The linearization of a power flow (PF) model is an important approach forsimplifying and accelerating the calculation of a power system's control,operation, and optimization. Traditional model-based methods derive linearizedPF models by making approximations in the analytical PF model according to thephysical characteristics of the power system. Today, more measurements of thepower system are available and thus facilitate data-driven approaches beyondmodel-driven approaches. This work studies a linearized PF model through adata-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 avoidoverfitting. The proposed approach is tested on a series of IEEE standardcases, which include both meshed transmission grids and radial distributiongrids, with both Monte Carlo simulated data and public testing data. Theresults show that the proposed approach can realize a higher calculationaccuracy than model-based approaches can. The results also demonstrate that theobtained regression parameter matrices of data-driven models reflect powersystem physics by demonstrating similar patterns with some power systemmatrices (e.g., the admittance matrix).
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