (V) TL (kw) THD I (%) THD V (%) Filter losses (kw) FP (%) FS (Ω) Mai capacitor duties with respect to omial values V C (%) V C, peak (%) I C (%) Q C (%) The power quality idices after compesatio ad the filter specificatio, which are obtaied for the system with lower (Case 1) ad higher (Case 2) short-circuit capacity with the same harmoic distortio levels, are give i Table 2, Table 3 ad Table 4, respectively. It is see from Table 2 ad Table 4 that the total distortio values of the harmoic currets, which flow through the supply side, have lower magitudes for Case 1 whe compared to Case 2 because of the higher Thevei impedace, which atteuate the curret source harmoics. Thus, it is oted from Table 3 that the filters desiged accordig to both approaches for Case 1 have higher R d ad lower X values, which results i higher filterig capability (or higher FP), lower resoace dampig capability (or higher FS) ad lower filter losses. Additioally, for ehacig the capabilities of harmoic atteuatio ad resoace dampig, it is oted for higher Thevei impedace systems (Case 1) that the proposed filter desig has cosiderably lower values of the tuig harmoic order h ad the mai capacitor reactace X C1 compared to the lower Thevei impedace systems. This is ot the case for the covetioal STPF filter desig. For both approaches, acceptable values of PF ad dpf are achieved, as show i Table 2 ad Table 4. Moreover, remarkable reductios i the values of THD V, TL, ad I S are obvious. The THD I percetages meet the IEEE limits. Besides, it is otable, as show i Table 3 ad Table 4, that the mai capacitors loadig values comply with the IEEE Stadard limits. Thus, all the costraits are satisfied. O the other had, the two approaches differ as give below: The THD V ad TL values observed for the proposed approach are lower tha the correspodig values observed for the covetioal oe i the two studied cases for the preseted passive filters. Additioally, their values observed for the CTPF are lower tha the correspodig values observed for the STPF for the two approaches i the two studied cases. The THD I values observed for the proposed approach are higher tha the THD I values observed for the covetioal oe i the two studied cases. However, the THD I values observed for both approaches comply with the IEEE 519 limits. Fig. 3 shows the simulated results of the compesated supply curret harmoic cotets for both approaches i the two cases for the 9

10 two preseted filters, respectively. Ulike what might be expected i such a case, the proposed CTPF desig is more cosistet with the idividual curret harmoic limits of the IEEE Stadard 519 compared to the covetioal oe, validatig that usig IHD I ad THD I limits i the optimizatio problem as costraits is usually better tha miimizig THD I as a objective fuctio, ad also showig that the filterig percetage is ot a good idex, sice it describes oly the filter effectiveess at oe frequecy umber but does ot describe the behaviour of the filter over a wide frequecy rage. However, this is ot true i the case of multiple-arm passive filters. Additioally, it ca be easily oted i Fig. 3 that the performace of the preseted CTPF ad STPF usig the proposed approach i the higher frequecy rage is more satisfactory tha that of the covetioal desig approach. However, the performace of the proposed CTPF appears more promisig, this is because the proposed CTPF absorbs much a broader rage of domiat harmoics. The proposed CTPF satisfies what is expected from it i the lower frequecy rage, while maitaiig its ability as a high-pass filter i the higher frequecy rage, compared to the covetioal approach ad the traditioal STPF. This is due to the fact that the FS values observed for the proposed approach are lower tha the correspodig values observed for the covetioal oe i the two studied cases. Moreover, the FS values observed for the CTPF are cosiderably lower tha the correspodig values observed for the STPF oe i the two studied cases. The differece betwee the FS values i the two approaches reflects the resoace dampig capabilities of each of them. It should be metioed that this differece was expected, sice the STPFs are ot damped filters. O the other had, the CTPFs attai less atteuatio tha sigle-tued filters for the same tuig frequecy, thus lower filterig percetages are provided with them. For the CTPF, it is evidet that the differece betwee the FS values i the two approaches caot be cosidered trivial. Thus, oe ca cosider that both approaches ca achieve similar performaces i harmoics mitigatio ad power factor correctio, but the proposed approach has a additioal advatage i dampig the series ad parallel resoaces. This is obvious i Fig. 4, which shows impedace-frequecy scas of the magitudes of the equivalet impedaces see from the harmoic source side for both filters i the two cases, respectively. As show i Fig. 4, the dampig resistace of the CTPFs ca reduce the peak of the parallel resoace effectively rather tha shiftig it to a less hazardous frequecy as i STPFs. Additioally, the same figure validates that the impedace-frequecy respose of the covetioal CTPFs ca be very similar to the STPFs, especially for distributio systems havig low shortcircuit capacities. For the STPF, despite it is ot a damped type filter, it is observed that the proposed approach may have a margial credit i dampig the parallel resoace. From the series resoace viewpoit, Fig. 5 shows the impedace-frequecy sca of magitudes of the equivalet impedaces see from the utility side for both filters i the two cases, respectively. It is obvious that resposes observed for the proposed approach have o tedecy to iitiate series resoace compared to resposes observed for the covetioal approach for both filters i the two studied cases. Besides, the proposed approach obviously has a better ability to atteuate a broad rage of harmoic frequecies geerated by oliear loads. However, the proposed CTPFs guaratee that harmoic-resoace risk is o-existet. It must be metioed that the harmoic umber is limited to 20 i Fig. 5 to give a close view of the cocered regio. Ref. [15] recommeds that values of m should be aroud 4 for harmoics mitigatio usig CTPFs, as they may be a suitable passive choice, ad less tha 20 to achieve the highest performace of the damped CTPFs. Recallig the m values give i Table 3, it is 10

11 obvious that the m values for the proposed approach are lower tha the correspodig values observed for the covetioal oe i the two studied cases. Hece, oe may coclude that the CTPF's resoace dampig rises as m ad FS values decrease. From aother viewpoit, the differece i m values observed betwee the two approaches for the system uder study i Case 2 was small, as they have similar resoace dampig capabilities, as show i Figs. 4(b) ad 5(b). Recallig Table 3 ad Table 4 agai, lower values of capacitive reactace or higher reactive power supplied by the filters are observed for the proposed approach, leadig to higher percetages of the true power factor compared to the covetioal oe. Thus, oe ca coclude that CTPFs may eed high reactive-power compared to the STPFs to ehace their harmoic compesatio ad resoace dampig capabilities ad thus to miimize the reactive-powers share of other filters combied with them, if they exist. From the poit of view of filter power losses, values observed for the proposed approach are higher (almost three times more) tha correspodig values for the covetioal approach because of the low values of R d, or the icreased resoace dampig capabilities for the CTPF. Additioally, for the proposed CTPF: Case 1, with the same harmoic tuig order h ad the same capacitor reactace X C1 but with R d varies from 1 till a value correspodig to m equals 20, Fig. 6 clarifies that the smaller the value of FS, the higher the value of eergy dissipated by the filter's resistace is. Thus, oe may coclude that the CTPF's ivestmet cost icreases as the resoace dampig capabilities rise because the eergy loss charges will icrease, due to the icreased loss of the CTPF. However, as m is less tha 20, these losses are still less (two or three times) tha the correspodig losses for the STPF. This is otable i the filter power loss values show i Table 3 ad Table 4 for both filters. Traditioally, passive filters struggle with system impedace chages. Also, a passive filter may sik specific harmoic currets from other eighbourig oliear loads o the same bus or from the power system upstream of the filter. This may cause a overload to the filter, ad the will be ieffective. Moreover, at light loadig coditios, the passive filters also cause problems of voltage regulatio, filter overloadig ad harmoic resoace betwee lie iductors ad shut capacitors istalled o the distributio system [19]. The traditioal solutio i such a case is to discoect the filters durig light load periods. Additioally, dyamic system chages, agig ad temperature effects modify the filter iductor ad capacitace values [20]. Thus, it is importat to aalyze the expected performace of the desiged filters i the presece of some parameter chages. Cosequetly, five tests have bee examied for the preseted filters parameters give i Table 3 ad Table 4: Case 1, as follows: Tests 1 ad 2: cosiderig egative ad positive 25% chage i the Thevei source impedace, respectively. Tests 3 ad 4: cosiderig 75% ad 50% loadig chage, respectively. Test 5: cosiderig positive tolerace of 5% o the capacitors ad 2% o the reactors. Fig. 7 shows the values of the THD V, THD I, ad FS durig the latter tests, where subscript 0 represets the actual system, filter ad load values. It ca be oted i Fig. 7(a) that the performace of the proposed CTPF has the advatages of preservig a acceptable voltage quality, while maitaiig its ability as a resoace damper filter compared to the covetioal oe ad the STPF for both approaches. Additioally, the lowest chage i FS values is provided by the proposed CTPF uder the differet tests, therefore, it decreases the effect of variatios i system impedace. Moreover, it was observed throughout the load perturbatio from full load to half load that the variatio i voltage has bee cotaied withi a regulatio of 3.6%, ad swell i the voltage due to light load coditio has bee averted for CTPF, usig both approaches. Additioally, the values of the mai capacitors loadig duties all comply with the IEEE Std limits. O the other side, the values of capacitor loadig duties for the sigle tued filters did ot comply with the IEEE Stadard limits for the differet 11

12 loadig percetages. This demostrates the ability of the CTPFs to work effectively for load-varyig coditios [7], where sofar traditioal passive filters fall short. It is obvious i Fig. 7(a) ad Fig. 7(c) that the THD I values observed for the proposed approaches are cosiderably lower tha the THD I values observed for the covetioal approaches, i case of half loadig percetage: Test 4. Moreover, the effect of the filter parameters chage is isigificat for the values of the THD V, THD I, ad FS uder the previous tests. Fially, [13] clearly states that most idustrial systems ca be aalyzed with a balaced represetatio. The loads are balaced three-phase loads, icludig the harmoic sources. However, balaced system aalysis is ot valid i may cases such as the use of large sigle-phase oliear loads [21, 22]. Accordigly, small ratig series passive/active filters combied with the proposed CTPF ca be employed to mitigate the adverse effects of ubalaced ad o-siusoidal voltages o the power quality sice they ca be used to adjust PCC phase voltages idividually. The employability of the series passive filters for the harmoic ad ubalace mitigatio will be cosidered i the future works. 6. Coclusio I additio to beig able to deal with high order harmoics, the CTPF is useful to create a resoace-free capacitor. I this paper, a ew use of a impedace-frequecy idex to assess the resoace dampig capability provided by the damped filters aalytically is proposed. The impedace-frequecy idex ca be employed as a idicator to describe the overall performace of the filter ad its resoace dampig capability. I additio to maitaiig harmoic voltage below their limits ad the otable reductio of trasmissio loss values; desig of the CTPF as a resoace damper filter offers a remarkably ehaced capability of resoace dampig, less cocer to parameter variatios ad filter overloadig. This may be useful for varyig load coditios i idustrial applicatios. Fially, more ivestigatios cosiderig the resoace dampig capability provided by the damped CTPF ad its power loss uder ubalaced ad o-siusoidal coditios should be performed. This poit is curretly uder study ad will be preseted i future work. 7. Refereces [1] Sher HA, Addoweesh KE, ad Kha KE (2013) Harmoics Geeratio, Propagatio ad Purgig Techiques i No- Liear Loads. I: Dr. Dyla Lu (Ed.) /53422 A Update o Power Quality, ITech, Croatia - Europea Uio. doi: [2] Das JC (2015) Power System Harmoics ad Passive Filter Desig. Wiley-IEEE Press, Hoboke, New Jersey, Uited States. [3] Abdel Aleem SHE, Ibrahim AM, ad Zobaa AF (2016) Harmoic assessmet-based adjusted curret total harmoic distortio. IET J Eg. doi: /joe [4] Saleh SM, Ibrahiem KH, Eiteba MBM (2016) Ecoomic aspects for multi-step LC compesator with ucertai load characteristics usig geetic algorithm. IET Geer Trasm Dis. doi: /iet-gtd [5] Nassif AB, Xu W, ad Freitas W (2009) A Ivestigatio o the Selectio of Filter Topologies for Passive Filter Applicatios. IEEE T Power Deliver 24: doi: /TPWRD [6] Zobaa AF (2014) Optimal multiobjective desig of hybrid active power filters cosiderig a distorted eviromet. IEEE T Id Electro 61: doi: /TIE [7] Duga RC, McGraagha MFS, ad Beaty HW (2002) Electric Power Systems Quality. McGraw-Hill, New York. 12

13 [8] Abdel Aleem SHE, Zobaa AF, ad Abdel Aziz MM (2012) Optimal C-Type Passive Filter Based o Miimizatio of the Voltage Harmoic Distortio for Noliear Loads. IEEE T Id Electro 59: doi: /TIE [9] Mohamed IF, Abdel Aleem SHE, Ibrahim AM, ad Zobaa AF (2014) Optimal Sizig of C-type Passive Filters uder No-siusoidal Coditios. Eergy Techology & Policy 1: doi: / [10] Balci ME (2014) Optimal C-Type Filter Desig to Maximize Trasformer's Loadig Capability uder No-siusoidal Coditios. Electr Pow Compo Sys 42: doi: / [11] Zhou JL, Tits AL, Lawrece CT (1997) User's Guide for FFSQP Versio 3.7: A FORTRAN Code for Solvig Optimizatio Problems, Possibly Miimax, with Geeral Iequality Costraits ad Liear Equality Costraits, Geeratig Feasible Iterates, TR r5, Istitute for Systems Research, Uiversity of Marylad, College Park, MD 20742, USA. [12] Abdel Aziz MM, El-Zahab EEA, Zobaa AF, ad Khorshied DM (2007) Passive harmoic filters desig usig FORTRAN feasible sequetial quadratic programmig. Electr Pow Syst Res 77: doi: /j.epsr [13] IEEE Stadard 519 (1992) IEEE Recommeded Practice ad Requiremets for Harmoic Cotrol i Electrical Power Systems. [14] Xiao Y, Zhao J, ad Mao S (2004) Theory for the Desig of C-type Filter. I 11th It. Cof. Harmoics ad Quality of Power, ICHQP 2004, Lake Placid, New York, Sept , pp doi: /ICHQP [15] Aravea P, Vallebuoa G, Mora L, Dixo J, ad Godoy O (2009) Passive Filters for High Power Cyclocoverter Gridig Mill Drives. I Idustry Applicatios Society Aual Meetig, IAS 2009, Housto, TX, Oct. 4 8, pp doi: /IAS [16] Zobaa AF, ad Abdel Aleem SHE (2014) A New Approach for Harmoic Distortio Miimizatio i Power Systems Supplyig Noliear Loads. IEEE T Id Iform 10: doi: /TII [17] IEEE Stadard 18 (2012) IEEE Stadard for Shut Power Capacitors. [18] Zheyu Huag, Wilsu Xu, Diavahi VR (2003) A Practical Harmoic Resoace Guidelie for Shut Capacitor Applicatios. IEEE T Power Deliver 18: doi: /TPWRD [19] Akagi H (1996) New Treds i Active Filters for Power Coditioig. IEEE T Id Appl 32: doi: / [20] Piceti P, ad Prado D (2015) Sesitivity of parallel harmoic filters to parameters variatios. INT J Elec Power 68: doi: /j.ijepes [21] Gokoza H, Taski S, Seker S, Ekiz H (2015) A eural etwork based approach to estimate of power system harmoics for a iductio furace uder the differet load coditios. Electr Eg. 97: doi: /s [22] Balci ME, Abdel Aleem SHE, Zobaa AF, ad Sakr S (2014) A Algorithm for Optimal Sizig of the Capacitor Baks uder No-siusoidal ad Ubalaced Coditios. Recet Advaces Elec. & Electroic. Eg. 7: doi: /

14 Figures Fig. 1. Mai features of C-type harmoic filters (a) CTPF (b) CTPF at the fudametal frequecy (c) The CTPF early works as a secod-order filter as the frequecy icreases (d) The CTPF at its resoat-frequecy acts as a resistace R F (e) At higher frequecies, the CTPF early acts as a first-order filter 14

15 Fig. 2. Cofiguratio of the compesated system 15

16 (a) Fig. 3. Harmoic cotets of the supply curret for both approaches usig CTPF ad STPF (a) Case 1 (b) Case 2 (b) 16

17 (a) (b) Fig. 4. The equivalet impedace see from the harmoic-source side versus harmoic umber of both approaches usig CTPF ad STPF (a) Case 1 (b) Case 2 17

18 (a) (b) Fig. 5. The equivalet impedace see from the utility- side versus harmoic umber of both approaches usig CTPF ad STPF (a) Case 1 (b) Case 2 18

19 Fig. 6. Illustratios of the FS idex ad the filter losses i case of variatio of the dampig resistace for the proposed approach usig CTPF: Case 1 19

20 (a) Proposed approach usig CTPF (b) Covetioal approach usig CTPF (c) Proposed approach usig STPF (d) Covetioal approach usig STPF Fig. 7. The THD V, THD I, ad FS values durig the tests: Case 1 (a) Proposed approach usig CTPF (b) Covetioal approach usig CTPF (c) Proposed approach usig STPF (d) Covetioal approach usig STPF 20