**5. Results and discussion**

The predictive DTC control scheme of DFIM has been implemented using MATLAB/Simulink. The specifications of DFIM are given in **Table 4**. The

*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque… DOI: http://dx.doi.org/10.5772/intechopen.89979*


**Table 4.**

*Specifications of DFIM and wind turbine.*

conditions of steady state, transient, tracking behavior, and performance near synchronism of DFIM are examined, which are given in three subsections.

#### **5.1 Transient and steady state analysis of DFIM**

The performance of proposed control strategy of DFIM is analyzed for steady state and transient conditions. For the transient conditions, the step change in electromagnetic torque i.e., from 0.4 pu to +0.4 pu at 0.6 s is considered. That means, from generator mode (negative torque) to motoring mode (positive torque), with constant switching frequency of 1 kHz, with speed reference of 1350 rev/min, and DC-link voltage of 1200 V. The DFIM is under steady state

operation up to 0.6 s with torque of 0.4 pu and at 0.6 s the DFIM enters into transient state, and again it reaches its steady state value of 0.4 pu.

The response of stator currents in stationary reference frame are shown in **Figure 3(a)**. Therefore, there are two waveforms which refer to α, β components of stator currents. From the **Figure 3(a)**, it is observed that there are no over currents in stator, which indicates the effectiveness of the proposed control scheme even at sudden variation in torque demand. This is possible because of selection of proper rotor voltage vectors with their respective time intervals.

**Figure 3(b)** shows the response of developed torque for the proposed strategy and classical DTC strategy (not expressed in p.u. value), from the figure, it is noticed that the torque response of the DFIM closely followed the torque command and also torque ripple is zero.

From the **Figure 3(c)**, it can be seen that stator active power has good dynamic response when the reference torque is changed suddenly. From the figure, it is observed that the stator active power follows the torque demand to make the DFIM to develop the torque to match its reference value.

The response of the stator flux is shown in **Figure 3(d)**, from the figure, it is clearly noticed that the stator flux response remains constant which is not affected by variation in torque command.

The response of the rotor flux is shown in **Figure 3(e)**, from the figure, it is observed that the rotor flux response is also not affected by change in reference torque and also the rotor flux response is sinusoidal in nature which is not distorted due to sudden change in torque command.

**Figure 3(f)** shows response of the rotor speed of DFIM. From the **Figure 3(f)**, it is observed that there is decrease in rotor speed due to step change in reference torque but decrease in rotor speed is very small.

The response of rotor currents is shown in **Figure 3(g)**. From the **Figure 3(g)**, it is observed that there are no over currents in rotor, which indicates the effectiveness of the proposed control scheme even at sudden variation in torque demand. This is possible because of selection of proper rotor voltage vectors with their respective time intervals.

#### **5.2 Performance analysis of DFIM during variable torque behavior**

In this section, the proposed control scheme of DFIM is investigated for variable speed operation implying wind energy applications, and at the same instant, the torque reference may also vary respectively with speed of DFIM. This kind of behavior of wind energy system is called as tracking behavior. At this condition, the actual values of the DFIM should follow the reference values as closely as possible and this is clearly guaranteed by proposed control strategy which can be seen clearly through the results presented in this section. To explore the tracking behavior of DFIM, sinusoidally varying reference torque with amplitude of 0.4 pu and frequency of 3 Hz is set to the DFIM. By this set reference torque, the DFIM operates in generating and motoring modes. In this mode of operation, the other parameters of DFIM are same as mentioned in Section 5.1.

The predictive DTC strategy has good tracking behavior and it is confirmed that the reduction in torque and flux ripples is achieved as there are absolute absence of over currents and reduced ripples in stator currents as shown in **Figure 4(a)**. From the **Figure 4(a)**, it is noticed that there is continuous increase and decrease in the amplitude of stator currents for maintaining the consistency due to variable behavior of torque command. The stationary reference frame stator currents are clearly noticed in **Figure 4(a)**.

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*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque… DOI: http://dx.doi.org/10.5772/intechopen.89979*

The torque produced by the DFIM follows as closely as the reference torque, which indicates good tracking behavior of the proposed control scheme comparative to classical DTC (not expressed in p.u. value), it can be seen in

*(a) Response of stator currents of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (b) Torque response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s, (i) proposed strategy (ii) classical DTC. (c) stator active power of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (d) Stator flux response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (e) Response of rotor flux of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (f) Rotor speed response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (g) Response of rotor currents of DFIM for step change in Tem from 0.4 pu*

*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque…*

*DOI: http://dx.doi.org/10.5772/intechopen.89979*

respectively. From the **Figure 4(c)** and **(d)**, it is observed that the variation in torque command is not having any influence on the stator and rotor fluxes

Stator flux and rotor flux responses of DFIM are shown in **Figure 4(c)** and **(d)**

**Figure 4(e)** shows the rotor speed response of DFIM. From the **Figure 4(e)**, it is observed that there is continuous variation in rotor speed; of course, this variation is

**Figure 4(b)**.

*to 0.4 pu at 0.6 s.*

**Figure 3.**

of DFIM.

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#### **Figure 3.**

*(a) Response of stator currents of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (b) Torque response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s, (i) proposed strategy (ii) classical DTC. (c) stator active power of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (d) Stator flux response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (e) Response of rotor flux of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (f) Rotor speed response of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s. (g) Response of rotor currents of DFIM for step change in Tem from 0.4 pu to 0.4 pu at 0.6 s.*

The torque produced by the DFIM follows as closely as the reference torque, which indicates good tracking behavior of the proposed control scheme comparative to classical DTC (not expressed in p.u. value), it can be seen in **Figure 4(b)**.

Stator flux and rotor flux responses of DFIM are shown in **Figure 4(c)** and **(d)** respectively. From the **Figure 4(c)** and **(d)**, it is observed that the variation in torque command is not having any influence on the stator and rotor fluxes of DFIM.

**Figure 4(e)** shows the rotor speed response of DFIM. From the **Figure 4(e)**, it is observed that there is continuous variation in rotor speed; of course, this variation is

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*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque… DOI: http://dx.doi.org/10.5772/intechopen.89979*

#### **Figure 4.**

*(a) Response of stator currents of DFIM with variable torque command. (b) Response of developed torque of DFIM with variable torque command (i) proposed strategy (ii) classical DTC. (c) Response of stator flux of DFIM with variable torque command. (d) Response of rotor flux of DFIM with variable torque command. (e) Response of rotor speed of DFIM with variable torque command. (f) Response of rotor currents of DFIM with variable torque command.*

very small it is because of variable torque command, but practically rotor speed almost constant.

The predictive DTC strategy has good tracking behavior and it is confirmed that the reduction in torque and flux ripples is achieved as there are absolute absence of over currents and reduced ripples in rotor currents as shown in **Figure 4(f)**. From the **Figure 4(f)**, it is noticed that there is continuous increase and decrease in the amplitude of rotor currents, similar to stator currents as shown in **Figure 4(a)**.

#### **5.3 Performance of DFIM near synchronous speed**

In this Section, the performance of the proposed control scheme of DFIM has been investigated near the synchronous speed. This is examined by varying the speed of DFIM from 1580 rpm (hyper synchronous value) to 1340 rpm (sub synchronous value) in terms of sine wave with frequency of 3 rads<sup>1</sup> and phase shift of 90°, with the reference values of torque and rotor flux are set to 0.4 pu and 1 pu respectively.

Even when the speed command is varied suddenly from hyper synchronous value to sub synchronous value no much transient peaks occur in stator currents, as shown in **Figure 5(a)**, which clearly emphasizes there is reduction in over currents in stator and this is because of proper selection of switching sequence of rotor voltage vectors.

As shown in **Figure 5(b)**, the torque developed by the machine for proposed strategy and classical DTC and it closely follows the reference torque which means the dynamic performance of the machine is quite satisfactory but when the rotor speed nears the synchronous speed at around 0.5 s, variable torque ripple is produced. This variability in the torque ripple is due to continuous selection of zero voltage vectors at that instant. It indicates, the smaller amplitude of rotor voltage vector is required at the instant of rotor speed nearing the synchronism, which

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actually causes the reduction in torque ripple and this leads to degradation of quality of control. As shown in **Figure 5(b)**, the ripples are reduced in electromag-

*(a) Response of stator currents of DFIM with variation in rotor speed from 1580 to 1340 rpm. (b) Torque response of DFIM with variation in rotor speed from 1580 to 1340 rpm (i) proposed strategy and (ii) classical DTC. (c) Response of stator flux of DFIM with variation in rotor speed from 1580 to 1340 rpm. (d) Response of rotor flux of DFIM with variation in rotor speed from 1580 to 1340 rpm. (e) Rotor speed of DFIM with variation in rotor speed from 1580 to 1340 rpm. (f) Response of rotor currents of DFIM with variation in rotor*

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The response of rotor flux is shown in **Figure 5(d)**, from the figure, it is observed that there is no effect on the rotor flux due to sudden change in the rotor

speed and rotor flux is also not affected by the changeover.

that the rotor speed response of DFIM follows the command speed.

Stator flux responses are shown in **Figure 5(c)**. From the figure, it is observed that the stator flux remains constant and is not affected by change in rotor speed

The response of rotor speed is as shown in **Figure 5(e)**, when reference speed is varied from hyper synchronous value to sub-synchronous value and it is observed

The proposed control method makes two general contributions to the predictive control techniques. Firstly, it shows that using instead of two voltage vectors operating three appropriate vectors, allows operating at low constant switching frequency. Secondly, it is crucial to achieve the whole good performance of the DFIM, in terms of torque and current ripples by reducing the ripples of both directly

Similar to stator currents as shown in **Figure 5(a)**, no much transient peaks occur in rotor currents, as shown in **Figure 5(f)**, that is, there is reduction in over currents in the rotor, which is because of proper selection of switching sequence of

netic torque response.

*speed from 1580 to 1340 rpm.*

**Figure 5.**

rotor voltage vectors.

**6. Conclusions**

**119**

and also it is sinusoidal in nature.

controlled variables instead of only one.

*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque… DOI: http://dx.doi.org/10.5772/intechopen.89979*

#### **Figure 5.**

*(a) Response of stator currents of DFIM with variation in rotor speed from 1580 to 1340 rpm. (b) Torque response of DFIM with variation in rotor speed from 1580 to 1340 rpm (i) proposed strategy and (ii) classical DTC. (c) Response of stator flux of DFIM with variation in rotor speed from 1580 to 1340 rpm. (d) Response of rotor flux of DFIM with variation in rotor speed from 1580 to 1340 rpm. (e) Rotor speed of DFIM with variation in rotor speed from 1580 to 1340 rpm. (f) Response of rotor currents of DFIM with variation in rotor speed from 1580 to 1340 rpm.*

actually causes the reduction in torque ripple and this leads to degradation of quality of control. As shown in **Figure 5(b)**, the ripples are reduced in electromagnetic torque response.

Stator flux responses are shown in **Figure 5(c)**. From the figure, it is observed that the stator flux remains constant and is not affected by change in rotor speed and also it is sinusoidal in nature.

The response of rotor flux is shown in **Figure 5(d)**, from the figure, it is observed that there is no effect on the rotor flux due to sudden change in the rotor speed and rotor flux is also not affected by the changeover.

The response of rotor speed is as shown in **Figure 5(e)**, when reference speed is varied from hyper synchronous value to sub-synchronous value and it is observed that the rotor speed response of DFIM follows the command speed.

Similar to stator currents as shown in **Figure 5(a)**, no much transient peaks occur in rotor currents, as shown in **Figure 5(f)**, that is, there is reduction in over currents in the rotor, which is because of proper selection of switching sequence of rotor voltage vectors.

#### **6. Conclusions**

The proposed control method makes two general contributions to the predictive control techniques. Firstly, it shows that using instead of two voltage vectors operating three appropriate vectors, allows operating at low constant switching frequency. Secondly, it is crucial to achieve the whole good performance of the DFIM, in terms of torque and current ripples by reducing the ripples of both directly controlled variables instead of only one.

From the proposed control method, it is possible to reduce the stress of the switching devices of the voltage source converter, in terms of low constant switching frequency behavior and switching power losses reduction, often demanded requirements in high power applications.

It presents good tracking behavior, capable of working at variable speed operation conditions, for both motoring and generating modes at sub- synchronous and hyper synchronous speeds when compared to DTC technique, making this control suitable for applications such as wind power generation.

The new DTC technique allows obtaining quick dynamic responses in respect to DTC method, with absolute absence of non-desired over currents in the machine. It ensures reduced torque and flux ripples, due to the control effect. The simulation results showed the effectiveness of the proposed method, to control the torque and the flux of the DFIM at considerably low constant switching frequency.

#### **7. Summary**

In this Chapter, new predictive DTC has been developed for DFIM. The proposed control scheme uses two voltage vectors instead of three voltage vectors and it allows operating at low constant switching frequency and reduces torque and flux ripples, and also capable of working at variable speed operating conditions for both motoring and generating modes at sub-synchronous and hyper synchronous speeds compared to classical DTC technique. The comparison of torque and flux ripple values (difference of maximum to minimum ripple value) and its reduction given by the difference of maximum value and minimum value to average value is given in the **Table 5** below.


**Author details**

**121**

Gopala Venu Madhav<sup>1</sup>

\* and Y.P. Obulesu<sup>2</sup>

\*Address all correspondence to: venumadhav.gopala@gmail.com

provided the original work is properly cited.

1 Department of EEE, Anurag Group of Institutions, Ghatkesar, TS, India

2 School of Electrical Engineering, VIT University, Vellore, Tamilnadu, India

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© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

#### **Table 5.**

*Torque and flux ripple reduction comparison.*

*Predictive Direct Torque Control Strategy for Doubly Fed Induction Machine for Torque… DOI: http://dx.doi.org/10.5772/intechopen.89979*
