The required standards for transformer efficiency in North American are U.S. DOE 2016 and CSA Publication C802.2-00 (Canada). The measurement and calculation methods, required by these standards, accurately determine a transformer’s losses and energy efficiency when supplying linear loads. The method used to determine the total losses requires the summation of excitation losses and impedance losses. These losses are determined by performing open-circuit and short-circuit tests.
Unfortunately, modern electrical distribution systems typically supply a high percentage of nonlinear electronic loads, particularly in 120/208-volt systems. As a result, transformer losses increase and energy efficiencies decrease. The level of deterioration is a function of harmonic voltage magnitudes at a transformer’s primary terminals, load-generated harmonic current magnitudes at its secondary terminals and their phase relationships. There are, unfortunately, no recognized standards or measurement methods for determining transformer losses or efficiency under nonlinear loading.
Nonlinear Efficiency – There is, and probably never will be, a standard for the measurement of losses and efficiency under nonlinear loading.
Measuring the energy efficiency of a transformer under nonlinear loading presents significant technical challenge. Unlike the conventional short-circuit test, which requires very little actual power (W), the measurement of nonlinear impedance losses would require a nonlinear load bank, with a specified harmonic current profile. Such a profile would be quite impossible to achieve, at any reasonable cost, for all transformer ratings and configurations.
‘Power-In – Power-Out Measurement Method’ – Several manufacturers have been publishing their transformers’ efficiencies under nonlinear loading. The decision to do so may have given them some ‘short-term’ marketing advantage, but their claims are quite deceiving. As already stated, there are no national or international standards. For this reason alone, it would be impossible for a specifying engineer to compare each manufacturer’s claims.
In addition to this obvious problem, the manufacturer’s claims have been based on the ‘Power-In – Power-Out Measurement Method’. Although mathematically sound, the method’s instrumentation can produce an efficiency measurement error of ±1.31%, when using ‘Revenue Class’ instrumentation or ±0.94%, when using ‘Laboratory Class’ instrumentation. These assessments may be found in a number of published IEEE papers, which are available upon request] In order to verify these claims, PQI conducted a number of tests at Liebert’s Columbus, Ohio laboratory, which has a large adjustable nonlinear load-bank and a selection of measuring systems, including precision ‘Laboratory Class’ instrumentation.
The PQI Calculator™ - As an alternative to measuring the losses and efficiencies of a transformer, PQI developed software based on IEEE Std C57.110.1998. This software was developed over an eight-year period so that it now measures losses and efficiency of harmonic mitigating transformers, with their more complex winding architectures. The present Revision 13 software, now called The PQI Calculator™, is capable of measuring and comparing the performance of any two transformers simultaneously, regardless if their kVA ratings or winding configurations. It can determine losses and efficiencies under any harmonic current profile. In addition to pre-programed load K-Factors, specific or measured profiles are easily programed.
Given the capital cost of each transformer, power costs and air conditioning requirements, the calculator will determine each transformer’s losses and efficiency, ‘penalty losses’ under any load factor, annual energy savings and financial benefits, in a new construction substitution scenario or before end-of-life replacement scenario. The calculator will also provide all EPA environmental benefits.
The Transformer Performance Analyzer™- To confirm the accuracy of The PQI Calculator™, PQI next developed The Transformer Performance Analyzer™, which is based on ‘The Voltage and Current Difference, Loss Measurement Method’.  This measuring instrument has an efficiency error of ±0.033%.  The results obtained by this instrument are in agreement with those produced with NEMA TP 2 measurements for linear loading and IEEE Std C57.110-1998 calculations for nonlinear loading.
 D. Lin, E.F. Fuchs, M. Doyle ‘Computer-Aided Testing of Electrical Apparatus Supplying Non-Linear Loads’, IEEE Transactions on Power Systems, Vol.12, No.1, February 1997
 A. Damnjanovic, G. Ferguson ‘The Measurement and Evaluation of Distribution Transformer Losses under Nonlinear Loading, IEEE PES, General Meeting, PESGM2004-000721, June 2004
 E.F. Fuchs, R. Fei ‘A New Computer-Aided Method for the Efficiency Measurement of Low-Loss Transformers and Inductors under Nonlinear Operation, Paper No. 95WM 097-PWRD, IEEE/PES Winter Meeting, January – February 1995
The CSA C802.5 Transformer Performance Calculator® - The CSA C802.5 Transformer Performance Calculator® is a spreadsheet tool for calculating the efficiency of a specified transformer under specified harmonic loading conditions. While the specified transformer may be K-Rated, it may not be harmonic mitigating.
Transformer efficiency calculations are based on IEEE C57.110, and are provided at the users desired loading percentage and operating temperature. The calculator can also determine the expected temperature rise of the specified transformer under the specified harmonic loading and percent full load (%FL).
Calculations are based on a number of assumptions that are noted in Annex C of the C802.5 guide. In the case that the calculator is permitted to determine the temperature rise without user-override, the calculator provides the transformer efficiency under the given harmonic loading condition across its entire loading profile. A graph is generated, illustrating the transformer’s efficiency versus loading percentage, with two super-imposed curves:
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