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# Battery voltage versus SOD, at temperatures of (top to bottom) 45 C, 34 C, 23 C, 10 C, 0 C, 010 C, and 020 C. The discharge rate is 0.7 A.

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Presents here a complete dynamic model of a lithium ion battery that is suitable for virtual-prototyping of portable battery-powered systems. The model accounts for nonlinear equilibrium potentials, rate- and temperature-dependencies, thermal effects and response to transient power demand. The model is based on publicly available data such as the m...

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In this paper, an accurate and comprehensive electrical battery model has been proposed and implemented in a Matlab environment. The proposed model considers the dynamic features of a battery, such as nonlinear Voc (open circuit voltage), charge and discharge current, and transient response time. The current model neglects the effects of cycle numb...

## Citations

... For the purpose of avoiding these disadvantages, in [77], some additional parameters were introduced linking their value to a specific rate factor f(i(t)), which accounts for the decrease in capacity caused by unwanted side reactions as the current increases. A more detailed analysis is also presented in [78]. ...

Considering the importance of lithium-ion (Li-ion) batteries and the attention that the study of their degradation deserves, this work provides a review of the most important battery state of health (SOH) estimation methods. The different approaches proposed in the literature were analyzed, highlighting theoretical aspects, strengths, weaknesses and performance indices. In particular, three main categories were identified: experimental methods that include electrochemical impedance spectroscopy (EIS) and incremental capacity analysis (ICA), model-based methods that exploit equivalent electric circuit models (ECMs) and aging models (AMs) and, finally, data-driven approaches ranging from neural networks (NNs) to support vector regression (SVR). This work aims to depict a complete picture of the available techniques for SOH estimation, comparing the results obtained for different engineering applications.

... In addition to ohmic loss, the loss due to surface kinetics becomes important at a low temperature regime [30]. Resistance due to both surface phenomena and concentration limitation are also significant in a high rate regime [32]. ...

Both operating current and ambient temperature have a great impact on heat generation and the available residual capacity of the lithium ion battery. The thermal response of the lithium ion battery is investigated under isothermal conditions. Six currents from 1 A to 6 A, with a 1 A interval, are investigated in order to discuss the effect of current under 25 °C; four temperatures from 10 °C to 55 °C, with a 15 °C interval, are investigated to study the effect of temperature under the current of 2 A. The heat generation rate increases with the current increasing during both the charge and discharge stage, but the charge capacity remains independent of current, while the discharge capacity decreases with increasing current. Heat generation decreases with increasing temperature in both the charge and discharge stage, while charge capacity and discharge capacity increase. with the temperature increasing from 10 °C to 55 °C. Heat generation of per charge/discharge capacity is also discussed, and in most cases, the heat generation of per charge capacity during the constant voltage charge stage is larger than that during the constant current charge stage. Heat generation increases at the expense of available capacity, during the discharge stage.

... where, n c denotes the number of stack cells, u o f c the no-load voltage, i f c fuel cell current, R f c ohmic resistance of the fuel cell, c 3 " 10, c 5 " 2, c 1 , c 3 , c 4 are defined according to quasi-static levels of fuel cell temperature using look-up tables [39,40], and the notation˚signifies in general the inputs to each DC/DC converter. Battery modeling has been conducted based on a second-order Thevenin model as illustrated in Fig. 3. Fig. 3: Equivalent circuit model of the battery based on secondorder Thevenin model [41] Second-order Thevenin model (also referred to in literature as PNGV model [42]) has been widely implemented for modeling of electric batteries in vehicular traction systems due to its ability to represent the ohmic behavior and electrochemical polarization with high fidelity and low computational requirements [43,44]. Terminal voltage of the battery ub (before the DC/DC converter) can be described as ...

Electric vehicles (EVs) are promising alternatives to carbonized propulsion-based vehicles. They are capable of reducing environmental degradation without compromising driving performance. Power management strategies (PMS) are particularly essential for electrified vehicles to ensure optimal power split between on-board energy storage sources and to meet operational requirements of each source. However, optimization concept in PMS, have been constantly addressed in literature to achieve optimal power handling decisions in real-time, particularly under unknown driving conditions. In this contribution, an intelligent rule-based PMS with embedded offline-optimized control parameters and online driving state recognition is proposed to achieve optimal power handling decisions for EVs situatively and adaptively. A set of characteristic variables defining driving states have been extracted from representative segments of several driving cycles, to which optimized control strategies are tuned offline. Three different driving cycles representing urban, highway, and mixed trip conditions have been implemented for comparative investigation of achieved results. The analysis of results reveals the potential of proposed PMS to reduce the energy consumption by 13.6-30.9 %.

... Electrical models [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] use electrical equivalent circuits for lithium-ion batteries. Moreover, these circuits combine voltage sources, resistors, and capacitors. ...

: Lithium-ion batteries are commonly used in electric vehicles, embedded systems, and portable devices, including laptops and mobile phones. Electrochemical models are widely used in battery diagnostics and charging/discharging control, considering their high extractability and physical interpretability. Many artificial intelligence charging algorithms also use electrochemical models for to enhance operation efficiency and maintain a higher state of health. However, the parameter identification of electrochemical models is challenging due to the complicated model structure and the high count of physical parameters to be considered. In this manuscript, a comprehensive electrochemical lithium-ion battery model is proposed for the charging and discharging process-es. The proposed model accounts for all dynamic characteristics of the battery, including the cell open-circuit voltage, cell voltage, internal battery impedance, charging/discharging current, and temperature. The key novelty of the proposed model is the use of simulated open-circuit voltage and simulated changes in entropy data instead of experimental data to provide battery voltage and temperature profiles during charging and discharging cycles in the development of the final model. An available experimental dataset at NASA for an LCO 18650 battery was utilized to test the proposed model. The mean absolute error for the simulated charging cell voltage and tem-perature values were 0.05 V and 0.3 °C, compared with 0.14 V and 0.65 °C for the discharging profile. The simulation results proved the effectiveness and accuracy of the proposed model, while simplicity was the key factor in developing the final model, as shown in the subsequent sections of the manuscript.

... A dynamic modeling of EV batteries was used for this simulation and was derived from the work of References [39,40]. Time factors for lithium batteries are presented in studies [41,42] and are incorporated into the battery model by [42] to better estimate SoC. The SoC, voltage, and power losses of the agent's battery are modeled as follows: (23) where T sec , T min , and T hour represent time-constant variables of the dynamic behavior of the battery. ...

... A dynamic modeling of EV batteries was used for this simulation and was derived from the work of References [39,40]. Time factors for lithium batteries are presented in studies [41,42] and are incorporated into the battery model by [42] to better estimate SoC. The SoC, voltage, and power losses of the agent's battery are modeled as follows: (23) where T sec , T min , and T hour represent time-constant variables of the dynamic behavior of the battery. ...

... The SoC, voltage, and power losses of the agent's battery are modeled as follows: (23) where T sec , T min , and T hour represent time-constant variables of the dynamic behavior of the battery. It should be noted that number of driving cycles, temperature and battery's discharge rate were assumed based on [42]. V terminal and V oc are both terminal and open circuit voltage levels for the battery's circuit; R int and R transient are the battery's internal and train set resistance; C battery and I battery represent the capacity and current of the battery, both modeled as a current source as follows [43]: Table 1 in Reference [42] shows the parameters utilized in our simulation, with the exception of the battery's degradation level that was disregarded, as the battery's life cyle is out of the scope of the study. ...

A real-time, metadata-driven electric vehicle routing optimization to reduce on-road energy requirements is proposed in this work. The proposed strategy employs the state–action–reward–state–action (SARSA) algorithm to learn the EV’s maximum travel policy as an agent. As a function of the received reward signal, the policy model evaluates the optimal behavior of the agent. Markov chain models (MCMs) are used to estimate the agent’s energy requirements on the road, in which a single Markov step represents the average energy consumption based on practical driving conditions, including driving patterns, road conditions, and restrictions that may apply. A real-time simulation in Python with TensorFlow, NumPy, and Pandas library requirements was run, considering real-life driving data for two EVs trips retrieved from Google’s API. The two trips started at 4.30 p.m. on 11 October 2021, in Los Angeles, California, and Miami, Florida, to reach EV charging stations six miles away from the starting locations. According to simulation results, the proposed AI-based energy minimization framework reduces the energy requirement by 11.04% and 5.72%, respectively. The results yield lower energy consumption compared with Google’s suggested routes and previous work reported in the literature using the DDQN algorithm.

... Therefore, the influence of temperature on battery capacity should be considered in SOC estimation. Since the available battery capacity is affected by temperature and the charge and discharge rate, the SOC calculation formula in Equation (1) has some errors in practical application [25]. Considering the influence of temperature on the available battery capacity, this paper introduces a capacity compensation factor to modify the calculation of SOC [19,20]. ...

The state of charge (SOC) of the battery is an important basis for the battery management system to perform state monitoring and control decisions. In this paper, by identifying the internal parameters of the battery model at different temperatures and SOCs of the lithium-ion battery, the specific factors that affect the change of the parameters are analyzed, the segmentation basis of the model and the fitting method of related parameters are discussed, the second-order equivalent circuit model of the lithium-ion battery whose parameters vary with SOC and temperature is established, the unscented Kalman filter (UKF) is used to estimate the SOC of the lithium-ion battery, and an improved SOC estimation method based on optimized equivalent circuit model is proposed. Simulation and experimental results show that the improved SOC estimation strategy can obtain high estimation accuracy in a wide temperature range.

... Such a mechanism can effectively inhibit the influence of noise on the long-term continuous prediction process. (2) Because reinforcement learning problems can often be described as Markov decision processes (MDPs) [31], DRL is suitable for constructing prediction models to investigate the degradation of Li-ion batteries [32]. (3) The successful introduction of deep neural networks has greatly improved the generalization of reinforcement learning algorithms. ...

In the design phase of Li-ion batteries for electric vehicles, battery manufacturers need to carry out cycle life tests on a large number of formulations to get the best one that meets customer demands. However, such tests take considerable time and money due to the long cycle life of power Li-ion batteries. Aiming at reducing the cost of cycle life tests, we propose a prediction method that can learn historical degradation data and extrapolate to predict the remaining degradation trend of the current formulation sample taking the initial stage of partial cycle life test results as input. Compared with existing methods, the proposed deep reinforcement learning based method is able to learn degradation trends with different formulations and predict long-term degradation trends. Based on the deep deterministic policy gradient algorithm, the proposed method builds a degradation trend prediction model. Meanwhile, an interactive environment is designed for the model to explore and learn in the training phase. The proposed method is verified with real test data from battery manufacturers under three different temperature conditions in the formulation design stage. The comparisons indicate that the proposed method is superior to traditional degradation trend prediction methods in both accuracy and stability.

... With the circular dependence of the battery's internal parameters and SOC, improving the estimation accuracy of one will lead to improvement in the other. Most equivalentcircuit models found in the literature represent the internal parameters mainly by a resistance connected in series with an RC filter [1][2][3][4], as shown in Figure 1b. In this figure, the series resistance, R k , represents the ohmic losses (I 2 R) in the form of heat, while the RC filter accounts for the time constant that emulates the transient behavior of the cell when exposed to charge/discharge pulses. ...

This paper proposes a state-of-charge estimation technique to meet highly dynamic power requirements in electric vehicles. When the power going in/out the battery is highly dynamic, the statistics of the measurement noise are expected to deviate and maybe change over time from the expected laboratory specified values. Therefore, we propose to integrate adaptive noise identification with the dual-Kalman filter to obtain a robust and computationally-efficient estimation. The proposed technique is verified at the pack and cell levels using a 3.6 V lithium-ion battery cell and a 12.8 V lithium-ion battery pack. Standardized electric vehicle tests are conducted and used to validate the proposed technique, such as dynamic stress test, urban dynamometer driving schedule, and constant-current discharge tests at different temperatures. Results demonstrate a sustained improvement in the estimation accuracy and a high robustness due to immunity to changes in the statistics of the process and measurement noise sequences using the proposed technique.

... The voltage measurement performed on the actual cell during the test allows us to compute the model parameters. This procedure is thoroughly described in [16][17][18][19]. With the pulse discharge test, only a few values are available; therefore, an interpolating function was used to make all the parameters continuous as a function of the SOC. ...

The state of health (SOH) is among the most important parameters to be monitored in lithium-ion batteries (LIB) because it is used to know the residual functionality in any condition of aging. The paper focuses on the application of the extended Kalman filter (EKF) for the identification of the parameters of a cell model, which are required for the correct estimation of the SOH of the cell. This article proposes a methodology for tuning the covariance matrices of the EKF by using an optimization process based on genetic algorithms (GA). GAs are able to solve the minimization problems for the non-linear functions, and they are better than other optimization algorithms such as gradient descent to avoid the local minimum. To validate the proposed method, the cell parameters obtained from the EKF are compared with a reference model, in which the parameters have been determined with proven procedures. This comparison is carried out with different cells and in the whole range of the cell’s SOH, with the aim of demonstrating that a single tuning procedure, based on the proposed GA process, is able to guarantee good accuracy in the estimation of the cell parameters at all stages of the cell’s life.

... In recent papers, variation of the phenomenological particle diameter is allowed [38] to simulate graded electrodes, for example. Equivalent electric circuit models (EECM) with fits of the open circuit potential from experimental data [39,40] are popular for the energy and power management, offering the advantage of rapid runs and easy integration with control algorithms in the s-domain (after the Laplace transform from the time t-domain). Both SPM and EECM are employed and evaluated in this study. ...

... At every timestep, V OC is expressed as a sixth order polynomial of the state of charge, SOC, where the empirical polynomial coefficients a k are fitted against the experimental data at very low C-rate (0.05 C in this study) following regression analysis [39,40]. The SOC is a function of the maximum capacity, Q max , of the battery which is adjusted with cycling, according to an artificial intelligence function that adjusts Q max at cycle ic on the basis of the Q max variation from the previous cycles obtained from historical experimental data. ...

Citation: Baboo, J.P.; Yatoo, M.A.; Dent, M.; Hojaji Najafabadi, E.; Lekakou, C.; Slade, R.; Hinder, S.J.; Watts, J.F. Exploring Different Binders for a LiFePO 4 Battery, Battery Testing, Modeling and Simulations. Energies 2022, 15, 2332.