Harmonc Detecton Algorthm based on DQ Axs wth Fourer Analyss for Hybrd Power Flters K-L. AREERAK Power Qualty Research Unt, School of Electrcal Engneerng Insttute of Engneerng, Suranaree Unversty of Technology Nakhon Ratchasma, 3 THAILAND kongpol@sut.ac.th Abstract: - The paper presents the DQ axs wth Fourer analyss (DQF) algorthm to dentfy harmonc quanttes for hybrd power flters. Ths algorthm s a combnaton of the advantages of DQ axs method and sldng wndow Fourer analyss (SWFA). Ths paper also presents the harmonc elmnaton by usng the DQF algorthm for both three-phase balanced and unbalanced systems. The results show that the unbalanced system becomes a balanced condton wth successfully reducng the quantty of system harmonc components after completely harmonc elmnaton by usng the proposed algorthm. The results confrm that the DQF algorthm s flexble and sutable n terms of desgn for hybrd power flters. Key-Words: - harmonc elmnaton, harmonc detecton, hybrd power flter, DQ axs wth Fourer 1 Introducton Presently, nonlnear loads are wdely used n ndustres n whch these loads manly generate the harmoncs nto the power system. These harmoncs cause a lot of dsadvantages nto the power system [1,,3,4]. Ths paper represents the new algorthm of harmonc detecton operated wth hybrd power flters for three-phase power systems called the DQF algorthm. Ths algorthm s a combnaton of the advantages of the DQ axs method [5] and the sldng wndow Fourer analyss (SWFA) [6]. The DQF algorthm has been reported snce 7 [7] n whch t s operated wth only the actve power flter to elmnate all harmonc components n the system. Ths paper extends the work n [7] to apply the DQF harmonc detecton wth hybrd power flters for elmnatng some harmonc components dependng on the engneerng desgn and the rest harmoncs can be cancelled by usng passve power flters. Ths s because the co-operaton of both power flters (hybrd power flters) s to reduce the rated of actve power flter as to acheve the lower cost. The hybrd power flter n ths paper s the combnaton between actve and passve power flters Fg.1 The system wth a resstve load connected to a three-phase dode rectfer representng a nonlnear load ISSN: 179-56 665 Issue 11, Volume 3, November 8
n whch the DQF harmonc detecton s operated wth actve power flters to elmnate some harmonc components and passve power flter s for the rest harmonc components. Theore, there are fve cases for studes n ths paper. The frst s to elmnate only the ffth harmonc of the system, whle the second case s the ffth and seventh harmonc elmnaton. The thrd case s for all harmonc elmnatons exceptng the ffth and seventh harmonc components and the fourth case s to cancel all system harmonc components. All four cases are for balanced three-phase power systems. currents ( u,, v,, w, ) for the actve power flter to elmnate system harmonc components. There are four cases for the balanced power system correspondng to Fg.1: Case I: 5 th harmonc elmnaton The dagram to represent the DQF harmonc detecton to elmnate the 5 th harmonc component of the system n Fg. 1 (Case I) s shown n Fg. 3. In Fg.3, three phase harmonc currents are transformed to the space vector currents on the αβo frame by usng (1). Fg. The system wth RL loads connected to three sngle-phase dode rectfers representng a nonlnear load The last case s to elmnate all harmonc components for unbalanced system to show how the power system becomes a balanced condton after completely harmonc elmnaton. The performance ndces of the proposed harmonc detecton are %THD and %unbalance of the compensated power system. The two nonlnear loads n ths paper are the three-phase dode rectfer wth a resstve load and three sngle-phase dode rectfers wth RL loads as depcted n Fg.1 and, respectvely. An deal current source s used to represent the actve power flter. The DQF harmonc detecton provdes the good results n terms of the harmonc elmnaton wth hgh accuracy and ths algorthm also makes the unbalanced system becomng to a balanced condton after completely harmonc elmnaton. Harmonc Detecton va the DQF Algorthm The DQF harmonc detecton n ths paper s the calculaton to defne the three phase erence 1 1 1 α Lu 3 3 = (1) β Lv 3 1 1 1 Lw Then only the currents on α and β axes are transformed to the synchronously rotatng dq frame, ) by usng (). ( dn qn dn qn cos( nt) sn( nt) α = () sn( nt) cos( nt) β where s the fundamental frequency of the system and n s the elmnated harmonc components of order n, n ths case n s set to 5. Consequently, usng (3) and (4) s to determne the dc component of d 5 and q5 called d 5 and q5, respectvely. Adn dn ( kt) = (3) ISSN: 179-56 666 Issue 11, Volume 3, November 8
Aqn qn ( kt ) = (4) where A dn and A qn n (3) and (4) can be calculated by usng (5) and (6), respectvely. Case II: 5 th and 7 th harmonc elmnaton The dagram for the DQF harmonc detecton to elmnate the 5 th and 7 th harmonc components of the system n Fg. 1 (Case II) s shown n Fg. 4. Fg. 3 DQF algorthm for 5 th harmonc elmnaton A A dn qn = N = N N+ N 1 dn k= N N+ N 1 qn k= N ( kt ) ( kt) (5) (6) where T s the samplng nterval, N s the startng pont for computng, N s the total number of sampled ponts n one cycle, and k s the tme ndex. A dn and A qn for the frst perod can be calculated as gven n (5) and (6) so as to acheve the ntal value for the DQF algorthm. For the next perod, these values can be calculated by usng (7) n whch ths approach called SWFA []. A A ( new) dn ( new) qn When A = A ( old ) dn ( old ) qn N [( N 1) T ] dn [( N + N) T] (7) + [( 1) ] N T N qn [( N + N) T] dn qn dn and qn are acheved va the SWFA approach n (7), the values of α n and β n can be calculated by usng (8) and the erence three-phase currents for the actve power flter are defned n (9). These erence currents are used for the actve power flter to generate the compensatng currents nto the system for the harmonc elmnaton. α n cos( nt) sn( nt) dn = (8) βn sn( nt) cos( nt) qn u, v, w, = 1 1 3 1 3 3 1 α n 1 (9) βn 1 It can be seen from Fg. 4 that α 5, β 5, α 7, and β 7 can be calculated from (1)-(8) by settng n equal to 5 and 7, respectvely. Consequently, α F s the current from the combnaton of elmnated harmonc currents on the α axs, whle β s the total njected harmonc currents on the β axs. Then, the three-phase erence currents for the actve power flter can be calculated from α, β, and o by usng (1). u, v, w, = 1 1 3 1 3 3 F F F 1 α F 1 (1) βf 1 Case III: All harmonc components elmnaton exceptng 5 th and 7 th The dagram for the DQF harmonc detecton to elmnate all harmonc components exceptng the 5 th and 7 th of the system n Fg. 1 (Case III) s shown n Fg. 5. In Fg.5, d1 and q1 are the fundamental currents of the system on the dq frame and these currents can be used to calculate all harmonc currents on the dq frame, dh and qh, as gven n (11) and (1), respectvely. These currents on the αβ frame can be calculated from dh and qh. However, ths case s to elmnate all harmoncs exceptng the 5 th and 7 th. Theore, α F and β F can be calculated by (13) and (14), respectvely. The three phase erence currents for the actve power flter can be calculated from α F, β F, and o by usng (1) the same as Case II. = (11) dh d1 d1 ISSN: 179-56 667 Issue 11, Volume 3, November 8
Fg. 4 DQF algorthm for 5 th and 7 th harmonc elmnaton Fg. 5 DQF algorthm for all harmonc elmnaton exceptng 5 th and 7 th Fg. 6 DQF algorthm for all harmonc elmnaton ISSN: 179-56 668 Issue 11, Volume 3, November 8
qh αf βf = (1) q1 q1 = (13) αh βh α 5 α 7 = (14) β 5 β 7 Case IV: All harmonc components elmnaton The dagram for the DQF harmonc detecton to elmnate all harmonc components of the system n Fg. 1 (Case IV) s shown n Fg. 6. From Fg. 6, the three phase erence currents for the actve power flter can be calculated from α, β, and o by F F Fg. 7 The block dagram for generalzed DQF harmonc detecton ISSN: 179-56 669 Issue 11, Volume 3, November 8
usng (1) the same as Case II and III n whch and α h and β F are equal to α h and h α F β, respectvely. The β h are all harmonc currents of the system on the αβ frame. The summary of generalzed harmonc detecton usng the DQF approach n ths paper s shown n Fg. 7. It can be seen from Fg. 7 that the proposed method can be appled to elmnate all harmonc, specfc n harmonc orders or all harmonc exceptng n harmonc order dependng on the desgners for general cases. For the rest harmonc, the passve power flter can be used to reduce the cost of power flter. 3 The Smulaton Results There are fve cases for the smulaton results n whch cases I-IV are for the three-phase balanced system as shown n Fg.1 wth L s = 1µ H and R = 5Ω. The case V s for the unbalanced system as shown n Fg. wth L s = 1µ H, L u = L = L = 1 H, R = Ω, R = 5Ω and v w u R w = 7Ω. Case I: 5 th harmonc elmnaton results The smulaton results for elmnatng the 5 th harmonc components of the system n Fg.1 by usng the DQF harmonc detecton operated wth an deal actve power flter are shown n Fg. 8. v It can be seen from Fg. 8 that the lne currents ( su, sv, sw ) are equal to the load currents ( Lu, Lv, Lw ) durng the frst perod (t=-. second). Ths s because the actve power flter s not operated durng the frst perod. Theore, %THD,u at phase u s equal to.54% as shown n Table 1. However, after t=. second the actve power flter njects the compensatng currents to the system to elmnate the 5 th harmonc (case I) n whch the erence currents can be calculated from the DQF algorthm as explaned n Secton. As a result, the 5 th harmonc n Table 1 s remarkable reduced from.58% to.6%, whle other orders are the same as the one before compensaton. For ths approach, the passve power flter can be used to elmnate other harmonc components dependng on the engneerng desgn so as to acheve the lower cost of actve power flters. Because of elmnatng the 5 th harmonc, %THD,u can be reduced from.54% to 8.44%. Hence, the lne currents after compensaton are nearly snusodal waveform. Case II: 5 th and 7 th harmonc elmnaton results The results for case II are shown n Fg. 9. It can be seen that the lne currents ( su, sv, sw ) after compensated are very close to the snusodal waveform compared wth the results n case I. Ths s because the 7 th harmonc component s elmnated for ths case n whch the 7 th harmonc s reduced from 7.43% to.3% to acheve the smaller %THD,u (4.89%). Fg.8 5 th harmonc elmnaton for the power system n Fg.1 ISSN: 179-56 67 Issue 11, Volume 3, November 8
Fg.9 5 th and 7 th harmonc elmnaton for the power system n Fg.1 Fg.1 All harmonc components elmnaton exceptng 5 th and 7 th Table 1. Harmonc Elmnaton Results for Balanced System case order 5 (%) order 7 (%) order 11 (%) order 13 (%) order 17 (%) order 19 (%) % THD, u before.58 7.43 4.47.5 1.53.67.54 compensated I.6 7.43 4.47.5 1.53.67 8.44 II.6.3 4.47.5 1.53.67 4.89 III.58 7.43.1..5.7. IV.4.7.3.4.1.. ISSN: 179-56 671 Issue 11, Volume 3, November 8
Fg.11 All harmonc components elmnaton results Fg.1 All harmonc components elmnaton results for unbalanced system Table. Harmonc Elmnaton Results for Unbalanced System THD, % THD, v % THD, w % THD, av u, rms v, rms w rms before compensated 17.11.79 4.4 1.38 4.1.58.5 4.71 after compensated (case V).1.8.7.9.85.85.85 % u, %unbalance ISSN: 179-56 67 Issue 11, Volume 3, November 8
Case III: All harmonc components elmnaton exceptng 5 th and 7 th results The results for case III are shown n Fg. 1. It can be seen that the lne currents s not nearly snusodal because the 5 th and 7 th harmonc components are not elmnated for ths case n whch the nonlnear load n Fg.1 manly generates the 5 th and 7 th harmonc components. Theore, the %THD,u s reduced from.54% to.%. Accordng to the results for ths case, t shows that the DQF harmonc detecton s flexble to operate wth actve power flters. Case IV: All harmonc components elmnaton results The results for case IV are depcted n Fg. 11. The %THD,u s very small compared wth the prevous cases because all harmonc components are elmnated. However, ths condton causes hgher ratng of actve power flters and consequently hgher cost. Theore, the hybrd power flter s more powerful n whch t s the combnaton between actve and passve power flters. The proposed harmonc detecton as presented n ths paper can provde the three-phase erence currents for the actve power flter to elmnate some harmonc components and the rest harmoncs can be cancelled by usng passve power flters. Case V: All harmoncs elmnaton for unbalanced power systems Accordng to the results from cases I-IV, the neutral current ( ) s equal to because the N, before system before compensaton s balanced. However, after compensaton, the neutral current ( ) s N, after stll equal to. For ths case, the DQF harmonc detecton operated wth the actve power flter to elmnate all harmonc components for the unbalanced system as shown n Fg. s depcted n Fg. 1. cause the damage n the neutral lne. Moreover, before compensaton, % THD, av s equal to 1.38% as addressed n Table calculated from (16). After compensaton, ths value s extremely reduced to.9% by usng the proposed harmonc detecton wth the deal actve power flter. In addton, t s nterestng that the unbalanced system can become a balanced condton after all harmoncs elmnated completely n whch %unbalance s equal to as shown n Table. Hence, the neutral lne current s because the zero sequence current s used for the DQF harmonc detecton as explaned n secton to acheve the erence currents for the actve power flter to generate the njected currents nto the system. From the lterature survey, there are many researches for the harmonc detecton methods usng artfcal ntellgent (AI) approaches such as genetc algorthm (GA) [8], adaptve lnear neural network (ADALINE) [9], and fuzzy logc [1]. Theore, for the future work, AI technques wll be appled wth DQF algorthm to obtan the better harmonc detecton methods compared wth the reported method n ths paper. 4 Concluson Ths paper presents the DQF harmonc detecton operated wth the actve power flter and passve power flters called the hybrd power flter. The proposed harmonc detecton can be successfully used to calculate the harmonc erence currents for elmnatng some or all harmonc components. After compensaton completely, the harmonc quanttes can be reduced and the system s balanced even through the system before compensaton s unbalanced. Theore, the proposed harmonc detecton s very flexble and sutable n terms of desgn for hybrd power flters. maxmum current devaton from average rms current % unbalance 1% average rms current = (15) 1 %THD, av = %THD, 3 k= u,v,w k (16) As can be seen from Fg. 1, the power system s unbalanced because the magntude of each phase s not the same. The %unbalance as shown n Table s 4.71% calculated from (15). Due to unbalanced stuaton, the neutral current s not zero and t may Acknowledgement The author would lke to thank Mr. Kongpan Areerak, lecturer n the School of Electrcal Engneerng, Suranaree Unversty of Technology, for hs knd suggeston of ths paper. ISSN: 179-56 673 Issue 11, Volume 3, November 8
References: [1] Indrajt P. and Paul J.S., Effect of Harmonc on Power Measurement, IEEE Petroleum and Chemcal Industry Conference, 1989, pp. 19-13. [] Elham B.M., Clarence L.W. and Adly A.G., A Harmonc Analyss of the Inducton Watthour Meter s Regstraton Error, IEEE Transacton on Power Delvery, Vol. 7, No. 3, 199, pp. 18-188. [3] Ho J.M., Lu C.C., The Effects of Harmoncs on Dfferental Relay for a Transformer, IEE Internatonal Conference and Exhbton on Electrcty Dstrbuton (CIRED), Vol., 1. [4] Wagner V.E., Balda J.C., Grfftk D.C., McEachern A., Barnes T.M., Hartmann D.P., Phlegg D.J., Emannuel A.E., Horton W.F., Red W.E., Ferraro R.J. and Jewell W.T., Effects of Harmoncs on Equpment, IEEE Transacton on Power Delvery, Vol.8, No., 1993, pp. 67-68. [5] Takeda M., Ikeda K., Teramoto A. and Artsuka T., Harmonc Current and Reactve Power Compensaton wth an Actve Flter, IEEE Power Electroncs Specalsts Conference (PESC '88). 1988, pp. 1174-1179. [6] EI-Habrouk M. and Darwsh M. K., Desgn and Implementaton of a Modfed Fourer Analyss Harmonc Current Computaton Technque for Power Actve Flter Usng DSPs, IEE Proc.-Electr. Power Appl., Vol. 148, No. 1, 1, pp. 1-8. [7]S. Sujtjorn,,and T.Kulworawanchpong, The DQ Axs Wth Fourer (DQF) Method for Harmonc Identfcaton, IEEE Transactons on Power Delvery, Vol., No. 1, 7, pp. 737-739. [8] S.G. Sefossadat, M. Razzaz, M. Moghaddasan and M. Monad, Harmonc Estmaton n Power Systems Usng Adaptve Perceptrons Based on a Genetc Algorthm, WSEAS Transactons on Power Systems, Vol., Issue 11, 7, pp.39-44. [9] Y. Han, Mansoor, G. Yao, L-D. Zhon and C. Chen, Harmonc Mtgaton of Resdental Dstrbuton System usng a Novel Hybrd Actve Power Flter, WSEAS Transactons on Power Systems, Vol., Issue 1, 7, pp.55-6. [1] A. Ghasem, S.S. Mortazav and R. Kannezhad, Fuzzy Logc Controlled Adaptve Actve Power Flter for Harmoncs Mnmzaton and Reactve Power Compensaton under Fast Load Varaton, WSEAS Transactons on Power Systems, Vol. 3, Issue 5, 8, pp.3-39. ISSN: 179-56 674 Issue 11, Volume 3, November 8