Model accuracy, computational complexity, and weighting factor dependency are three primary challenges associated with model predictive control (MPC) in controlling multilevel inverters (MLIs). This paper proposes an enhanced discrete-time model of MLI by using Heun's integration method, resulting in a more precise formulation and indirect minimization of CMV. Unlike the existing methods, this method does not employ a cost function with weighting factor or offline selection of voltage vectors (VVs) to minimize common-mode voltage (CMV). This approach allows per-phase control philosophy, and it can be easily to extended to higher-level of MLIs without significant modifications. Experimental studies are conducted on a four-level MLI system to validate the efficacy of the proposed MPC, and its performance is compared with the existing MPC methods.