Due to the repeated switching, the detailed switchlevel models of electrical machines coupled with power-electronic converters are computationally expensive and hard to linearize for small-signal frequency-domain analysis. Average-value modeling (AVM) has become an effective tool for small-signal analysis of power electronic systems and time-domain transient studies where the details of switching are not important and can be neglected. Recently, a parametric AVM (PAVM) approach has been developed for machine/diode rectifier systems. This paper extends the parametric approach to the machine/thyristor-controlled-rectifier systems, where the thyristor firing may be referenced to either the line voltages or the rotor position. An analytical average model for this system is also developed based on the recently proposed constantparameter voltage-behind-reactance synchronous machine model. The new PAVM is compared against the original switching system, as well as the analytical AVM. It is shown that the PAVM can accurately predict both small-signal characteristics and largesignal transients of the original switching system in light and heavy modes, which represents an advantage over the analytical models which are typically implicit.Index Terms-Average-value model (AVM), impedance characterization, synchronous machine, thyristor rectifier, voltage behind reactance (VBR) model.