Apparent Power and Power Factor Measurement by Using FPGA-based Chip Considering Nonsinusoidal and Unbalanced Conditions

Transcription

1 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms pparnt Powr and Powr Factor Masurmnt by Using FPG-basd Cip Considring Nonsinusoidal and Unbalancd Conditions HU-CHEN WNG Dpartmnt of Computr and Communication Enginring aipi Collg of Maritim cnology aipi, aiwan scwang@mail.tcmt.du.tw CHI-JUI WU, Dp. of Elctrical Enginring, National aiwan Univrsity of cinc and cnology aipi, aiwan cjwu@mail.ntust.du.tw HENG-WEN YNG Dp. of Elctrical Enginring, National aiwan Univrsity of cinc and cnology aipi, aiwan bstract: - Load caractristics of armonic and unbalanc can not b xprssd in t traditional apparnt powr and powr factor wic only considr t fundamntal and tr-pas balancd sinusoidal conditions. is papr utilizs t Xilinx partan- FPG (XC500-4FG676) cip to dvlop t platform to implmnt t calculation mtods of apparnt powrs and powr factors. is papr discussd t ffctiv powr and powr factor, t aritmtic powr and powr factor, and t fundamntal powr and powr factor. Modlim is usd at first to simulat t calculation of apparnt powrs and powr factors to nsur t accuracy of timing and function. sarc rsults sow tat t dsignd cip can comput accuratly t apparnt powrs and powr factors considring t ffcts of nonsinusoidal and unbalancd conditions. Ky-Words: - FPG, oc, Powr Factor, Harmonic, Unbalancd Powr ystm. Introduction valu of powr factor gnrally is an important pnalty factor in t rvnu of lctricity customrs. Howvr, t traditional powr factor dfinition always assums tat t load condition is sinusoidal. ffcts of load unbalanc and armonic distortion ar nglctd. It as bn rportd tat if traditional lctro-mcanical mtrs ar usd in circumstancs of nonsinusoidal and tr-pas unbalancd voltags or currnts, t rrors can rac 0%~0%[]. In rcnt yars, tr ar many discussions rgarding t powr dfinitions and calculations [-7]. vral dfinitions ar givn in t IEEE td. 459, suc as ffctiv apparnt powr, aritmtic apparnt powr, and vctor apparnt powr. inc armonic pollution, load unbalanc, and ractiv powr fluctuation could affct t powr factor valus of customrs, six diffrnt dfinitions of powr factor valus av bn invstigatd for t sam rcordd masurmnt data of customrs in [8]. diffrnt rsults of calculation ar dpndnt on t load caractristics. In [9], it is sown tat t currntly usd apparnt powr dfinitions, namly t ritmtic and t ctor, bot lack an important proprty. inc good dfinitions of apparnt powrs and powr factors may wll rflct t practical situations of tr-pas unbalancd and non-sinusoidal circuits, t ffctiv powr, ffctiv powr factor, aritmtic powr, and aritmtic powr factor ar invstigatd in tis papr. calculation algoritms will b implmntd by using a FPG-basd cip. ffcts of nonsinusoidal and unbalancd conditions ar considrd. Powr Factor Dfinition. ingl-pas systm For a singl-pas load undr sinusoidal condition, t instantanous voltag and currnt ar, rspctivly, v(t) sin( ωt+ α) () i(t) Isin( ωt+ β) () IN: IBN:

2 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms Hnc t apparnt powr, activ powr, and ractiv powr ar, rspctivly, I () P Icosθ (4) wr θ α β is t pas angl diffrnc btwn voltag and currnt. Q Isinθ (5) P P (6) P + Q Wn a singl-pas systm is undr non-sinusoidal situation, t instantanous voltag and currnt valus can b v( t) + sin( ω +α ) (7) t 0 ( t) I + I sin( ω +β ) i t 0 wr 0 avrag voltag I 0 avrag currnt, rms valus of armonic voltags I, rms valus of armonic currnts α pas angls of armonic voltags β pas angls armonic currnts root man squard (rms) valus ar giv by 0 M 0 I M I (8) (9) (0) apparnt powr, activ powr, and ractiv powr ar M M () P I cos( α β ) () 0 ( α β ) Q I sin () B n t powr factor is dfind as P P (4) P + QB Bcaus P + Q. r is a dfinition of t distortion powr as D P Q (5) B. r singl-pas systm () ritmtic apparnt powr and aritmtic powr factor ar, rspctivly + + I + I + I (6) P B (7) () Effctiv apparnt powr and ffctiv powr factor ar, rspctivly I (8) P (9). In a tr-pas four-wir systm Effctiv currnt I + I+ I + IN I Effctiv voltag [ ( ) ( )].4 In a tr-pas tr-wir systm Effctiv currnt I Effctiv voltag I + I+ I (0) () () + + () 9 fundamntal apparnt powr and fundamntal powr factor ar, rspctivly + + I + I + I (4) P (5) r ar tr dfinitions for t avrag powr factor (a) avrag aritmtic powr factor P( t) (6) ( t) (b) avrag ffctiv powr factor P t ( ) ( t) (c) t avrag fundamntal powr factor P( t) ( t) (7) (8).5 Evaluat of armonic and unbalanc load ffctiv voltag and currnt of fundamntal componnts of t tr-pas four-wir systm ar givn by [ ( ) ( )] (9) I+ I+ I+ IN I (0) os of t tr-pas tr-wir systm ar givn by () IN: IBN:

3 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms I+ I+ I I () fundamntal ffctiv apparnt powr is I () Wr N is t nonfundamntal ffctiv apparnt powr. (4) N normalizd nonfundamntal ffctiv apparnt powr is N N (5) Wn tr is an unbalancd tr-pas situation, t fundamntal positiv-squnc apparnt powr is ( ) ( ) I P + Q (6) wr + ( + a + a ) I ( I + ai + a I ),a unbalancd fundamntal apparnt powr is + ( ) U (7) normalizd fundamntal unbalancd apparnt powr is U (8) U + tructur of imulation ystm. Matlab imulation tructur simulation block to gnrator t tst data is dvlopd by using t imulink and im Powr ystms, wic work togtr wit t MLB [0]. simulation modl is sown in Fig.. r ar four givn loading cass in invstigating t tr-pas systm as sown in abl and abl, basd on t proprtis of fundamntal powrs and armonic currnts. 0 rs BLE r-pas load cass Load Cas Cas Cas Cas 4 catgory U () 0 0~00 0 0~00 N () 0 0 0~00 00 Loading Condition s balancd unbalanc d inductiv inductiv inductiv witout armonics witout armonics balancd unbalancd Wit armonics inductiv Wit armonics. Matlab simulation procdurs. 0 (lin-to-lin) symmtrical tr-pas voltag sourc block is usd.. tr-pas loads ar composd of sris LC load blocks and t armonic currnt sourc blocks. sris LC load blocks can b assignd t fundamntal activ and ractiv powrs. n it is to us t sim command to adjust unbalanc lvl and armonic lvl.. instantanous lin-to-lin voltags and lin currnts of t tr-pas cass can b obtaind by t masurmnt blocks. sampling rat is 840 sampl/scond. 4. n t instantanous voltags and currnt valus ar snt to calculat t valus of apparnt powr and powr factors. Bcaus float-point calculations nd larg M capacity and long opration tim, t instantanous voltag and currnt valus ar mappd to intgral valus. procdurs ar as follows: () Normalizing to pr-unit valus rms valu of t voltag is 0 and tat of t fundamntal currnt is 4.45 in cas, so tat all instantanous valus ar dividd by t rms valu. () n all pr-unit valus ar multiplid by 000 to incras t ffctiv bit numbr in FPG. () calculation rror by FPG is dfind as givn valu(matlab)-calculatd valu( FPG) (%) 00 givn valu( Matlab) ε (9). FPG imulation tructur In calculation of t fundamntal componnts, t FI filtr is usd to obtain t fundamntal frquncy componnts and rjct armonic componnts. impuls rspons of t filtr is computd by Matlab. Fig. r-pas four-wir simulation modl BLE Load paramtr oltag f (Hz) P (W) Q () Load 0() Inductiv IN: IBN:

4 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms Fig. ystmatic structur diagram of calculation (d) componnts, t armonic distortion is disrgardd. rfor, t valus ar qual to tos in Cas. analytical rsults rval tat. igr t armonic distortion is, t lss and ar. Cas 4 simultanously considrs t ffcts of armonic distortion and unbalanc. om powr factor valus ar givn in BLE 7. analytical rsults rval tat U (%) Fig.4. vs U () in Cas Fig.5. vs N (%) N () in Cas. Fig. flowcart of FPG dsign circuit 4 Calculation sults Figs. 4-6 sow t trnd of, and vrsus U and N. utilization conditions of FPG ar givn in BLE -5. om obsrvations can b obtaind. (a) In Cas, t tr-pas systm is balancd and witout armonic loads. powr factor valus ar givn in BLE 6. o t valus of tr powr factors ar t sam. (b) In Cas, t tr-pas systm is unbalancd but wit armonic loads. distortion powr is zro. Bcaus and do not drop wit U, ty do not rflct t unbalanc dgr. Only drops wit of U, so tat it can rflct t ffct of unbalanc dgr. analytical rsults rval tat. (c) Cas considrs t ffcts of armonic distortion. analytical rsults rval tat sinc only considrs t fundamntal U (%) Fig.6. vs U () in Cas 4. BLE Utilization conditions of FPG in calculating ffctiv powr factor Logic Utilization Usd vailabl Utilization lic Flip Flops LUs lics 77 0 IOBs MUL Clk 8 Global iming Constraints Priod Offst in Offst out.4(ns) 4.899(ns) 8.896(ns) IN: IBN:

5 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms BLE 4 Utilization conditions of FPG in calculating aritmtic powr factor Logic Utilization Usd vailabl Utilization lic Flip Flops LUs lics 4 6 IOBs MUL Clk 8 Global Priod 9.87(ns) iming Offst in 4.899(ns) Constraints Offst out 7.4(ns) BLE 5 Utilization conditions of FPG in calculating fundamntal powr Logic Utilization Usd vailabl Utilization lic gistrs LUs lics IOBs MUL Clk 8 Global iming Constraints Priod Offst in Offst out.0(ns) 0.6(ns) 8.59(ns) BLE 6 Powr factor valus in Cas Matlab FPG Error( ) Conclusion calculation of apparnt powrs and powr factors ar implmntd in FPG considring t ffcts of armonic and unbalancd conditions. lot of algoritms ar writtn into IP on FPG. calculation rsults of powr factors av t avrag rror about 0.5. In t FPG cip utilization rats, t calculation procdurs of fundamntal powr factor ar t igst, and t calculation mtod of aritmtic t lowst. In calculating tim of t procdurs of t aritmtic factor is t fastst. rsults rval tat t FPG cip can b usd to calculat t powr factor valus accuratly. frncs: [] IEEE Working Group on Nonsinusoidal ituations: Effcts on Mtr prformanc and Dfinitions of Powr, Practical dfinitions for powrs in systms wit nonsinusoidal wavforms and unbalancd loads: a discussion, IEEE rans. on Powr Dlivry, ol., No., 996, pp [] P.. Filipski, Y. Bagzouz, and M. D. Cox, Discussion of powr dfinitions containd in t IEEE dictionary, IEEE rans on Powr Dlivry, ol. 9, No., 994, pp [] IEEE Working Group on Nonsinusoidal ituations, survy of Nort mrican lctric utility concrns rgarding nonsinusoidal wavforms, IEEE rans. on Powr Dlivry, ol., No., 996, pp [4] IEEE td , IEEE rial-us tandard Dfinitions for t Masurmnt of Elctric Powr Quantitis Undr inusoidal, Nonsinusoidal, Balancd, or Unbalancd Conditions, Nw York, 000. [5]. E. Emanul, pparnt powr dfinitions for tr-pas systms, IEEE rans. on Powr Dlivry, ol. 4, No., 999, pp [6] L.. Czarncki, Powr rlatd pnomna in tr-pas unbalancd systms, IEEE rans. on Powr Dlivry, ol. 0, No., 995, pp [7] C. J. Wu,. H. Fu, J. and L. Yn, Powr Factor Invstigation and nalysis of Larg-siz Customrs, rsarc rport, Powr sarc Institut, aiwan Powr Company, 99. [8]. E. Emanul, pparnt powr dfinitions for tr-pas systms, IEEE rans. on Powr Dlivry, ol. 4, No., 999, pp [9] C. J Wu, C. P. Huang,. H. Fu,. C. Zao and H.. Kuo, Powr Factor Invstigation of Elctric rc Furnac Loads: Comparison of IEEE tandard nd Otr Dfinitions, Intrnational Journal of Elctrical Enginring, ol., No., 004, PP.9-0. [0] Lysvski, Enginring and cintific Computation Using MLB, Nw York Wily, 00. IN: IBN:

6 Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms U (%) N BLE 7 om powr factor valus in Cas 4 (%) Matlab FPG ε (%) Matlab FPG ε (%) Matlab FPG ε (%) Error( ) 0.0 Error( ) -0.4 Error() IN: IBN: