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This study proposes a novel network sensitivity-based approach to solving complex power flow calculation problems in real time. A new sensitivity factor, named Jacobian-based distribution factor (JBDF), is used for the calculation of active and reactive power flow in transmission systems. It is derived from the Jacobian matrix of the base case Newton-Raphson power flow solution, and kept constant during real-time line flow calculation. Unlike well-known distribution factors, such as generation shift distribution factor (GSDF), generalised generation shift distribution factor (GGDF) and Z-bus distribution factor (ZBD), this approach reflects changes in complex injection power. Changes in load conditions from base case loads, with either conforming or non-conforming changes in complex power in each bus, can be used to rapidly compute active and reactive power flow without iterations. The proposed approach was tested on IEEE 14-Bus and 30-Bus systems. Numerical results demonstrate that the proposed approach is not only superior to previous distribution factors, but also compares favourably with the Newton-Raphson power flow method. It is well suited to real-time applications in steady-state security control and optimal dispatch.