This paper clarifies the operating principles of a controllable reactor of transformer type (CRT). In nature, a CRT is equivalent to a multi-winding transformer for which the low-voltage windings (control windings) operate at short-circuited states in turn. This kind of reactor possesses such advantages as smooth power regulation, low current harmonic content, and fast response. Taking account of the coupling of the control windings, this paper examined the current harmonic content for the work winding by Fourier series decomposition, and thus derived the current harmonic coefficients. Based on the solution of the branch current equation of a multi-winding transformer, and introduction of the concept of equivalent winding impedance, a polygon-type equivalent circuit is proposed for a multi-winding transformer. Subsequently, formulae for the branch impedances of the equivalent circuit are presented. According to the harmonic content constraints, the number of control steps is determined. Then, by combining the MMF and branch current equations, an expanded equation about the winding currents and current-limiting reactances is obtained. According to the feature that the control windings are short-circuited in turn, the current-limiting reactances are calculated for each control winding step by step. At last, based on the proposed equivalent circuit for a multi-winding transformer, a simulation model for a CRT is fabricated with MATLAB/SIMULINK/PSB. The simulation results confirmed the presented work, which underpins the further analysis and design of a CRT.