Mixed-Integer Real-Time Control of a Building Energy Supply System

Abstract

We present a methodology based on mixed-integer nonlinear model predictive control for a real-time building energy management system in application to a single-family house with a combined heat and power (CHP) unit. The developed strategy successfully deals with the switching behavior of the system components as well as minimum admissible operating time constraints by use of a special switch-cost-aware rounding procedure. The quality of the presented solution is evaluated in comparison to the globally optimal dynamic programming method and conventional rule-based control strategy. Based on a real-world scenario, we show that our approach is more than real-time capable while maintaining high correspondence with the globally optimal solution. We achieve an average optimality gap of 2.5% compared to 20% for a conventional control approach, and are faster and more scalable than a dynamic programming approach.

Mixed‐integer NMPC for real‐time supervisory energy management control in residential buildings

“…The solution strategy is described here in a general and condensed form. For a detailed description, refer to [8].…”

“…Therefore, we omit the interim problem formulation here. Following the convexification and relaxation procedures from Section 2, we introduce one-hot encoding similar to [8] here 𝝎(𝑡) ∶ 𝕊 4 → Ω ∶= {0, 1} 2 , but for the integer inputs for the boiler and the heat pump on/off states. Relaxation procedure then replaces 𝝎 ∈ {0, 1} 4 with 𝜶 ∈ [0, 1] 4 .…”

“…To determine an appropriate binary control $$\bm{\omega }^N$$ from an optimal solution $$(\bm{x}^N,\bm{u}^N,\bm{\alpha }^N)$$ that was obtained by discretizing (2) into N time elements, we utilize the novel SCARP procedure using a shortest‐path approach, initially introduced in [15, 16] and successfully applied in [8]. One of the limitations of SCARP is the inability to consider disturbances to the system's states $$x(t)$$ when computing the binary solution from a relaxed optimal one.…”

“…A terminal constraint to keep the heat storage and the battery state on certain levels at the end of the prediction horizon is also imposed. The resulting system control problem is a MIOCP of the same form as in [8] but with a more‐dimensional and complex model described above. Therefore, we omit the interim problem formulation here.…”

“…We shortly summarize the results of a simulation study for the energy system of a single‐family house performed in [8]. The real‐time performance and the resulting quality of the solution have been proved by their high correspondence to the globally optimal solution calculated by the computationally costly dynamic programming (DP) method.…”