A Scalable Semidefinite Relaxation Approach to Grid Scheduling

TL;DR

This paper introduces a scalable semidefinite relaxation method for large-scale power grid scheduling that accurately models nonlinear electricity flow, leading to more reliable and efficient power system operations.

Contribution

It presents the first polynomial-time semidefinite relaxation capable of solving large-scale, nonlinear power scheduling problems with thousands of units.

Findings

Successfully applied to real-world European grid data

Achieves near-global optimal solutions

Improves power system reliability and market transparency

Abstract

Determination of the most economic strategies for supply and transmission of electricity is a daunting computational challenge. Due to theoretical barriers, so-called NP-hardness, the amount of effort to optimize the schedule of generating units and route of power, can grow exponentially with the number of decision variables. Practical approaches to this problem involve legacy approximations and ad-hoc heuristics that may undermine the efficiency and reliability of power system operations, that are ever growing in scale and complexity. Therefore, the development of powerful optimization methods for detailed power system scheduling is critical to the realization of smart grids and has received significant attention recently. In this paper, we propose for the first time a computational method, which is capable of solving large-scale power system scheduling problems with thousands of generating units, while accurately incorporating the nonlinear equations that govern the flow of electricity on the grid. The utilization of this accurate nonlinear model, as opposed to its linear approximations, results in a more efficient and transparent market design, as well as improvements in the reliability of power system operations. We design a polynomial-time solvable third-order semidefinite programming (TSDP) relaxation, with the aim of finding a near globally optimal solution for the original NP-hard problem. The proposed method is demonstrated on the largest available benchmark instances from real-world European grid data, for which provably optimal or near-optimal solutions are obtained.