Atomic Scheduling of Appliance Energy Consumption in Residential Smart Grid

TL;DR

This paper introduces an atomic scheduling approach for appliance energy consumption in smart grids, modeling the problem as a Boolean-convex optimization and proposing a successive convex relaxation method for efficient approximate solutions.

Contribution

It formulates the atomic scheduling problem using an optimal routing framework and develops a successive convex relaxation technique for efficient suboptimal solutions.

Findings

The proposed method achieves solutions close to the global optimum.

It effectively minimizes cost and peak-to-average ratio.

Numerical results validate the approach's efficiency and accuracy.

Abstract

The current formulation of the optimal scheduling of appliance energy consumption uses as optimization variables the vectors of appliances' scheduled energy consumption over equally-divided time slots of a day, which does not take into account the atomicity of appliances' operations (i.e., the unsplittable nature of appliances' operations and resulting energy consumption). In this paper, we provide a new formulation of atomic scheduling of energy consumption based on the optimal routing framework; the flow configurations of users over multiple paths between the common source and destination nodes of a ring network are used as optimization variables, which indicate the starting times of scheduled energy consumption, and optimal scheduling problems are now formulated in terms of the user flow configurations. Because the atomic optimal scheduling results in a Boolean-convex problem for a convex objective function, we propose a successive convex relaxation technique for efficient calculation of an approximate solution, where we iteratively drop fractional-valued elements and apply convex relaxation to the resulting problem until we find a feasible suboptimal solution. Numerical results for the cost and peak-to-average ratio minimization problems demonstrate that the successive convex relaxation technique can provide solutions close to, often identical to, global optimal solutions.