## 4 Grid-Forming Control by Wind Turbine Generators
* **FRT unit**, which generates a discrete FRT signal that is applied to the active power control block for angle correction control as well as to the voltage control block for suspending the integration action during a fault. The FRT signal is set to 1 when the wind terminal's voltage drops below 0.9 p.u. * **Active power control**, which controls active power according to a droop characteristic. During a fault, it is switched to a fault-mode angle correction control. It generates the transformation angle \(\theta_{\text{GSC}}\), which is used in the transformation between the real-imaginary frame and the dq frame and vice versa. * **Modulation unit**, which transforms obtained converter internal voltage references \(u_{\text{c,dq}}^{*}\) from dq-frame into the network oriented frame and generates \(u_{\text{c,xy}}^{*}\) as inputs for the grid side converter of the wind turbine generator. For the active power control, the common droop control concept is applied [57]. To explain the choice of the droop control, an equivalent electric circuit for a grid-forming converter connected to a grid is shown in Figure 10. It includes a grid-forming converter modelled as a voltage source \(u_{\text{c}}\angle\delta\) in series with the impedance \(z_{\text{f}}\) connected to the grid \(u_{\text{g}}\angle 0\) with impedance \(z_{\text{g}}\). The active and reactive power flows from converter to the grid are calculated as:  
\[p=\frac{u_{\text{c}}}{r^{2}+x^{2}}[r(u_{\text{c}}-u_{\text{g}}\cos\ \delta)+xu_{\text{g}}\sin\ \delta] \tag{2}\]  
\[q=\frac{u_{\text{c}}}{r^{2}+x^{2}}[-ru_{\text{g}}\sin\ \delta+x(u_{\text{c}}-u_{ \text{g}}\cos\ \delta)] \tag{3}\]  
where \(r=r_{\text{f}}+r_{\text{g}}\) and \(x=x_{\text{f}}+x_{\text{g}}\). For the high voltage transmission systems, we can assume that \(x\gg r\), also if the power angle \(\delta\) is small, so that \(\sin\ \delta\approx\delta\) and \(\cos\ \delta\approx 1\). Therefore, Equations (2) and (3) can be written as:  
\[\delta\approx\frac{xp}{u_{\text{c}}u_{\text{g}}} \tag{4}\]  
\[u_{\text{c}}-u_{\text{g}}\approx\frac{xq}{u_{\text{c}}} \tag{5}\]  
The above analysis shows a correlation between \(q\) and \(u\) as well as \(p\) and \(\delta\). Therefore, in such grids, the voltage angle or the frequency can be controlled by active power control; the droop characteristic of which can be defined as:  
\[\omega=k_{\text{D}}(p^{*}-p)+\omega_{\text{g}} \tag{6}\]  
Figure 9.0 Power control of a grid-forming converter connected to a grid. in which \(\omega\) is the converter output frequency, \(p\) is the converter active power, \(p^{*}\) is the converter active power set-point, \(k_{\text{D}}\) is the proportional droop gain and \(\omega_{\text{g}}\) is the rated frequency (all in p.u.). The grid-forming droop control mimics the synchronous generators' self-regulation, which means a PLL or other synchronisation unit is not required. Unlike synchronous generators that have over-current capability during a fault, grid-forming converters should be protected against over-current operation. This issue is illustrated by Figure 9.1 In the event of grid faults, \(u_{\text{pc}}\) dips, but the grid-forming controller tends to maintain its inner voltage \(u_{\text{c}}\). As a result, \(i\) increases instantaneously (Figure 11[58]). On the one hand, the grid-forming converter should ride through a fault, and on the other hand, its fault current should be limited by a suitable current limiting strategy. Therefore, a feedback compensator for the active power control is applied here. The active power control block is shown in Figure 9.2 \(k_{\text{cor}}\) is the proportional correction gain and \(f_{0}\) is the base rated frequency of (i.e., 50 Hz). When there is an AC grid fault _and_ the discrete FRT signal is 1, the control mode is changed from droop-control to angle correction control. This control will keep the phase angle of the wind terminal voltage fixed at the pre-fault values. The FRT unit activates the switch when the voltage drops below the threshold.