A Compact Qubo Formulation For Solving Transmission Expansion Planning

Long-term infrastructure planning involves high costs and has become increasingly complex, making cost-effective strategies essential. Within this context, mathematical optimisation represents a viable tool. However, the discrete nature of investment decisions in Transmission Expansion Planning (TEP) renders the problem NP-hard, with solution space growing exponentially as investment options increase. Given recent advances in quantum computing and the potential of higher computational power, we explore the use of Quantum Annealing (QA) for optimising the Mixed-Integer Nonlinear Programming problem (MINLP) formulation of TEP. We propose a method for incorporating various types of constraints into the Quadratic Unconstrained Binary Optimization problem (QUBO) formulation required by QA, considering current hardware limitations in computational memory and topology. The approach is refined to mitigate infeasibility and tested on a 3-node test network using the D-Wave Advantage2 system1.6, owing the small test network size to the previously mentioned hardware limits.