**1. Introduction**

Induction motors (IM) are very common because they are inexpensive and robust, finding use in everything from industrial applications such as pumps, fans, and blowers to home appliances. In recent years, the control of high-performance IM drives for general industrial applications and production areas has received a lot of research interests.

The most modern technique, for the induction machine, is the direct torque and the stator flux vector control method (DTC). It has been realized in an industrial way by ABB, using the theoretical background proposed by *Takahashi* [1] and Depenbrock [2] in the middle of 1980's. Over the years, DTC method becomes one of the high-performance control strategies for AC machines to provide a very fast torque and flux control [3, 4].

The DTC has been selected in order to fulfill the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the gusts of wind. This positioning system can be introduced in the multi-sources hybrid system, in order to allow high efficiencies of photovoltaic systems. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. In what follows, the chapter will be focused on the problem of position regulation of an induction motor under DTC and DTC-SVM strategies.

considering that subscripts *s* and *r* refer to stator and rotor, subscripts *α* and *β* refer to components in ð Þ *α*, *β* frame, *v*, *i* and ð*ρ* refer to voltage, current and flux, *Rs* and *Rr* refer to stator and rotor resistances, and *ω<sup>m</sup>* refers to the machine speed

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications*

*ϕα<sup>s</sup>* ¼ *Lsi<sup>α</sup><sup>s</sup>* þ *Mi<sup>α</sup><sup>r</sup> ϕα<sup>r</sup>* ¼ *Mi<sup>α</sup><sup>s</sup>* þ *Lri<sup>α</sup><sup>r</sup> ϕβ<sup>r</sup>* ¼ *Mi<sup>β</sup><sup>s</sup>* þ *Lri<sup>β</sup><sup>r</sup> ϕβ<sup>s</sup>* ¼ *Lsi<sup>β</sup><sup>s</sup>* þ *Mi<sup>β</sup><sup>r</sup>*

The made constant DC voltage by the rectifier is delivered to the inverter input, which thanks to controlled transistor switches, converts this voltage to three-phase AC voltage signal with wide range variable voltage amplitude and frequency. The voltage vector of the three-phase voltage inverter can be represented as

*Sa* <sup>þ</sup> *Sbe <sup>j</sup>*

where *Sa*, *Sb* and *Sc* are three-phase inverter switching functions, which can take

The implementation scheme of the *Takahashi* basic DTC strategy applied to the

Referring to [5, 6], it has been found that the *Takahashi* basic DTC strategy is penalized at low speeds by the so-called "demagnetization phenomenon" which is caused by the systematic application of zero voltage vectors when the torque regulator output is zero, independently of the flux regulator output state. Indeed, the application of these voltage vectors during a sampling period *Ts* yields a slight decrease of the stator flux at high speeds. However, at low speeds, the application of

2*π* <sup>3</sup> <sup>þ</sup> *Sce <sup>j</sup>*

4*π* 3 h i (4)

*dt* <sup>Ω</sup>*<sup>m</sup>* <sup>¼</sup> *Tem* � *Tl* (3)

(2)

(*ω<sup>m</sup>* ¼ *Np*Ω*<sup>m</sup>* ¼ *ω<sup>s</sup>* � *ω<sup>r</sup>* and *Np* is the pole pair number). Relationships between currents and flux are:

*DOI: http://dx.doi.org/10.5772/intechopen.94436*

8 >>><

>>>:

where *L* and *M* refer to the inductance and the mutual one. The mechanical part of the machine is described by:

*J d*

where *J* is the motor inertia and *Tl* represent the load torque.

ffiffiffi 2 3 r

position regulation of an induction motor drive is shown in **Figure 1**.

zero voltage vectors leads to a high reduction of the stator flux, yielding the

In order to overcome this shortcoming, the zero-voltage vectors can be substituted by active ones. For a given stator flux vector and when the torque regulator output is "0", the active vector around which is located the sector including the stator flux vector, is applied. The resulting look-up table is given in **Table 1**. Nevertheless, this substitution is associated to an other crucial problem: that is an increase of the inverter switching frequency which compromises the drive

demagnetization problem which affects the electromagnetic torque.

*V* ! *<sup>s</sup>* ¼

**2.4 Basic concept of DTC based position control**

**2.3 Voltage source inverter**

a logical value of either 0 or 1.

follows:

efficiency.

**41**

#### **2. A case study: solar panel positioning**

#### **2.1 Problem heading**

Photovoltaic panels are commonly exposed to the sun in a fixed position corresponding to the maximum sunshine recorded during a day that is the position of the sun at midday. Nevertheless, this strategy does not allow the extraction of the maximum power during a day and therefore a high efficiency of photovoltaic systems, which can be integrated with the multi-source hybrid system, described above. An approach to solve this problem consists in moving photovoltaic panels according to the maximum sunshine position. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. Accounting for the high perturbation amplitude applied to the panel, the control strategy to be implemented in the drive is of great importance [5].

The proposed tracking system has two freedom degrees in such a way that it allows the displacement of the photovoltaic system within latitudes and meridians: the first degree of freedom is controlled automatically by an IM drive under the control of a DTC strategy.

The DTC approach has been selected in order to full the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the gusts of wind.

The following work will be focused on the study of the first freedom degree. Special attention is paid to the implementation of a suitable DTC strategy in the IM drive.

#### **2.2 Mathematical model of induction machines**

The dynamic behavior of an induction machine is defined in terms of space variables in the sequel:

$$\begin{cases} \frac{d}{dt}\phi\_{\alpha\varepsilon} = v\_{\alpha\varepsilon} - R\_s i\_{\alpha\varepsilon} \\ \frac{d}{dt}\phi\_{\beta\varepsilon} = v\_{\beta\varepsilon} - R\_s i\_{\beta\varepsilon} \\ \frac{d}{dt}\phi\_{ar} = -R\_r i\_{ar} - \alpha\_m \phi\_{\beta r} \\ \frac{d}{dt}\phi\_{\beta r} = -R\_r i\_{\beta r} + \alpha\_m \phi\_{\alpha r} \end{cases} \tag{1}$$

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications DOI: http://dx.doi.org/10.5772/intechopen.94436*

considering that subscripts *s* and *r* refer to stator and rotor, subscripts *α* and *β* refer to components in ð Þ *α*, *β* frame, *v*, *i* and ð*ρ* refer to voltage, current and flux, *Rs* and *Rr* refer to stator and rotor resistances, and *ω<sup>m</sup>* refers to the machine speed (*ω<sup>m</sup>* ¼ *Np*Ω*<sup>m</sup>* ¼ *ω<sup>s</sup>* � *ω<sup>r</sup>* and *Np* is the pole pair number).

Relationships between currents and flux are:

$$\begin{cases} \phi\_{\alpha r} = L\_s i\_{\alpha r} + M i\_{\alpha r} \\ \phi\_{\alpha r} = M i\_{\alpha s} + L\_r i\_{\alpha r} \\ \phi\_{\beta r} = M i\_{\beta s} + L\_r i\_{\beta r} \\ \phi\_{\beta s} = L\_s i\_{\beta s} + M i\_{\beta r} \end{cases} \tag{2}$$

where *L* and *M* refer to the inductance and the mutual one. The mechanical part of the machine is described by:

$$J\frac{d}{dt}\Omega\_m = T\_{em} - T\_l \tag{3}$$

where *J* is the motor inertia and *Tl* represent the load torque.

#### **2.3 Voltage source inverter**

The DTC has been selected in order to fulfill the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the gusts of wind. This positioning system can be introduced in the multi-sources hybrid system, in order to allow high efficiencies of photovoltaic systems. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. In what follows, the chapter will be focused on the problem of position regulation of an induction motor

Photovoltaic panels are commonly exposed to the sun in a fixed position corresponding to the maximum sunshine recorded during a day that is the position of the sun at midday. Nevertheless, this strategy does not allow the extraction of the maximum power during a day and therefore a high efficiency of photovoltaic systems, which can be integrated with the multi-source hybrid system, described above. An approach to solve this problem consists in moving photovoltaic panels according to the maximum sunshine position. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. Accounting for the high perturbation amplitude applied to the panel, the control strategy to be implemented in the drive

The proposed tracking system has two freedom degrees in such a way that it allows the displacement of the photovoltaic system within latitudes and meridians: the first degree of freedom is controlled automatically by an IM drive under the

The DTC approach has been selected in order to full the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the

The following work will be focused on the study of the first freedom degree. Special

attention is paid to the implementation of a suitable DTC strategy in the IM drive.

The dynamic behavior of an induction machine is defined in terms of space

*dt ϕα<sup>s</sup>* <sup>¼</sup> *<sup>v</sup><sup>α</sup><sup>s</sup>* � *Rsi<sup>α</sup><sup>s</sup>*

*dt ϕβ<sup>s</sup>* <sup>¼</sup> *<sup>v</sup><sup>β</sup><sup>s</sup>* � *Rsi<sup>β</sup><sup>s</sup>*

*dt ϕα<sup>r</sup>* ¼ �*Rri<sup>α</sup><sup>r</sup>* � *<sup>ω</sup>mϕβ<sup>r</sup>*

(1)

*dt ϕβ<sup>r</sup>* ¼ �*Rri<sup>β</sup><sup>r</sup>* <sup>þ</sup> *<sup>ω</sup>mϕα<sup>r</sup>*

**2.2 Mathematical model of induction machines**

*d*

8

>>>>>>>>>><

>>>>>>>>>>:

*d*

*d*

*d*

under DTC and DTC-SVM strategies.

**2.1 Problem heading**

is of great importance [5].

control of a DTC strategy.

gusts of wind.

**40**

variables in the sequel:

**2. A case study: solar panel positioning**

*Direct Torque Control Strategies of Electrical Machines*

The made constant DC voltage by the rectifier is delivered to the inverter input, which thanks to controlled transistor switches, converts this voltage to three-phase AC voltage signal with wide range variable voltage amplitude and frequency.

The voltage vector of the three-phase voltage inverter can be represented as follows:

$$\overrightarrow{\mathbf{V}}\_{s} = \sqrt{\frac{2}{3}} \left[ \mathbf{S}\_{a} + \mathbf{S}\_{b} e^{j\frac{2\pi}{3}} + \mathbf{S}\_{c} e^{j\frac{4\pi}{3}} \right] \tag{4}$$

where *Sa*, *Sb* and *Sc* are three-phase inverter switching functions, which can take a logical value of either 0 or 1.

#### **2.4 Basic concept of DTC based position control**

The implementation scheme of the *Takahashi* basic DTC strategy applied to the position regulation of an induction motor drive is shown in **Figure 1**.

Referring to [5, 6], it has been found that the *Takahashi* basic DTC strategy is penalized at low speeds by the so-called "demagnetization phenomenon" which is caused by the systematic application of zero voltage vectors when the torque regulator output is zero, independently of the flux regulator output state. Indeed, the application of these voltage vectors during a sampling period *Ts* yields a slight decrease of the stator flux at high speeds. However, at low speeds, the application of zero voltage vectors leads to a high reduction of the stator flux, yielding the demagnetization problem which affects the electromagnetic torque.

In order to overcome this shortcoming, the zero-voltage vectors can be substituted by active ones. For a given stator flux vector and when the torque regulator output is "0", the active vector around which is located the sector including the stator flux vector, is applied. The resulting look-up table is given in **Table 1**. Nevertheless, this substitution is associated to an other crucial problem: that is an increase of the inverter switching frequency which compromises the drive efficiency.

**2.6 Simulations and discussions: A comparative study**

they have been selected as *εϕ* ¼ 0*:*02*Wb* and *ετ* ¼ 3*:*5*N*.

calculated and has been found equal to 57.762 N.m.

*Induction motor position regulation based on the DTC-SVM strategy.*

Power 10 kW Voltage 380 V/220 V Efficiency 80% Current 24A/41A Speed 1500 rpm Frequency 50 Hz

study, are listed in **Tables 2** and **3** respectively.

*DOI: http://dx.doi.org/10.5772/intechopen.94436*

chosen equal to 100*μ*s.

under study.

**Figure 2.**

**Table 2.**

**43**

*Induction machine ratings.*

The ratings and parameters of the induction machine, used in the simulation

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications*

• The sampling period *Ts* has been chosen equal to 50*μs* in the cases of the first and the second strategies, whereas in the case of the third strategy, it has been

• Bandwidths of flux and torque hysteresis regulators have been chosen as: *εϕ* ¼ 0*:*02*Wb* and *ετ* ¼ 5*N* for the two first strategies, whereas for the third one,

• The load torque is given by the following expression: *Tl* ¼ *K* sin *θ: K* has been

• The modulation period has been fixed to *Tmod* ¼ 150*μs* in DTC-SVM approach

**Figure 1.** *IM position regulation based on basic DTC strategy.*


#### **Table 1.**

*Look-up table with zero-voltage vectors substituted by active ones.*

#### **2.5 Concept of DTC-SVM with hysteresis controllers based position control**

The implementation scheme of the DTC-SVM strategy with hysteresis controllers applied to the position regulation of an induction motor drive is shown in **Figure 2**. It has the same layout as the one of the basic DTC strategy proposed in section II, except that the SVM bloc is added to the control system that ensures an imposed switching frequency [7–12].

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications DOI: http://dx.doi.org/10.5772/intechopen.94436*
