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Electric forklifts are extremely important for the world’s logistics and industry. Lead acid batteries are the most common energy storage system for electric forklifts; however, to ensure more energy efficiency and less environmental pollution, they are starting to use lithium batteries. All lithium batteries need a battery management system (BMS) for safety, long life cycle and better efficiency. This system is capable to estimate the battery state of charge, state of health and state of function, but those cannot be measured directly and must be estimated indirectly using battery models. Consequently, accurate battery models are essential for implementation of advance BMS and enhance its accuracy. This work presents a comparison between four different models, four different types of optimizers algorithms and seven different experiment designs. The purpose is defining the best model, with the best optimizer, and the best experiment design for battery parameter estimation. This best model is intended for a state of charge estimation on a battery applied on an electric forklift. The nonlinear grey box model with the nonlinear least square method presented a better result for this purpose. This model was estimated with the best experiment design which was defined considering the fit to validation data, the parameter standard deviation and the output variance. With this approach, it was possible to reach more than 80% of fit in different validation data, a non-biased and little prediction error and a good one-step ahead result.

The past few years have seen strong growth of solar-based off-grid energy solutions such as Solar Home Systems (SHS) as a means to ameliorate the grave problem of energy poverty. Battery storage is an essential component of SHS. An accurate battery model can play a vital role in SHS design. Knowing the dynamic behaviour of the battery is important for the battery sizing and estimating the battery behaviour for the chosen application at the system design stage. In this paper, an accurate cell level dynamic battery model based on the electrical equivalent circuit is constructed for two battery technologies: the valve regulated lead–acid (VRLA) battery and the LiFePO 4 (LFP) battery. Series of experiments were performed to obtain the relevant model parameters. This model is built for low C-rate applications (lower than 0.5 C-rate) as expected in SHS. The model considers the non-linear relation between the state of charge ( S O C ) and open circuit voltage ( V OC ) for both technologies. Additionally, the equivalent electrical circuit model for the VRLA battery was improved by including a 2nd order RC pair. The simulated model differs from the experimentally obtained result by less than 2%. This cell level battery model can be potentially scaled to battery pack level with flexible capacity, making the dynamic battery model a useful tool in SHS design.

Storing energy efficiently is one of the main factors of a more sustainable world. The battey management system in energy storage plays an extremely important role in ensuring these systems’ efficiency, safety, and performance. This battery management system is capable of estimating the battery states, which are used to give better efficiency, a long life cycle, and safety. However, these states cannot be measured directly and must be estimated indirectly using battery models. Therefore, accurate battery models are essential for battery management systems implementation. One of these models is the nonlinear grey box model, which is easy to implement in embedded systems and has good accuracy when used with a good parameter identification method. Regarding the parameter identification methods, the nonlinear least square optimization is the most used method. However, to have accurate results, it is necessary to define the system’s initial states, which is not an easy task. This paper presents a two-outputs nonlinear grey box battery model. The first output is the battery voltage, and the second output is the battery state of charge. The second output was added to improve the system’s initial states identification and consequently improve the identified parameter accuracy. The model was estimated with the best experiment design, which was defined considering a comparison between seven different experiment designs regarding the fit to validation data, the parameter standard deviation, and the output variance. This paper also presents a method for defining a weight between the outputs, considering a greater weight in the output with greater model confidence. With this approach, it was possible to reach a value 1000 times smaller in the parameter standard deviation with a non-biased and little model prediction error when compared to the commonly used one-output nonlinear grey box model.

This work introduces a sophisticated impedance-based equivalent circuit model of the electrochemical processes inside a lithium-ion battery cell. The influence on the electrical voltage response is derived and merged into a mathematical calculation framework describing all fundamental phenomena inside a battery. The parameters, whose sole influences on the electric behaviour cannot be separated at the cell level, are summarised to derive a model with purely electrical quantities. We significantly reduce the model order compared to a physicochemical model while ensuring a minimal approximation error. Utilising the findings from the model derivation, we develop a parameterisation procedure to separate the individual processes occurring in the battery and to support a hypothesis of the assignment to positive and negative electrodes based on several indicia. For this purpose, electrochemical impedance spectroscopy and correlation analysis are used to calculate the distribution of the time constants. The final parameterised model has physics-based parameter variations, which ensures that the simulation over broad ranges of temperatures and states of charge results in a reasonable voltage response. The model’s physical basis enables extrapolation beyond the measured operation area, and the model verification shows less than a 10 mV root mean square error over a wide range of operations.

Finding the cost-optimal battery size in the context of parcel delivery with Electric Vehicles (EVs) requires solving a tradeoff between using the largest possible battery (so as to maximize the number of deliveries over a given time) and the relative costs (initial investment plus the unnecessary increase of the truck weight during delivery). In this paper, we propose a framework for the optimal battery sizing for parcel delivery with an electric truck; we implement an electric truck simulator including a nonlinear battery model to evaluate revenue, battery cost, charging cost, and overall profit for annual delivery. Our framework finds the cost-optimal battery size for different parcel weight distributions and customer location distributions. We analyze the effect of battery sizing on the profit, which is up to 56%.

This paper proposes a battery voltage model that is suitable for variable operation. The model combines the features of the Kinetic Battery Model (KiBaM) and voltage model (VM), and it improves the accuracy and quality of the solution, addressing four characteristics of operation: charging, discharging, rest after charge, and rest after discharge. This model will be known as 4-KiVM and shows low impact on computational burden. The proposed model can keep track of the voltage even when the load is inverted or turned off. To calibrate and validate the model, a NASA-provided dataset was used composed of a battery with variable charges and discharges, simulating real applications. A metaheuristic method based on tabu search is used to extract constants from this dataset and validate this hybrid model. In addition, a comparison of performance of the 4-KiVM against KiBaM, VM, and the electric circuit model (ECM) was made, showing its advantages. The results of the simulations showed a good prediction of the battery voltage response and SOC prediction in random (variable) use.

Since the evolution of the electric and hybrid vehicle, the analysis of batteries’ characteristics and influence on driving range has become essential. This fact advocates the necessity of accurate simulation modeling for batteries. Different models for the Li-ion battery cell are reviewed in this paper and a group of the highly dynamic models is selected for comparison. A new open circuit voltage (OCV) model is proposed. The new model can simulate the OCV curves of lithium iron magnesium phosphate (LiFeMgPO4) battery type at different temperatures. It also considers both charging and discharging cases. The most remarkable features from different models, in addition to the proposed OCV model, are integrated in a single hybrid electrical model. A lumped thermal model is implemented to simulate the temperature development in the battery cell. The synthesized electro-thermal battery cell model is extended to model a battery pack of an actual electric vehicle. Experimental tests on the battery, as well as drive tests on the vehicle are performed. The proposed model demonstrates a higher modeling accuracy, for the battery pack voltage, than the constituent models under extreme maneuver drive tests.

A battery management system (BMS) plays a crucial role to ensure the safety, efficiency, and reliability of a rechargeable Li-ion battery pack. State of charge (SOC) estimation is an important operation within a BMS. Estimated SOC is required in several BMS operations, such as remaining power and mileage estimation, battery capacity estimation, charge termination, and cell balancing. The open-circuit voltage (OCV) look-up-based SOC estimation approach is widely used in battery management systems. For OCV lookup, the OCV–SOC characteristic is empirically measured and parameterized a priori. The literature shows numerous OCV–SOC models and approaches to characterize them and use them in SOC estimation. However, the selection of an OCV–SOC model must consider several factors: (i) Modeling errors due to approximations, age/temperature effects, and cell-to-cell variations; (ii) Likelihood and severity of errors when the OCV–SOC parameters are rounded; (iii) Computing system requirements to store and process OCV parameters; and (iv) The required computational complexity of real-time OCV lookup algorithms. This paper presents a review of existing OCV–SOC models and proposes a systematic approach to select a suitable OCV–SOC for implementation based on various constraints faced by a BMS designer in practical application.

Owing to high oil prices and the efforts to reduce greenhouse gases according to the United Nations Framework Convention on Climate Change, there has been active research and development on environmentally friendly, high-efficiency vehicles. In developing the system design and specifications of an environmentally friendly vehicle, various simulations have been performed on the different components and the overall system. Although a precise modelling of each part and the system as a whole is necessary for an accurate simulation, detailed modelling of a high-capacity battery system – which directly affects the performance of an environmentally friendly vehicle – is difficult to achieve owing to the non-linear electrochemical properties of the battery. In this study, an electrochemical impedance measurement technique is used to implement a battery cell model, upon which a battery system model for environmentally friendly vehicles that takes into account the ancillary components of the battery pack is developed. And we used an actual battery system that requires complex and difficult modelling owing to non-linear and irreversible properties of the battery. In addition, to verify the developed battery system model, we used models implemented for other vehicle components and systems to construct a hardware-in-the-loop simulation of a battery reflecting an actual driving environment.

Battery state estimation is fundamental to battery management systems (BMSs). An accurate model is needed to describe the dynamic behavior of the battery to evaluate the fundamental quantities, such as the state of charge (SOC) or the state of health (SOH). This paper presents an overview of the most commonly used battery models, the equivalent electrical circuits, and data-driven ones, discussing the importance of battery modeling and the various approaches used to model lithium batteries. In particular, it provides a detailed analysis of the electrical circuit models commonly used for lithium batteries, including equivalent circuit and thermal models. Furthermore, a comprehensive overview of data-driven approaches is presented. The advantages and limitations of each type of model are discussed. Finally, the paper concludes with a discussion of current research trends and future directions in the field of battery modeling.