The increasing share of renewable generation leads to new challenges in reliable power system operation, such as the rising volatility of power generation, which leads to timevarying dynamics and behavior of the system. To counteract the changing dynamics, we propose to adapt the parameters of existing controllers to the changing conditions. Doing so, however, is challenging, as large power systems often involve multiple subsystem operators, which, for safety and privacy reasons, do not want to exchange detailed information about their subsystems. Furthermore, centralized tuning of structured controllers for large-scale systems, such as power networks, is often computationally very challenging. For this reason, we present a hierarchical decentralized approach for controller tuning, which increases data security and scalability. The proposed method is based on the exchange of structured reduced models of subsystems, which conserves data privacy and reduces computational complexity. For this purpose, suitable methods for model reduction and model matching are introduced. Furthermore, we demonstrate how increased renewable penetration leads to timevarying dynamics on the IEEE 68 bus power system, which underlines the importance of the problem. Then, we apply the proposed approach on simulation studies to show its effectiveness. As shown, a similar system performance as with a centralized method can be obtained. Finally, we show the scalability of the approach on a large power system with more than 2500 states and about 1500 controller parameters.