Multi-objective dynamic programming for constrained optimization of non-separable objective functions with application in energy storage

Western China has good conditions for constructing large-scale photovoltaic (PV) power stations; however, such power plants with large fluctuations and strong randomness suffer from the long-distance power transmission problem, which needs to be solved. For large-scale PV power stations that do not have the conditions for simultaneous hydropower and PV power, this study examined long-distance delivery mode and energy storage optimization. The objective was to realize the long-distance transmission of electrical energy and maximize the economic value of the energy storage and PV power storage. For a large-scale PV power station, the energy storage optimization was modelled under a given long-distance delivery mode, and the economic evaluation system quantified using the net present value (NPV) of the battery was based on the energy dispatch optimization model. By contrast, a lithium battery performance model was developed. Therefore, further analysis of the economics of the energy storage and obtaining the best capacity of the energy storage battery and corresponding replacement cycle considered battery degradation. The case study of Qinghai Gonghe 100 MWp demonstration base PV power station showed that the optimal energy storage capacity was 5 MWh, and the optimal replacement period was 2 years. Therefore, the annual abandoned electricity was reduced by 3.051 × 10 4 MWh compared with no energy storage. The utilization rate of both the PV power station and quality of the delivered electricity were modelled to realize a long-distance transmission to the grid net. This will have an important guiding significance to develop and construct large-scale single PV power stations.

Climate change and the pressing need for sustainable energy solutions have propelled smart grids to the forefront of technological innovation. The emergence of prosumers in smart grids, coupled with the integration of battery energy storage systems (BESS), has significantly enhanced the potential for harnessing renewable energy and optimizing energy consumption patterns. This thesis presents a novel evolutionary game-theoretic (EGT) framework for energy storage scheduling in smart grids, addressing the complex dynamics of local energy markets (LEMs) and the strategic interactions between prosumers equipped with photovoltaic (PV) systems and BESS.At the core of this research is a holistic energy management system (EMS) for prosumers with PV and BESS. This comprehensive framework serves as the foundation for optimizing energy consumption, storage, and trading within a smart grid community (SGC). It considers various factors such as stochastic energy generation, consumption patterns, and fluctuating market conditions to maximize the benefits for individual prosumers and the community as a whole. We propose a novel decentralized EGT approach for exploring a vast action space for battery scheduling over a 24-hour horizon. This innovative algorithm enhances energy management while preserving privacy and scalability. By leveraging EGT, the approach allows for adaptive decision-making in response to changing market conditions and prosumer behaviors, significantly improving upon market stability over traditional scheduling methods.A comprehensive comparative analysis evaluates our proposed EGT algorithm against established methods such as centralized optimization, game theory, and auction-based approaches. This comparison focuses on key performance metrics, including peak-to-average ratio, price volatility, economic efficiency, and computational performance. Results demonstrate the superiority of our EGT approach in terms of both effectiveness and efficiency.The research implements a modified fitness function within the EGT framework that balances technical and economic objectives through the analytic hierarchy process (AHP) approach. This novel fitness evaluation considers both the prosumer's electricity bill and battery degradation, measured by the depth of discharge (DoD). By incorporating these dual objectives, the framework enables prosumers to make informed decisions that balance immediate economic benefits with long-term battery health and sustainability.Building on this enhanced framework, we present a detailed techno-economic analysis that evaluates the financial viability of BESS investments within the SGC. Through considering metrics such as the net present value (NPV) and payback periods, we provide valuable insights into the economic implications of different battery utilization strategies. Our analysis reveals how varying the weights between economic and technical objectives impacts both immediate economic returns and long-term system sustainability. By incorporating these economic metrics alongside technical considerations in our EGT framework, we achieve a balanced approach that addresses both financial viability and system longevity.Extensive simulations demonstrate the effectiveness of our EGT algorithm in stabilizing market conditions under various Feed-in Tariff (FiT) scenarios and prosumer penetration rates. The results show how increased prosumer participation leads to more predictable investment outcomes and stable market conditions. This thesis provides an in-depth analysis of a demand-side management scheme that can be employed by prosumers worldwide in the near future, contributing to the global effort in combating climate change through advanced energy management solutions

Charging up Stationary Energy Storage

With the acceleration of globalization and economic development, the microgrid combining renewable energy generation, storage and load has become the unit controlling the entire system, through the autonomous microgrid cluster to more efficient, reliable and economical use of renewable energy to meet the multiple needs of the power system. This paper proposes a scheme to optimize energy storage strategy by using consistency algorithm. By improving sag control, optimizing energy storage unit design and adjusting SOC balance between the same/different capacities, the efficiency and stability of DC microgrid can be improved. The scheme can achieve SOC balance and voltage regulation, avoid voltage quality degradation, and improve the reliability and practicability of distributed energy storage system. In the simulation experiment, no matter the capacity of Distributed Energy Storage Unit(DESU) is the same or different, the energy storage state can be balanced and the output active power ratio can be maintained, which further verifies the feasibility and advantages of the scheme.

Against the backdrop of imbalanced urban–rural spatial structures and energy resource allocation, along with the continuous increase in distributed photovoltaic (PV) penetration rate, achieving orderly PV expansion and optimal energy storage (ES) configuration has become an urgent requirement for urban–rural distribution network planning. Existing research generally overlooks regional differences between urban and rural areas, making multiregional collaborative optimization difficult to achieve. Therefore, this paper proposes a distributed collaborative planning model for PV and ES (PV–ES) in multiregional urban–rural distribution networks based on the analytical target cascading (ATC) algorithm. By establishing a collaborative planning model that accounts for urban–rural differences, system decoupling is achieved through decomposition modeling and distributed parallel solution is accomplished using the ATC algorithm. Case validation demonstrates that the proposed model can coordinately optimize PV–ES configuration across multiple urban–rural regions, simultaneously enhancing system economics and significantly reducing impact on the upper‐level grid.The study further proposes a three‐level planning implementation pathway of “municipal–county–township” transmission, providing systematic technical methods and planning support for promoting the integration of urban–rural energy infrastructure.

The LA100 Equity Strategies project integrates community guidance with robust research, modeling, and analysis to identify strategy options that can increase equitable outcomes in Los Angeles' clean energy transition.This chapter focuses on utility rates and low-income bill assistance programs as means to improve energy affordability, which is one of the community's highest priorities.Specifically, NREL developed a model using Los Angeles Department of Water and Power (LADWP)-specific inputs to test 2035 rate design and low-income assistance program scenarios.Utility bills were modeled based on the hourly household energy usage (electricity and gas) of each of the 50,000 prototypical LADWP residential households NREL developed with unique combinations of housing types (single-family, multifamily), climate zones, insulation levels, appliances, heating and cooling systems, solar adoption and generation, renter or owner occupancy, and income levels.We evaluated the results to assess the relative efficacy of each approach in reducing bills for LADWP's low-income households using customer affordability and equity metrics including energy burden and hours worked at minimum wage.NREL modeling and results are bounded by LADWP-provided projected revenue requirements as of March 2023.Revenue forecasts were not validated due to lack of data and thus may overstate or understate actual future costs.Also, because we focused solely on affordability and equity impacts to low-income households, this work does not represent a holistic analysis of rate design.Research was guided by input from the community engagement process, and associated equity strategies are presented in alignment with that guidance. Community GuidanceGuidance from the LA100 Equity Strategies Steering Committee, listening sessions with community-based organizations and community members, and community meetings yielded the following:1 Federal Weatherization Assistance Program-eligible households are those living at or below 200% of U.S. federal poverty guidelines. 2 These funds were spent as part of the EZ-SAVE program. 3 Lifeline program eligibility is based on income qualification for customers who are 62 years of age or older or who are permanently disabled.viii communities, 4 and mostly non-White, Hispanic, renter, and lower-income census tracts.Despite these significant program investments, the same demographic groups have the most utility disconnections stemming from bill payment failures.In 2022, LADWP ended its practice of disconnects for a limited set of customers (primarily EZ-SAVE enrollees and Lifeline customers) as a debt collection tool (Haley Smith 2022).Although long-term low-income assistance investments have been significant, LADWP's January 2022 Rates and Equity Metrics Board Package noted the low-income assistance program has "minimal outreach efforts by LADWP to customers," "no targeted communications to customers," "no formal engagement with community-based organizations," and has experienced a "reduction in customers recertifying for the program" (Santilli, Ann and Adams, Martin 2022). Key FindingsContinuing LADWP's current rate design and low-income assistance programs through 2035 is estimated to result in low-income 5 households experiencing disproportionately higher bill increases.Under the existing LADWP rate design and low-income assistance programs, modeling indicates average electricity bills will increase by $83/month across all households between 2019 and 2035 (a 79% increase), while low-income households see an average expected increase of $110/month (a 131% increase). 6Electricity bill affordability metrics modeled for 2035 include: Average electricity burdens, or the percentage of income spent on electricity bills, by income level. Average monthly electricity bills by income level. Average hours worked at minimum wage required to pay for monthly electricity bills, per income level.7 The 15 rate periods are based on the intersection of (1) a three-tier, two-season set of tiered rates and (2) a fourseason set of incremental ordinances (see Appendix C). 8 NREL modeled a tiered "inclining block rate" structure recommended by the California Public Utilities Commission, which charges customers more per kilowatt-hour as their usage increases past certain thresholds (or blocks). 9LADWP does not currently have the smart meter infrastructure required to implement default TOU rates, but it is assumed that by 2035 sufficient metering infrastructure is in place. 10Note that even customers eligible for CARE and FERA that are not ultimately enrolled shoulder the transfer costs associated with participating customers.

The transition from internal combustion engine vehicles to electric vehicles (EVs) is gaining momentum due to their significant environmental and economic benefits. This study addresses the challenges of integrating renewable energy sources, particularly solar power, into EV charging infrastructures by using deep learning models to predict photovoltaic (PV) power generation and EV charging demand. The study determines the optimal battery energy storage capacity and charging schedule based on the prediction result and actual data. A dataset of a 15 kWp rooftop PV system and simulated EV charging data are used. The results show that simple RNNs are most effective at predicting PV power due to their adept handling of simple patterns, while bidirectional LSTMs excel at predicting EV charging demand by capturing complex dynamics. The study also identifies an optimal battery storage capacity that will balance the use of the grid and surplus solar power through strategic charging scheduling, thereby improving the sustainability and efficiency of solar energy in EV charging infrastructures. This research highlights the potential for integrating renewable energy sources with advanced energy storage solutions to support the growing electric vehicle infrastructure.

The present paper proposes a novel methodology for the optimisation of energy storage allocation strategies within wind-solar storage microgrid systems. Firstly, a framework for the joint optimization and configuration of photovoltaic power generation, energy storage, and the power grid within the park has been developed. Secondly, the optimal energy storage allocation strategy for the wind-solar-storage microgrid system is determined based on the particle swarm algorithm (PSO). The potential of collaborative scheduling in joint parks is then verified by comparing the self-sufficiency of power supply in independent parks. The optimal energy storage configuration scheme for A park without energy storage configuration, B, C, and D parks with 153.81kW/400.13kWh, 54.74kW/68.42kWh, and 83.7kW/200kWh, was ultimately determined. It reveals the operation law of the joint operation mode to realize the optimal system operation through the energy sharing mechanism.

Virtual storage capability of residential buildings for sustainable smart city via model-based predictive control

Utilization of early retiring coal-fired power plants as a cold reserve in South Korea: A public perspective

An optimal design model for residential photovoltaic (PV) systems in South Korea was proposed. In the optimization formulation, the objective function is composed of three costs, including the monthly electricity bill, the PV system construction cost (including the government’s subsidy), and the PV system maintenance cost. Here, because the monthly electricity bill is not differentiable (it is a stepped piecewise linear function), it cannot be solved by using traditional gradient-based approaches. For details considering the residential electric consumption in a typical Korean household, consumption was broken down into four types (year-round electric appliances, seasonal electric appliances, lighting appliances, and stand-by power). For details considering the degree of PV generation, a monthly generation dataset with different PV tilt angles was analyzed. The optimal design model was able to obtain a global design solution (PV tilt angle and PV size) without being trapped in local optima. We hope that this kind of practical approach will be more frequently applied to real-world designs in residential PV systems in South Korea and other countries.

Ferroelectric ceramics have the potential to be widely applied in the modern industry and military power systems due to their ultrafast charging/discharging speed and high energy density. Considering the structural design and electrical properties of ferroelectric capacitor, it is still a challenge to find out the optimal energy storage of ferroelectric ceramics during the phase-transition process of amorphous/nanocrystalline and polycrystalline. In this work, a finite element model suitable for the multiphase ceramic system is constructed based on the phase field breakdown theory. The nonlinear coupling relationship of multiple physical fields between multiphase ceramics was taken into account in this model. The basic structures of multiphase ceramics are generated by using the Voronoi diagram construction method. The specified structure of multiphase ceramics in the phase-transition process of amorphous/nanocrystalline and polycrystalline was further obtained through the grain boundary diffusion equation. The simulation results show that the multiphase ceramics have an optimal energy storage in the process of amorphous polycrystalline transformation, and the energy storage density reaches the maximum when the crystallinity is 13.96% and the volume fraction of grain is 2.08%. It provides a research plan and idea for revealing the correlation between microstructure and breakdown characteristics of multiphase ceramics. This simulation model realizes the nonlinear coupling of the multiphase ceramic mesoscopic structure and the phase field breakdown. It provides a reference scheme for the structural design and performance optimization of ferroelectric ceramics.

Li-ion batteries (LiBs) are widely adopted in electric vehicles (EVs) owing to their superior properties, such as high energy density, low discharge rate, long lifespan, and lightweight construction. Since the battery pack is the sole energy source for an EV, its performance is critical for optimal vehicle operation. However, the battery's calendar life, cycle life, and overall performance are significantly affected by temperature variations. The Li-ion batteries used in EVs may encounter challenging working conditions, leading to thermal problems such as significant capacity and power loss. In contrast, thermal runaways can occur at temperatures above a specific threshold, leading to severe health deterioration and sometimes catastrophic safety hazards such as fires and explosions. As the temperature significantly impacts Li-ion batteries, a battery thermal management system that can efficiently dissipate heat is crucial to ensure the battery's optimal performance and longevity. Hence, it is crucial to develop accurate algorithms for battery thermal management systems to precisely and dynamically estimate the temperature dynamics of the batteries integrated within the battery pack.While experimental data can be used to estimate battery temperatures, the dynamic and diverse operating conditions of electric vehicles (EVs) present a significant challenge. Therefore, accurately predicting thermal response within batteries is critical. Various thermal models have been developed to predict the thermal behavior of batteries and quantify the amount of heat generated. The simplified thermal model only considers joule heating and reversible entropic heating. However, more accurate physics-based models consider reversible heat caused by the side reactions, heat generated by mass transport loss, and even mixing-induced heat. The amount of heat generated inside a Li-ion battery is determined by its equivalent internal resistance, open circuit voltage, and entropy change, which are in turn influenced by temperature and depth of discharge (DoD). To the best of the authors' knowledge, previous research on the heat generation of Li-ion batteries has been limited in some respects. Specifically, there has been little investigation into the combined impact of temperature and depth of discharge (DoD) across a wide temperature range. Most studies have been conducted under ambient temperature conditions, and only a few have focused on high temperatures within a narrow range with low discharge rates.Thus, this study aims to address the research gap regarding the impact of temperature and depth of discharge (DoD) on heat generation in Li-ion batteries by analyzing these parameters using a transient battery thermal model. The research intends to improve the accuracy and precision of battery thermal behavior prediction, which has broad implications for battery-powered applications. This study aims to evaluate the impact of different resistance models on heat generation in Li-ion batteries, explicitly comparing a constant resistance model with a model that considers resistance as a function of temperature and depth of discharge (DoD). Investigating the interdependent impact of battery temperature and DoD on heat generation is crucial to create an accurate battery thermal model with high fidelity. The current study uses a two-dimensional battery thermal model to comprehensively analyze thermal behavior of a LiFePO4-20Ah Li-ion pouch cell. In this research study, heat generation in a Li-ion battery is evaluated by estimating the internal resistance and entropic change obtained from experimentation. The energy equation is then solved using the finite difference method in MATLAB to obtain the transient thermal response of the battery. The developed transient electrothermal model is validated against experimental data under varying C rates to assess the accuracy and precision of the proposed model. The simulation results show that the thermal response obtained considering the effect of temperature and DoD on heat generation shows more accurate results than the constant resistance values. The thermal behavior of a LiFePO4 pouch cell, considering constant values for heat generation, has a maximum relative error of roughly 19.99% compared to experimental data at a 4C discharge rate. While this maximum relative error was reduced to 6.29% when considering the effect of temperature and DoD on heat generation. In the constant resistance model, more significant errors can be attributed to the fact that the resistance of a Li-ion battery varies with the depth of discharge (DoD). While the initial discharge phase of the battery exhibits minimal changes in resistance values, a substantial increase in resistance occurs during the final stages of discharge. This contrasts with the actual behavior of Li-ion batteries, which demonstrate significant variations in resistance values throughout the discharge process. Thus, coupling the effects of DoD and temperature on heat generation is necessary to accurately predict the thermal behavior of Li-ion battery. Figure 1

Battery degradation reduces the performance and lifetime of electric vehicles (EVs). Using energy storage devices with different characteristics alongside the battery can minimize degradation while satisfying driving demands. However, this introduces the additional complexities of sizing multiple storage devices and controlling them in real time. In this brief, we first provide a computationally tractable method to manage power-sharing between dual energy storages using approximate linear programming (ALP), an approximation of infinite horizon dynamic programming (DP). We formulate a procedure to determine the optimal sizes of the two storages based on the solution to the energy management problem to account for the tradeoff between vehicle range, storage size, and weight. We validate our approaches on a numerical case study. Numerical results show that our controller shares power efficiently between the storages, and our sizing procedure provides a design with minimal cost.

Many factors affect the degradation behavior of lithium-ion (Li-ion) batteries and one of these is the depth of discharge (DOD). As Li-ion batteries are used, a reasonable DOD can not only extend their service life (by reducing the degradation rate) but can also reduce the frequency of the re-charging. Therefore, to investigate and clarify the effect of the DOD on cathode performance, we performed cycle aging tests on coin cells considering three DODs. Furthermore, we proposed a degradation mechanism, to account for the influence of the DOD on the cathode performance, through ex-situ post-mortem analysis.The investigated positive electrode was from a commercial cathode NMC 532, assembled with a lithium metal anode in a 2016 type coin cell. The initial discharge capacity was about 163 mAh g–1 at a 1 C rate (1C taken as 160 mAh g–1). After every certain number of cycles, the 100% DOD (2.75 – 4.3 V) capacity was measured and recorded for all DOD ranges.Our cycle aging test experiment results (in the below Figure) show that the capacity fades faster in the higher DOD range (i.e., 3.65 – 4.3 V); the capacity of coin cells showed an initial increase due to the initial activation and a rapid decline thereafter. In contrast, the battery capacity faded slower in the two lower DOD ranges (i.e., 2.75 – 4.3 V and 3.55 – 4.3 V). The results also show that the higher DOD makes the battery more active during the initial cycles, as shown in the Figure.We refined and analyzed the XRD results of different states of the charged cathode to calculate the change in unit cell volume in initial different DOD cycles. By calculating the Li-ion diffusion coefficient through the EIS measurements, it was found that it is larger in the higher state of charge (SOC) state, which explains the higher activity of the cathode in a higher DOD range. Furthermore, we disassembled and analyzed the coin cells, after the same numbers of equivalent full cycles. Surface microcracks of the cathode were observed by SEM, and the cathode-electrolyte interphase (CEI) film was analyzed and quantified by XPS technology.Based on these results, we concluded that higher DODs enable the material to maintain a faster Li-ion diffusion rate and are always in a highly activated state. At the same time, it leads to a faster cathode decay. The post-mortem analysis showed the detailed mechanism of degradation. Looking at the results of this study, frequent charging, making the battery operation at a higher voltage, aggravates deterioration of the cathode.AcknowledgmentsThis project has received funding from the China Scholarship Council (no. 202006370035; no. 202006220024). Furthermore, the authors would like to thank Haidi company for providing the cathode material. Figure 1