A Critical Study of Using the Peukert Equation and Its Generalizations for Determining the Remaining Capacity of Lithium-Ion Batteries  
[PERSON]  
1 Laboratory of Electrochemical and Hydrogen Energy, Don State Technical University, 346500 Town of Shakhty, Rostov Region, Russia; [EMAIL_ADDRESS] (N.  
evaluation is using models based on the Kalman filter and fuzzy logic [8; 9; 10; 11; 12; 13]. These models provide much better SoC evaluation [11] than the previous methods, especially at dynamic loads. However, in our experiments, the relative error of SoC evaluation by this method was about 10%, which is quite high.  
The modern method of SoC evaluation relies on the combination of the following two methods: counting of ampere hours and use of voltage profiles. However, this method makes the SoC calculation a difficult problem, and it has known accuracy problems [1].  
From the theoretical point of view, the most accurate battery models can be obtained only with use of the electrochemical laws of molecules and ions transport with due account of all the internal characteristics of batteries, i.e., with use of the electrochemical method of modeling [14; 15; 16; 17]. However, for their service, these models require powerful computing systems not typical for modern mobile vehicles and appliances. Thus, they are unacceptable for electric vehicles, airplanes and other mobile systems containing the batteries. They are inconvenient to use in practice, too, as they require a long calibration and finding out of all internal parameters of a battery [18].  
An alternative to the above-described methods can be the analytical models based on various generalizations of the Peukert equation [18; 19; 20; 21] or on other empiric equations [22]. However, even when modeling batteries by the electrochemical method, one is often forced (within the frameworks of those models) to use additional analytical models when it is necessary to take into account such poorly studied processes as the thermal runaway [23; 24; 25], the accumulation of hydrogen in battery electrodes [26; 27] and the gas generation during lithium-ion battery cycling [28; 29].  
Analytical models are often used for SoC evaluation in the lithium-ion batteries [18; 19]; moreover, the temperature of the batteries is also taken into account. We believe the most promising method is the analytical model of [PERSON] [18]. This model is specifically designed to evaluate the remaining capacity of batteries in electric vehicles. This model is based on the classic Peukert equation. However, the classic Peukert equation does not correspond to experimental data for lithium-ion batteries at any discharge current.  
The purpose of this paper is to find the ranges of discharge currents in which the classic Peukert (and Liebenow) equation is applicable for lithium-ion batteries, since the classic Peukert equation is very often used in various analytical models of lithium-ion batteries [18]. In addition, this paper aims at weighing the advantages and disadvantages of the most popular generalized Peukert equations and choosing an optimal equation for SoC evaluation in the lithium-ion batteries (at any discharge current), for example, based on the analytical models proposed in [18; 19].