Model predictive control

Model Predictive Control (MPC) is the backbone of our control and optimisation algorithms. MPC is an algorithm for controlling a system that uses a mathematical model of that system, in this case a building and its Heating, Ventilation and Air Conditioning (HVAC) equipment. The model predicts the impact of control options on the system cost over a period of time in the future. Using this model, the MPC finds the control setpoints that lead to the lowest system cost over the considered period, while satisfying a number of operational constraints that are also computed by the model. The cost function can be operational cost, CO₂ emission, primary energy use or something else. For example, a building MPC computes the control variables that minimize the heat pump electrical power use for the next three days while maintaining a minimum temperature constraint within the building.

Many different types of models exist. In academic literature, models are often classified based on the type of information that they use. ‘Black box’ models require measurement data from a building - such as building temperature measurements - while ‘white box’ models require physical information about the building, such as the building geometry and the used building materials. Grey box models use a combination of both. For a short introduction into these model types, see this link. Discover in the section below what is unique about our white-box MPC technology.

Our approach & challenge

We have developed an MPC approach that uses white box modelling, implemented using a high level of detail. For this purpose we develop the in-house Modelica library IDEAS, which is available open-source. Instead of modelling a whole building as one zone, each room or group of rooms that has its own HVAC equipment is modelled individually. Furthermore, each building HVAC component is modelled individually. Consequently, the solar heat gains through each window, all heat flow rates, mass flow rates, pressure drops and efficiencies in pumps, fans, valves, heat pumps are computed and can be compared or benchmarked to building measurements. When implemented in an MPC, the mismatch between a model and the real building is corrected over time using measurement data. In fact, we thus use a grey-box approach. The level of detail however creates a clear distinction between what model parts are black or white, so feel free to call it a zebra-box model.

The resulting models typically consist of tens of thousands of equations, compared to a few tens of equations in less detailed models. While computationally much more demanding, these models can be optimised using our Toolchain for Automated Control and Optimisation (TACO). It is the heart and soul of our software, which has been developed and tested over the past years.

MPC in action

A simple example model is illustrated in the figure below. The top right illustrates the schematic that is optimised, which consists of a water-water heat pump, two circulation pump and a valve. Note that the building envelope model is not shown in the figure. We minimise the electrical power of both pumps and the heat pump. Since the valve affects the system pressure drops, it also affects the pump power. The MPC looks for the best control actions (valve position, pump speeds and heat pump power) that still achieve the minimum room temperature of 21 ˚C (red line in top left).

The animation illustrates the process where the solver searches for the correct control actions. Along the way, the floor heating temperature (top right, green), the electrical powers (bottom left) and system mass flow rates (bottom right) fluctuate, but the final solution is a smooth profile where the zone temperature (top left) touches the temperature limit.

Advantages

The main advantage of (white-box) MPC and the focus of Builtwins is to reduce energy use and the associated costs and CO₂ emissions, and to improve thermal comfort. Our approach is designed to be scalable in size and complexity such that it is future-proof, with native support for exploiting time-of-use pricing, self-consumption of locally produced electrical power, etc. The large level of detail has numerous side-effects and potential for future development. To name a few:

1. We only use measurement data during operation such that the controller can be developed and tested during building construction.
2. We do not require an existing BMS implementation since we can directly provide set-points for each physical device. To clarify, we do need an existing BACnet system.
3. We can learn individual component efficiencies from measurement data, monitor them through time and benchmark them to datasheet specifications to monitor the system health.
4. We can identify air filter clogging and component malfunctions by benchmarking the system behavior to the white-box model, flag these malfunctions and compute the associated operational cost increase, which is a valuable input for maintenance scheduling.
5. We unlock flexibility by exploiting the building energy storage.