This chapter describes the system modelling of two predominant three-phase AC controller configurations, three-phase AC controllers with back-to-back silicon-controlled rectifiers (SCRs) in series with the AC lines with star-connected resistive load and isolated neutral. It discusses the three-phase AC controllers with back-to-back SCRs in series with resistive load connected in delta to the AC lines. System models for three-phase back-to-back connected thyristor AC controllers in series with lines connected to star-connected resistive load with isolated neutral. A single-phase AC controller uses a pair of SCRs connected back-to-back or antiparallel between the supply and the load. Several configurations for three-phase AC controllers are available employing three single-phase AC controllers. There are two categories of AC to AC converters. One is the cycloconverter, which converts the AC input voltage with a given frequency and peak value to a variable amplitude AC output voltage at a desired frequency, different from the frequency of the AC input voltage.