Sizing Neutrals for Transformers - lanecoburn.com

1 |PURE POWER// FALL 200524K-rated Transformers are typically usedwhere anticipated loads include non-linear power supplies. They don tremove harmonic distortion from thesystem. Rather, they handle the addedcurrent and heating effects resultingfrom nonlinear loads without Laboratories has estab-lished ratings of 1, 4, 9, 13, 20, 30, 40and 50 as standard K-factor ratings. K-rated Transformers include neutral lugsthat allow for 200% neutral connec-tions; smaller parallel windings on thesecondary side of the transformer tocompensate for the skin effect associ-ated with high frequency harmonics;transposed delta winding conductors;and electrostatic shielding between theprimary and secondary windings.

2 Harmonic load currents cause addi-tional heating, primarily in the form ofadditional winding eddy current provides methodsto de-rate a transformer for a given har-monic load profile. ANSI found that anon-K-rated transformer would have tobe de-rated to about 70% in an envi-ronment requiring K-13 load actual K rating of a transformerdescribes the ratio of linear and non-linear load that it can handle. As theamount of nonlinear load increases inrespect to the linear load, higher K-rated Transformers will be required. Aspecific K-factor rating indicates that atransformer can supply its rated kVAload output to a load of specifiedamount of harmonic content.

3 K-factoris a scale of the harmonic currentswith respect to their effects on trans-former heating based on A. For example, the followingdata is from the Federal Pacific website( ): K-4 transformer will handle 100%plus 50% nonlinear load. K-13 transformer will handle100% plus 100% nonlinear load. K-20 transformer will handle100% plus 125% nonlinear load. K-30 transformer will handle100% plus 150% nonlinear transformer will be able tooperate without overheating within itsrating while supplying a nonlinearload percentage. For instance, for a K-13 transformer, the total current fromthe frequencies above 60 Hz (funda-mental) is equal to the total currentfrom the fundamental of the K ratings noted above(4, 13, 20 and 30) have an associatedharmonic profile.

4 Utilizing the har-monic content load profile, the totalharmonic distortion (THD) can be cal-culated by the following equation:%THD =100 * (I2 + I3 + I4 +I5 ..+ Ih ) / I1 This is the square root of the sum ofthe square of all harmonic currentspresent in the load, excluding the 60Hz fundamental. The total harmonicdistortion for each of the K-ratingsabove can be used to calculate the totalbalanced and unbalanced neutral cur-rent with the following formulas:Balanced: % Neutral current < 300 * % THD (10,000 + (% THD) ) (Cannot exceed 173% of neutral.)Unbalanced: % Neutral current < 200 * (2,500 + (% THD) )(10,000 + (% THD) ) (Cannot exceed 141% of neutral.)

5 The per unit harmonic currents usedfor the calculations in the accompany-ing charts are arbitrary. But when theper unit harmonic current is squaredand multiplied by the harmonicSizing Neutrals forTransformersCorrectly Sizing Neutrals for transformer secondaries is essential for handling harmonicsBY KEITH LANE, Coburn & Associates, , 9/13/2005 1:35 PM Page 24frequency number squared for each ofthe harmonic frequencies and thesums of these values added together,they equal the K-factor amounts of per unitharmonic currents can exist at thevarious harmonic frequencies for thesame K-factor level, but using thefigures noted should give a goodapproximation of the anticipated levelof THD associated with various K-ratedtransformers.

6 Actual harmonic currentlevels at the various harmonicfrequencies would have to beevaluated to determine the actual THDfor a specific location in a distributionsystem. Charts 1 through 4 show thecalculations for various AND HIGHAt lower levels of harmonic content,the unbalanced situation will producemore neutral current. As harmoniccontent increases to the K-13 level, theunbalanced neutral content is aboutequal to the balanced neutral one approaches even higher levels,the balanced situation will producemore neutral current than in theunbalanced situation. The additiveeffects of the harmonics coupling onthe neutral from all three-phase con-ductors start to have more of an effectthan the canceling effect on the neu-tral of the balanced one can see from the charts,200% Neutrals from the secondaryside of a 480-208/120-volt, delta-wye,3-phase, 4-wire transformer to the208/120-volt distribution panel are notalways required.

7 Theoretically themaximum neutral current can only be173% of the phase conductors basedon worst case condition of rectifierconduction angles of 60 degrees. Evenin the widely used K-13 transformer,the associated load profile dictatesonly a maximum of a 126% neutralcurrent. It may be prudent to provide200% neutral feeders from the trans-former to the distribution panel in anenvironment requiring a K-30 trans-former where the calculated maximumneutral current can be as high as171% of the phase neutral current can theoreticallybe as much as 173% based on worstcase condition of rectifier conductionangles of 60 degrees of the balancedungrounded conductor (phase) currentdue to nonlinear loads.

8 The NationalElectrical Code (NEC) does not haveany specific codes that call for theneutral conductors to be larger thanthe ungrounded the 1996 NEC code cycle, anad hoc subcommittee studied manyinstallations and hundreds of feedersinvolving 3-phase 4-wire, wye-con-nected systems with nonlinear found that only about 5% hadneutral current ampacities exceeding125% of the phase conductors. As aresult, the subcommittee indicatedthat there was not enough evidence torequire neutral conductors to be over-sized by any typical factor. [CHART 1]Neutral Current with K-4 Transformer The per unit harmonic current for the various harmonics =100 * ( + + + + + + + + + + + ) / 1 = : % Neutral < 300 * / (10,000 + (% ) ) = 68%Unbalanced: % Neutral 200 * (2,500 + (% ) ) / (10,000 + (% ) ) = 107%[CHART 2]Neutral Current with K-13 Transformer The per unit harmonic current for the various harmonics are: =100 * ( + + + + + + + + + + + ) / 1 = : % Neutral 300 * / (10,000 + (% ) ) = 126%Unbalanced.

9 % Neutral 200 * (2,500 + (% ) ) / (10,000 + (% ) ) = 124%25 | 9/13/2005 1:35 PM Page 25|PURE POWER// FALL 200526 NEC dictates that the demand calcu-lations for a system will be based on100% of the non-continuous load plus125% of the continuous load. Thephase conductors are sized based onthe system demand calculations. Sincethe neutral conductors are typicallysized at a minimum the same as thephase conductors they are sized tohandle 125% of the continuous cur-rent. Per NEC, a continuous load iswhere maximum current is expected tolast for three or more JUDGMENTT here are times when applying a 200%neutral to the secondary of every K-rated transformer can be avoided byusing logic and mathematical formulasto determine the actual size of therequired neutral conductor.

10 Reducingthe size of neutral conductor from thesecondary of the 480-208/120-voltdelta-wye 3-phase, 4-wire transformerto the 120/208-volt distribution panelwill not provide much cost savings ifthe panel is close to the if the electrical distribution con-tains several feed-through panels orextended lengths of 208-volt 3-phasefeeders to distribution panels, reducingthe size of neutral conductors can pro-vide installation cost is not uncommon to feed four tosix receptacles for computer loads froma single 20-amp, 1-pole breaker. Thisindividual branch can be fed independ-ently with a single hot and a neutral orcan be combined with two otherbranch feeders in what is called a fullboat.