IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 3, JULY 2013 1813 Harmonic Analysis in Frequency and Time Domain IEEE Task Force on Harmonics Modeling and Simulation A. Medina, J. Segundo-Ramirez, P. Ribeiro, W. Xu, K. L. Lian, G. W. Chang, V. Dinavahi, and N. R. Watson Abstract—This paper presents a review with a concise de- scription and analysis of the fundamentals, characteristics, analytical details, merits, and drawbacks associated with existing methods in frequency and time domain for harmonic analysis in practical power networks. The description and analysis are centered on methods developed in the harmonic domain, hybrid frequency-time domain, and time domain, respectively. Validation of the reviewed methods for harmonic analysis, against one of the widely accepted digital simulators, such as EMTP, EMTDC, or MATLAB/SIMULINK, is reported in the cited individual contributions. Index Terms—Harmonic domain, Hartley transform, hybrid frequency-time domain, nonlinear elements, time varying. I. INTRODUCTION A POWER system, operating under ideal conditions, is ex- pected to be perfectly balanced, of a single frequency, and with sinusoidal current and voltage waveforms of constant amplitude. However, in practical power systems, this ideal op- erational mode is not encountered, since the network compo- nents, at a lesser or greater extent, have the undesirable effect of distorting the original sinusoidal waveforms. Nonlinear compo- nents and loads, such as power converters, flexible ac transmis- sion systems (FACTS) devices, nonlinear saturation and hys- teresis in components with magnetic cores, fluorescent lamps and arc furnaces, among others, represent the main contribution to this effect, known as harmonic distortion. Adverse quality of power effects due to harmonic distortion are, for instance, in- terference with communication, control and protection systems, reduction of the equipment’s life span, and additional losses in the power system. Diverse harmonic distortion issues, such as its causes, effect on quality of power, standards and mitigation techniques, are described in literature [1], [2]. Digital harmonic analysis relies on harmonic detection and prediction, respectively. The first processes in real-time data of the monitored harmonic content in the network, while the last Manuscript received November 07, 2012; accepted February 19, 2013. Date of publication May 07, 2013; date of current version June 20, 2013. Paper no. TPWRD-01209-2012. Task Force on Harmonics Modeling and Simulation is with the Harmonics Working Group under Power Quality Subcommittee, IEEE Power and Energy Society T&D Committee. Task Force members: R. Burch, G. Chang (Chair), V. Dinavahi, A. Emanuel, R. Langella (Vice Chair), K. Lian, P. Lehn, A. Medina (corresponding author), B. Moncrief, T. Ortmeyer, I. Papic, S. Ranade, P. Ribeiro, H. Sharma, A. Testa, N. R. Watson, X. Wang, W. Xu, and X. Yang (e-mail: amedinr@gmail.com). Digital Object Identifier 10.1109/TPWRD.2013.2258688 relies on computer simulations to predict the harmonic distor- tion through implemented analytical models. The methods to be described in this paper belong to this second category. Harmonic analysis has been carried-out using frequency, time and hybrid time-frequency domain methods. The conceptual and analytical details of these methods are concisely detailed in this contribution. A concise overview on simulation methods for harmonic analysis has been previously reported [3]. Their application was illustrated in a companion paper with examples and sample systems [4]. Further advances on methods for har- monic analysis in frequency and time domain are detailed in [5], [6] and more recently in [7], where in addition to the above, an alternate sub-division of methods for harmonic analysis is proposed. This paper presents a concise yet detailed revision of theoret- ical fundamentals and principles of classical methods for har- monic analysis. A precise and simple classification of methods is given. II. METHODS FOR HARMONIC ANALYSIS Different methods for harmonic analysis in frequency domain and time domain are currently detailed in the open literature. Hybrid frequency and time domain methods have been devel- oped with the purpose of combining the individual advantages of the frequency and time domain methods. The fundamentals and theoretical principles of these methods are given next. A. Frequency Domain In general, available methods for harmonic analysis in the frequency domain are divided into direct method, iterative har- monic analysis and harmonic power flow methods, respectively. 1) Direct Method: The frequency response of the power system, as seen by the bus of interest, is obtained through injec- tion of a one per-unit current or voltage at discrete frequency steps for the particular range of frequencies. The process is based on the solution of the network equation (1) where is the network admittance matrix, is the nodal voltage vector and is vector of current injections, with only one nonzero entry. The simplest current source method uses the sequence com- ponent framework by injecting ideal current sources into the power network [8]. In a later contribution, the solution is di- rectly obtained in the phase domain for three-phase unbalanced systems [9]. Harmonic decoupled circuits are assumed in both methods. 0885-8977/$31.00 © 2013 IEEE