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Determination of the most economic strategies for supply and transmission ofelectricity is a daunting computational challenge. Due to theoretical barriers,so-called NP-hardness, the amount of effort to optimize the schedule ofgenerating units and route of power, can grow exponentially with the number ofdecision variables. Practical approaches to this problem involve legacyapproximations and ad-hoc heuristics that may undermine the efficiency andreliability of power system operations, that are ever growing in scale andcomplexity. Therefore, the development of powerful optimization methods fordetailed power system scheduling is critical to the realization of smart gridsand has received significant attention recently. In this paper, we propose forthe first time a computational method, which is capable of solving large-scalepower system scheduling problems with thousands of generating units, whileaccurately incorporating the nonlinear equations that govern the flow ofelectricity on the grid. The utilization of this accurate nonlinear model, asopposed to its linear approximations, results in a more efficient andtransparent market design, as well as improvements in the reliability of powersystem operations. We design a polynomial-time solvable third-ordersemidefinite programming (TSDP) relaxation, with the aim of finding a nearglobally optimal solution for the original NP-hard problem. The proposed methodis demonstrated on the largest available benchmark instances from real-worldEuropean grid data, for which provably optimal or near-optimal solutions areobtained.

A Scalable Semidefinite Relaxation Approach to Grid Scheduling