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This paper discusses the extension of electromechanical stability models of voltage source converter high voltage direct current (VSC HVDC) to multi-terminal (MTDC) systems. The paper introduces a control model with a cascaded DC voltage control at every converter that allows a two-terminal VSC HVDC system to cope with converter outages. When extended to an MTDC system, the model naturally evolves into a master-slave set-up with converters taking over the DC voltage control in case the DC voltage controlling converter fails. It is shown that the model can be used to include a voltage droop control to share the power imbalance after a contingency in the DC system amongst the converters in the system. Finally, the paper discusses two possible model reductions, in line with the assumptions made in transient stability modeling. The control algorithms and VSC HVDC systems have been implemented using both MatDyn, an open source MATLAB transient stability program, as well as the commercial power system simulation package EUROSTAG.