An Efficient Method for the Optimal Control of Microgrids Under Uncertainties using Local Reduction
Summary
Proposes and compares two mathematical formulations for robust microgrid sizing and power scheduling under uncertainties, using a local reduction algorithm that achieves high feasibility rates in Monte Carlo simulations.
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Paper page - An Efficient Method for the Optimal Control of Microgrids Under Uncertainties using Local Reduction
Source: https://huggingface.co/papers/2606.12345
Abstract
Two mathematical formulations for robust microgrid sizing and power scheduling are proposed and compared, with one using binary variables and big-M constraints and the other using continuous nonlinear programming with smooth reformulation of logical constraints.
The problem of optimal sizing and power scheduling in microgrids subject to uncertainties is well known to the control community. Commonly, the optimal control problem is cast as a mixed-integer program to model thelogical constraintsarising in energy storage systems, and is then solved approximately using numerical methods such as the scenario approach. In this paper, we propose and compare two formulations of a robust microgrid sizing and power scheduling optimal control problem withlogical constraintsand uncertainties in the user’s power demand, solar power generation, grid electricity prices and battery efficiencies. The first formulation uses binary variables andbig-M constraints, leading to amixed-integer linear program. The second formulation casts the problem as acontinuous nonlinear programthrough an exactsmooth reformulationof thelogical constraints, consisting of additional modelling variables and non-convex constraints. We then propose a novellocal reduction algorithm, extending an existing method, to solve both problems. The two formulations are compared by evaluating the solutions returned by local reduction using 100,000-sampleMonte Carlo simulationsand achieve promising results, with both averagingfeasibility rates above 90%.
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