Complex-domain Design and Robustness Analysis for the Control of SSCI in DFIG-based Wind Farms

The paper proposes a complex domain control and robustness analysis approach to damping of Sub-Synchronous Control Interactions (SSCI) in the IEEE first and second benchmark models and is applied to wind farms with Doubly-Fed Induction Generators (DFIG). Two complex pole-placement control laws are proposed to eliminate oscillations at different levels of compensation as well as at varying speed conditions. The complex domain framework reduces the system dimensions by half and facilitates the direct placement of the system poles in the left-half plane, ensuring stability and performance. An observer is designed to estimate the variables that would be difficult to measure at a high sampling rate but are useful to stabilize the systems. Time-domain simulations in MATLAB/Simscape show that the proposed controllers are successful in eliminating oscillations. By leveraging a complex domain representation, the feedback system is analyzed as a single-input single-output (SISO) system. This simplifies the visualization of the robustness of the controllers and makes it possible to compute the gain, phase, and delay margins of the feedback system. These margins are validated in simulations on the full-scale model. The proposed complex pole-placement controller is then compared to other excitation control-based approaches to demonstrate its effectiveness.