Tuning of Synchronous-Frame PI Current Controllers in Grid-Connected Converters Operating at a Low Sampling Rate by MIMO Root Locus

Current controller performance is key in grid-connected power converters for renewable energy applications. In this context, a challenging scenario is arising in multi-megawatt 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 proportional-integral 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. First, 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.