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This paper develops a mathematical model for the dynamic simulation of ac-dc systems. The basic features of the proposed model are: All the subsystems and components of a realistic HVDC scheme are included in the model. The power system components are modelled using the exact differential equations derived from their three phase equivalent networks and therefore the model can give the instantaneous values of voltage, current and power at any point of the system. The considerable amount of computation involved is substantially reduced using tensor techniques as the differential equations of the system are automatically assembled to deal with the time varying topology of the network caused by the switching action of the valves. Line and bus faults are also simulated using tensor techniques and this increases considerably the flexibilty of the computer program. The basic disadvantage of the model is the extensive computation required and is, therefore, suitable only for applications where accuracy is essential, as for the final testing of new converter control systems.