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This paper deals with the validation and design analysis of Matrix converter for variable frequency using mathematical equations. The analysis was done using Venturini modulation algorithm. The PI controller is used for Matrix converter to reduce Total Harmonic Distortion (THD) in the output current. The comparative study is done for open loop and closed loop PI compensation in MATLAB-Simulink. Furthermore, the output waveforms are produced with significant reduction in the Total Harmonic Distortion.