Optimal Battery Capacity Research Articles

Performance Investigations on All-Solid-State Polymer-Ceramic Sodium-Ion Batteries through a Spatially Resolved Electrochemical Model

Rechargeable batteries are crucial in modern energy storage, with lithium-ion batteries dominating the market. However, the scarcity and environmental concerns associated with lithium have spurred interest in alternative battery chemistries, particularly sodium-ion batteries (SIBs), which utilize abundant sodium resources. Despite extensive experimental research on all-solid-state SIBs (ASSSIBs), theoretical investigations have primarily focused on molecular-level analyses, overlooking the impact of cell composition on overall performance. This paper aims to address this gap by developing a physical model for simulating ASSSIBs at the particle scale. Our methodology involves integrating experimental data with simulation results to identify key factors influencing battery performance. The study reveals slow sodium ion transport as a significant bottleneck, attributed to factors such as low porosity of the half-cell and limited electrolyte ionic conductivity. Simulation outcomes emphasize the importance of advancing fast-ion-conducting solid electrolytes to enhance ASSSIB performance. Moreover, the results suggest that electrodes with high electrolyte active filler content and reduced thickness are necessary for achieving optimal battery capacity utilization. Overall, this research underscores the intricate relationship between electrode microstructure and battery performance, offering valuable insights for the design and optimization of sustainable sodium-ion battery systems suitable for stationary and mobile applications.

Analysis of power load tracking and regulation performance in a distributed multi-energy coupled system with nuclear and solar sources

This paper presents a novel distributed multi-energy coupled system that combines solar PV, nuclear power, and energy storage systems to address the power supply challenges in remote regions. Through parameter analysis and multi-objective optimization, the study aims to minimize the need for frequent reactor adjustments during system operation. The key findings indicate that by regulating the rotational speed of the main-compressor, it is possible to meet the power load requirements for a single nuclear power system. The battery capacity and the number of PV panels have a significant impact on the adjustment frequency of the reactor and the power output of the nuclear power system, respectively. The optimal battery capacity is determined to be 183 kWh, while the optimal number of PV panels is 327. These configurations result in an average power output of 20.86 kW for the PV system and 3458.28 kW for nuclear power system. To maximize the utilization of PV energy and minimize reactor adjustments, an energy dispatch strategy is proposed. With the optimal configuration, the adjustment frequency of the reactor decreases to 339 and 276 during the winter and summer months, respectively. Overall, this paper offers a feasible configuration and energy dispatch method for regional power supply.

Optimal Capacity Model for Battery Swapping Station of Electric Taxis: A Case Study in Chengdu

Battery swapping station (BSS) technology can provide electric taxis (ETs) with more economical and high-efficiency operating services. However, the battery-swapping market needs to be more organized due to unpredictable swapping periods for ETs, resulting in more requirements for batteries of BSSs needing multiple batteries simultaneously. To address these challenges, this paper first analyzed two operation patterns of taxis to estimate the demand for swapping ETs. Then, an optimal capacity model of BSS is proposed to optimize the battery capacity of BSSs to meet the swapping demand of ETs. Finally, a genetic algorithm (GA) is utilized to solve the proposed model. The real operating data of taxis with GPS routes in Chengdu city are used as a case study to validate the proposed method. The results show that the proposed method could obtain the optimal battery capacity of a BSS and improve the economic benefits of BSSs.

Research on Optimal Configuration of Integrated Energy Storage for Source Network, Load Storage Considering Carbon Emissions

This study endeavors to construct an optimized operation model for a Combined Heat and Power Microgrid that utilizes renewable distributed power generation. The model decouples the thermoelectric connection via energy storage equipment and takes into account carbon emissions based on multi-energy complementarity. This approach offers an optimization space for the thermal and electrical production of microgrids. Numerical simulation verification demonstrates that the optimization strategy proposed in this study enhances the flexibility of the system’s energy supply and improves the operational economy. Furthermore, the study explores the optimal storage battery capacity under the integration of a specific area’s source-grid-load-storage.

Uncertainty aware optimal battery sizing for cloud energy storage in community microgrid

Cloud energy storage systems (CES) are a new paradigm for the application of consumer-side energy storage in residential community microgrids. By transforming traditional consumers into self-sustaining and utility consumers, CES facilitates interaction between consumers and utilities as well as between consumers. Residential CES development is complicated by the flexible capacity of CES batteries and the uncertainty of supply. This paper recommends the CES system for residential prosumers. A machine learning-based uncertainty quantization and an artificial ecosystem optimization (AEO) method are used to determine optimal battery capacity considering PV, load, and price uncertainty. Compare this algorithm to the other four optimization algorithms to find out how well it works. The feasibility and profitability of deploying CES with residential PV are assessed. This problem minimizes the user’s cost and maximizes the profit of the CES operator. The sensitivity analysis of CES is analyzed for various storage capacity penetrations. Further, optimal battery capacity determines the use of an AEO algorithm. Based on a PJM dataset of residential PV, load, and electricity price, simulation results demonstrate that the suggested framework integrated with a distributed PV system is more economical to DES.

Multi-objective optimization of battery capacity of grid-connected PV-BESS system in hybrid building energy sharing community considering time-of-use tariff

The use of renewable energy and storage systems in energy sharing communities relieves the strain on the grid and reduces the cost of electricity, making the design of community energy management strategies particularly important. In this paper, a shared energy storage operation strategy considering the time-of-use tariff is proposed for the grid-connected PV-BESS system of hybrid building community including factories, offices and dormitories. Aiming at maximizing the photovoltaic self-consumption ratio, minimizing the payback period and power transportation loss, the system is optimized by non-dominated sequencing genetic algorithm II to obtain the optimal battery capacity of each building under the designed strategy. The results show that when the total battery capacity of the community is determined, the photovoltaic power generation of each building and the building load are the main factors that affect the allocation of battery capacity, and the proportion of battery allocation in each building changes little when the values of other influencing parameters are changed. The photovoltaic array area of the building, the difference between peak and valley electricity price and the power input and output limits of the grid are the main factors affecting the optimal battery capacity and system performance. When the photovoltaic array area increases from 65% to 80%, the difference between peak and valley price increases from 0.52RMB/kWh to 0.82RMB/kWh, and the grid power output limit increases from 7500 kW to 9000 kW, the total optimal battery capacity is increased by 9.8%, 20%, 2.2%, the corresponding payback period is increased by 4%, 3.1%, 2%, the photovoltaic self-consumption ratio is increased by 3.3%, 1.9%, 0.2%, and the electricity transportation loss is increased by 6%, 21%, 2.4%, respectively. On the contrary, when the grid power input limit increases from 5500 kW to 7000 kW, the optimal total battery capacity, the corresponding payback period, photovoltaic self-consumption ratio, and power transport loss are reduced by 2.8%, 2.5%, 0.3% and 3.3%, respectively. This study provides theoretical guidance for community battery capacity optimization and energy scheduling design under the peak-valley policy of power grid.

Optimal sizing and lifetime investigation of second life lithium-ion battery for grid-scale stationary application

The renewable energy sources (RESs) integration into the grid system aims to solve the problem of power shortage and satisfy the increasing demand with the production of surplus energy. However, the intermittent nature of these RESs (solar and wind) is a challenge to integrate with the grid system without the deployment of mitigating solutions. The re-use of first life-end-of-life (FL_EoL) electric vehicle batteries known as second life batteries (SLBs) is therefore proposed as a reliable solution to resolve this problem, satisfying the techno-economic requirements of stationary applications. Though various studies performed on the technical viability evaluation of SLBs, most of them have not considered the field data of existing stationary plants and were found to be limited with simulation-based aging results. On the other hand, few of the studies have performed the second life aging test with limited cycles considering the end of test conditions rather than using the cells reached to their end of first life criteria. Therefore, in this paper, the prolonged cycling aging of SLBs is conducted (both cell-level and module-level aging), focusing on aging characteristics of SLBs by using a real-life renewable power smoothing profile extracted from an existing photovoltaic grid-connected system (PVGCS) installed in Ethiopia. Prior to the aging characterization of SLBs, assessment of the selected stationary application requirement, optimal sizing of the storage battery and cycling profile definition are performed using advanced moving average ramp rate controller (MARRC) algorithm. The proposed method of MARRC is used to determine the optimal SLBs capacity by analyzing the relationship between ramp-rate, initial battery capacity and window sizes of moving average control method in terms of time series. The algorithm addresses the main objectives of reducing unnecessary battery cycling, mitigating ramp-rate violations and meeting minimum storage requirements for the second-life application. From the result of the battery sizing study, the desired optimal battery capacity and the permissible ramp-rate limit below 10 %/minute is achieved. Moreover, the aging characterization and lifetime model validation results with a root mean square error (RMSE) of 1.5 % shows that, the technical performance of the SLBs is found to be promising with an efficiency of >90 % interpreted in terms of the service year that the SLBs can provide. Therefore, SLBs can be regarded as a viable solution for integrating RESs with the grid system for the power variability smoothing application.

Optimal battery and hydrogen fuel cell sizing in heavy-haul locomotives

Global supply chains must be decarbonised as part of meeting climate targets set by the United Nations and world leaders. Rail networks are vital infrastructure in passenger and freight transport, however, have not received the same push for decarbonisation as road transport. In this investigation, we used real world data from locomotives operating on seven rail corridors to identify optimal battery capacity and hydrogen fuel cell (HFC) power in hybrid systems. We found that the required battery capacity is dependent on both the available regenerative braking energy and on the capacity required to buffer surpluses and deficits from the HFC. The optimal system for each corridor was identified, however it was found that one 3.6 MWh battery and 860 kW HFC system could service six of the seven corridors. The optimal systems presented in this work suggest an average of around 5 h of battery storage for the HFC power, which is larger than the 2 h previously reported in literature. This may indicate a gap between purely theoretical works that use only route topography and speed, and those that employ real world locomotive data.

Comparison of Tender Criteria for Electric and Diesel Buses in Poland—Has the Ongoing Revolution in Urban Transport Been Overlooked?

The electrification of public transport is an overwhelming trend, representing the first step in the energy transition of the transport sector. The transport sector is characterized by the prevalence of public ownership and the significant influence of the public sector. Accordingly, tendering procedures are widely utilized to identify the most efficient bus delivery options. This paper compares, evaluates, and identifies the differences in criteria used in tenders for battery electric buses and diesel buses in Poland based on a deep bus market analysis supported by in-depth individual interviews. The article also attempts to determine whether the weight of the “vehicle price” criterion corresponds to the share of the vehicle price in its life cycle cost or total cost of ownership. The results indicate no significant difference in the tender criteria between battery electric buses and diesel buses. In the vast majority of cases, institutions that had previously developed diesel bus acquisition patterns transferred these patterns to tenders for battery electric bus purchases. Therefore, the criteria and their weights used in tenders do not consider the advantages and disadvantages of both technologies. Tendering procedures are adapted to local conditions and operational requirements. Electric buses often replace conventionally powered vehicles on existing routes and schedules. Thus, operational requirements are known. As a result, the necessary number of vehicles and the basic technical and operational parameters (e.g., selection of the optimal charging method and battery capacity) can be determined. In turn, the charging method will influence the total cost of ownership, with overnight charging favored for shorter assignments and opportunity charging favored for longer mileages.

Techno-economic assessment of battery storage with photovoltaics for maximum self-consumption

Abstract The study provided a techno-economic optimization technique for acquiring the ideal battery storage capacity in conjunction with a solar array capable of meeting the desired residential load with high levels of self-sufficiency. Moreover, the viability of a proposed photovoltaic battery system was evaluated. With a resolution of one minute, the annual energy consumption, irradiance, and ambient temperature for 2021 have been measured. Simulations of a stationary economic model are run from 2021 to 2030. Based on the experimental evaluation of the annual energy consumption, which was 3755.8 kWh, the study reveals that the photovoltaic array with a capacity of 2.7 kWp is capable of producing an annual energy production of 4295.5 kWh. The optimal battery capacity determined was 14.5 kWh, which can satisfy 90.2% of self-consumption at the cost of energy $0.25/kWh. Additionally, two third-order polynomial relationships between self-consumption and net present costs and energy cost were established.

Local Interpretable Explanations of Energy System Designs

Optimization-based design tools for energy systems often require a large set of parameter assumptions, e.g., about technology efficiencies and costs or the temporal availability of variable renewable energies. Understanding the influence of all these parameters on the computed energy system design via direct sensitivity analysis is not easy for human decision-makers, since they may become overloaded by the multitude of possible results. We thus propose transferring an approach from explaining complex neural networks, so-called locally interpretable model-agnostic explanations (LIME), to this related problem. Specifically, we use variations of a small number of interpretable, high-level parameter features and sparse linear regression to obtain the most important local explanations for a selected design quantity. For a small bottom-up optimization model of a grid-connected building with photovoltaics, we derive intuitive explanations for the optimal battery capacity in terms of different cloud characteristics. For a larger application, namely a national model of the German energy transition until 2050, we relate path dependencies of the electrification of the heating and transport sector to the correlation measures between renewables and thermal loads. Compared to direct sensitivity analysis, the derived explanations are more compact and robust and thus more interpretable for human decision-makers.

Global Product Design Platforming: A Comparison of Two Equilibrium Solution Methods

AbstractGlobal product platforms can reduce production costs through economies of scale and learning but may decrease revenues by restricting the ability to customize for each market. We model the global platforming problem as a Nash equilibrium among oligopolistic competing firms, each maximizing its profit across markets with respect to its pricing, design, and platforming decisions. We develop and compare two methods to identify Nash equilibria: (1) a sequential iterative optimization (SIO) algorithm, in which each firm solves a mixed-integer nonlinear programming problem globally, with firms iterating until convergence; and (2) a mathematical program with equilibrium constraints (MPEC) that solves the Karush Kuhn Tucker conditions for all firms simultaneously. The algorithms’ performance and results are compared in a case study of plug-in hybrid electric vehicles where firms choose optimal battery capacity and whether to platform or differentiate battery capacity across the US and Chinese markets. We examine a variety of scenarios for (1) learning rate and (2) consumer willingness to pay (WTP) for range in each market. For the case of two firms, both approaches find the Nash equilibrium in all scenarios. On average, the SIO approach solves 200 times faster than the MPEC approach, and the MPEC approach is more sensitive to the starting point. Results show that the optimum for each firm is to platform when learning rates are high or the difference between consumer willingness to pay for range in each market is relatively small. Otherwise, the PHEVs are differentiated with low-range for China and high-range for the US.

Collective self-consumption of solar photovoltaic and batteries for a micro-grid energy system

The paper carried out a techno-economic analysis in order to obtain the optimum battery storage capacity in conjunction with a photovoltaic array that can match the desired household load at highest possible self-consumption. In addition, it determined the economic feasibility of a proposed micro-system. Annual energy consumption, irradiance, and ambient temperature were measured at 1-min resolution for the year 2021. Simulations of a stationary economic model are performed for the years 2021 through 2030.The results showed that the photovoltaic array at 2.7 kWp capacity can generate an annual energy of approx. 4295.4 kWh and the optimal battery capacity which can satisfy 91.1% of self-consumption and energy cost of $0.256/kWh is 14.4 kWh. Furthermore, two third-order polynomial relationships between self-consumption and net present cost with energy cost were solved.

Solar Self-Sufficient Households as a Driving Factor for Sustainability Transformation

We present a model to estimate the technical requirements, including the photovoltaic area and battery capacity, along with the costs, for a four-person household to be 100% electrically self-sufficient in Germany. We model the hourly electricity consumption of private households with quasi-Fourier series and an autoregressive statistical model based on data from Berlin in 2010. Combining the consumption model and remote-sensed hourly solar irradiance data from the ERA5 data set, we find the optimal photovoltaic area and battery capacity that would have been necessary to be self-sufficient in electricity from July 2002 to June 2022. We show that it is possible to build a self-sufficient household with today’s storage technology for private households and estimate the costs expected to do so.

Energy management strategy and optimal battery capacity for flexible PV-battery system under time-of-use tariff

An appropriate battery capacity and a reasonable energy management strategy can improve the techno-economic characteristics and the energy flexibility for building energy systems. In this study, integrating the battery roles of the PV self-consumption maximum, peak shifting, and price arbitrage, a new operation strategy defined as MF strategy is proposed by setting the charging/discharging ratios for PV-battery system with time-of-use tariff. Compared with the single-objective optimization based on the MINLP model, the calculating time based on the MF strategy is reduced by 45 h, and the SCR is increased by 8.73%. Compared with the multi-objective optimization based on the SCM strategy, the optimal battery capacities based on the proposed MF strategy have a lower total cost, and the optimal SCR range is 77%–86%. Moreover, the sensitivity of 14 parameters on the energy system performance is analyzed by local and global sensitivity analysis. The analyses showed that the important parameters for the total cost include the charging/discharging ratio for the shoulder period. The important parameters for the SCR include the charging/discharging ratio for the shoulder period and discharging ratio for the peak period. This study provides a new operation strategy and algorithm for battery capacity optimization and energy management.

Optimal Energy Storage Systems for Long Charge/Discharge Duration

The interest for long-term energy storage in electrical grid provided with renewable energy sources is presently growing, because of the wide range of service that such systems can offer [1,2]. Although the choice of optimal duration of the charge / discharge cycles of energy storage systems for stationary applications is still an open question, among the different energy storage technologies available at a high readiness level (TRL), a few fit particularly well this kind of services [3,4]. Depending on the application and the market in which the energy storage systems are applied, the optimal duration can have different values and call for different technologies. Among electrochemical energy storage systems Vanadium Redox Flow Batteries (VRFBs) are emerging as a very promising solution for long-term stationary applications [5]. In order to find an optimal duration value for applications, the development of a physical-economic model becomes essential. Indeed, the optimal duration of energy storage systems not only depends on the technical features of each energy storage device (e.g. life cycle, self-discharge, ecc...), but also on the specific services required by the market. VRFBs devices which may be very expensive for a specific market, could be a competitive solution for a different one. The purpose of this work is to size the optimal duration of VRFB system according to the specific applications and the reference market.Reference Wu Y, Liu Z, Liu J, Xiao H, Li, R, Zhang L, Optimal battery capacity of grid-connected PV-battery systems considering battery degradation, Renewable Energy, 2022,181:10-23. DOI: 1016/j.renene.2021.09.036.Simoglou CK, Biskas PN, Marneris IG, Roumkos CG, Long-term electricity procurement portfolio optimization, Electric Power Systems Research, 2022, 202:107582. DOI: 1016/j.epsr.2021.107582Alotto P, Guarnieri M, Moro F, Redox Flow Batteries for the storage of renewable energy: a review, Renewable & Sustainable Energy Reviews, 2014,29:325-335. DOI: 1016/j.rser.2013.08.001.Ibrahim H, Ilinca A, Perron J, Energy storage systems-Characteristics and comparisons, Renewable and Sustainable Energy Reviews, 2008,12,5:1221-1250. DOI:10.1016/j.rser.2007.01.023Guarnieri M, Mattavelli P, Petrone G, Spagnuolo G, Vanadium Redox Flow Batteries: Potentials and Challenges of an Emerging Storage Technology, IEEE Industrial Electronics Magazine, 2016,10,4:20-31. DOI: 1109/MIE.2016.2611760. Figure 1

If Electric Cars Are Good for Reducing Emissions, They Could Be Even Better with Electric Roads.

This research investigates carbon footprint impacts for full fleet electrification of Swedish passenger car travel in combination with different charging conditions, including electric road system (ERS) that enables dynamic on-road charging. The research applies a prospective life cycle analysis framework for estimating carbon footprints of vehicles, fuels, and infrastructure. The framework includes vehicle stock turnover modeling of fleet electrification and modeling of optimal battery capacity for different charging conditions based on Swedish real-world driving patterns. All new car sales are assumed to be electric after 2030 following phase-out policies for gasoline and diesel cars. Implementing ERS on selected high-traffic roads could yield significant avoided emissions in battery manufacturing compared to the additional emissions in ERS construction. ERS combined with stationary charging could enable additional reductions in the cumulative carbon footprint of about 12–24 million tons of CO2 over 30 years (2030–2060) compared to an electrified fleet only relying on stationary charging. The range depends on uncertainty in emission abatement in global manufacturing, where the lower is based on Paris Agreement compliance and the higher on current climate policies. A large share of the reduction could be achieved even if only a small share of the cars adopts the optimized battery capacities.

Optimal utilization strategy of the LiFePO[formula omitted] battery storage

The paper provides a comprehensive battery storage modeling approach, which accounts for operation- and degradation-aware characteristics and can be used in optimization problem formulations. Particularly, Mixed-Integer Linear Programming (MILP) compatible models have been developed for the lithium iron phosphate (LiFePO4) battery storage using the Special Order Sets 2 to represent the nonlinear characteristics, including efficiency, internal resistance growth, and capacity fade. Such formulation can be used in problems related to various applications, i.e., power systems, smart grid, and vehicular applications, and it allows finding the globally optimal solution using off-the-shelf academic and commercial solvers. In the numerical study, the proposed modeling approach has been applied to realistic scenarios of peak-shaving, where the importance of considering the developed models is explicitly demonstrated. Operation- and degradation-aware techno-economic analysis showed that the optimal battery capacity is driven by operating rather than service requirements. Particularly, a considerable battery over-sizing becomes economically feasible when the battery storage is used more extensively. Another finding suggests that to achieve the maximum value from battery storage, its operation strategy needs to be significantly modified during the course of its lifetime. In the scenarios considered, the charging time gradually increased from four to seven hours, while the average SoC decreased by 20%. Such an adaptable scheduling results in reduced battery degradation and a longer lifetime, which may provide as much as 12.1% of savings in the battery storage system project.

Optimal battery capacity in electrical load scheduling

With a rapid decline in cost of battery energy storage, a battery system plays an increasingly important role in managing imbalance between ordering and consumption in the electricity wholesale market. We develop an innovative electricity demand forecasting framework for calculating the optimal battery capacity that maximizes the profit of an electricity retailer. The framework allows different costs associated with over- and under-prediction errors, and two insensitive parameters to capture the battery residual capacity and remaining storage space. An application to Australia National Electricity Market in New South Wales shows that the use of a battery system with the optimal capacity can save up to AUD $65 millions annually under reasonable battery unit cost assumptions.

Optimal fleet, battery, and charging infrastructure planning for reliable electric bus operations

• Propose optimal single-route bus electrification planning. • Jointly optimize battery capacity, fleet size, and charging infrastructure. • Explicitly identify five major constraints in bus electrification. • Develop a tractable two-stage sequential solution method. • Investigate economic and environmental advantages of operating electric buses. The electrification of bus systems offers the potential to reduce fossil fuel consumption. Motivated by this, we assume a scenario in which a single existing bus route is operated by battery-electric buses and find the optimal planning by determining the number of chargers, the electric bus fleet size, and the battery capacity. While decision-making, it is necessary to guarantee that all scheduled tasks are completed with reliability against stochastic electricity consumption. We discover that a large fleet size and a high charging infrastructure capacity can reduce the minimum necessary battery capacity, and this tradeoff is crucial in the optimization. We demonstrate the proposed framework using electric bus operation data collected in Jeju, Korea, and find that the optimal electrification of a bus route can be economically and environmentally beneficial.