With the rapid development of power system, applications of classical AC power flow model are limited in the power system industry for its problems of nonlinearity, difficulty to converge and low computational efficiency, especially in large-scale systems. Thus the research of linear power flow is of great significance. Several linear models are introduced in this paper, which have their own advantages and disadvantages. Classical DC power flow model is of great interest in field of online operation for its fast calculation with reasonable accuracy in active power flow, but the voltage magnitude and branch power losses are ignored. This gap is closed by proposing the concept of network losses equivalent power and decoupling of variables which respectively make the calculation of active power flow and voltage magnitude more accurate. Finally, the decoupled linearized equivalent power flow model is proposed, which has a high computational efficiency without the loss of accuracy, and its applicability and robustness are proved in case studies including radial distribution systems and large-scale meshed systems.