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

F.J. Casares, M. Varo, R. López-Luque , M. Torres-Roldán, D. Muñoz-Rodríguez



Stochastic simulation methods are normally extended as the only available to assess the reliability of the PV system 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 forgenerating 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.

Published in: Renewable Energy & Power Quality Journal (RE&PQJ, Nº. 14)
Pages:531-536 Date of Publication: 2016/5/20
ISSN: 2172-038X Date of Current Version:2016/05/04
REF:383-16 Issue Date: May 2016
DOI:10.24084/repqj14.383 Publisher: EA4EPQ

Authors and affiliations

F.J. Casares , M. Varo, R. López-Luque , M. Torres-Roldán, D. Muñoz-Rodríguez
Research Group on Physics for Renewable Energy and Resources. University of Córdoba. Spain

Key words

SAPV, LLP, Aguiar matrixes, PV sizing.


[1] Egido M, Lorenzo E. The sizing of a stand-alone PV systems: a review and a proposed new method. Solar Energy
Materials and Solar Cells 1992; 26: 51-69.
[2] Posadillo R, LópezLuque, R. Approaches for developing a sizing method for stand-alone PV systems with variable demand. Renew Energy 2008; 33: 1037 – 48.
[3] Posadillo R, LópezLuque, R. A sizing method for standalone PV installations with variable demand. Renew Energy
2008; 33: 1049 – 55.
[4] Lorenzo E, Araujo G, Cuevas A, Egido M.A, Miñano R, Zilles R. 1994. Electricidad Solar. Ed. Progensa.
[5] Sidrach-de-Cardona M, Mora López Ll. A simple model for sizing stand alone photovoltaic systems.Solar Energy Materials and Solar Cells 1998; 55: 199-214.
[6] Barra L, Catalanotti S, Fontana F, Lavorante F. An analytical method to determine the optimal size of a photovoltaic
plant.Solar Energy 1984; 33: 509-14.
[7] Bartoli B, Cuomo V, Fontana F, Serio C, Silvestrini V. The design of photovoltaic plants: an optimization procedure.
Applied Energy 1984; 18: 37-47.
[8] Bucciarelli L.L. Estimating loss-off-power probabilities of stand-alone photovoltaic solar energy systems.Solar Energy 1984; 32: 205-09.
[9] Bucciarelli L.L. The effect of day-to-day correlation in solar radiation on the probability of loss-of-power in a standalone photovoltaic energy system.Solar Energy 1986; 36: 11-14.
[10] Negro E. On PV simulation tools and sizing techniques: a comparative analysis toward a reference procedure. Proc. 13th Europ. PV Solar Energy Conf., Nice,1995; 687-90.
[11] Aguiar R, Collares-Pereira M, Conde J. Simple procedure for generating sequences of daily radiation values using a library of Markov Transition Matrices. Solar Energy 1988; 40: 269-79.
[12] Casares, F. , Lopez-Luque R, . Posadillo R., Varo-Martínez M. Mathematical approach to the characterization of daily energy balance in autonomous photovoltaic solar systems.Energy 2014; 72: 393-404.