LAUSR

Abstract The planning and development of a hybrid energy source network is based on an optimal analysis which takes into account the connection costs and the production facilities. This paper aims at modeling a hybrid multisource system by employing the methods of the thermostatted kinetic theory. Specifically a network of energy sources is allocated into a geographical domain, which is divided into different regions each of them containing different energy sources. A hybrid kinetic theory framework is proposed where the energy source is identified by a quality parameter which can attain discrete values, whereas the energy supplied by the source is modeled by defining a continuous variable. The mathematical framework consists into a system of partial integro-differential equations with quadratic type nonlinearities whose parameters are interaction rates and probability density functions. The storage system is also modeled by introducing an external force field coupled with a mathematical thermostat for ensuring the conservation of the activation energy of the energy network. The existence and uniqueness of the solution is investigated by employing fixed point arguments and integration along the characteristic curves. A critical analysis and research perspectives conclude the paper showing that the proposed thermostatted kinetic theory frameworks can be considered as general paradigms for the derivation of specific models.