In high voltage direct current power transmission, the need to filter the non-sinusoidal current wave forms drawn by the converters from the ac supply has long been acknowledged. Assessment of the harmonic content of these waveforms to the best accuracy possible is a desirable objective to aid filter design. The conventional analytical technique necessitates making simplifying assumptions and produces only approximate results. Such practical considerations as system unbalance cannot be taken into account. The objective of the research was to perform in-depth analyses of hvdc transmission links, by developing a mathematical model which, in addition to perfectly balanced conditions, allows for the following practical operational abnormalities: (i) Unbalanced 3-phase ac supply voltages (ii) Unbalanced converter transformer impedances (iii) Asymmetrical thyristor valve triggering, whilst not making the usual assumptions of infinite dc side inductance and zero ac system impedance. In other words to develop a completely comprehensive mathematical model. The initial approach was to develop the tensor analysis of a six-pulse Graetz bridge supplied first by a star-star, and then by a star-delta connected transformer. A twelve-pulse converter system was then investigated by modelling the series connection of these two arrangements. The technique of diakoptlcs was introduced and combined with the previous tensor analysis to model a complete dc link with a twelve pulse converter at each end of a transmission line. The diakoptic approach enables the full circuit to be torn, for the purpose of the analysis, into the two twelve pulse converters and the dc line. Summary The final stage of the development of the model involved the inclusion of a more sophisticated representation of the ac system impedance and the addition of tuned or damped filters at the ac busbars. To verify the program, computed results from the mathematical model are compared with corresponding experimental results obtained from a laboratory-scale model of a typical hvdc link configuration. Comparisons are also made with conventionally based calculations involving the assumptions included in the computer-based results, in order to investigate the relative accuracy of the computed solution.