Robust Design of Multi-Energy Systems Accounting for Mixed-Integer Operational Problems

TL;DR

This paper analyzes how nonconvexities affect the robustness of multi-energy system designs identified by heuristics and proposes a hybrid method for verification.

Contribution

It investigates the impact of common nonconvexities on heuristic robustness and introduces a hybrid approach to verify design robustness in multi-energy systems.

Findings

Noncurtailment of surplus energy can cause heuristic failure due to nonconvexities.

Storage complementarity does not compromise robustness if curtailment is allowed.

The proposed hybrid method can verify the robustness of heuristic-identified designs.

Abstract

Identifying robust designs for multi-energy systems is computationally challenging. As rigorous approaches are often computationally intractable, heuristics are employed to generate candidate designs. One example is the feasibility time-step heuristic by Teichgraeber et al. [Appl. Energy, 275, 115223, 2020]. We theoretically investigate how three common nonconvexities, i.e., piecewise-linear energy inflow-outflow relationships, minimal part-loads, and storage complementarity, affect the robustness of designs identified by this heuristic. We find that, if surplus energy cannot be curtailed, any of these nonconvexities may cause the heuristic to fail. If curtailment is allowed, storage complementarity does not compromise robustness, and convex piecewise-linear inflow-outflow relationships can be reformulated linearly. However, minimal part loads may lead to failure of the heuristic. Furthermore, if the objective function of the operational problem is not jointly convex in the uncertain variables and the operational variables, the heuristic may fail. We consider an illustrative multi-energy system, where minimal part-loads and nonconvex dependence of the objective function on heat-pump efficiency are identified as possible failure modes. We propose a hybrid method that discretizes integer variables and embeds the dual of the lower-level problem into a single-level formulation to verify whether a design identified by the heuristic is robust. The results show that the feasibility time-step heuristic may identify robust designs despite the presence of nonconvexities, but the success is case-dependent. Hence, the heuristic can serve as a first step in identifying robust designs; however, when robustness guarantees are required, rigorous methods are necessary.