2010 NCSL International Workshop and Symposium

Transcription

1 Impact of Harmonc Current on Energy Meter Calbraton Speaker: Steven Wenzerl, Radan Research, Inc., 852 Fortune Drve, Lafayette, IN, 47905, USA, (765) , Authors: Shannon Edwards, Dave Bobck, and Steven Wenzerl, Radan Research, Inc. Abstract: Ths paper compares and contrasts dfferent methods to quantfy VAR for sngle and polyphase energy meters. The results for the dfferent methods wll be compared n the presence of dfferent realstc harmonc content scenaros, wth sometmes a 0x dfference seen n results between the methods. By understandng the dfferences between VAR methodologes n the presence of harmoncs, we can take the next steps towards metrology consensus and standardzaton on how to measure and calculate them. 1. Introducton As countres update ther energy polcy and nfrastructure and ncrease nvestment n smart grd technologes, there s greater awareness of power and energy measurements. Wth that comes greater awareness of the ncreasng gap between consumed real power (watts) and generated apparent power (VA). Furthermore, as electronc devces become more sophstcated wth ncreased semconductor content, there s a rapd prolferaton of hghly non-resstve and nonlnear loads. In fact, many of these new non-resstve and non-lnear devces are energyconservng devces such as dmmers, energy-effcent motors n new applances, and compact fluorescent lghts that are beng deployed as part of the new energy polces. Hstorcally, reactve power (VAR) has been used to quantfy the gap between consumed real power and generated apparent power of an AC electrc power system [1]. Reactve power comes from 2 man sources: 1. Phase angle dfference between the voltage and current sne waves, prmarly due to non-resstve behavor such as devce nductance or capactance. 2. Waveform dstorton from non-lnear behavor, prmarly due to harmonc content. VAR s easy to determne n the frst case of phase angle (non-resstve) contrbuton va a scalng factor of sn( ); therefore there s consensus among metrologsts and measurement experts on how to quantfy t. However, VAR n the second case due to harmonc currents from non-lnear loads s more complcated. Combned wth the fact that reactve power n general does not transfer energy, there s a lack consensus amongst metrologsts on how to measure and calculate VAR n the presence of harmonc content. Ironcally, the ssue s further compounded by the observaton that compared to older electromechancal meters, newer sold state meters have much smaller measurement error of actve energy (watts) when suppled wth actve harmonc energy [2]. However, the sold state meters have shown wdespread varaton n VAR results, hence a call for for an urgent nternatonal agreement [2]. Because the utltes that produce energy need to buld expensve base or peak generaton plants based on VA and are begnnng to charge consumers based on the VAR component, t s an mportant ssue of far commerce for a consensus to be acheved amongst metrologsts NCSL Internatonal Workshop and Symposum

2 Ths paper wll: Comple and revew the most common VAR calculatons. 9 dfferent ones are dentfed and dscussed. Propose 6 representatve waveforms (theoretcal and actual recorded) wth dfferng levels of harmoncs n them to compare the results of the 9 dfferent VAR calculatons. Contrbutons from harmoncs out to the 100 th order are ncluded. Compare the results of the 9 dfferent VAR calculatons across the 6 dfferent representatve waveforms. Make suggestons for next steps on how to proceed. 2. Complaton and revew of best-known VAR calculatons Because there s no standardzed nomenclature, the names for the methods were created by the authors and are now beng used wthn the ANSI C12.24 commttee. The 9 dentfed VAR calculatons are classfed nto broad types: Pure fundamental calculaton approprate for a pure snusodal whch by defnton ncludes the effects of only the frst harmonc and dscards contrbutons from hgher harmonc orders. Phase shft calculatons. Ths category has 5 varants wthn t: o Integral Phase Shft Method Fxed Frequency o Integral Phase Shft Method Exact Frequency o Dfferental Phase Shft Method o Quarter Cycle Delay Method o Cross Connected Phase Shft Method Vector calculatons. Ths category has 4 varants wthn t: o Vector Method usng VA RMS o Vector Method usng VA Average Respondng o Vector Method usng VA RMS & Fundamental Waveforms A glossary of symbols used n the formulae s gven at the end of the paper Fundamental calculaton VARs for each element are calculated by multplyng the fundamental of the voltage tmes the fundamental of the current tmes the sne of the phase angle between them: ~ ~ VAR = V I sn( θ) Where the fundamental RMS Voltage and Current are calculated: kt kt ~ 1 ~ V = V 2 ~ 1 ~ and I = I 2 kt kt 2010 NCSL Internatonal Workshop and Symposum

3 2.2. Phase shft VAR calculatons The geness behnd ths calculaton type s prmarly hstorcal: Early analog electromechancal meters could only measure actve (real) watthours. By ntroducng a known reactve element (typcally capactor and resstor network) nto the crcut to create a known 90 phase shft on the voltage axs, the watt-hour measurements of the meter could n essence be trcked nto measurng the reactve component. The added reactve element made the reactve porton of the power actve so the meter could measure t, and made the actve part reactve to be nvsble to the meter. Once two sdes (watts and VARs) of the power trangle are known, the thrd (VA) can be easly calculated from the power trangle as shown n Fg. 1 []: Fgure 1 Whle the phase shft method was a resourceful way to make the best use of avalable technology at the tme, ths method has shortcomngs because the selecton of the C and R values are frequency specfc: Although the phase shft was correct, t would cause ampltude dstorton as frequency changed. The prolferaton of the phase-shft technques was the result of future more sophstcated teratons of t to mnmze ts shortcomngs. Wthn the phase shft methods, there are ntegral (ntegraton) methods and dfferental (dfferentaton) methods. The concept s based on: sn cos and cos I.e., ntegratng the voltage axs gves a 90 phase shft. Dfferentaton works n a smlar manner. However: Integraton attenuates the ampltude of the harmoncs Dfferentaton amplfes the ampltude of the harmoncs Wth both, the ampltude dstorton s proportonal to the frequency. So whle the phase shft was acheved, t was at the expense of ampltude dstorton. These methods then renormalze the ampltude of the ntegrated (phase-shfted) voltage to create a voltage whose fundamental voltage would be dentcal n ampltude to the fundamental component of the voltage axs. Orgnally the frequency could not be measured n real tme so a fxed value (60Hz or 50Hz as approprate) was assumed; later the frequency was measured and used n the calculaton or the equvalent R and C values were assgned adaptvely n real tme NCSL Internatonal Workshop and Symposum

4 The equaton for the Integral Phase Shft Method Exact Frequency method s: kt VAR = ω I V kt Substtutng (2 60) or (2 50) as approprate for Method Fxed Frequency. The equaton for Dfferental Phase Shft Method s analogously: 1 kt dv VAR = I kt + ω 2010 NCSL Internatonal Workshop and Symposum gves the formula for Integral Phase Shft The Quarter Cycle Delay Method could be dgtally mplemented wth charge-coupled devces to acheve the phase shftng. Its advantage over the earler ntegral/dfferental phase shft methods s that t doesn t mpact the ampltude. Compared to the ntegraton method, t appeared to perodcally flp the sgn of a gven harmonc s contrbuton, and so more often than not wll make the VAR calculaton be more negatve. Its equaton s: kt 1 VAR = I ( t) V ( t T / 4) kt + Fnally, the Cross Connected Phase Shft Method s based on creatng a voltage that s 90 delayed from the voltage axs and adjustng the ampltude to match the ampltude of the voltage axs nput. The 90 delay s created by subtractng the voltage phase that s 240 behnd from the voltage phase that s 120 behnd. The ampltude s then adjusted by dvdng by. Ths phase shft and ampltude adjustment assumes that the voltages are balanced and spaced 120 apart. VARs for each element are calculated by multplyng the 90 -delayed ampltude-adjusted voltage tmes the current and ntegratng over the fundamental perod: ω kt VAR I [ xv ] kt = Where the 90 delayed and ampltude corrected voltages are: xv1 = ( V2 V ), xv2 = ( V V1 ), xv = ( V1 V2 ) Ths method has been used extensvely n -phase electromechancal meters. Its bggest shortcomngs are: The assumpton of balanced voltages across the phases. Ths s rarely true, gvng the wrong ampltude value n the calculaton. The assumpton that the voltage phases are exactly 120 apart (rarely true). 2.. Vector VAR calculatons These methods are all based on measurng VA and Watts, and calculatng VAR for each phase from the power trangle (Fg. 1):

5 where: VAR = VA 2 WATT 1 VA = V I and WATT = V I kt 2 kt VAR, Vector Method usng VA RMS uses the fundamental and all harmoncs n the calculaton: 1 kt V V kt 2 1 kt = and I I kt 2 = (Eq. 1) and then substtutng nto Eq. 1 and Eq. 2. (Eq. 2) VAR, Vector Method usng VA Average Respondng works smlarly n concept to the Smpson meter wth a D Arsonval meter movement [4]. It s worth a menton for hstorcal reasons: π 2 kt V V 4kT π 2 kt = and I I 4kT = One artfact s that the calculated average respondng VA can be less than the watts value, contradctng the power trangle shown n Fg. 1. Ths s because, for example, a voltage sgnal whch s 0 for some tme as n the case of a dmmer ends up wth a low average value. Hence why the RMS method s better. VAR, Sgned Vector Method usng VA RMS, & Fundamental Waveforms for polyphase meters attempts to prevent cancellng of sgns of dfferent harmoncs by gettng the sgn correct sn( θ ) wth a multplyng factor of : sn( θ ) VAR sn( θ ) = sn( θ ) VA 2010 NCSL Internatonal Workshop and Symposum 2 WATT 2 The rest of the equatons are the same as for VAR, Vector Method usng VA RMS. One practcal and obvous dffculty wth ths method s when =0 and the sgnng factor blows up. L Hôptal s rule [5] must be nvoked n realtme to determne whch nfnte value s smaller.. Waveforms The sx representatve waveforms used to compare the results of the calculatons consst of three theoretcal ones and three actual ones recorded n the feld. Ther names and short descrptons are gven here, wth pctures of them n the followng subsectons: Theoretcal: o Sne wave voltage, Sne wave current -60 lag. Current s laggng voltage, smulatng an nductor present n the load. Ths waveform s used as a realty check all VARs calculatons should be scaled by sn(60 ), or

6 o Sne wave voltage, Phase dmmng 90 conducton angle. Ths represents an energy-conscous consumer usng a lght dmmer at ½ power. o Narrow Current Pulse. Wth the prolferaton of swtchng and Pulse Wh Modulated (PWM) power supples [6], ths type of waveform mght be reflected back from the load to the lne. Actual ones: The Natonal Research Councl Canada (NRC) recorded actual waveforms (WF) at a varety of stes n the feld; labeled them to anonymze them; archved them; and made them avalable upon request. Whle the waveforms may look unbelevable, they are ndeed real. Usng a dgtal frequency transformer, we parameterzed them nto harmoncs components out to 100 th order to run them through varous closed-form VARs calculatons gven n Secton 2. o NRC WF 2. Actual waveform recorded n the feld. Its V and I waveforms are farly symmetrc, wth the V waveform havng smaller hgh frequency spkes and I waveform have larger ampltude, lower frequency harmoncs. o NRC WF Actual waveform recorded n the feld. Its V waveform s asymmetrc, ndcatng the presence of more even harmoncs. o NRC WF Actual waveform recorded n the feld. Its V waveform s mostly symmetrc but has sgnfcant spkes and sags. The I waveform s nearly square, ndcatng many hgh order harmoncs. To better enable comparsons, all waveforms have been normalzed to 1Vrms and 1Arms,.e., 1VArms..1. Sne wave voltage, Sne wave current -60 Lag.2. Sne wave voltage, Phase dmmng 90 conducton angle 2010 NCSL Internatonal Workshop and Symposum

7 .. Narrow Current Pulse.4. NRC WF 2.5. NRC WF NRC WF NCSL Internatonal Workshop and Symposum

8 4. Results and dscusson A graphcal summary of the results comparng the dfferent VARs calculatons for the dfferent waveforms s gven below: Calculated VAR (watts) Sne Wave, 60 Lag Phase Dmmng, 90 Conducton Angle Imagnary, VA < W Narrow Current Pulse Fundamental Waveform Method Integral Phase Shft Method 60 Hz Fxed Integral Phase Shft Method Exact Frequency Dfferental Phase Shft Method Quarter Cycle Delay Method Cross Connected Phase Shft Method Vector Method usng VA RMS Vector Method usng VA Average Respondng Sgned Vector Method usng VA RMS & Fundamental Waveforms NRC WF 2 NRC WF19140 NRC WF16216 Observatons on the results for each of the waveforms are as follows: Sne wave voltage, Sne wave current -60 lag. As expected and hoped, all VARs methods return the same value of 0.866, so ths realty check s passed. Sne wave voltage, Phase dmmng 90 conducton angle. o All ntegral phase shft methods gave the same value of because the ~ voltage waveform used was a pure sne wave (no harmoncs),.e., V = 0 n ~ ~ VAR = V I sn( θ ) for 1. o The vector methods gave notceably hgher values versus the phase-shft methods because the phase-shft methods mss the contrbutons of the harmoncs. o All the vector RMS methods gave dentcal values of However the vector average respondng method was the clear outler wth a much lower value of because the voltage sgnal s 0 for an apprecable tme, causng a lower average value. Narrow Current Pulse. Smlar comparson as the prevous case of phase dmmng: 2010 NCSL Internatonal Workshop and Symposum

9 o All ntegral phase shft methods gave the same value, but t s 0 they totally mssed the energy. Ths s because the voltage waveform used was a pure sne ~ wave (no harmoncs),.e., V = 0 for NCSL Internatonal Workshop and Symposum o The vector methods gave notceably hgher values versus the ntegral methods the ntegral methods were mssng energy contrbutons from hgher harmoncs. o All the vector RMS methods gave dentcal methods of The vector average respondng method was agan the clear outler of the group wth a much smaller value because the voltage sgnal s 0 for an apprecable tme. In fact, ts VAR value was magnary because erroneously VA < Watt n the radcal. NRC WF 2. The RMS vector methods show hghest magntude because they detect the hgher harmoncs on both the V and I axes. The dfferental phase shft method s notceably lower, most lkely because harmoncs wth negatve sgns got amplfed by the dfferental phase-shft method and erroneously over-subtracted from the overall total. The vector average respondng s lower because the I waveform s near zero for an apprecable tme. NRC WF Here s a case wth 0x dfferences between results. The phase-shft methods are erroneously lower because a pure voltage sne wave was assumed and they re mssng the contrbutons from the hgher even harmoncs. Agan the dfferental phase-shft method s lower as t s lkely amplfyng a negatve harmonc and oversubtractng ts contrbuton. NRC WF Fnally, a case where there s dsagreement between the vector VA RMS methods. VA RMS s by defnton usng all postve quanttes, so n ths case the VAR, Sgned Vector Method usng VA RMS, & Fundamental Waveforms (last green bar) accounts for contrbutons from negatve harmoncs and could be more correct. 5. Conclusons Sgnfcant dfferences are seen n VAR results on a varety of waveforms. Dfferences are seen n both sgn and order of magntude, and the agreement gets worse as the harmonc content ncreases. Due to the prolferaton of already-nstalled electrc meters wth the dfferent VARs methods, suggestng or mandatng a sngle standard method and then retrofttng the feld s mpractcal. The best course of acton s for manufacturers, utltes, and consumers to be aware of the dfferences and act accordngly. The core ssue s equty n bllng n the presence of large harmonc content n both the voltage and current waveforms n the power grd. The power trangle (Eq. 1) only works for snusodal waveforms and so s no longer vald. Measurng real consumed power (watts) and reactve power (VARs) separately s n a sense a hstorcal crutch whch started out because the orgnal meters could only measure real power.

10 The technology now exsts to measure meter VA and VA-h at the pont of use. Whle there stll needs to be consensus among metrologsts on VA measurements, that t much more lkely to happen than achevng consensus on VAR measurements. Because VA s more drectly related to actual cost of generaton and more lkely to acheve consensus on ts measurement, t mght make sense to start wth VA and address VARs later. 6. Acknowledgements The authors gratefully acknowledge the excellent nputs from, and dscussons wth, the members of the ANSI C12.24 commttee. 7. References The Regstraton of Harmonc Power by Analog and Dgtal Power Meters, Johan Dresen, Therry Van Craenenbroeck, and Danel Van Dommelen, IEEE Transactons on Instrumentaton and Measurement, vol. 47, no. 1, Feb. 1998, pp Handbook for Electrcty Meterng, 10 th eon, Edson Electrc Insttute, pp. 1-21, Glossary Index represents the th phase n the poly-phase network. =1 sngle-phase, maxmum s for three-phase. V ~ I ~ ˆ V ( h ) ˆ I ( h) = Potental component fundamental (1 st harmonc order) = Current component fundamental (1 st harmonc order) = Potental component for harmonc order (h) = Current component for harmonc order (h) (h) = Phase angle of the potental for harmonc order (h) (h) = Phase angle of the current for harmonc order (h) V = Generalzed potental waveform (fundamental and all harmoncs) I = Generalzed current waveform (fundamental and all harmoncs) = Phase angle between the fundamental potental and current, (1) mnus (1) t = VAR-hour and VA-hour ntegraton nterval measured n seconds T = Fundamental perod k = Number of fundamental perods = Fundamental angular frequency = 2 f 0, where f 0 s the fundamental frequency = Start tme of ntegraton = Generally represents the norm of the wave functon: 1-norm (Average) or 2010 NCSL Internatonal Workshop and Symposum

11 2-norm RMS. X = Absolute value of X bv = Blondel Theorem transformed Voltages bv =, bv 2 = 0, bv = V V2 1 V1 V NCSL Internatonal Workshop and Symposum