Design and analysis of capacity models for Lithium-ion battery
Introduction
The research on battery-powered electric vehicles is the primary focus of experts to ensure sustainable, cleaner and noise-free environment [1], [2], [3]. The main unit responsible for transmission of power to vehicle is the battery pack. The main problems associated with the battery packs are overcharging, overheating, thermal runway, etc. Many modelling methods were developed to formulate the physics-based-models, the empirical models and the equivalent circuit models The main factors responsible for the problems is the abnormal voltage and abnormal temperature, which directly results in material degradation of battery and capacity fading and loss of cycle life [4]. In this context, a gamut of research studies [5], [6], [7] has been conducted classifying the modelling methods with their pros and cons for predicting battery/battery pack states [8], [9], [10]. The following is the important literature review conducted in area of battery models.
Basically, many review studies summarize that there exist three types of models [11]. Firstly, the empirical model based on only the data obtained from the experiments or simulation. These models have disadvantage of having the poor accuracy and does not incorporate physics into a model. Secondly, the models based on physics generally represents the fundamentals mechanisms taking place inside the battery. These models are known as electrochemical models or physics-based models. These are computationally expensive and the error accumulates over the time. The third category of models are equivalent circuit models which requires good understanding of circuit system in the battery pack. The broad discussion on these models were based on the two types of batteries: lead acid and lithium-ion [12], [13], [14]. The models are a part of battery management systems whose functions is to monitor and control the battery pack by the prediction of voltage, temperature distribution, battery SOC, battery SOH, etc. In this context, the review on key issues in battery management system was conducted and the findings were discussed [15], [16], [17].
Among the main issues in the battery management system, the emphasizes was paid to the prediction of SOC and SOH in real time. Past studies suggests that the prediction SOH is most difficult since it is difficult to visualize the mechanisms/material degradation inside battery in real time that results in capacity fading of the battery. In this context, the theory of fuzzy mathematics in combination of human knowledge was used because it considers the imprecise information of battery [18].
Several prognostic and health management (PHM) methods for the battery states estimation were reviewed [19]. The methods were categorized into battery type, operating condition and driving conditions. The models were classified into empirical, physics-based, equivalent circuit models and fusion models [20], [21]. A thorough review on the battery management system, vehicle energy management and the vehicle control was conducted by Cuma and Koroglu [14]. Battery management system comprises of the battery modelling methods, learning algorithms, controller, etc. Fundamental study on temperature and thermal life estimation, state of power estimation and recovery estimation methods are part of vehicle energy management system with objective to lower emissions and the higher efficiency. Besides, the vehicle control consists of methods for the prediction of orque, speed, range, slideslip angle, roll angle, road friction condition and the electric motor parameters with objective to ensure smooth vehicle control [22].
The critical review of the past studies reveals that the methods applied for battery modelling includes the physics-based modelling, empirical modelling based on artificial intelligence (AI) and the fusion modelling methods. Among these methods, the physics-based models developed using the finite element software’s were used to understand the physical/chemical aspects at cell level. However, the knowledge attributes such as the performance and durability derived from these physics based models are difficult to be incorporated in the electric vehicle system since they are built on different languages/platforms. The fusion and AI based methods are mainly used for battery modelling to estimate the battery states such as the battery capacity, discharge capacity, SOC, SOH, SOF, temperature distribution, voltage, etc. for fault diagnosis and prognostics to mitigate the safety risk [14]. It was found that the AI based models can be integrated in the system however, their robustness and accuracy with respect to the input variations still possesses the main challenge. For e.g., Any systematic/non-systematic variations in the inputs such as the structure of the battery modelling method can directly influence the robustness of the models in context of any smaller variation in inputs values. In addition, the models built must represent explicitly the relationships between the battery capacity and the inputs. The pre-assumption of the model structure for the battery capacity introduces an uncertainty in the predictive ability of the model [23]. Therefore, it would be interesting to develop a robust approach that can explicit represent and estimate the battery capacity of the models based on the variations in temperature, rate of discharge rate and the structure of the modelling method.
In this context, the AI category of evolutionary approach of Genetic programming (GP) can be applied for generation of explicit models for battery capacity based on the given inputs [24]. Past studies in GP reveals that the state-of-the-art of the work was mainly on developing the new variants of GP by hybridising it with other methods such as the neural network, support vector regression and probabilistic based methods. New selection and genetic operators were developed to improve the evolutionary search mechanism [25], [26], [27]. To the best of authors knowledge, very few or hardly any research studies were found focussing on evaluation of the complexity measures in objective functions. The performance of the generated models depends highly on the objective functions chosen in GP. This is because the objective function is responsible for monitoring the search for the optimum models from one generation to the next. Improper search throughout the execution can results in evolution of the poor generalized models. Therefore, it is highly essential to design a new objective functions incorporating an appropriate complexity term in GP. The same is shown by dotted line in Fig. 1. The form of existing objective functions takes into account the number of data samples and/or nodes of the model, and, thereby penalizes the accuracy of the model as the complexity of the model increases. The complexity of the GP model is measured by the number of nodes as shown in Fig. 2. The number of nodes as the complexity may not be appropriate because it will then imply that sin (x) and -x have the same complexity value, which is not true. The polynomial having the fixed degree of complexity can be considered as a complexity measure of GP models in its objective function during the evolutionary search. Thus, it would be interesting to investigate the effect of each objective function on GP having polynomial as its complexity.
Therefore, the present work proposes the evolutionary approach of GP based on polynomial as its complexity measure in modelling of the battery capacity of the electric vehicle. The seven objective functions are referred and influence of each having polynomial complexity measure on the evolution of GP models is investigated. The inputs considered for measurement of battery capacity are the temperature and discharge rate. The research problem including the design of experiment for battery capacity is described in Section 2. Section 3 introduces the evolutionary approach of GP and the seven objective functions having the polynomials as its complexity measure. Section 4 discusses the performance of the GP based battery capacity models. Section 5 provides the 2-D and 3-D surface analysis for the battery capacity models based on the temperature and discharge rate. Finally, Section 6 concludes with the scope for future work.
Section snippets
Battery capacity data acquisition
This section discusses the problem statement including the acquisition of the battery capacity data. The experiment is designed in such a way that the battery capacity is estimated based on the varying temperature and discharge rates of the lithium battery. The temperature varied from 0 K to 55 K, whereas the discharge rate is varied from C/10 to 5C. The experimental details are kept the same as those discussed in study on Lithium-ion battery modelling conducted by Chandrasekaran et al. [28].
Principle and design of new objective functions
Evolutionary approach of GP which works on the principle of “Survival of the fittest” is proposed to design the battery capacity estimation model [29]. The mechanism is similar to that of genetic algorithm (GA), except the fact that the GP evolves model structures but GA evolves solutions in crisp form. The steps needed for the implementation of GP is as follows.
- 1.
First step involves the definition of functional and terminal set. Functional includes the airthematic operations while the terminal
Performance analysis of the GP based battery capacity models
The statistical evaluation of the models is conducted using the two metrics: the coefficient of determination (R2) and the mean absolute percentage error (MAPE). Higher the value of R2 and lower the value of MAPE, higher the performance of the model. The battery capacity estimation is directly related to the performance of the model. This work investigated the influence of new objective functions designed by incorporating the polynomial based complexity. To ensure the robustness of the
2-D and 3-D surface analysis of GP based battery capacity models
This section discusses the nature of influence of the temperature and discharge rate on the battery capacity by analysing the GP model. Analysis of the GP model shall include the 2-D and 3-D surface plots to evaluate the main and interaction effects of the inputs on the battery capacity respectively. The technical details of the analysis can be found in [25]. Fig. 6 shows the nature of main effect of the inputs on the battery capacity. Fig. 6 clearly shows that there is a higher non-linear
Conclusions
The present work highlights the motivation behind formulation of explicit and robust models for battery capacity for the battery packs in electric vehicle. The evolutionary approach of GP based on design of new objective functions having polynomial as complexity factor is proposed. The quantitative analysis of the seven objective functions reveals that the SRM objective function when used in GP framework has resulted in evolution of accurate and robust battery capacity models. PRESS objective
Acknowledgement
The authors wish to acknowledge that this research has been supported by Shantou University Scientific Research Foundation (Grant Nos. NTF 16002, NTF 16011) and the Sailing Plan of Guangdong Province, China. This work was also supported by Viet Nam National University through research grant number: NV2018-18-01.
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