Optimization and Engineering

, Volume 20, Issue 2, pp 575–603 | Cite as

Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm

  • Landen Blackburn
  • Aaron Young
  • Pratt Rogers
  • John Hedengren
  • Kody PowellEmail author
Research Article


As more renewable energy is integrated into the power grid, it is increasingly important to exploit variable electricity pricing structures to minimize commercial utility costs and enable more intermittent renewables on the grid through proactive management of energy storage. Using data from a large campus district energy system, equipped with centralized chilled water plants and a thermal energy storage tank, a novel technique is proposed to optimize this system in real-time, formulated as a mixed-integer quadratic programming problem. This method, titled Quadratic Programming Hybrid with Augmented Constraints, is sufficiently fast to be computed in real-time for a district chiller system. This method is compared to both Branch and Bound and a simple logical decision algorithm in both speed and optimality. The proposed method for solving this mixed-integer quadratic programming problem proves very successful at achieving a near-optimal solution when compared to a standard Branch and Bound (BnB) algorithm. Although suboptimal, the proposed algorithm takes 99.96–99.99% less computational time than the standard BnB and computes an answer to within 29.9% of the BnB objective function. When compared to a simple logical decision algorithm, which represents an operator manually controlling the plant, the proposed method is estimated to yield 8.10–33.7% in savings on chiller energy costs. The Quadratic Programming Hybrid with Augmented Constraints algorithm shows potential for use in a real-time optimization application to exploit variable electricity pricing and significantly reduce the costs of running a chiller plant with thermal energy storage.


Dynamic optimization Chiller Mixed-integer quadratic programming Thermal energy storage 



The authors wish to thank the USTAR Energy Research Triangle program for funding this project and the University of Utah for providing generous access to facilities and historic data.


  1. Afram A, Janabi-Sharifi F (2014) Theory and applications of HVAC control systems-a review of model predictive control (MPC). Build Environ 72:343–355CrossRefGoogle Scholar
  2. Ahn B, Mitchell J (2001) Optimal control development for chilled water plants using a quadratic representation. Energy Build 33(4):371–378. Special Issue: Building Simulation’99
  3. Al-Rabghi OM, Akyurt MM (2004) A survey of energy efficient strategies for effective air conditioning. Energy Convers Manag 45(11–12):1643–1654CrossRefGoogle Scholar
  4. Bonami P, Lee J (2007) Bonmin users manual. Numer Math 4:1–32Google Scholar
  5. Braun JE (2007) A near-optimal control strategy for cool storage systems with dynamic electric rates (rp-1252). HVAC&R Res 13(4):557–580. CrossRefGoogle Scholar
  6. Chang YC (2004) A novel energy conservation methodoptimal chiller loading. Electr Power Syst Res 69(2):221–226.
  7. Chang YC (2007) Optimal chiller loading by evolution strategy for saving energy. Energy Build 39(4):437–444.
  8. Chow T, Zhang G, Lin Z, Song C (2002) Global optimization of absorption chiller system by genetic algorithm and neural network. Energy Build 34(1):103–109.
  9. dos Santos Coelho L, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278.
  10. dos Santos Coelho L, Klein CE, Sabat SL, Mariani VC (2014) Optimal chiller loading for energy conservation using a new differential cuckoo search approach. Energy 75:237–243.
  11. Fan B, Jin X, Du Z (2011) Optimal control strategies for multi-chiller system based on probability density distribution of cooling load ratio. Energy Build 43(10):2813–2821.
  12. Geem ZW (2011) Solution quality improvement in chiller loading optimization. Appl Therm Eng 31(10):1848–1851.
  13. Gordon J, Ng KC, Chua HT (1995) Centrifugal chillers: thermodynamic modelling and a diagnostic case study. Int J Refrig 18(4):253–257CrossRefGoogle Scholar
  14. Hart WE, Watson JP, Woodruff DL (2011) Pyomo: modeling and solving mathematical programs in python. Math Program Comput 3(3):219–260MathSciNetCrossRefGoogle Scholar
  15. Hart WE, Laird CD, Watson JP, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD (2017) Pyomo-optimization modeling in python, vol 67, 2nd edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
  16. Huang S, Zuo W, Sohn MD (2016) Amelioration of the cooling load based chiller sequencing control. Appl Energy 168:204–215.
  17. Koeppel E, Klein S, Mitchell J, Flake B (1995) Optimal supervisory control of an absorption chiller system. HVAC&R Res 1(4):325–340CrossRefGoogle Scholar
  18. Kota NN, House JM, Arora JS, Smith TF (1996) Optimal control of HVAC systems using DDP and NLP techniques. Optim Control Appl Methods 17(1):71–78CrossRefzbMATHGoogle Scholar
  19. Lee WS, Lin LC (2009) Optimal chiller loading by particle swarm algorithm for reducing energy consumption. Appl Therm Eng 29(8):1730–1734.
  20. Li X, Wen J, Malkawi A (2016) An operation optimization and decision framework for a building cluster with distributed energy systems. Appl Energy 178:98–109CrossRefGoogle Scholar
  21. Lu YY, Chen J, Liu TC, Chien MH (2011) Using cooling load forecast as the optimal operation scheme for a large multi-chiller system. Int J Refrig 34(8):2050–2062.
  22. Lu Y, Wang S, Sun Y, Yan C (2015) Optimal scheduling of buildings with energy generation and thermal energy storage under dynamic electricity pricing using mixed-integer nonlinear programming. Appl Energy 147:49–58CrossRefGoogle Scholar
  23. Ma Z, Wang S (2011) Supervisory and optimal control of central chiller plants using simplified adaptive models and genetic algorithm. Appl Energy 88(1):198–211CrossRefGoogle Scholar
  24. Mojica JL, Petersen D, Hansen B, Powell KM, Hedengren JD (2017) Optimal combined long-term facility design and short-term operational strategy for CHP capacity investments. Energy 118:97–115CrossRefGoogle Scholar
  25. Patel NR, Rawlings JB, Wenzel MJ, Turney RD (2016) Design and application of distributed economic model predictive control for large-scale building temperature regulation. In: 4th International High Performance buildings Conference at Purdue, West LafayetteGoogle Scholar
  26. Powell KM, Cole WJ, Ekarika UF, Edgar TF (2013a) Optimal chiller loading in a district cooling system with thermal energy storage. Energy 50:445–453.
  27. Powell KM, Hedengren JD, Edgar TF (2013b) Dynamic optimization of a solar thermal energy storage system over a 24 hour period using weather forecasts. In: American control conference (ACC), 2013, IEEE, pp 2946–2951Google Scholar
  28. Powell KM, Sriprasad A, Cole WJ, Edgar TF (2014) Heating, cooling, and electrical load forecasting for a large-scale district energy system. Energy 74:877–885CrossRefGoogle Scholar
  29. Powell KM, Kim JS, Cole WJ, Kapoor K, Mojica JL, Hedengren JD, Edgar TF (2016) Thermal energy storage to minimize cost and improve efficiency of a polygeneration district energy system in a real-time electricity market. Energy 113:52–63CrossRefGoogle Scholar
  30. Prez-Lombard L, Ortiz J, Pout C (2008) A review on buildings energy consumption information. Energy Build 40(3):394–398.
  31. Rawlings JB, Patel NR, Risbeck MJ, Maravelias CT, Wenzel MJ, Turney RD (2018) Economic MPC and real-time decision making with application to large-scale HVAC energy systems. Comput Chem Eng 114:89–98CrossRefGoogle Scholar
  32. Risbeck MJ, Maravelias CT, Rawlings JB, Turney RD (2016) Closed-loop scheduling for cost minimization in HVAC central plants. In: International High Performance Buildings Conference, Paper 177.
  33. Risbeck MJ, Maravelias CT, Rawlings JB (2018) Real-time mixed-integer optimization for improved economic performance in HVAC systems. Comput Aided Chem Eng 44:33–42. CrossRefGoogle Scholar
  34. Touretzky CR, Baldea M (2016) A hierarchical scheduling and control strategy for thermal energy storage systems. Energy Build 110:94–107CrossRefGoogle Scholar
  35. Yu F, Chan K (2007) Optimum load sharing strategy for multiple-chiller systems serving air-conditioned buildings. Build Environ 42(4):1581–1593.
  36. Yu F, Chan K (2008) Improved energy performance of air cooled centrifugal chillers with variable chilled water flow. Energy Convers Manag 49(6):1595–1611.
  37. Zhao Y, Lu Y, Yan C, Wang S (2015) MPC-based optimal scheduling of grid-connected low energy buildings with thermal energy storages. Energy Build 86:415–426CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Landen Blackburn
    • 1
  • Aaron Young
    • 2
  • Pratt Rogers
    • 2
  • John Hedengren
    • 3
  • Kody Powell
    • 1
    Email author
  1. 1.Department of Chemical EngineeringUniversity of UtahSalt Lake CityUSA
  2. 2.Department of Mining EngineeringUniversity of UtahSalt Lake CityUSA
  3. 3.Department of Chemical EngineeringBrigham Young UniversityProvoUSA

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