Due to the significance of hybrid energy systems, selecting the appropriate sizing-energy management strategy combination represents a key factor to ensure the efficient operation while offering a competitive operating cost. This paper presents an integrated framework for finding the best size-energy management strategy combination for a hybrid energy system. Fundamental to this framework is utilizing finite automata to develop multiple energy management strategies that fully take into consideration the dynamic relationship between all the assets in the hybrid energy system. The proposed integrated framework consists of three main steps. First, an analytical and economic sizing approach is performed to find the initial sizes of the hybrid energy system assets based on an initial energy management strategy; second, using finite automata to implement the initial energy management strategy and instantiate different energy management strategies; and third, an evaluation model is developed to assess the instantiated energy management strategies and extract the featured conditions to create new-improved one. This new energy management strategy is used to re-exercise the analytical and economic sizing to obtain the best size-energy management strategy combination. The novelty in this work can be summarized as taking the impact of selecting the right energy management strategy on the sizing of a hybrid energy management. This can lead to better performance and can be explained in our integrated framework by reducing the cost, reducing the diesel generator and fuel cell working hours and increasing the photovoltaic utilization. Moreover, using finite automata in implementing and instantiating multiple energy management strategies to attain an improved one has not been reported. A comparison between the results of the proposed framework and the results of the analytical and economic sizing approach is carried out. The size of the photovoltaic is reduced from 140 kW to 60 kW when using the integrated framework and therefore the size of the electrolyzer and the hydrogen tank reduced to the half. Moreover, a reduction in the diesel generator working hours by 35% and in the levelized cost of energy by 40% are achieved.