## 2 Combined Inertial Control of Wind Turbine
### Principle of Combined Inertial Control
However, at the end of the frequency regulation phase, as the absolute value of the rate of change of frequency becomes smaller, the output power support is further reduced, which hinders the restoration of the power system frequency. Therefore, the virtual inertia control method is mostly used to support the transient frequency and cannot continuously participate in the frequency regulation, and it is necessary to avoid the problem of secondary frequency drop in the speed recovery phase. Droop control is a simulation of the power-frequency static characteristic curve of the primary frequency regulation of a synchronous generator, which is also referred to as proportional control or ramp control. It responds directly to the power system frequency deviation and can provide continuous support for the frequency deviation. The input signal is the power system frequency deviation, and the output signal is the increment of electrical power output from the WT. The increment of electrical power output of the WT varies linearly with the deviation of the power system frequency. As shown in the following equation:  
\[\Delta P=-\frac{1}{R}\Delta f \tag{5}\]  
where \(R\) is the droop coefficient. The specific control implementation of droop control is shown in Figure 3.  
Figure 3: Schematic diagram of droop control. Figure 2: Virtual inertia control. In contrast to virtual inertia control, droop control employs the frequency deviation signal as its input, which provides greater power assistance in the vicinity of the frequency nadir. However, it has a slower response time compared to virtual inertia control and is disadvantaged by inadequate power support during the initial stages of frequency regulation. Virtual inertia control can have a suppressive effect on the high frequency deviation rate in the power system, while droop control mainly serves to reduce the power system frequency deviation, but both have their own drawbacks when acting individually. When the system frequency changes, if only the virtual inertia control is used, the output power involved in the process of frequency regulation fluctuates greatly and stops working after the system frequency drops to the lowest point, so it cannot continuously participate in frequency regulation. If droop control is used alone, the frequency response is slow and cannot provide support at the beginning of the frequency change, and the effect of frequency regulation is poor when the amount of frequency change is small. In order to better realize the participation of the WT in primary frequency regulation and ensure system frequency security, the existing research introduces a combined inertial control strategy consisting of both virtual inertia control and droop control. The introduction of both frequency deviation and frequency change rate in the WT active control link, so that the rotor kinetic energy actively responds to the system frequency change, can further improve the frequency tuning capability of the WT. Its additional active reference values are expressed as follows:  
\[\Delta P=-K_{\text{df}}\frac{\text{d}f}{\text{d}t}-K_{\text{pf}}\Delta f \tag{6}\]  
where \(K_{\text{df}}\) is the virtual inertia control parameter and \(K_{\text{pf}}\) is the droop control parameter. The values of \(K_{\text{df}}\) and \(K_{\text{pf}}\) can be adjusted to change the values of \(\Delta P\), which can further affect the WT inertia support capacity and speed recovery time after frequency regulation. The basic control block diagram of the combined inertial control is shown in Figure 4. The high-pass filter allows only the transient component of the frequency to pass, and the low-pass filter is used to avoid interference from noise during the measurement. Combined inertial control combines virtual inertia control and droop control, which can provide powerful power support in both the initial phase of the system frequency response and the range near the frequency nadir. However, the setting of the control parameters in the application is complicated and subject to external influence.