Summary Few switching transition in high‐power and medium‐voltage application of power converters is desirable. The optimal pulse‐width modulation (OPWM) at fundamental switching frequency offers a better quality waveform at lower switching losses. It is a preprogrammed modulation technique where certain amounts of lower order harmonics are controlled and fundamental voltage is maintained. Here, a set of nonlinear transcendental equations is obtained, which exhibits multiple, unique, or no solution in different range of modulation index (MI). This paper proposes an advanced and fast method to obtain switching instants for OPWM equations. Moreover, it can solve a large number of such equations as computation of Jacobian matrix in the subsequent iteration is estimated from the previous values. Moreover, the proposed method also removes the singularity problem especially for large OPWM equations. The computational, simulation, and hardware results are provided to validate the concept for various cases.