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The discontinuous conduction operating mode of three-phase diode bridge rectifiers that apply third-harmonic current injection is analysed. A piecewise linear rectifier model suitable for application of numerical methods is developed in order to analyse the circuit. A method to normalise the rectifier variables is proposed, such that numerically obtained results can easily be generalised to any rectifier applying denormalisation. Four special cases of rectifier operation in the discontinuous conduction mode are analysed, at the boundaries of the region. An approximate method of rectifier analysis is proposed. The rectifier is also analysed applying numerical methods, and the results of such analysis are presented illustrating dependence of the rectifier operation parameters on the load current and the component tolerances. The results are compared to the previously proposed approximate method. Experimental verification of the rectifier analysis is performed. It is shown that the discontinuous conduction mode is a suitable choice for applications that tolerate a total harmonic distortion ≈ 10%.