Multi-Objective Building Energy Management Optimization with Model Predictive Control

Today’s goals for the reduction of CO2 emissions are significantly impacting both the civil and the industrial sector. The increasing share of renewable energy sources leads to more volatile and challenging conditions for power consumption. The building sector is responsible for approximately a third of both CO2 emissions and energy consumption in Germany. At the same time, it offers the potential to adapt to the changing conditions by the intelligent use of energy storage systems. These can, e. g., be stationary batteries, electric vehicles at charging stations, heat tanks or the building itself. The control system for the power flow between these elements is called a building energy management (BEM) system. As the control strategy, Model Predictive Control (MPC) is an obvious choice. It allows optimal control while incorporating forecasts of, e. g., power demand, renewable energy production and air temperature. However, in a complex control setting such as BEM, multiple contradicting objectives are to be minimized. For example, next to the reduction of monetary costs, the building’s temperature is supposed to be kept at a comfortable level, electric vehicles have to be charged sufficiently, battery degradation should be kept low and CO2 emissions have to be reduced. To directly optimize real-world objectives such as the examples given above, Economic Model Predictive Control (EMPC) can be utilized, in which the cost function for the optimal control problem (OCP) does not need to be quadratic, but can be of arbitrary form. However, if multiple objectives have to be respected, usually this is done in form of a weighted sum. Thereby, the weights are chosen either from experience or such that all objectives are of the same magnitude. While this is a reasonably simple approach, it neglects that, especially for BEM systems, the OCP varies significantly with the volatile outer conditions. Therefore, the trade-off which is chosen by the fixed weights varies over time, too. The simultaneous optimization of contradicting objectives is called multi- objective optimization (MOO). Usually, the set of all ’optimal’ solutions is approximated and a (human) decision maker (DM) afterwards selects a solution which represents his preferences the most. This is appropriate in the case of one-time optimizations, which is usually the case in MOO. However, we want to use MOO for the permanent control of a BEM system. Therefore, we propose an extended conceptualization of dynamic MOO, which is the systematic combination of MPC and MOO. At every time step, a multi-objective OCP is formulated and an approximation of the Pareto front is derived as its solution, i. e. the set of all optimal compromises. Then, a solution is automatically chosen. To this end, we present two different options. In the metric-based automatized decision making strategy, the Pareto front is first normalized. Then, a metric is calculated for every solution and the solution with the best value is chosen. We present two normalization schemes and three metrics a DM can choose from. In the preference-based automatized decision making strategy, preferences formulated by the DM a priori are utilized. First, a knee region is determined from the normalized Pareto front to exclude solutions which are too extreme. Then, the preferences are used to construct a hyperplane with which a solution from the knee region is finally selected. The applicability of the proposed methods to the BEM problem is shown in long-term simulations. To this end, we show how the most important elements in a BEM system can be modeled while obtaining well-solvable convex optimization problems. Furthermore, we present a new method to determine an approximation of the Pareto front which is more apt for the case of dynamic MOO and its varying conditions