Tropical climate is characterized by hot temperatures throughout the year. In areas subject to this climate, air conditioning represents an important share of total energy consumption. In some tropical islands, there is no electric grid; in these cases, electricity is often provided by diesel generators. In this study, in order to decarbonize electricity and cooling production and to improve autonomy in a standalone application, a microgrid producing combined cooling and electrical power was proposed. The presented system was composed of photovoltaic panels, a battery, an electrolyzer, a hydrogen tank, a fuel cell, power converters, a heat pump, electrical loads, and an adsorption cooling system. Electricity production and storage were provided by photovoltaic panels and a hydrogen storage system, respectively, while cooling production and storage were achieved using a heat pump and an adsorption cooling system, respectively. The standalone application presented was a single house located in Tahiti, French Polynesia. In this paper, the system as a whole is presented. Then, the interaction between each element is described, and a model of the system is presented. Thirdly, the energy and power management required in order to meet electrical and thermal needs are presented. Then, the results of the control strategy are presented. The results showed that the adsorption cooling system provided 53% of the cooling demand. The use of the adsorption cooling system reduced the needed photovoltaic panel area, the use of the electrolyzer, and the use of the fuel cell by more than 60%, and reduced energy losses by 7% (compared to a classic heat pump) for air conditioning.