Effect of prediction uncertainties on the performance of a white-box model predictive controller for district heating networks

Abstract

The performance of a model predictive controller (MPC) depends on the accuracy of the controller model and predictions of system disturbances. This paper studies the effect of prediction uncertainties and/or an imperfect state observer on the performance of a white-box MPC applied to a small-scale district heating network by performing a co-simulation with a detailed emulator model. This effect is studied for both a non-linear program (NLP)-based MPC and a mixed-integer NLP (MINLP)-based MPC. The results show a limited impact of prediction uncertainties when using a perfect state observer, with electricity use and thermal discomfort changing by only ▪ to ▪ and ▪/day/building to 0.56 ▪/day/building. An MPC with perfect predictions and a simple state observer only impacts the MPC's trade-off between electricity use and thermal discomfort: the former increases by 2–▪ but the latter decreases by 0.01–▪/day/building. The combined effect of both simplifications has a significant impact with an increase in electricity use and thermal discomfort of 2–▪ and 0.35–▪/day/building, but MPC still outperforms a conventional rule-based controller. The MINLP-based MPC better predicts the actual system behaviour, but its performance is similar compared to the NLP-based MPC in terms of electrical energy use and thermal comfort.