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This paper and a companion paper  develop the digital-computer techniques for the dynamic representation of HVDC power links. A digital-computer program is developed which may represent many circuit configurations, different modes of control, and protective devices, and provides a model which offers both accuracy and flexibility. The formation of a mathematical model which represents the converters and their associated ac systems by differential, algebraic, and Boolean equations is described. The requirements of a computer calculation have been born in mind during the construction of this mathematical model. A new topological technique for the representation of converters is introduced. This technique overcomes the problems of representing the discrete switching processes which occur in converter operation. The utilization of tensor analysis and diakoptics facilitates the construction of a flexible mathematical model of the complete systems of multiconverter stations and associated ac circuitry. The techniques presented are specifically designed for the dynamic simulation of HVDC systems; however the theory may be applied to other circuit prolems where switching processes occur.