This thesis describes a novel harmonic domain approach for assessing the steady state performance of Flexible AC Transmission System (FACTS) devices. Existing harmonic analysis techniques are reviewed and used as the basis for a novel iterative harmonic domain model for PWM FACTS devices. The unified Newton formulation adopted uses a combination of positive frequency real valued harmonic and three-phase fundamental frequency power-flow mismatches to characterise a PWM converter system. A dc side mismatch formulation is employed in order to reduce the solution size, something only possible because of the hard switched nature of PWM converters. This computationally efficient formulation permits the study of generalised systems containing multiple FACTS devices. This modular PWM converter block is applied to series, shunt and multi-converter FACTS topologies, with a variety of basic control schemes. Using a three-phase power-flow initialisation and a fixed harmonic Jacobian provides robust convergence to a solution consistent with time domain simulation. By including the power-flow variables in the full harmonic solution the model avoids unnecessary assumptions regarding a fixed (or linearised) operating point, fully modelling system imbalance and the associated non-characteristic harmonics. The capability of the proposed technique is illustrated by considering a range of harmonic interaction mechanisms, both within and between FACTS devices. In particular, the impact of transmission network modelling and operating point variation is investigated with reference to ac and dc side harmonic interaction. The minor role harmonic distortion and over-modulation play in the PWM switching process is finally considered with reference to the associated reduction in system linearity.