Mathematical model of an off-grid hybrid solar and wind power generating system

The dynamics of an off-grid power generating system, coupled to a storage unit and to household appliances, is described by means of an analytic hydrodynamic analog. Following this analogy, by noticing that the effux rate from a leaking bucket is described, in terms of the liquid content, by Torricelli's formula, we denote as “Torricelli's smart consumer” a user being able to calibrate its energy consumption rate with respect to the energy level in the storage unit as if the hydrodynamic model would strictly apply. Simple solutions to the nonlinear dynamic problem associated to this type of smart consumer are found and generalization to other types of smart consumers are sought.