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A four-leg pulse width modulation (PWM) voltage source converter (VSC) is used to supply three phase balanced voltage even under an unbalanced load condition in three phase four wire power distribution network. A novel carrier-based modulation technique for the converter is described with the concept of an offset voltage and also is extended to so called 'discontinuous PWM (DPWM)' to minimize switching losses of VSC. As a practical application example of the four-leg VSC, a line interactive uninterruptible power supply (UPS) system is chosen. The feasibility of the proposed PWM strategies and control algorithms has been verified by the simulation and experimental results.