Currents' physical components (CPC) concept in wind farm harmonic current studies

Cu en s’ Physical Componen s (CPC) concep in wind a m ha monic cu en s udies L. Sainz1 and J. Cunill-Solà2 1 Depa men o Elec ical Enginee ing E.T.S.E.I.B, Technical Uni e si y o Ca alonia (UPC) A . Diagonal 647, 08028 Ba celona (Spain) Phone/Fax numbe :+0034 93 4011759/+0034 93 4017433, e-mail: [email p o ec ed] 2 Depa men o Elec ical Enginee ing E.P.S.E.M, Technical Uni e si y o Ca alonia (UPC) A . de les Bases 61-73, 08240 Man esa (Spain) Phone/Fax numbe :+0034 93 8777263/+0034 93 8777202, e-mail: [email p o ec ed] Abs ac . Ve y li le in o ma ion abou ac ual wind a m ha monic measu emen s is a ailable in he li e a u e. This pape analyzes he ha monic measu emen s o an 18 MW wind a m wi h he CPC concep o de e mine i hey a e consumed o injec ed by he wind a m and o s udy he di e en eac i e powe de ini ions. The CPC concep is an app oach o powe heo y ha p o ides a physical in e p e a ion o powe phenomena in elec ical sys ems wi h linea , ime-in a ian (LTI) loads and ha monic gene a ing loads (HGLs) such as wind a ms. Key wo ds Wind powe gene a ion, ha monics, powe heo y. 1. In oduc ion The inc easing numbe o wind a ms wo ldwide causes powe quali y p oblems such as ha monic cu en emissions [1]-[6]. These emissions p oduce ol age dis o ion in ne wo ks, and hei measu emen and inclusion in WT powe ce i ica es a e he e o e equi ed by cu en s anda ds [7], [8]. Knowledge o hese emissions is undamen al o s udy he in luence o wind a ms on ne wo k ha monic dis o ion. Al hough hey a e a well-known opic, e y ew s udies based on ac ual measu emen s ha e been published [2]-[5]. Recen ly, he ha monic cu en beha io o an 18 MW wind a m was in es iga ed om a la ge numbe o measu emen s in [9]. The wind a m ha monic emissions we e s udied, and he in luence o he wind a m wo king poin on hese emissions was ex ensi ely analyzed. In addi ion, he p obabili y densi y unc ions o he ha monic magni udes and phase angles we e discussed and compa ed in de ail wi h analy ical and empi ical dis ibu ions in he li e a u e. Wind a m ha monics and, in pa icula , powe ansmission phenomena can be analyzed by he CPC concep . The CPC concep is cu en ly he mos ad anced o m o powe heo y o elec ic sys ems wi h pe iodic and semi-pe iodic ol ages and cu en s. I explains powe p ope ies o single- and h ee-phase sys ems wi h LTI loads and HGLs [10]-13]. The pape analyzes he ha monic cu en measu emen s in [9] and ela ed powe phenomena by he CPC concep . 2. Wind Fa m Measu emen s A. Wind Fa m The ha monic cu en s o he wind a m in he one-line diag am o Fig. 1 we e ex ensi ely s udied in [9]. The a m consis s o 30x600 kW WT squi el-cage induc ion gene a o s (SCIGs) connec ed o he MV collec o wi h 20/0.69 kV ans o me s. The a ed powe o he wind a m is PN = 18 MW and he a ed cu en a he MV collec o is IN = 522 A. A 110/20 kV ans o me subs a ion connec s he MV and HV busba s. B. Ha monic cu en measu emen s Measu emen s we e ca ied ou a he wind a m MV collec o (Fig. 1) wi h he powe ne wo k analyze AR5−L o CIRCUTOR (Fig. 2) acco ding o he equi emen s o IEC 61400-21 [7] and IEC 61000-4-7 [8] s anda ds. The analyze has a 0.5% ol age and cu en HV Busba MV Busba (ac collec o ) 110 kV 20 kV To al wind a m powe : 10 x 1.8 MW Powe analyze measu emen s ⋅⋅⋅ N = 30 WTs ⋅⋅⋅ 50-Hz S y s em i 20 kV 0.69 kV WT SCIG PN = 600 kW 20 kV 0.69 kV Fig. 1. One-line diag am o he wind a m. accu acy class, a sampling equency su icien o e alua e up o he 63 d ha monic o de and a 1Mb on- boa d memo y o sa e all measu ed o calcula ed pa ame e s o u u e e ie ing. The cu en clamps employed in he measu emen s ha e a o al ull-scale accu acy o 1% wi h a bandwid h o 10 Hz o 5 kHz. The ac i e powe , P, and ol age and cu en wa e o ms, and i, espec i ely, we e eco ded o e a 6-day pe iod wi h a 10-minu e ime in e al be ween eadings, each eco d being he 10-min a e age alue. The long s o age pe iod made i possible o eco d da a o he whole powe ange o he wind a m, and he 10-min a e age alues p o ided su icien accu acy o he ol age and cu en measu emen s. All he eco ded ol age and cu en alues we e s o ed on a ha d disk and ea ed wi h cus omized MATLAB so wa e o ha monic analysis. Thus, assuming ha he magni ude o he cu en s is s a iona y, he Fou ie ans o m was applied o a 20-ms ec angula window p o iding a 50-Hz equency esolu ion. The cu en and ol age ha monics ( h and ih, espec i ely) we e e alua ed up o he i ie h o de (2.5 kHz o 50-Hz sys ems): () 1, ,50 ( ,). h hx h x xx h x i φ ⇒=∠ = =…(1) The wind a m ha monic cu en s and he in luence o he wind a m wo king poin on hem we e analyzed. In addi ion, sca e plo s o he ha monics (magni ude and phase angle) e sus he wind a m ou pu powe we e p o ided and he andom beha io o he ha monics was examined om he expe imen al measu emen s. I could be obse ed ha he dominan ha monics belonged o he low-o de se (in pa icula , he highes we e 5 h and 7 h) and ha a high-o de ha monic pa e n exis ed in he cu en spec um be ween 1.0 and 2.0 kHz. A summa y o he measu emen s in [9] is gi en in Fig. 3 o Fig. 5 conside ing he o al and indi idual ha monic cu en dis o ions as ollows [7]: P/PN (pu) 0.2 0.4 0.6 0.8 10 P/PN (pu) 0.2 0.4 0.6 0.8 10 − 180 0 180 φ i5 (º) φ i7 (º) Fig. 5. Phase angles o he wind a m 5 h and 7 h ha monic cu en s e sus ou pu powe o he o al measu emen pe iod cou se. P/PN (pu) 0.2 0.4 0.6 0.8 10 THDI (%) 0 1 3 2 P/PN (pu) 0.2 0.4 0.6 0.8 10 0 0.4 0.8 1.2 HDI1 (%) 0 1 3 2 HDI5 (%) 0 0.4 0.8 2 1.2 1.6 HDI7 (%) Fig. 4. Wind a m ha monic dis o ion e sus ou pu powe o he o al measu emen pe iod cou se. P/PN (pu) 0 0.2 0.4 0.8 1 0.6 Da e and Time 11.30 7.4.08 23.00 10.30 22.00 9.30 21.00 8.30 20.00 7.30 19.00 6.30 18.00 5.30 8.4.08 9.4.08 10.4.08 11.4.08 12.4.08 13.4.08 0.6 0 1.2 1.8 2.4 3 THDI (%) P/PN THDI Fig. 3. Time cou se o he o al ha monic dis o ion and ou pu powe a io. Fig. 2. Powe ne wo k analyze AR5-L o CIRCUTOR. 50 2 2 NN ,(1,3), h hh h ii THDI HDI h II = === ∑ …(2) whe e IN is he wind a m a ed cu en and ih he undamen al and ha monic magni udes o he cu en a he MV collec o . Fig. 3 shows he ime cou se o he THDI and he wind a m ou pu powe . Fig. 4 shows he sca e plo o he THDI and HDIh (h = 1, 5 and 7) e sus he wind a m ou pu powe . Fig. 5 con ains he phase angle sca e plo s o he mos signi ican ha monic cu en s (i.e., 5 h and 7 h ha monics) e sus he ou pu powe . The ollowing ema ks on he measu emen s can be made: - The undamen al cu en inc eases p opo ionally wi h he wind a m ou pu powe while he ha monic cu en s a y s ochas ically. - In spi e o he andom beha io o wind a m ha monic cu en s, hese a e usually modeled as ixed cu en injec ions due o hei small a ia ion wi h espec o he wind a m ope a ing poin . In acco dance wi h IEC 61000 s anda ds, he magni udes adop ed o ha monic cu en injec ions a e gene ally he 95% non-exceeding p obabili y alues o hese cu en s. - De e minis ic models a e usually based on he a i hme ic sum o he a e age o he 95% pe cen ile alues o measu ed wind a m ha monic cu en s. These models a e he simples ones and compensa e o he lack o in o ma ion abou ha monic cu en phase angles. Ne e heless, hey lead o o e es ima ion o sys em ha monic dis o ion because he andom a ia ion o ha monics (in pa icula hei phase angles) is dis ega ded. In [9], a comple e s udy o he wind a m ha monic cu en s ochas ic beha io was pe o med om he ield measu emen s. The analysis o he wind a m ha monic measu emen s in [9] can be heo e ically suppo ed wi h he CPC concep . In pa icula , he o igin o he ha monic cu en s measu ed in he abo e s udy can be analyzed (i.e. we he hese cu en s a e consumed o injec ed by he wind a m). The CPC concep is an ad anced o m o powe heo y sys ems wi h non-sinusoidal ol age and cu en s [10]-[13]. Thus, he nex Sec ion summa izes some o he powe heo y concep s in oduced by he CPC app oach in he p esence o HGL [12]. 3. CPC in Single-Phase Ci cui s wi h HGLs Le us conside he single-phase ne wo k in Fig. 6, o med by wo subne wo ks, he dis ibu ion sys em and he cus ome load, and he ol age and cu en , ( ) and i( ), measu ed a he c oss-sec ion be ween he dis ibu ion sys em and he cus ome load. I ( ) and i( ) belong o he linea space LT 2, i.e. 2 0 1 () ( ), () ( ,), T x x kT x d x i T =± <∞ = ∫(3) whe e k is any in ege numbe and T, called he pe iod o x( ), is a nonze o eal numbe , hey can be exp essed wi h he Fou ie se ies: 0 1 () 2Re () ( ,), h j h h hh x X Xe x x i ω ∞ =∈Η =+ = = ∑∑ (4) whe e xh( ) is he ha monic o o de h o he quan i y x( ), Η ep esen s he se o ha monic o de s h, including h = 0, o ha monics wi h nonze o complex ms alues . Xh j h h XXe α =(5) The ins an aneous powe a he c oss-sec ion in Fig. 6 is he a e o elec ic ene gy W( ) low om he dis ibu ion sys em o he cus ome load and can be exp essed as a sum o ha monics as ollows: () () ()() () (). hh hh dW p i i d ∈Η ∈Η === ∑∑ (6) The ac i e powe is he a e age alue o he ins an aneous powe o e a single pe iod o he ol age and cu en : * 0 1 () ()() Re cos ( ), hh T h h h hh h h h V I hh Pp i VI T VI P ϕϕαα ∈Η ∈Η ∈Η == = = ===− ∑ ∫ ∑∑ (7) whe e cos hhh h PVI ϕ = (8) is he ac i e powe o he h h ha monic o de . The appa en powe is de ined as he p oduc o he ol age and cu en ms alues: 2 () ( ,), h h x Xx i ∈Η == ∑(9) ( ) i( ) Dis ibu ion sys em Cus ome load Fig. 6. C oss-sec ion be ween dis ibu ion sys em and cus ome load. and i can be exp essed as ollows: 22 2 222 22 222 () () 1 2 , sh s h s h s s S i PQ P PVV V VV PDQ ∈Η ∈Η ∈Η ==   =+ − + =      =++ ∑∑ ∑ (10) whe e Ds and Q a e he sca e ed and eac i e powe in oduced by L. S. Cza necki [13] and sin hhh h QVI ϕ =(11) is he eac i e powe o he h h ha monic o de . The powe de ini ions in oduced in (10) by he CPC concep p o ide be e unde s anding o ene gy low and powe phenomena in elec ic sys ems and s udy p ocedu es o he enhancemen o powe ansmission e iciency and quali y. The e o s in he de ini ions in oduced in powe heo y by di e en au ho s ha e also been cla i ied om he CPC concep , o example he de ini ion o eac i e and dis o ion powe in oduced in 1927 by Budeanu and suppo ed by he IEEE S anda d Dic iona y [14]: 222 sin , . BhhhB B h QVI DSPQ ϕ ∈Η ==−− ∑(12) The physical phenomena ha cha ac e ize he ha monic ene gy lows in non-sinusoidal condi ions a he c oss- sec ion in Fig. 6 can be analyzed om he phase angle ϕ h be ween he ol age and he cu en ha monics, h and ih, a he c oss-sec ion, o om he ha monic ac i e powe Ph (8). Thus, i | ϕ h | ≤ π/2, he e is an a e age componen o ene gy low a he h h ha monic o de om he dis ibu ion sys em owa ds he cus ome load, i.e. Ph ≥ 0. I | ϕ h | > π/2, he e is an a e age componen o ene gy low a he h h ha monic o de om he cus ome load back he dis ibu ion sys em, i.e. Ph < 0. Conside ing he p e ious analysis, he se Η o all he ha monic o de s can be decomposed in o sub-se s ΗA and ΗB (ΗA ∪ ΗB = Η) as ollows A B i o 0, 2 i o 0, 2 hh hh hP hP π ϕ π ϕ ∈ Η≤≥ ∈ Η>< (13) and he ol age and cu en s can be exp essed as AB () () () () ( ,). hhh hh h x x x x x i ∈Η ∈Η ∈Η == + = ∑ ∑∑ (14) Tha is, he consume load can be conside ed as a ecei e o a ha monic sou ce o he ha monics belonging o he sub-se ΗA o ΗB, espec i ely. This (b) (a) h ih Zh jCh Ph h ih eh Zh ZCh Ph Fig. 7. Equi alen ci cui s: a) Fo ha monics h ∈ ΗA. b) Fo ha monics h ∈ ΗB. Da e and Time 11.30 7.4.08 23.00 10.30 22.00 9.30 21.00 8.30 20.00 7.30 19.00 6.30 18.00 5.30 8.4.08 9.4.08 10.4.08 11.4.08 12.4.08 13.4.08 P5 (kW) − 2.5 − 2 − 1.5 − 0.5 0 − 1 P7 (kW) − 1 − 0.75 − 0.5 0.5 0 − 0.25 0.25 P1 (MW) − 25 − 20 − 15 − 5 0 − 10 Fig. 8. Time cou se o he undamen al, i h and se en h ha monic ac i e powe s. decomposi ion allows he ne wo k in Fig. 6 o be desc ibed as a supe posi ion o he wo ne wo ks in Fig. 7 since sub-se s ΗA and ΗB do no con ain common ha monic o de s h (ΗA ∩ ΗB = 0) and he ol age and cu en s belonging o hem a e mu ually o hogonal. In Fig. 7(a) and Fig. 7(b), he cus ome load is modeled as an LTI load and a ha monic cu en sou ce, espec i ely, and he dis ibu ion sys em is modeled as a ha monic ol age sou ce and a passi e ene gy ecei e , espec i ely. 4. CPC in Wind Fa m S udy A. Ac i e powe s udy As men ioned in he p e ious Sec ion, he sign o he ha monic ac i e powe s Ph (8) allows de e mining whe he he wind a m ha monic cu en s occu because o he supply ha monic ol ages o hey a e gene a ed in he wind a m. Thus, Fig. 8 shows he ime cou se o he undamen al and he mos signi ican ha monic ac i e powe s measu ed a he MV collec o o he wind a m. F om his igu e, i can be no ed ha - The ac i e undamen al powe P1 lows om he wind a m back he dis ibu ion sys em because i s sign is nega i e. This powe nea ly coincides wi h he ou pu powe in Fig. 3 because he ha monic powe con ibu ion is small. - The ac i e i h and se en h ha monic powe s P5 and P7 low om he wind a m back he dis ibu ion sys em because hei sign is nega i e, oo. This means ha he measu ed ha monic cu en s a e gene a ed by he wind a m. B. Reac i e powe s udy Fig. 9 shows he ime cou se o he eac i e powe s calcula ed om he de ini ions p esen ed in he p e ious Sec ion [Cza necki, ha monic and Budeanu eac i e powe s, i.e. (10), (11) and (12)]. F om his igu e, i can be no ed ha - The Cza necki eac i e powe Q is always posi i e and i s cancella ion is achie ed only when all ha monic eac i e powe s a e cancelled. - The Budeanu eac i e powe QB is simply he sum o he ha monic eac i e powe s o all ha monics and i s cancella ion does no necessa ily mean he cancella ion o such ha monic powe s. In ac , he physical meaning o he ha monic eac i e powe s [i.e., he ampli ude o he al e na ing componen o he ins an aneous powe (6)] is los in he Budeanu de ini ion. - This undamen al eac i e powe Q1 nea ly coincides wi h he Budeanu eac i e powe because he ha monic powe con ibu ion is small. This undamen al powe co esponds o an induc i e consume and does no change signi ican ly o e he ime cou se, i.e. wi h he di e en wind a m ou pu powe s. 5. Conclusion The pape p esen s he measu emen s o SCIGs wind a m ha monic beha io and analyzes he powe ha monic phenomena om hese measu emen s and he CPC concep . The ha monic cu en injec ed om he wind a m back he dis ibu ion sys em is demons a ed wi h he obse a ion o he ac i e ha monic powe sign. Da e and Time 11.30 7.4.08 23.00 10.30 22.00 9.30 21.00 8.30 20.00 7.30 19.00 6.30 18.00 5.30 8.4.08 9.4.08 10.4.08 11.4.08 12.4.08 13.4.08 Q (M a ) 0 2 8 4 6 QB (M a ) −8 −6 0 4 8 2 −4 −2 6 Q1 (M a ) −8 −6 0 4 8 2 −4 −2 6 Q5 (k a ) −16 −14 −8 −4 0 −6 −12 −10 −2 Q7 (k a ) −3 −2.5 −2 −1 0 −1.5 −0.5 Fig. 9. Time cou se o he eac i e powe s. The eac i e powe is calcula ed om i s di e en de ini ions and he esul s a e discussed and compa ed. Acknowledgemen This esea ch is ca ied ou wi h he inancial suppo o g an DPI2010-15448, which he au ho s g a e ully acknowledge. Re e ences [1] S. A. Papa hanassiou and M. P. 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