Convex optimisation of phase-shifting transformer taps in a high-throughput, topology-changing congestion management

Sammanfattning

Electricity grid congestion management requires transmission system operators to implement non-costly remedial actions -- including topological changes and phase-shifting transformer adjustments -- to prevent line overloads. Real-time operational constraints necessitate efficient computational approaches like linearised power flow approximations on high-throughput architectures to perform a combinatorial search for remedial actions. While an existing topology optimiser for congestion management addresses bus splits, coupler openings, and line switching, phase-shifting transformer set point adjustments have been neglected. This thesis extends the existing high-throughput combinatorial topology optimiser to include phase-shifting transformer set points, which can be modelled as a convex, box-constrained, non-differentiable optimisation problem. By summarising the literature and performing numerical experiments on real-world grids, we compare three algorithmic classes of ascending mathematical complecity: direct search, proximal subgradient-based, and proximal primal-dual methods. We conclude that the proximal subgradient method with constant step length performs best when considering quality of results, speed, and integration into the existing software.