Analysis of Distribution Transformer Performance under Non-linear Balanced Load Conditions and Its Remedial Measures

Transcription

1 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Analysis of Distribution Transformer Performance under Non-linear Balanced Load Conditions and ts emedial Measures Sanjay A. Deokar, Laxman M. Wagmare Dnyanganga College of Engineering and esearc, Pune University, Pune-44 S.G.G.S., nstitute of Engineering and Tecnology, Nanded s_deokar@rediffmail.com lmwagmare@yaoo.com Abstract n recent years tere as been very extensive use of power electronic devices, wic result in armonic proliferation in te power distribution system. n tis paper, as per EEE C 57. standards, procedure to calculate total loss in te distribution transformer under non-linear distortion environment is proposed. Te power factor capacitor performance under non-linear load conditions is also analyzed. Te relation of total current armonic distortion in te distribution system wit load power factor, transformer losses, efficiency and maximum current delivered is also analyzed. Te mitigation metods are proposed to minimize te non-linear load impact on te distribution transformer performance. nstead of K-factor transformer approac, a passive armonic filter metod is developed based on iger savings in energy losses. Te simulation studies, are performed using Mat works MATLAB 7.. for distribution system at /.44 k, ka distribution transformer under non-linear balanced load conditions. t is observed tat te power factor capacitor bank acts as a source of armonic under te nonlinear load conditions in te presence of passive filters. Keywords Harmonic Proliferation, k-factor, Non-linear Load, Power Factor, Mitigation.. NTODUCTON Te transformers are designed and manufactured to be used for non-linear load, at rated frequency and balanced supply voltage. Te present design trend in electrical load devices is to increase energy efficiency wit solid-state electronics. One of te major drawbacks of tis trend is te injection of armonics into te power systems. Almost all te utilities ave expressed concern about overeating of oil immersed distribution transformers, wic supply te non-linear loads. A transformer termal response to sinusoidal loads is properly evaluated at te transformer design stage, but it s actual response to 5 non-linear loads sould be estimated after proper evaluation of present load conditions[].te increasing usage of non-linear loads on electrical power systems is causing greater concern for te possible loss of transformer life. Manufacturers of distribution transformers ave developed a rating system called K- factor, a design wic is capable of witstanding te effects of armonic load currents. An application of tis rating system to specify a transformer for a particular environment requires knowledge of te fundamental & armonic load currents predicted. n almost all te cases, te field measurements are required to diagnose problems at a specific location, by analyzing load currents. Electrical insulation used in distribution transformers gets degraded wen it is subjected to te termal, electrical, environmental, mecanical and combined stresses during its operation. Electrical stresses are caused by voltage gradient. Te average life expectancy of a transformer is decided by te average life of insulating materials. Te steady-state power quality problem like armonics and variation in frequency are responsible for accelerated aging of its insulating material. A transformer designed witout considering all tese issues will result into premature failure. n [], a different metod to calculate te impact of non-linear loads as been discussed. t also gives an overview of impact of nonlinear load on te distribution transformer winding losses. Te standard K-factor transformer ratings and typical loads as well as its design guidelines are given in [3]. n [4], measurement metods for reactive power demand under non-linear loads ave been presented. n [5], on line monitoring of all losses of bot single and tree-pase transformers as been investigated under a different percentage of load conditions.

2 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Harmonics and its impact on te power factor wit teir relation ave been investigated in [6]. t also explains te important to te true power factor compared wit displacement power factor under non-linear load. Te transformer de-rating metods during non-linear load supply conditions are given in [7].n [8], transformer modeling under te non-linear load conditions is investigated and tested under non-linear load conditions. Te measurement of te losses for estimation of te transformer de-rating and armonic loss factor comparison as been discussed in [9]. Te measurement of eddy current loss coefficient and de-rating of single pase transformers as well as comparison wit K-factor as been presented in []. Te transformer design and application considerations for non-sinusoidal load currents as been discussed in [].Te impact of nonlinear loads on temperature rise of small oil filled distribution transformers as been analyzed in [3]. A dry type distribution transformer specifications and calculations of winding temperatures in distribution transformers under armonic load conditions ave been elaborated in [4], [5].Considering all tese issues it is necessary to study and analyze te various effects of nonlinear load on distribution transformers. Te power factor during linear load condition is called displacement power factor and during non-linear load condition, it is called distorted power factor. f armonic currents are introduced in te system, true or total power factor is always less tan te displacement power factor. n tis paper, a case study of ka, k/44, 3-pase distribution transformer wit balanced load nature is simulated using Mat works MATLAB-7.. for analyzing te impacts of non-linear loads. Te relation between current armonics in te distribution system and losses, efficiency, maximum current delivered, apparent power capacity of te distribution transformer as been analyzed and presented. Te impact of ordinary power factor capacitor bank on total current armonic distortion is also analyzed. A mitigation measures like K-rated transformers and application of passive filters are presented and results are compared wit armonic content base case. From tis comparison, instead of K-factor transformer, passive filter metod is recommended.. LOSSES DUNG NON-LNEA LOADNG OF DSTBUTON TANSFOME An easy way to comply wit te conference paper formatting requirements is to use tis document as a template and simply type your text into it. 53 As per ANS/EEE C [7],[], te transformer losses are mainly no-load loss (excitation loss); load loss (impedance loss); and total loss. Tis can be written by using PTOTAL PCOE PLOAD L () Were, P Total loss, P Core or No load loss and TOTAL COE P LOADL Load loss Te total load loss can be given as, PLOAD L DC PWEC L P () OSLL Were, PWEC is te winding eddy current loss and L POSL is L te oter stray loss. Total stray losses include winding eddy current losses and structural part stray losses. Tese are given by te following expressions [4], PTotal ST PWECLPOSLL PLOAD L P (3) POSLL PTotal ST P (4) WECL Te winding eddy current loss can be calculated using te PWEC L. 33P (5) Total ST Losses during non- linear loading of a distribution transformer n modern power systems, te total armonic voltage distortion ( THD v ) is normally below 5% and te magnitudes of te voltage armonic components are small compared to fundamental components(% to 3%).Terefore voltage armonics effects are neglected. Te current armonics are more significant. Tese armonic load current components cause additional losses in te winding and oter structural parts. Hence total load losses under armonics load condition can be given by te PLOAD L PCU PWEC L P (6) OSLL Te armonic component of load current increases te r.m.s. value of te load current and ence P CU loss will be increased accordingly. PWEC is te winding L eddy current loss due to te non-sinusoidal load current. t can be given as follows, max P WECL PWEC (7) T

3 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Were, P is te rated eddy current loss under full load WEC conditions, is te armonic order, is te r.m.s. current at armonic order and is te rated T fundamental current at full load conditions and rated frequency. Te increased winding eddy current losses produced by a non-sinusoidal load current can cause excessive winding losses and ence abnormal temperature rise. POSL are te stray losses in te structural parts due L to non-sinusoidal current. t can be calculated by te max.8 P OSLL POSL (8) Were, POSL are te structural part stray losses under rated conditions. Te factor.8 is accepted by EEE after manufacturer s verification. For oil filled transformers, tese stray losses increase te oil temperature and tus te ot spot temperature. Total load losses in bot oil cooled and dry type transformer under non-sinusoidal load condition wit current armonics are calculated by te P LOSDL P OSL P max CU max.8 P WEC max. DE-ATNG OF DSTBUTON TANSFOME According to te EEE dictionary, de-rating is defined as "te intentional reduction of te stress/strengt ratio (e.g., real or apparent power) in te application of an item (e.g., transformer), usually for te purpose of reducing te occurrence of stress-related failure (e.g., reduction of lifetime of transformer due to increased temperature beyond te rated temperature)."harmonic currents and voltages result in armonic losses increasing te temperature rise. Tis rise beyond its rated value results in a reduction of lifetime. (9) 54 Te distribution transformer must be de-rated under non-sinusoidal load conditions [].Te transformers derating can be performed using following metods: a) Direct loss measurement. b) Using K-Factor and c) Based on armonic loss factor ( F HL ). A. Distribution Transformer De-rating Based on K- Factor Te impact of nonlinear loads on distribution transformers greatly depends on te nature and te armonic spectrum caused by te nonlinear load, wic is not considered by te manufacturers. Te EEE standard. C [7] introduced a term called te K-factor for rating a transformer as per teir capability to andle load currents wit significant armonic contents.t is an alternate tecnique for transformer de-rating wic considers load caracteristics. t is a rating optionally applied to a transformer indicating its suitability for use wit loads tat draw non-sinusoidal currents. t is an index tat determines te canges in conventional transformers must undergo so tat tey can dissipate eat due to additional iron and copper losses because of armonic currents at rated power. Hence te K-factor can be written as, K max () Tis K-factor is only an indicative value. Te main objective is to design and manufacture an oil filled distribution transformer wic can operate for a specific K-factor value witout loosing its expected life span. Terefore, te maximum amount of.m.s. armonic load current tat te transformer can deliver is given by te max PECL ( ) () kp EC Were te fundamental rms current under is rated load conditions, P is te eddy current loss to rated ECL loss in wic is te total rms current. Te reduction in apparent power is given by te P Non linear ms. u. e ( ) p KA duction max atedms ()

4 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Were, Non linear ms te total rms is value of te secondary voltage including armonics and is te rated atedms.m.s. value of te secondary winding witout armonics. B. Distribution Transformer De-rating Based on F HL Factor As per EEE Std. C57./D7-998[7], tis represents an alternative approac for assessing transformer capability supplying non-linear loads. Hence F Factor HL can be defined using max F (3) HL max Te stray loss armonic factor can be given as, max.8 F (4) HL STAY max Hence, te relation between K-factor and as follows, K max F HL F is given HL (5) Terefore, te maximum amount of.m.s. armonic load current tat te transformer can deliver is given as, PLOAD L max (6) [ FHL PECL ] [ FHLSTAY POSL ] Under armonic load condition, te new load loss can be calculated by te PLOAD LNEW [ FHL PECL FHLSTAY POSL ] (7) Te reduction in te apparent power rating is given by te equation ().. MODELNG AND SMULATON OF DSTBUTON TANSFOME A ka tree-pase distribution transformer is modeled and simulated using Matlab-7. for different load caracteristics. All parameters wen te transformer is tested at balanced linear full load were taken from Maarastra State Electricity Distribution Company Limited (MSEDCL) manual. All tese parameters are given in Table. TABLE ALL PAAMETES AND LOSSES OF KA TANSFOME WOKNG AT FULL LOAD Parameters KA ating oltage ange KA K/44.5A 66.7A No load iron loss Full Load Cu Loss at 75 C 5W 3W 4.75Ω.6Ω L.3H L c L m.67mh 78 kω 35H ating A transformer is tested for te following load caracteristics at full loads. A. Base Case of ka Distribution Transformer wit Linear Nature of Load at.8 P.F. n tis case ka distribution, transformer is loaded at its full capacity wit non-linear load. 55

5 Amplitude of current (A) 'a' pase current(a) nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Te single-line diagram of te simulated power system is sown in Fig. (a).bot primary and secondary full load currents, current THD, and total losses are calculated. t is matcing wit standard full load test data of te ka distribution transformers wit 5% tolerance given by distribution Company. Efficiency of te transformer under tis case is 98.% at.8 lagging power factor and current armonics are below te EEE standard. X/=.5 Supply k, f rom power utility /.433k ka =4.75om L =.3H =.6om L =.67H m =78kom L m =35H BUS BA t is observed tat te losses are reduced and ence efficiency is also improved about 98.4%.For te same load, current to be supplied by a transformer is reduced by 6%. Tis arrangement is simulated in matlab-7. as sown in Fig. (b), and results are sown in Table.. A CASE OF KA DSTBUTON TANSFOME FEEDNG NON-LNEA NATUE OF LOAD WTHOUT P.F. MPOEMENT n tis case transformer, performance is cecked witout power factor improvement for non-linear load only in wic load is adjusted at THDi=8.9% up to 35 t armonics level. From te simulation, it is observed tat te losses are increased drastically, wic results in efficiency at 96.6%. Te transformer maximum current delivery capacity is reduced by 5% as compared to secondary full load current. Te voltage profile is also reduced due to increased voltage drop in distribution lines. Tis arrangement is simulated and is sown in Fig.(c). Te current spectrum and its armonic current level of a single pase are sown in Fig. (a) and (b) respectively. Te results are sown in Table. 4 3 S S S3 S4 Linear Load Full load ka p.f.=.8lagging Non-Linear Load %THDi=8 Capacitor bank 67.4kA Passiv e Filters,5t, 3kA/Pase 7t and 5t onwardska/ pase Time (sec) Fig.. A distribution transformer feeding a linear/non-linear full load; (a) Te linear nature of load at.8 lagging p.f.; (b) Te linear nature of load wit.95 p.f. improvement using capacitor bank; (c) Non-linear nature of load witout p.f. improvement wit % THD =8%.; (d) Te Non-linear nature of load wit p.f. improvement (e) Non-linear nature of load wit passive armonic filters for p.f improvement and %THD mitigation (a) B. Base Case of ka Distribution Transformer Feeding Linear Nature of Load wit P.F. mprovement at.95 n tis case, a transformer performance is cecked wen a capacitor bank of 67 47kA. is installed at te point of common coupling (PCC ) to improve power factor of.95 lagging witout canging load nature Harmonic order Fig.. (a) Harmonic current spectrum of pase A ; (b)current armonic bar cart of pase A at non-linear full load witout power factor improvement. (b)

6 Amplitude of current (A) 'a' pase current(a) nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ). A CASE OF KA DSTBUTON TANSFOME FEEDNG NON-LNEA LAD WTH P.F.MPOEMENT n tis case transformer, performance is cecked wit power factor improvement capacitor and non-linear load nature at full load. From te simulation results it is observed tat te THDi is increased to 35.4%.t is also observed tat te current armonics are increased in eac level compared to previous case. Te losses are increased drastically results in efficiency reduction at 9.8%. For te same load distribution, line is overloaded by 4.5% and te load carrying capability of a transformer is reduced by 3% compared to previous case. Te transformer maximum current delivery capacity is reduced by 44% as compared to secondary full load current. Te voltage profile is also disturbed due to increased voltage drop in distribution lines results in reduction in apparent power capacity. Here under non-sinusoidal load condition, power factor improvement is impossible wit simple capacitor banks only. An ordinary capacitor bank also acts as a source of armonics as current THD is increased. Tis arrangement is simulated and is sown in Fig.(d). Te current spectrum and armonics level is sown in Fig.3(a)&(b) respectively.te results are sown in Table TABLE SMULATON ESULTS OF KATANSFOME TESTED AT DFFEENT LOAD CHAACTESTCS Load Caracteris tics Base case (Total Linear nature of Load).3Am p 66.6A mp Total Load Losses Watts Base Case+ Capacitor Banks for P.F. improvem ents Total Non- Linear Load witout...p.f... improveme nt Nonlinear Load+ P.F. Capacit or. 8.67Amp.3Amp 9.38 Amp 8.4Amp 6.5Amp 73.5 Amp 85.9 Watts 56.5 Watts 347 Watts THD i <5% <5% 8.9% 35.5% 6 4 max ated Capacit y ated Capacity.78 Amp 55.3 Amp - -4 K-rating No Derating No Derating Time (sec) (a) % Efficiency Total Power Factor 97.73% 98.4% 96.6% 9.8%.8 lagging.95 lagging.77 lagging.94 lagging % ka Capacity reduction.%.% 7.% 4.87% Harmonic order (b) Fig.3. (a) Harmonic current spectrum of pase A wen distribution transformer is feeding non-linear full load wit capacitor bank for p.f. improvement up to.95 lagging. (b) Current armonic level bar cart of pase A wen base case feeding non-linear full load wit capacitor bank. 57

7 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ). POWE FACTO UNDE NON-LNEA LOAD ENONMENT Under te armonic load conditions, total armonic distortion or distortion factor is used for its level measurement. t is te ratio of te rms value of te armonics (voltage or current) above fundamental to te rms value of te fundamental. t can be given by te THD O THD max max (8) Hence, correct form of true power factor under linear and non-linear load environments is given by te TUE PF P ( THD fun Avg fun ) ( THD ) (9) Normally in most of armonic load cases, average power variations are negligible and voltage total armonic distortion is also less tan 5%, ence it is also neglected[],[6].by considering tese assumptions te approximate equation for true power factor is given as, TUE PF P fun fun fun ( THD DisplacementPF Distortion PF Were, P fun, fun and fun are te fundamental power, voltage and currents. ) () 58 Since displacement power factor is always less tan unity, ence true power factor is always less tan te distorted power factor. Te true power factor variation under different non-linear load conditions is depicted Table and Table respectively. t is seen tat te armonic loads, especially current armonic content as a significant impact on te true power factor and te transformer efficiency. Te true or total power factor variations wit current total armonic distortions are plotted in Fig.6.. MTGATON MEASUES A. Harmonic filter design-a sunt passive filters t can be seen tat te sunt capacitor acts as a source of armonics wen load nature is non-linear. Wit incorporation of te power factor capacitor, total current armonic distortion level is increased from 8.9% to 35.5%. t is important to note tat just by adding a sunt capacitor poor distortion power factor can t be compensated. Te displacement power factor can be improved wit sunt capacitors. Here existing power factor capacitor is removed, and it is converted into armonic passive filter. A single tuned band pass passive filter for 5 t and 7 t armonic level and ig-pass filter from 5 t armonic onwards are designed and simulated for 8.9 % of current THD. Harmonic filters are designed to be capacitive at fundamental frequency, so tat tey are also used for producing reactive power required by non-linear loads and for power factor correction. Hig-pass filters, wic are used to filter igorder armonics and cover a wide range of frequencies. A sunt filter is said to be tuned to te frequency wic makes its inductive and capacitive reactance s equal. Tree-pase armonic filter are sunt elements tat are used in power systems for decreasing bot current and voltage distortion as well as for power factor correction. Te ig-pass filter is a single-tuned filter were te L and elements are connected in parallel instead of series. Tis connection results in a wide-band filter aving impedance at ig frequencies limited by te resistance. Te quality factor is adjusted according to te armonic order wic determines te sarpness of tuning. t is observed tat te armonic filters reduce te THD of te current injected in te system from 8.9% to 4.8% wic is bellow EEE standard [9]. Te total 7 KA is adjusted as per te following configuration: 3 KA low-pass filter tuned to te 5 t armonic wit quality factor of and KA low-pass filter tuned to te 7 t armonic wit quality factor of as well as KA

8 a pase Current (Amp) Amplitude of Current (Amp) nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) ig-pass filter tuned to 5 t armonics onward. Te total load losses are reduced by 44% compared to 8.9% of THDi case and 74.5% compared to 35.5% of THD i case. Te corresponding simulation results are sown in Table 3. From te table, it observed tat te transformer maximum current delivery capacity is close to be rated current capacity and efficiency at full load is 98.37%. Te current spectrum and current armonic bar cart of pase A is sown in Fig. 4 (a) and (b) respectively. TABLE SMULATON ESULTS OF KA TANSFOME TESTEDWHEN PASSE FLTES AE TESTED Load Caracteristics Total Load losses Non-linear Loads+ 343 Watts THDi.43% max Passive Filters 64. Amp K-rating.43 % Efficiency 98.37% Total Power Factor.95 lagging eduction in ka capacity.97% Harmonic order (b) Fig.4. (a) Harmonic current spectrum of pase A; (b) Current armonic level bar cart of pase A at non-linear full load wit passive filters. B. Transformer De-rating using K-Factor and F HL Factor f te filters are not installed ten transformer derating using K-factor and F HL factor can be implemented. Some of te canges in te design of K-rated transformers are given below: ) Optimum increase in te delta connected primary winding conductor size wic can tolerate te circulating triplen armonics. ) Core design flux density sould be minimum to protect against voltage distortion. 3) Multiple and transposed secondary winding conductor to reduce resistance to avoid eating due to skin effect from ig frequency currents. Tese design factors can improve te termal dissipation to minimize te additional losses. 4) Heavier conductors and transposition of winding conductor to reduce magnetic losses ) Electrostatic sielding between primary and secondary winding to reduce eddy current losses and eating Time (sec) (a) 6 Double sized neutral conductor to protect against triplen armonics. As per reference [], te standard K-factor transformer ratings for specific loads are given in Table. 59

9 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) Type of Loads TABLE TANASFOME K-ATNGS ncandescent ligting Electric resistance eating, Motors, Control transformers witout solid state controllers. K- Electric discarge ligting UPS, nduction eating equipment, Welders, PLC s. Telecommunication Equipments, UPS witout filtering, General ealt care and classrooms of scools, arious testing equipments. Mainframe computer loads, Moters wit FD s, Healt care equipments in critical care areas and operating rooms of ospitals. Multi-wire receptacle circuits in industrial,medical, educational laboratories etc. K-factor K-4 K-3 K- K-3 Loads producing ig order armonics K-4 Te calculations sown in Table and Table, it can be observed tat te K-factor rating increases wit total current armonic distortion. Te relation between K- factor and THDi is sown in Fig.5, as given below. 5 %THDi K-FACTO Fig.5. elation between K-Factor and THDi. Power factor capacitor contributes for increase in total current armonic distortion level wit non-linear load. t alone doesn t elpful for improving total power factor but can improve displacement power factor. Tis relation is plotted in Fig 6..9 Total pf %THDi Fig.6. elation between total power factor and THDi. Te maximum current delivered by te transformer is inversely proportional to te total current armonic distortion. Transformer KA capacity also reduced wit current armonic level. Wen total current armonic distortion level is 8.9%, K-3 rating and for THDi=35.5%, K- rating transformer is recommended. Wen passive filters are used, te K-factor is reduced to K-.Oter mitigation measures suggested are given below: ) f te filters are not installed ten transformer derating using K-factor and F HL factor can be implemented. ) Use energy efficient transformers to control temperature rise and losses. t will extend te life of transformer. 3) Design of proper sizing of distribution transformer neutral conductor. 4) Use of Star-delta connected transformer to block triplen armonics. X. CONCLUSONS A tree -pase distribution transformer was simulated for critical analysis under balanced non-linear load. t was sown tat te THDi as a significant impact on te transformer efficiency as compared wit linear nature of te load. t is observed tat power factor, KA capacity and transformer efficiency decreases wit non-linear load. t is also sown tat te power factor capacitors act as a source of armonics during non-linear loading. Te K- factor de-rating of te distribution transformer increases wit an increase in % THDi. f te load THDi is increased in suc a way tat te load K-factor greater tan te rated K-factor, ten te transformer can t be operated at its full KA capacity, and ence it would require de-rating. 6

10 nternational Journal of Emerging Tecnology and Advanced Engineering Website: (SSN 5-459, olume, ssue, December ) From tis analysis, it is concluded tat as compared to K-factor transformer, a passive filter tecnique is effective for armonic mitigation and power factor improvement. Wen ever te passive filter is used te transformer apparent power capacity and distribution line loading capability can be improved for te same nature of load. Wit te implementation of passive filters, tere is significant reduction in te energy losses. n case of unbalanced non-linear load, an active filter can be used to improve te power system performance. EFEENCES [] EEE ecommended Practices & equirements for Harmonic Control in Electrical Power Systems, EEE Std [3] A.W Galli, M.D Cox, Temperature rise of small oil filled distribution transformers supplying non-sinusoidal load currents, EEE transactions on Power Delivery, vol., no.,pp 83-9, January 996. [4] sadoro Kerzenbaum, Alexander Mazur, Maendra Mistry, Jerome Frank Specifying Dry type Distribution Transformers for Solid- State Applications, EEE Transactions on ndustry Application, vol.7, no., pp , January/ February 99. [5] M.D.Hwang,, W.M.Grady, H.W.Sanders Jr., Calculation of winding temperatures in distribution transformers subjected to armonic currents, EEE Transactions on Power Delivery,vol.3, no.3, pp , July 988. [] E.F Fucs, A. Moammad, S.Masoum Power Quality in Power Systems and Electrical Macines, Elsevier nc, SBN , Marc- 8. [] G.W.Massey, Estimation metods for power system armonic effects on power distribution transformers, EEE Trans.ndistrial Application,vol.3,no.,pp ,Mar/Apr.994.` [3] Underwriters Laboratories, UL-56, Proposed requirements and proposed effective dates for te first edition of te standard for dry type general purpose and power transformers, Santa Clara, CA, 99. [4] E.F Fucs, D. Lin, and J Martynaitis, Measurement of tree-pase transformer derating and reactive power demand under nonlinear loading conditions, EEE Transactions on Power Delivery, vol., no., pp , 6. [5] D.Lin, E.F Fucs, eal-time monitoring of iron-core and copper losses of tree-pase transformers under non-sinusoidal operation, EEE Transactions on Power Delivery, vol., no.3, pp , July 6. [6] W.M.Grady, obert J. Gilleskie, Harmonics and ow tey are relate to power factor, Proceedings of te EP power quality issues & opportunities conference (PQA-93), San Diego, CA, November-993. [7] EEE Standard, ecommended practice for establising transformer capability wen supplying non-sinusoidal load currents, ANS/EEE C57., February 998. [8] J Pedra, F Corcoles, L Sainz, Harmonic nonlinear transformer modeling, EEE Transactions on Power Delivery, vol. 9, no., pp , 4. [9] E.F Fucs, D Yildirim, Measured transformer derating and comparisons wit armonic loss factor FHL approac, EEE Transaction on Power Delivery, vol. 5, no., pp.86-9, January-. [] E.F.Fucs, D.Yildirim, W.M. Grady, Measurement of eddy current loss coefficient PEC-,derating of single pase transformers, and comparison wit K-factor approac, EEE Transaction on Power Delivery, vol. 5, no.,pp-48-54, January-. [] W.P.Linden, Transformer Design and Application Considerations for non-sinusoidal Load Currents, EEE Transactions on ndustry Applications, vol.3, no., pp , May/June