  The linearization of a power flow (PF) model is an important approach for
simplifying and accelerating the calculation of a power system's control,
operation, and optimization. Traditional model-based methods derive linearized
PF models by making approximations in the analytical PF model according to the
physical characteristics of the power system. Today, more measurements of the
power system are available and thus facilitate data-driven approaches beyond
model-driven approaches. This work studies a linearized PF model through a
data-driven approach. Both a forward regression model ((P, Q) as a function of
(theta, V)) and an inverse regression model ((theta, V) as a function of (P,
Q)) are proposed. Partial least square (PLS)- and Bayesian linear regression
(BLR)-based algorithms are designed to address data collinearity and avoid
overfitting. The proposed approach is tested on a series of IEEE standard
cases, which include both meshed transmission grids and radial distribution
grids, with both Monte Carlo simulated data and public testing data. The
results show that the proposed approach can realize a higher calculation
accuracy than model-based approaches can. The results also demonstrate that the
obtained regression parameter matrices of data-driven models reflect power
system physics by demonstrating similar patterns with some power system
matrices (e.g., the admittance matrix).
