The International Electrotechnical Commission Standard 61400-27-1 was published in February 2015. This standard deals with the development of generic terms and parameters to specify the electrical characteristics of wind turbines. Generic models of very complex technological systems, such as wind turbines, are thus defined based on the four common configurations available in the market. Due to its recent publication, the comparison of the response of generic models with specific vendor models plays a key role in ensuring the widespread use of this standard. This paper compares the response of a specific Gamesa dynamic wind turbine model to the corresponding generic IEC Type III wind turbine model response when the wind turbine is subjected to a three-phase voltage dip. This Type III model represents the doubly-fed induction generator wind turbine, which is not only one of the most commonly sold and installed technologies in the current market but also a complex variable-speed operation implementation. In fact, active and reactive power transients are observed due to the voltage reduction. Special attention is given to the reactive power injection provided by the wind turbine models because it is a requirement of current grid codes. Further, the boundaries of the generic models associated with transient events that cannot be represented exactly are included in the paper.