Modelling state spaces and discrete control using MILP: computational cost considerations for demand response

Abstract

INTRODUCTION: Demand response (DR) has been proposed as a mechanism to induce electricity cost reductions and is typically assumed to require the adoption of time-differentiated electricity prices. Making the most of these requires using automated energy management systems to produce optimised DR plans. Mixed-integer linear programming (MILP) has been used for this purpose, including by modelling dynamic systems (DS).

OBJECTIVES: In this paper, wecompare the computational performance of MILP approaches for modelling state spaces and multi-level discrete control (MLDC) in DR problems involving DSs.

METHODS: A state-of-the-art MILP solver was used to compute solutions and compare approaches.

RESULTS: Modelling state spaces using decision variables proved to be the most efficient option in over 80% of cases. In turn, the new MLDC approaches outperformed the standard one in about 60% of cases despite performing in the same range.

CONCLUSION: We conclude that using state variables is generally the better option and that all MLDC variants perform similarly.