This article considers the data-driven modeling of a class of phase-controlled wireless power transfer (WPT) systems, where the load may vary slowly with respect to time. The dominant mode analysis suggests that a model of the Hammerstein type, which consists of a static nonlinearity function, followed by a linear time-varying model with a pure time delay, is the best structure to describe the input-output relationship of the system. On this basis, we derive a small-signal model that is linear in the variables in order to aid control design and allow the associated model parameters to be estimated from sampled input-output data using the standard refined instrumental variable (RIV) method. In the presence of a time-varying load, however, the plant model parameters may not be correctly estimated if the load response is not removed. In order to address this problem, a new recursive RIV method is proposed, in which an effective technique is introduced to track the load response, so allowing the parameters and time delay of the time-varying model to be accurately estimated. The effectiveness of the proposed method is verified by applying it to both a simulation model and a laboratory system.