A novel method on estimating the degradation and state of charge of lithium-ion batteries used for electrical vehicles
Introduction
Lithium-ion batteries are important energy storage devices that have been widely applied to various types of electric vehicles (EVs). Battery health assessment and efficient energy management are basic principles pertaining to battery application. As an electric vehicle core technology, accurate estimations of battery capacity and state of charge (SoC) are very important. Battery SoC is residual capacity and usually described by percentage. Battery capacity, defined as the maximum energy in ampere-hours that the battery can hold, is generally referred to as the maximum available capacity of the battery at the current aging level. After repeated cycling, battery capacity diminishes due to the modification of the positive and negative structural properties, growth on the solid electrolyte interface (SEI), and variation of the electrolyte chemical composition or reduction in active materials [1], [2], [3]. It is necessary to obtain an accurate estimation of battery capacity and SoC for the battery during its service life [4]. Otherwise, battery abuse including over-charging, over-discharging, or even thermal runaway may occur. Therefore, accurate and high-efficiency estimation of battery capacity and SoC can prolong battery service life and improve overall battery performance.
With increased popularity and application of Li-ion batteries, the estimation of battery SoC has received much attention, resulting in improved estimation precision. The SoC estimation methods are summarized and evaluated in Refs. [1], [2]; these methods are often divided into four types: conventional methods [3], [4], [5] (OCV, ampere-hour counting, and others), adaptive filter algorithms, learning algorithms [6] and non-linear observers [7]. The OCV based method is a simple approach to obtain the battery SOC, which is not suitable for EVs for batteries are required to have long time resting in order to reach balance. The ampere-hour counting method is also simple and general way for low-cost sensors and computing, which is often combined with other model based estimation approaches. But it has accumulated error and is hard to calibrate the initial error. The learning algorithms can be employed for SoC estimation. The disadvantages of this method are a great number of training data are needed and a lot of computations are required. The method of non-linear observers is not complex but when the system is observable the method can be used. Among these SoC estimation methods, adaptive filter algorithms are more suitable for EV application, and the methods proposed by the authors in Refs. [8], [9], [10] result in a SoC estimation error precision within 5%. However, most of the battery SoC estimation methods mentioned previously are based on a known capacity. Because battery capacity diminishes and performance degrades in an unpredictable and random manner, also the degradation paths of batteries are difficult to capture accurately. SoC estimation using a known capacity has obvious limitations to practical applications. Therefore, it is important that calibrate battery capacity on-line to estimate SoC accurately for practical applications.
Another important battery parameter is battery capacity. Capacity estimation techniques can be divided into two categories [11], [12], [13], [14]: SoC-correlative and SoC-independent. The methods from the SoC-correlative category consider that battery capacity estimation is concerned with SoC. Ref. [15] uses the ratio of ampere-hour accumulation and SoC variation to estimate the battery capacity for the current aging condition. The relationship between battery OCV and SoC is used to calculate battery capacity in Refs. [16], [17], [18]. The advantage of this method is that fewer parameters are needed in the battery capacity estimation, because only the OCV-SoC relationship is used. The accuracy of this method is high for different aging states during the entire battery application lifespan if the cell inconsistency of the OCV-SoC relationship is very small. The disadvantage of this method is that accurately measured OCV is difficult to obtain during the entire battery service life. Therefore, this method is difficult to use on-line. A joint estimation or dual estimation method is used to estimate battery capacity and SoC concurrently, and in Refs. [3], [19], [20], [21], [22], [23], the extended Kalman filter (EKF), in Ref. [24], the unscented Kalman filter (UKF), in Ref. [25], the particle filter (PF), in Ref. [26], the unscented particle filter (UPF) and in Ref. [27], the recursive least square (RLS) algorithms are employed. These methods can potentially estimate battery capacity accurately as the battery is modeled, and SoC is thereby estimated [2]. However, these methods performance could increase when the system and observation noise satisfy the Gaussian distribution and the model parameters are accurate. The disadvantage of these methods is that the algorithms suffer from high complexity, high computational cost and instability.
The methods that use the SoC independently can avoid the need for a complex model. In Ref. [28], the change in battery voltage is observed to estimate the battery capacity. This estimation method is suitable for identical charging conditions, but electric vehicles subject to dynamic operating conditions could be charged inconsistently with different current. Battery impedance can also reveal capacity fade of the battery current state condition [29]. In Refs. [30], [31], [32], [33], [34], the authors use incremental capacity analysis (ICA) and differential voltage analysis (DVA) techniques to investigate the behavior of a battery and estimate the battery capacity. These methods can estimate battery capacity accurately only for constant current charging and discharging conditions. Consequently, they cannot be used in EVs directly.
Both the capacity and the SoC are important parameters for the battery management system (BMS) in EVs. Their accurate estimations have recently been the focus of research, particularly the capacity estimation. The accessible capacity is the base of accurate battery health assessment and efficient energy management. In this paper, the three-dimensional response surface (TRS)-based SoC-OCV capacity estimator has been constructed covering the entire lifetime of a battery, based on a GA estimator for accurate estimation of battery capacity and SoC. As a state-of-the-art optimal algorithm, the GA method is able to obtain the global optimum very efficiently. Except for the SoC-OCV-capacity response surface constructed in the beginning, limited on-board data is needed to accurately determine the battery capacity and initial SoC, even during the entire battery application lifespan. Additionally, because of its high reliability and portability, the GA algorithm is expected to be more applicable in practice compared with traditional advanced estimators such as Kalman filters. For electric vehicles application, we can send a certain period of time data of driving cycles stored in BMS on-line to a powerful computer off-line or even a cloud computing platform to compute the battery capacity and SoC. Then the calculation results are returned to the BMS via a SIM card or other mediums. We use an on-line and off-line computing manner in combination to reduce computational cost of BMS.
Section 2 first describes the flow diagram of the optimization algorithm. Next, the specific computation procedure for the capacity and SoC is presented. Section 3 introduces the configuration of the battery test bench, the schedule and the results. A battery with four different aging states and two different operating conditions is analyzed in the six case studies in Section 4 before conclusions are drawn in Section 5.
Section snippets
An equivalent circuit model of a battery
Lithium-ion battery characteristics can be described by an equivalent circuit model for different operating conditions. Plett [27] and Hu [35] have proposed several equivalent circuit models, including the simple, one-state hysteresis, enhanced self-correcting, first-order RC, first-order RC with one-state hysteresis models, etc., and Hu has presented a comparative study of the 12 equivalent circuit models. Based on their previous research experience, we consider the first-order RC model, also
Experiments
An equivalent circuit model for a battery can be based upon data obtained from a variety of battery experiments. In this section, the configuration and basic principles of the battery test bench are introduced. A lithium-ion battery cell database is established, which records test data for a battery from the beginning of service to the end of its service life in an EV. This database is a basis for building an OCV model.
Case studies
This section presents six cases to demonstrate the effectiveness of the proposed methods for battery capacity and SoC estimation for different aging states (nearly fresh battery, lightly cycled, heavily cycled and near end of service life) and different operating conditions. In case01 and case02, the battery cell has an aging level of 100 cycles and an operating condition identical to that in the UDDS test. The duration for calculating and storing data is 3600 s for case01 while the duration is
Conclusion
A battery capacity and SoC estimation approach is proposed in this paper. To verify the effectiveness of the estimation approach, many battery experiments were implemented. From the battery experiments, a battery cell test database is established, and a three-dimensional response surface-based battery OCV versus SoC battery capacity model is established for different aging states. The battery capacity and initial SoC which are taken as battery parameters are estimated using a genetic algorithm
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China (Grant No. 51507012), Beijing Nova Program (Grant No. Z171100001117063), the National High Technology Research and Development Program of China (2015BAG01B01) and Joint Funds of the National Natural Science Foundation of China (Grant No. U1564206). The systemic experiments of the lithium-ion batteries were performed at the Advanced Energy Storage and Application (AESA) Group, Beijing Institute of Technology.
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