## Materials and Methods
### Developed Model for WTGSs
While looking at the positive-sequence equivalent circuit and the bi-quadratic equation, which was used to model the CFSIG based WTGSs for balanced systems in [9], the referred rotor positive-sequence voltage's magnitude, \(V_{rp}\), can be written as  
\[V_{rp}=\sqrt{\frac{{V_{sp}}^{2}-2R_{sc}P_{rp}+\sqrt{\big{(}{V_{sp}}^{2}-2R_{sc }P_{rp}\big{)}^{2}-4Z_{sc}^{2}P_{rp}^{2}}}{2}}, \tag{4}\]  
where \(Z_{sc}\) stands for the induction generator's short-circuit impedance:  
\[Z_{sc}=\sqrt{R_{sc}^{2}+X_{sc}^{2}}. \tag{5}\]  
The magnitude of the negative sequence current (\(I_{sn}\)), which flows from \(r\) bus to s bus in the negative-sequence equivalent circuit, and negative-sequence active power at \(r\) bus (\(P_{m}\)) can be expressed in terms of the impedance parameters (\(R_{r}\), \(R_{sc}\), \(X_{sc}\)), the magnitudes of the rotor positive-sequence and stator negative-sequence voltages (\(V_{rp}\), \(V_{sn}\)) and positive-sequence active power at \(r\) bus (\(P_{rp}\)):  
\[I_{sn}=I_{rn}=\frac{V_{sn}}{\sqrt{\bigg{(}\big{(}R_{sc}-R_{r}\cdot\frac{{V_{ rp}}^{2}}{2{V_{rp}}^{2}+P_{rp}\cdot R_{r}}\big{)}^{2}+X_{sc}^{2}\bigg{)}}}, \tag{6}\]  
\[P_{rn}={I_{rn}}^{2}\cdot R_{r}\cdot\frac{-V_{rp}^{2}}{2V_{rp}^{2}+P_{rp}R_{r}}. \tag{7}\]  
The positive- and negative-sequence active powers at \(s\) bus can be expressed as in Equations (8) and (9):  
\[P_{sp}=P_{rp}+\bigg{(}\frac{P_{rp}}{V_{rp}}\bigg{)}^{2}R_{sc}+\frac{{V_{sp}}^{ 2}}{R_{m}}, \tag{8}\]  
\[P_{sn}=P_{rn}+{I_{sn}}^{2}R_{sc}. \tag{9}\]  
Hence, the total active power at \(s\) bus can be calculated as:  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]0On the other hand, the positive- and negative-sequence reactive powers at s bus can be expressed as follows:  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]1  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]2  
By regarding both reactive powers, the total reactive power at \(s\) bus can be calculated:  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]3  
Since \(P_{rp}\) and \(P_{m}\) have unknown values, the model needs an iterative solution algorithm. The algorithm of the Developed model is summarized below:  
* Step 1: Determine initial value of \(P_{rp}\) by assuming all of the mechanical power (\(P_{T}\)) delivered to the positive-sequence circuit. * Step 2: Calculate \(V_{rp}\) via Equation (4). * Step 3: Find \(I_{m}\) and \(P_{m}\) by substituting the \(V_{rp}\) and the \(P_{rp}\) values in Equations (6) and (7). * Step 4: Calculate \(P_{s}\) and \(Q_{s}\) values by means of Equations (8)-(13). * Step 5: Find the relative difference value of \(P_{s}\) and the relative difference value of \(Q_{s}\), which are calculated for the last two iterations (\(i+1\). and \(i\). iterations), via Equations (14) and (15). * Step 6: If both calculated relative difference values are larger than tolerance value (\(\varepsilon\)), update the \(P_{rp}\) value by substituting the last calculated \(P_{m}\) value in Equation (3), and return to the \(V_{rp}\) calculation step. Otherwise, finalize the solution algorithm: \[\lambda=\frac{\omega R}{u}, \tag{2}\]4 (14) \[\lambda=\frac{\omega R}{u}, \tag{2}\]5 (15)  
Note that the magnitudes (\(V_{sp}\), \(V_{sn}\)) and angles (\(\varphi_{sp}\), \(\varphi_{sn}\)) of the sequence voltages at the s bus have known values, and sequence active powers (\(P_{sp}\), \(P_{sn}\)), sequence reactive powers (\(Q_{sp}\), \(Q_{sn}\)) and magnitudes (\(I_{sp}\), \(I_{sn}\)) of sequence currents at the \(s\) bus are found after completing the iterative algorithm. Additionally, the angles of the positive- and negative-sequence currents measured at the s bus, denoted as \(\beta_{sp}\) and \(\beta_{sn}\), can be calculated by considering Equations (16) and (17):  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]6  
\[\lambda=\frac{\omega R}{u}, \tag{2}\]7  
Finally, sequence voltages and currents of the stator side can be converted to the phase values of those quantities by means of the symmetrical components method.