## 4 Grid-Forming Control by Wind Turbine Generators  
The grid-forming converter is a power converter that controls the voltage magnitude and the angle at the point of common coupling (PCC). Contrary to grid following converters, grid-forming converters do not need the fundamental frequency of the grid voltage as input. Grid-forming converters are mainly beneficial in islanded operation and in weak (i.e., low short circuit power) grids. Moreover, they can also support the grid by injecting an instantaneous active and reactive power. The required characteristics for the grid-forming controller in this paper are specified as follows:  
* It has frequency and voltage regulation;
* The controller needs to be capable of operating in both strong and weak-grid conditions;
* The controller needs to be able to limit the current during the fault condition while successfully riding through the fault in both grid-connected and islanded operations. Due to the increasing number of converter-based generators in the grid, several European countries have issued requirements for these generators to support the stability of the power system [8]. One of the requirements is for FRT capability: converter-based generators should stay connected to the grid when the voltage drops significantly and sometimes need to inject reactive current into the power system during voltage dips (e.g., the German grid code [53]). Considering the above-mentioned requirements, a droop-based grid-forming control is implemented [7; 8]. The high-level schematic of the grid-forming converter is shown  
Figure 8: Workflow diagram of the co-simulation setup using mosaik and the FMI. in Figure 9. It contains a grid side converter supplied by a DC voltage source. On the AC side, the converter is connected to an AC grid through an \(l_{\text{rf}}\) filter and a step-up transformer. The AC grid is modelled by an ideal AC voltage source \(u_{\text{g}}\) in series with its equivalent impedance \(z_{\text{g}}\). The function of the grid-forming control is to modulate the converter internal voltage \(u_{\text{c}}^{*}\) in such a way that the voltage difference across the filter can produce the desired exchange of active and reactive power with the grid. As this work focuses on the transient stability studies for a generic transmission systems, the switching effect of power electronics is not modelled, which is considered a plausible assumption [5]. As the fast phenomena are not involved, root mean square (RMS) models are selected which effectively evaluate the transient stability of the power system in the grid-planning phase [34]. As can be seen in Figure 9, the grid-forming control system consists of following blocks:  
* **Measurement unit**, which transforms the wind turbine terminal current \(i_{\text{t}}\) and terminal voltage \(u_{\text{t}}\) from the network oriented frame (i.e., \(xy\)) to the dq-frame using wind terminal voltage angle \(\theta_{\text{GSC}}\) coming from the active power control block. Furthermore, the active power \(p\) is calculated as \[p=u_{\text{t,x}}i_{\text{t,x}}+u_{\text{t,y}}i_{\text{t,y}}\] (1)
* **Voltage control**, which controls the wind terminal voltage \(u_{\text{t}}\) with a PI controller and provides current references \(i_{\text{t,dq}}^{*}\). * **Current limit**, which limits the current references and produces limited current references \(i_{\text{t,dq}}^{**}\). Figure 9: Single line and control block diagram of a grid-forming converter. All variables are in p.u. * **Voltage reference generation**, which generates voltage references \(u_{\text{c,dq}}^{*}\) based on the limited current reference provided by the current limitation block. Moreover, to ensure adequate damping of the low frequency oscillations especially in the weak-grid and islanded operations, an auxiliary damping signal is added to the voltage references.