As more non-synchronous renewable energy sources participate in power systems, the system's inertia decreases and becomes time dependent, challenging the ability of existing control schemes to maintain frequency stability. System operators, research laboratories, and academic institutes have expressed the importance to adapt to this new power system paradigm. However, power dynamics have been modeled as time-invariant, by not modeling the variability in the system's inertia. To address this, this work proposes a new modeling framework for power system dynamics to simulate a time-varying evolution of rotational inertia coefficients in a network. Power dynamics are modeled as a hybrid system with discrete modes representing different rotational inertia regimes of the network. Using this new modeling framework for power dynamics we study a framework to design a fixed learned controller based on datasets of optimal time-varying LQR controllers. We test the performance of the controller in a twelve-bus system. By adding virtual inertia we can guarantee stability of high-renewable (low-inertia) modes. The novelty of our work is to propose a design framework for a stable controller with fixed gains for time-varying power dynamics. This is relevant because it would be simpler to implement a proportional controller with fixed gains compared to a time-varying control.




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