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

Abstract

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).

Analysis and Comparison of Notch Filter and Capacitor Voltage Feedforward Active Damping Techniques for LCL Grid-Connected Converters

“…Furthermore, Fig. 1 shows the current controller structures for both active damping strategies, where K(z) is the main current controller, F vd (z) and F n f (z) the two analysed damping actions, which shape the converter admittances [15], [27].…”

“…In practice, L t is set by the transformer leakage. Typical values for the secondary inductance are then in the range [0.06, 0.1] p.u: (wind turbine rated power is used for base calculations) [15].…”

“…where k ad is the active damping gain, and C the nominal value of the LCL filter capacitor. The discrete time implementation, based on the Backward-Euler rule, provides a dominant derivative action only for frequencies below 0.2ω s ; however, in practise ω lcl < 0.2ω s is a quite reasonable assumption to the hardware design constraint [6], [15]. Alternatively, the nonideal generalized integrators have been proposed for scenarios with higher ω lcl [16].…”

“…Active damping techniques, on the contrary, mitigate the effects of the LCL resonance by proper control actions [5], [9]- [11], [13]- [21]; where the use of a filtered capacitor voltage feed-forward [5], [15]- [18] as well as second order notch filters in cascade with the main current controller [21]- [25] are very common approaches, for which the implementation is straightforward.…”

Conformal mapping of impedance stability models for system-level dynamics assessments

“…1. This approach gives an immediate description of system dynamics, which, by some basic design assumptions, can be employed for the design of power electronics controllers [3]. In principle, it is also suitable for an accurate assessment of large power systems [4].…”