The complicated modulation algorithm and the high switching frequency are two main hindrances in the analysis and simulation of matrix converters (MCs) based systems. To simplify the analysis and accelerate the simulation of MCs, a unique dynamic model is presented for the MC, which is independent of MC type (direct or indirect) and the modulation algorithm. All the input and output variables are transferred to the respective reference frames and their relations and limits are calculated. Based on the proposed equations, an equivalent circuit model is presented which can predict all the direct and indirect matrix converters dynamic and steady state behaviors without the need for small simulation time steps. Validity of the proposed model is evaluated using simulation of the precise model. Moreover, experimental results from a laboratory matrix converter setup are provided to verify the accuracy of the simulation results. 1. Introduction The need for AC-AC power conversion is, rapidly, increasing. The power electronics converters are used for generating variable amplitude, frequency, and phase voltages and currents [1]. Matrix converter (MC) is an all-switch power converter with interesting properties such as controllable input power factor, bidirectional power flow, and high quality input and output currents. Moreover, because of the absence of the bulky DC link energy storage component, it benefits from the possibility of a compact design [2, 3]. As shown in Figure 1, there are two main types for the MC, namely, direct matrix converter (DMC) and indirect matrix converter (IMC). The application of these converters are extensive: motor drive [4, 5], FACTS devices [6–8], distributed generation systems [9, 10], and wind energy conversion systems [11, 12]. Figure 1: Schematic circuit of (a) direct matrix converter, and (b) indirect matrix converter. The MC switching states are determined by modulation algorithms. Different modulation algorithms such as Alesina-Venturini (AV) method, optimum AV method, space vector modulation (SVM) [13], and duty cycle space vector (DCSV) [14, 15] have been proposed. In all cases, the modulation of the matrix converter is a complicated task and the switching frequency is usually in order of kHz (up to 45？kHz) [16]. Therefore, simulation of any MC based system is a time-consuming process, specially when the switching frequency is high. However, in dynamic and steady state studies, there is no need to consider the switching behavior of the converter regarding the study timescale. Moreover, in analytical methods for dynamic and
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