The electric power grid is undergoing a rapid change predominantly driven by high penetration levels of renewable energy resources (RERs) such as wind and solar. These resources are interfaced with the power grid through power electronic inverters that use control algorithms to define their performance characteristics. As a group, these types of resources are commonly referred to as inverter-based RERs (IB-RERs). While IB-RERs use power electronic controls to change active and reactive power injection, the fast inverter controls, separating the power source from the grid, have changed grid dynamics and posed new challenges to maintaining reliable and safe grid operation. Moreover, the variable nature of IB-RERs generation under uncertain weather conditions further challenge the grid operation under uncertain operating conditions resulting from an imbalance in electricity generation and demand. To effectively manage IB-RERs for providing reliable grid services, this dissertation studies the impact of IB-RERs on grid operation at the transmission- and distribution- levels while considering uncertain operating conditions. More specifically, the probabilistic collocation method is introduced to quantify the uncertainty of renewable generation and load demands on the distribution system operation. Also, the probabilistic collocation method is integrated with grid assessment to assess the grid stiffness under uncertain operating conditions. In addition, the impact of transmission-level disturbances on solar generator operation in distribution systems is investigated by a real-time electromagnetic simulator. The proposed method and analysis results are useful for guiding grid planning and operation to address the emerging issues of integrating the high penetration of IB-RERs into the power grid for reliable grid services.