A framework of topology-agnostic probabilistic power flow with Gaussian processes

The integration of large-scale renewable energy and distributed generation significantly increases the uncertainty in both power injection and network topology in modern power systems. Traditional Probabilistic Power Flow (PPF) methods, such as Monte Carlo Simulation (MCS), incur prohibitive computational costs and time when exhaustive topological scenarios must be considered. This study presents a robust topology-agnostic probabilistic framework that combines Gaussian Mixture Model (GMM) clustering with cluster-level Gaussian Process Regression (GP). The method utilizes a subset of bus voltage measurements (𝑉𝑚𝑒𝑎𝑠) to form operational mode clusters, thereby bypassing explicit topology encoding. In the prediction phase, new samples are routed via the GMMand evaluated by the corresponding local GP model. This report details the mathematical foundations, engineering implementation, and rigorous validation of the Case9 and IEEE30 test systems. The results indicate that the method achieves extremely low generalization errors (e.g., 𝑀𝐴𝐸 ≈ 2 × 10−4 p.u. in the Case9 system), validating its effectiveness and scalability.