Abstract: The variable speed constant frequency（USCF） electrical power system is a new type of aircraft power supply, which contains an alternating generator and a cycloconverter. This paper has summed up the work of cycloconverter, and obtained four fundamental classes of circuit construction of the closed-loop system, which have twelve operating models. The mathematical model for each fundamental class of the circuit construction has been introduced in thia paper. These mathematical models can be used in digital simulation. The result of the simulation will be significant for the optimal design of the whole system.