Stability and Uncertainty Propagation in Power Networks: A Lyapunov-Based Approach With Applications to Renewable Resources Allocation

The rapid increase in the integration of intermittent and stochastic renewable energy resources (RER) introduces challenging issues related to power system stability. Interestingly, identifying grid nodes that can best <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">support</i> stochastic loads from RER has gained recent interest. Methods based on Lyapunov stability are commonly exploited to assess the stability of power networks. These strategies approach quantifying system stability while considering: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> simplified reduced order power system models that do not model power flow constraints, or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> data-driven methods that are prone to measurement noise and hence can inaccurately depict stochastic loads as system instability. In this paper, while considering a nonlinear differential algebraic equation (NL-DAE) model, we introduce a new method for assessing the impact of uncertain renewable power injections on the stability of power system nodes/buses. The identification of stable nodes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">informs</i> the operator/utility on how renewables injections affect the stability of the grid. The proposed method is based on optimizing metrics equivalent to the Lyapunov spectrum of exponents; its underlying properties result in a computationally efficient and scalable stable node identification algorithm for renewable energy resources allocation. The developed framework is studied on various standard power networks.