  Linear power flow (LPF) models are essential in power system analysis.
Various LPF models are proposed, but some crucial questions are still remained:
what is the performance bound (e.g., the error bound) of LPF models, how to
know a branch is applicable for LPF models or not, and what is the best LPF
model. In this paper, these crucial questions are answered and a general
formulation (GF) for evaluating the performance of LPF models is proposed. The
GF actually figure out two core difficulties, the one is how to define the
definition range of the LPF models, and the second is how to analytically
obtain the best LPF model and evaluate the performance of a given LPF model.
Besides, the key factors that affect the performance of LPF models are also
analyzed through the proposed framework. The case studies compare the proposed
LPF model with the DC power flow model, the physical-model-driven LPF model,
and the data-driven LPF model, and the results show the effectiveness as well
as the superiority of the proposed method.
