## 2 Modeling and Analysis of Wind Storage Systems
### Modeling of Wind Farm and Analysis of Its Working Characteristics
\tag{4}\]  
In the equations: \(\beta\) is the pitch angle; \(\beta_{\rm ref}\) is the reference value of the pitch angle; \(T_{\rm\beta}\) is the time constant of the pitch angle control system; \(K_{\rm p}\), \(K_{\rm i}\) is the proportional and integral parameter of the PI link to obtain the given value of the pitch angle from the rotational speed; \(\omega_{\rm r}\) is the generator rotor speed; \(\omega_{\rm ref}\) is the reference value of generator rotor speed. In the modeling of doubly fed wind turbines, using dual mass blocks is more effective in describing the mechanical characteristics of the DFIG shaft system in detail than using single mass blocks. Therefore, the wind turbine and low-speed shaft are treated as one  
Figure 2: Control strategies for DFIG: characteristic for Maximum Power Point Tracking. mass block, and the gearbox and high-speed shaft are treated as another mass block. The torsion between multiple mass blocks in DFIG will generate shafting oscillation [9], and the shafting model of the two mass modules is:  
\[\left\{ \begin{array}{l}\frac{d\omega_{\rm t}}{dt}=\frac{T_{\rm m}}{2H_{\rm t}}- \frac{K\gamma}{2H_{\rm t}}-\frac{D(\omega_{\rm t}-\omega_{\rm t})}{2H_{\rm t}}\\ \frac{d\omega_{\rm t}}{dt}=\frac{K\gamma}{2H_{\rm t}}+\frac{D(\omega_{\rm t}- \omega_{\rm t})}{2H_{\rm t}}-\frac{T_{\rm e}}{2H_{\rm r}}\\ \frac{d\gamma}{dt}=\omega_{\rm FB}(\omega_{\rm t}-\omega_{\rm r})\end{array} \right. \tag{5}\]  
In the equations: \(\omega_{t}\) is the angular velocity of the wind turbine; \(\omega_{r}\) is the rotor speed of the double-fed asynchronous generator; \(\gamma\) is the torque angle of the transmission shaft; \(H_{t}\), \(H_{r}\) are the inertial time constants of the wind turbine and the double-fed asynchronous generator; \(T_{m}\) is the output torque of the wind turbine; \(T_{e}\) is the electromagnetic torque of the double-fed asynchronous generator; \(K\) is the stiffness coefficient of the shaft system; \(D\) is the damping coefficient; and \(\omega_{FB}\) is the reference value of the speed. If the electromotive force and the d, q axis carries out of the stator are selected as the state variables after the transient reactance is decided, the dynamic equation of the doubly fed induction motor can be expressed (See Appendix A for the specific derivation process):  
\[\left\{\begin{array}{l}\frac{d\omega_{\rm d}}{dt}=-\frac{\omega_  
In the equation, \(u_{dg}\) and \(u_{dg}\) are the \(d\) and \(q\) axis components of the grid voltage; \(i_{dg}\) and \(i_{qg}\) are the \(d\) and \(q\) axis components of the grid side converter current, respectively; \(u_{dg}\) and \(u_{qg}\) are the \(d\) and \(q\) axis components of the grid side converter voltage, respectively. This article assumes that both the stator and rotor sides adopt the motor convention. The control objective of RSC is to achieve decoupling and independent control of active and reactive power on the stator side by controlling the excitation voltage. The control block diagram on the RSC side is shown in Figure 3, and the dynamic model is as follows:  
\[\left\{ \begin{array}{l}\frac{dx_{\mathrm{r}}}{dt}=P_{\mathrm{s}}^{*}-P_{ \mathrm{s}}\\ \frac{dx_{\mathrm{r}}}{dt}=Q_{\mathrm{s}}^{*}-Q_{\mathrm{s}}\\ \frac{dx_{\mathrm{r}}}{dt}=I_{\mathrm{dr}}^{*}-I_{\mathrm{dr}}=K_{\mathrm{P1}} (P_{\mathrm{s}}^{*}-P_{\mathrm{s}})+K_{\mathrm{i1}}x_{\mathrm{P}}-I_{\mathrm{ dr}}\\ \frac{dx_{\mathrm{r}}^{2}}{dt}=I_{\mathrm{qr}}^{*}-I_{\mathrm{qr}}=K_{\mathrm{ p3}}(P_{\mathrm{s}}^{*}-P_{\mathrm{s}})+K_{\mathrm{i3}}x_{\mathrm{Q}}-I_{\mathrm{qr}} \end{array} \right. \tag{11}\]  
The output voltage is:  
\[\left\{