Mathematical approach to the characterization of daily energy balance in autonomous photovoltaic solar systems

Sizing SAPV techniques try to assess the reliability of the system from the stochastic simulation of the energy balance. This stochastic simulation implies the generation, for an extended period of time, of the main state variables of the physical equations describing the energy balance of the system, that is, the energy delivered to the load and the energy stored in the batteries. Most of these methods consider the daily load as a constant over the year and control the variables indicating the reliability associated with the supply of power to the load. Furthermore, these methods rely on previous random models for generating solar radiation data and, since the approximations of the simulation methods are asymptotic, when more precise reliability indicators are required, the simulation period needs to be extended. This paper presents a mathematical methodology to address the daily energy balance without resorting to simulation methods. This method is directly based on daily solar radiation series modelled according to Markov stochastic processes and Aguiar matrices. The characterization presented is the base of a rational method in which reliability does not depend on the number of iterations but on the precision of the conditional probabilities included in Aguiar matrices. •A new SAPV sizing method is presented and validated.•This model relates the PV sizing methods to the autocorrelative Aguiar model.•This statistical approach is only limited by Markov matrixes.•It permits the study of PV systems with variable daily demands or solar tracking.•LLP for a SAPV can be estimated quickly and in an analytic and precise way.