Nonlinear Model Order Reduction of Power Grid Networks using Quadratic Manifolds

Abstract: The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is essential for reducing this complexity, conventional approaches in power systems predominantly rely on linear projection methods. Such linear subspaces have limited capability for representing the inherently nonlinear swing dynamics of synchronous machines, often resulting in poor approximations and inefficient compression. To address these limitations, this paper introduces a quadratic manifold-based model order reduction (MOR) framework to accelerate the transient dynamic simulations in power systems. The proposed method combines the linear proper orthogonal decomposition (POD) basis with a learned quadratic correction term that minimizes the reconstruction error. This yields a scalable MOR strategy capable of handling strongly nonlinear behaviors, particularly those arising during fast-acting faults, where linear techniques typically fail. The method is tested on a range of benchmark power system models of increasing size and complexity. In addition, we provide a detailed numerical algorithm for constructing the quadratic manifold, along with the corresponding implementation code.