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The aim of this study is to present a set of closed-form analytical equations in order to enable the computation of the three-phase bridge rectifier steady-state performance estimation. The proposed method presented in this study is a fast, accurate and effective mathematical model for analysing three-phase full-wave controlled rectifiers. The steady-state mathematical model is based on the derivation of an appropriate set of switching functions using the general switching matrix circuit (GSMC) techniques. Once the switching functions are derived, the output current, input current and output dc voltage can all be easily derived and generated from the application of this technique. The effect of overlap is accurately modelled and the distortion (notches), frequency content on the input (voltage and current) and output voltage distortion are derived. The proposed mathematical model, unlike conventional analytical methods, can be integrated in the design of active filters. Furthermore, the output voltage reduction, the rms, average and peak values of voltages and currents for the thyristors and any other semiconductor devices used are readily available for the designer by direct substitution into closed-form equations without any need for the waste of time for worst-case scenario simulations. This method can also be applied to other types of converters, specifically to all voltage fed power converters.