Loading transformers with non sinusoidal currents

Transcription

1 LES00070-ZB rev. Loading transformers wit non sinusoidal currents K Factor Loading transformers wit non sinusoidal currents... Interpretation / example... 6 Copyrigt 007 ABB, All rigts reserved.

2 LES00070-ZB rev. / 7 Loading transformers wit non sinusoidal currents All ratings for transformers are based on sinusoidal rms values, rated power, rated voltage, losses, temperature rise, etc. For a tree pase transformer te main ratings, rated power; r, rated voltage: U r ; and rated current; I r, are linked troug te well known equation: r I r = [] U 3 r Load losses and temperature rise are based on sinusoidal rms rated current. Load losses can be expressed as follows: LL = DC + WE OS [] Being: DC DC losses produced by a DC current of te same value tat rms fated current. WE - 50 Winding eddy losses at te rated frequency produced by circulation current (eddy) in te windings due to leakage flux. OS Oter stray losses, produced in bus bars and steel parts due to leakage flux, tese losses ave not any influence on winding temperature rise. All losses referred to te reference temperature. Wen transformer supply a non sinusoidal load current wit te same rms value tan rated current, DC losses remain constant but winding eddy losses increase due to te iger frequency of te armonics, as a result, winding temperature rise increases and temperature limits can be exceed. A transformer requested to supply non sinusoidal loads, sall be oversized in order to guarantee tat windings temperature limits are not exceed in service. Te value K of suc over sizing factor wic means tat temperature rise limits are guaranteed wen test current is K times rated current is calculated as follows: K = DC DC + + EW H EW 50 [3] EW-H Winding eddy losses at load current wit armonics. Usually winding eddy losses are given in per unit of DC losses, tat is: EW 50 EW 50 = [4] DC EW H EW H = [5] DC

3 LES00070-ZB rev. 3 / 7 Remark: For HD 538 Factor K calculation metod, EW-50 and DC are total eddy winding losses and total DC losses for te transformers because anyting else is specified. Oter standards, suc as UL 56 or IEEE C57.0 use individual winding values, calculated according to te metod proposed in te applicable standard. Te following ratio, EW H EW 50 = H = H = = q K EF WE I + I = = q [6] Hereafter referred as K EF-WE, is te enancement factor for winding eddy losses, being: I rms current for armonic in pu of rms rated current I rated is te armonic number q Exponent for armonic number, for transformer wit foil windings in LV, q =.5 as recommended in HD 538. Eddy losses in conductors exposed to external flux, suc as leakage flux in transformers, vary wit te product (conductor widt x frequency) q, q value varies between for lower values of product and for larger values. Tis is te reason wy for foil LV windings, were leakage flux as a big radial component perpendicular to foil surface, a value equal to.5 is recommended. Remark: according to te UL 56, tis exponent is equal to, owever suc value is very conservative leading to a transformer over size beyond te actual needs. On tis basis, eddy losses enancement factor K EF-WE sall be calculated using te equation [6] and considering q equals to.5, tat is: K EF WE = + = H.5 I ( pu) [6B] = Taking into account tat: rated = H I = ( pu) I [7] referably, customer sould specify te full armonic content. In suc case, te calculation of eddy losses enancement factor and rated current can be done by using equations [6B] and [7].

4 LES00070-ZB rev. 4 / 7 Alternatively, customer can specify rated power and total armonics distortion THD (refer to IEC paragrap 3..7) in p.u. of fundamental rms current. In tis case armonics spectrums are assumed to be as follows: Harmonics: 3 rd, 5 t, 7 t, 9 t, t, 3 t, 5 t, 7 t, 9 t, st, 3 rd and 5 t Harmonic (from 3 to 5), p.u. value of fundamental rms, as follows: αi I = [8] I ( THD) = [9] + ( THD) α = [0] And finally, eddy losses enancement factor is found out by using te equation [6B]. In case customer specifies a certain K-Factor calculated according UL wit exponent q=, ten, te armonic spectrum sall be defined as above, and α calculated as follows: K = 0,45 K α [] K= K-Factor Terefore, te eddy losses enancement factor sould be found out by using te equation [6B].

5 LES00070-ZB rev. 5 / 7 As a summary of te previous explanation, te following table is starting te equivalence between te K-Factor according to te UL standards and te transformer over rating factor, te factor K. Table. Equivalence table between K-Factor (UL 56) and over rating factor, Factor K (HD 538) THD K-Factor UL OVER RATING FACTOR K HD 538 Eddy = 0.5 RI loss I (pu I rated ) I 3 (pu I rated ) I 5 (pu I rated ) I 7 (pu I rated ) I 9 (pu I rated ) I (pu I rated ) I 3 (pu I rated ) I 5 (pu I rated ) I 7 (pu I rated ) I 9 (pu I rated ) I (pu I rated ) I 3 (pu I rated ) I 5 (pu I rated ) Remark: tis equivalence list is valid up to 350kVA transformers

6 LES00070-ZB rev. 6 / 7 Interpretation / example Assuming a transformer is requested to supply 000kVA (called as fundamental power according to te IEC 6378-) wile te armonic content of te net is defined as per K- Factor 7, te equivalent power (wic includes te armonic effect) of suc unit sall be equal to te fundamental power multiplied by te proper Factor K according to te table attaced above. Tat is: Fundamental ower MVA Net armonic content K-7 => Factor K equals to.8 THD K-Factor UL OVER RATING FACTOR K HD 538 Eddy = 0.5 RI loss I (pu I rated ) I 3 (pu I rated ) I 5 (pu I rated ) Equivalent ower 000 x.8 = 560kVA As a result of tis, te transformer sall be pysically sized as 560kVA rated power and te temperature rise limit sall be guaranteed at suc equivalent power as well. Terefore, sould te temperature rise test is requested, during te full load part of te test te current must be equal to te rated current multiplied by te proper Factor-K, i.e. assuming te no load voltage level on LV side is 47V (Dyn), rated current will be 000/ (47*3) =.77kA, owever test must be run at.77x.8= 3.54kA (corresponding to 560kVA).

7 Document Title Loading transformers wit non sinusoidal currents Document No. Date & Rev. Ind. No. of ages age LES00070-ZB 7 7