IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 49, NO. 2, APRIL 2000 315 Measurement of Harmonic Losses in Transformers Supplying Nonsinusoidal Load Currents Lorenzo Peretto, Member, IEEE, Renato Sasdelli, Member, IEEE, and Giovanni Serra, Member, IEEE Abstract—The spread of the load control techniques based on power electronics is causing the increase of harmonic losses in power distribution systems. A digital method for the evalua- tion of these losses in power transformers, which only requires measurements taken at the transformer output terminals, is discussed in this paper. The accuracy of the method, along with the performance of a virtual-instrumentation-based instrument implementing it, is also discussed. The results of some experi- mental work are reported. Index Terms—Digital measurements, harmonic distortion, non- linear systems, power transformer losses, testing. I. INTRODUCTION I NDUSTRIAL equipment and household appliances based on power electronics are aimed at more efficient uses of elec- tricity. Nevertheless, the ever-increasing use of electric loads that contain nonlinear and time-varying devices also results in growing harmonic distortion of the line currents in power distri- bution systems. The harmonic currents determine the increase of losses in power apparatus and systems. Owing to this increase, neutral conductors may need to be resized, and power apparatus, such as transformers, may need to be derated. Indeed, the current distortion determines the increase of the following transformer losses: • the losses ( being the dc winding resistance), by increasing the rms value of the load current; • the winding eddy current losses, which are proportional to the square of the frequency (both losses can cause ab- normal winding temperature rise); • other stray losses in the core, clamps, and other structural parts. The traditional metering practices fail to account for these costs that are therefore shared by all electric energy purchasers. Investigation methodologies able to provide information about the impact of new technologies on distribution systems in terms of harmonic losses are therefore searched for. New test methods would also be useful to validate the conventional procedures, such as those endorsed by standards [1], [2], for establishing the capability of transformers when supplying nonsinusoidal load currents. A method to measure the transformer losses in oper- ating conditions was proposed in [3]. It allows obtaining the total losses as the sum of two powers measured at the trans- former input and the output terminals, respectively. To reach this Manuscript received May 26, 1999; revised November 22, 1999. The authors are with Dipartimento di Ingegneria Elettrica, Università degli Studi di Bologna, Bologna I-40136 Italy (e-mail: lorenzo.peretto@mail.ing. unibo.it; renato.sasdelli@mail.ing.unibo.it; giovanni.serra@mail.ing.unibo.it). Publisher Item Identifier S 0018-9456(00)02439-6. Fig. 1. (a) Circuit where a distorting load is supplied by a sinusoidal source and (b) active-power flow in the circuit. goal, the voltage and current transducers must have the same nominal ratio, and this must be very close to the transformer ratio. Moreover, the transducers must feature the same transfer function in the frequency bandwidth of the signals. Meeting this requirement can be very difficult in the case of the pri- mary-voltage transducers. A method to measure the harmonic losses and their effect on the efficiency of power transformers is discussed in this paper. It only requires measurements at the output terminals of the trans- former under test, so that high-voltage transducers are not neces- sary. This paper also deals with the performance of a measuring instrument based on the virtual instrumentation (VI) technique that implements the method. Finally, the results of some exper- imental work for the method’s validation are presented. II. THEORETICAL BACKGROUND The measurement method recalled here relies on the flow analysis of the harmonic active powers in circuits supplied by sinusoidal generators (see [4]). It only requires power measure- ments at the transformer output terminals; hence it makes un- necessary the use of high-voltage transducers. Let us refer to the schematic diagram in Fig. 1(a), where a load that draws a distorted current Re (1) is supplied by a source of sinusoidal electromotive force . We assume that the Thevenin equivalent impedance of the source is independent of . Each current component causes a voltage drop across ; hence, the voltage in Re (2) i.e., the voltage applied to the load, is also distorted. In (1) and (2), is the angular frequency of ; is the complex rms 0018-9456/00$10.00 © 2000 IEEE