The system comprises a main cogeneration module which can be supplied with a flow of fuel for a combustion process and is able to generate electrical energy and thermal energy in the form of a flow of at least one first hot fluid, preferably water. The main module has an electrical output terminal or node which can be directly connected to electrical user appliances and can be connected in parallel to an external electric power generating and supply network via a controlled switching device. The system comprises moreover a bottoming cycle recovery cogeneration apparatus able to recover, and partially convert into useful work, thermal energy from the products of the combustion process; an auxiliary generation module which can be supplied with thermal energy produced by the main module and is able to provide thermal energy at a lower temperature in the form of a flow of at least one second chilled fluid; and management and control devices preset to manage in a predetermined manner operation of the main module and the auxiliary module.