4. Simulation results

The generator is tested under single line to ground fault condition on phase 'a'; at 1.5 s an unbalanced voltage drop of 20% is created for a time of 0.1 s as shown in Figure 3. In this section, all the physical quantities are in per unit values, and the quantities of the rotor are referred to the stator side. Figure 7 shows the Simulink block diagram of the DFIG wind turbine model. The switching frequency of converter is set to 1 kHz; the nominal DC converter is set to 2000 V. Wind speed varies from 10 to 11 m/s. To examine the validity of the proposed

Figure 7. Simulink block diagram of the DFIG wind turbine model.

Dual Robust Control of Grid-Connected DFIGs-Based Wind-Turbine-Systems under Unbalanced Grid Voltage… http://dx.doi.org/10.5772/intechopen.75518 93

Figure 8. Stator active power (pu): (a) conventional single RCS, (b) proposed dual RCS.

<sup>V</sup>\_ <sup>¼</sup> STð Þ<sup>x</sup>

92 Stability Control and Reliable Performance of Wind Turbines

current controller and the calculation of the current references.

Figure 7. Simulink block diagram of the DFIG wind turbine model.

4. Simulation results

H<sup>1</sup> H<sup>2</sup> H<sup>3</sup> H<sup>4</sup>

0

BBBBB@

�

It is worth mentioning that if the positive control gains satisfy the following condition, specifically, K1 > |H1|, K2 > |H2|, K3 > |H3| and K4 > |H4| the time derivative of Lyapunov function V\_ is still definitely negative. Consequently, the control law features are robust. Figure 6 shows the block diagram of the VC scheme for DFIG using Lyapunov-based robust control (RC). In this block diagram, the Phase-Locked-Loop (PLL) estimates the frequency, the grid voltage magnitude and the stator angle. The block of separate positive and negative sequences of the current and the voltage shown in Figure 1 is used in this schema for the dual

The generator is tested under single line to ground fault condition on phase 'a'; at 1.5 s an unbalanced voltage drop of 20% is created for a time of 0.1 s as shown in Figure 3. In this section, all the physical quantities are in per unit values, and the quantities of the rotor are referred to the stator side. Figure 7 shows the Simulink block diagram of the DFIG wind turbine model. The switching frequency of converter is set to 1 kHz; the nominal DC converter is set to 2000 V. Wind speed varies from 10 to 11 m/s. To examine the validity of the proposed

K1sat Sð Þ<sup>1</sup> K2sat Sð Þ<sup>2</sup> K3sat Sð Þ<sup>3</sup> K4sat Sð Þ<sup>4</sup>

1

CCCCCA

≤ 0 (34)

Figure 9. Harmonic spectra of the stator active power (pu): (a) conventional single RCS, (b) proposed dual RCS.

dual Lyapunov based robust control scheme (RCS), these results are compared with the conventional single Lyapunov-based RCS published in [15].

Figures 8(a) and (b), 9(a) and (b), 10(a) and (b) and 11(a) and (b), show that, during grid voltage unbalance, if conventional control is applied, the active and reactive powers contain important oscillations due to the nature of the second harmonic at twice the grid frequency (100 Hz) with magnitude of 0.78 pu. The conventional control does not provide adequate control of the negative sequence current during the occurrence or removal of voltage unbalance. Whereas, by using the proposed control method, these oscillations are dramatically reduced because of the negative sequence current compensation, during grid fault, by the dual current control loops which can indirectly control these powers.

Figure 10. Stator reactive power (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 11. Harmonic spectra of the stator reactive power (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 12. Electromagnetic torque (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 13. Harmonic spectra of the electromagnetic torque (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figures 12(a) and (b) and 13(a) and (b) show that the ripples of the electromagnetic torque are also mitigated with the proposed control. On the contrary, when we use the conventional control method, the electromagnetic torque has oscillations with magnitude of 0.74 pu and frequency of 100 Hz, which might be harmful to the mechanical parts.

control method. This is due to the fact that the conventional control cannot control the negative component introduced by the unbalanced voltage in the stator flux and current vectors to zero. In that situation, interaction of these components in the generator develops motoring and generating behavior resulting in excessive oscillations. The stator flux amplitude is constant at the steadystate and rotates synchronously with the grid voltage. Instantly after the occurrence of the unbalanced voltage dip (see Figure 3), two voltages cause a positive and negative flux in the stator. Unlike the case of balanced voltage dip, where two components will be induced in the stator flux: the forced component is rotating with the grid frequency; afterward, the natural flux is

Figure 15. Harmonic spectra of the stator currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

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Figure 14. Stator currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 16. Rotor currents (pu): (a) conventional single RCS, (b) proposed RCS.

static with the stator.

Figures 14(a) and (b) and 15(a) and (b) show that the stator currents have important harmonics with conventional control, which are injected into grid, but these currents are quite sinusoidal and symmetrical with the proposed control.

Figures 16(a) and (b) and 17(a) and (b) show that the currents at the rotor side are also unbalanced with conventional control, but these oscillations are attenuated by using the proposed

Dual Robust Control of Grid-Connected DFIGs-Based Wind-Turbine-Systems under Unbalanced Grid Voltage… http://dx.doi.org/10.5772/intechopen.75518 95

Figure 14. Stator currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 15. Harmonic spectra of the stator currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 16. Rotor currents (pu): (a) conventional single RCS, (b) proposed RCS.

Figures 12(a) and (b) and 13(a) and (b) show that the ripples of the electromagnetic torque are also mitigated with the proposed control. On the contrary, when we use the conventional control method, the electromagnetic torque has oscillations with magnitude of 0.74 pu and

Figure 13. Harmonic spectra of the electromagnetic torque (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 11. Harmonic spectra of the stator reactive power (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figures 14(a) and (b) and 15(a) and (b) show that the stator currents have important harmonics with conventional control, which are injected into grid, but these currents are quite sinusoidal

Figures 16(a) and (b) and 17(a) and (b) show that the currents at the rotor side are also unbalanced with conventional control, but these oscillations are attenuated by using the proposed

frequency of 100 Hz, which might be harmful to the mechanical parts.

Figure 12. Electromagnetic torque (pu): (a) conventional single RCS, (b) proposed dual RCS.

and symmetrical with the proposed control.

94 Stability Control and Reliable Performance of Wind Turbines

control method. This is due to the fact that the conventional control cannot control the negative component introduced by the unbalanced voltage in the stator flux and current vectors to zero. In that situation, interaction of these components in the generator develops motoring and generating behavior resulting in excessive oscillations. The stator flux amplitude is constant at the steadystate and rotates synchronously with the grid voltage. Instantly after the occurrence of the unbalanced voltage dip (see Figure 3), two voltages cause a positive and negative flux in the stator. Unlike the case of balanced voltage dip, where two components will be induced in the stator flux: the forced component is rotating with the grid frequency; afterward, the natural flux is static with the stator.

Figure 17. Harmonic spectra of the rotor currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 18. Stator flux (pu): (a) conventional single RCS, (b) proposed dual RCS.

Figure 18(a) and (b) shows the trajectory of the stator flux. Before the voltage unbalance, the stator flux traces a circle with radius equal to 1 pu. The flux of the stator with the proposed dual RCS is very well centered compared with that obtained with the conventional single RCS. When the voltage unbalance starts, the ellipse trajectory drawn by the flux is due to the presence of positive and negative flux in the stator rotating in opposite directions, which is a common characteristic in unbalanced voltage sags. Whereas, the natural flux brings the ellipse to be off-center. After the clearance of the voltage unbalance, the natural component of the stator flux is attenuated and the trajectory of the stator flux turns into the center again. However, it is noticed from these figures that compared with the proposed dual RCS, the stator flux trajectory of the conventional single RCS is not well centered with an important transient with a slow decay.

ripples compared with the conventional method. In addition, the proposed dual RCS is able to reduce the harmonics of the rotor and stator currents. It can be concluded from these strategies that the proposed control method can effectively reduce the torque oscillations which inciden-

Figure 19. Comparison of ripples in electromagnetic torque, stator active and reactive power between the two control

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Figure 20. Comparison of harmonics in stator and rotor currents between the two control strategies.

In this chapter, an improved control strategy for doubly fed induction generator (DFIG)-based wind turbine under unbalanced grid voltage is presented. The dynamic behavior of DFIG by the proposed control algorithm proved to be suitable by a set of simulation tests using the MATLAB®/Simulink® environment. The results obtained imply that with the conventional single robust control scheme (RCS), the magnitude of the second harmonic oscillations can become high, intolerable and may lead to electrical and mechanical failure in function. After

tally may lead to a decrease of the fatigues on the turbine shaft.

5. Conclusions

strategies.

For clear illustrations, Figures 19 and 20 are included to show the comparative results of ripples pulsating at twice the grid frequency (100 Hz) in the stator active/reactive powers and electromagnetic torque among these different control strategies during network unbalance. As presented, the proposed dual RCS aims at mitigating the torque pulsations and the power Dual Robust Control of Grid-Connected DFIGs-Based Wind-Turbine-Systems under Unbalanced Grid Voltage… http://dx.doi.org/10.5772/intechopen.75518 97

Figure 19. Comparison of ripples in electromagnetic torque, stator active and reactive power between the two control strategies.

Figure 20. Comparison of harmonics in stator and rotor currents between the two control strategies.

ripples compared with the conventional method. In addition, the proposed dual RCS is able to reduce the harmonics of the rotor and stator currents. It can be concluded from these strategies that the proposed control method can effectively reduce the torque oscillations which incidentally may lead to a decrease of the fatigues on the turbine shaft.

#### 5. Conclusions

Figure 18(a) and (b) shows the trajectory of the stator flux. Before the voltage unbalance, the stator flux traces a circle with radius equal to 1 pu. The flux of the stator with the proposed dual RCS is very well centered compared with that obtained with the conventional single RCS. When the voltage unbalance starts, the ellipse trajectory drawn by the flux is due to the presence of positive and negative flux in the stator rotating in opposite directions, which is a common characteristic in unbalanced voltage sags. Whereas, the natural flux brings the ellipse to be off-center. After the clearance of the voltage unbalance, the natural component of the stator flux is attenuated and the trajectory of the stator flux turns into the center again. However, it is noticed from these figures that compared with the proposed dual RCS, the stator flux trajectory of the conventional single RCS is not well centered with an important

Figure 17. Harmonic spectra of the rotor currents (pu): (a) conventional single RCS, (b) proposed dual RCS.

96 Stability Control and Reliable Performance of Wind Turbines

Figure 18. Stator flux (pu): (a) conventional single RCS, (b) proposed dual RCS.

For clear illustrations, Figures 19 and 20 are included to show the comparative results of ripples pulsating at twice the grid frequency (100 Hz) in the stator active/reactive powers and electromagnetic torque among these different control strategies during network unbalance. As presented, the proposed dual RCS aims at mitigating the torque pulsations and the power

transient with a slow decay.

In this chapter, an improved control strategy for doubly fed induction generator (DFIG)-based wind turbine under unbalanced grid voltage is presented. The dynamic behavior of DFIG by the proposed control algorithm proved to be suitable by a set of simulation tests using the MATLAB®/Simulink® environment. The results obtained imply that with the conventional single robust control scheme (RCS), the magnitude of the second harmonic oscillations can become high, intolerable and may lead to electrical and mechanical failure in function. After removing the voltage unbalance, in the conventional control method, small oscillations appear in the powers and currents waveforms. On the contrary, when the proposed dual RCS is used, these power oscillations are effectively damped to a reasonable level. Furthermore, the proposed control strategy shows good performances and robustness by eliminating the pulsations in the torque which maybe preferred by wind farm operators since it will mitigate the fatigue of the turbine shaft as well as the gearbox. Moreover, symmetrical and sinusoidal stator and rotor currents are also obtained, in turn minimizing the copper losses in the rotor circuit, when the grid voltage is unbalanced. All computer simulations have been designed with a fixed-step size of 0.5 ms in order to consider digital implementation in future works.

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