## 4 Grid-Forming Control by Wind Turbine Generators
Consequently, the voltage angle is locked to a value dictated by the feedback compensation block. The rest of the controller details are shown in Figure 9.3 In the proposed control scheme, the reactive power control is not specifically included. The angle of the voltage is controlled by the droop-based active power control as explained before and the magnitude of the voltage is controlled in the voltage control with a PI controller. The voltage vector is aligned with the d-axis, so the d-axis wind terminal voltage set-point \(u_{\text{t,d}}^{*}\) is equal to the wind turbine nominal voltage in p.u., and the q-axis wind terminal voltage set-point \(u_{\text{t,d}}^{*}\) is zero. For voltage controlling purposes, a PI controller is applied. For mitigating the integrator wind-up phenomena, a conditional integration technique is implemented [59]. This technique stops the integration when the error is high. Consequently, the FRT signal is added to the PI block as shown in Figure 13 to freeze the integrator during faults. After obtaining the current references, as a complimentary current limiting strategy, a hard  
Figure 9.4 Phasor diagram after fault occurrence in the grid. Figure 9.5 Active power control with a feedback compensator activated during a fault. limiter is applied to limit the amplitude of the current references. In the current limitation block, the maximum current for the d-axis in p.u. is calculated as:  
\[i_{\text{d,max}}= \begin{cases}\sqrt{t_{\text{lim}}},&\text{if }\;i_{\text{lim}}= \sqrt{i_{\text{max}}{}^{2}-i_{\text{t,q}}^{*}{}^{2}}>0\\ 0,&\text{otherwise}\end{cases}  \tag{7}\]  
where \(i_{\text{max}}\) is the maximum permitted wind turbine current and assumed 1.1 p.u., and \(i_{\text{t,q}}^{*}\) is the q-axis current reference in p.u. To comply with reactive current injection requirements, reactive current is given priority over active current. Then a limiter is applied for \(i_{\text{t,d}}^{*}\) in the range of \((-i_{\text{d,max}},i_{\text{d,max}})\) and \(i_{\text{t,q}}^{*}\) in the range of \((-i_{\text{max}},i_{\text{max}})\) (middle of Figure 13). The next control block is the voltage reference generation block, which supplies the converter internal voltage references of the grid side converter of the wind turbine. As the network elements (i.e., step-up transformer) are represented by complex phasors in the grid simulator, the voltage reference modulation (\(u_{t}\) and \(u_{c}\)) can be calculated by the following algebraic entities:  
\[u_{\text{c,d}}^{*}+ju_{\text{c,q}}^{*}=u_{\text{t,d}}+ju_{\text{t,q}}+(r_{ \text{f}}+jx_{\text{f}})(i_{\text{t,d}}^{**}+ji_{\text{t,q}}^{**}) \tag{8}\]  
where \(r_{\text{f}}\) is neglected. The converter internal voltage references in d-axis and q-axis can be calculated as:  
\[u_{\text{c,d}}^{*}=u_{\text{t,d}}-x_{\text{f}}i_{\text{t,q}}^{**} \tag{9}\]  
\[u_{\text{c,d}}^{*}=u_{\text{t,q}}+x_{\text{f}}i_{\text{t,d}}^{**} \tag{10}\]  
The analysis of weak grid conditions and islanded operation revealed that there are low-frequency oscillations after transient events. Power system stabilizer (PSS) can help in eliminating such oscillations [60]. The PSS is extensively applied in power systems dominated by synchronous generators and introduced for converter-based generators as well [61]. The auxiliary damping signals are produced based on the difference between the wind turbine currents \(i_{\text{t,dq}}\) and the limited current references \(i_{\text{t,dq}}^{**}\) and they resemble a virtual series resistor. The objective of the PSS is to provide adequate damping of transient responses originating from the interconnected power system. A resistor can play a damping role, which unfortunately comes with losses. Therefore, the voltage drop is emulated by a virtual resistor. Moreover, in order to activate this damping effect only in transient situations, a washout filter is added according to [62]. The stabiliser consists of a damping gain \(k_{\text{w}}\) and a washout filter with time constant \(T_{\text{w}}\).