Mixed-integer optimization methods for online scheduling in large-scale HVAC systems

  • Michael J. Risbeck
  • Christos T. MaraveliasEmail author
  • James B. Rawlings
  • Robert D. Turney
Original paper


Due to time-varying utility prices, peak demand charges, and variable-efficiency equipment, optimal operation of heating ventilation, and air conditioning systems in campuses or large buildings is nontrivial. Given forecasts of ambient conditions and utility prices, system energy requirements can be reduced by optimizing heating/cooling load within buildings and then choosing the best combination of large chillers, boilers, etc., to meet that load while accounting for switching constraints and equipment performance. With the presence of energy storage, utility costs can be further reduced by temporally shifting production, which adds an additional layer of complexity. Furthermore, due to changes in market and weather conditions, it is necessary to revise a given schedule regularly as updated information is received, which means the problem must be tractable in real time (e.g., solvable within 15 min). In this paper, we present a mixed-integer linear programming model for this problem along with reformulations, decomposition approaches, and approximation strategies to improve tractability. Simulations are presented to illustrate the effectiveness of these methods. By removing symmetry from identical equipment, decomposing the problem into subproblems, and approximating longer-timescale behavior, large instances can be solved in real time to within 1% of the true optimal solution.


Large-scale HVAC systems Online optimization Closed-loop scheduling 



Funding, equipment models, and sample data provided by Johnson Controls, Inc. Additional funding provided by the National Science Foundation (Grant #CTS-1603768).

Supplementary material

11590_2018_1383_MOESM1_ESM.pdf (248 kb)
Supplementary material 1 (pdf 248 KB)


  1. 1.
    Powell, K.M., Cole, W.J., Ekarika, U.F., Edgar, T.F.: Optimal chiller loading in a district cooling system with thermal energy storage. Energy 50, 445–453 (2013)CrossRefGoogle Scholar
  2. 2.
    Albadi, M.H., El-Saadany, E.F.: Demand response in electricity markets: an overview. In: 2007 IEEE Power Engineering Society General Meeting, IEEE, pp. 1–5 (2007)Google Scholar
  3. 3.
    Touretzky, C.R., Baldea, M.: Integrating scheduling and control for economic MPC of buildings with energy storage. J. Process Control 24(8), 1292–1300 (2014)CrossRefGoogle Scholar
  4. 4.
    Henze, G.P.: Energy and cost minimal control of active and passive building thermal storage inventory. J. Sol. Energy Eng. 127(3), 343–351 (2005)CrossRefGoogle Scholar
  5. 5.
    Henze, G.P., Felsmann, C., Knabe, G.: Evaluation of optimal control for active and passive building thermal storage. Int. J. Therm. Sci. 43(2), 173–183 (2004)CrossRefGoogle Scholar
  6. 6.
    Henze, G.P., Biffar, B., Kohn, D., Becker, M.P.: Optimal design and operation of a thermal storage system for a chilled water plant serving pharmaceutical buildings. Energy Build. 40(6), 1004–1019 (2008)CrossRefGoogle Scholar
  7. 7.
    Rawlings, J., Patel, N., Risbeck, M., Maravelias, C., Wenzel, M., Turney, R.: Economic MPC and real-time decision making with application to large-scale hvac energy systems. Comput. Chem. Eng. 114, 89–98 (2017)CrossRefGoogle Scholar
  8. 8.
    Ma, J., Qin, J., Salsbury, T., Xu, P.: Demand reduction in building energy systems based on economic model predictive control. Chem. Eng. Sci. 67(1), 92–100 (2012)CrossRefGoogle Scholar
  9. 9.
    Oldewurtel, F., Parisio, A., Jones, C.N., Gyalistras, D., Gwerder, M., Stauch, V., Lehmann, B., Morari, M.: Use of model predictive control and weather forecasts for energy efficient building climate control. Energy Build. 45, 15–27 (2012)CrossRefGoogle Scholar
  10. 10.
    Ma, Y., Matuško, J., Borrelli, F.: Stochastic model predictive control for building HVAC systems: complexity and conservatism. IEEE Trans. Control Syst. Technol. 23(1), 101–116 (2015)CrossRefGoogle Scholar
  11. 11.
    Ma, Y., Borrelli, F., Hencey, B., Coffey, B., Bengea, S.C., Haves, P.: Model predictive control for the operation of building cooling systems. IEEE Control Syst. Technol. 20(3), 796–803 (2012)CrossRefGoogle Scholar
  12. 12.
    Touretzky, C.R., Baldea, M.: A hierarchical scheduling and control strategy for thermal energy storage systems. Energy Build. 110, 94–107 (2016)CrossRefGoogle Scholar
  13. 13.
    Kapoor, K., Powell, K.M., Cole, W.J., Kim, J.S., Edgar, T.F.: Improved large-scale process cooling operation through energy optimization. Processes 1(3), 312–329 (2013)CrossRefGoogle Scholar
  14. 14.
    Risbeck, M.J., Maravelias, C.T., Rawlings, J.B., Turney, R.D.: A mixed-integer linear programming model for real-time cost optimization of building heating, ventilation, and air conditioning equipment. Energy Build. 142, 220–235 (2017)CrossRefGoogle Scholar
  15. 15.
    Maravelias, C.T.: General framework and modeling approach classification for chemical production scheduling. AIChE J. 58(6), 1812–1828 (2012)CrossRefGoogle Scholar
  16. 16.
    Harjunkoski, I., Maravelias, C.T., Bongers, P., Castro, P.M., Engell, S., Grossmann, I.E., Hooker, J., Méndez, C., Sand, G., Wassick, J.: Scope for industrial applications of production scheduling models and solution methods. Comput. Chem. Eng. 62, 161–193 (2014)CrossRefGoogle Scholar
  17. 17.
    Kondili, E., Pantelides, C., Sargent, R.: A general algorithm for short-term scheduling of batch operations–I MILP formulation. Comput. Chem. Eng. 17(2), 211–227 (1993)CrossRefGoogle Scholar
  18. 18.
    Pantelides, C.C.: Unified frameworks for optimal process planning and scheduling. In: Proceedings on the Second Conference on Foundations of Computer Aided Operations, pp. 253–274 (1994)Google Scholar
  19. 19.
    Méndez, C.A., Cerdá, J., Grossmann, I.E., Harjunkoski, I., Fahl, M.: State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comput. Chem. Eng. 30(6–7), 913–946 (2006)CrossRefGoogle Scholar
  20. 20.
    Velez, S., Maravelias, C.T.: Reformulations and branching methods for mixed-integer programming chemical production scheduling models. Ind. Eng. Chem. Res. 52(10), 3832–3841 (2013)CrossRefGoogle Scholar
  21. 21.
    Vin, J.P., Ierapetritou, M.G.: A new approach for efficient rescheduling of multiproduct batch plants. Ind. Eng. Chem. Res. 39(11), 4228–4238 (2000)CrossRefGoogle Scholar
  22. 22.
    Mendez, C.A., Cerdá, J.: An milp framework for batch reactive scheduling with limited discrete resources. Comput. Chem. Eng. 28(6–7), 1059–1068 (2004)CrossRefGoogle Scholar
  23. 23.
    Touretzky, C.R., Harjunkoski, I., Baldea, M.: Dynamic models and fault diagnosis-based triggers for closed-loop scheduling. AIChE J. 63(6), 1959–1973 (2017)CrossRefGoogle Scholar
  24. 24.
    Rawlings, J.B., Mayne, D.Q., Diehl, M.M.: Model Predictive Control: Theory, Computation and Design. Nob Hill Publishing, Madison (2017)Google Scholar
  25. 25.
    Gupta, D., Maravelias, C.T.: On deterministic online scheduling: major considerations, paradoxes and remedies. Comput. Chem. Eng. 94, 312–330 (2016)CrossRefGoogle Scholar
  26. 26.
    Gupta, D., Maravelias, C.T., Wassick, J.M.: From rescheduling to online scheduling. Chem. Eng. Res. Des. 116, 83–97 (2016)CrossRefGoogle Scholar
  27. 27.
    Lee, T.-S., Liao, K.-Y., Lu, W.-C.: Evaluation of the suitability of empirically-based models for predicting energy performance of centrifugal water chillers with variable chilled water flow. Appl. Energy 93, 583–595 (2012)CrossRefGoogle Scholar
  28. 28.
    Li, Z., Ierapetritou, M.G.: Process scheduling under uncertainty: review and challenges. Comput. Chem. Eng. 32(4–5), 715–727 (2008)CrossRefGoogle Scholar
  29. 29.
    Li, Z., Floudas, C.A.: A comparative theoretical and computational study on robust counterpart optimization: III improving the quality of robust solutions. Ind. Eng. Chem. Res. 53(33), 13112–13124 (2014)CrossRefGoogle Scholar
  30. 30.
    Shi, H., You, F.: A computational framework and solution algorithms for two-stage adaptive robust scheduling of batch manufacturing processes under uncertainty. AIChE J. 62(3), 687–703 (2016)CrossRefGoogle Scholar
  31. 31.
    Lappas, N.H., Gounaris, C.E.: Multi-stage adjustable robust optimization for process scheduling under uncertainty. AIChE J. 62(5), 1646–1667 (2016)CrossRefGoogle Scholar
  32. 32.
    Du, J., Park, J., Harjunkoski, I., Baldea, M.: A time scale-bridging approach for integrating production scheduling and process control. Comput. Chem. Eng. 79, 59–69 (2015)CrossRefGoogle Scholar
  33. 33.
    Nie, Y., Biegler, L.T., Villa, C.M., Wassick, J.M.: Discrete time formulation for the integration of scheduling and dynamic optimization. Ind. Eng. Chem. Res. 54(16), 4303–4315 (2015)CrossRefGoogle Scholar
  34. 34.
    Feng, J.D., Chuang, F., Borrelli, F., Bauman, F.: Model predictive control of radiant slab systems with evaporative cooling sources. Energy Build. 87, 199–210 (2015)CrossRefGoogle Scholar
  35. 35.
    Mendoza-Serrano, D.I., Chmielewski, D.J.: HVAC control using infinite-horizon economic MPC. In: IEEE 51st Annual Conference on Decision and Control (CDC), pp. 6963–6968 (2012)Google Scholar
  36. 36.
    Vielma, J.P., Ahmed, S., Nemhauser, G.: Mixed-integer models for nonseparable piecewise-linear optimization: unifying framework and extensions. Oper. Res. 58(2), 303–315 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison (2009)Google Scholar
  38. 38.
    Wolsey, L.A.: Integer Programming. Wiley, New York (1998)zbMATHGoogle Scholar
  39. 39.
    Patel, N.N.R., Risbeck, M.J., Rawlings, J.B., Wenzel, M.M.J., Turney, R.D.: Distributed economic model predictive control for large-scale building temperature regulation. In: American Control Conference, Boston, MA, pp. 895–900 (2016)Google Scholar
  40. 40.
    Zavala, V.M., Constantinescu, E.M., Krause, T., Anitescu, M.: On-line economic optimization of energy systems using weather forecast information. J. Process Control 19(10), 1725–1736 (2009)CrossRefGoogle Scholar
  41. 41.
    ElBsat, M.N., Wenzel, M.J.: Load and electricity rates prediction for building wide optimization applications. In: 4th International High Performance Buildings Conference at Purdue, West Lafayette, IN (2016)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Wisconsin–MadisonMadisonUSA
  2. 2.Johnson ControlsMilwaukeeUSA
  3. 3.University of California–Santa BarbaraSanta BarbaraUSA

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