Data Based Linearization: Least-Squares Based Approximation

Abstract: 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.