**4. Results**

This section presents a comparison of the responses of the generic Type 3 WT model implemented in both software tools during two different voltage dips, and also the calculation of the validation errors according to Section 2.1. Moreover, it performs a comprehensive analysis of the reasons for such errors. The values of the main parameters that are part of the generic Type 3 WT model are shown in Table 2.


**Table 2.** Main parameters of the generic Type 3 WT model.


**Table 2.** *Cont.*

#### *4.1. Validation of the Generic Type 3 WT Model*

The WT dynamic model (implemented in MATLAB/Simulink and DIgSILENT-PowerFactory) was submitted to two different voltage dips, the residual voltage (*u*), and dip duration (*t*), of which are *u* = 0.50 pu and *t* = 920 ms for the Test Case 1, and *u* = 0.25 pu and *t* = 625 ms for the Test Case 2. In order to do so, the field data series were converted to positive sequence values, since the generic WT models must be studied for fundamental frequency-positive sequence response analyses. Thus, the positive sequence values of the voltage dips were reproduced in the generic WT models.

Figures 9 and 10 show the active and reactive power responses and their validation errors in Test Case 1, while Figures 11 and 12 show those corresponding to Test Case 2. The value of the more than a hundred parameters which are part of the generic Type 3 WT model do not vary from one software to the other. This explains the excellent correlation between the two simulation data series (in blue and black), in both the active power (Figures 9a and 11a) and the reactive power (Figures 10a and 12a), for both Test Cases. In these figures, a red line represents the measured data from the field tests. As might be expected, the differences between measured and simulation data are higher than the differences between both simulation responses, despite the generic Type 3 WT model having been adjusted to the field data series to the maximum extent.

In the graphics of the error data series, Figures 9b–12b, vertical lines and red bars at the top indicate the transient periods of 140 ms and 500 ms that must not be considered in the calculations of errors at the start of fault and post-fault periods, respectively, as explained in Section 2.1. As can be observed in these figures, error lines between simulation models and measured data for all cases (in red and blue) show sharp peaks. In addition, Figure 9 shows how an aerodynamic imbalance may affect the error between the field data and the simulation responses. The real response shows an undershoot during the post-fault period due to a wind speed fluctuation, which can be emulated by neither of the generic WT models. Nevertheless, as will later be explained drawing on Tables 3 and 4, the maximum errors obtained do not exceed 13% in either case (the *MXE* values are marked in the figures as small circles). Finally, the black lines represent the error obtained between both simulation models, which is at around 0% in all cases.

**Figure 9.** Active power in Test Case 1: *u* = 0.50 pu, *t* = 920 ms.

**Figure 10.** *Cont*.

 **Figure 10.** Reactive power in Test Case 1: *u* = 0.50 pu, *t* = 920 ms.

In general, the graphic representation of the errors obtained is a good way to provide a general but comprehensive overview of the results. Thus, a quick glance reveals the performance of the simulation models, since the higher the deviation from 0%, the lower is the accuracy of the simulation models compared with each other and with the field measurements.

Furthermore, the numerical results of the validation errors are presented in Table 3 for Test Case 1 and Table 4 for Test Case 2. Different trends may be observed. First, as expected, lower errors are obtained for the 'MATLAB-PowerFactory' comparison (third column of Tables 3 and 4), since the behavior of both simulation models is very similar. In these cases, the *ME* and the *MAE* do not exceed 1% either in the active power or in the reactive power of the two test cases analyzed, in both fault and post-fault periods. Regarding the *MXE*, it does not exceed 2% in either case for the 'MATLAB-PowerFactory' comparison. It can therefore be stated that, despite the slight deviations which will be analyzed in Section 4.2, there is very little difference between the MATLAB and the PowerFactory simulation responses.

**Figure 11.** *Cont*.

**Figure11.**ActivepowerinTestCase2:*u*=0.25pu,*t*=625ms.

(**b**) Error series and *MXE* values.

**Figure 12.** Reactive power in Test Case 2: *u* = 0.25 pu, *t* = 625 ms.


**Table 3.** Validation errors of Test Case 1: *u* = 0.50 pu, *t* = 920 ms.

**Table 4.** Validation errors of Test Case 2: *u* = 0.25 pu, *t* = 625 ms.


In light of the above, the values of the errors between the 'MATLAB-Field' and 'PowerFactory-Field' data series are very similar, as can be observed in Tables 3 and 4. Moreover, in general, the *ME*, the *MAE* and the *MXE* are lower in the reactive power responses than in the active power responses for both test cases. This means that the reactive power simulation response of the generic Type 3 WT model is better adjusted to the field measurements. Despite this, there also exists a good correlation between the simulation and the field measurements in active power for both test cases.

Hence, as the generic WT models developed by IEC 61400-27-1 are not intended to be studied during the transient periods appearing at the start and the clearance of the faults, higher error values may be obtained. Indeed, most of the *MXE* errors obtained are near the transient periods of the responses (see the small circles in Figures 9b–12b and the red bars at the top, respectively), where the accuracy of the model with regard to the field measurements is usually lower. This is because transient periods of the actual WTs are not adequately represented by the generic models.

The efficient performance of the simulation models is also supported by the good correlation in the amplitude and the phase shift of the active power responses after the voltage dip clearance (Figures 9a and 11a). This is mainly due to the good fit to the parameters of the two-mass mechanical model. Moreover, the reactive power responses provided by the generic WT models are highly accurate (Figures 10a and 12a), since they present a very similar behavior to that of the field measurements (including the reactive power injection period during the voltage dips to stabilize the voltage).

Therefore, in view of the explanations above and the low values of the validation errors obtained, it can be concluded that the simulation responses of the generic Type 3 WT model yield satisfactory results, since, on the one hand, both emulated responses are very similar (with errors around 0%) and, on the other hand, both models are adjusted adequately to the field measurements.

#### *4.2. Analysis of the Limitations of the Software Tools: Causes of the Differences in the Simulated Response*

Section 4.1 analyzed the values of the validation errors calculated according to the validation guidelines issued by IEC 61400-27-1 in the three cases considered: (i) MATLAB Model—Field Data, (ii) PowerFactory Model-Field Data, (iii) MATLAB Model—PowerFactory Model. This section aims to explain the main differences in the software tools that may cause the errors found between both simulation responses of the generic WT model. However, it is worth noting that the validation errors are smaller than 2% for all cases. The explanations included in this Section intend to clarify the small differences between both simulation responses (from the two software tools used) at the time of conducting dynamic simulations, but always considering that the results are equally valid for both of them.

Figure 13 shows one of the constraints when comparing both simulation tools. Specifically, the response of a signal passing through a built-in rate limiter in PowerFactory and Simulink is analyzed. The rising rate was set to 5 and the falling rate was set to –999. It can be observed that the PowerFactory response is not the expected behavior, while the Simulink response is correct. Basically, PowerFactory applies a first-order filter to the input signal of the block, the time constant of which can also be adjusted. Thus, setting a lower time constant should dampen the effect of this filter. Nevertheless, this filter has an effect on the signal and, hence, the responses from PowerFactory and Simulink when using these limiters (which are several in IEC 61400-27-1 models) are not the same. More precisely, the generic Type 3 WT model includes a total of five rate limiters, two in the generator system model and three in the active power control model, so that the combined effect of these blocks on the output signals also explains the differences between the responses of both software tools. These filters are not implemented in Simulink since IEC 61400-27-1 does not include them in the models.

**Figure 13.** Rate limiters responses for the same input signal.

Additionally, despite the PowerFactory solver being set to 'fixed step' with a time step of 1 ms, the time step varies during the simulations. Regarding Simulink, the solver was set to ode4 (Runge–Kutta) with a fixed time step of 1 ms. This type of solver is widely used due to its balance between accuracy and simulation time. This is shown in Figure 14, which represents the time step at each sample, as well as the active power response for that simulation. When the active power response varies greatly, the time step decreases to improve the accuracy. In fact, this is the appropriate behavior for a variable step solver. However, for comparison purposes, a real fixed-step simulation time would be desirable. Therefore, this variable time step used by DIgSILENT-PowerFactory for the simulation of the WT model was identified as another one of the main causes of the slight differences between the simulation responses of the two software tools.

**Figure 14.** Simulation time steps during a fault in PowerFactory.

Therefore, differences in the rate limiter responses in both software tools, and the variable time step used by DIgSILENT-PowerFactory during the simulation, are identified as the key factors explaining the errors between the responses of the generic Type 3 WT dynamic model.
