The Measurement and Evaluation of Distribution Transformer Losses Under Non-Linear Loading

Transcription

1 IEEE ower Engineering Society General Meeting, Denver CO, June 9, 4 / ESGM 4-7 e Measureent and Evaluation of Distribution ransforer Losses Under Non-Linear Loading Aleksandar Danjanovic,.D., Meber IEEE and Gregory Ferguson, BSc., Life Meber IEEE Abstract Haronic currents, generated by non-linear electronic loads, produce penalty losses in every eleent of an electrical distribution syste. [] ese aronic-related losses reduce syste efficiency, cause apparatus overeating, and increase power and air conditioning costs. [] Haronic currents effectively de-rate existing systes and, wen accoodated, add substantially to te capital cost of new distribution systes. e easureent and evaluation of transforer losses under linear and non-linear load conditions will be discussed. In addition, typical financial benefits tat result fro te application of ig efficiency aronic itigating distribution transforers, under non-linear loading, will be calculated. Index ers efficiency, aronics, non-linear load, penalty losses, transforer losses I. INRODUCION Existing Standards e igest standards for transforer efficiency in Nort Aerican are found in NEMA Standard ublication -, [3] CSA ublication C8.- and EA s Energy Star requireents. e easureent and calculation etods required by tese standards accurately deterine a transforer s losses and energy efficiency, wen it supplies linear resistive and/or inductive loads. e Non-Linear Load Reality Modern electrical distribution systes typically supply a ig percentage of nonlinear electronic loads, particularly in /8-volt systes. As a result, transforer losses increase and energy efficiency decrease. e level of deterioration is a function of aronic voltage agnitudes at a transforer s priary terinals, loadgenerated aronic current agnitudes at its secondary terinals and teir pase relationsips. ere are, unfortunately, no recognized standards for deterining transforer losses or efficiency under tese nonlinear conditions. Misleading Clais A nuber of ig efficiency distribution transforer anufacturers now clai efficiencies tat eet or exceed te requireents of NEMA - and CSA C8.- under severe but unspecified nonlinear loading. Several anufacturers ave even publised teir efficiency test etods. At best, tese clais are isleading since: (i ere is no recognized standard guide for deterining te energy efficiency of a distribution transforer or a standard test etod for easuring its energy consuption under nonlinear load conditions and (ii e anufacturers publised ower-in ower-out Measureent Metod, wic boasts ±.3% revenue class instruentation accuracy and ±.% watteter accuracy, will, in reality, produce an error of ±.5%,wen easuring te efficiency of a transforer under linear or nonlinear loading. As a result, teir claied efficiency of 98%, for a 75kVA transforer, ay, in fact, be only 96.5%. II. RANSFORMER LOSSES Haronic voltages and currents increase transforer losses. More specifically, aronic voltages increase losses in its agnetic core wile aronic currents increase losses in its windings and structure. e effect of aronic voltages is relatively sall since losses in te agnetic core are norally only % of te winding losses. A transforer s penalty losses are ainly due to aronic currents. Unfortunately, aronics currents are typically uc iger in /8-volt subsystes. ransforers operating at tese voltage levels require special consideration. IEEE SD and IEEE SD categorize transforer losses as No-Load Losses ( NL or Excitation Losses and Load Losses ( LL or Ipedance Losses. e su of tese losses is referred to as otal Losses ( LOSS : LOSS ( NL LL Excitation Losses [4] are priarily losses in te agnetic core and are due to agnetic ysteresis and eddy currents. Load Losses are divided into I R Losses and Stray Losses. I R Losses can be obtained, as follows: ax I R I R ( Eddy-currents, wic produce stray electroagnetic flux in te transforer s windings, agnetic core, core claps, enclosure and oter structural parts, cause Stray Losses. Wit ig aronic currents, te Eddy-Current Losses in te windings are te ost doinant losses in te transforer. otal Stray Losses ( S are proportional to te product of Fundaental Stray Losses ( S and te square of te product of te aronic currents and teir corresponding frequencies, as follows: S ax S I III. MEASURING OF RANSFORMER LOSSES (3 e easureent of a transforer s losses and calculation of its efficiency is very well understood and applied in te power and distribution transforer industry. However,

2 conventional No-Load Loss and Load Loss easureent etods only confir a transforer s perforance under linear load conditions. IEEE Std Standard est Code for Dry-ype Distribution and ower ransforers and NEMA -998 A Standard est Metod for Measuring te Energy Consuption of Distribution ransforers [5] specify te testing procedure for te easureent of losses and te calculation of efficiency under linear loading. e easureent of No-Load Losses is ade during an Open-Circuit est and te easureent of Load Losses is ade during a Sort-Circuit est. ese easureents can be used to calculate efficiency as follows: OU (4 OU LOSS Were: ransforer Efficiency Output ower (Watts OU ransforer ower Losses (Watts LOSS Conventional Metod of Measureents ransforer Losses and Efficiency - A transforer s otal Losses are obtained by calculating te difference between input and output power. A single-pase transforer can be considered as a twoport network (Figure, in wic te transforer losses are obtained as te difference between two products: p loss p p p (5 v in out p vi vi i i RANSFORMER Kt=N/N A ransforer as a wo-ort Network Figure e instruentation and connection diagra, for testing a single-pase transforer, is sown in Figure. v i V v INU OWER C A ESING RNASFORME RANSFORMER R C v i A v V OUU OWER Connection Diagra for a Single-ase ransforer Figure Depending on its kva rating, te efficiency of a distribution transforer is usually in te 9% to 98% range. o coply wit NEMA, CSA C8.- and te EA Energy Star. rogra, efficiencies ust be in te 97% to 98.9%. However, v NEMA, and all oter current standards, specifically excludes transforers tat supply nonlinear loads. We can derive te axiu full scale errors for te voltages and currents, and te axiu errors for losses and efficiency, for 75 kva 48/:8 tree-pase transforer, as follows: No-Load Losses = 86 Watts, Load Losses at % load =,74 Watts, Efficiency = wen te instruent transforers are.3% accuracy class, te volteter and aeters ave an accuracy of.%fs, and te watteters ave an accuracy of.%fs, as sown in Figure. e instruentation is suarized in able. Instruents Full Scale Full Scale Error V 48/.36 V - - C /5.5 C 4/5.5 V 3.3 V 3.3 A 5.5 A 5.5 able Losses and efficiency easureent errors, at unity power factor and % load can be calculated as follows: loss ( vt V(5 C A x ( V (5 Ct A x kW 74.6kW.3kW e losses easureent error is: Loss Loss.3 x 5.6% e efficiency easureent error is: eff.34% New Metod of Measureents ransforer Losses and Efficiency [6] Considering te transforer as a two-port network (Figure, instantaneous power absorbed by te transforer is defined by equation (5. By creating a new twoport network, wic is sown in Figure 3, we introduce a * current generator ( i i i / K, wic is parallel to port * p-p, and voltage generator ( v v / K v, wic is in series wit port p-p. Bot Input and Output ower coincide wit v i / K. e overall absorbed power troug ports p-p and p-p is zero. e instantaneous power absorbed will be equal to te su of te power delivered by tese generators. e power losses of te transforer can be expressed by: " p L ( i i / K v ( v / K v i p p (6

3 p v p i /K i * = i -i / K RANSFORMER Kt = N/N " Second ter is: ( v vk t idt i v * = v /K-v p i v Adt " iv AC v i v /K A ransforer as a wo-ort Network Figure 3 Average power for soe period of tie can be expressed by: " L ( i i / K vdt ( v / Kv idt (7 Equation (6 is valid for any constant K. Based on tis forulation, a new easuring etod is presented, wit te connection diagra sown in Figure 4. is etod also requires two watteters, or two sets of volteters and aeters. One set for a full range of voltages and sall currents and te oter set for sall voltages and full range of currents. ysical interpretation of tis etod can be explained using Figure 4. INU v V C v i i i i -i A A RANSFORMER ESING RNASFORMER v A V C p OUU v -v Connection Diagra for a Single-ase ransforer Figure 4 Based on te diagra as sown in Figure 4. ( i i / Kt vdt i v Adt iv AB e ter corresponds to te losses due to te circulation of agnetizing current in te priary added to agnetic core losses. at is equivalent to te transforer open circuit test. i dt dt v (8 (9 Equation (9 represents te su of te losses in te priary and secondary of te transforer, due to load current, wic is equivalent to a transforer sort-circuit test. Wit tis etod, it is possible to separately easure te core and copper losses of te transforer. Measureent under nonlinear load conditions is also possible. o evaluate te new easuring etod, using te proposed connection diagra in Figure 4, we analyze te sae exaple evaluated wit te conventional easuring approac, wit standard Metering Class Cs and Vs, and specially design differential Cs and Vs. e instruentation is suarized in able. Instruents Full Scale Full Scale Error V 48/.36 V /.36 C 5/5.5 C 5/5.5 V. V. A. A. Exciting current error is: able ( i i C A.6 ( i i ( i i / Input Voltage is easured wit te error: v V V.7 v v e core losses are easured wit te error: Fe v ( i i.33 Fe v ( i i e series voltage drop is easured wit te error: ( v v V V.68 ( v v ( v v Output current is easured wit error: i C A.79 i i / e copper losses are easured wit te error: Cu i ( v v.4 Cu i ( v v e core losses are easured wit te error: Fe v ( i i.33 Fe v ( i i e total losses are easured wit te error: Loss cu Fe.3.3% Loss Loss e efficiency easureent error is: eff.33% 3

4 IV. EVALUAION OF LOSSES AND MEASUREMEN Based on te presented two easureent etods, we will plot te losses and efficiency for bot etods. Figures 5a and 5b present Losses (kw vs. Load (pu wile Figures 6a and 6b present Efficiency (pu vs. Load (pu V & C Difference lus & Minus Error ower-in ower-out Minus Error ower-in ower-out lus Error V & C Difference lus & Minus Error lus Losses Measureent Error Figure 5a V & C Difference lus & Minus Error ower-in ower-out lus Error Minus Losses Measureent Error Figure 5b ower-in ower-out lus Error V & C Difference lus & Minus Error lus Efficiency Measureent Error Figure 6a Minus Efficiency Measureent Error Figure 6b IV. CONCLUSION A conventional approac to te easureent of losses in distribution transforers is based on te difference of two nuerically large ters tat are quite close in value. e easureent error in tis approac is significant and cannot be used to calculate efficiency of a igly efficient transforer. e error in deterining te losses and calculating te transforer s efficiency can be greatly reduced by using a new etod tat is based on te addition of two ters, wic are in te sae region of value. Fro tis presentation, it is obvious tat te easureent of transforer losses and calculation of transforer efficiency, wic is based on te ower-in ower-out Measureent Metod, is very inaccurate. Using current and voltage transforers wit Metering Class accuracy (.3% can lead to a easureent error in te.3% range. Wit te ore accurate current and voltage transforers (.%, te accuracy of easureent is iproved to.94%, wic is still not satisfactory for te easureent of transforer losses. Clais of ig transforer efficiencies under nonlinear loading, wen tested by tis conventional etod, tat is, by easuring te input and output power, will not be valid or tecnical eaningful, since it produces an error of.3% or.94% best case. By coparison, te etod based on Voltage and Current Difference as an error of less ten.35%. e ower-in ower-out Metod, for deterining a transforer s energy losses in a nonlinear load environent, is isleading and witout tecnical erit. e etod based on Voltage and Current Difference will accurately deterine a transforer s efficiency in any nonlinear load environent. V. REFERENCE []. Key & J-S. Lai, Costs and Benefits of Haronic Current Reduction for Switc-Mode ower Supplies in Coercial Office Buildings. IEEE Annual Meeting, October 995, Orlando, Florida. [] G.N.C. Ferguson, e Costs and Benefits of Haronic Current Reduction in Low Voltage Distribution Systes. International ower Quality Conference (IQC, October, Singapore. 4

5 [3] NEMA Standard ublication -, Guide for Deterining Energy Efficiency for Distribution ransforers. [4] IEEE Standard C , est Code for Dry- ype Distribution ower ransforers. [5] NEMA Standard ublication -998, Standard est Metod for Measuring te Energy Consuption of Distribution ransforers [6] D. Lin, E.F. Fucs, M. Doyle Coputer-Aided esting of Electrical Apparatus Supplying Non-Linear Loads, IEEE ransactions on ower Systes, Vol., No., February 997. VI. BIOGRAHIES Aleksandar Danjanovic was born in Yugoslavia in 96. He received a B.S. Degree in Electrical Engineering fro te University of St. Kiril and Metodij, Skopje, Yugoslavia, and a Master Degree and D in Electrical Engineering fro swine University of ecnology, retoria, Sout Africa. His experience includes eployent wit ABB &D, Sout Africa, Instruent ransforers, Inc., USA, and asetronics, Inc., USA. Mr. Danjanovic joined ower Quality International, Inc., USA, in, as its Vice-resident, Engineering. His researc interests include electroagnetics, power syste odeling, analysis and design. Gregory Ferguson was born in oronto, Canada in 937. He received a B.Sc. Degree in Engineering ecnology fro Ryerson olytecnic University, oronto. His experience includes eployent wit te Ontario Hydro-Electric ower Coission and Scarboroug ublic Utilities, Canada. He is te founder of Ferguson Engineering Services, Inc., Canada, Electrical esting Instruents, Ltd., Canada, ower Quality International, Inc., USA and FES International, Inc., Canada & USA. Mr. Ferguson is a Life Meber in IEEE. His interests include electrical power syste analysis, design, optiization and forensics. 5