Capturing State‐of‐Charge‐Dependent Efficiency in Battery Energy Storage Systems: A Bernoulli Model Approach
ABSTRACT Accurate modelling of battery energy storage systems (BESSs) is critical for optimising their integration into power grids with high penetration of renewable energy. Conventional stochastic models often assume constant charging and discharging efficiencies, an oversimplification that neglects the significant dependence of battery performance on its state‐of‐charge (SOC). This paper introduces a novel analytical model for BESS based on a discrete‐time discrete‐state Markov chain that explicitly incorporates SOC‐dependent efficiencies and charge acceptance limitations. The BESS is modelled as a finite‐state buffer subject to stochastic energy inflows and outflows, where the transition probabilities are functions of the current SOC. We derive a closed‐form analytical solution for the steady‐state probability distribution of the battery's charge levels. Through an illustrative numerical study, the comparative analysis demonstrates that, when charge acceptance is limited at high SOC (e.g., for State Of Health preservation), our model predicts a significant shift in operational behaviour compared to ideal or constant‐efficiency models. The system's probability mass tends to concentrate in an intermediate range, a behaviour that simpler models often overlook. This has significant implications for BESS sizing and control strategies, indicating that the selected operating strategy greatly affects the appropriate usable capacity. The proposed model provides a computationally efficient and more realistic framework for analysing these dependencies.
- Research Article
37
- 10.1016/j.energy.2011.01.019
- Mar 5, 2011
- Energy
Integrated battery controller for distributed energy system
- Conference Article
- 10.1109/isgt-asia.2014.6873841
- May 1, 2014
This paper studies a harmonized energy management strategy for houses with highly penetrated photovoltaic (PV) based on low temporal-spatial resolution state of charge (SOC) scheduling and high temporal-spatial resolution power balancing control. Energy market in residential sector is rapidly growing due to highly penetrated PV. It requires safety, reliability, economic efficiency, environment-friendly and fair control. Our target is to develop the energy management system (EMS) satisfying previous requirements. In this paper, load aggregator's targets are to decrease peak-to-peak interconnection point power flow and achieving harmonized battery energy storage system (BESS) control. Load aggregator makes SOC schedule and interconnection point power flow bandwidth based on hourly forecasting data in a day ahead. On the day, BESSs are minutely controlled to decrease excess power flow compare to the scheduled power flow bandwidth based on SOC schedule. Simulation results show reduction of the peak-to-peak interconnection point power flow and power fluctuation due to smoothing effect and discuss about fairness of the BESS control.
- Research Article
3
- 10.1016/j.meaene.2025.100048
- Jun 1, 2025
- Measurement: Energy
Electrical modelling of a grid-connected battery energy storage system via EMS and BMS data
- Conference Article
11
- 10.1109/isgt-europe47291.2020.9248945
- Oct 26, 2020
In islanded microgrid, fluctuating operations and intermittency of renewable energy sources (RES) are the challenges of its operation. When droop control is applied on fossil-fueled generator, those challenges can be overcome. However, droop control makes the system working outside the permissible frequency range. Installing battery energy storage system (BESS) could be an option of frequency problem which its ability to regulate the frequency. In BESS operation, battery state-of-charge (SOC) is an important issue since it reflects BESS availability. Hence, a proper of BESS control is needed that it can participate actively to the system called Load Frequency Control (LFC). Furthermore, SOC control in BESS should be included to ensure BESS availability. In this paper, a BESS control that able to regulate system frequency and keep its SOC in certain range is introduced. In order to actualize these functions, shifted-LFC is used. This control will be simulated on diesel-fueled generator-photovoltaic (PV)-BESS microgrid system to observe the impact of installing the proposed control. Under this control, BESS can participate in regulating microgrid frequency and maintaining SOC level within a certain range.
- Research Article
140
- 10.1016/j.segan.2016.03.004
- Apr 1, 2016
- Sustainable Energy, Grids and Networks
Battery energy storage system for primary control reserve and energy arbitrage
- Research Article
19
- 10.11591/ijpeds.v11.i1.pp398-408
- Mar 1, 2020
- International Journal of Power Electronics and Drive Systems (IJPEDS)
<span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Renewable Energy (RE) penetration is a new phenomenon in power systems. In the advent of high penetration of RE in the systems, several issues have to be addressed especially when it involves the stability and flexibility of the power systems. Battery Energy Storage System (BESS) has gained popularity due to its capability to store energy and to serve multiple purposes in solving various power system concerns. Additionally, several BESS can be combined to operate as Virtual Power Plant (VPP). This study will involve the design and implementation of BESS for five potential customer sites for the demonstration project and to be possibly integrated into one VPP system. The study is expected to demonstrate bill savings to the customers with BESS due to peak demand reduction and energy arbitrage savings.</span><table class="MsoNormalTable" style="width: 444.85pt; border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext;" width="593" border="1" cellspacing="0" cellpadding="0"><tbody><tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes; mso-yfti-lastrow: yes; height: 63.4pt;"><td style="width: 290.6pt; border: none; border-top: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; height: 63.4pt;" valign="top" width="387"><p class="MsoNormal" style="margin-top: 6.0pt; text-align: justify;"><span style="font-size: 9.0pt; color: black; mso-bidi-font-style: italic;">Renewable Energy (RE) penetration is a new phenomenon in power systems. In the advent of high penetration of RE in the systems, several issues have to be addressed especially when it involves the stability and flexibility of the power systems. Battery Energy Storage System (BESS) has gained popularity due to its capability to store energy and to serve multiple purposes in solving various power system concerns. Additionally, several BESS can be combined to operate as Virtual Power Plant (VPP). This study will involve the design and implementation of BESS for five potential customer sites for the demonstration project and to be possibly integrated into one VPP system. The study is expected to demonstrate bill savings to the customers with BESS due to peak demand reduction and energy arbitrage savings.</span></p></td></tr></tbody></table>
- Research Article
32
- 10.1016/j.ijepes.2019.105463
- Aug 6, 2019
- International Journal of Electrical Power & Energy Systems
Control of a population of battery energy storage systems for frequency response
- Research Article
- 10.1149/ma2016-02/3/417
- Sep 1, 2016
- Electrochemical Society Meeting Abstracts
The usage of renewable energy to supply electricity demands is expected to increase drastically in the coming years. This is attribute to the encouragement of the government through policies such as RPS(renewable energy portfolio standards) and FIT(feed-in-tariffs). However, the performance of power system is sometimes critically constrained by stability characteristics. It is very challenging for system operators to manage a high penetration of renewable energy resources in a bulk power system, as they are known to deteriorate the dynamic performance of power systems.Therefore, it has been proposed that the large-scale Energy Storage System (ESS) of which power output can be controlled accurately and quickly can be applied to a bulk power system for securing the stability of the system despite a high penetration of the renewable energy resources. By increasing deployment of renewable energy, importance of power grid stability has been increased. For example, Wind Power has characteristics of difficult prediction and rapid variation depending on the regional climate characteristics. Energy Storage System aims to transform an uncontrollably variable and partially unpredictable renewable energy into a controlled and predictable one. For these purpose, a quickly responsive and highly efficient control-algorithm is essential. It is for using such a high performance of ESS when a disturbance occurs on a electrical grid system.KEPCO implemented a demonstration project on large-scale grid connected 4 MW / 8 MWh Battery ESS (BESS) using Lithium-Ion Battery (LIB). Fig. 1 shows the interconnection of ESS at the demonstration site. The 4 MW / 8 MWh BESS is connected to both the 22.9kV substation bus and the distribution line in Jocheon, Jeju Island for offshore wind turbines. In this study, Operation strategies for the BESS were developed for frequency regulation of the grid-system. Fig. 1 Interconnection of ESS at Jocheon Substation For power system frequency regulation, There are two kinds of control strategies through ESS here. One is for the normal status that the ratio of frequency change is not bigger than reference ratio of frequency change(ξ). The reference ratio is frequency changes per second when the smallest power supply was failed from the power system. The other is for the dynamic status that the ratio of frequency change is bigger than the reference ratio. In case of South Korea, it is about -0.306 Hz/sec. It could be variable every year because the total amount of power supply in the grid-system would be different. In this paper, we researched briefly about the normal status.At normal control mode, the power output(P) of the ESS is proportional to the change in frequency(f). kd is a proportional coefficient set by the droop characteristics of a battery generation.P=kd(60-f) In order to distribute output power of each battery, this study established a SOC(State Of Charge) weighted control strategy that can consider the SOC of each battery. The following factors were considered to provide frequency regulation service while considering the SOC :1) Set proportional coefficient (kd) for calculating total output demand2) Set priority at output distribution according to SOC3) Consider rating output of each battery when distributing outputAt normal status, the proportional coefficient(kd) was set by applying the droop of a general generator. This is to control the ESS output with a performance similar to the droop of the general generator. When allocating output demand determined by each battery SOC through this strategy, the battery with a higher SOC have priority in distribution. This is more efficient way to fulfill the total output demand cost-effectively. The SOC weighted control result is shown in Figure 2.Fig. 2 Result of battery output during SOC weighted control (simulation)It can be found that the distributed quantity of output was provided depending on the SOC level of each battery. It's likely to be seen that a battery with a higher SOC has priority in the distribution of output.SOC management effect of the control algorithm was analyzed through a 5-hour too. The result obtained from a simulation frequency of five hours before and after a credible accident. We can find that, in the range within dead band, the control of battery was conducted in order to reach a SOC sustainment section. When the frequency is in the dead band, ESS is not working for frequency regulation. In the outside range of the frequency dead band, it was observed that control capacity was distributed according to SOC in order to provide frequency regulation.
- Conference Article
3
- 10.1109/poweri.2012.6479471
- Dec 1, 2012
This paper endeavours an investigation of voltage and frequency (VF) based BESS (battery energy storage system) controller used in micro grid for analyzing the optimum capability of plant under transient conditions. Micro grid is formed by using three hydro power plants feeding linear and non linear loads. The BESS VF controller used is for load balancing, harmonic suppression, load leveling and neutral current minimization. The proposed BESS controller permits the selection of an optimized battery voltage level and allows independent current control of each phase. The main emphasis is given on maintaining constant voltage and frequency within the micro grid under transient conditions. Micro grid with power plant and BESS controller is modeled in MATLAB/Simulink using Sim Power System Library.
- Research Article
41
- 10.1016/j.epsr.2022.108037
- May 2, 2022
- Electric Power Systems Research
Coordinated control of Incentive-Based Demand Response Program and BESS for frequency regulation in low inertia isolated grid
- Conference Article
5
- 10.1109/ipemc.2016.7512294
- May 1, 2016
The rapid development of battery energy storage technology has provided a new solution for integrating large scale renewable power generation; however, the accurate model of battery energy storage system (BESS) in multi-time scales has not been developed yet. The BESS model consists of battery model, power electronics interface model and controller model. There are still no certain math expressions about the parameters of battery model, the model of power electronics and controller are also different in different applications. Considering different applications in power system, the multi-time scales model of BESS should be established to take account of the transient, steady and dynamic state. In this paper, an equivalent modeling method of BESS was developed. First, the different equivalent circuit models of battery were summarized, according to the comparison, the thevenin equivalent circuit model was supposed as the effective model for power system application. So, taking into account the relations between the parameters such as current, internal resistance, and state of charge (SOC), the battery parameters were fitted based on experimental date. Then, the power electronics interface model including DC/AC and DC/DC converter were introduced, and the control method with different operations were proposed. Finally, the BESS model were built and verified on the platform of BESS experiment. The results show that the model can represent the multi-state characteristics of battery and has quick response.
- Research Article
87
- 10.35833/mpce.2020.000743
- Jan 1, 2021
- Journal of Modern Power Systems and Clean Energy
Large-scale renewable energy integration decreases the system inertia and restricts frequency regulation. To maintain the frequency stability, allocating adequate frequency-sup-port sources poses a critical challenge to planners. In this context, we propose a frequency-constrained coordination planning model of thermal units, wind farms, and battery energy storage systems (BESSs) to provide satisfactory frequency supports. Firstly, a modified multi-machine system frequency response (MSFR) model that accounts for the dynamic responses from both synchronous generators and grid-connected inverters is constructed with preset power-headroom. Secondly, the rate-of-change-of-frequency (ROCOF) and frequency response power are deduced to construct frequency constraints. A data-driven piecewise linearization (DDPWL) method based on hyperplane fitting and data classification is applied to linearize the highly nonlinear frequency response power. Thirdly, frequency constraints are inserted into our planning model, while the unit commitment based on the coordinated operation of the thermal-hydro-wind-BESS hybrid system is implemented. At last, the proposed model is applied to the IEEE RTS-79 test system. The results demonstrate the effectiveness of our co-planning model to keep the frequency stability.
- Research Article
- 10.1149/ma2018-02/4/213
- Jul 23, 2018
- Electrochemical Society Meeting Abstracts
Battery Energy Storage Systems (BESSs) can facilitate renewable energy sources integration onto the grid. For this application, these systems are expected to last for a decade or more, but the actual battery degradation under different real-world conditions is still largely unknown. In this work, three years of lithium titanate BESS usage in Hawai'i were analyzed. In addition, the representative usage was subjected on individual cells under controlled laboratory conditions to study the degradation mechanisms and enable life prognosis. The BESS was found to be operational 90% of the time and it stored a cumulative 1.5 GWh of energy, which represented more than 5000 equivalent full cycles on the cells. From this BESS usage data, an initial estimate of BESS degradation was provided and a representative duty cycle was developed. The analysis of the maintenance cycles indicated that these 5000 equivalent cycles induced an estimated 5-10% degradation of the single cells. The battery duty cycle was characterized based on 5 parameters: pulses duration, pulses intensity (current), state of charge (SOC) swing range, SOC event ramp rate, and temperature. The average usage consisted of several 9-second C/2 charge and discharge pulses organized to generate 5% SOC swings with a 0.75% SOC/min ramp rate at 35°C. However, extreme values such as currents up to 4C, swings of 100% SOC, and temperatures above 50°C were also recorded. Laboratory testing and analysis, in conjunction with a more thorough SOH estimation protocol, resulted in a detailed description of degradation that improved the predictions of the remaining useful battery life. Based on the BESS representative usage profile, cycle-aging and calendar-aging experiments were designed to test the degradation of the associated Li-ion cells in a controlled fashion. It was proven that the cell temperature history had the strongest impact on battery degradation followed by the C-rate and the state of charge. Interestingly, the impact of SOC, both on the cycle-aging and the calendar-aging experiments, was revealed to be counterintuitive. During cycle aging, small SOC swings were more detrimental than larger ones. During calendar aging, batteries lost capacity faster at low SOC than at high SOC. The associated degradation mechanisms and their path dependency were analyzed using incremental capacity analysis.
- Research Article
- 10.1149/ma2019-03/1/75
- Feb 1, 2019
- Electrochemical Society Meeting Abstracts
Battery Energy Storage Systems (BESSs) can facilitate renewable energy sources integration onto the grid. For this application, these systems are expected to last for a decade or more, but the actual battery degradation under different real-world conditions is still largely unknown. In this work, three years of lithium titanate BESS usage in Hawai'i were analyzed. In addition, the representative usage was subjected on individual cells under controlled laboratory conditions to study the degradation mechanisms and enable life prognosis. The BESS was found to be operational 90% of the time and it stored a cumulative 1.5 GWh of energy, which represented more than 5000 equivalent full cycles on the cells. From this BESS usage data, an initial estimate of BESS degradation was provided and a representative duty cycle was developed. The analysis of the maintenance cycles indicated that these 5000 equivalent cycles induced an estimated 5-10% degradation of the single cells. The battery duty cycle was characterized based on 5 parameters: pulses duration, pulses intensity (current), state of charge (SOC) swing range, SOC event ramp rate, and temperature. The average usage consisted of several 9-second C/2 charge and discharge pulses organized to generate 5% SOC swings with a 0.75% SOC/min ramp rate at 35°C. However, extreme values such as currents up to 4C, swings of 100% SOC, and temperatures above 50°C were also recorded. Laboratory testing and analysis, in conjunction with a more thorough SOH estimation protocol, resulted in a detailed description of degradation that improved the predictions of the remaining useful battery life. Based on the BESS representative usage profile, cycle-aging and calendar-aging experiments were designed to test the degradation of the associated Li-ion cells in a controlled fashion. It was proven that the cell temperature history had the strongest impact on battery degradation followed by the C-rate and the state of charge. Interestingly, the impact of SOC, both on the cycle-aging and the calendar-aging experiments, was revealed to be counterintuitive. During cycle aging, small SOC swings were more detrimental than larger ones. During calendar aging, batteries lost capacity faster at low SOC than at high SOC. The associated degradation mechanisms and their path dependency were analyzed using incremental capacity analysis.
- Research Article
1
- 10.1088/1757-899x/446/1/012009
- Dec 1, 2018
- IOP Conference Series: Materials Science and Engineering
With increasing penetration of renewable source in power system, higher requirements for power quality are put forward. Energy storage system represented by chemical battery and flywheel energy storage system is fast-ramping and responses quickly in frequency regulation market. It shows outstanding performance in frequency regulation comparing with the traditional frequency regulation resource. This paper reports a review of the energy storage system participating in frequency regulation, including frequency regulation market and energy storage technology. Also, it contrasts the frequency regulation characteristics and total costs between battery energy storage system (BESS) and flywheel energy storage system (FESS) both applied widely in the projects. The operation mode and Simulink modelling of energy storage system, along with the control strategy and capacity configuration, are also discussed through relative literature.