*2.3. Implementation of RSC Control*

The control block implemented the DFIG vector control in the synchronous reference frame as shown in Figure 3. The id reference and speed reference were initially set to zero. I<sup>r</sup> and vs. were obtained from the three-phase measurements block and ω<sup>m</sup> were obtained from the measurement signals output of the DFIG model.

**Figure 3.** Stator flux-oriented Vector Control of RSC of DFIG.

The two inner current control loops use the transformation blocks dq to DQ, DQ to abc, abc to DQ, and DQ to dq. The PWM generator used a normalized triangular wave (−1 to 1), so the control block output was also normalized using the gain block with value 1/(Vbus/2). A third harmonic injection at the control output was used to extract more voltage for a given dc–dc bus voltage. It allowed the output voltage to be improved by 15%. The transformation angle θ<sup>r</sup> was obtained from the stator voltages angle thetas and rotor angle θm. It was given as inputs to the transformation blocks. In the outer loop, a speed PI regulator was implemented to control the speed of the machine. The upper and lower limits were defined by Tem. In the inner loop, two PI regulators were required to control the id and i<sup>q</sup> currents according to the reference values. The k<sup>p</sup> and k<sup>i</sup> values were found using the transfer function of the designed system. The upper and lower limits were defined by Vbus/sqrt (3). The cross-coupling terms were cancelled using the cancellation of cc block. The idr and iqr were obtained from the output of transformation blocks of the rotor current Ir. The output of the speed PI regulator was multiplied by the gain to give the iqr\_ref. Thus, the stator flux-oriented vector control was implemented.

## **3. SS Performance Analysis of DFIG**

The DFIG's working characteristics are influenced by both the applied stator voltage and the injected rotor voltage. The direct and quadratic components of the injected rotor voltage are defined as proportional to the stator voltage for simulation purposes and are varied to observe the effect of changes in the active and reactive powers, copper losses, electromagnetic torque, power factor, and fluxes characteristics. In this article, the different operational points are used to depict DFIG's behavior. For analyzing the performance of DFIG under SS operating conditions, the following steps are involved in the programming:


Step 10: Program executed.

The SSA is mainly about the representative magnitudes of the DFIG model. The torquespeed data array as an input that emulates a 3-blade WT obtained from a 2 MW "Mitsubishi-MWT 92" wind turbine datasheet. The obtained parameters are provided in Table A1. During the execution, the SS magnitudes from a minimum speed of 900 rpm to a maximum speed of 1800 rpm are calculated. Further, through the MATLAB program, the parameters are calculated for different rotor speeds and plotted as per the Equations (1)–(29). Figure 4 shows the rotor generation strategy, that makes the d-axis rotor current zero (Idr = 0).

**Figure 4.** SS Characteristics of 2 MW DFIG Idr = 0; (**a**) Torque, (**b**) Total Power, (**c**) Stator and Rotor Power, (**d**) Stator Current, (**e**)Rotor Current, (**f**) Stator and Rotor Voltage, (**g**) Stator Reactive Power, (**h**) Rotor Reactive Power, (**i**) Efficiency.

Here in Figure 4a, the torque (Tem) is negative so the machine in this case operates as a generator. In Figure 4b, we have the mechanical power (Pt), which is nothing but the product of torque and speed. Then in Figure 4c, we have the active power of the rotor and stator (Pr and Ps). The maximum active power is around 2 MW. Max rotor power is around 400 kW. The active power of the rotor is negative and positive depending on the rotational speed. In Figure 4d,e, we have the stator (Is) and rotor currents (Ir). The rotor current is bigger than the stator current. Accordingly, in Figure 4g,h, we have the stator reactive power (Qs) and rotor reactive power (Qr). We can see that Qs increase with the rise in rotor speed whereas Qr decreases with a rise in rotor speed. Then, in Figure 4f we have the stator (Vs) and rotor voltages (Vr). We can see that the stator is directly connected to the grid, so the stator voltage amplitude is always constant. Whereas the rotor voltage magnitudes depend on the speed. At synchronous speed, it is minimum. At the two extremes, we have high voltages. We are working with a rotor referred to as the stator, so these magnitudes are not real magnitudes. If we convert to the rotor side and work, we will have the voltages very near to stator voltages. Finally, in Figure 4i we have the efficiency of the DFIG at a SS.

Here, we have the mechanical power (Pm), which is nothing but the product of torque and speed. Then we have the active power of the rotor and stator (P<sup>r</sup> and Ps). The stator active power is much bigger than the rotor active power. The maximum active power is around 2 MW. Max rotor power is around 400 kW. The active power of the rotor is negative and positive depending on the rotational speed: the stator currents, red Q<sup>r</sup> = 0 and blue for Idr = 0. When we make Q<sup>r</sup> = 0, the I<sup>s</sup> is lower than when Idr = 0. On the contrary, for the rotor current, we see that with Idr = 0, the rotor current is lower. Then we have the stator and rotor voltages. We can see that the stator is directly connected to the grid, so the stator voltage amplitude is always constant. Whereas the rotor voltage magnitudes depend on the speed. At synchronous speed, it is minimum. At the two extremes, we have high voltages. We are working with a rotor referred to as the stator, so these magnitudes are not real magnitudes. If we convert to the rotor side and work, we will have the voltages very near to stator voltages. Then we have the reactive power. With Idr = 0, we have high reactive power, and with the other generation strategy, which has 0 reactive power. Finally, rotor reactive power behavior in both cases, and finally, we have the efficiency.

The steps followed for the analysis using SS equations are discussed as a flowchart in Figure 5. The left branch discusses the computational method using mathematical equations. The right branch discusses the performance analysis of DFIG using the MATLAB/Simulink model. In the end, the results are compared to validate the simulation.

**Figure 5.** SS response of the simulated system with a rotor speed of 188.5 rad/sec; (**a**) Speed, (**b**) Torque, (**c**) Stator Voltage, (**d**) q-axis Current, (**e**) d-axis Current, (**f**) Stator Current, (**g**) d-axis voltage, (**h**) q-axis Voltage, (**i**) Rotor Current.

#### **4. Results and Discussion**

The developed model is simulated in the following procedure for obtaining the results,


#### *4.1. Simulation Results*

The simulation results of SSA at two different operating points of 1800 rpm with load torque of −10,894 and 1273.21 rpm with a torque of −5285, can be seen in Figure 6a,b. The change in operating point is initiated at a time instant of 6 s through a step signal. For a smooth transition, a rate limiter has been used with a rate of 100/seconds. The model is run with a reference speed of 1273.21 rpm and torque of −5285 Nm and at 6 s, the rotor reference speed is changed to 188.4 rad/s ((1364 rev/min × 2π rad/rev)/(60s/min) = 188.4 rad/s) corresponding to 1800 rpm. The operating point shifts from subsynchronous mode to super-synchronous mode. The synchronous speed of the machine is 1500 rpm. The new SS is reached at 6.5 s. The speed controller tracks the reference value for both subsynchronous and super-synchronous modes. The machine operates in subsynchronous mode and later switches to super-synchronous speed as per the reference. The rotor and stator currents have the value corresponding to the specific operating point in Figure 5 corresponding to a rotational speed of 1273.2 rpm and 1800 rpm with rotor magnetizing technique (idr = 0). The rotor voltages (sqrt(Vdrˆ2 + Vqrˆ2)) also follow the same. The absolute active power and reactive powers of the system will be obtained with correct voltages and currents.

The Idref (Figure 5e) is maintained at 0, as we maintain reactive power at zero during a SS. The I<sup>q</sup> current (Figure 5d) varies from 1176 A to 2103 A, to reach the new operating point corresponding to a speed-torque (1800 rpm & −10,602 Nm). I<sup>q</sup> is responsible for controlling the torque. The current controllers work properly as the d and q component currents follow the reference. The rotor voltages V<sup>d</sup> and V<sup>q</sup> (Figure 5g,h) vary in such a way that along with the rotor current, the generator generates the required real power of approximately 130 kw and 323 kw. The stator voltage in Figure 5c is constant with a peak amplitude of 563 V as no variation is made at the stator. The stator current in Figure 5f changes from 1362 A to 2079 A as the stator of the generator nearing synchronous speed draws less power. The rotor current in Figure 5i changes from 1174.5 A corresponding to a SS of 133 rad/sec and during synchronous speed, the frequency of rotor current becomes zero (DC). After crossing synchronous speed, the generator operates at super synchronous speed with a rotor current of 2019 peak amplitude. The machine operates as a conventional 3 phase synchronous generator.

#### *4.2. Comparative Analysis*

The steps followed for the analysis using SS equations are discussed in the flowchart, depicted in Figure 6. The left branch discusses the computational method using mathematical equations. The right branch discusses the performance analysis of DFIG using the MATLAB/Simulink model. In the end, the results are compared to validate the simulation.

**Figure 6.** Process of DFIG's SS performance analysis.

The most representative SS magnitudes of DFIG and they are compared to the calculated SS values available in Figure 5 corresponding to Idr = 0 for a rotational speed of 1800 rpm and 1273.21 rpm. It is observed that the SS magnitudes both computed and simulated are similar in Figures 7–14. The results are tabulated for further analysis. The SS magnitudes obtained through programming for two different operating points corresponding to a speed of 1800 rpm and 1273.21 rpm are shown in Figures 7a, 8a, 9a, 10a, 11a, 12a, 13a and 14a. The simulation model is run for these two operating points from 0 s to 6 s for a speed of 1273.21 rpm and from 6 s to 10 s for a speed of 1800 rpm. The most significant magnitudes are shown in Figures 7b, 8b, 9b, 10b, 11b, 12b, 13b and 14b. The values of stator current are calculated to be 1200.52 A, which is similar to the simulated SS value of 1362.82 A for a speed of 1273.21 rpm. Again, for a speed of 1800 rpm, the calculated value of stator current is 2124.85 A and the SS value of 2079.7 A is within comparable limits. Figure 7a,b show the values for comparison.

**Figure 7.** (**a**) Calculated stator current; (**b**) Stator current of the designed system.

The values of rotor current are calculated to be 1011.98 A, which is similar to the simulated SS value of 1214.42 A for a speed of 1273.21 rpm. Again, for a speed of 1800 rpm, the calculated value of stator current is 2076.2 A and the SS value of 2114.37 A is within comparable limits. Figure 8a,b show the values for comparison.

**Figure 8.** (**a**) Calculated rotor current; (**b**) Rotor current of the designed system.

The values of stator voltage are calculated to be 563.383 V, which is similar to the simulated SS value of 563.382 V for all operating points as the stator voltage remains constant. Figure 9a,b show the values for comparison.

**Figure 9.** (**a**) Calculated stator voltage; (**b**) Stator voltage of the designed system.

The values of rotor voltages are calculated to be 86.0158 V, which is similar to the simulated SS value of 87.1958 V for a speed of 1273.21 rpm. Again, for a speed of 1800 rpm, the calculated value of stator current is 106.294 V and the SS value of 104.47 V is within comparable limits. Figure 10a,b show the values for comparison.

**Figure 10.** (**a**) Calculated rotor voltage; (**b**) Rotor voltage of the designed system. **Figure 10.** (**a**) Calculated rotor voltage; (**b**) Rotor voltage of the designed system.

The stator real power in Figure 11b, varies from 824.698 kW to 1693.45 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec (1800 rpm) and is comparable with the calculated value of −824.545 kW and −1693.620 kW as shown in Figure 11a. The stator real power in Figure 12b, varies from 824.698 kW to 1693.45 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec (1800 rpm). With a transition peak of 261.395 kW. The stator reactive power in Figure 13b, remains constant at 589.357 kVAR. The rotor real power in Figure 11b varies from 130.217 kW to 319.068 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec(1800 rpm). The rotor reactive power in Figure 13b changes from 14.067 kVAR to −64.57 kVAR to meet the reactive power demands during subsynchronous and super-synchronous conditions. The stator real power in Figure 11b, varies from 824.698 kW to 1693.45 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec(1800 rpm) and is comparable with the calculated value of −824.545 kW and −1693.620 kW as shown in Figure 11a. The stator real power in Figure 12b, varies from 824.698 kW to 1693.45 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec(1800 rpm). With a transition peak of 261.395 kW. The stator reactive power in Figure 13b, remains constant at 589.357 kVAR. The rotor real power in Figure 11b varies from 130.217 kW to 319.068 kW corresponding to a speed of 133.33 rad/sec (1273.21 rpm) to 188.5 rad/sec(1800 rpm). The rotor reactive power in Figure 13b changes from 14.067 kVAR to −64.57 kVAR to meet the reactive power demands during subsynchronous and super-synchronous conditions.

**Figure 11.** (**a**) Calculated stator real power; (**b**) Stator real power of the designed system. **Figure 11.** (**a**) Calculated stator real power; (**b**) Stator real power of the designed system.

**Figure 12.** (**a**) Calculated rotor real power; (**b**) Rotor real power of the designed system. **Figure 12.** (**a**) Calculated rotor real power; (**b**) Rotor real power of the designed system.

The stator reactive power in Figure 13b, varies from 589.357 kVAR to 590.238 kVAR for change in speed from 1273.21 rpm to 1800 rpm. This is similar to the calculated values of 591.097 kVAR and 596.696 kVAR in Figure 13a.

**Figure 13.** (**a**) Calculated stator reactive power; (**b**) Stator reactive power of the designed system.

The rotor reactive power in Figure 14b changes from 14.067 kVAR to −64.57 kVAR to meet the reactive power demands during subsynchronous and super-synchronous conditions. The values are comparable to the calculated values of 12.4827 kVAR and −69.5111 kVAR in Figure 14a.

**Figure 14.** (**a**) Calculated rotor reactive power; (**b**) Rotor reactive power of the designed system.

The values of Is, Ir, Vs, Vr, Ps, Pr, Qs, and Q<sup>r</sup> obtained through computation and simulation for the specific operating point are tabulated in Table 1. The error between the computed and simulated values are calculated and it is found that an overall error of less than 10% is observed for a speed of 1800 rpm and an error of less than 20% is observed for an operating speed of 1273.21 rpm. Hence, it is established from the acquired results that the designed system is working properly and can be used for future analysis.


**Table 1.** Comparison of SS magnitudes.


**Table 1.** *Cont.*

↑↑ indicates percentage increased from computed value; ↓↓ percentage decreased from the computed value.

#### **5. Conclusions**

In this paper, the SS performance analysis of the DFIG based WT with rotor magnetizing strategy Idr = 0 and the DFIG system design in MATLAB/Simulink is presented. For the analysis, a 2 MW DFIG WT was chosen with torque-speed datasets of an MWT 92 Mitsubishi WT design. The SS magnitudes of the DFIG were computed based on SS equations and the values were plotted. These SS values were further used for the validation of the designed system for a specific operating mode corresponding to a rotor speed of 1800 rpm. The simulation results were, in turn, compared with the calculated value and the overall error in SS magnitudes was found to be less than 10% which shows the acceptable performance of the designed system. The designed system can be used by the scientific community for a detailed study of the wind turbine based DFIG such as WT behavior under fault, performance under various test conditions, and for further research on the topic.

**Author Contributions:** All authors contributed equality in each task towards the paper. More specifically: B.A. and J.P.S.: Page: 16 conceptualization; I.V.: methodology; J.P.S.: software; R.S.R.: validation; J.P.S.: formal analysis; R.S.R.: investigation; B.A.: resources; J.P.S.: data curation; J.P.S. and I.V.: writing—original draft preparation; R.S.R.: writing—review and editing; J.P.S.: visualization; I.V.: supervision; I.V.: project administration; B.A.: funding acquisition; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Deanship of Scientific Research at Najran University Research Funding Program under the General Research Funding program, grant code (NU/- /SERC/10/649).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work under the General Research Funding program grant code (NU/- /SERC/10/649).

**Conflicts of Interest:** The authors declare that they have no conflict of interest to report regarding the present study.

#### **Nomenclature**

