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High-voltage direct-current (HVDC) systems play an important role in modern energy grids, whereas efficient and accurate models are often needed for system-level studies. Due to the inherent switching in HVDC converters, the detailed switch-level models are computationally expensive for the simulation of large-signal transients and hard to linearize for small-signal frequency-domain characterization. In this paper, a dynamic average-value model (AVM) of the first CIGRE HVDC benchmark system is developed in a state-variable-based simulator, such as Matlab/Simulink, and nodal-analysis-based electromagnetic transient program (EMTP), such as PSCAD/EMTDC. The 12-pulse converters in the HVDC system are modeled with a set of nonlinear algebraic functions that are extracted numerically. The results from the average-value models are compared with the results of the detailed simulation to verify the accuracy of the AVMs in predicting the large-signal time-domain transients. The

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