Precise knowledge of the plant time constant L/R is essential to perform a thorough analysis and design of the current control loop in voltage source converters (VSCs). From the perspective of the current controller dynamics in the low-frequency range, such plant time constant is also suitable for most cases in which an LCL filter is used. As the loop behavior can be significantly influenced by the VSC working conditions, the effects associated to converter losses should be included in the model, through an equivalent series resistance. In addition, the plant inductance may also present important uncertainties with respect to the value of the VSC L/LCL interface filter measured at rated conditions. Thus, in this paper, a method is presented to estimate both parameters of the plant time constant, i.e., the equivalent inductance and resistance in the plant model of current-controlled VSCs. The proposed technique is based on the evaluation of the closed-loop transient responses of both axes of the synchronous reference frame when a proportional-integral current controller is implemented. The method gives a set of resistance and inductance values that should be employed for a rigorous design of the current controllers. Experimental results validate the approach.