N-$k$ Security Assessment With Quantum Annealing

Suppose one is interested in identifying the weakest link of the electrical system at 3 simultaneous faults caused by an extreme weather event. Current techniques cannot identify this; however, knowing such information can help reinforce the system at the weakest link to increase system security. Current techniques typically apply a forward process to the security assessment: assign a contingency list, study its impact, analyse the list to obtain a shortlist, and improve the system. However, this process does not scale well to the number of contingencies, specifically, when one is interested in the combination of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> faults, as the process needs to run once per combination. This paper proposes a new backwards process using quantum effects from quantum annealing (QA). Our proposal formulates a quadratic optimisation to find the worst-case N-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> contingency using disjunctive power transfer distribution factors. Then, we use a quantum annealer and propose a search algorithm to solve the problem, using the distribution of solutions to obtain the shortlist of contingencies. We propose a meta-heuristic to make the approach feasible on quantum computers with limited qubits. The case studies focus on the IEEE 118-bus system, showing a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$200 \times$</tex-math></inline-formula> speed-up for 50 faults compared to exhaustive search. The case study extrapolates to the 2383wp system, showing the approach scales well to larger power systems; however, the current quantum hardware limits the number of single faults to consider to around 50. Case studies demonstrate weak lines can be identified for reinforcement by analysing the QA solution distribution, potentially improving system security for multiple N-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> faults.