## 3 Basic Principle of Additional Damping Control for DFIG  
The low-frequency oscillation of the power system is mainly caused by the unbalanced torque of the synchronous generator rotor. For inter-area power oscillations that occur between two clusters, the two clusters can be considered as equivalent two-machine systems for analyzing inter-area oscillations. This section will explain the principle of increasing the system damping of the DFIG according to the simple power system model shown in Figure 2. The two areas, each with a local load, are connected through a transmission line. The wind farm based on DFIG is integrated in area 1. The dynamic model of the two-area power system without wind generation connection can be described with the swing equation in (11), which is widely used in [17]:  
\[\left\{ \begin{array}{l}\frac{d\delta_{12}}{dt}=\omega_{12}\\ \frac{d\omega_{12}}{dt}=\frac{1}{H_{1}}(P_{m1}-P_{L1})-\frac{1}{H_{2}}(P_{m2}- P_{L2})-\big{(}\frac{1}{H_{1}}+\frac{1}{H_{2}}\big{)}\frac{V_{1}}{V_{2}}sin \delta_{12}\end{array} \right., \tag{11}\]  
Figure 2: Simple power system model. where \(\omega\) is the generator rotor speed; \(\delta\) is the generator rotor angle; \(\delta_{13}=\delta_{1}-\delta_{3}\) and \(\omega_{13}=\omega_{1}-\omega_{3}\) are the relative rotor angle and relative rotor speed, respectively, between the two areas; \(H_{1}\) and \(H_{2}\) are the equivalent inertia of areas 1 and 2, respectively; \(P_{m1}\) and \(P_{m2}\) are the mechanical power of generator 1 and generator 2, respectively; \(X\) is the total impedance of the transmission line; and \(V_{1}\) and \(V_{2}\) are the voltages of Bus 1 and Bus 2, respectively. The damping coefficient of synchronous machine is not considered. When the wind farm is linked to area 1, as illustrated in Figure 2, the system dynamic behavior can be described as [10]  
\[\left\{ \begin{array}{l}\frac{d\delta_{12}}{dt}=\omega_{12}\\ \frac{d\omega_{12}}{dt}=\frac{1}{H_{1}}(P_{m1}+P_{w}-P_{L1})-\frac{1}{H_{2}}( P_{m2}-P_{L2})-\left(\frac{1}{H_{1}}+\frac{1}{H_{2}}\right)\frac{V_{1}}{V_{2}} sin\delta_{12}\end{array} \right., \tag{12}\]  
where \(P_{w}\) is the active power generated from the wind farm. As shown in Equation (12), by adding auxiliary power control to the DFIG, the DFIG can inject dynamic damping power into the system, thereby suppressing the electromechanical oscillation of the power system. The low-frequency oscillation is also affected by the bus voltage, and the voltage amplitude is affected by the transmission of reactive power. The equation is related to (13). Power damping can be improved by modulating the bus voltage with reactive power control [18]:  
\[Q_{t}=Q_{g}+Q_{1}=\frac{V_{2}^{2}-V_{1}V_{2}\cos\delta_{12}}{X}, \tag{13}\]  
where \(Q_{t}\), \(Q_{g}\), and \(Q_{1}\) are the reactive power transmitted from area 1 to area 2, reactive power injection of DFIG, and the reactive power generated by synchronous generator 1, respectively. Bus voltage increases or decreases with the reactive power of the DFIG. The generator accelerates when voltage increases and decelerates when voltage decreases. The amplitude of oscillations can be reduced. DFIG has two voltage-source PWM converters, i.e., a rotor side converter (RSC) and a grid side converter (GSC). The DFIG control includes RSC and GSC controllers for governing its active and reactive power. Figure 3 shows the block diagram of RSC controller. The reactive power outer loop is cascaded with the q-axis rotor current inner loop, and the active power outer loop is cascaded with the d-axis rotor current inner loop. The q-axis loop is used to regulate the active power of DFIG (P) and the axis loop is utilized to control the reactive power of DFIG stator (Q). Active and reactive powers are regulated with the classical PI controllers. Output is closely related to the d-axis and q-axis currents of the rotor due to the active and reactive power of the DFIG.