382 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 49, NO. 2, APRIL 2000 On the Selection of the “Best” Test Waveform for Calibrating Electrical Instruments Under Nonsinusoidal Conditions Alessandro Ferrero, Fellow, IEEE, and Carlo Muscas, Member, IEEE Abstract—The paper deals with a test method, based on the generation of signals with known and pre-assigned harmonic con- tent, for calibrating measurement devices to be used under non- sinusoidal conditions. The attention is concentrated on selecting the most suitable waveforms for the characterization of measure- ment instruments, by considering both the amplitude and the rel- ative phase of the different harmonics. The aim is to identify the situations that cause, more than others do, uncertainty problems while measuring different quantities. This investigation is theoret- ically performed by means of a number of numerical simulations, in which pre-defined values for each uncertainty source have been added to the voltage and current acquisition channels. Index Terms—Calibration, electric variable measurements, har- monic distortion, uncertainty analysis. I. INTRODUCTION T HE PRESENCE of nonsinusoidal voltages and currents in electric power systems is steadily increasing, owing to the increasing number of nonlinear or time-variant apparatus and devices which cause harmonic pollution in the system. A lot of theoretical and practical measurement problems arise from this new situation, such as the redefinition of the com- monly used electrical quantities (especially power quantities) [1], the definition and measurement of power quality indices [2], [3], and many others. However an important problem should be preliminary con- sidered in order to solve the above-mentioned problems, i.e., the metrological characterization of the measuring instruments im- plemented to perform measurements under nonsinusoidal con- ditions [4]. Since these measurements are usually performed by means of instruments based on digital signal processing techniques, the uncertainties introduced by each step (analog signal con- ditioning, sampling and A/D conversion, measurement algo- rithms, etc.) have to be taken into account. The classical specifications of measurement devices are often valid only under sinusoidal steady state conditions. The frequency-domain characterization of these instruments allows only for knowing their behavior with sinusoidal waveforms at different frequencies, but not under nonsinusoidal conditions, Manuscript received May 26, 1999; revised February 2, 2000. A. Ferrero is with the Dipartimento di Elettrotecnica, Politecnico di Milano University, Milano, Italy. C. Muscas is with the Dipartimento di Ingegneria Elettrica ed Elettronica, Università di Cagliari, I-09123, Cagliari, Italy (e-mail: carlo@diee.unica.it). Publisher Item Identifier S 0018-9456(00)03430-6. owing to their intrinsically nonlinear behavior. Therefore, when distorted signals are dealt with, it becomes necessary to establish new and more general characterization procedures. Up to now, very few attempts have been proposed to find a solution to this problem [5], [6], and no clear recommendations are provided by the standardization organizations. Some important respects of this problem are dealt with in the paper. In particular, the paper focuses on a test method based on the generation of calibrated test signals with known and pre-as- signed harmonic content. This method is aimed at obtaining, starting from a limited number of tests, information that could be useful in order to assess measurement uncertainties in a more general situation. The critical point, with this method, is the se- lection of the test signals. Therefore, this paper concentrates the attention on how to select the most suitable waveforms to be used for the characterization of measurement instruments. First, the different possible kinds of distortion typical of the electrical systems [7] are briefly investigated. A further investi- gation is needed in order to identify the waveforms that cause, more than others do, uncertainty problems while measuring dif- ferent quantities. Here in particular the uncertainty in the cal- culation of power quality indices suggested by standards or re- cently proposed in the literature [2] is considered. For this purpose it is necessary to evaluate which signal fea- tures are the most “dangerous” as far as the overall measurement uncertainty is concerned. The investigation should therefore regard, for instance, the amplitude of the harmonic components, referring either to the differences between harmonic order (e.g., odd or even) or to the possible interaction between neighboring harmonics. In addition, also the relative phase of the different harmonics has to be considered with particular attention. Indeed it has been many times demonstrated [2], [3] that many quantities to be measured (e.g., those based on the analysis of harmonic powers) strictly depend on the time relations between the frequency components of different signals. For this purpose it should be useful to study the uncertainty variations versus changes in the relative phase of one or more harmonic compo- nents and check the results of this study in realistic situations. In this initial stage of the investigation numerical simulations have been used to estimate the measurement uncertainty, since they are a useful and time-saving tool. With this method, pre-de- fined values for each uncertainty source have to be added to the voltage and current signals, so that their composition in com- puting the considered quantities can be assessed. Once all the- oretical respects of the problem will be better understood, ex- 0018-9456/00$10.00 © 2000 IEEE