**Applications**

122 Sustainable Growth and Applications in Renewable Energy Sources

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Viladrich, M. 2004. Las principales aportaciones a la teoría de la regulación medioambiental. Los últimos cuarenta años. Economía Agraria y Recursos Naturales, 4(8), 41-62 Wiesenthal, T, Leduc, G, Christidis, P, Schade, B, Pelkmans, L, Govaerts, L, and

the Netherlands. Applied Economics, 39, 2465–2482

K., Meibom P., Lescot D., Hoffman T., Stronzik M., Gual M., del Rio P., Hernández P., 2003. Renewable electricity market developments in the European Union, Final Report of the Admire Rebus Project, ECN-C-03-082. ECN: Pettern, Netherlands. Van Beers, C., Van den Bergh, J.C., De Moor, A and Oosterhuis, F. 2007. Determining the

environmental effects of indirect subsidies: integrated method and application to

Georgopoulos, P. 2009. Biofuel support policies in Europe: Lessons learnt for the long way ahead. Renewable and Sustainable Energy Reviews, 13 (4), 789-800*.* 

**7** 

*Guyane Française* 

**Structural Design of a Dynamic Model of the** 

For a standard interconnected electrical power network, the problem of optimal management of production arises from randomness of users demand. When using renewable energies, an additional critical problem is that the resource itself is random. The difficulty is still more pregnant when dealing with small isolated production networks, in locations where photovoltaic systems or wind generators should be a promising solution. To resolve the difficulties induced by intermittent production or consumption, these systems must make a consistent use of the energy storage. For example, in the case of an individual photovoltaic system, storage is essential to the scale of at least 24h, in order to overcome the

Among the various methods used to store electrical energy, electrochemical batteries constitute the most readily available, with good performance and a reasonable cost (Riffonneau et al.,2008). Renewable Energies are concerned by stationary storage, for which lead acid batteries are a good choice. Despite decades of use and its apparent simplicity, the battery maintains a complex and poorly understood dynamical behavior. Moreover, possible degradation of the battery is largely related to poor control of periods of deep discharge or full load with gassing. For efficient use of this device, a detailed knowledge of operation, and thus a good electrochemical modeling, is essential. Otherwise, it could constitute the most fragile element in a photovoltaic or wind systems because of premature

aging resulting in a loss of capacity or a failure risk (Garche et al.,1997).

A lot has been done in the domain of batteries modeling from two opposite ways.

On the one hand, a purely phenomenological approach has been developed by engineers. In particular, very valuable tests are commonly performed using battery cycling with constant charge and discharge currents. In particular, there appears a reduction of the effective capacity when the cycling current increases (Peucker's law (Manwell Jams, 2003)). These results may have direct application for charge monitoring in systems with alternate charging and discharging sequences (for instance traction vehicles); unfortunately, they do not apply to wind turbines or photovoltaic applications subject to random electrical current

On the other hand, extensive physical studies have been made by electrochemists concerning the physics of electrochemical cells. Descriptions of the cell behavior have been

**1. Introduction** 

daily fluctuations.

variations.

**Battery for State of Charge Estimation** 

Frédéric Coupan, Ahmed Abbas, Idris Sadli, Isabelle Marie Joseph and Henri Clergeot

*UMR ESPACE-DEV, Université des Antilles et de la Guyane* 
