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Synchronous reluctance machines with solid rotor construction have advantages in certain high-speed applications such as flywheel energy storage systems. However, the solid rotor allows the flow of eddy currents, resulting in rotor loss and heat generation. The switching harmonics in the stator voltage supplied by a pulsewidth modulation (PWM) inverter are one of the sources of the rotor loss. This paper performs an analysis for the time harmonic loss in a solid-rotor synchronous reluctance machine, and investigates design and control issues associated with the inclusion of a three-phase LC filter for reduction of the rotor loss in solid rotor. A two-phase dynamic model of the machine which incorporates the LC filter dynamics is presented. This model is used to predict rotor losses due to switching harmonics generated by the three-phase PWM inverter. A model-based current regulator is utilized, which is modified to include the effects of the LC filter. Experimental results validate the proposed approach.