An Original Investigation into Quantum Computing Algorithms for Optimisation Problems in Nigerian Power Grid Management

The optimal scheduling of generation dispatch, power flow optimisation, and fault location in Nigeria's complex and fragmented power grid constitute large combinatorial optimisation problems for which quantum computing algorithms offer theoretical advantages over classical approaches, yet no investigation of quantum algorithm applicability to Nigerian grid optimisation problems has been conducted. This study investigated the applicability and performance of quantum computing algorithms for Nigerian power grid optimisation, developing original algorithm adaptations suited to the structural characteristics of the Nigerian grid. Three optimisation problems were formalised: generation unit commitment for the NBET capacity market, voltage stability optimisation in the 330 kV TCN transmission network, and fault localisation in distribution networks. A systematic mapping of these problems onto quantum algorithm frameworks was performed, including the Quantum Approximate Optimisation Algorithm for unit commitment, Variational Quantum Eigensolver for voltage stability, and Grover's amplitude amplification for fault search. Simulations were run on IBM Qiskit Aer simulators and selected circuits executed on the IBM Quantum ibmq_manila 5-qubit hardware. QAOA depth-6 for unit commitment on a 10-unit problem achieved solutions within 3.1 percent of the classical MILP optimal with 10,000 circuit shots. Noise characterisation on real IBM hardware confirmed that current quantum hardware limitations prevent scaling beyond approximately 20 variables for NISQ-era devices. A theoretical complexity analysis demonstrated quantum advantage in the fault localisation problem for network sizes above 500 nodes, providing a concrete threshold above which quantum approaches become computationally competitive. The study constitutes an original quantum-power grid optimisation theoretical contribution.