This paper introduces a sensitivity-based approach for the efficient calculation of the post-disturbance, steady-state conditions in VSC-based MTDC power grids subject to generation outages and VSC disconnections. This approach is useful for the N-1 contingency analysis, a crucial tool in power system control centres. In order to maintain a high degree of fidelity, the approach considers state-of-the-art VSC control strategies: converters with DC voltage regulation, power-injection control, DC voltage/power droop control, and converters imposing frequency regulation on passive grids. The speed-governing response of power plants is also considered, enabling accurate calculations of AC/DC power flows and AC system frequencies. Indeed, the derived sensitivity factors permit the primary frequency response of the AC systems and DC grid to be efficiently assessed, something that would require several hours of simulation by standard electromagnetic transient (EMT) simulators. Evidently, this novel approach allows a much faster calculation of the AC/DC network’s post-disturbance conditions than is possible with dynamic simulation tools. A formulation with such modelling versatility and practicality does not currently exist elsewhere.The usefulness of this novel formulation has been confirmed using an MTDC system comprising six VSC-connected AC grids and a 13-bus DC grid. The disconnections of VSC units and power plants have also been evaluated. The study shows that the post-disturbance, steady-state conditions computed by the sensitivity-based approach agree well with those obtained by full dynamic simulations, because the relative errors between the two fundamentally different methods are smaller than 0.1% for the AC system frequencies and smaller than 4% for the AC and DC transmission line power flows.