## 1 Introduction  
Monitoring battery operation and measuring battery aging in real life have been a challenging goal that includes a number of complex processes under complicated operating conditions. The state of charge (SOC) and state of health (SOH) of the lithium-iron-phosphate (LiFePO4) battery must be estimated with an accurate method [1, 2]. In addition, batteries work under variable aging and thermal conditions. Therefore, a battery observation system to monitor the aging and the operation needs to be built. This is a multi-controlproblem that needs to be expressed via mathematical equations and a combined thermal model, electrical model, and an aging model. It is difficult to predict the behavior of batteries because of their non-linearity. Also, many attempts have been conducted to estimate and model the system's inner state [3; 4; 5]. Recently, battery modeling has been introduced using many approaches to achieve accurate SOC estimation [6]. The model introduced in [7] took into consideration the robustness, accuracy, and low-cost hardware requirements. It was based on the online parameter identification of an electrical model using recursive least square (RLS) with the application of an unscented Kalman filter (UKF) to estimate SOC. The model parameters used in the filter were updated by the algorithm. An improved extended Kalman filter (EFK) algorithm was introduced to estimate lithium-iron-phosphate (LiFePO4) battery SOC [8]. That model incorporated a second-order RC circuit with a fuzzy controller to adjust the noise variance. The results of that model showed better observable accuracy of the estimation than EKF. A third-order RC circuit model was introduced [9] based on sampling point Kalman joint algorithm in order to SOC estimation error correction. The error was controlled within 2% and that model was better than the second-order RC circuit model. The temperature effect under dynamic load on the LiFePO4 battery SOC has been studied experimentally [10]. The estimation approach was based on the RLS method, along with a model of an open-circuit voltage to SOC under different ranges of temperature. The results showed a remarkable accuracy with an error below 5.2%. Moreover, the dynamic characteristic of the LiFePO4 battery under different rates of current was studied [11]. The proposed model to estimate the SOC showed reduced error results. It was based on both current rates and direction. The electrochemical-thermal model introduced in [12] was developed to simulate the temperature and voltage distribution three-dimensionally. The comparison between the predicted variables was made to validate the model accuracy. It was found that the main element for electrochemical performance improvement was the self-heating in the large-sized cells. In the recent years, advanced artificial intelligence and machine learning algorithms have been utilized in many worldwide practical applications with superior performance in diverse power system topics, e.g., [13; 14; 15; 16; 17; 18; 19; 20] while renewables and storage systems are simulated intensively [21; 22; 23; 24; 25]. In [26], a single-particle model (SPM) was used to introduce a physical-chemical model of the lithium-ion battery, which governed its performance. The curves of charging and discharging were obtained for different cycle depths and current rates. The effect of the high number of cycles on the aging was introduced, as well as the electrolyte dynamics. The three-parameter method (TPM) was implemented for comparison purposes to validate the proposed model. The paper concluded that the used models had included a method to protect the battery via cutting the current in charge and discharge based on the electrode maximum stoichiometric concentration ranges of lithium. Besides, different values of the \(r_{\textit{eff}}\) parameter were used to study the direct influence on the discharge voltage. The aging performances of different batteries including LiFePO4 were tested and compared in [27] through a series of start-stop micro cycles.