A Geometric Approach to a Battery Electrochemical Model Using Specific Tools from the Poisson Geometry

Abstract

Abstract. Through this paper is presented a geometric approach of a battery electrochemical model using specific tools from the Poisson geometry. IntroductionThe area of remote sensing and controlling based on smart wireless sensors, is currently facing a trend from specific, highly customized applications, toward generic applications tailored for the use of a more general public. The new wireless motes are able to concurrently handle a variety of sensing units, but their flexibility is increasing the energy consumption and inevitable, the lifetime of the wireless sensors network will decrease dramatically when the motes will be equipped with several energy hungry sensors, as there is a limited energy that batteries can deliver. To overcome these limitations, different approaches are required for energy optimization like dynamic voltage and/or frequency scaling, powering off the sensing modules for the time intervals when they are not used, dynamic scaling of the radio transceiver power to limit the range of the transmitted signal to the actual communication partners and not waste energy, etc.In this context, we are working on the energy optimization in wireless sensor networks through online monitoring of the energy consumption at a node level and runtime accounting of the battery state-of-charge based on accurate battery models. The mathematical models of battery are generally used in wireless sensor networks simulations or during the design and development phases of these networks for life-time estimation, to analyze the impact of various strategies on energy consumption, for sizing the batteries in terms of price and performance at the application level. A less common usage of the battery mathematical models is for online battery state-of-charge monitoring even though it was proven that using the battery state-of-charge information in decision making can lead to an extended network lifetime of three times than the case in which decisions are taken on the basis of probabilities [1].There are several types of battery models available, each being characterized by a different accuracy -computational effort ratio. Differences between the actual battery models arise from the way in which the battery parameters are taken into account: the physical characteristics of the batteries (like material of the electrodes, electrolyte and separator, the size and the geometry of these electrodes, the distance between them and the internal resistance), the variations of load and of the temperature, etc.Some other aspects that are covered by the battery mathematical models are related to the real batteries behavior like self-discharge (effect caused by internal resistance of the battery, as a reduction of the state-of-charge over time even when no load is connected), relaxation effect (at very low consumption rates, the concentration of electrons became homogeneous by the electrons diffusion across the electrolyte, this behavior being seen from outside the battery as a partial