A Root-Locus Design Methodology Derived from the Impedance/Admittance Stability Formulation and Its Application for LCL Grid-Connected Converters in Wind Turbines

This paper presents a systematic methodology for design and tuning of the current controller in LCL gridconnected converters for wind turbine applications. The design target is formulated as a minimization of the current loop dominant time constant, which is in accordance with standard design guidelines for wind turbine controllers (fast time response and high stability margins). The proposed approach is derived from the impedance/admittance stability formulation, which, on one hand, has been proved to be suitable for controller design when active damping is implemented and, on the other hand, it has been also proved to be very suitable for system level studies in applications with a high penetration of renewable energy resources. The tuning methodology is as follows: firstly, the physical system is modelled in terms of the converter admittance
and its equivalent grid impedance; then, a sensitivity transfer function is derived, from which the closed-loop eigenvalues can be calculated; finally, the set of control gains that minimize the dominant time constant are obtained by direct search optimization. A case study that models the target system in a low power scale is provided and experimental verification validates the theoretical analysis. More specifically, it has been found that the solution that solves the minimization of the current controller time constant (wind turbine controller target) also corresponds to a highly damped electrical response (robustness provided by the active damping).