This study presents a frequency-domain model of an high voltage direct current (HVDC) transmission link with a line-commutated current-source converter. Using space-vector transfer functions between superimposed oscillations in the control signal and the AC and DC sides, expressions for voltages and currents have been derived. The dynamic properties of the HVDC link, taking the characteristics of the networks on both the AC and the DC sides into consideration, can be studied by applying classical Bode/Nyquist/Nichols control methods. The resulting model was validated by time-domain studies in PSCAD/EMTDC. The model is described in two papers. In this paper (Part I), it has been assumed that the overlap angle during commutation remains constant. It is shown in the validation that this assumption introduces resonances that cause severe errors at certain network conditions. In the second paper (Part II), the model is extended so as to cope with the varying overlap angle in order to bring the frequency-domain model into agreement with the results obtained from time-domain simulations.