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# Hysteresis phenomenon

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This paper presents an improved and easy-to-use battery dynamic model. The charge and the discharge dynamics of the battery model are validated experimentally with four batteries types. An interesting feature of this model is the simplicity to extract the dynamic model parameters from batteries datasheets. Only three points on the manufacturer’s di...

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... particularity of this model is the use of a filtered current ( i ∗ ) flowing through the polarisation resistance. In fact, experimental results show a voltage slow dynamic behaviour for a current step response. This filtered current solve also the algebraic loop problem due to the simulation of electrical systems in Simulink. Finally, the OCV varies non-linearly with the SOC. This phenomenon is modelled by the polarisation voltage term. The exponential zone of equation (1) is valid for the Li-Ion battery. For the other batteries (Lead-Acid, NiMH and NiCD), there is a hysteresis phenomenon between the charge and the discharge, no matter the SOC of the battery [6], [7]. This behaviour occurs only in the exponential area, as shown in Fig. 2. This phenomenon can be represented by a non-linear dynamic ...

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... The present paper proposes equations using proper physical units, which include the SoC-dependent behavior of internal resistance. Tremblay et al. stated for [20], as well as their extended version from 2009 [23], that the sets of equations would not model the so-called Peukert effect, which means the discharge current would not change the predicted available capacity under constant current discharge [12]. Nevertheless, the present paper will demonstrate that this kind of equation can well describe the main reasons for the Peukert-effect of lithium-ion cells. ...
... In 2018, Song et al. [14] Tremblay et al. stated for [20], as well as their extended version from 2009 [23], that the sets of equations would not model the so-called Peukert effect, which means the discharge current would not change the predicted available capacity under constant current discharge [12]. Nevertheless, the present paper will demonstrate that this kind of equation can well describe the main reasons for the Peukert-effect of lithium-ion cells. ...
... The classic Peukert equation (1) leads to a straight-line representation (negative linear slope −k) when plotting the employed constant current I versus the reached discharge time t end , and both axes are scaled in a logarithmic order. The experiments and application of the proposed equations using (20)- (22) with the exemplary specimen showed its validity for reflecting the Peukert behavior up to discharge C-rates of approximately 5 C n (see Figures 4 and 5), in which the Peukert exponent can be derived from (23). ...
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... Similarly, another research uses modelica methodologies to model EV pickup attributes to study the dynamic response of an electric vehicle [3]. Other such models for battery dynamics and solar hybrid vehicles have been given in [4] and [5] respectively. In conclusion, there is enough research material that can be found for developing a model to study the vehicle dynamics of an electric vehicle. ...
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... Alat penelitian terdiri dari perangkat keras dan perangkat lunak. Perangkat keras yang digunakan dalam penelitian ini terangkum pada Tabel 1. Persamaan 4 dan 5 merupakan model baterai [18]. Nilai dan secara berturut-turut adalah resistansi internal baterai dan tegangan baterai. ...
... Tabel 4. Spesifikasi baterai [18] Parameter Nilai ...
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... Alat penelitian terdiri dari perangkat keras dan perangkat lunak. Perangkat keras yang digunakan dalam penelitian ini terangkum pada Tabel 1. Persamaan 4 dan 5 merupakan model baterai [18]. Nilai dan secara berturut-turut adalah resistansi internal baterai dan tegangan baterai. ...
... Tabel 4. Spesifikasi baterai [18] Parameter Nilai ...
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... The circuit is based off the work of Zhu et al. [37]. and Tremblay et al. [36] (see Fig. 10). The internal resistance is assumed to be constant during the charge and discharge cycles and does not vary with the amplitude of the current. ...
... Input/output given to the fuel cell model from Njoya[34].Fig. 10e Equivalent circuit of the battery included in the model[36]. ...
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... Given this, it is advisable to use the Shepherd's parametric model [8,9], which describes the chargedischarge characteristic of SB. This system of equations, is implemented in the Simscape Simulink model and has the form (2) ...
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... The discharging process is therefore divided into exponential zone, nominal zone, B Q and fast-discharging zone to reflect this dynamic feature. 16 Fig. 2 Typical discharging curve of lithium ion battery 15 Currently, there are a variety of models describing the dynamic characteristic of the battery, e.g., Equivalent Circuit Model (ECM), [16][17][18] electrochemical model, 19 and intelligent mathematical model. 20 With the high fidelity and complexity, the electrochemical model is mainly utilized in the battery design and manufacturing. ...
... The discharging process is therefore divided into exponential zone, nominal zone, B Q and fast-discharging zone to reflect this dynamic feature. 16 Fig. 2 Typical discharging curve of lithium ion battery 15 Currently, there are a variety of models describing the dynamic characteristic of the battery, e.g., Equivalent Circuit Model (ECM), [16][17][18] electrochemical model, 19 and intelligent mathematical model. 20 With the high fidelity and complexity, the electrochemical model is mainly utilized in the battery design and manufacturing. ...
... is the internal resistance, is the filtered current, is the nominal capacity, K is B R F I N Q the polarization resistance, A is the exponential zone voltage amplitude, and B is the exponential zone time constant inverse. Oliver and Louis 16 derived the equations to determine the coefficients K, A and B 16 (6) ...
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... Batteries are modelled based on their charging and discharging cycles. The number of lifecycles reduces with the Depth of Discharge (DOD) [46]. Also, a few models use the currentvoltage characteristics of a battery as a function of State of Charge (SOC) [47]. ...
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