## 2 Combined Inertial Control of Wind Turbine
### Principle of Combined Inertial Control  
The energy source of the WT is the wind energy captured by the blade rotation, according to the knowledge of aerodynamics, the mechanical power of the WT can be expressed as follows:  
\[P_{\rm m}=\frac{1}{2}C_{\rm p}(\lambda,\beta)\rho\pi R^{2}v^{3} \tag{1}\]  
where \(C_{\rm p}(\lambda,\beta)\) is the wind energy utilization coefficient; \(\lambda\) is the blade tip speed ratio; \(\beta\) is the pitch angle; \(\rho\) is the air density; \(R\) is the wind wheel radius; \(v\) is the wind speed. The wind energy utilization coefficient reflects the ability of the WT to capture wind energy, and a commonly used functional expression is as follows [16]:  
\[\left\{ \begin{array}{l}C_{\rm p}(\lambda,\beta)=0.22\Big{(}\frac{116}{\pi}- 0.4\beta-5\Big{)}{\rm e}^{-\frac{12.5}{2}}\\ \frac{1}{\pi}=\frac{1}{\lambda+0.08\beta}-\frac{0.035}{\beta^{3}+1}\\ \lambda=\frac{R\omega_{\rm w}}{p}\end{array} \right. \tag{2}\]  
where \(\omega_{\rm w}\) is the WT speed. In order to be able to capture the maximum amount of wind energy and achieve the maximum utilization of wind energy, the WT will generally operate in the maximum power point tracking mode under normal conditions. When the electromagnetic power and mechanical power reach equilibrium, the WT is in a stable operating condition, and the amount of active power produced can be represented by the following equation:  
\[P=P_{\rm m}=0.5\rho\pi R^{2}v^{3}C_{\rm p(opt)}=k\omega_{\rm w(opt)}^{3} \tag{3}\]  
where \(C_{\rm p(opt)}\) and \(\omega_{\rm w(opt)}\) denote the optimal wind energy utilization coefficient and the corresponding optimal WT speed, respectively; \(k\) is the maximum power tracking coefficient of the WT, and \(k=\rho\pi R^{5}C_{\rm p(opt)}/2\lambda_{\rm opt}^{3}\), where \(\lambda_{\rm opt}\) is the optimal blade tip speed ratio. As the penetration of wind power in the power system continues to increase, the proportion of traditional thermal power plants also decreases accordingly, and the inertia level of the power system continues to decrease. At this time, in order to provide sufficient inertia support to the power system, the WT also needs to have the corresponding frequency regulation capability. To enable the WT to provide inertial response, additional control loops with frequency differentiation and frequency deviation feedback are introduced in the converter active control link to enable the WT to provide power support through rotor kinetic energy control during the power system frequency deviation. Rotor kinetic energy control generally consists of virtual inertia control, droop control, combined inertial control, and virtual synchronous generator techniques. In this paper, a combined inertial control method consisting of virtual inertia control and droop control is used. Virtual inertia control enables the WT to adjust the active reference instruction according to the rate of frequency change when the power system frequency changes by simulating the inertia characteristics of the synchronous machine to release or absorb the rotor kinetic energy for the purpose of participating in the power system frequency regulation. Specific control implementation can be referred to in Figure 2.  
In Figure 2, \(\Delta P\) is the additional active reference signal obtained by the virtual inertia control. It can be acquired through a direct correlation with the fluctuation rate of the power system frequency. The active reference signal can be expressed as follows:  
\[\Delta P=-K_{\text{f}}\frac{\text{d}f}{\text{d}t} \tag{4}\]  
where \(K_{\text{f}}\) is the scale coefficient. Virtual inertia control provides a fast active output response when the power system is disturbed. In the initial phase of the power system frequency response, the frequency deviation is small, while the absolute value of the frequency rate of change is large. Therefore, the WT with virtual inertia control can provide faster and stronger power support during the initial phase.