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This paper presents a study of modeling and simulation of a twelve-pulse circuit rectifier taking into consideration the effects of the voltage source impedance on the commutation angle for the system operating under a balanced and unbalanced three-phase supply. Three conduction modes are formed in this analysis. Based on the source inductances, the converter conduction modes will change including mode 3 overlap when the angle overlap μ extends beyond 60° and the number of conducting devices alternate between 3 & 4 devices in each state for both upper and lower bridges. These results are verified using a detail proposed analytical matlab model simulation. Also, the proposed analytical model results are compared to Simulink Powersys Toolbox model results and they are corresponded very well. The analytical method clearly shows the conduction states in all cases which could not identified using the simulink powersys toolbox model.