Electric energy storage is a crucial problem for autonomous systems powered by photovoltaic installations. The excess of produced energy under favourable conditions is normally stored into batteries. For large scale applications, where more than one battery is used, the correct utilization of the storing bank plays an important role in order to extend the batteries' lifetime. The context of this work is related to the research on a solar assisted domestic heating application, which includes an autonomous photovoltaic installation and a software-driven resistance load which represents a dwelling heated by a heat pump. The load stands as a sink with time-varying energy consumption. The energy pattern resulting from the climate condition and the user driving behaviour implies a hard float cycling work of the storing bank. Moreover, in such applications, due to the tolerances on the internal parameters, the interactions between the batteries are unavoidable. As a result, some storage units work under constant discharge conditions whereas the others take on the overcharge current and imbalances occur. Therefore, a state-of-charge monitoring scheme of an individual unit can provide an essential information in order to improve energy management. The notion of State-Of-Charge (SOC) can be explained in terms of the energy available to the user in given charge/discharge conditions. Knowing the amount of energy left in a battery compared with the energy it had when it was new gives the user an indication of how much longer a battery will continue to perform before it needs recharging. The SOC is a fictitious variable which embodies the physical phenomena that occur in the battery and it cannot be explicitly measured. Hence, many modelling approaches have been developed to determine the SOC (Jossen et al., 2001; Sabatier et al., 2006; Rodrigues et al., 2000; Sauer, 1997). Unfortunately, none of the existent model assures a reliable estimation of it and new approaches are under development. Typically, the procedure of SOC determination involves the modelling of the battery behaviour under operating conditions. Generally, several methods of SOC estimation are used: SOC as a linear/non-linear function of the battery open circuit voltage. Ampere-counting techniques such as current integration. SOC as a function of the battery impedance. Each technique has its disadvantages. Since the SOC is a non-linear function depending on many parameters it is difficult to design an adequate model. The open circuit voltage represents the SOC function but is not though available under load. Thus, different observers based on the equivalent electric circuit have been designed to reconstruct this state in order to determine the SOC. The current integration method stands as a better solution to determine the SOC and it takes into account all charging and discharging currents. But also ampere counting does not allow an adequate SOC processing due to the errors accumulated during integration. The Electrochemical Impedance Spectroscopy (EIS) methods (Rodrigues et al., 2000) are commonly used to determine the physical parameters of the equivalent electric circuit and therefore give the essential information about SOC. Nevertheless, the battery impedance does not altogether reflect the SOC but provides in turn knowledge about faults, battery age, corrosion of electrodes, and other active mass properties. Besides, its practical implementation with systems that constantly work under load is complicated too. Since the battery exhibits a non-linear behaviour and its parameters may contain uncertainties, it appears interesting to study and compare two approaches of SOC calculation: robust state estimation, based on the sliding mode technique; fuzzy logic observation, based on the black-box modelling.
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