A Two-Layer Network Equivalent With Local Passivity Compensation With Applications to Hybrid Simulations of MMC-Based AC–DC Grids

A frequency-dependent network equivalent (FDNE) is essential to capture wide-band frequency dynamics in the hybrid simulation of large-scale modular multi-level converter based ac-dc grids. The FDNE model must be enforced to be passive, ensuring the numerical stability in time-domain simulations. However, existing passive enforcement techniques based on global optimization perturbations cannot guarantee convergence, accuracy, and efficiency simultaneously. To address the issues, a two-layer FDNE (T-FDNE) model is developed for the ac grids. The two layers, namely, detailed layer and equivalent layer, have their admittances derived by perturbation test and analytical approach, respectively. The passivity of the T-FDNE model is guaranteed by the proposed local passivity compensation technique using auxiliary rational functions. Since no optimization is required and the passivity is enhanced locally, the convergence, accuracy, and efficiency can be improved considerably. By incorporating the T-FDNE model into the interface model of transient (TS) and electromagnetic transient hybrid simulations, wide-band frequency interactions, especially those of very high frequency, can be reflected effectively. The performance (efficiency and accuracy) of the T-FDNE model as well as of the hybrid simulation method has been validated on a modified and practical ac-dc system in China.