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The output voltage of a Multilevel Inverter (MLI) can be controlled using various low and high frequency modulation strategy. Apart from meeting the load voltage demand, the modulation strategy also tries to reduce the harmonics present in the output voltage waveform. In this paper, a novel modulation strategy, a Variable Structure Nearest Level Modulation (VSNLM) has been proposed with the objective to reduce the Total Harmonic Distortion (THD) thus giving better output voltage quality and smoother control. The development of the mathematical model and subsequent analysis has been carried out. Moreover, the proposed modulation scheme has been implemented on 7, 9, 11, and 13 level Cascaded H Bridge inverter and a generalized mathematical model of the proposed scheme has been developed. A comparison of the proposed strategy with the conventional NLC is presented in the paper. The results confirm the superior performance of proposed strategy in terms of THD. Experimental results have also been presented for validation.