A mixed-integer linear programming model for real-time cost optimization of building heating, ventilation, and air conditioning equipment

Abstract In this paper, we present a framework for the formulation and solution of mixed-integer linear programming (MILP) models for operational planning of HVAC systems in commercial buildings. We introduce the general concepts of generators (e.g., chillers, boilers, cooling towers) and resources (e.g., electricity, chilled water), which allow us to model a wide range of central plants. By using discrete variables for on/off states of central plant equipment and continuous variables for equipment load, storage tank usage, and building temperature trajectory, all critical-to-cost decisions are taken into account. In addition, we consider both time-varying use charges and peak demand charges as well as building models of varying complexity. Because equipment models are often nonlinear, piecewise-linear approximations are used, which can be made arbitrarily accurate and enable real-time solution to the resulting optimization problems. We also employ a symmetry-free formulation to enhance the solution of the MILP model. Such features lead to improved performance compared to approaches employing heuristics or optimization without discrete variables. We demonstrate optimization for a small-scale cooling system and show favorable scaling of solution time with respect to number of units and temperature zones. In addition, we show simultaneous optimization of heating and cooling loops when a forecast of resource demand is available. Finally, we demonstrate closed-loop operation of our proposed optimization scheme. In all cases examined, a solution with an optimality gap below 1% can be obtained within 5 min, and thus the proposed optimization can be solved in real time, allowing for rapid response to changing weather, price, or demand forecasts.

[1]  Lino Guzzella,et al.  Optimal design and operation of building services using mixed-integer linear programming techniques , 2013 .

[2]  Mesut Avci,et al.  Demand Response-Enabled Model Predictive HVAC Load Control in Buildings using Real-Time Electricity Pricing , 2013 .

[3]  Xinhua Xu,et al.  A supervisory control strategy for building cooling water systems for practical and real time applications , 2008 .

[4]  Gregor P. Henze.  Energy and Cost Minimal Control of Active and Passive Building Thermal Storage Inventory , 2005 .

[5]  Singiresu S Rao,et al.  Energy optimization in chiller plants: A novel formulation and solution using a hybrid optimization technique , 2013 .

[6]  Christos T. Maravelias,et al.  General framework and modeling approach classification for chemical production scheduling , 2012 .

[7]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations */I , 1993 .

[8]  Frauke Oldewurtel,et al.  Building modeling as a crucial part for building predictive control , 2013 .

[9]  Prodromos Daoutidis,et al.  Dynamic real‐time optimization and control of a hybrid energy system , 2014 .

[10]  Christos T. Maravelias,et al.  Cost optimization of combined building heating/cooling equipment via mixed-integer linear programming , 2015, 2015 American Control Conference (ACC).

[11]  Giuliano Fontanella,et al.  Energy analysis of chilled water system configurations using simulation-based optimization , 2013 .

[12]  Riccardo Minciardi,et al.  Modeling and optimization of a hybrid system for the energy supply of a “Green” building , 2012 .

[13]  Kevin J. Kircher,et al.  On the lumped capacitance approximation accuracy in RC network building models , 2015 .

[14]  Donald J. Chmielewski,et al.  Controller and system design for HVAC with thermal energy storage , 2012, 2012 American Control Conference (ACC).

[15]  Nathan Mendes,et al.  Predictive controllers for thermal comfort optimization and energy savings , 2008 .

[16]  Moncef Krarti,et al.  Optimal control of building storage systems using both ice storage and thermal mass – Part I: Simulation environment , 2012 .

[17]  Wen-Shing Lee,et al.  Optimal chiller loading by differential evolution algorithm for reducing energy consumption , 2011 .

[18]  Gregor P. Henze,et al.  Optimal design and operation of a thermal storage system for a chilled water plant serving pharmaceutical buildings , 2008 .

[19]  José A. Candanedo,et al.  Model-based predictive control of an ice storage device in a building cooling system , 2013 .

[20]  Atila Novoselac,et al.  Use of model predictive control to enhance the flexibility of thermal energy storage cooling systems , 2012, 2012 American Control Conference (ACC).

[21]  Gregor P. Henze,et al.  Evaluation of optimal control for active and passive building thermal storage , 2004 .

[22]  Rubiyah Yusof,et al.  Review of HVAC scheduling techniques for buildings towards energy-efficient and cost-effective operations , 2013 .

[23]  Jaime Cerdá,et al.  State-of-the-art review of optimization methods for short-term scheduling of batch processes , 2006, Comput. Chem. Eng..

[24]  Francesco Borrelli,et al.  Model Predictive Control of thermal energy storage in building cooling systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[25]  Zhiqiang John Zhai,et al.  A simplified method to predict hourly building cooling load for urban energy planning , 2013 .

[26]  Michael Baldea,et al.  A hierarchical scheduling and control strategy for thermal energy storage systems , 2016 .

[27]  Philip Haves,et al.  Model predictive control for the operation of building cooling systems , 2010, Proceedings of the 2010 American Control Conference.

[28]  Kody M. Powell,et al.  Optimal chiller loading in a district cooling system with thermal energy storage , 2013 .

[29]  James E. Braun.  A General Control Algorithm for Cooling Towers in Cooling Plants with Electric and/or Gas-Driven Chillers , 2007 .

[30]  J. E. Braun,et al.  Near-optimal control of cooling towers for chilled-water systems , 1990 .

[31]  M. Kintner-Meyer,et al.  Optimal control of an HVAC system using cold storage and building thermal capacitance , 1995 .

[32]  Wan-Chen Lu,et al.  Evaluation of the suitability of empirically-based models for predicting energy performance of centrifugal water chillers with variable chilled water flow , 2012 .

[33]  Lazaros G. Papageorgiou,et al.  Efficient energy consumption and operation management in a smart building with microgrid , 2013 .

[34]  Truong Nghiem,et al.  Green Scheduling for Energy-Efficient Operation of Multiple Chiller Plants , 2012, 2012 IEEE 33rd Real-Time Systems Symposium.

[35]  Mohammed H. Albadi,et al.  Demand Response in Electricity Markets: An Overview , 2007, 2007 IEEE Power Engineering Society General Meeting.

[36]  Peng Xu,et al.  Demand reduction in building energy systems based on economic model predictive control , 2012 .

[37]  J. Mitchell,et al.  Optimal control development for chilled water plants using a quadratic representation , 2001 .

[38]  Wenjian Cai,et al.  A simplified modeling of mechanical cooling tower for control and optimization of HVAC systems , 2007 .

[39]  Kody M. Powell,et al.  Improved Large-Scale Process Cooling Operation through Energy Optimization , 2013 .

[40]  Tsutomu Sasao,et al.  On the number of segments needed in a piecewise linear approximation , 2010, J. Comput. Appl. Math..

[41]  Zong Woo Geem,et al.  Solution quality improvement in chiller loading optimization , 2011 .

[42]  Alejandro Toriello,et al.  Fitting piecewise linear continuous functions , 2012, Eur. J. Oper. Res..

[43]  Pedro M. Castro,et al.  Scope for industrial applications of production scheduling models and solution methods , 2014, Comput. Chem. Eng..

[44]  Francesco Borrelli,et al.  Implementation of model predictive control for an HVAC system in a mid-size commercial building , 2014 .

[45]  Michael Baldea,et al.  Integrating scheduling and control for economic MPC of buildings with energy storage , 2014 .

[46]  James E. Braun.  A Near-Optimal Control Strategy for Cool Storage Systems with Dynamic Electric Rates (RP-1252) , 2007 .

[47]  Stig-Inge Gustafsson,et al.  Mixed integer linear programming and building retrofits , 1998 .

[48]  Seyed Hossein Hosseinian,et al.  A novel approach for optimal chiller loading using particle swarm optimization , 2008 .

[49]  Donald J. Chmielewski,et al.  HVAC control using infinite-horizon economic MPC , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[50]  Shmuel Rippa,et al.  Adaptive Approximation by Piecewise Linear Polynomials on Triangulations of Subsets of Scattered Data , 1992, SIAM J. Sci. Comput..

[51]  Lihua Xie,et al.  HVAC system optimization––condenser water loop , 2004 .