Selective Harmonics Elimination Pulse width modulation (SHE PWM) presents an alternative modulation technique to operate medium voltage medium and high power converters as it reduces the switching losses. SHE PWM generates high-quality output waveform at the low switching frequency. Its application to multilevel converters furthers leads to improvement in output waveforms with lower switching losses, lesser dv/dt and lowers switching devices ratings. In this Paper SHE PWM for an asymmetrical cascaded H-bridge multilevel inverter under unequal DC voltage condition for fundamental and multiple switching cases are investigated. More harmonics can be eliminated by considering multiple switching's. The Solution of the Nonlinear transcendental SHE equation is obtained using an advanced derivative free numerical technique which. The method is simple in implementation with fast calculations per iteration as it avoids the evaluation of Jacobian and its matrix. Also the need for precise initial guess in the proximity of actual solution is not needed as an identity matrix of the size of designed variable serves the purpose. Different inequality in the dc voltages is taken to eliminate the lower order harmonics from the output. Only exact solutions for the switching angles which ensure the complete elimination of targeted harmonics are reported. Simulation and Hardware results are presented to confirm the validity of the proposed technique.