Data Based Linear Power Flow Model: Investigation of a Least-Squares Based Approximation

Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow (LPF) model while the model error is the main concern. Therefore, various linear power flow models have been proposed in literature and dedicated to seek better linear models. Many linear power flow models are based on some kind of transformation/simplification/Taylor expansion of AC power flow equations. In this paper, numerical performance and theoretical explanation of the data-based linear power flow model are investigated. The direct least-squares method with complete orthogonal decomposition is designed for addressing collinear data and big data. The resulted linear power flow model is named as least-squares distribution factors (LSDF) and its performance is investigated in cold-start applications. It is found that LSDF is in fact an approximation of the optimal LPF with minimum mean square error. It is also proved that the LSDF can give an accurate estimation of total system losses. Comprehensive numerical testing show that the LSDF can work very well for system with large load variations. The average error of LSDF is only about 1% of the average error of power transfer distribution factor (PTDF) in numerical testing.