In recent years, multi-generation systems (MGS) have been at the centre of attention for incorporating various energy sources and technologies to provide a reliable and sustainable energy supply. However, deciding on the most suitable configuration and optimal operation strategy of MGSs has always been a challenging issue due to the nonlinear and complex interactions between different energy converters. Cogeneration solutions offer excellent energy efficiency through the coproduced heat from the electricity generation process. This will lead to significant economic profitability compared to conventional independent heat and power production plants. This paper presents a mixed-integer quadratic based multi-objective structural design strategy for grid-connected cogeneration systems comprising combined heat and power (CHP) devices, ancillary boiler, and energy storage devices in presence of nonlinear and dynamic behaviour of the energy storage systems. The power fluctuations smoothing index (PFSI) and energy storage depreciation factor (ESDF) are defined to effectively mitigate the power grid fluctuations and extend the lifetime of the energy storage systems. Presenting three case scenarios, the obtained results demonstrate the efficacy and applicability of the developed technique and reflect the impact of the introduced factors on the optimal configuration and operation of cogeneration systems.