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Three-phase voltage- and current-source converters are the building blocks of a great number of power electronic systems. The origin of difficulties in the control of the above converters is in their nonlinear nature. In this paper, a novel modeling technique is introduced to derive the linear models of the converters from the nonlinear transformations of the conventional nonlinear models. Then, based on the derived linear models, a high-performance linear controller with satisfactory performances is designed. The bold feature of the new model is the independence of the controller design from the operating point. A DSP-based control system has been built in the lab to verify the performance of the new models and the control algorithm. The simulation and experimental results are in close agreement. The results show that the DC term and the AC-side reactive power can be controlled independently in less than one cycle.