The lifetime of wireless sensor nodes and implicit of the network they form is one of the elements driving the WSN design. There is also a related metric used during network employment, time to live, which has a major impact in selecting predefined strategies for nodes behavior. Although the energy consumption, the most important thing behind that metric, has influence on all the node components, the actual research mainly focuses on development of application oriented energy efficient functionalities and many authors use a less accurate energy approach for modules they did not concentrate on. Through this paper we try to gather the relevant factors for energy consumption that need to be taken into account with high accuracy regardless the analyzed component or functionality, and propose some relations for lifetime estimations based on identified factors which can be also utilized in energy balancing strategies.

Through this paper we will concentrate on battery powered electronic devices, able to integrate an on-line, software based, state of charge monitoring system. We propose a novel approach of the Lithium-ion battery mathematical model that provides accurate information about batteries behavior. Using the differential equations related to the cathode electrode from the battery electrochemical model, a Hamilton-Poisson realization is provided to point out some of the geometrical and dynamical properties. The shortcomings of Runge-Kuta numerical integration versus the proposed approach are highlighted. Keywords-energy monitoring; battery mathematical models; differential geometry. I. INTRODUCTIONThe widespread use of small electronic devices capable of receiving, transmitting and/or processing information is among the relevant elements defining the contemporary society, especially over the last decade. In this context, actual research is focused on improving performances of these devices in terms of functionality and autonomy. Through this paper we take into consideration the efforts done to prolong the systems autonomy and will concentrate on the constraints specific to battery powered electronic devices that are able to integrate an on-line, software based, state of charge monitoring system, using the sensor nodes of Wireless Sensor Networks constraints as reference.The key elements in providing precise information about the energy available in the batteries of electronic devices are the battery mathematical models and the methods used for determination of the power consumption in a context aware manner. Most of the existing WSN applications are using a simplified approach for run-time energy consumption, advances in this area being made through improvement of simulators, emulators and other types of development and testing environments.A brief glance on existing test-beds is performed in [1], where the authors propose a solution for energy run-time monitoring. There is also a software on-line monitoring method presented in [2]. The drawback on both methods for energy run-time monitoring is related to the absence of an accurate battery model for estimating available energy, even if the first system [1] relies on a fuel gauge electronic device which can be configured to compensate and minimize errors from variations in device temperature and supply voltage.In this paper, after a general view over the methods used for the battery state-of-charge determination, some types of battery models are enumerated with focus on a simplified electrochemical model. In order to outline some properties of this battery model, we provide a representation of the numeric integration solutions

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