With the access to a large number of new energy sources, the fault characteristics of multi-terminal HVDC based on MMC (MMC-MTDC) become increasingly complex. One of the key problems that urgently needs to be solved is the fast and accurate fault identification and fault location. To this end, a fault identification and location method for wind-photovoltaics-electrochemical energy storage-pumped storage hydropower complementary power plant transmitted by flexible DC transmission was proposed. Firstly, the flexible transmission system of the wind-solar-storage-storage-complementary power station was constructed. Based on this, a new method of Teager energy operator energy entropy was proposed, and the ratio of Teager energy operator energy entropy of positive and negative poles of measurement points was used to construct fault pole selection and section identification criteria. Then, a fault location method combining variational mode decomposition (VMD) and Teager energy operator (TEO operator) was proposed for the identified fault lines. Finally, PSCAD/EMTDC was used for simulation. The results show that the proposed identification method can accurately determine the fault line, and the proposed fault location method can realise fault location within 2 ms time window of fault occurrence. The error rate is not more than 2.55%, and it has strong ability to withstand transition resistance.