Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases.
We optimize the operation of a fuel cell hybrid train using convex optimization. The main objective is to minimize hydrogen fuel consumption for a target journey time while considering battery thermal constraints. The state trajectories: train speed, energy management system, and battery temperature, are all optimized concurrently within a single optimization problem. A novel thermal model is proposed in order to include battery temperature yet maintain formulation convexity. Simulations show fuel savings and better thermal management when temperature is optimized concurrently with the other s…
User-centric Vehicle-to-Grid Optimization with an Input Convex Neural Network-based Battery Degradation Model
Delft Center for Systems and Control (DCSC), Department of Mechanical Engineering, Delft University of Technology (TU Delft)（代尔夫特系统与控制中心（DCSC）、机械工程系、代尔夫特理工大学）
We look into modeling fuel cell hybrid trains for the purpose of optimizing their operation using convex optimization. Models and constraints necessary to form a physically feasible yet convex problem are reviewed. This effort is described as holistic due to the broad consideration of train speed, energy management system, and battery thermals. The minimized objective is hydrogen fuel consumption for a given target journey time. A novel battery thermal model is proposed to aid with battery thermal management and thus preserve battery lifetime. All models are derived in the space-domain which a…
This paper presents a novel battery modeling framework based on the enhanced single particle model (ESPM) to account for degradation mechanisms of second-life batteries. While accounting for the transport and electrochemical phenomena in the battery solid and electrolyte phases, the dominant anode-related aging mechanisms, namely, solid electrolyte interphase (SEI) layer growth and lithium plating, are modeled. For the first time, the loss of active material (LAM), which describes the tendency of anode and cathode, over time, to reduce the electrode material available for intercalation and dei…
In this letter, we model the day-ahead price-based demand response of a residential household with battery energy storage and other controllable loads, as a convex optimization problem. Further using duality theory and Karush-Kuhn-Tucker optimality conditions, we derive a sufficient criterion which guarantees non-simultaneous charging and discharging of the battery energy storage, without explicitly modelling it as a constraint
In this manuscript, we have investigated the response of the State of Charge (SoC) and the open-circuit voltage across the dynamic battery model under the variable voltage and current during the charging cycle of the battery. These variable input voltage and current have been obtained using the variable irradiance and surface temperature of a Solar PV array which is connected as an input of the dynamic battery model to store the energy within it. In order to match the Simulation result with reality, these variable irradiance and surface temperature of Solar PV Array with respect to time has be…
Modeling And Control Battery Aging in Energy Harvesting Systems
The Donald Bren School of Information and Computer Science, UC Irvine（加州大学欧文分校唐纳德·布伦信息与计算机科学学院）；Dept. of Information Engineering, Computer Science and Mathematics, University of L’Aquila（拉奎拉大学信息与工程、计算机与数学系）
This paper instantiates a convex electric powertrain design optimization framework, bridging the gap between high-level powertrain sizing and low-level components design. We focus on the electric motor and transmission of electric vehicles, using a scalable convex motor model based on surrogate modeling techniques. Specifically, we first select relevant motor design variables and evaluate high-fidelity samples according to a predefined sampling plan. Second, using the sample data, we identify a convex model of the motor, which predicts its losses as a function of the operating point and the de…
Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Virtual battery (VB) models are often used to quantify the predictive flexibility in thermostatic loads (e.g. residential air-conditioners, electric water-heaters), which model the temporal evolution of a (virtual) energy state via a first order dynamics including self-dissipation rate, and power and energy capacities as parameters. Uncertainties and lack of information regardi…
Redox Flow Batteries are a promising option for large-scale stationary energy storage. The vanadium redox flow battery is the most widely commercialized system thanks to its chemical stability and performance. This work aims to optimize the scheduling of a vanadium flow battery that stores energy produced by a renewable power plant, keeping into account a thorough characterization of the battery performance, with variable efficiencies and capacity fade effects. A detailed characterization of the battery performance improves the calculation of the optimal number of cycles and revenue associated…
Vehicle-to-grid (V2G) is a promising approach to solve the problem of grid-level intermittent supply and demand mismatch, caused due to renewable energy resources, because it uses the existing resource of electric vehicle (EV) batteries as the energy storage medium. EV battery design together with an impetus on profitability for participating EV owners is pivotal for V2G success. To better understand what battery device parameters are most important for V2G adoption, we model the economics of V2G process under realistic conditions. Most previous studies that perform V2G economic analysis, assu…
This paper presents a convex optimization framework to compute the minimum-lap-time control strategies of all-wheel drive (AWD) battery electric race cars, accounting for the grip limitations of the individual tyres. Specifically, we first derive the equations of motion (EOM) of the race car and simplify them to a convex form. Second, we leverage convex models of the electric motors (EMs) and battery, and frame the time-optimal final-drives design and EMs control problem in space domain. The resulting optimization problem is fully convex and can be efficiently solved with global optimality gua…
Mercedes-Benz AG（梅赛德斯-奔驰股份公司）；Institute of Automotive Technology Dresden（德累斯顿汽车技术研究所）
Dynamic models of the battery performance are an essential tool throughout the development process of automotive drive trains. The present study introduces a method making a large data set suitable for modeling the electrical impedance. When obtaining data-driven models, a usual assumption is that more observations produce better models. However, real driving data on the battery's behavior represent a strongly non-uniform excitation of the system, which negatively affects the modeling. For that reason, a subset selection of the available data was developed. It aims at building accurate nonline…
The widespread adoption of Electric Vehicles (EVs) is limited by their reliance on batteries with presently low energy and power densities compared to liquid fuels and are subject to aging and performance deterioration over time. For this reason, monitoring the battery State Of Charge (SOC) and State Of Health (SOH) during the EV lifetime is a very relevant problem. This work proposes a battery digital twin structure designed to accurately reflect battery dynamics at the run time. To ensure a high degree of correctness concerning non-linear phenomena, the digital twin relies on data-driven mod…
North Carolina A&T State University（北卡罗来纳农工州立大学）；Arizona State University（亚利桑那州立大学）
Given the high power density low discharge rate and decreasing cost rechargeable lithium-ion batteries LiBs have found a wide range of applications such as power grid level storage systems electric vehicles and mobile devices. Developing a framework to accurately model the nonlinear degradation process of LiBs which is indeed a supervised learning problem becomes an important research topic. This paper presents a classical-quantum hybrid machine learning approach to capture the LiB degradation model that assesses battery cell life loss from operating profiles. Our work is motivated by recent a…
This article proposes an offline Energy Management System (EMS) for Parallel Hybrid Electric Vehicles (PHEVs). Dividing the torque between the Electric Motor (EM) and the Internal Combustion Engine (ICE) requires a suitable EMS. Batteries are vital to HEVs and significantly impact overall vehicle cost and performance. High temperature and high battery State of Charge (SOC) are the main factors that accelerate battery aging. SOC is the most critical state variable in EMS and was usually considered the only dynamic variable in previous studies. For simplicity, the battery temperature was often a…
Islanded microgrids powered by renewable energy require costly energy storage systems due to the uncontrollable generators. Energy storage needs are amplified when load and generation are misaligned on hourly, monthly, or seasonal timescales. Diversification of both loads and generation can smooth out such mismatches. The ideal type of battery to smooth out remaining generation deficits will depend on the duration(s) that energy is stored. This study presents a controls co-design approach to design an islanded microgrid, showing the benefit of hybridizing tidal and solar generation and hybridi…
This paper presents a novel modular, reconfigurable battery energy storage system. The proposed design is characterized by a tight integration of reconfigurable power switches and DC/DC converters. This characteristic enables isolation of faulty cells from the system and allows fine power control for individual cells toward optimal system-level performance. An optimal power management approach is developed to extensively exploit the merits of the proposed design. Based on receding-horizon convex optimization, this approach aims to minimize the total power losses in charging/discharging while a…
Cities all around the world struggle with urban air quality due to transportation related emissions. In public transport networks, replacing internal combustion engine buses by electric buses provides an opportunity to improve air quality. Hence, many bus network operators currently ask for an optimal transformation plan to integrate battery electric buses into their fleet. Ideally, this plan also considers the installation of necessary charging infrastructure to ensure a fleet's operational feasibility. Against this background, we introduce an integrated modeling approach to determine a cost-…
Frequency response and voltage support are vital ancillary services for power grids. In this paper, we design and experimentally validate a real-time control framework for battery energy storage systems (BESSs) to provide ancillary services to power grids. The objective of the control system is to utilize the full capability of the BESSs to provide ancillary services. We take the voltage-dependent capability curve of the DC-AC converter and the security requirements of BESSs as constraints of the control system. The initial power set-points are obtained based on the droop control approach. To …
This paper investigates the impact of implantable cardioverter defibrillator (ICD)'s load on its lithium battery power sources through a coupled electro-thermal dynamic model simulation. ICDs are one of the effective treatments available to significantly improve survival of patients with fatal arrhythmia (abnormal heart rhythm) disorders. Using a lithium battery power source, this life-saving device sends electrical shocks or pulses to regulate the heartbeat. The service life and reliability of an ICD is primarily expressed by its battery's lifespan and performance. In this paper we investigat…
Motivated by the need of assessing the optimal allocation of battery energy storage services across various markets and the corresponding impact on market operations, an optimization framework is proposed in this work to coordinate the operation of an independent utility-scale price-maker battery energy storage system (BESS) in the energy, spinning reserve and performance-based regulation markets. The entire problem is formulated as a bi-level optimization process, where the structure of all markets is modeled considering the joint operation limits. The strategic bidding behavior of a price-ma…
This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by compar…
Profit-Maximizing Planning and Control of Battery Energy Storage Systems for Primary Frequency Control
The Chinese University of Hong Kong（香港中文大学）；Shenzhen Research Institute, The Chinese University of Hong Kong（香港中文大学深圳研究院）；California Institute of Technology（加州理工学院）
