Hybrid energy plants (HEPs), which include both fossil fuel technologies and renewable energy systems, can provide an important step toward a sustainable energy supply. In fact, the hybridization of renewable energy systems with gas turbines (GTs), which are fed by fossil fuels allows an acceptable compromise, so that high fossil fuel efficiency and high share of renewables can be potentially achieved. Moreover, electrical and thermal energy storage systems increase the flexibility of the energy plant and effectively manage the variability of energy production and demand. This paper investigates the optimal sizing of a HEP, which combines an industrial GT, renewable energy systems, and energy storage technologies. The considered renewable energy system is a photovoltaic system (PV), while the energy storage technologies are electrical energy storage and thermal energy storage. Moreover, a compression chiller and a gas boiler (GB) are also considered. For this purpose, the load profiles of electricity, heating, and cooling during a whole year are taken into account for the case study of the Campus of the University of Parma (Italy). The sizing optimization problem of the different technologies composing the HEP is solved by using a genetic algorithm, with the goal of minimizing the primary energy consumption (PEC). Moreover, different operation strategies are analyzed and compared so that plant operation is also optimized. The results demonstrate that the optimal sizing of the HEP, coupled with the optimized operation strategy, allows high average cogeneration efficiency (up to 84%), thus minimizing PEC.