This thesis describes a new algorithm for the harmonic analysis of power systems. Existing non-linear models are incorporated into a structure that allows very general configurations that are linked by linear ac and dc systems. A three phase loadflow is included at the power frequency and the steady-state is solved iteratively using a real-valued, positive frequency, full Newton technique. This structure allows electrical and non-electrical variables to be solved simultaneously. The resultant process is fast, robust and shows excellent comparison with time domain simulation. The harmonic characteristics of large power conversion installations such as HVdc and high-pulse LVdc are investigated. The effects of system operation on the harmonic transfer through an HVdc link are investigated using the multiple run feature of the algorithm. Also, the representation of bipolar HVdc links is investigated and justifications for accurate dc system representation shown. The harmonic domain converter has been generalised, and a representation of the zigzag transformer developed. Using this the effects of outage conditions of a high-pulse installation are modelled, and a proposal is given for the minimisation of low order harmonic generation during this condition. Finally, a fast numerical technique for the accurate calculation of non-linear device impedances is described. This is used in conjunction with simplified converter models to assess the impact of the converter on the linear ac system impedance. A comparison is made between the different methods of harmonic analysis and a quantitative assessment of their accuracy given.