(60d) Mixed-Integer Model Predictive Control for Online Scheduling of HVAC Equipment in Commercial Buildings

With increased attention toward the negative impact of carbon and other greenhouse gas emissions on global climate, it is clear that broad changes need to be made to primary energy consumption habits. Within commercial buildings, heating, ventilation, and air conditioning (HVAC) systems are a prime target for improved supervisory control, as they are active with time-varying intensity throughout the day and combined to account for 51% of commercial building energy use in 2010. While across-the-board reduction would be ideal, existing architecture often precludes any sweeping cuts without sacrificing performance. Furthermore, due to cyclic occupation, resource consumption in buildings is highly time-varying, and specifically for electricity, the onus of meeting transient demand profiles is placed directly on suppliers who in turn pass extra costs on to consumers. Unfortunately, complicated and possibly uncertain pricing structures leave central plant operators largely adrift with only minimal feedback in the form of a monthly utility bill. Thus, existing heuristics for large-scale HVAC operation result in high cost and low efficiency, and so we propose a scheduling and control formulation to make equipment use and energy purchase decisions in a systematic manner without sacrificing occupant comfort.

In campuses or large buildings, major HVAC equipment is typically grouped in a “central plant,” with thermal demand being met by producing hot or chilled water centrally (in the “waterside system”) and piping it to local air-handlers where it ultimately affects air temperatures (the “airside system”). By utilizing both active and passive storage, this equipment can temporally shift energy consumption to take advantage of time-varying utility price structures and significantly reduce costs. Thus, we formulate an optimization- and model-based control system to operate central plant equipment at the lowest energy cost while meeting relevant constraints. This approach represents integration of model predictive control (MPC) and traditional production scheduling. MPC has enjoyed great success in the chemical process industries, but the binary on/off choices needed to pick from among the available equipment mean existing techniques using only continuous inputs are not directly applicable. By contrast, although many of the decisions made in scheduling problems are binary, yes-or-no choices, they are typically made on a much slower time scale, and thus care is required to balance complexity and online tractability.

Our proposed model applies to two similar cases: (1) when a model for building temperature is available to determine online how much heating or cooling is required to meet temperature constraints; and (2) when a forecast of heating and cooling demand is provided and thus a building model is not needed. In the first case, models must be able to predict with reasonable accuracy the rate of cooling that is required to maintain temperature within established comfort bounds. Since actual temperature regulation is handled by local zone controllers, model accuracy is not critical to maintaining comfort, but better airside models result in better waterside decisions. A benefit to this methodology is that pre-cooling and other passive storage techniques appear implicitly in optimal solutions insofar as they are economically optimal. For the second case, following a known demand forecast eliminates the need for an airside model, thus reducing problem size. This means that more accurate equipment models can be used, leading to better performance. However, the formulation need not change beyond removing variables and constraints that are no longer necessary. By addressing both cases with the same formulation, we ensure that our approach is modular and thus can be applied to the widest variety of buildings.

In either case, the objective is to minimize economic cost while meeting relevant production constraints (i.e., maintaining comfort levels in the building and/or meeting heating and cooling forecasts). This optimization requires making on/off and setpoint decisions for central plant equipment such as chillers, heat-recovery chillers, pumps, etc. Furthermore, the optimization must decide how to make use of active thermal storage tanks to temporally shift production to more favorable times. Thus, each optimization must consider a sufficiently long horizon to capture available cost savings. However, because of uncertainty inherent in forecasts of demand and ambient conditions, the controller must also be able to quickly re-optimize when provided with new data. This fast, closed-loop implementation avoids an overly conservative policy that would be required by slow, intermittent optimization, but it also imposes restrictions on model complexity. To this end, we formulate our optimization as a mixed-integer linear program (MILP) for which sophisticated solvers are available, allowing large instances to be solved in real time. A key consideration is the nonlinear dependence of heating/cooling production on resource consumption in process equipment. To ensure that the controller accurately predicts economic cost, nonlinear equipment models are approximated as piecewise-linear to enable use in the MILP formulation without introducing significant error to the cost calculation. This approximation scheme provides the flexibility to trade accuracy for computational speed.

After describing the mathematical formulation of the optimization problem, we present a case study for the proposed control architecture. For a system with four chillers and two temperature zones, we show that computation is sufficiently fast to find provably optimal solutions. For a larger number of temperature zones, we show that, although provably optimal solutions are much harder to find, it is still relatively easy to find quality sub-optimal solutions suitable for feedback control. For a system with a forecast for simultaneous chilled and hot water demand, we show that our model can include heat-recovery chillers with no modifications. This allows rejecting heat to process streams where it can be reused instead of simply venting to the ambient. Using a prediction horizon of 48 h with a 1 h timestep, these optimizations can be solved to optimality within 5 min, which is suitably fast to implement online. We also show improved performance relative to existing heuristic methods. A key advantage of this approach is that it makes few assumptions about the central plant equipment and can thus be applied to existing buildings without expensive retrofit. Whereas existing methods make scheduling decisions using heuristics on a slow time scale, our approach, by augmenting a scheduling model with feedback control techniques, allows equipment utilization schedules to be created and revised online and in real time, resulting in improved economic performance.