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battery-soc-prediction-journal

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`TVLSI-00029-2003.R1 1 An Analytical Model for Predicting the Remaining Battery Capacity of Lithium-Ion Batteries Peng Rong, Student Member, IEEE and Massoud Pedram, Fellow, IEEE Abstract — Predicting the residual energy of the battery source that powers a portable electronic device is imperative in designing and applying an effective dynamic power management policy for the device. The paper starts up by showing that a 30% error in predicting the battery capacity of a Lithium-ion battery can result in up to 20% performance degradation for a dynamic voltage and frequency scaling algorithm. Next, this paper presents a closed-form analytical expression for predicting the remaining capacity of a lithium-ion battery. The proposed high-level model, which relies on online current and voltage measurements, correctly accounts for the temperature and cycle aging effects. The accuracy of the high-level model is validated by comparing it with DUALFOIL simulation results, demonstrating a maximum of 5% error between simulated and predicted data. Index Terms—Remaining battery capacity, accelerated rate capacity, temperature, cycle aging and dynamic voltage scaling I. INTRODUCTION1 HE battery service life of mobile battery-powered electronic systems is a major concern of designers of such systems. Attempts for extending the battery lifetime have traditionally focused on minimizing the power consumption of the electronic circuits powered by these batteries. These circuit-oriented techniques tend to be inadequate because they ignore important characteristics of the battery source itself e.g., the dependency of the remaining capacity of a secondary (rechargeable) battery on its current discharge rate and internal temperature, the charge recovery phenomenon, and the cycle aging effect. In the recent years, a number of researchers have begun to investigate the characteristics of battery sources and their impact on low-power circuit optimization techniques and power management strategies. A survey of battery-aware design techniques can be found in reference [1][2]. A number of researchers have reported models for predicting the battery remaining capacity or battery service life. A low-level detailed electrochemical model based on concentrated-solution theory was reported in [3]. This model is accurate and general enough to handle a wide range of lithium-ion cells, which also explains the wide-spread use of its companion simulator software. A multi-dimensional coupled thermal-electrochemical model was presented in [4]. Electrochemical models are accurate but inherently suffer from the long simulation time required in practice. Manuscript received February 2, 2003, revised July 14, 2005 and accepted January 23, 2006. This work was funded in part by a grant from the NSF CSR-EHS program (contract # 0509564.) P. Rong is with Department of Electrical Engineering, University of Southern California, CA 90089, USA (email: [email protected]). M. Pedram is with Department of Electrical Engineering, University of Southern California, CA 90089, USA (email: [email protected]). Consequently, more efficient battery models have been proposed in recent years. A macro-model for lithium-ion batteries was presented in [5], where the battery is modeled by a PSPICE circuit comprising of voltage sources and linear passive elements. Since simulation of the electrical circuit model is still time consuming, the authors of reference [6] proposed a discrete-time battery simulation model, which approximates a continuous-time circuit model by using VHDL language. Reference [7] studied the battery discharge efficiency under different loading conditions and approximated this dependency as a linear or quadratic function. In this paper, the authors also presented a discharge rate-based method to estimate the battery lifetime under a variable load. The battery discharge efficiency was used as the weighting coefficient in the lifetime estimation equation. Reference [8] presented a stochastic battery model based on discrete Markovian process which captures battery recovery and rate capacity effects. Reference [9] proposed a high-level diffusion based analytical model. This model aims to predict the battery lifetime given the discharge profile. The authors consider the concentration evolution of the active materials in the battery during a discharge process and model it as a one-dimensional diffusion process in a finite region. In this model, a battery is considered exhausted when the active material concentration at the electrode surface drops below a preset threshold. This model is quite successful in terms of prediction accuracy, efficiency and generality. However, a prerequisite to use this model is that the load of a battery should be known exactly from the beginning of a discharge process. And this model does not take temperature dependence and cycle aging effects in account. So each time when a battery works in a different situation the model parameters needs to be reset, which may cause inconvenience in practice due to the overhead. An extensive review of battery models and battery aware low power techniques can be found in the [10]. The battery temperature and the cycle life of a secondary battery have a large impact on the battery lifetime after a full charging step. As temperature increases, the full discharge capacity of a secondary battery tends to increase. Unfortunately, higher temperature also results in much lower cycle-life for the battery (the cycle-life denotes the number of full charge/discharge cycles that a secondary battery can go thru before its output voltage drops below an acceptable threshold even after a full charging cycle.) The battery cycle aging effect denotes the phenomenon by which the full deliverable capacity of a rechargeable battery decreases as the number of battery charge/discharge cycles (which is referred to as the cycle-age of the battery) increases. As shown in work [11], the full deliverable capacities of commercial lithium-ion batteries shrink by 10-40% during the first 450 T`TVLSI-00029-2003.R1 2 charge/discharge cycles. Without knowledge about temperature and cycle life of a battery, it is therefore impossible to obtain an accurate prediction of the battery remaining capacity. Commercially deployed battery estimation techniques can be generally classified into three categories according to their expected accuracy: load voltage technique [12], coulomb counting technique [13], and


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