# Dynamic Frequency Support from a DFIG-Based Wind Turbine Generator via Virtual Inertia Control
## 4 Proposed Virtual Inertia Control Method of the DFIG-based WTG  
As in [15; 18], the additional power, \(\Delta P_{in}\), calculated by the virtual inertia control is expressed:  
\[\Delta P_{in}=K\times f_{sys}\times\frac{df_{sys}}{dt}, \tag{11}\]  
where \(K\) indicates the control gain of virtual inertia control loop. The effect of different control gains on the virtual inertia control is investigated under a low wind speed condition (see Figure 4). Three different control factors of 0, 10, and 50 are considered in the investigation under a low wind speed. The use of a large control gain displays better performance on the maximum _df/dt_ and frequency nadir, as more power is injected to the grid during the initial stage of disturbance. However, when a larger control gain is applied, such as 50 in the investigation, the rotor speed decreases to the minimum value; as a result, stalling of the DFIG-based WTG occurs. Even the released energy in the initial stage of disturbance is more than that when control gain is set to 10, and the maximum frequency deviation is large. Therefore, the use of a large gain can improve the dynamic frequency stability; however, it may have a possibility of causing stalling of the DFIG-based WTG and further worsening the frequency nadir. The use of a small fixed control gain for the conventional strategy is inevitable to prevent the stalling of the DFIG-based WTG, thereby restricting the contribution to improving the frequency stability during disturbance. To improve the maximum _df/dt_ and frequency nadir and prevent the DFIG-based WTG from stalling, this paper proposes a kinetic energy-dependent control gain. The following sections describe how to define the proposed control gain. The kinetic energy available of the DFIG-based WTG (\(E_{av}\)) at \(\omega_{r}\) can be expressed as:  
\[E_{\mathrm{av}}=0.5\times J_{DFIG}\times(\omega_{r}^{2}-\omega_{\mathrm{min} }^{2}), \tag{12}\]  
where \(J_{DFIG}\) indicates the moment of inertia of the DFIG-based WTG. In this study, the kinetic energy of a DFIG-based WTG is normalized by its rated capacity; thus, the unit of the normalized kinetic energy is seconds. For the DFIG-based WTG, the capability of virtual inertia control is dependent on the \(E_{av}\), thus, the control gain, \(K_{pro}\), in the proposed strategy can be represented as:  
\[K_{pro}=C\times(\omega_{0}^{2}-\omega_{\mathrm{min}}^{2}), \tag{13}\]  
where \(C\) and \(\omega_{0}\) mean the virtual inertia control factor and the rotor speed before disturbance, respectively; the second term of (13) indicates the kinetic energy available from the DFIG-based WTG prior to disturbance. Figure 3: Mechanical power curves and MPPT operation curve of a DFIG-based WTG. Figure 5 displays the proposed control gain at various rotor speeds when \(C\) is set to 100. The control gain is proportional to the rotor speed of the DFIG-based WTG. In the high-rotor-speed region, the use of a large control gain releases more kinetic energy to improve the frequency stability; the use of a small control gain for the low speed region can release suitable energy to support the dynamic system frequency while preventing the DFIG-based WTG from stalling. As shown in Figure 1, to remove the noise components of the measured system frequency in the virtual inertia control loop, a first order low pass filter is implemented; \(T\) is set to 100 ms in this research. Further, \(P_{n\!f}\) calculated by virtual inertia control strategy is limited by the rate of change of power and maximum power limiters to prevent the excessive mechanical stress. The setting of the maximum power limiter is 1.1 times that of the nominal power of the DFIG-based WTG; the setting of the rate of change of power limiter is 0.45 p.u./s [27]. Figure 4: Influence of different control gains of the virtual inertia control strategy at the wind speed of 6.5 m/s: (**a**) system frequencies; (**b**) active powers; (**c**) rotor speeds. Synchronous generators with the IEEEG1 steam governor model (type B) are selected.