Linearization Error of Power Flow Model Considering the Distribution of State Variables

Linear power flow models are widely used in power system analysis. However, finding the linear power flow model with the minimized error is still a difficult task. Actually, the linearization error of the power flow model is influenced by the power flow formulation and the distribution of variables. In this paper, we focus on the linearization of v
_i
v
_j
in the power flow model, which is a major origin of the linearization error. Based on the general linear power flow model, we derive the linearization of v
_i
v
_j
using different formulation of independent variables. The Copula method is used to describe the joint distribution of (v
_i
, v
_j
). We propose a method to find the optimal Copula function that best fits the actual distribution of the historical data. Finally, an algorithm to obtain the linearization of v
_i
v
_j
with the minimized error is presented. Case studies in the IEEE 118-bus system validate the proposed method.