Convex Relaxations of Probabilistic AC Optimal Power Flow for Interconnected AC and HVDC Grids

TL;DR

This paper develops a robust chance constrained AC-OPF method for interconnected AC and HVDC grids, incorporating wind uncertainty, HVDC control, and scalable solution techniques, demonstrated on large realistic systems.

Contribution

It introduces a novel chance constrained AC-OPF formulation for AC and HVDC grids with a tractable approximation, joint constraints, and scalable solution methods.

Findings

Achieves near-global optimality guarantees on large systems

Ensures compliance with joint chance constraints under uncertainty

Outperforms DC-OPF in probabilistic violation metrics

Abstract

High Voltage Direct Current (HVDC) systems interconnect AC grids to increase reliability, connect offshore wind generation, and enable coupling of electricity markets. Considering the growing uncertainty in power infeed and the complexity introduced by additional controls, robust decision support tools are necessary. This paper proposes a chance constrained AC-OPF for AC and HVDC grids, which considers wind uncertainty, fully utilizes HVDC control capabilities, and uses the semidefinite relaxation of the AC-OPF. We consider a joint chance constraint for both AC and HVDC systems, we introduce a piecewise affine approximation to achieve tractability of the chance constraint, and we allow corrective control policies for HVDC converters and generators to be determined. An active loss penalty term in the objective function and a systematic procedure to choose the penalty weights allow us to obtain AC-feasible solutions. We introduce Benders decomposition to maintain scalability. Using realistic forecast data, we demonstrate our approach on a 53-bus and a 214-bus AC-DC system, obtaining tight near-global optimality guarantees. With a Monte Carlo analysis, we show that a chance constrained DC-OPF leads to violations, whereas our proposed approach complies with the joint chance constraint.