{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T20:41:51Z","timestamp":1774989711891,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T00:00:00Z","timestamp":1546560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>This paper addresses an optimized management of a storage energy battery which is part of a microgrid with a connection to the main grid and is supplied by a photovoltaic (PV) power plant. The main contribution of this paper is to consider uncertainty in electricity price while managing the battery storage. The forecasted value for demand and PV unit are predicted by a seasonal autoregressive integrated moving average model (SARIMA)\u2014capable of accurately characterizing both seasonality effects and tail fatness. The optimal operation of the battery is determined by resolving a linear optimization program in which the objective function comprises the conditional value at risk (CVaR). Using CVaR ensures that the demand is fully supplied while minimizing the risk and operational cost. The cost function is the difference between power sold and bought subject to the charging and discharging rates for the battery and defining upper and lower bounds for the level of battery charge. The simulation results confirm that the risk consideration has a significant effect on the optimized management of a storage energy battery in a photovoltaic grid-connected microgrid.<\/jats:p>","DOI":"10.3390\/app9010169","type":"journal-article","created":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T11:34:26Z","timestamp":1546601666000},"page":"169","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Optimal Management of an Energy Storage Unit in a PV-Based Microgrid Integrating Uncertainty and Risk"],"prefix":"10.3390","volume":"9","author":[{"given":"Mehdi","family":"Tavakkoli","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2217-5293","authenticated-orcid":false,"given":"Edris","family":"Pouresmaeil","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1244-5624","authenticated-orcid":false,"given":"Radu","family":"Godina","sequence":"additional","affiliation":[{"name":"UNIDEMI - Department of Mechanical and Industrial Engineering, Faculty of Science and Technology (FCT), New University of Lisbon, 2829-516 Caparica, Portugal"}]},{"given":"Ionel","family":"Vechiu","sequence":"additional","affiliation":[{"name":"ESTIA Institute of Technology, ESTIA, F-64210 Bidart, France"}]},{"given":"Jo\u00e3o P. S.","family":"Catal\u00e3o","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, and INESC TEC, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.energy.2018.02.088","article-title":"A unified index for power quality evaluation in distributed generation systems","volume":"149","author":"Elbasuony","year":"2018","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1016\/j.energy.2017.06.055","article-title":"Centralized vs distributed generation. A model to assess the relevance of some thermal and electric factors. Application to the Spanish case study","volume":"134","author":"Rivier","year":"2017","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"26291","DOI":"10.1109\/ACCESS.2017.2766233","article-title":"Event-Driven Energy Trading System in Microgrids: Aperiodic Market Model Analysis With a Game Theoretic Approach","volume":"5","author":"Park","year":"2017","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.scs.2018.04.001","article-title":"A multiagent based decentralized energy management system for power exchange minimization in microgrid cluster","volume":"40","author":"Harmouch","year":"2018","journal-title":"Sustain. Cities Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.enconman.2015.05.049","article-title":"Joint energy demand and thermal comfort optimization in photovoltaic-equipped interconnected microgrids","volume":"101","author":"Baldi","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.apenergy.2015.10.140","article-title":"Occupancy-based demand response and thermal comfort optimization in microgrids with renewable energy sources and energy storage","volume":"163","author":"Korkas","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.solener.2017.04.019","article-title":"Multi-agent based operational cost and inconvenience optimization of PV-based microgrid","volume":"150","author":"Rahmani","year":"2017","journal-title":"Sol. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1016\/j.rser.2016.09.082","article-title":"Grid-connected isolated PV microinverters: A review","volume":"67","author":"Hasan","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.energy.2014.01.042","article-title":"Dynamic operation and control of microgrid hybrid power systems","volume":"66","author":"Ou","year":"2014","journal-title":"Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/TSTE.2013.2255135","article-title":"Robust Energy Management for Microgrids with High-Penetration Renewables","volume":"4","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5250","DOI":"10.1109\/TIE.2017.2777401","article-title":"PWM Common Mode Reference Generation for Maximizing the Linear Modulation Region of CHB Converters in Islanded Microgrids","volume":"65","author":"Lamb","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1016\/j.apenergy.2018.04.103","article-title":"Microgrids energy management systems: A critical review on methods, solutions, and prospects","volume":"222","author":"Zia","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.epsr.2017.05.042","article-title":"A demand power factor-based approach for finding the maximum loading point","volume":"151","author":"Contreras","year":"2017","journal-title":"Electr. Power Syst. Res."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pourakbari-Kasmaei, M., Mantovani, J.R.S., Rashidinejad, M., Habibi, M.R., and Contreras, J. (2017, January 6\u20139). Carbon footprint allocation among consumers and transmission losses. Proceedings of the 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC\/I&CPS Europe), Milan, Italy.","DOI":"10.1109\/EEEIC.2017.7977512"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1049\/iet-gtd.2014.1195","article-title":"Multi-area environmentally constrained active\u2013reactive optimal power flow: a short-term tie line planning study","volume":"10","author":"Rider","year":"2016","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/TSTE.2018.2828778","article-title":"Adaptive Robust Short-Term Planning of Electrical Distribution Systems Considering Siting and Sizing of Renewable Energy-based DG Units","volume":"10","author":"Mantovani","year":"2019","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ref.2017.12.002","article-title":"PV based distributed generation power system protection: A review","volume":"24","author":"Bansal","year":"2018","journal-title":"Renew. Energy Focus"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s12667-018-0282-z","article-title":"A stochastic mixed-integer conic programming model for distribution system expansion planning considering wind generation","volume":"9","author":"Ortiz","year":"2018","journal-title":"Energy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.scs.2018.01.052","article-title":"Energy storage key performance indicators for building application","volume":"40","author":"Aste","year":"2018","journal-title":"Sustain. Cities Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.apenergy.2016.12.007","article-title":"Modelling electrochemical energy storage devices in insular power network applications supported on real data","volume":"188","author":"Rodrigues","year":"2017","journal-title":"Appl. Energy"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Su, H.-I., and Gamal, A. (2011, January 28\u201330). El Modeling and analysis of the role of fast-response energy storage in the smart grid. Proceedings of the 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA.","DOI":"10.1109\/Allerton.2011.6120239"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3226","DOI":"10.1109\/TPWRS.2013.2245925","article-title":"Optimal Power Flow in Microgrids With Energy Storage","volume":"28","author":"Levron","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TPEL.2010.2095040","article-title":"Composite Energy Storage System Involving Battery and Ultracapacitor with Dynamic Energy Management in Microgrid Applications","volume":"26","author":"Zhou","year":"2011","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1109\/TPWRS.2014.2344859","article-title":"Optimal Management and Sizing of Energy Storage Under Dynamic Pricing for the Efficient Integration of Renewable Energy","volume":"30","author":"Harsha","year":"2015","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.cor.2018.03.002","article-title":"Load-frequency control in a multi-source power system connected to wind farms through multi terminal HVDC systems","volume":"96","author":"Tavakoli","year":"2018","journal-title":"Comput. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Tavakkoli, M., Adabi, J., Zabihi, S., Godina, R., and Pouresmaeil, E. (2018). Reserve Allocation of Photovoltaic Systems to Improve Frequency Stability in Hybrid Power Systems. Energies, 11.","DOI":"10.3390\/en11102583"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.ijepes.2006.03.003","article-title":"Optimal operation of dispersed generation under uncertainty using mathematical programming","volume":"28","author":"Handschin","year":"2006","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1109\/TSG.2011.2177282","article-title":"Application of Model Predictive Control for Active Load Management in a Distributed Power System With High Wind Penetration","volume":"3","author":"Zong","year":"2012","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1109\/TCST.2013.2295737","article-title":"A Model Predictive Control Approach to Microgrid Operation Optimization","volume":"22","author":"Parisio","year":"2014","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijepes.2018.02.022","article-title":"CVaR-based energy management scheme for optimal resilience and operational cost in commercial building microgrids","volume":"100","author":"Tavakoli","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.scs.2018.05.035","article-title":"A Two Stage Hierarchical Control Approach for the Optimal Energy Management in Commercial Building Microgrids Based on Local Wind Power and PEVs","volume":"41","author":"Tavakoli","year":"2018","journal-title":"Sustain. Cities Soc."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, Z., Zang, C., Zeng, P., and Yu, H. (2016). Combined Two-Stage Stochastic Programming and Receding Horizon Control Strategy for Microgrid Energy Management Considering Uncertainty. Energies, 9.","DOI":"10.3390\/en9070499"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.apenergy.2012.05.039","article-title":"Virtual power plant mid-term dispatch optimization","volume":"101","author":"Kuzle","year":"2013","journal-title":"Appl. Energy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/TSG.2014.2368077","article-title":"Toward Optimal Day-Ahead Scheduling and Operation Control of Microgrids Under Uncertainty","volume":"6","author":"Farzan","year":"2015","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1109\/TSG.2014.2302396","article-title":"An Optimal Energy Storage Control Strategy for Grid-connected Microgrids","volume":"5","author":"Malysz","year":"2014","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Sheikhahmadi, P., Mafakheri, R., Bahramara, S., Damavandi, M., and Catal\u00e3o, J. (2018). Risk-Based Two-Stage Stochastic Optimization Problem of Micro-Grid Operation with Renewables and Incentive-Based Demand Response Programs. Energies, 11.","DOI":"10.3390\/en11030610"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.ijepes.2012.05.061","article-title":"Risk-based performance analysis of microgrid topology with distributed energy generation","volume":"43","author":"Gabbar","year":"2012","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.apenergy.2012.01.070","article-title":"Estimating risk for the carbon market via extreme value theory: An empirical analysis of the EU ETS","volume":"99","author":"Feng","year":"2012","journal-title":"Appl. Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1111\/1467-9965.00068","article-title":"Coherent Measures of Risk","volume":"9","author":"Artzner","year":"1999","journal-title":"Math. Financ."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.apenergy.2018.01.051","article-title":"A risk-based approach for modeling the strategic behavior of a distribution company in wholesale energy market","volume":"214","author":"Sheikhahmadi","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1109\/TPWRS.2011.2170442","article-title":"Wind Power Trading Under Uncertainty in LMP Markets","volume":"27","author":"Botterud","year":"2012","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/TSTE.2015.2500539","article-title":"Risk-Constrained Offering Strategy for Aggregated Hybrid Power Plant Including Wind Power Producer and Demand Response Provider","volume":"7","author":"Aghaei","year":"2016","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.renene.2018.05.014","article-title":"Tailoring large-scale electricity production from variable renewable energy sources to accommodate baseload generation in Europe","volume":"129","author":"Reichenberg","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2555","DOI":"10.1109\/TII.2017.2662069","article-title":"CVaR-Constrained Optimal Bidding of Electric Vehicle Aggregators in Day-Ahead and Real-Time Markets","volume":"13","author":"Yang","year":"2017","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.energy.2017.02.063","article-title":"Application of CVaR risk aversion approach in the dynamical scheduling optimization model for virtual power plant connected with wind-photovoltaic-energy storage system with uncertainties and demand response","volume":"124","author":"Tan","year":"2017","journal-title":"Energy"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1016\/j.apenergy.2018.02.157","article-title":"A decentralized trading algorithm for an electricity market with generation uncertainty","volume":"218","author":"Bahrami","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1109\/TSG.2015.2469134","article-title":"Stochastic Unit Commitment in Isolated Systems with Renewable Penetration Under CVaR Assessment","volume":"7","author":"Asensio","year":"2016","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"21","DOI":"10.21314\/JOR.2000.038","article-title":"Optimization of conditional value-at-risk","volume":"2","author":"Rockafellar","year":"2000","journal-title":"J. Risk"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1109\/TSTE.2016.2543024","article-title":"Optimal Control of Energy Storage in a Microgrid by Minimizing Conditional Value-at-Risk","volume":"7","author":"Khodabakhsh","year":"2016","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Conejo, A.J., Carri\u00f3n, M., and Morales, J.M. (2010). Decision Making Under Uncertainty in Electricity Markets, Springer US.","DOI":"10.1007\/978-1-4419-7421-1"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Box, G.E.P., Jenkins, G.M., and Reinsel, G.C. (2008). Time Series Analysis: Forecasting and Control, Wiley.","DOI":"10.1002\/9781118619193"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Lasnier, F. (2017). Photovoltaic Engineering Handbook, CRC Press.","DOI":"10.1201\/9780203743393"},{"key":"ref_53","unstructured":"(2018, December 16). NYISO (Markets & Operations\u2014Market Data\u2014Pricing Data). Available online: http:\/\/www.nyiso.com\/public\/markets_operations\/market_data\/pricing_data\/index.jsp."},{"key":"ref_54","unstructured":"NREL (2018, December 16). Data and Tools. Concentrating Solar Power, Available online: https:\/\/www.nrel.gov\/csp\/data-tools.html."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/9\/1\/169\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:23:39Z","timestamp":1760185419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/9\/1\/169"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,4]]},"references-count":54,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["app9010169"],"URL":"https:\/\/doi.org\/10.3390\/app9010169","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,4]]}}}