## 3 Results and Discussion  
### Validation of Model  
To show the validity of the Developed model, its results are comparatively evaluated with the experimental results obtained in a test system. In addition, the results of the SCP model [12] are also provided. The equivalent circuit parameters of the test machine are given in Table 11, and these parameters are obtained by standard no-load and blocked rotor tests. In the system, active and reactive powers of the asynchronous generator are measured under unbalanced voltages. For the same unbalanced voltages, the results of the Developed model and SCP model [12] are calculated, and they are comparatively evaluated by considering the measurement results as reference values. In the comparative analysis, the voltage unbalance factor (_VUF_) [24,25] is considered to quantify the unbalance level of the test voltages. The expression of _VUF_ can be written as:  
\[VUF(\%)=\frac{V_{sn}}{V_{sp}}\cdot 100. \tag{20}\]  
A schematic representation and a photograph of the test system, which are used for validity tests of the model, are taken and provided in Figure 4. In the first part of the validity tests, for the induction generator working with the constant rotor slip value (\(s=-1.2\%\)) under the _VUF_ values between \(0\%\) and \(5\%\), the injected active and demanded reactive powers are plotted in Figure 5. Thus, the Developed model and SCP model [12] are examined in how they responded to _VUF_ changes. In the second part of the tests, the asynchronous generator working with the slip values between \(-0.4\%\) and \(-1.2\%\) under the unbalanced terminal voltage with _VUF_ = \(5\%\), the injected active and demanded reactive powers are plotted in Figure 6. The _VUF_ values have been obtained by changing the magnitudes of phase voltages while the phase angle differences remained constant at \(120\) degrees. In addition to that, the tolerance value (\(\varepsilon\)) of the machine iterations for validity tests has been determined as \(10^{-9}\) for both models. Figure 4: Schematic representation (**a**), and a photograph (**b**) of the test system. The obtained and calculated reactive power demand results at _VUF_ 0% given in Figure 5a are 0.720 pu, 0.665 pu and 0.655 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. In the same figure, reactive power demand results at _VUF_ 5% are 0.653 pu, 0.582 pu and 0.608 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. Similarly, injected active power results at _VUF_ 0% seen in Figure 5b are 0.405 pu, 0.366 pu and 0.358 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. In the same figure, injected active power results at _VUF_ 5% are 0.364 pu, 0.347 pu and 0.320 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. In the light of this information, as a result of neglecting _Rm_ and _Xm_ values which are not readily available and difficult to determine, for simplification in the negative sequence equivalent circuit, at higher _VUF_ values, the reactive power demand results obtained by the Developed Model are moving away from the trend of the measured values. For higher _VUF_ values, a similar situation is also observed in the results obtained by the SCP model [12]. The obtained and calculated reactive power demand results at \(-0.4\%\) slip value given in Figure 6a are 0.596 pu, 0.557 pu and 0.571 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. In the same figure, reactive power demand results at \(-1.20\%\) slip value are 0.653 pu, 0.582 pu and 0.608 pu, respectively, for Measurement, the Developed Model and the SCP Model [12]. Figure 5: Variation of the reactive power demand (**a**) and injected active power (**b**) of the generator at the \(-1.20\%\) slip value for various unbalanced terminal voltages (_VUF_%).