Reconstructable dynamic simulation models of modern variable-speed wind turbines (WTs), which are integrable into any simulation software, are crucial to the scientists investigating the contribution of WTs to counteracting the current power system stability issues. The structural similarity between a doubly fed induction-generator-based (DFIG-based) WT model and a full-scaleconvertor-based (FSC-based) WT model using induction generator offers the possibility of integrating them into a combined modular model with little effort and the same used parameter set. This article presents a combined root mean square (RMS) WT model, which contains a DFIG-based WT and a FSC-based WT using induction generator. The model is designed based on fundamental machine and converter equations and can be applied for classical network stability analyses. Furthermore, analogous well-performing initialization procedures for both DFIG-based and FSC-based WT models are also introduced. As an example, to demonstrate the performance of the WT model in frequency stability studies, the model is extended with a droop-based fast frequency response (FFR) controller and is implemented in a MATLAB-based RMS simulation tool. The results of the case studies confirmed a solid functionality of initialization procedures. Furthermore, they illustrate feasible and comparable general behavior of both WT models as well as their plausible responses in the event of a frequency drop in a 220 kV test system.