A Principal Component Analysis-Based Dimension Reduction Method for Parametric Power Flow

Probabilistic power flow is a fundamental tool for analyzing the probability uncertainty of system states caused by uncertainty factors. A similar and also important topic is to acquire an explicit expression of the implicit function relationship between uncertainty factors (called parameters) and system states, which is termed parametric power flow problem in this paper. However, a great challenge of solving this problem is the curse of dimensionality, i.e., the computational cost increases rapidly with the number of parameters. This paper proposes a principal component analysis-based dimension reduction method for parametric power flow. The proposed method firstly separates parameter directions with large and small function variability by principal component analysis, and then obtains the dimension-reduced parametric power flow model by eliminating directions with small function variability. Results of the IEEE 118-bus system validate accuracy of the reduced model and remarkable computational efficiency improvement of solving the dimension-reduced model.