## 2 Modeling and Analysis of Wind Storage Systems
### Modeling of Wind Farm and Analysis of Its Working Characteristics
\begin{array}{l}U_{\mathrm{dr}}=K_{\mathrm{p2}}(K_{\mathrm{p1}}\Delta P _{\mathrm{s}}+K_{\mathrm{i1}}x_{\mathrm{P}}-I_{\mathrm{dr}})+K_{\mathrm{i2}}x _{\mathrm{idr}}-(1-\omega_{\mathrm{r}})L_{\mathrm{m}}I_{\mathrm{qs}}-(1- \omega_{\mathrm{r}})L_{\mathrm{m}}I_{\mathrm{qr}}\\ U_{\mathrm{qr}}=K_{\mathrm{p2}}(K_{\mathrm{p3}}\Delta Q_{\mathrm{s}}+K_{ \mathrm{i3}}x_{\mathrm{Q}}-I_{\mathrm{qr}})+K_{\mathrm{i2}}x_{\mathrm{idr}}-(1 -\omega_{\mathrm{r}})L_{\mathrm{m}}I_{\mathrm{ds}}-(1-\omega_{\mathrm{r}})L_{ \mathrm{rr}}I_{\mathrm{dr}}\end{array} \right. \tag{12}\]  
In the equation, \(p\), \(i\), respectively, represent the proportional gain and integral gain in the PI parameters, \(x_{\mathrm{P}}x_{\mathrm{P}}x_{\mathrm{Q}}\), \(x_{\mathrm{idr}}x_{\mathrm{iqr}}\) are intermediate state variables introduced in the control loop. The control objective of GSC is to stabilize the DC link voltage and maintain the constant power factor operation of the main network. The control block diagram of the GSC side is shown in Figure 4, and the dynamic model is as follows:  
\[\left\{ \begin{array}{l}\frac{dx_{\mathrm{d}}}{dt}=U_{\mathrm{dc}}^{*}-U_{ \mathrm{dc}}\\ \frac{dx_{\mathrm{r}}}{dt}=Q_{\mathrm{g}}^{*}-Q_{\mathrm{g}}=0\\ \frac{dx_{\mathrm{d}}}{dt}=K_{\mathrm{p5}}(U_{\mathrm{dc}}^{*}-U_{\mathrm{dc}} )+K_{\mathrm{i5}}x_{\mathrm{dc}}-I_{\mathrm{dg}}\\ \frac{dx_{\mathrm{qg}}}{dt}=0-I_{\mathrm{qs}}\end{array} \right. \tag{13}\]  
The output voltage is similar to the machine-side converter, and the dynamic model of the control part of the energy storage converter is similar to the fan-side, which will not be repeated here. The dynamic model of the DC side of the intermediate capacitor is:  
\[U_{\mathrm{dc}}C\frac{dU_{\mathrm{dc}}}{dt}=P_{\mathrm{s}}-P_{\mathrm{g}}=P_ {\mathrm{s}}-\frac{3}{2}u_{\mathrm{dg}}i_{\mathrm{dg}} \tag{14}\]  
The synchronous generator includes the second-order rotor Equations of motion, the first-order rotor electromagnetic transient equation, the first-order excitation system equation, and the first-order speed governing system equation. This article studies the  
Figure 3: RSC Side Converter Control Block Diagram. characteristics of low-frequency oscillation, ignoring the prime mover and its speed control system. The dynamic differential equation is described as:  
\[\left\{ \begin{array}{l}\frac{d\xi}{dt}=\omega_{0}(\omega-\omega_{0})\\ T_{\rm d}\frac{d\omega}{dt}+D(\omega-\omega_{0})=P_{\rm m}-P_{\rm e}\\ T_{\rm d0}^{\prime}\frac{dE_{\rm d}^{\prime}}{dt}=E_{\rm fd}-E_{\rm q}^{\prime }-(x_{\rm d}-x_{\rm d}^{\prime})i_{\rm d}\\ T_{\rm A}\frac{dE_{\rm fd}}{dt}=-E_{\rm fd}-K_{\rm A}(U_{\rm pref}-U_{\rm f}) \end{array} \right. \tag{15}\]  
In the equation,\(\omega\) is the generator rotor angular velocity, \(\omega_{0}\) is the synchronous angular velocity of the generator rotor, \(T_{\rm J}\) is the inertia time constant of the generator rotor, \(D\) is the damping torque coefficient of the generator, \(P_{\rm m}\) is the mechanical power of the prime mover, \(P_{\rm e}\) is the electromagnetic power of the generator;\(T_{\rm d0}^{\prime}\) is the time constant of the excitation winding; \(E_{\rm fd}\) is excitation electromotive force for the generator; \(E_{\rm q}^{\prime}\) is the transient electromotive force of the generator; \(x_{\rm d}\) and \(x_{\rm d}^{\prime}\) is the synchronous reactance and transient reactance of the stator; \(K_{\rm A}\) and \(T_{\rm A}\) is the gain and time constant of the excitation system; \(U_{\rm t}\) and \(U_{\rm pref}\) are the terminal voltage and its reference value of the synchronous machine.