Current controller performance is key in grid-connected power converters for renewable energy applications. In this context, a challenging scenario is arising in multi-MW wind turbines, where sampling and switching frequencies tend to be lower and lower as power ratings increase. This strongly affects achievable control time constant. With this perspective, this paper presents a systematic procedure for accurate dynamics assessment and tuning of synchronous-frame PI current controllers, which is based on linear control for multiple input multiple output (MIMO) systems. The dominant eigenvalues of the system are calculated with explicit consideration of time-delay and cross-coupling terms, two factors which clearly impair the system dynamics when considering a low sampling frequency. The proposed methodology is summarized as follows. Firstly, the plant and controller matrices are modeled in state-space. Subsequently, the characteristic polynomial of the closed-loop system is obtained and a computer-aided parametric analysis is performed to calculate the MIMO root locus as a function of the control gain. By its inspection, it is possible to identify the gain which minimizes the current closed-loop time constant. This tuning is suitable for wind turbine applications, taking into consideration cascaded-control structures and grid-code requirements. The validity and accuracy of the analysis is fully supported by experimental verification. Index Terms—Ac/dc power conversion, current control, pulse width modulation converters, wind power generation.