Optimal Sizing Of Energy Storage System Research Articles

Game theoretical approach for critical sizing of energy storage systems for residential prosumers

The integration of Energy Storage Systems (ESS) into the distribution system has resulted in changes in the behavior of energy management systems. The primary objective of ESS management on the consumer side is to minimize operational costs reflected in energy bills, while the main goal for the Distribution System Operator (DSO) is to improve and smooth the aggregated load profile. Utilizing ESSs in distribution systems requires thorough research, as incorrect implementation can reduce controllability of distribution networks. This paper investigates the relationship between energy cost and the load responsiveness index of PV-ESS equipped residential loads using game theoretic approach. Sensitivity analysis is conducted to examine the relationship between load responsiveness and factors such as load profile, PV size, and energy cost. The goal of the paper is to propose a new approach for optimal sizing of ESS.

Composite Demand-Based Energy Storage Sizing for an Isolated Microgrid System

This paper presents a comprehensive model for optimal energy storage system (ESS) design for an isolated microgrid. The model presented is a mixed integer linear program (MILP) that considers seasonal varying generation (VG) demand, more specifically seasonal solar cell generator (SCG) demand, SCG maintenance (failure and restoration) rates, and practical operation of conventional generation (CG) while satisfying the required demand and reserve. The model is based on unit commitment (UC) to simulate real operations and physical constraints of CG units, the power balance, and reserve requirements. The objective function aims at minimizing the associated cost of CG, namely, production (fuel), costs of startup and shutdown procedures, and the investment cost of power and energy. The proposed model is assessed on a case study system consisting of multiple SCGs in addition to CG to meet a specific demand. The proposed model showed that the ESS sizing when considering Li-Ion technology and a SCG penetration of 25% was on average approximately 3 MWh and 1.70 MW. Meeting the demand and reserve requirements were the two major constraints when determining the optimal ESS sizing. Moreover, introducing the ESS substantially reduced the operating cost of the system.

Multi-Objective Optimization of PV and Energy Storage Systems for Ultra-Fast Charging Stations

The installation of ultra-fast charging stations (UFCSs) is essential to push the adoption of electric vehicles (EVs). Given the high amount of power required by this charging technology, the integration of renewable energy sources (RESs) and energy storage systems (ESSs) in the design of the station represents a valuable option to decrease its impact on the grid and the environment. Therefore, this paper proposes a multi-objective optimization problem for the optimal sizing of photovoltaic (PV) system and battery ESS (BESS) in a UFCS of EVs. The proposed multi-objective function aims to minimize, on one side, the annualized cost of the station, and on the other side, the produced pollutant emissions. The decision variables are the number of PV panels and the capacity of the ESS to be installed. The optimization problem is reduced to a single-objective problem by applying the linear scalarization method. Then the equivalent single-objective function is optimized through a genetic algorithm (GA). The proposed optimization framework is applied to a study case and the results prove that PV and ESS could lead to a significant reduction of both the annualized cost and the pollutant emissions. Finally, a sensitivity analysis is also presented to validate the effectiveness of the proposed solution.

A Flexible Operation and Sizing of Battery Energy Storage System Based on Butterfly Optimization Algorithm

There is a surge in the total energy demand of the world due to the increase in the world’s population and the ever-increasing human dependence on technology. Conventional non-renewable energy sources still contribute a larger amount to the total energy production. Due to their greenhouse gas emissions and environmental pollution, the substitution of these sources with renewable energy sources (RES) is desired. However, RES, such as wind energy, are uncertain, intermittent, and unpredictable. Hence, there is a need to optimize their usage when they are available. This can be carried out through a flexible operation of a microgrid system with the power grid to gradually reduce the contribution of the conventional sources in the power system using energy storage systems (ESS). To integrate the RES in a cost-effective approach, the ESS must be optimally sized and operated within its safe limitations. This study, therefore, presents a flexible method for the optimal sizing and operation of battery ESS (BESS) in a wind-penetrated microgrid system using the butterfly optimization (BO) algorithm. The BO algorithm was utilized for its simple and fast implementation and for its ability to obtain global optimization parameters. In the formulation of the optimization problem, the study considers the depth of discharge and life-cycle of the BESS. Simulation results for three different scenarios were studied, analyzed, and compared. The resulting optimized BESS connected scenario yielded the most cost-effective strategy among all scenarios considered.

Optimal power system design and energy management for more electric aircrafts

Recent developments in fuel cell (FC) and battery energy storage technologies bring a promising perspective for improving the economy and endurance of electric aircraft. However, aircraft power system configuration and power distribution strategies should be reasonably designed to enable this benefit. This paper is the first attempt to investigate the optimal energy storage system sizing and power distribution strategies for electric aircraft with hybrid FC and battery propulsion systems. First, a novel integrated energy management and parameter sizing (IEMPS) framework is established to co-design aircraft hardware and control algorithms. Under the IEMPS framework, a new real-time power distribution algorithm with a flexible ratio is established to facilitate integrated parameter optimization, which can adapt to different power system configurations. Based on the comprehensive analysis of hydrogen economy, FC aging cost, and aircraft stability, a multi-objective parameter optimization model is established to decide the size of aircraft energy storage systems and hyper-parameters in the power controller. The X-57 Maxwell, an experimental electric aircraft designed by NASA, is employed to verify the developed methods. This work provides a novel power system configuration, sizing, and power management method for future commercial aircraft design, and it can further promote the aviation electrification process.

Optimal Placement and Sizing of an Energy Storage System Using a Power Sensitivity Analysis in a Practical Stand-Alone Microgrid

The energy storage system (ESS) is developing into a very important element for the stable operation of power systems. An ESS is characterized by rapid control, free charging, and discharging. Because of these characteristics, it can efficiently respond to sudden events that affect the power system and can help to resolve congested lines caused by the excessive output of distributed generators (DGs) using renewable energy sources (RESs). In order to efficiently and economically install new ESSs in the power system, the following two factors must be considered: the optimal installation placements and the optimal sizes of ESSs. Many studies have explored the optimal installation placement and the sizing of ESSs by using analytical approaches, mathematical optimization techniques, and artificial intelligence. This paper presents an algorithm to determine the optimal installation placement and sizing of ESSs for a virtual multi-slack (VMS) operation based on a power sensitivity analysis in a stand-alone microgrid. Through the proposed algorithm, the optimal installation placement can be determined by a simple calculation based on a power sensitivity matrix, and the optimal sizing of the ESS for the determined placement can be obtained at the same time. The algorithm is verified through several case studies in a stand-alone microgrid based on practical power system data. The results of the proposed algorithm show that installing ESSs in the optimal placement could improve the voltage stability of the microgrid. The sizing of the newly installed ESS was also properly determined.

Energy storage sizing in plug-in Electric Vehicles: Driving cycle uncertainty effect analysis and machine learning based sizing framework

Transportation electrification has been considered as one of the promising solutions towards clean environment. On-board Energy Storage System (ESS) has significant influence on the cost and reliability of Electric Vehicles (EVs). Furthermore, the choice of the ESS in terms of type and size, i.e., its capacity heavily depends on the driving patterns which, usually, vary significantly depending on factors like driver characteristics, geographical locations and traffic congestion. Hence, it is crucial to understand the effect of driving patterns/cycles on the sizing of ESS in order to avoid over/under-sizing. In this context, we investigate the effect of driving cycle uncertainties on the optimal sizing of ESS in EVs. We specifically focus on the uncertainty arising from the unpredictability of the future state of speed and acceleration and model the same as a scaling factor on velocity-magnitudes and time-windows of the velocity profile. Subsequently, (i) we derive the quantitative relationship between uncertainty and corresponding change in ESS size based on four thousand test driving cycles; (ii) we develop a framework which provides a guideline towards the choice of appropriate sizing of ESS in EVs subject to uncertainty in driving cycle; and (iii) we propose a machine-learning based framework that can enable a data-driven approach for ESS sizing with lower computational requirement. We choose a city bus application to illustrate our approach and consider three different ESS configurations: (i) Li-ion battery alone, (ii) Supercapacitor alone, and (iii) Battery–Supercapacitor hybrid ESS.

Chance Constraints Optimal Planning Strategy of Energy Storage Systems and Tie-Lines under Wind Power Uncertainties to Improve the Reliability

The energy storage devices and renewable energy integration have great impacts on modern power system. The optimal site selection and network expansion under several uncertainties, however, are the challenging tasks in modern interconnected power system. This paper proposes a robust optimal planning strategy to find the location and the size of the energy storage system (ESS) among the power network buses and transmission lines expansion to accommodate the wind power energy integration to serve the future demand growth under uncertainties. The proposed methodology provides the optimal location concerning the required size of ESS at each bus, along with the optimal selections to reinforce existing lines or recommending new ones in a single solving stage. The co-optimization problem is formulated as a mixed-integer linear programming problem, in which the power balance constraint is developed as an optimal power flow. The stochastic optimization problem is solved robustly using the chance-constrained method. Furthermore, the load shedding and wind curtailment are taken into account in the cost function. The methodology is tested in the IEEE RTS-96 system. The simulation results demonstrate the effectiveness of the proposed strategy to find optimal size and location of ESS. The optimal candidates and transfer capacity for the tie-lines expansion planning are also determined. The results are found using different confidence levels to assess the optimality when the confidence level changes. The primary generation adequacy indices are evaluated to highlight the effectiveness of the proposed methodology. The optimally sized batteries allocated in the optimally selected locations around the system enhance the system’s performance economically and reliably.

Utilization of in-pipe hydropower renewable energy technology and energy storage systems in mountainous distribution networks

Million miles of gravity-fed drinking water and sewage pipelines around the world, especially in rural and urban areas in mountain ranges, have introduced a new renewable energy sources (RES), i.e., in-pipe hydropower systems (IHS). Output power of this technology, similar to other types of RES, suffers from intermittency, while it is still more predictable in comparison to other technologies of RESs. Besides, energy storage systems (ESS) are introduced as a pivotal technology for dealing with the intermittent and non-dispatchable characteristics of IHS through spatio-temporal arbitrage. This paper aims to develop a stochastic mixed-integer linear programming (MILP) formulation that simultaneously determines the optimal location and size of ESS and IHS in a microgrid (MG) considering the correlation between prevailing uncertainties. In this regard, the proposed optimization problem minimizes the expected social cost of MG considering the AC power flow equations and operation constraints. Finally, the efficiency and applicability of the proposed model are illustrated using numerical simulations on the IEEE 33-bus distribution test system.

Optimal sizing and placement of energy storage system in power grids: A state-of-the-art one-stop handbook

• Critical review on ESS planning covering ESS selection, modelling and algorithms. • Thorough discussion on requirements of ESS techniques in different sub-systems. • Systematic methodology of problem formulation for optimal ESS planning. • Comparison of algorithms focusing on optimization and uncertainty management. • Research directions on ESS planning considering demands in future grid. Energy storage system (ESS) has been expected to be a viable solution which can provide diverse benefits to different power system stakeholders, including generation side, transmission network (TN), distribution network (DN) and off-grid microgrid. Prudent ESS allocation in power grids determines satisfactory performance of ESS applications. Optimal sizing and placement of ESS are crucial for power quality improvement of DN and transmission system protection setting. To solve this issue, considerable researches have been done either in modelling or algorithms. However, various options and complex characteristics in different sub-systems make it difficult to appraise a specific method for an ESS application, while the existing reviews only focus on ESS applications in DN. This paper provides a critical one-stop handbook related to one hundred and four methods in six categories covering all kinds of networks and tailored applications. Meanwhile, a systematic methodology is presented with an extensive latest literature review, including ESS selection, evaluation criteria, modelling and solution methods. Particularly, different technical requirements and modelling methods of different sub-systems are outlined. Besides, pros and cons of optimization methods are thoroughly analysed and compared to reveal state-of-the-art studies. Finally, key points in optimal ESS sizing and placement are concluded along with recommendations for future research.

Enhancing the reliability of a microgrid through optimal size of battery ESS

Reliability is one of the most important factors to judge a power system. So, assessing reliability is an important task in power system planning. Many techniques have been developed to enhance the reliability of a power system. Some of those techniques depend on integrating new components and other techniques depend on changing some characteristics of existing components. One of the techniques depending on integrating new components is to integrate an energy storage system (ESS) with a power system. If the ESS is optimally sized to minimise the investment and operating cost, it enhances the reliability of the power system with a notable difference. This paper illustrates how to optimally size an ESS to be integrated with a grid-connected microgrid using the mixed-integer linear programming method. Moreover, load uncertainty is considered and the optimisation problem is solved using two different approaches to optimally size the ESS. Reliability indices of the microgrid are calculated before integrating it with the ESS and after integrating it to illustrate the enhancement of the reliability indices. Simulation results depict the effectiveness of the proposed approach.

Optimal sizing of energy storage considering the spatial‐temporal correlation of wind power forecast errors

Energy storage is considered as an effective approach to deal with the power deviation that caused by the stochastic wind power forecast error. Because of the spatial-temporal correlation of forecast errors for wind farms, which locate close to each other and integrate into the same regional power grid, energy storage could be deployed effectively and economically. Therefore, this study proposes an optimisation method to size the capacity of energy storage system (ESS) considering the spatial-temporal correlation of forecast errors for multiple nearby wind farms. The copula theory based correlation model of high-dimensional forecast errors is built to capture the spatial-temporal characteristics of forecast error. Then, according to multiple scenarios technique, an optimal ESS sizing model is established to minimise the investment and operation costs of the ESS. Meanwhile, an operation strategy considering the trend of prediction and correlation of errors is used to implement rolling operation strategy of ESS. The case studies demonstrate the effectiveness of the new method and illustrate the significant impact of the correlation of forecast error on the capacity of ESS.

Economic Value Assessment and Optimal Sizing of an Energy Storage System in a Grid-Connected Wind Farm

This study identifies the optimal management policy of a given energy storage system (ESS) installed in a grid-connected wind farm in terms of maximizing the monetary benefits and provides guidelines for defining the economic value of the ESS under optimal management policy and selecting the optimal size of the ESS based on economic value. Considering stochastic models for wind power and electricity price, we develop a finite-horizon periodic-review Markov decision process (MDP) model to seek the optimal management policy. We also use a simple optimization model to find the optimal storage capacity and charging/discharging capacity of the ESS. By applying our analytic approach to a real-world grid-connected wind farm located in South Korea, we verify the usefulness of this study. Our numerical study shows that the economic value of the ESS is highly dependent on management policy, wind electricity variability, and electricity price variability. Thus, the optimal size of ESS should be carefully determined based on the locational characteristics and management policy even with limited investments. Furthermore, this study provides a meaningful policy implication regarding how much of a subsidy the government should provide for installing ESS in a wind farm.

Modeling the temporal correlation of hourly day-ahead short-term wind power forecast error for optimal sizing energy storage system

Due to the inherent stochastic and intermittent nature of wind generation, it is very difficult to sharply improve the wind power forecasting accuracy. The sizing of energy storage system (ESS) for wind farm can effectively reduce the uncertainty caused by the inevitable forecast error of wind power. However, optimal sizing of ESS is a multi-period decision-making problem and it is the key point that exactly captures the variation magnitude and speed of forecast error. This paper proposes a method to establish the multivariate joint cumulative distribution function (JCDF) of hourly day-ahead short-term multi-period forecast errors using Normal/t copula. Based on the proposed JCDF and multiple scenarios technique, a model of optimal sizing of ESS is proposed in which the temporal correlation relationship between different time period forecast errors and probability distribution of each time period forecast error are both considered. The simulation results verify the effectiveness of the proposed methods and show that if the temporal correlation of wind power short-term forecast error is ignored, the rated energy and power capacity of sizing of ESS will be significantly misestimated.

Novel Adaptive Multi-Clustering Algorithm-Based Optimal ESS Sizing in Ship Power System Considering Uncertainty

The optimal sizing of an energy storage system (ESS) in a power generation system that incorporates photovoltaic (PV) generation is crucial in a power grid for which the reduction of CO2 emissions is important. This problem is particularly challenging when it relates to the power system of a ship because it involves uncertain meteorological and load data along a navigation route. This paper proposes a novel method for multi-objective minimization of investment/replacement cost, fuel cost, and CO2 emissions, to find the optimal size of the ESS considering life-span of the ESS. The generation of power by PV modules on a ship is affected by temporal and geographical variations of irradiation along the navigation route. In particular, operating load conditions and irradiation are uncertain. This paper proposes a novel algorithm for partitioning high-dimensional uncertain data into tractable clusters solved by deterministic optimization method. Case studies of an all-electric ship along a route from Dalian in China to Aden in Yemen are shown to demonstrate the applicability of the proposed clustering-based stochastic optimization method.

An optimal sizing method for energy storage system in wind farms based on the analysis of wind power forecast error

Energy storage system (ESS) in a wind farm can effectively compensate the fluctuations of wind power. How to determine the size of ESS in wind farms is an urgent problem to be solved. A novel method is proposed for designing the optimal size of ESS considering wind power uncertainty. This approach uses non-parametric estimation method to analysis the wind power forecast error (WPFE) and the cumulative wind power deviation (CWPD) within the scheduling period. Then a cost-benefit analysis model is established to obtain the optimal size of ESS based on the analysis of WPFE and CWPD. A series of wind farm data in California are used as numerical cases, which presents that the algorithm presented in this paper has good feasibility and performance in optimal ESS sizing in wind farms.

A heuristic approach for optimal sizing of ESS coupled with intermittent renewable sources systems

In this paper a techno-economic comparison of an energy storage system (ESS) sizing for three intermittent renewables, wind, wave and PV power, with regard to two electricity grid services is presented. The first service consists of output hourly smoothing, based on day-ahead power forecasts (S1). The second service supplies year-round guaranteed power (S2). This leads to an annual default time rate (DTR) for which the actual power supplied to the grid does not match the day-ahead power bid within a given tolerance. A heuristic optimization based on an Adaptive Storage Operation (ASO) scheduling is developed in this study. ASO enables the minimal 5%-DTR ESS capacity, power, energy and feed-in-tariffs to be inferred from the operating conditions, depending on tolerance. The simulations assess and compare the techno-economic viability and efficiency of every renewable sources coupled with ESS. PV power is more efficient with daylight hours restricted services and higher power levels can be guaranteed for S1. Wind and wave power are more suitable than PV for services dedicated to full-day power delivery, as in the case of S2. For hourly smoothing the forecast accuracy influence is studied and yields a high impact on techno-economic sizing.

Value of the energy storage system in an electric bus fast charging station

Electric buses (EBs) are undergoing rapid development because of their environmental friendliness. Different from private electric vehicles, EBs are scheduled by a public transport company and required to be charged as soon as possible during operation hours. Consequently, the implementation of fast charging stations (FCSs) is essential to support the operation of EBs. Usually, the size of an FCS is constrained by the residual capacity of the connected distribution network and the investment budget. An energy storage system (ESS) is considered as a potential supplement not only to reduce the network integration cost for FCSs but also to reduce the charging cost of EBs through electricity price arbitrage. To quantify the value of ESS in an electric bus FCS, a mixed integer nonlinear programming (MINLP) formulation for optimal sizing and control of FCS and ESS is built. A simplification method is proposed to convert the MINLP problem to a linear one without any loss in optimality, which accelerates the solving process. Simulations are performed based on historical data of a practical FCS. Numerical results indicate that ESS can significantly help reduce the overall investment and charging cost of the FCS. Meanwhile, the parameters of investment cost, lifespan and time-of-use electricity price have significant influences on the overall value of ESS for an FCS.

Statistical distribution for wind power forecast error and its application to determine optimal size of energy storage system

Accurate wind power forecast is an important tool for wind farm to participate in day-ahead or hours-ahead energy markets. However, forecast errors with any methodology are so large that they cannot be neglected. The forecast error needs to be analyzed individually for single wind farm to estimate the impact of this error on trading wind energy in electricity market. Although forecast error is always assumed as normal distribution, it can be demonstrated that it is not proper with a simple statistical analysis. In this paper, a mixed distribution is proposed based on laplace and normal distribution to model forecast errors associated with persistence forecast for single wind farm over multiple timescales. Then the proposed distribution is used to estimate the penalties for prediction errors in the electricity market. Energy storage system (ESS) can smooth the wind power output and make wind power more “dispatchable”. A probabilistic method is proposed to determine optimal size of ESS for wind farm in electricity markets. The results indicate that the proposed distribution and probabilistic method is efficient to find optimal size of ESS.

Reliability-Constrained Optimal Sizing of Energy Storage System in a Microgrid

This paper presents a model for calculating the optimal size of an energy storage system (ESS) in a microgrid considering reliability criterion. A larger ESS requires higher investment costs while reduces the microgrid operating cost. The optimal ESS sizing problem is proposed which minimizes the investment cost of the ESS, as well as expected microgrid operating cost. Utilizing the ESS, generation shortage due to outage of conventional units and intermittency of renewable units is handled; hence microgrid reliability criterion is satisfied. A practical model for ESS is utilized. Mixed-integer programming (MIP) is utilized to formulate the problem. Illustrative examples show the efficiency of the proposed model.