Optimization and Engineering

, Volume 20, Issue 1, pp 179–213 | Cite as

Optimal design and dispatch of a hybrid microgrid system capturing battery fade

  • Gavin Goodall
  • Michael Scioletti
  • Alex Zolan
  • Bharatkumar Suthar
  • Alexandra NewmanEmail author
  • Paul Kohl
Research Article


Microgrids provide power to remote communities and at operational sites that are not connected to a grid. We consider such a microgrid that consists of batteries, photovoltaics, and diesel generators, and optimize the components it comprises and a corresponding dispatch strategy at hourly fidelity so as to minimize procurement, operations and maintenance, and fuel costs. The system is governed by constraints such as meeting demand and adhering to component interoperability and capability. Our contribution lies in the introduction to this optimization model of a set of constraints that incorporates capacity fade of a battery and temperature effects. We show, using data from a forward operating base and solving the corresponding instances for a time horizon of 8760 h, that higher temperatures decrease resistance, leading to better round-trip energy efficiency, but at the same time increase capacity fade of the battery, resulting in a higher overall operating cost. In some cases, the procurement strategy is robust to the fade of the battery, but fade can influence battery state of charge and power output as the available battery capacity degrades over time and with use.


Design optimization Dispatch optimization Microgrids Batteries Mixed-integer linear programming Systems analysis 



The authors would like to thank Dr. Mark Spector, Office of Naval Research (ONR) for full support of this research effort under contract Award #N000141310839, and several anonymous referees whose comments significantly improved the paper.


  1. Androulakis I, Maranas C, Floudas C (1995) \(\alpha \)BB: a global optimization method for general constrained nonconvex problems. J Glob Optim 7(4):337–363MathSciNetzbMATHGoogle Scholar
  2. Ashok S (2007) Optimised model for community-based hybrid energy system. Renew Energy 32(7):1155–1164Google Scholar
  3. Bala B, Siddique S (2009) Optimal design of a PV–diesel hybrid system for electrification of an isolated island in Sandwip, Bangladesh using a genetic algorithm. Energy Sustain Dev 13(3):137–142Google Scholar
  4. Buller S (2002) Impedance based simulation models for energy storage devices in advanced automotive power systems. Ph.D. thesis, ISEA RWTH Aachen, Aachen, GermanyGoogle Scholar
  5. Das T, Krishnan V, McCalley JD (2015) Assessing the benefits and economics of bulk energy storage technologies in the power grid. Appl Energy 139:104–18Google Scholar
  6. Daud AK, Ismail MS (2012) Design of isolated hybrid systems minimizing costs and pollutant emissions. Renew Energy 44:215–224Google Scholar
  7. Dufó-Lopez R, Bernal-Agustin JL (2005) Design and control strategies of PV–diesel systems using genetic algorithms. Sol Energy 79(1):33–46Google Scholar
  8. Engels M, Boyd PA, Koehler TM, Goel S, Sisk DR, Hatley DD, Mendon VV, Hail JC (2014) Smart and green energy (SAGE) for base camps final report. Technical report, Pacific Northwest National Laboratory (PNNL), Richland, WA (US)Google Scholar
  9. Fourer R, Gay DM, Kernighan BW (2003) AMPL—a modeling language for mathematical programming. Thomson Brooks/Cole Academic Publisher, Pacific GrovezbMATHGoogle Scholar
  10. Givler T, Lilienthal P (2005) Using HOMER software, NREL’s micropower optimization model, to explore the role of gen-sets in small solar power systems. Technical report, National Renewable Energy LaboratoryGoogle Scholar
  11. Goodall GH, Hering AS, Newman AM (2017) Characterizing solutions in optimal microgrid procurement and dispatch strategies. Appl Energy 201:1–19Google Scholar
  12. Hua S, Zhou Q, Kong D, Ma J (2006) Application of valve-regulated lead-acid batteries for storage of solar electricity in stand-alone photovoltaic systems in the northwest areas of China. J Power Sources 158(2):1178–1185Google Scholar
  13. Husted M, Suthar B, Goodall G, Newman A, Kohl P (2018) Coordinating microgrid procurement decisions with a dispatch strategy featuring a concentration gradient. Appl Energy 219:394–407Google Scholar
  14. IBM ILOG CPLEX Optimization Studio CPLEX User’s Manual (2013).
  15. Ikeda S, Ooka R (2015) Metaheuristic optimization methods for a comprehensive operating schedule of battery, thermal energy storage, and heat source in a building energy system. Appl Energy 151:192–205Google Scholar
  16. Kaldellis JK, Zafirakis D, Kavadias K (2011) Minimum cost solution of wind-photovoltaic based stand-alone power systems for remote consumers. Energy Policy 42:105–117Google Scholar
  17. Kamel S, Dahl C (2005) The economics of hybrid power systems for sustainable desert agriculture in Egypt. Energy 30(8):1271–1281Google Scholar
  18. Karimi G, Li X (2013) Thermal management of lithium-ion batteries for electric vehicles. Int J Energy Res 37:13–28Google Scholar
  19. Katsigiannis Y, Georgilakis P (2008) Optimal sizing of small isolated hybrid power systems using tabu search. J Optoelectron Adv Mater 10(5):1241–1245Google Scholar
  20. Koutroulis E, Kolokotsa D, Potirakis A, Kalaitzakis K (2006) Methodology for optimal sizing of stand-alone photovoltaic–wind-generator systems using genetic algorithms. Sol Energy 80(9):1072–1088Google Scholar
  21. Liu G, Ouyang M, Lu L, Li J, Hua J (2015) A highly accurate predictive-adaptive method for lithium-ion battery remaining discharge energy prediction in electric vehicle applications. Appl Energy 149:297–314Google Scholar
  22. Manwell JF, McGowan JG (1993) Lead acid battery storage model for hybrid energy systems. Sol Energy 50(5):399–405Google Scholar
  23. McCormick G (1976) Computability of global solutions to factorable nonconvex programs: part I—convex underestimating problems. Math Progr 10(1):147–175zbMATHGoogle Scholar
  24. Merei G, Berger C, Uwe Sauer D (2013) Optimization of an off-grid hybrid PV–wind–diesel system with different battery technologies using genetic algorithm. Sol Energy 97:460–473Google Scholar
  25. MIT Electric Vehicle Team (2008) A guide to understanding battery specifications. MIT, BostonGoogle Scholar
  26. Morais H, Kadar P, Faria P, Vale ZA, Khodr H (2010) Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming. Renew Energy 35(1):151–156Google Scholar
  27. Pinson MB, Bazant MZ (2013) Theory of SEI formation in rechargeable batteries: capacity fade, accelerated aging and lifetime prediction. J Electrochem Soc 160(2):A243–A250Google Scholar
  28. Pruitt KA, Leyffer S, Newman AM, Braun RJ (2014) A mixed-integer nonlinear program for the optimal design and dispatch of distributed generation systems. Optim Eng 15(1):167–197MathSciNetzbMATHGoogle Scholar
  29. Rehman S, Al-Hadhrami LM (2010) Study of a solar PV diesel battery hybrid power system for a remotely located population near Rafha, Saudi Arabia. Energy 35(12):4986–4995Google Scholar
  30. Scioletti M, Goodman J, Kohl P, Newman A (2016) A physics-based integer-linear battery modeling paradigm. Appl Energy 176:245–257Google Scholar
  31. Scioletti M, Newman A, Goodman J, Leyffer S, Zolan A (2017) Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations. Optim Eng 18(3):755–792MathSciNetzbMATHGoogle Scholar
  32. Shaahid S, El-Amin I (2009) Techno-economic evaluation of off-grid hybrid photovoltaic diesel battery power systems for rural electrification in Saudi Arabia as a way forward for sustainable development. Renew Sustain Energy Rev 13(3):625–633Google Scholar
  33. Tan X, Li Q, Wang H (2013) Advances and trends of energy storage technology in microgrid. Int J Electr Power Energy Syst 44(1):179–91Google Scholar
  34. Wang J, Liu P, Hicks-Garner J, Sherman E, Soukiazian S, Verbrugge M, Tataria H, Musser J, Finamore P (2011) Cycle-life model for graphite-LiFePO\(_4\) cells. J Power Sources 196(8):3942–3948Google Scholar
  35. Zachar M, Daoutidis P (2015) Understanding and predicting the impact of location and load on microgrid design. Energy 90:1005–1023Google Scholar
  36. Zhao H, Wu Q, Hu S, Xu H, Rasmussen CN (2015) Review of energy storage system for wind power integration support. Appl Energy 137:545–553Google Scholar
  37. Zolan A, Scioletti M, Morton D, Newman A (2018) Decomposing loosely coupled mixed-integer programs for optimal microgrid design. Submitted for publicationGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Gavin Goodall
    • 1
  • Michael Scioletti
    • 1
  • Alex Zolan
    • 2
  • Bharatkumar Suthar
    • 3
  • Alexandra Newman
    • 1
    Email author
  • Paul Kohl
    • 3
  1. 1.Department of Mechanical EngineeringColorado School of MinesGoldenUSA
  2. 2.Department of Mechanical EngineeringUniversity of Texas at AustinAustinUSA
  3. 3.School of Chemical and Biomolecular EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations