# Fast Stepwise Inertial Control Scheme of a DFIG for Reducing Second Frequency Drop
## 1 Introduction  
The increase in the penetration of renewable energy in electric power systems is expected and planned. Wind power generation has the highest proportion of employment and potential for renewable energy generation. However, wind power generation is a power electronic-based resource that minimally contributes to the inertia response of electric power systems. In addition, increasing the amount of wind power generation can replace traditional synchronous generators (TSGs), leading to low system inertia and primary frequency response [1, 2, 3, 4, 5]. In a low-inertia electric power system, an insufficient inertia response increases the rate of change of frequency and the maximum frequency deviation [6, 7, 8]. In a traditional electric power system, a frequency disturbance, including load connection or generator tripping, reduces the system frequency since TSGs immediately respond to the power imbalance. Initially, the inertia of TSGs supplies the deficit power of the electric power system, and after a few seconds, the generator's governor response activates to prevent the system frequency from further decreasing, thereby stabilizing the system frequency [9]. In a high wind power penetration electric power system, low inertia response and primary frequency response increase the maximum frequency deviation, which drops below the reliability standard. A wide-area power failure may occur during the activation of under-frequency relays [10]. To solve this frequency stability issue, the fastfrequency response (FFR) of the wind turbine generators (WTGs), which improves the lower frequency, was introduced as an auxiliary service [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The present strategies of the WTGs for providing FFR are roughly divided into two types based on their input signals: frequency-based FFR and fixed-trajectory FFR [27; 28; 29; 30; 31; 32; 33]. The use of frequency based FFR modifies the additional control signals to imitate the inertial response and emulate the droop response based on frequency deviation [27; 28; 29]. The authors of [7] suggest a timing-varying droop control coefficient to reduce the SFD. An optimized power point tracking method is suggested, the coefficient of the optimized power point tracking scheme is defined based on the frequency deviation and rate of change of frequency [30]. Fixed trajectory FFR is determined by the predefined power reference rather than the measured frequency; it can also sustain the system frequency better than the frequency-based FFR [31]. Nevertheless, after sustaining the grid frequency, the rotor speed is required to regain optimal speed; this process creates a secondary dip in the system frequency [32]. To lessen the depth of the SFD, the authors of [33] suggested a power reference that decays in a ramp manner. Regaining rotor speed addresses a small constant power reference, reducing the depth of the SFD [34; 35]. However, it is difficult to counterbalance the performance of the second frequency drop and rotor speed recovery. In addition, to reduce the SFD, the authors of [36] suggest a power reference based on mechanical power. However, it is difficult to obtain accurate mechanical power information. Therefore, a two-stage variable coefficient-based controller was constructed for DFIGs [37]. However, the effectiveness of the two-stage scheme strongly relies on the predetermined training of the fuzzy controller. Furthermore, the rotor speed is regained by adjusting the setting of the primary frequency response, and an energy storage system counterbalances the absorbed power. However, these two strategies require more investment. We suggest a fast stepwise inertial control scheme of a DFIG to preserve the FN with less energy released and reduce both the depth of the SFD and the mechanical stress on the wind turbine. A piecewise function for the frequency support phase and rotor speed recovery phase is needed to address these issues.