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The high-power self-commutated voltage-source converter (VSC) and current source converter (CSC) are the key control devices in HVDC, flexible ac transmission systems (FACTS) and distribution FACTS systems. To achieve the expected control objectives, suitable control strategies must be implemented based on the available devices, system, and control techniques. The self-commutated ac/dc converters control the electrical power by generating controllable ac fundamental and dc average outputs. These controllable outputs are controlled by the conducting state combinations of the converter switching devices, driven by their gate signals. The gate signals are specified by fundamental parameters of frequency, amplitude, and phase angle. The converter system model for describing the relation between the system-state variables and the gate signal parameters is essential for the converter system control. This paper (part I) derives the state variable equations for transmission systems using VSC while the second paper (part II) is for the transmission systems using CSC. The self-commutated converter systems provide active and reactive power control flexibility, but their nonlinearity makes their control difficult. The linearized state equations by using feedback linearization are presented to enable the controller design by using linear control theory.