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The doubly fed induction generator (DFIG) is the most widely applied wind turbine in practice and contains a dc-link capacitance in its back-to-back converter to deliver the generated power and to provide dc-link voltage for converters. In small-signal analysis, fluctuations in dc-link voltage can be caused by perturbations injected at the ac-terminals of DFIG system and the dc-link voltage fluctuations can affect the outputs of ac-terminals in reverse. It has been found in former publications that this dc-link dynamic behavior is able to shape the small-signal characteristics of DFIG system and influence the system stability. However, the modeling and analysis for the dc-link dynamic behavior is lacked, which makes it difficult to indicate the influencing factors of dc-link dynamics and how to suppress the negative influence of weakly-damped dc-link dynamics on the DFIG system. In this paper, the mechanism of dc-link dynamics and how dc-link dynamics affect the small-signal characteristics of DFIG system are described at first. Then, an indicator function that models the dc-link dynamic behavior is firstly defined and then obtained based on harmonic linearization method. The proposed indicator function will be applied to describe the impedance shaping effect of dc-link dynamics on DFIG system, indicate the influencing factors of dc-link dynamics and analyze the influence of weakly-damped dc-link dynamic behavior. Several experiments based on Control-hardware-in-loop (CHIL) platform will also be carried out to verify the analytical models and theoretical analysis in this paper.INDEX TERMS Control-hardware-in-loop (CHIL), dc-link dynamics, doubly fed induction generator (DFIG), impedance modeling, indicator.

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With the increasing penetration of renewable energy, wind turbines based on doubly fed induction generators (DFIG) are becoming more and more important in the power system. The impedance reshaping control strategy based on the virtual impedance method can be utilized to solve the stability problem of DFIG-grid interconnected system under the weak grid. However, the stability issues caused by phase locked loop (PLL) is more complicated due to the frequency coupling characteristic. This paper presents an improved control strategy of DFIG system based on a symmetrical PLL, in which the frequency coupling characteristic can be avoided and the system can be simplified as a SISO system that facilitates the design of virtual impedance. The influence of symmetrical PLL on the operation of DFIG system is studied, and an improved impedance reshaping control strategy is proposed. Simulation and experimental results are conducted to verify the effectiveness of the proposed impedance reshaping control strategy.

When grid side converter (GSC) is connected to weak grid, the small signal instability can happen due to terminal characteristics of the GSC that are incompatible with the grid impedance. This issue is not of wide concern in previous studies of direct power control (DPC) of GSC. By small signal analysis, it is shown that the impedance characteristic of the conventional direct power control GSC is not compatible with the inductive grid impedance in weak grid due to its constant power load behavior. To solve the problem, instead of feeding the DPC controller with direct measured voltage and current, a Kalman filter (KF) is used to obtain filtered output current and a double second-order generalized integrator (DSOGI) is used to obtain filtered voltage at the point of common coupling (PCC). These strategies change the impedance characteristic of the GSC dramatically and make it suitable to operate in weak grid where SCR is 2, while the rapid power response is preserved. The proposed strategy is verified through simulation and controller hardware in loop (CHIL) tests.