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Abstract In this study, the implementation of different corona discharge models in a transient program for overhead multiconductor lines based on the implicit Crank‐Nicolson Finite Difference Time Domain method is presented. Among different corona models available in the literature, two empirical models (Gary's and Suliciu's models) and a physics‐based model (Malik's model) are discussed, which are broadly used in EMT programs, and their predictions under fast‐front lightning surges and slow‐front switching impulses are assessed. The authors critically review the dynamic capacitance approach in terms of numerical accuracy, when dealing with slowly varying voltages, and applicability, regarding dispersive models assuming a non‐instantaneous charge‐voltage relation. The alternative voltage‐controlled generator approach is proposed, which is successfully included in the implicit Crank‐Nicolson scheme. One of the objectives of this study is to show how different corona models may predict overvoltages with huge discrepancies, depending on the transient waveform and the propagation distance, despite the similarity of the q‐v hysteresis curves. More evident discrepancies between models under fast‐front voltage waves are reported, rather than for switching impulses. The consistency of these results in terms of the models' features and q‐v curves is analysed, highlighting the necessity for new engineering tools for corona simulation of general predictive capability.