Control of Energy Storage William Holderbaum www.mdpi.com/journal/energies Edited by Printed Edition of the Special Issue Published in Energies Control of Energy Storage Special Issue Editor William Holderbaum MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor William Holderbaum University of Reading and Manchester Metropolitan University UK Editorial Office MDPI AG St. Alban ‐ Anlage 66 Basel, Switzerland This edition is a reprint of the Special Issue published online in the open access journal Energies (ISSN 1996 ‐ 1073) from 2015–2017 (available at: http://www.mdpi.com/journal/energies/special_issues/control ‐ energy ‐ storage). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: Author 1; Author 2. Article title. Journal Name Year , Article number , page range. First Edition 2017 ISBN 978 ‐ 3 ‐ 03842 ‐ 494 ‐ 9 (Pbk) ISBN 978 ‐ 3 ‐ 03842 ‐ 495 ‐ 6 (PDF) Articles in this volume are Open Access and distributed under the Creative Commons Attribution license (CC BY), which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book taken as a whole is © 2017 MDPI, Basel, Switzerland, distributed under the terms and conditions of the Creative Commons license CC BY ‐ NC ‐ ND (http://creativecommons.org/licenses/by ‐ nc ‐ nd/4.0/). iii Table of Contents About the Special Issue Editor ..................................................................................................................... v Preface to “Control of Energy Storage” ...................................................................................................... vii Timur Yunusov, Maximilian J. Zangs and William Holderbaum Control of Energy Storage Reprinted from: Energies 2017 , 10 (7), 1010; doi: 10.3390/en10071010 ..................................................... 1 Enrico Telaretti, Mariano Ippolito and Luigi Dusonchet A Simple Operating Strategy of Small ‐ Scale Battery Energy Storages for Energy Arbitrage under Dynamic Pricing Tariffs Reprinted from: Energies 2016, 9 (1), 12; doi: 10.3390/en9010012 ............................................................. 6 Zuchang Gao, Cheng Siong Chin, Wai Lok Woo and Junbo Jia Integrated Equivalent Circuit and Thermal Model for Simulation of Temperature ‐ Dependent LiFePO4 Battery in Actual Embedded Application Reprinted from: Energies 2017 , 10 (1), 85; doi: 10.3390/en10010085 ......................................................... 26 Stefano Pietrosanti, William Holderbaum and Victor M. Becerra Optimal Power Management Strategy for Energy Storage with Stochastic Loads Reprinted from: Energies 2016 , 9 (3), 175; doi: 10.3390/en9030175 ........................................................... 48 Fei Lin, Xuyang Li, Yajie Zhao and Zhongping Yang Control Strategies with Dynamic Threshold Adjustment for Supercapacitor Energy Storage System Considering the Train and Substation Characteristics in Urban Rail Transit Reprinted from: Energies 2016 , 9 (4), 257; doi: 10.3390/en9040257 ........................................................... 65 Huan Xia, Huaixin Chen, Zhongping Yang, Fei Lin and Bin Wang Optimal Energy Management, Location and Size for Stationary Energy Storage System in a Metro Line Based on Genetic Algorithm Reprinted from: Energies 2015 , 8 (10), 11618–11640; doi: 10.3390/en81011618....................................... 83 Thomas Bruen, James Michael Hooper, James Marco, Miguel Gama and Gael Henri Chouchelamane Analysis of a Battery Management System (BMS) Control Strategy for Vibration Aged Nickel Manganese Cobalt Oxide (NMC) Lithium ‐ Ion 18650 Battery Cells Reprinted from: Energies 2016 , 9 (4), 255; doi: 10.3390/en9040255 ........................................................... 104 Thai ‐ Thanh Nguyen, Hyeong ‐ Jun Yoo and Hak ‐ Man Kim Application of Model Predictive Control to BESS for Microgrid Control Reprinted from: Energies 2015 , 8 (8), 8798–8813; doi: 10.3390/en8088798 ............................................... 124 Woo ‐ Kyu Chae, Hak ‐ Ju Lee, Jong ‐ Nam Won, Jung ‐ Sung Park and Jae ‐ Eon Kim Design and Field Tests of an Inverted Based Remote MicroGrid on a Korean Island Reprinted from: Energies 2015 , 8 (8), 8193–8210; doi: 10.3390/en8088193 ............................................... 137 Linas Gelažanskas and Kelum A. A. Gamage Distributed Energy Storage Using Residential Hot Water Heaters Reprinted from: Energies 2016 , 9 (3), 127; doi: 10.3390/en9030127 ........................................................... 153 iv Alexander Kies, Bruno U. Schyska and Lueder von Bremen The Demand Side Management Potential to Balance a Highly Renewable European Power System Reprinted from: Energies 2016 , 9 (11), 955; doi: 10.3390/en9110955 ......................................................... 166 Rong Fu, Yingjun Wu, Hailong Wang and Jun Xie A Distributed Control Strategy for Frequency Regulation in Smart Grids Based on the Consensus Protocol Reprinted from: Energies 2015 , 8 (8), 7930–7944; doi: 10.3390/en8087930 ............................................... 180 Fabio Massimo Gatta, Alberto Geri, Regina Lamedica, Stefano Lauria, Marco Maccioni, Francesco Palone, Massimo Rebolini and Alessandro Ruvio Application of a LiFePO4 Battery Energy Storage System to Primary Frequency Control: Simulations and Experimental Results Reprinted from: Energies 2016 , 9 (11), 887; doi: 10.3390/en9110887 ......................................................... 193 Jin ‐ Sun Yang, Jin ‐ Young Choi, Geon ‐ Ho An, Young ‐ Jun Choi, Myoung ‐ Hoe Kim and Dong ‐ Jun Won Optimal Scheduling and Real ‐ Time State ‐ of ‐ Charge Management of Energy Storage System for Frequency Regulation Reprinted from: Energies 2016 , 9 (12), 1010; doi: 10.3390/en9121010 ....................................................... 209 Yuqing Yang, Weige Zhang, Jiuchun Jiang, Mei Huang and Liyong Niu Optimal Scheduling of a Battery Energy Storage System with Electric Vehicles’ Auxiliary for a Distribution Network with Renewable Energy Integration Reprinted from: Energies 2015 , 8 (10), 10718–10735; doi: 10.3390/en81010718....................................... 222 Maximilian J. Zangs, Peter B. E. Adams, Timur Yunusov, William Holderbaum and Ben A. Potter Distributed Energy Storage Control for Dynamic Load Impact Mitigation Reprinted from: Energies 2016 , 9 (8), 647; doi: 10.3390/en9080647 ........................................................... 237 Zhihao Zhao, Yue Sun, Aiguo Patrick Hu, Xin Dai and Chunsen Tang Energy Link Optimization in a Wireless Power Transfer Grid under Energy Autonomy Based on the Improved Genetic Algorithm Reprinted from: Energies 2016 , 9 (9), 682; doi: 10.3390/en9090682 ........................................................... 257 Yao ‐ Liang Chung A Novel Power ‐ Saving Transmission Scheme for Multiple ‐ Component ‐ Carrier Cellular Systems Reprinted from: Energies 2016 , 9 (4), 265; doi: 10.3390/en9040265 ........................................................... 273 Seungmin Jung and Gilsoo Jang Development of an Optimal Power Control Scheme for Wave ‐ Offshore Hybrid Generation Systems Reprinted from: Energies 2015 , 8 (9), 9009–9028; doi: 10.3390/en8099009 ............................................... 291 v About the Special Issue Editor William Holderbaum received the Ph.D. degree in automatic control from the University of Lille, Lille, France, in 1999. He was a Research Assistant with the University of Glasgow, Glasgow, UK, from 1999 to 2001. He was lecturer (2001–2009), Senior Lecturer (2009–2014) and currently a Professor at the University of Reading, Reading, UK and Manchester Metropolitan University since 2016. His current research interests include control theory and its applications. In particular in the area of energy in smarter grid to help reduce peak demand and increase the stability of the grid, current techniques involve charge incentives for users to cut load at peak periods as well as researching and developing optimal storage devices. He is a member of the IEEE and he has published over 100 papers in leading journals and international conferences. vii Preface to “Control of Energy Storage” Energy storage can provide numerous beneficial services and cost savings within the electricity grid, especially when facing future challenges like renewable and electric vehicle (EV) integration. Public bodies, private companies and individuals are deploying storage facilities for several purposes, including arbitrage, grid support, renewable generation, and demand ‐ side management. Storage deployment can therefore yield benefits like reduced frequency fluctuation, better asset utilisation and more predictable power profiles. Such uses of energy storage can reduce the cost of energy, reduce the strain on the grid, reduce the environmental impact of energy use, and prepare the network for future challenges. This Special Issue of Energies explore the latest developments in the control of energy storage in support of the wider energy network, and focus on the control of storage rather than the storage technology itself. Specifically, this book encompass: • Control of energy storage (e.g., for flywheels, batteries or supercapacitors) • Energy storage systems for transport (e.g., for automotive, shipping and aircraft) • Energy storage systems for grid support including use with ancillary services • Intelligent coordination of storage elements in the grid both at micro (i.e., low voltage) and macro (i.e., high voltage) scales • Monitoring, modelling and other performance assessment methodologies for the control of storage • Explorations of the future of energy storage systems and associated control problems. The contributions are based on leading research, as well as cutting ‐ edge exemplars from industrial practice that can be used to encourage sustainable development and performance of control of energy storage systems. William Holderbaum Special Issue Editor energies Editorial Control of Energy Storage Timur Yunusov 1, ∗ , Maximilian J. Zangs 1 and William Holderbaum 2 1 Technologies for Sustainable Built Environments Centre, School of Built Environment, University of Reading, Reading RG6 6AF, UK; m.j.zangs@pgr.reading.ac.uk 2 School of Engineering, Manchester Metropolitan University, Manchester M1 5GD, UK; w.holderbaum@mmu.ac.uk * Correspondence: t.yunusov@reading.ac.uk Received: 30 May 2017; Accepted: 10 July 2017; Published: 16 July 2017 1. Introduction In the attempt to tackle the issue of climate change, governments across the world have agreed to set global carbon reduction targets. For instance, the UK has agreed to reduce the green house gas emissions by 80% of 1990 levels by 2050 [ 1 ]. In the pursuit of the carbon reduction, there has been a continuous shift towards the de-carbonisation of major infrastructures such as transport and energy, and an uptake of renewable power generation. An increasing proportion of renewable energy introduces new challenges for the transmission and distribution system operators. The intermittent nature of the renewable energy resources impacts their power output, causing imbalance in supply and demand across the power system. Since the proportion of inverter-fed generation is also likely to increase, the natural inertia of the system would reduce. This in turn causes the grid’s frequency to become less stable and deviate from its target more rapidly than in the present day. Electrification of major infrastructures will cause an additional demand for electricity, which could potentially coincide with existing demand peaks. Furthering this peak demand imposes additional strain on the distribution network, which pushes both its thermal limits and its voltage constraints. Energy storage is often viewed as a silver bullet to buffer the differences between the demand and supply. Additionally, it can improve network operation. With advancements in energy storage technologies, today’s catalogue of energy storage systems offers a wide range of applications to choose from, where all yield some benefit at different levels throughout the entire network. The collection of manuscripts in this editorial provides an insight into some of the cutting edge research on the control of energy storage for power systems. 2. Short Review of the Contributions in This Issue The special issue of the MPDI Energies on “Control of Energy Storage” is focused on the control methods of energy storage for a range of applications and degrees of complexity. Specifically, the this special issue addresses the following topics: • Control of energy storage. • Energy storage systems for transport. • Energy storage systems for grid support. • Intelligent coordination of storage elements in the grid at micro and macro levels. • Monitoring, modelling, and other performance assessment methodologies for the control of energy storage. • Explorations of the future of energy storage systems and associated control problems. The success of energy storage relies on the inclusion of the technical constraints and economic feasibility into the control strategies for the energy storage applications. The research articles included Energies 2017 , 10 , 1010 1 www.mdpi.com/journal/energies Energies 2017 , 10 , 1010 in this special issue cover the full range of aspects for the energy storage applications: from energy storage technology modelling for more predictable performance in real-life applications to micro and macro control strategies for energy storage in power systems of a range of sizes. 2.1. Modelling Telaretti et al. [ 2 ] developed a multi-vector model for energy storage operation taking into account technical, economic, and financial aspects. Along with the model, the paper proposes an energy storage scheduling strategy designed to maximise the profit for the energy storage owner by providing price arbitrage services subject to the technical constraints of the energy storage system (e.g., rating, efficiency, and depth-of-discharge). The performance of the proposed strategy was assessed in a simulation of three energy storage technologies: lithium-ion (Li-ion), sodium-sulfur (NaS), and lead acid. Looking into more detailed modelling, the performance and lifespan of modern battery chemistries depend on the internal temperature and the voltages on individual cells during the operation. Gao et al. [ 3 ] proposed a thermal model and equivalent circuit of a LiFePO 4 battery to accurately estimate the state-of-charge and temperature of the battery during operation. The proposed model have been validated on experimental results and shown to have high accuracy cell voltage estimation on a multi-cell LiFePO 4 battery. 2.2. Automotive Industry Energy storage application in automotive industry is presented with unique operational conditions. Bruen et al. [ 4 ] presented a study on the effect of vibration on the lifespan and performance of nickel manganese cobalt oxide (NMC) Li-ion batteries, commonly found in electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEV). The results of the study were used to develop an equivalent circuit model for the cells and provide recommendation on the battery management strategies. Moving on to control strategies for energy storage integrated into power systems, three research articles addressed the application of energy storage for improving the performance and economic efficiency of transport systems. Pietrosanti et al. [ 5 ] proposed a power management strategy for the control of a flywheel energy storage system on a rubber tyre gantry crane. A power management strategy was proposed in order to reduce the overall cost of energy that is required to operate the gantry crane. This strategy balances the power demands for container lifting operations, and the recovered energy when lowering the same. Due to the random duration of each such operation, the developed power management strategy was implemented using statistical load distributions. Numerical calculations using MATLAB/Simulink models of the required systems show increased energy savings and reduced peak power demand with respect to current control strategies. Lin et al. [ 6 ] proposed a control strategy for super-capacitor installation to recover breaking energy fromurban rail trains. Introducing variable thresholds for the wayside energy storage system allowed the recuperation to make best use of the train’s breaking V - I characteristics. Using a dual-loop control method enabled the authors to achieve the best energy-saving effect, which was verified through simulations and an experimental test on the Batong Line of the Beijing subway, using 200 kW wayside supercapacitor energy storage prototypes. Xia et al. [ 7 ] proposed a solution for super-capacitor sizing, placement, and control strategy for improving the efficiency of a metro line and improving voltage profile. The proposed solution is based on a novel optimisation method, combining genetic algorithms and simulation platform of an urban rail power system, including network, train, and energy storage system modelling. 2.3. Network Support Energy storage also has potential to perform energy management and network support in standalone or grid-connected electricity distribution system—microgrids. Zangs et al. [ 8 ] proposed an improvement on the additive increase multiplicative decrease (AIMD) algorithm for enabling voltage support services from distributed energy storage devices in a low-voltage distribution network. 2 Energies 2017 , 10 , 1010 The improved algorithm—AIMD + —uses local voltage measurements against location-adjusted thresholds to improve voltage and thermal constraints on the network whilst providing more equal energy storage utilisation. Nguyen et al. [ 9 ] proposed a model predictive control (MPC) system for power control of battery energy storage systems (BESS) in a micro-grid environment. Two variations of MPC—the proposed purely predictive power control and predictive current control with proportional-integral (PI )—are compared against the traditional PI control technique for BESS inverter control. The performance of the control techniques was assessed using MATLAB/Simulink models of a microgrid with a mix of generation sources, two energy storage systems, and a lump load, both in grid-connected and islanded modes. Results showed that MPC-based power control methods are best applied for BESS applications in power import/export control and frequency regulation in a microgrid, and the predictive current with inner PI control loop is more suitable BESS control for smoothing the wind power fluctuations. Chae et al. [ 10 ] highlighted the difference between simulated and actual performance of islanded power systems. Authors presented results from economic feasibility studies of typical island power systems and microgrid island power systems. A representative model of a typical island power system supplied with diesel generators was assessed in a feasibility study tool called HOMER. The results of the study showed that the most economical operational costs remained the same—between 20% and 70% of energy supplied from renewable resources. Study of a planned power system on the test island showed that 91% of the energy will be supplied from the renewable resources, giving an 81% reduction in average fuel consumption. The real operational data showed the 82% of the energy was supplied from renewable resources, achieving fuel consumption savings of 80%. Discussion by the authors highlights the differences between the feasibility study against the actual observations and the effect of microgrid operation on the power quality and operational efficiency of the power system. 2.4. Demand-Side Management One of the fundamental functions of energy storage is to shift energy usage in time. Demand-side management (DSM) can be viewed as equivalent to energy storage: the energy usage by a controllable load is managed with an aim to minimise the impact on the network (e.g., supply unbalance, frequency regulation, or network support) whilst maintaining the required function of the load for the benefit of the consumer. Gelazanskas and Gamage [ 11 ] proposed a method for scheduling of domestic hot water heaters to compensate for the errors in day-ahead wind generation forecasts. The control system schedules the heating periods every 5 min for the next 12 h to adjust the demand to fill the gap or absorb the excess in supply. An artificial neural network is used to predict the loading of the water heater, allowing the heating periods to be scheduled without causing discomfort to the user. Results showed that the forecasting of energy usage by water heaters combined with scheduling lowers the energy requirement for hot water preparation and reduces the imbalance in supply for wind power generation. On a larger scale, Kies et al. [ 12 ] addressed the issue of demand and supply unbalance in a simplified model of a fully renewable European power system by investigating the impact of DSM on the need for backup generation. Authors use ten years of weather and historical data to perform power flow analysis of several combinations of scenarios for transmission links capacities and distribution of generation capacity across Europe to assess DSM as an energy storage equivalent. 2.5. Frequency Regulation Imbalance in supply and generation at the grid level causes deviation of frequency from the statutory range. Excess power generation allows the speed of rotating machines (e.g., steam turbines on coal and gas power plants) to increase, which in turn increases the grid frequency. Similarly, lack of supply leads to a decrease in frequency. Significant deviation from the statutory limits could lead to blackouts, as the generation plants and loads will be disconnected from the network by frequency-sensitive relays. Large-scale energy storage devices or coordinated behaviour of multiple small-scale energy 3 Energies 2017 , 10 , 1010 storage devices could provide frequency regulation services to assist with maintaining the frequency within the nominal range. Fu et al. [ 13 ] proposed a distributed control algorithm for the coordination of frequency regulation provided by multiple distributed resources. The algorithm uses an agent-based consensus control protocol, where each agent represents a system component capable of providing active power support and, through communication, aims to converge to a new common frequency state. Gatta et al. [ 14 ] present an application of LiFePO 4 BESS for primary frequency control. Electrical-thermal circuit models were developed for evaluation purposes, taking into account the cycle-life and auxiliary energy consumption. Numerical simulations then showed the trade-off between expected lifetime and overall system efficiency when performing droop controlled frequency control. Yang et al. [ 15 ] presented an optimal scheduling algorithm for an energy storage device providing frequency regulation service. The control algorithm uses particle swarm optimisation to compensate for the errors in state of charge estimation and adjust the operation of the energy storage device to maximise profit whilst ensuring availability for the automatic generation control signal. 3. Conclusions The research articles in the special issue on “Control of Energy Storage” presented contributions from micro to macro scale of energy storage applications. Several works presented models for the prediction of performance and lifespan of the selected energy storage technologies. Control techniques for energy storage applications in transport and microgrid were presented, focusing on improvement of operation efficiency and power quality. On the larger scale, three articles addressed the aspects of frequency regulation provided by energy storage and demand response systems. The collection of the research articles included in this special issue have demonstrated the wide range applications for energy storage and the role of modelling in delivering effective control systems for energy storage. Energy storage is expected to play an important role in keeping the lights on in the future low-carbon electricity networks. Further integration of renewable generation and low carbon technologies would require greater flexibility from the energy consumers and producers to ensure balance of supply and demand. Energy storage deployed throughout the network levels has the potential to provide the required flexibility and support network operation. Acknowledgments: The authors are grateful to the MDPI Publisher and the members of the editorial team of “ Energies ” for the invitation to act as guest editors for the special issue. Author Contributions: Timur Yunusov and Maximilian J. Zangs have reviewed the works included in the MDPI special issue on Control of Energy Storage and wrote the editorial. William Holderbaum is the academic editor for the special issue and have guided and reviewed the writing of the editorial. Conflicts of Interest: The authors declare no conflict of interest. References 1. The Stationary Office. Climate Change Act (c. 27) ; The Stationary Office: London, UK, 2008. 2. Telaretti, E.; Ippolito, M.; Dusonchet, L. A simple operating strategy of small-scale battery energy storages for energy arbitrage under dynamic pricing tariffs. Energies 2016 , 9 , 12, doi:10.3390/en9010012. 3. Gao, Z.; Chin, C.S.; Woo, W.L.; Jia, J. Integrated equivalent circuit and thermal model for simulation of temperature-dependent LiFePO 4 battery in actual embedded application. Energies 2017 , 10 , 85, doi:10.3390/en10010085. 4. Bruen, T.; Hooper, J.M.; Marco, J.; Gama, M.; Chouchelamane, G.H. Analysis of a battery management system (BMS) control strategy for vibration aged nickel manganese cobalt oxide (NMC) lithium-ion 18650 battery cells. Energies 2016 , 9 , 255, doi:10.3390/en9040255. 5. Pietrosanti, S.; Holderbaum, W.; Becerra, V.M. Optimal power management strategy for energy storage with stochastic loads. Energies 2016 , 9 , 175, doi:10.3390/en9030175. 4 Energies 2017 , 10 , 1010 6. Lin, F.; Li, X.; Zhao, Y.; Yang, Z. Control strategies with dynamic threshold adjustment for supercapacitor energy storage system considering the train and substation characteristics in urban rail transit. Energies 2016 , 9 , 257, doi:10.3390/en9040257. 7. Xia, H.; Chen, H.; Yang, Z.; Lin, F.; Wang, B. Optimal energy management, location and size for stationary energy storage system in a metro line based on genetic algorithm. Energies 2015 , 8 , 11618–11640. 8. Zangs, M.J.; Adams, P.B.E.; Yunusov, T.; Holderbaum, W.; Potter, B.A. Distributed energy storage control for dynamic load impact mitigation. Energies 2016 , 9 , 647, doi:10.3390/en9080647. 9. Nguyen, T.T.; Yoo, H.J.; Kim, H.M. Application of model predictive control to bess for microgrid control. Energies 2015 , 8 , 8798–8813. 10. Chae, W.K.; Lee, H.J.; Won, J.N.; Park, J.S.; Kim, J.E. Design and field tests of an inverted based remote microgrid on a Korean Island. Energies 2015 , 8 , 8193–8210. 11. Gelazanskas, L.; Gamage, K.A.A. Distributed energy storage using residential hot water heaters. Energies 2016 , 9 , 127, doi:10.3390/en9030127. 12. Kies, A.; Schyska, B.U.; Bremen, L.V. The demand side management potential to balance a highly renewable European power system. Energies 2016 , 9 , 955, doi:10.3390/en9110955. 13. Fu, R.; Wu, Y.; Wang, H.; Xie, J. A distributed control strategy for frequency regulation in smart grids based on the consensus protocol. Energies 2015 , 8 , 7930–7944. 14. Gatta, F.; Geri, A.; Lamedica, R.; Lauria, S.; Maccioni, M.; Palone, F.; Rebolini, M.; Ruvio, A. Application of a LiFePO 4 battery energy storage system to primary frequency control: Simulations and experimental results. Energies 2016 , 9 , 887, doi:10.3390/en9110887. 15. Yang, J.S.; Choi, J.Y.; An, G.H.; Choi, Y.J.; Kim, M.H.; Won, D.J. Optimal scheduling and real-time state-of-charge management of energy storage system for frequency regulation. Energies 2016 , 9 , 1010, doi:10.3390/en9121010. c © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). 5 Article A Simple Operating Strategy of Small-Scale Battery Energy Storages for Energy Arbitrage under Dynamic Pricing Tariffs Enrico Telaretti *, Mariano Ippolito and Luigi Dusonchet Department of Energy, Information Engineering and Mathematical Models, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy; ippolito@dieet.unipa.it (M.I.); dusonchet@dieet.unipa.it (L.D.) * Correspondence: telaretti@dieet.unipa.it; Tel.: +39-091-238-602-62; Fax: +39-091-488-452 Academic Editor: William Holderbaum Received: 9 October 2015; Accepted: 16 December 2015; Published: 25 December 2015 Abstract: Price arbitrage involves taking advantage of an electricity price difference, storing electricity during low-prices times, and selling it back to the grid during high-prices periods. This strategy can be exploited by customers in presence of dynamic pricing schemes, such as hourly electricity prices, where the customer electricity cost may vary at any hour of day, and power consumption can be managed in a more flexible and economical manner, taking advantage of the price differential. Instead of modifying their energy consumption, customers can install storage systems to reduce their electricity bill, shifting the energy consumption from on-peak to off-peak hours. This paper develops a detailed storage model linking together technical, economic and electricity market parameters. The proposed operating strategy aims to maximize the profit of the storage owner (electricity customer) under simplifying assumptions, by determining the optimal charge/discharge schedule. The model can be applied to several kinds of storages, although the simulations refer to three kinds of batteries: lead-acid, lithium-ion (Li-ion) and sodium-sulfur (NaS) batteries. Unlike literature reviews, often requiring an estimate of the end-user load profile, the proposed operation strategy is able to properly identify the battery-charging schedule, relying only on the hourly price profile, regardless of the specific facility’s consumption, thanks to some simplifying assumptions in the sizing and the operation of the battery. This could be particularly useful when the customer load profile cannot be scheduled with sufficient reliability, because of the uncertainty inherent in load forecasting. The motivation behind this research is that storage devices can help to lower the average electricity prices, increasing flexibility and fostering the integration of renewable sources into the power system. Keywords: price arbitrage; battery energy storage system; optimal operation; hourly electricity prices; energy management 1. Introduction Electricity customers will face significant challenges in the near future due to the most recent developments in the energy market sector. These changes have been mainly driven by the increasing penetration of renewable and distributed energy sources in the power system, which can positively contribute to a reduction of CO 2 emissions. The diffusion of renewable sources has been made possible thanks to the introduction of support policies, such as those put in place for the photovoltaic (PV) and wind technology [ 1 – 4 ]. Clearly, the transition from the current centralized electricity market structure towards a decentralized market model will require major investments in the electricity grid infrastructure, in order to ensure an adequate level of quality and reliability of the energy supply. Energies 2016 , 9 , 12 6 www.mdpi.com/journal/energies Energies 2016 , 9 , 12 In the spot markets, the electricity price varies stochastically from one day to the next and systematically between seasons. The marginal cost of producing energy has become much more volatile in the last decade, mainly due to the recent moves toward competitive liberalized markets. Indeed, the competition among actors has increased the range of variability in electricity prices, expanding the difference between on-peak and off-peak prices. Normally, electricity users are not exposed to these fluctuations but pay a constant price. In an attempt to reduce demand peaks, several utilities are moving from a conventional fixed-rate pricing scheme to new market-based models, where the electricity cost is free to fluctuate depending on the balance between supply and demand. Such dynamic pricing schemes reflect the prices of the wholesale market and are able to lower demand peaks and the volatility of the wholesale prices [ 5 ]. A first example of dynamic pricing tariff is time-of-use (TOU) pricing, which provides two or three periods of different electricity price (generally “on-peak”, “mid-peak” and “off-peak” prices), depending on the hour of day. Electricity users are advised in advance about electricity prices that are not normally modified more than once or twice per year. A more flexible electricity-pricing scheme is real-time pricing ( RTP ), for which the retail electricity price closely reflects the wholesale energy price. In this case, customer electricity prices can vary hourly depending on the wholesale market and electricity users can manage their power consumption in a more flexible and economical manner, taking advantage of the price differential. The real-time prices can be notified to electricity customers with different timing, depending on the specific utility’s RTP program. For example, with Ameren’s RTP program (an Illinois’ Electric Utility), hourly prices for the next day are set the night before and are communicated to customers so they can modify their power consumption in advance. Differently, with ComEd’s RTP program (another Illinois’ Electric Utility), hourly prices are based on the average of the twelve five-minute prices for each hour, and electricity users are notified in real-time, only when the hour has passed. Later on in this article, the RTP prices will be considered as day-ahead hourly prices, so electricity customers are advised a day before and can modify their power consumption accordingly. The highly volatile behavior of the electricity price can be exploited by using an energy storage device in order to capture the price differential. Indeed, if an electricity customer is charged at an hourly-dependent rate, a storage system can be adopted with the aim to shift portions of consumption to different hours than those where they actually occur. The electricity is simply stored when it is inexpensive and resold back to the grid at a higher price [6,7]. The object of this article is to analyze, develop and demonstrate a charge/discharge scheduling method able to maximize the arbitrage benefit of a storage system, subject to technical constraints. The storage system is described by means of its performance parameters, such as the charge and generation capacity, the charge/discharge efficiency, the rated charge/discharge rate, the depth-of-discharge ( DOD ), etc. , which are sufficient to evaluate the arbitrage potential of a storage system. The scheduling strategy is based on the definition of an objective function, able to maximize the arbitrage benefit of the storage owner subject to technical constraints, allowing the battery to be charged/discharged at different DOD , as further detailed in Section 4. The developed model is valid for any kind of storage, although the simulations refer to a lead-acid, a lithium-ion (Li-ion) and a sodium-sulfur (NaS) battery. Test results show that the proposed operating strategy is effective to maximize the profit for the customer. Unlike the studies reported in the literature, often requiring an estimate of the end-user load profile, the proposed operation strategy is able to properly identify, for each daily period, the charge/discharge hours relying only on the hourly spot market price profile, regardless of the specific facility’s consumption. This is made possible thanks to some simplifying assumptions in the sizing and the operation of the battery energy storage system (BESS), as further details in Section 3. This could be particularly useful when the customer load profile cannot be scheduled with sufficient reliability because of the uncertainty inherent in load forecasting. In these cases, identifying a BESS operating strategy that does not depend on the user’s power profile can be an important task, since the deviation of the scheduled power profile from the effective one could affect the results obtained using more complete methods. Furthermore, the proposed management 7 Energies 2016 , 9 , 12 strategy requires a low computational burden and can be implemented in simple and available software, for instance in a spreadsheet, representing a friendly but effective instrument to optimize the charge/discharge schedule of a storage device. The next section summarizes existing literature on the topic of optimal operation of storage systems. In Section 3, the customer energy system used in this paper is briefly described and the basic operational assumptions are outlined. In Section 4, the problem formulation is provided, showing the objective function to be maximized and defining the constraint equations. In Section 5, a case study is presented and the technical and economic parameters for each storage device are provided. Section 6 shows the simulation results and some important remarks about the operating schedule of the storage devices. Finally, Section 7 summarizes the conclusion of the work. 2. Current Literature Traditionally, most of the studies address the optimal operation of a storage system based on linear programming [ 8 – 11 ], nonlinear programming [ 12 ], dynamic programming [ 13 – 16 ] and multipass iteration particle swarm optimization approach [ 17 ]. Other charge/discharge strategies are described in [18–25]. 2.1. Linear and Nonlinear Programming In [ 8 ], the authors study the optimal operation of an energy storage unit installed in a small power producing facility using a conventional linear programming technique. In [ 9 ], the authors determine the optimal charge/discharge schedule by using a linear optimization model of the battery systems (based on Li-ion and lead-acid technology) for arbitrage accommodation. They found that the cost and the efficiency of the storage systems have the highest impact on simulation results. The developed model is linear and can thus be solved without much computational effort. Bradbury et al. [10] studied seven real-time US electricity markets and 14 different storage technologies, finding that the optimal profit-maximizing size of a storage device ( i.e. , hours of energy storage) depends largely on its technological characteristics (round-trip charge/discharge efficiency and self-discharge), rather than the magnitude of market price volatility, which instead increases internal rate of return (IRR). The arbitrage benefit is maximized using a simple linear programming, subject to technical constraints. Graves et al. [ 11 ] emphasize the fact that using average peak and off-peak prices does not account for the variability in prices and thus leading to significant errors in the optimal management strategy. They also discuss the use of a linear programming for determining the optimal operation strategy. In [ 12 ], the authors present an optimal operation strategy of BESSs to the real-time electricity price in order to achieve maximum profits of the BESS. The algorithm is based on a sequential quadratic programming method as to maximize the profits for the customer. The stra