Economic MPC and real-time decision making with application to large-scale HVAC energy systems
Introduction
Control of heating and cooling systems has become an active area of research due to the significant energy expenditures associated with commercial buildings. Most commercial applications use on/off and PID controllers for control of their heating, ventilation, and air conditioning (HVAC) systems (Afram and Janabi-Sharifi, 2014). Recent work has proposed model predictive control (MPC) as a promising solution for controlling HVAC systems (Oldewurtel et al., 2012, Mendoza-Serrano and Chmielewski, 2012).
Large commercial buildings are often subject to dynamic utility prices, most notably for electricity. These structures, aimed at flattening peaks in electricity consumption, come in the form of varying time-of-use charges, as well as peak demand charges based on the overall maximum rate of electricity usage over the course of a month (Ma et al., 2012a, Cole et al., 2012). MPC is able to take advantage of these price structures to shift the energy load from peak hours to off-peak hours using thermal energy storage (TES). Through load shifting, energy costs can be decreased by running equipment during periods of low resource prices. The mass of the building can be readily used as passive TES (Oldewurtel et al., 2010, Avci et al., 2013). Active TES, e.g., chilled water or ice tanks, can also be utilized for load shifting, generally at higher energy efficiency than passive storage (Henze, 2005, Hajiah and Krarti, 2012). It is important that such systems are effectively controlled, as some heuristic-based control strategies can actually lead to increased operating costs when a storage tank is added (Braun, 2007). Due to storage inefficiency, time-shifting production may actually increase secondary energy consumption (i.e., electricity usage). However, overall primary efficiency consumption is likely to decrease, as the additional electricity is produced during off-peak hours at higher efficiency. Thus, economic optimization can lead to both decreased costs and higher primary energy efficiency for building operators.
As shown in Fig. 1, there are two main parts of most large-scale HVAC systems: the airside and waterside systems. The airside system includes the zones in all of the buildings along with the associated air-handler units (AHUs) used in temperature regulation. The waterside system includes the central plant equipment used to meet heating and cooling loads. The aim of the control system is to decide zone temperature setpoints in the airside problem and equipment operation schedules in the waterside problem, which includes both continuous and discrete variables.
One barrier to the widescale deployment of MPC-based control systems in industry is the scale of commercial systems. Large-scale applications, such as the one depicted in Fig. 1, involve hundreds of buildings each with tens of zones. Solving a single optimization problem for these large systems is neither practical nor desirable.
To divide the single optimization problem into smaller ones, distributed MPC can be used as discussed by Rawlings and Mayne (2009, Chapter 6) and Christofides et al. (2013). Typically, iterative methods have been used for this purpose (Cai et al., 2016, Elliott and Rasmussen, 2012, Scherer et al., 2014, Lamoudi et al., 2011). However, these methods may involve many information exchanges and iterations, which are undesirable in practice due to the limitations to information exchanges based on existing HVAC communication protocols (Moroşan et al., 2010). Additionally, the computation time to convergence may be longer than solving the single large optimization. Finally, demand charges require coordination amongst the zones in the airside system in order to avoid a high peak cost. Existing distributed methods do not address the full complexity of commercial applications, including peak demand charges, active TES, or detailed waterside equipment models.
In the central plant, the key challenge is the combinatorial problem that must be solved to sequence the multiple chillers, pumps, etc., while accounting for variable equipment efficiency. Although near-optimal heuristics are available (Braun, 2007), additional benefit can be achieved via optimization. Global search heuristics like particle swarm optimization (Ali et al., 2013) or optimization methods like mixed-integer linear programming (MILP) (Deng et al., 2015) have been applied to make the necessary discrete choices. Due to its small contribution to total cost, auxiliary equipment like pumps and cooling towers can be modeled to relatively low accuracy, e.g., in a single lumped model (Kapoor et al., 2013). This simplification reduces the number of discrete choices and thus also the computation time. For models where system dynamics depend on whether the TES is charging or discharging, an additional discrete decision variable can be added, often leading to a linear switched-system model (Mayer et al., 2015, Feng et al., 2015). Many strategies for the waterside subsystem assume that the total cooling load is a known parameter (Ma et al., 2012b, Powell et al., 2013, Deng et al., 2015), which effectively decouples the two subsystems, assuming the load estimate is near-optimal.
A final challenge is the presence of nonlinearities throughout the system. For the airside system, bilinear terms arise from the product of temperatures and flow rates (Ma et al., 2015), while for the waterside, equipment models are often polynomial in input variables (Lee et al., 2012). These difficulties can be eliminated by linearizing along a reference trajectory (Deng et al., 2015), but the resulting solution can be inaccurate if the reference trajectory is suboptimal. Successive linearizations can be performed until convergence (Oldewurtel et al., 2012), although convergence to a global optimum is not guaranteed. For both the airside and waterside systems, care is needed to balance model accuracy with computational complexity.
The remainder of this paper is organized as follows. In the next section, we present the hierarchical structure for the proposed controller and compare to other approaches in the literature. We then discuss some of the practical considerations for this controller. Next we present a brief case study simulating the proposed controller on a large cooling plant. The paper concludes with a brief description of the first, recently completed large-scale application of the ideas in the Stanford Energy Systems Innovations Project, and a discussion of what new control theoretic results might prove useful in this new class of applications.
Section snippets
Control structure
Due to the large number of zones on the airside and the discrete decisions on the waterside, a monolithic optimization problem considering all aspects of the problem in detail would be difficult to maintain and computationally intractable for online use. Therefore, we decompose the problem into a high-level subproblem that considers both the airside and waterside subsystems in approximate form and two low-level subproblems that consider each of the subsystems in more detail. Setpoints
Assumptions and simplifications
In the high-level problem, both the airside and waterside systems are modeled in only approximate form. For the airside system, two main simplifications are made. First, it is assumed that the decision variable is the cooling load delivered to the zone, rather than temperature setpoint for a local controller. This reduction allows the local controller model to be omitted. Second, the detailed zone models are reduced by assuming certain collections of zones are completely coupled and can thus be
System description
As an example system, we consider a large central cooling plant serving a campus of buildings. The cooling plant consists of eight conventional chillers with supporting pumps and cooling towers. Each chiller has minimum and maximum cooling capacities of 2.5 MW and 12.5 MW for a total plant capacity of 100 MW cooling. The nonlinear model and piecewise-linear approximation for each chiller is shown in Fig. 3. Chilled water supply temperature is fixed at 5.5 °C. The central plant also contains a
Application – Stanford Energy Systems Innovations project
Stanford University recently completed a $485-million Stanford Energy System Innovations (SESI) project to replace completely their 155-building campus heating and cooling system (Fig. 9). Johnson Controls, Inc. designed the control system for the new system. The deployed control system is approximately one-half of the top and bottom levels shown in Fig. 2. The waterside system is modeled similarly to the approach described in this paper, while the airside load is determined from historical
Economic versus tracking problems
After even a cursory examination of Figs. 5–, we can conclude that there is no tracking problem of the type considered in the vast majority of the MPC theory literature. Traditional MPC theory (stabilize the origin) was fashioned after the dominant application in the chemical process industries, which was to maintain a plant for reasonably long times at a fixed steady-state setpoint determined by another layer, the so-called real-time optimization (RTO) layer. One can debate whether this early
Conclusions and future outlook
Large-scale commercial applications provide a great opportunity for cost savings through optimal control of their HVAC systems. The existing industry-standard technology is not capable of achieving these savings. In this paper, a scalable decomposition has been presented for control of the coupled airside and waterside systems. The simulation results show that this control architecture can be used for large-scale applications with a large central plant and hundreds of zones.
Future research
Acknowledgments
The authors are grateful to Johnson Controls, Inc. for sample data, equipment models, and research funding. The authors gratefully acknowledge the financial support of the NSF through grant #CTS-1603768.
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