Semi-dynamic optimal placement and relocation of protection and control devices in electrical distribution grids considering protective device failure rates using the 3D-GRAM framework and Double Genetic Algorithm

This study introduces the 3D Distribution Grid Representation and Analysis Model (3D-GRAM) as the foundation for a semi-dynamic approach to the optimal placement and relocation of protection and control devices in distribution networks. Unlike conventional methods that often lack scalable and generalizable topology representations, 3D-GRAM provides a structured modeling framework capable of capturing up to two levels of lateral branching. Its three-dimensional array-based structure integrates seamlessly with optimization algorithms such as the proposed two-phase Double Genetic Algorithm (Double-GA) enhancing convergence in computationally intensive tasks while offering a reusable foundation for broader planning applications. A key contribution of this work lies in the integration of 3D-GRAM with semi-dynamic planning, which divides the economic horizon into shorter intervals to account for time-varying operating conditions and enable adaptive decision-making. Although semi-dynamic optimization typically increases computational complexity, the efficiency of the 3D-GRAM framework mitigates these challenges, ensuring scalability for large-scale systems. The proposed method was validated on an IEEE 85-bus distribution network under four distinct scenarios. Numerical results demonstrated that the Double-GA consistently outperformed the Single-GA, achieving total cost reductions ranging from 0.48% to 2.97% across the evaluated scenarios and sensitivity analyses, while requiring 2–4 fewer devices. Sensitivity analyses further confirmed the robustness of the approach under varying failure probabilities of protection devices, demonstrating that the Double-GA effectively balances additional investment in new devices against the reduction of outage costs while maintaining system reliability. Despite the increase in computation time, the proposed framework remains computationally tractable for planning studies and provides a scalable, adaptive, and economically efficient solution for modern distribution grid planning.