Risk-Constrained Optimization Framework for Generation and Transmission Maintenance Scheduling Under Economic and Carbon Emission Constraints

Power generation and transmission systems face increasing challenges in coordinating maintenance planning under economic pressure and carbon emission constraints. This study proposes an optimization framework that integrates preventive maintenance scheduling with operational dispatch decisions, aiming to achieve both cost efficiency and emission reduction. A bi-layer scenario-based mixed-integer optimization model is formulated, where the upper layer determines annual preventive maintenance windows, and the lower layer performs hourly economic dispatch considering renewable generation and demand uncertainty. To manage the exposure to extreme carbon outcomes, a Conditional Value-at-Risk (CVaR) constraint is embedded, jointly controlling economic and environmental risks. A parallel cut-generation decomposition algorithm is developed to ensure computational scalability for large-scale systems. Numerical experiments on six-bus and IEEE 118-bus systems demonstrate that the proposed model reduces total carbon emissions by up to 32.1%, while maintaining cost efficiency and system reliability. The scenario analyses further show that adjusting maintenance schedules according to seasonal carbon intensity effectively balances operation and emission targets. The results confirm that the proposed optimization framework provides a practical and scalable approach for achieving low-carbon, reliable, and economically efficient power system maintenance planning.