Alternative definitions of energy for power meters in non-sinusoidal systems q M. Ponce-Silva, E.A. Moreno-Basaldúa ⇑ Centro Nacional de Investigación y Desarrollo Tecnológico, Int. Internado Palmira S/N, Palmira, C.P. 62490 Cuernavaca, Morelos, Mexico article info Article history: Received 20 November 2013 Received in revised form 4 September 2014 Accepted 12 September 2014 Keywords: Active power Electric energy Energy measurement Power definitions Power measurement Power theory abstract Energy flow in sinusoidal systems is analyzed without problems by means of the traditional power def- initions such as: apparent, active, and reactive, but these definitions are not properly applied in nonlinear loads. These loads present several distortions which are not correctly measured with the prevailing instruments designed for measuring energy and power. This is because a generalized set of power defi- nitions is not available. In this paper, an alternative set of energy and power definitions is suggested for non-sinusoidal systems. Each definition is obtained through the analysis of power in the time domain. The proposed definitions add information to alleviate the power and energy measurement problem of the power meters, offer alternative indexes to measure the energy distribution, and allow calculations in transient and steady states. Furthermore, an experimental measurement of the proposed powers by means of a half-wave rectifier is shown. Ó 2014 Elsevier Ltd. All rights reserved. Introduction The measurement of electrical energy plays an important role in the industry. Power meters provided appropriate values when the measurement was based on the analysis of the observed phenom- enon. For example, in single-phase sinusoidal passive loads, the power meters ran adequately when their design was based on the analysis of sinusoidal signals. From that analysis, the defini- tions of apparent, active and reactive power were defined [1]. However, the use of these definitions in nonlinear loads was inappropriate. With the growth of nonlinear loads, an urgent redesign was required for power meters to correctly measure the electrical energy. This redesign was generally based on the definitions of Budeanu [2,3]. They were not only an extension of the analysis of sinusoidal signals [4], but also they were not appropriate in all nonlinear loads, mainly because the orthogonally of the power components was only valid in some special loads [5]. Consequently, other definitions and power theories were devel- oped by many researchers as: Fryze [6], Akagi [7], Czarnecki [8], Emanuel [9], Tenti [10], among others. Different theories were suitably employed in certain loads and fulfill certain specific objectives [11], but as the standard IEEE 1459-2010 states [12]: ‘‘There is not yet available a generalized power theory that can provide a simultaneous common base for – Energy billing. – Evaluation of electric energy quality. – Detection of the major sources of waveform distortion. – Theoretical calculations for the design of mitigation equipment such as active filters or dynamic compensators.’’ In this paper, the points two and three of the standard IEEE 1459-2010 are considered the most important. The just energy billing and the correct design of mitigation equipment depend on them. Evaluation of electric energy quality The power quality (PQ) assessment is quantified by means of indexes or limit values of disturbances. The most known indexes are the THD of voltage or current and the power factor (PF) [13]. The limit values of disturbances are specified in terms of the volt- age signal such as sags (or dips), swells, notches, etc. The most sig- nificant is the voltage dip which is a short duration reduction in amplitude voltage [14]. This disturbance reduces the lifetime of several sensitive devices such as computers, and fluorescent lamps. Several European standards such as the EN 50160 [15] and the IEC 61000-4-30 [16], and American standards such as the IEEE 519 [17] put efforts to classify and to establish allowable levels of dis- turbances [18]. Also, the parts 1, 2, and 3 of the IEC 61000 series http://dx.doi.org/10.1016/j.ijepes.2014.09.019 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. q Thanks to the Consejo Nacional de Ciencia y Tecnología (CONACYT) for the support received in this research. ⇑ Corresponding author. Tel.: +52 777 271 71 57. E-mail address: edwing-ie@outlook.es (E.A. Moreno-Basaldúa). Electrical Power and Energy Systems 64 (2015) 1206–1213 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes