On the Use of Harmonc Detecton Algorthms for Actve Power Flterng Control BOUSSAID Abdlfettah, MAOUCHE Yassne, NEMMOUR Ahmed Lokmane, KHEZZAR Abdelmalek Laboratore d électrotechnque de Constantne Département d électrotechnque Unversté Constantne 1, 5, Constantne, Algera abdlfettah.boussad@lec-umc.org Abstract In the present work a techncal revew of several algorthms of harmonc currents compensaton has been presented. The nstantaneous reactve power theory (PQ theory), the Mult-Varable Flter and Synchronous Reference Frame have been analyzed and compared under dstorted and unbalanced condtons. The adopted strategy conssts n frst tme n mposng a constant tme response then the THD of the fundamental sgnal delvered by each method s computed; n second tme the reversal case s consdered; a THD value s mposed then the tme response constant of each method wll be computed. The smulaton results obtaned have been verfed epermentally usng Dspace 114 platform. 1. Introducton The electrc and electronc equpments are very welldeveloped n the recent years; generally those devces consttute non-lnear loads and absorb currents polluted wth harmoncs. Ths fact causes serous problems to the power network sources such as power factor and power qualty degradaton, loses ncreasng, the communcaton nterferences... etc [1]. For that reason, a several and effectve solutons have been provded to permt an optmal, economc and safety operatng condtons of the power dstrbuton networks. One of the most popular solutons to elmnate the harmonc presence s the passve flters []. The prncpal knds of these flters are the sngle-tuned and the hgh-pass passve flters [][]. The frst one s used to flter determned harmonc components or to attenuate ther ampltudes, the hgh-pass flters are used to cancel the hgh frequency ones. Passve flters are also used to provde fundamental reactve power compensaton [4]. Nevertheless ths soluton s not sutable when the mpedance of the non-lnear loads vares; n addton t may form seres and parallel resonances whch wll result n amplfcaton of harmonc currents n the power network [5]. In 1976, Gyugy and Strycula ntroduced the frst power qualty devces; denomnated Actve Flters [6]. Accordng to ther connecton to the network the actve flter can be seres, shunt or combned of these types and passf flters to weaken the harmonc component n the network [7]. Fgure 1 llustrates the confguraton of the shunt actve flter type. The actve power flter (APF) s connected n parallel wth the network and njects n real tme the harmonc components of the currents absorbed by the nonlnear loads connected to the network. Thus, the current provded by the source of energy becomes snusodal. Fgure 1. Shunt actve flter structure. We deal n the present paper wth an mportant part that allows to the APF workng perfectly. We are gong to compare some etracton algorthms whch have been used to detect the harmonc components; frstly we wll begn by the algorthm based on the nstantaneous reactve power theory (PQ theory) [8]; several papers have presented the applcaton of the method; t could be employed for a sngle-phase system [9, 1, 11], for three-phase or for three-phase four-wre systems wth a modfed pq theory [1]. Second, we wll use the synchronous reference frame method whch has many uses too [1, 14, 15], and fnally we end by the FVM flter that could be ntegrated wth the PQtheory [16]. Many crtera have been used n the lterature to evaluate the performance of each method, some crtera use deal/unbalanced source voltages and dstorted/unbalanced load currents [17]; others use non-symmetrcal load and a symmetrcal/unsymmetrcal voltage [18] -[19]. So t s clearly notceable that all APF reference detecton strateges have been compared wth the same condtons but how about the parameters of each algorthm? In ths work, we wll attempt to answer to ths queston and precse whch method s more performer than another by consderng the followng approach: n the frst way we mpose for them the same tme response value then the computed THD% of the etracted fundamentals are compared; n the second way, we mposee a same THD% value then the calculated tme response values wll be compared.. Control Strateges.1. Instantaneous Reactve Power Theory Akag et al. [8] proposed a soluton based on nstantaneous values n three-phase power systems wth or wthout 5
neutral wre, known as nstantaneous power theory or actvereactve (PQ) theory whch conssts of an algebrac transformaton (Concorda transformaton) of the three-phase voltages n the abc coordnates to the αβ coordnates, followed by the calculaton of the PQ values of nstantaneous power components: [ ] vα v β [ α ] β [ 1 1 [ 1 1 1 1 ] va (1) v b v c ] a () Thus, the nstantaneous actve and reactve power are gven by: [ [ ][ ] p vα v β α () q] v β v α β In the general case, each power p and q contan a contnuous part and an alternatve part, whch enables us to wrte: { p p + p (4) q q + q wth : p, q: contnuous components related to the fundamental components of p and q. p, q: alternate components relatng to the harmoncs. The current references are then gven by: [ ] [ ] α 1 vα v β (5) β vα + vβ v β v α ][ p q Fnally, t s easy to obtan the reference currents along the abc aes by the nverse transformaton of Concorda: 1 [ ] a b 1 α c 1 (6) β Fgure shows the current references computaton correspondng to the PQtheory... Synchronous Reference Frame Based Controller (SRF) Ths method generally appled n flterng applcatons [1] conssts n transformng the current from the abc frame to the b c dq frame usng the Park transformaton where ths last beng synchronzed wth the source voltages, so: [ ] d q (7) [ cos(ωt) cos(ωt π ) cos(ωt + π ) ] sn(ωt) sn(ωt π ) sn(ωt + π ) a b As for the theory of the nstantaneous reactve power, the terms d and q contan a DC components and a multple of AC components, such as: { d ī d + ĩ d (8) q ī q + ĩ q The synchronzaton of the currents wth the frequency of the network transforms the fundamental current component nto a contnue component. However the harmonc components undergo a shft n frequency spectrum. The elmnaton of the contnuous component s carred out by a low/hgh-pass flter and the harmonc currents references could be obtaned by: a b c cos(ωt) sn(ωt) ] cos(ωt π ) sn(ωt π ) [ĩd cos(ωt + π ) sn(ωt + π ) ĩq Fgure summarzes the current references computaton correspondng to the SRF method... The Flter Mult-Varable () Hong-scok Song had defned the equvalent transfer functons of the ntegraton n the synchronous references frame as [16]: V y(t) e jωt e jωt U y(t)dt (1) The Laplace form of relaton (1) s epressed by: H(s) Vy(s) U s + jωc (11) y(s) s + ωc In [1] authors had ntroduced a constant k n the transfer functon H(s) to obtan the wth a cut-off frequency, so the prevous transfer functon H(s) becomes: (s + k)+jωc H(s) k (1) (s + k) + ωc Now t s clear that the s smlar to other flters lke hgh Pass-flter or low Pass-flter wth a cut-off frequency ω c and a gan k. c (9) Fgure. Harmonc current references generaton based on the pq theory. Fgure. Harmonc current references generaton based on the SRF method. 54
After some smplfcatons the followng epressons could be obtaned: { α(s) k(s+k) kω (s+k) +ωc α(s) c (s+k) +ωc β (s) β (s) k(s+k) kω (s+k) +ωc β (s)+ c (1) (s+k) +ωc α(s) The scheme relatve to the algorthm based on the s shown n Fg. 4. Several confguratons of the flter were presented n the lterature. It s possble to use t drectly accordng to aes αβ gven by (1) to etract the harmonc components from the current sgnals [],[16].. Smulaton Study The three methods mentoned above have been put n same condtons to show the performance of each technque. Frst, for the same tme response we compare the THD. After that, for the same THD we compare the tme response. In the frst case, we mpose a constant tme response for the three methods and the THD s measured; therefore we took the cut-off frequency ω c 5Hz, ξ.7and k 19 to compute the fundamental references of the rectfer lne currents as a no-lnear load (Fg. 5). The results obtaned are shown n the Fg. 6 and summarzed n Table 1. Table 1. Smulaton results. The THD of each method when the tme response s consdered constant. PQ & SRF ξ.7, ω c 5Hz, LPF HPF k 19 Tme response (s).15.14.19 THD %.746 6..574 Table. Smulaton results. The tme response of each method when the THD s consdered constant. PQ & SRF LPF HPF Parmeters ξ. ξ.7 K 57 ω c 5Hz ω c 5Hz ω c 5Hz THD %.746.7497.716 Tme(s).15.51.446 Fgure 4. Harmonc current references generaton based on the method. FFT sc sb sa - - -.5...4.6.8.1 THD % 7.6. 5 1 15 5 Harmonc order Fgure 5. Load currents (top) and ther normalzed spectrum (bottom). f sa f sa f sa FFT - - -.1..4.8.1.16. THD % constant.7. 5 1 15 5 Harmonc order t(s) LPF HPF Fgure 6. The transent reference of the fundamental component. Top flter, mddle LPF et HPF respectvely wth PQ and SRF methods ther normalzed spectrum (bottom) In the second case, the THD s kept constant at.7% and the tme response calculaton for the three methods s summarzed n Table. Accordng to [] the SRF s certanly a partcular case of the PQ theory, for that n both cases we notced the same results for both methods. We can notced that low pass flter LPF s more perform than the hgh pass flter HPF used wth the PQ and SRF flters. On the other hand, the and the PQ performances can consdered close and are drectly nfluenced by the chosen parameters. The LPF for both methods PQand SRF when an unbalance s ntroduced n the voltage source. Table summarzed the obtaned results where we can see a degradaton of the performance of PQmethods as t uses drectly the unbalanced voltage n ts algorthm. The SFR s not dsturbed, as the pulsaton ω s obtaned usng a PLL and at the last we notced that the performance of the s dsturbed but reman acceptable. 4. Epermental valdaton For the epermental part, the Dspace 114 platform s used, n addton to the rectfer as polluted load (FIG.6). Fgure 8 shows the transent part of the current fundamental etracton. t(s) 55
Table. Smulaton results. The THD of each method when the unbalance n the voltage source s ntroduced. THD % load THD % fundamental etracted PQ SRF Phase1 7.96 18.1 1..89 Phase.9 17.6.7.9 Phase.64.64.71.8 Table 4 gves the THD value obtaned for the dfferent methods when the tme response s consdered constant and the Table 5 gves the tme response when the THD value s constant. Table 6 summarzed the results when the unbalanced s ntroduced on the voltage source. It s clear that the epermental results are n total concordance wth that of smulaton ones. Table 4. Epermental results. The THD of each method when the tme response s consdered constant. PQ&SR ξ.7, ω c 5Hz, LPF HPF K 19 Tme response (s)...1 THD %.849 6.676.8645 Table 5. Smulaton results. The tme response of each method when the THD s consdered constant. PQ&SR LPF HPF Parmeters ξ. ξ.7 K 57 ω c 5Hz ω c 5Hz ω c 5Hz THD %.886.8897.8894 Tme(s).145.989.65 Table 6. Epermental results. The THD of each method when the unbalance n the voltage source s ntroduced. THD % load THD % etracted fundamental PQ SRF Phase1 7.6.46.4.99 Phase.84 19.4.9.59 Phase.44.8.9.46 Fgure 7. Epermental setup for the etracton of the fundamental components wth the dfferent methods. Fgure 8. Epermental results. The tme response of each method when the THD s consdered constant. (top), HPF (mddle) and LPF (bottom) 5. Concluson Ths paper presents a comparatve study of three strateges of harmoncs detecton, the man crtera for the dfferent methods s to have a constant tme response and measured the THD n frst tme, n second tme and for the same THD value the tme response s measured. From the smulaton and epermental results t s clear that the LPF n the case of PQ and SFR s more performer than the HPF and the flter under balanced voltages. On the other hand, the PQ method become obsolete when the unbalance s ntroduced n the voltage source. 6. References [1] Yaow-Mng Chen, Passve Flter Desgn Usng Genetc Algorthms, IEEE Transactons On Industral Electroncs, vol. 5, no.1, Febrary,. [] Darwn Rvas, Lus Moran, Juan W. Don, José R. Espnoza, Improvng Passve Flter Compensaton Performance wth Actve Technques, IEEE Transactons on Industral Electroncs, vol. 5, no.1,no.1,febrary,. [] Aleandre B. Nassf, Wlsun Xu Walmr Fretas, An Investgaton on the Selecton of Flter Topologes for Passve Flter Applcatons, IEEE Transactons on Power Delvery, vol. 4, no., July, 9. [4] Subhashsh Bhattacharya, Deepak M. Dvan, B. Ben Banerjee, Control And Reducton Of Termnal Voltage Total Harmonc Dstorton (THD) In A Hybrd Seres Actve And Parallel Passve Flter System, Power Electroncs Specalsts Conference, 199. PESC 9 Record., 4th Annual IEEE, pp: 779-786, -4 Jun 199. [5] Stan George Dan, Donga Danel Benjamn, R. Magureanu, L. Asmnoae, R. Teodorescu, F. Blaabjerg, Control 56
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