In this paper we construct an energy function for multi-machine power systems with doubly-fed induction generator-based wind turbine (DFIGWT) according to a synchronous-generator-mimicking (SGM) model of the DFIGWT. An SGM model is proposed to approximate the dynamics of a DFIGWT. Similar to the modelling of a synchronous generator (SG)

the internal dynamics of a DFIGWT are also described with differential equations of newly constructed virtual rotor angle and internal electromotive force (EMF) in the SGM model. Moreover

the power flow of a DFIGWT is expressed by nonlinear functions of its virtual rotor angle and internal EMF. The SGM model bridges the gap between the irregular and complex modelling of DFIGWTs and the well-developed energy function construction techniques for SG models. Based on the SGM model

a numerical energy function is constructed for power systems with DFIGWT generation. Both theoretical analysis and numerical studies were undertaken to validate that the proposed energy function satisfies the necessary conditions for an energy function of a power system.