With deployment of measurement units

fitting static equivalent models of distribution networks (DNs) by linear regression has been recognized as an effective method in power flow analysis of a transmission network. Increasing volatility of measurements caused by variable distributed renewable energy sources makes it more difficult to accurately fit such equivalent models. To tackle this challenge

this letter proposes a novel data-driven method to improve equivalency accuracy of DNs with distributed energy resources. This letter provides a new perspective that an equivalent model can be regarded as a mapping from internal conditions and border voltages to border power injections. Such mapping can be established through 1) Koopman operator theory

and 2) physical features of power flow equations at the root node of a DN. Performance of the proposed method is demonstrated on the IEEE 33-bus and IEEE 136-bus test systems connected to a 661-bus utility system.