**1. Introduction**

Energy storage systems (ESSs) store electricity when surplus electricity is generated or electricity rates are low and supply the stored electricity to the unit when electricity is in high demand or prices are high; therefore, for the efficient operation of power facilities, the development of an energy management system (EMS) algorithm is imperative.

Battery characteristics [1–3] and the sizing of ESSs have been extensively investigated [4–6] because the battery accounts for most of the budget when designing ESSs; therefore, battery selection and management are important, as the aging problems caused by inappropriate battery management costs account for a large part of the replacement budget.

Many ESSs use lithium-ion batteries, since they offer a high energy density and high efficiency [7,8]; however, it is crucial to identify the charging state of batteries because there is a risk of fire during charge-discharge cycles and because there is a need to predict the state of health (SoH) and state of charge (SoC) for battery state management [9]. The ESS consists of cells in series-parallel [10,11] with a large capacity. To solve the safety problems related to fires and explosions [12], a system that manages the battery status is required [13].

The purpose of a battery management system (BMS) is to manage the battery [14,15]. To improve the reliability and safety of the battery [16,17], many BMS functions are being developed [18]. The functions of BMS can be classified as real-time monitoring, calculation and prediction, protection, and optimization. The battery voltage, current, temperature, SoC,

**Citation:** Lee, J.; Kim, J.-M.; Yi, J.; Won, C.-Y. Battery Management System Algorithm for Energy Storage Systems Considering Battery Efficiency. *Electronics* **2021**, *10*, 1859. https://doi.org/10.3390/ electronics10151859

Academic Editors: Shailendra Rajput, Moshe Averbukh and Noel Rodriguez

Received: 7 July 2021 Accepted: 30 July 2021 Published: 2 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

SoH, and other factors can be confirmed via monitoring [19–21]. In addition, the SoC, SoH, and internal impedance can be calculated and predicted [19,22–25]. The protection process limits overcurrent, overvoltage, and overheating and performs fault diagnosis [26–29]. The optimization process maintains the optimal state of charge of a battery by considering the amount of charge between cells [30–32]. As the cycle of a battery increases, the battery ages and its state changes [33]; therefore, to manage a battery, it is necessary to improve the performance of BMSs. The performance of a BMS varies according to the estimation accuracy of the SoC and SoH, indicators of the battery state [10,34,35].

Charge-discharge cycles, temperature, overcharge and overdischarge, and increased internal resistance cause batteries to age, which reduces their capacity. The calculation of battery efficiency can be performed based on the current and SoC [36], via aging analysis based on charge-discharge capacities [37], or via charging-discharging power differences [38,39]; however, it is difficult to accurately estimate the battery state using this approach, as it does not consider the internal resistance changes arising from the aging phenomenon.

Since the internal resistance increases along with the aging phenomenon of the battery, it should be estimated during the operation, therefore, a battery efficiency estimation method is proposed in this paper. The efficiency of the battery is obtained based on the charging and discharging power losses. Since the internal resistance varies according to the battery efficiency, the battery states can be identified using this variation of internal resistance.

A battery efficiency calculation formula is used to predict the SoC and SoH of the battery. The conventional methods used for estimating battery SoC for BMS performance improvements include deep neural network-based methods for error rating reduction [40], extended Kalman filter (EKF)-based methods with the Thevenin model [41], particle swarm optimization (PSO) [42], and hysteresis voltage of the open circuit voltage (OCV) [43]. Additionally, SoC and internal resistance estimation methods based on an unscented Kalman filter (UKF) with analysis of model parameters [44] and estimation based on the adaptive cubature Kalman filter (ACKF) with neural networks are proposed in [45]. In addition, there are other related studies on SoC estimation, such as equivalent circuit model (ECM)-based estimation with noise compensation [46], OCV error compensation based on DNN [47], the open circuit voltage–charge amount (OCV-Q) curve fitting method using a convolutional neural network (CNN) [48], the event-driven Coulomb counting method (CCM) algorithm for unbalanced SoCs [49], and CCM based on modified parameters [50]; however, DNN- and KF-based methods require high computational power and an additional learning process. The OCV and CCM are primarily used to indicate the charging state of a battery [51,52]; however, because OCV is used when the internal battery state is stabilized, it is not sufficiently stable for a nonlinear battery [9]. Furthermore, because another CCM calculates the SoC by accumulating the charge current, the CCM has the disadvantage of increasing the SoC if an error occurs in the initial current measurement value [53].

In this paper, an SoC estimation method combining OCV with CCM is proposed to improve upon the drawbacks of both OCV and CCM. This estimation algorithm does not require excessive computational power and can improve the estimation accuracy. The proposed algorithm uses the OCV equation with the internal resistance and efficiency of the battery. Additionally, the equation can calculate the charge-discharge of the battery by accurately considering the initial value of the CCM by applying OCV while considering the state of the battery.

Based on the battery efficiency formula, a formula that predicts the SoH of a battery based on the charging time required to safely operate the battery is also applied to the BMS algorithm to improve the reliability.

Research related to SoH estimation to improve BMS performance includes the multilayer perceptron (MLP)-based method [54], the self-adaptive weight particle swarm optimization (SWPSO)-based estimation method using a dynamic recurrent neural network

(DRNN) with the ability to conduct dynamic mapping [55], and the XGBoost-based estimation method [56]. Additionally, a state estimation method combining the battery model with a data-based method [57] and a voltage–power-curve-based estimation method [58] has been researched. In [59], a more accurate SoH estimation method was proposed by considering the charging time of the battery, although it did not consider the internal resistance variation and showed estimation error; however, as the SoH estimated without considering the internal resistance is incorrect, some researchers have considered it a constant value [60,61]. Although the SoH is also predicted based on its constant current (CC) charging time [62–64], the internal resistance and temperature [65] of a battery are considered when a system is operated for a long time, while the accurate characteristics of a battery cannot be numerically represented; however, this research used the battery efficiency equation, allowing for a more accurate estimation of the battery state by numerically defining the capacity reduction and the internal resistance of a battery.

The BMS measures the battery's initial SoH and stores the value. The BMS stores the current SoH by comparing the current values with the initial SoH based on the changing values as the battery is used. According to the battery status, the temperature of the battery arises and internal resistance increases along with it. Because of the increase in the internal resistance, the SoH of a battery decreases and it takes less time to chargedischarge the battery; therefore, the CC time period decreases. Based on this time period difference among the charge-discharge cycles, the SoH estimation method is proposed in this paper. The proposed SoH estimation method uses the integral value of the CC time period difference among the charge-discharge cycles for more accurate SoH estimation. In this paper, the battery efficiency equation is used to predict the SoH of a battery considering the decrease in the CC charging time of the SoH due to the increase in the internal resistance of the battery and the fact that the capacity of a battery decreases when it heats up.

An algorithm for predicting battery-related system safety and accurate SoC and SoH by determining a battery fault using the battery efficiency equation is proposed.

The literature on the fault diagnosis of batteries shows that the estimated SoH method is typically used. Many studies on battery fault diagnosis have focused on SoH estimation, since it is a major part of fault diagnosis. For example, in [66], the fault diagnosis method is based on the estimated SoH using the surface temperature of the battery, while fault detection is performed using the SoH estimated based on a multilayer neural network (MNN) in [67].

In this paper, a novel fault diagnosis algorithm that detects the fault state based on the SoH and the efficiency of the battery is proposed for more accurate fault detection. With the proposed method, the battery can be managed more safely because battery faults can be detected beforehand, since the battery efficiency plummets in the fault state before the SoH reaches its fault range.

In this study, we implement the SoC calculation combined with the OCV and CCM, SoH based on the charging time, as well as a fault diagnosis algorithm in a 3 kW ESS. Furthermore, the validity of the proposed BMS algorithm is investigated.
