Optimal Virtual Inertia Placement Considering Battery Degradation Cost in Microgrids

Decreasing system inertia in microgrids due to high penetration of inverter-based resources necessitates enhancing system stability with virtual inertia. Optimal placement of virtual inertia significantly impacts system frequency behavior, making it a crucial consideration in virtual inertia provision. While some studies have employed relatively comprehensive storage device models for optimal virtual inertia placement, they often overlook the cost of battery degradation. The cost of battery degradation should be considered in optimization problem with respect to the importance of battery lifetime. This paper formulates an optimal cost function integrating virtual inertia technology costs, including installation, operation, battery degradation, and replacement. Incorporating battery degradation costs enhances battery health within the grid and provides a more accurate cost estimate for virtual inertia provision. By addressing the non-linearity of optimal virtual inertia placement, previous studies used genetic algorithms to find optimal solutions. with linear optimization methods thereby reducing non-linearity. In this paper replaced genetic algorithms with linear optimization methods to simplify the process of determining the optimal placement of virtual inertia, thereby linearized model for optimal virtual inertia placement problem.