Hybrid Polygeneration Energy Systems (HPES) can be effective solutions to reach COP26 goals. In particular, Combined Heat and Power (CHP) systems can increase the total system efficiency when both electrical and thermal power are required. The integration of a Battery Energy Storage System (BESS) can further improve the plant efficiency and economy, assuring higher operational flexibility. Configuration, sizing and control strategy definition are of primary concern for these systems when the best possible performances are sought. This work aims to quantitatively assess the importance of the adopted control strategy in the operation and performance of a possible sub-system of a grid-connected Hybrid Polygeneration Energy Systems (HPES), consisting in this study of a CHP plant assisted by a BESS. A simulation code of the plant from an energetic point of view was used, and the main economic indicator was also calculated according to the legislative reference scenario. Then a Prescient Model Predictive Control (MPC) was coded to achieve near-optimal plant operation, using a novel system state description to reduce the computational burden linked to the Optimal Control Problem (OCP) solution. The BESS system was modelled, including cycle battery ageing. Subsequently, the performances of the adopted prescient MPC have been compared to the previous results given by a multi-objective plant sizing with a rule-based control. The results show that the control strategy can enhance the performance of the CHP system, achieving remarkable overall better performances, with up to 12% higher Primary Energy Savings. Moreover, the research findings highlight how the proposed control variable ensure a reduction of the computational time by more than 70%, also improving the quality of the found solutions to the OCP. The results also suggest that proper control strategies should be adopted even in a preliminary optimal sizing phase of the CHP plant, since there is a large room of improvement in predicting the achievable plant performance when more basic rule-based control strategies are overcome and replaced by MPC.