Thomas Schmitt, Tobias Rodemann, Jürgen Adamy, "Application of Pareto Frontiers in an Economic Model Predictive Controlled Microgrid", GMA-Fachausschuss Treffen, 2019.

The increase of renewable energies and a trend to decentralization lead to a need of managable strategies for energy commitment in small microgrids. Intuitively, economic model predictiv control (EMPC) is a profound approach for this task, due to its capabilities of optimizing an control sequence with respect to constraints and future predictions. To apply EMPC, we model a medium-sized company building as a second-order linear time-discrete model. The microgrid in grid-connected mode includes storage systems, renewable energies and couplings between the electrical and heat energy system. As states we use the energy of a stationary battery and the building’s temperature. All uncontrollable impacts such as the critical power demand or air temperature are respected as disturbances acting on the system. For the MPC control approach, a cost function consisting of two competing objectives is formulated, i. e. resulting monetary costs and comfort costs in form of quadratic temperature deviations from a given setpoint. Furthermore, to respect the many-objective nature of the optimization problem in the single objective framework of model predictive control, Pareto optimization is applied. I. e., in every time step, the 2D-Pareto frontier is constructed. Then, a human decision maker (HDM) can decide which weighting to choose. Since this methodology shall be used to support the HDM in charge over a microgrid, the Pareto frontiers are obtained for filtered objectives in a decision space, which is easier to relate to (in contrast ot the objective space). Using real-world data from 2018, the model is simulated with auto-detection of the Pareto frontier’s knee point. The results show that the chosen trade-off varies significantly over time. However, once long-time simulations are at hand, taking the mean of the chosen weights for a complete year does give similar results to using the auto-detection of knee points, i. e. monetary costs are reduced slightly in cost of a small higher temperature deviation. Simulations with data from the first six months in 2019 show that the detected mean weighting still works well with new data. In summary, our results show that using Pareto optimization over long periods is useful to obtain mean weights. Once they are determined, they can be used for future control resulting in similar costs like the Pareto frontiers knee points.