Multi-objective optimization of smart grid operations via preventive maintenance scheduling using time-dependent unavailability

This paper presents a method for multi-criteria optimization of system operations using transient operation models. Real systems often combine long-living components with rapid repairs, creating challenges for numerical integration due to fine discretization requirements. These challenges significantly increase the computational cost when evaluating renewal processes with recurrent terms of quadratic complexity in mission time. To address this, we derive new mathematical formulas for evaluating unavailability and operational costs of components under periodic, age-based preventive restoration. The key innovation is a decomposition of the renewal equation: repair-related terms are approximated analytically, eliminating the need for fine discretization throughout the process. A special formula is introduced for components with uniformly distributed repair times and mean time to repair much shorter than mean time to failure, applicable to many real-world systems. The accuracy of the proposed approach is validated against Monte Carlo simulations, showing significant reduction in computational effort. This efficiency enables repeated evaluations in optimization tasks, demonstrated on a real-world case involving interconnected energy and communication infrastructure in the Czech Republic. A multi-objective NSGA-II algorithm is employed to optimize the preventive replacement policy, minimizing both system maintenance cost and expected downtime. We also explore systems with components of non-zero initial age. Results show that relying solely on asymptotic approximations may lead to suboptimal strategies, potentially worsening performance. However, allowing preventive renewal of selected components at time zero enables identification of superior solutions.