  Linearization of power flow is an important topic in power system analysis.
The computational burden can be greatly reduced under the linear power flow
model while the model error is the main concern. Therefore, various linear
power flow models have been proposed in literature and dedicated to seek the
optimal approximation. Most linear power flow models are based on some kind of
transformation/simplification/Taylor expansion of AC power flow equations and
fail to be accurate under cold-start mode. It is surprising that data-based
linearization methods have not yet been fully investigated. In this paper, the
performance of a data-based least-squares approximation method is investigated.
The resulted cold-start sensitive factors are named as least-squares
distribution factors (LSDF). Compared with the traditional power transfer
distribution factors (PTDF), it is found that the LSDF can work very well for
systems with large load variation, and the average error of LSDF is only about
1% of the average error of PTDF. Comprehensive numerical testing is performed
and the results show that LSDF has attractive performance in all studied cases
and has great application potential in occasions requiring only cold-start
linear power flow models.
