**5. Theory of double-feed induction machine**

The beginning of the work in the field of the theory of DFIA was initiated by the research in the late 1960s — early 1970s by the laboratory of double feeding machines under the guidance of doctors of technical sciences M. Botvinnik and Yu. G. Shakaryan [20].

The results of these works were the development of the foundations of the theory, structural schemes, principles of construction, as well as the creation of a number of experimental and industrial installations.

In a double-feed machine, energy is supplied (or withdrawn) to both the stator and rotor windings. This allows you to control the flow of active and reactive power of the dual-feed machine. The expediency of using DFIA is observed in the construction of alternator sets with a variable speed of rotation of the shaft, which is very important for wind power plants.

The stator windings of the machine are connected to the power supply network (U1 = const, f1 = const), and the rotor windings are connected to a separate controlled power source (active semiconductor converter ASC).

There are various options for implementing a controlled power supply in the rotor circuit. A scheme of independent rotor power supply is interested in wind power plants (**Figure 13**).

The active Converter is a three-phase bridge circuit of the inverter, made on transistors. The main property of the active Converter is the ability to two-way transmission of active power. When transmitting power from an AC source, ASC acts as an active controlled rectifier (ACR). When transmitting power from the DC link, ASC acts as an Autonomous Inverter (AI). Such structures allow you to control the flow of active and reactive power between the supply network and the machine.

We write down the equations for the G-shaped equivalent circuit (3)

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

*Equivalent circuit of the DFIA: a) T-shaped equivalent circuit; b) G-shaped equivalent circuit.*

2; *U*<sup>1</sup> ¼ *jX*1*mIm*,*Im* ¼ *I*<sup>1</sup> þ *I*

The following should be taken into account when assessing energy flows

1.The active power in the source is positive when the source gives energy and

2.The reactive power in the source is positive (inductive) when the voltage is ahead of the current, and negative (capacitive) when the voltage is behind the

3.The mechanical power on the shaft is positive in the motor mode of your operation and negative in the generator mode of your operation. Active and

<sup>2</sup> *cos <sup>φ</sup>*2; *<sup>Q</sup>*<sup>1</sup> <sup>¼</sup> <sup>3</sup>

The mechanical power reported to the shaft of the machine at n < n0

2

In the direction of the mechanical power acting on the shaft, the modes can be

(**Figure 15**) and the electrical power obtained by the rotor through a semiconductor converter, are transmitted to the stator and after deduction of losses are recovered

∣

2; *R*<sup>2</sup> ¼ *RsC* þ

<sup>2</sup> are determined from the expressions.

2 *U*∣ 2*I* ∣

<sup>2</sup> *sin φ*<sup>2</sup> (4)

*<sup>U</sup>*1*I*<sup>1</sup> *sin <sup>φ</sup>*1; *<sup>Q</sup>* <sup>¼</sup> <sup>3</sup>

*Rr s*

*<sup>C</sup>*<sup>2</sup> <sup>≈</sup>*Rs* <sup>þ</sup>

*Rr s* ;

(3)

*U*∣

**Figure 14.**

<sup>2</sup> ¼ *U*<sup>1</sup> þ *R*2*I*

current.

*<sup>P</sup>*<sup>1</sup> <sup>¼</sup> <sup>3</sup> 2

to the grid.

**Figure 15.**

**13**

∣ <sup>2</sup> þ *jX*2*I* ∣

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

*<sup>X</sup>*<sup>2</sup> <sup>¼</sup> *XlsC* <sup>þ</sup> *XlrC*<sup>2</sup> <sup>≈</sup>*Xls* <sup>þ</sup> *Xlr*; *<sup>X</sup>*1*<sup>m</sup>* <sup>¼</sup> *Xls* <sup>þ</sup> *Xm*

negative when the source consumes energy.

reactive power sources *<sup>U</sup>*<sup>1</sup> and *<sup>U</sup>*<sup>∣</sup>

divided into motor mode and generator mode.

2 *U*∣ 2*I* ∣

*Vector diagram and energy diagram of DFD in generator mode at n < n0.*

We consider only all generator modes for a wind turbine.

*<sup>U</sup>*1*I*<sup>1</sup> *cos <sup>φ</sup>*1; *<sup>P</sup>*<sup>2</sup> <sup>¼</sup> <sup>3</sup>

**Figure 13.** *Controlling of rotor power.*

The main advantages of DFIA are as follows:


Modes of operation, vector and energy diagrams. Theoretically, the following operating modes of DFIA are possible:


In all these modes, the system of equations describing the electromagnetic processes of the machine in a steady state using the method of the resulting vector [21], has the form:

$$
\overline{U}\_1 = R\_r \overline{I}\_1 + jX\_b \overline{I}\_1 + \overline{E}\_1 \qquad \frac{\overline{U}\_2^\dagger}{s} = \frac{R\_r}{s} \overline{I}\_2^\dagger + jX\_l \overline{I}\_2^\dagger + \overline{E}\_2 \qquad \overline{I}\_m = \overline{I}\_1 + \overline{I}\_2^\dagger,\tag{1}
$$

where *U*<sup>1</sup> is the line voltage; *I*1, *E*<sup>1</sup> ¼ *jω*1*Ψ <sup>m</sup>* ¼ *jXmIm* is the current and EMF in anchor winding; *U*<sup>∣</sup> 2,*I* ∣ 2, *E* ∣ <sup>2</sup> ¼ *jω*1*Ψ <sup>m</sup>* ¼ *jXmIm* is the led voltage, current and EMF in rotor winding; *Im* magnetizing current; *Rs*, *Xls* ¼ *ω*1*Lls* is the active and inductive resistance of the stator; *Rr*, *Xlr* ¼ *ω*1*Llr* is the led active and inductive resistance of the rotor; *Xm* ¼ *ω*1*Lm* is the inductive reactance of magnetization circuit; *s* is the slide. The T-shaped equivalent circuit based on Eq. (1) is shown in **Figure 14a**.

Let us transform the T-shaped equivalent circuit into a G-shaped equivalent circuit. Conversion factor is:

$$\mathbf{C} = \mathbf{1} + \frac{\mathbf{X}\_{ls}}{\mathbf{X}\_{m}}.\tag{2}$$

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*

**Figure 14.** *Equivalent circuit of the DFIA: a) T-shaped equivalent circuit; b) G-shaped equivalent circuit.*

We write down the equations for the G-shaped equivalent circuit (3)

$$\begin{aligned} \overline{U}\_{2}^{\parallel} &= \overline{U}\_{1} + R\_{2}\overline{I}\_{2}^{\parallel} + jX\_{2}\overline{I}\_{2}^{\parallel}; \ \overline{U}\_{1} = jX\_{1m}\overline{I}\_{m}, \overline{I}\_{m} = \overline{I}\_{1} + \overline{I}\_{2}^{\parallel}; R\_{2} = R\_{i}C + \frac{R\_{r}}{s}C^{2} \approx R\_{i} + \frac{R\_{r}}{s}; \\ X\_{2} &= X\_{l}C + X\_{lr}C^{2} \approx X\_{ls} + X\_{lr}; X\_{1m} = X\_{ls} + X\_{m} \end{aligned} \tag{3}$$

The following should be taken into account when assessing energy flows


$$P\_1 = \frac{3}{2} U\_1 I\_1 \cos \,\rho\_1; P\_2 = \frac{3}{2} \overline{U}\_2^\dagger \overline{I}\_2^\dagger \cos \,\rho\_2; Q\_1 = \frac{3}{2} U\_1 I\_1 \sin \,\rho\_1; Q = \frac{3}{2} \overline{U}\_2^\dagger \overline{I}\_2^\dagger \sin \,\rho\_2 \tag{4}$$

In the direction of the mechanical power acting on the shaft, the modes can be divided into motor mode and generator mode.

We consider only all generator modes for a wind turbine.

The mechanical power reported to the shaft of the machine at n < n0 (**Figure 15**) and the electrical power obtained by the rotor through a semiconductor converter, are transmitted to the stator and after deduction of losses are recovered to the grid.

**Figure 15.** *Vector diagram and energy diagram of DFD in generator mode at n < n0.*

The main advantages of DFIA are as follows:

Modes of operation, vector and energy diagrams.

• motor mode at a speed below synchronous;

• motor mode at a speed above synchronous;

• alternator mode at a speed higher than synchronous;

*U*∣ 2 *<sup>s</sup>* <sup>¼</sup> *Rr s I* ∣ <sup>2</sup> þ *jXlrI*

• alternator mode at a speed below synchronous.

efficiency of the system.

wind turbines.

**Figure 13.**

*Aerodynamics*

*Controlling of rotor power.*

[21], has the form:

anchor winding; *U*<sup>∣</sup>

**12**

Conversion factor is:

*U*<sup>1</sup> ¼ *RsI*<sup>1</sup> þ *jXlsI*<sup>1</sup> þ *E*<sup>1</sup>

2,*I* ∣ 2, *E* ∣

1.Control is carried out on the rotor circuit; this makes the high energy

Theoretically, the following operating modes of DFIA are possible:

In all these modes, the system of equations describing the electromagnetic processes of the machine in a steady state using the method of the resulting vector

where *U*<sup>1</sup> is the line voltage; *I*1, *E*<sup>1</sup> ¼ *jω*1*Ψ <sup>m</sup>* ¼ *jXmIm* is the current and EMF in

Let us transform the T-shaped equivalent circuit into a G-shaped equivalent circuit.

*Xls Xm*

rotor winding; *Im* magnetizing current; *Rs*, *Xls* ¼ *ω*1*Lls* is the active and inductive resistance of the stator; *Rr*, *Xlr* ¼ *ω*1*Llr* is the led active and inductive resistance of the rotor; *Xm* ¼ *ω*1*Lm* is the inductive reactance of magnetization circuit; *s* is the slide. The T-shaped equivalent circuit based on Eq. (1) is shown in **Figure 14a**.

*C* ¼ 1 þ

∣

<sup>2</sup> ¼ *jω*1*Ψ <sup>m</sup>* ¼ *jXmIm* is the led voltage, current and EMF in

<sup>2</sup> þ *E*<sup>2</sup> *Im* ¼ *I*<sup>1</sup> þ *I*

*:* (2)

∣

2, (1)

2.DFIA can operate at speeds above and below synchronous, both in motor mode and in alternator mode. Therefore, when using DFIA as a alternator, there are no difficulties with stabilizing the parameters of the generated voltage when changing the speed of the shaft rotation, which is important for

Energy diagrams of the generator mode DFIA at n > n0 are shown in **Figure 16**. In this mode, the mechanical power supplied to the shaft from the rotor side is converted into electrical power. Part of this power is given to the network from the rotor side. The other part is given to the stator circuit in the form of electromagnetic power and after deduction of losses is recovered in the network.

The balances of power in the various modes are summarized in **Table 1**.

A system of equations should be solved to quantify the properties of DFIA. This solution is carried out in a rotating coordinate system x (real axis) and y (imaginary axis). In this case, the voltage U1 is combined with the real axis x, and for the secondary voltage the ratio U2m<sup>¼</sup> *<sup>ω</sup>*1*U*<sup>2</sup> *<sup>ω</sup>*<sup>2</sup> and the phase ϭ are given. It is important to emphasize that when the real axis is combined with the voltage vector, the real component of the current is the active current of the stator, and the imaginary component is the reactive current of the stator.

$$I\mathbf{1} = \frac{\overline{(U\mathbf{1})} \left(\frac{\mathbf{R}r}{s} + j\mathbf{X}s\right) - j\frac{\overline{U\mathbf{2}}}{s}\mathbf{X}m}{(\mathbf{R}s + j\mathbf{X}s)\left(\frac{\mathbf{R}r}{s} + j\mathbf{X}s\right) - \mathbf{X}\_m^2}; \quad \overline{\mathbf{T}} = \frac{\frac{\overline{U\mathbf{2}}}{s}(\mathbf{R}s + j\mathbf{X}) - j\overline{U\mathbf{1}}\mathbf{X}m}{(\mathbf{R}s + j\mathbf{X}s)\left(\frac{\mathbf{R}r}{s} + j\mathbf{X}s\right) - \mathbf{X}\_m^2}. \tag{5}$$

The total current of the rotor and stator are calculated by the formula:

$$I\mathbf{1} = \sqrt{I\_{\mathbf{1x}}^2 + I\_{\mathbf{1y}}^2}; \quad I\mathbf{2} = \sqrt{I|\_{\mathbf{2x}}^2 + I|\_{\mathbf{2y}}^2} \tag{6}$$

*P*<sup>1</sup> ¼ 1*:*5*U*1*I*1*x*; *Q*<sup>1</sup> ¼ �1*:*5*U*1*I*1*y*; *Q*<sup>2</sup> ¼ 1*:*5 *U*2*yI*2*<sup>x</sup>* � *U*2*xI*2*<sup>y</sup>*

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

ð Þ 1 � *s ω*<sup>1</sup> *p*

Δ*P* ¼ *I* 2 <sup>1</sup>*Rs* þ *I* 2

We present the main characteristics obtained on the model.

from the network is mainly positive (inductive).

*Virtual laboratory setup for DFIA studies with independent controlling.*

*Electromagnetic and electromechanical characteristics of DFIA with independent control in generator mode at*

These equations can be used to model DFIA in Mathlab (**Figures 17**–**19**).

Assessing the properties of DFIA in the generator mode, we can draw the

1.The area of unstable operation is in a rather narrow zone of positive slides.

2.At U2m ≤ U1 in the sliding range from 0 to �1, the reactive power consumed

*Pm* ¼ *Teω<sup>m</sup>* ¼ *Te*

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

following conclusions:

**Figure 17.**

**Figure 18.**

*U2m < U1.*

**15**

Electromagnetic losses are calculated by the expression

;

(8)

<sup>2</sup>∣*Rr* (9)

; *P*<sup>2</sup> ¼ 1*:*5 *U*2*xI*2*<sup>x</sup>* þ *U*2*yI*2*<sup>y</sup>*

The electromagnetic moment is determined from the equation:

$$T\_e = \frac{3}{2} p L\_m \left(\overline{I\_2} \cdot \overline{I\_1}\right) = 1.5 p L\_m \left(I\_{2\mathbf{x}} I\_{1\mathbf{y}} - I\_{2\mathbf{y}} I\_{1\mathbf{x}}\right) \tag{7}$$

The energy properties of the MIS are determined after the calculation of the currents from the equations according to the following expressions.

**Figure 16.** *Vector diagram and energy diagram of DFD in generator mode at n > n0.*


**Table 1.**

*Balance of DFIA active powers depending on operating modes.*

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*

$$\begin{aligned} P\_1 &= \mathbf{1.5U\_1I\_{1x}}; Q\_1 = -\mathbf{1.5U\_1I\_{1y}}; Q\_2 = \mathbf{1.5}(U\_{2y}I\_{2x} - U\_{2x}I\_{2y}); \\ P\_m &= T\_\epsilon \alpha\_m = T\_\epsilon \frac{(\mathbf{1} - \mathbf{s})\alpha\_1}{p}; P\_2 = \mathbf{1.5}(U\_{2x}I\_{2x} + U\_{2y}I\_{2y}) \end{aligned} \tag{8}$$

Electromagnetic losses are calculated by the expression

$$
\Delta P = I\_1^2 R\_s + I\_2^2 |R\_r| \tag{9}
$$

These equations can be used to model DFIA in Mathlab (**Figures 17**–**19**). We present the main characteristics obtained on the model.

Assessing the properties of DFIA in the generator mode, we can draw the following conclusions:


**Figure 17.** *Virtual laboratory setup for DFIA studies with independent controlling.*

**Figure 18.**

*Electromagnetic and electromechanical characteristics of DFIA with independent control in generator mode at U2m < U1.*

Energy diagrams of the generator mode DFIA at n > n0 are shown in **Figure 16**.

A system of equations should be solved to quantify the properties of DFIA. This solution is carried out in a rotating coordinate system x (real axis) and y (imaginary axis). In this case, the voltage U1 is combined with the real axis x, and for the

*<sup>ω</sup>*<sup>2</sup> and the phase ϭ are given. It is important to

*<sup>s</sup>* ð Þ� *Rs* þ *jX jU*1∣ *Xm*

*<sup>s</sup>* <sup>þ</sup> *jXs* � � � *<sup>X</sup>*<sup>2</sup>

� � (7)

*m*

*:* (5)

(6)

In this mode, the mechanical power supplied to the shaft from the rotor side is converted into electrical power. Part of this power is given to the network from the rotor side. The other part is given to the stator circuit in the form of electromagnetic

The balances of power in the various modes are summarized in **Table 1**.

emphasize that when the real axis is combined with the voltage vector, the real component of the current is the active current of the stator, and the imaginary

; *I*2 ¼

; *I*2∣ ¼

The energy properties of the MIS are determined after the calculation of the

*U*2∣

r

� � <sup>¼</sup> <sup>1</sup>*:*5*pLm <sup>I</sup>*2*xI*1*<sup>y</sup>* � *<sup>I</sup>*2*yI*1*<sup>x</sup>*

ð Þ *Rs* <sup>þ</sup> *jXs Rr*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *I* 2 <sup>2</sup>*<sup>x</sup>* <sup>þ</sup> *<sup>I</sup>* � � � � 2 2*y*

power and after deduction of losses is recovered in the network.

*U*2∣ *<sup>s</sup> Xm*

*m*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *I* 2 <sup>1</sup>*<sup>x</sup>* þ *I* 2 1*y*

The electromagnetic moment is determined from the equation:

*pLm I*<sup>2</sup> � *I*<sup>1</sup>

currents from the equations according to the following expressions.

The total current of the rotor and stator are calculated by the formula:

*<sup>s</sup>* <sup>þ</sup> *jXs* � � � *<sup>X</sup>*<sup>2</sup>

q

*I*1 ¼

*Vector diagram and energy diagram of DFD in generator mode at n > n0.*

*Balance of DFIA active powers depending on operating modes.*

**Slide Generator mode** s . 0 P1 + Pm=�P1+Δ*P* s , 0 Pm= �P1þΔ*P*�P2

*Te* <sup>¼</sup> <sup>3</sup> 2

secondary voltage the ratio U2m<sup>¼</sup> *<sup>ω</sup>*1*U*<sup>2</sup>

ð Þ *Rs* <sup>þ</sup> *jXs Rr*

*<sup>I</sup>*<sup>1</sup> <sup>¼</sup> <sup>ð</sup>*U*1∣<sup>Þ</sup> *Rr*

*Aerodynamics*

**Figure 16.**

**Table 1.**

**14**

component is the reactive current of the stator.

*<sup>s</sup>* <sup>þ</sup> *jXs* � � � *<sup>j</sup>*

#### **Figure 19.**

*Electromagnetic and electromechanical characteristics of DFIA with independent control in generator mode at U2m > U1.*

3.At U2 > U1 in the sliding range from 0 to �1, the reactive power consumed from the network is always negative (capacitive).

4. In case of significant sliding, the DFIA is a source of torque.

This property is extremely useful when performing the DFIA generator function when the shaft speed varies widely.

## **6. DFIA design basics**

The design of complex technical systems such as DFIA in the digital age should be based on the application of nonlinear programming techniques for synthesis and analysis.

subjective and the success of their application depends on the experience of the developer. For this reason, we formulate a one-criterion optimization problem for the generator. Practice shows that such problems are solved successfully and efficiently. It should be noted that the optimality criterion can be changed depending

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

We formulate the problem of single-criterion optimization of DFIA in the classical formulation [2, 3]: for the given parameters (specific performance, materials, initial data of the technical task), under the given restrictions, it is necessary, making a search of independent variables by a certain algorithm, to determine the geometry that would provide the extreme value of the selected criteria. There can be several optimality criteria, but depending on the project situation one is chosen

The flowchart of the single-criterion optimization problem is shown in **Figure 20**.

As constraints are the technical requirements for dimensions and permissible loads. As criteria of optimality it is possible to accept the quality indicators which have received the greatest distribution in practice, for example: the minimum mass of active materials; the minimum volume of magnetic system, the maximum possible

The choice of independent variables is a separate and rather complex task.

The independent variables for the optimization problem must meet the follow-

• they should be effective, that is, their change should bring the calculation closer to the optimal design in the minimum number of iterations;

**6.2 Selecting independent variables for the optimization problem**

• they should be visual and have a clear physical meaning;

The data of the technical task are taken as constants in the problem.

at the set electromagnetic loadings of efficiency.

on the current project situation.

*Block diagram of the single-criterion optimization problem.*

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

for optimization.

**Figure 20.**

ing basic requirements:

**17**

There are a large number of CAD systems for the analysis of electromagnetic and thermal state of electric machines. Application of the Ansys software package will be shown below.

For the synthesis of electric machines, there are no fully developed techniques. Developers are forced to form a design system for each new type of machine.

DFIA operates in a wide range of mechanical and electrical loads. For its effective operation in all modes, it is necessary to determine the optimal geometry of the magnetic system and the anchor windings.

It should be noted that the problem of optimal design of electric machines remains quite complex and not fully solved [5, 12–18]. This is due to the choice of optimization method, the formalization of independent variables and the definition of quality indicators of the electric machine. Until now, the optimal design problems remain very important and relevant in electrical engineering.

#### **6.1 Problem statement of optimal design of DFIA**

Optimizations should be understood as the process of selecting the best option for a large number of possible options. Indicators of the quality of the best option are the optimality criteria. As a rule, there are several optimality criteria in the computational model, and in the most General case there is a need to solve a multicriteria problem. It should be noted that the solution of multi-criteria problem is quite difficult. This is due to the fact that the optimality criteria are in a contradictory relationship. Improvement of one criterion leads to deterioration of others. So the increase in efficiency leads to an increase in the mass and volume of the product, the improvement of the output voltage parameters to the complication of electronics, cost reduction to a decrease in reliability. The experience of optimal design in electrical engineering shows that the task of multi-criteria optimization is quite complex. It is poorly formalized. The existing methods of its solution are

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*

#### **Figure 20.**

3.At U2 > U1 in the sliding range from 0 to �1, the reactive power consumed

*Electromagnetic and electromechanical characteristics of DFIA with independent control in generator mode at*

This property is extremely useful when performing the DFIA generator function

The design of complex technical systems such as DFIA in the digital age should be based on the application of nonlinear programming techniques for synthesis and

There are a large number of CAD systems for the analysis of electromagnetic and thermal state of electric machines. Application of the Ansys software package will

For the synthesis of electric machines, there are no fully developed techniques.

DFIA operates in a wide range of mechanical and electrical loads. For its effective operation in all modes, it is necessary to determine the optimal geometry of the

Optimizations should be understood as the process of selecting the best option for a large number of possible options. Indicators of the quality of the best option are the optimality criteria. As a rule, there are several optimality criteria in the computational model, and in the most General case there is a need to solve a multicriteria problem. It should be noted that the solution of multi-criteria problem is quite difficult. This is due to the fact that the optimality criteria are in a contradictory relationship. Improvement of one criterion leads to deterioration of others. So the increase in efficiency leads to an increase in the mass and volume of the product, the improvement of the output voltage parameters to the complication of electronics, cost reduction to a decrease in reliability. The experience of optimal design in electrical engineering shows that the task of multi-criteria optimization is quite complex. It is poorly formalized. The existing methods of its solution are

Developers are forced to form a design system for each new type of machine.

It should be noted that the problem of optimal design of electric machines remains quite complex and not fully solved [5, 12–18]. This is due to the choice of optimization method, the formalization of independent variables and the definition

of quality indicators of the electric machine. Until now, the optimal design problems remain very important and relevant in electrical engineering.

from the network is always negative (capacitive).

when the shaft speed varies widely.

magnetic system and the anchor windings.

**6.1 Problem statement of optimal design of DFIA**

**6. DFIA design basics**

analysis.

**16**

**Figure 19.**

*Aerodynamics*

*U2m > U1.*

be shown below.

4. In case of significant sliding, the DFIA is a source of torque.

*Block diagram of the single-criterion optimization problem.*

subjective and the success of their application depends on the experience of the developer. For this reason, we formulate a one-criterion optimization problem for the generator. Practice shows that such problems are solved successfully and efficiently. It should be noted that the optimality criterion can be changed depending on the current project situation.

We formulate the problem of single-criterion optimization of DFIA in the classical formulation [2, 3]: for the given parameters (specific performance, materials, initial data of the technical task), under the given restrictions, it is necessary, making a search of independent variables by a certain algorithm, to determine the geometry that would provide the extreme value of the selected criteria. There can be several optimality criteria, but depending on the project situation one is chosen for optimization.

The flowchart of the single-criterion optimization problem is shown in **Figure 20**. The data of the technical task are taken as constants in the problem.

As constraints are the technical requirements for dimensions and permissible loads. As criteria of optimality it is possible to accept the quality indicators which have received the greatest distribution in practice, for example: the minimum mass of active materials; the minimum volume of magnetic system, the maximum possible at the set electromagnetic loadings of efficiency.

The choice of independent variables is a separate and rather complex task.

#### **6.2 Selecting independent variables for the optimization problem**

The independent variables for the optimization problem must meet the following basic requirements:


• they should have clear boundaries of change, it is desirable that the optimum is not on the border. This will make it difficult to choose optimization methods.

Analysis of the characteristics of the DFIA generator shows that its energy efficiency and specific energy performance are less dependent on specific linear dimensions, such as the height and width of the slot, the size of the back of the stator and inductor. To a greater extent, the energy of the machine depends on the ratio of the areas of the active zones, for example, the ratio of the cross-sectional area of the anchor to the cross-sectional area of the machine, the ratio of the area of the slotted zone to the area of the anchor, the ratio of the area of the slots to the area of the slotted zone, etc. Selecting these relative parameters as independent variables is very convenient. They have clear boundaries of change from 0 to 1, show the optimal ratio of the active zones involved in the energy conversion; their optimal values vary in a small range when the size changes over a wide range.

The idea of using these variables is not new. It was used for the synthesis of traction motors of rolling stock [22], and later, for the development of design methods of valve torque DC motors [3]. However, for dual power generators, this technique has not previously been used. Let us give these variables the term "generalized variables", which reflect their physical nature, and define them for DFIA.

### **6.3 Definition of generalized variables for DFIA**

For the asynchronous-synchronous machine, it is convenient to allocate 6 generalized variables:

1. Variable *fs* shows how much of the cross-sectional area of the electric machine without shaft is occupied by the total machine cross section (**Figure 21**);

$$f\_s = \frac{\mathcal{S}\_{ring}}{\mathcal{S}\_{circle}} = \frac{\mathcal{S}\_{machine\ cross\ section\ without\ shaft}}{\mathcal{S}\_{total\ machine\ cross\ section}};\tag{10}$$

3. Variable *f er* shows the ratio of the area of cross section of rotor slot-tooth

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

*<sup>f</sup> es* <sup>¼</sup> *Scross section of rotor slot*�*tooth layer Srotor cross section*

*<sup>f</sup> zr* <sup>¼</sup> *Scross section of rotor slots*

4. Variable *f zr* reflects the ratio of the area of cross section of rotor slots by the

*Scross section of rotor slot*�*tooth layer*

5. Variable *f es* shows the ratio of the area of stator slot-tooth layer by the area of

6. Variable *f zs* reflects the ratio of the area of cross section of stator slots by the

*<sup>f</sup> es* <sup>¼</sup> *Scross section of stator slot*�*tooth layer Sstator cross section*

; (12)

; (13)

; (14)

layer by the area of rotor cross section (**Figure 23**);

area of cross section of rotor slot-tooth layer (**Figure 24**)

area of cross section of stator slot-tooth layer (**Figure 26**);

stator cross section (**Figure 25**);

**Figure 22.** *Variable f <sup>а</sup>.*

**Figure 23.** *Variable f es.*

**19**

2. Variable *f <sup>а</sup>* reflects the ratio of area of the rotor cross section by the area of total machine cross section (**Figure 22**)

**Figure 21.** *Variable fs .*

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*

**Figure 22.** *Variable f <sup>а</sup>.*

• they should have clear boundaries of change, it is desirable that the optimum is not on the border. This will make it difficult to choose optimization methods.

Analysis of the characteristics of the DFIA generator shows that its energy efficiency and specific energy performance are less dependent on specific linear dimensions, such as the height and width of the slot, the size of the back of the stator and inductor. To a greater extent, the energy of the machine depends on the ratio of the areas of the active zones, for example, the ratio of the cross-sectional area of the anchor to the cross-sectional area of the machine, the ratio of the area of the slotted zone to the area of the anchor, the ratio of the area of the slots to the area of the slotted zone, etc. Selecting these relative parameters as independent variables is very convenient. They have clear boundaries of change from 0 to 1, show the optimal ratio of the active zones involved in the energy conversion; their optimal

The idea of using these variables is not new. It was used for the synthesis of traction motors of rolling stock [22], and later, for the development of design methods of valve torque DC motors [3]. However, for dual power generators, this technique has not previously been used. Let us give these variables the term "generalized variables", which reflect their physical nature, and define them for DFIA.

For the asynchronous-synchronous machine, it is convenient to allocate 6 gen-

<sup>¼</sup> *Smachine cross section without shaft Stotal machine cross section*

2. Variable *f <sup>а</sup>* reflects the ratio of area of the rotor cross section by the area of

*<sup>f</sup>* <sup>а</sup> <sup>¼</sup> *Srotor cross section Stotal machine cross*\_*section* ; (10)

; (11)

1. Variable *fs* shows how much of the cross-sectional area of the electric machine without shaft is occupied by the total machine cross section

values vary in a small range when the size changes over a wide range.

**6.3 Definition of generalized variables for DFIA**

*fs* <sup>¼</sup> *Sring Scircle*

total machine cross section (**Figure 22**)

eralized variables:

*Aerodynamics*

**Figure 21.** *Variable fs .*

**18**

(**Figure 21**);

**Figure 23.** *Variable f es.*

3. Variable *f er* shows the ratio of the area of cross section of rotor slot-tooth layer by the area of rotor cross section (**Figure 23**);

$$f\_{es} = \frac{\mathbb{S}\_{cross\text{ section of}} \text{ }\,\,\,\text{rotor\, slot-tooth\,\, layer}}{\mathbb{S}\_{rotor\,cross\text{ section}}};\tag{12}$$

4. Variable *f zr* reflects the ratio of the area of cross section of rotor slots by the area of cross section of rotor slot-tooth layer (**Figure 24**)

$$f\_{xr} = \frac{\text{S}\_{cross\text{ section of}}\text{ of}\begin{array}{c} \text{rotor slot} \\ \text{rotor slot} \end{array}}{\text{S}\_{cross\text{ section of}}\text{ of}\begin{array}{c} \text{rotor slot} \\ \text{rotor slot} \end{array}};\tag{13}$$

5. Variable *f es* shows the ratio of the area of stator slot-tooth layer by the area of stator cross section (**Figure 25**);

$$f\_{\text{et}} = \frac{\text{S}\_{\text{cross\\_section\\_of\\_stator\\_slot}-\text{both layer}}{\text{S}\_{\text{starator\\_cross\\_section}}};\tag{14}$$

6. Variable *f zs* reflects the ratio of the area of cross section of stator slots by the area of cross section of stator slot-tooth layer (**Figure 26**);

*Aerodynamics*

$$f\_{xs} = \frac{\text{S}\_{\text{cross section of}} \text{ of star slot}}{\text{S}\_{\text{cross section of}} \text{ of star slot} - \text{both layer}};\tag{15}$$

Once again, we emphasize the visibility and clear physical meaning of the introduced generalized variables.

**Figure 24.** *Variable f <sup>z</sup>.*

**Figure 25.** *Variable f er.*

**Figure 26.** *Variable f zr.*

**6.4 The determination of the geometry of DFIA using generalized variables**

of reference.

*hzr* (18):

*hzr* ¼ 0*:*5 � *Dout* �

*bzr* <sup>¼</sup> *<sup>π</sup>* � *Dout* � *<sup>f</sup> zr* 2 � *z*<sup>р</sup>

**Figure 27.**

**21**

*Cross-sectional sketch of DFIA.*

The above six generalized variables allow us to accurately calculate the basic dimensions of the magnetic circuit of the DFIA but for the product of this calculation it is necessary to set the initial parameter from which the further calculation will be made. As this parameter, it is most convenient to take the outer diameter of the stator of the electric machine, since most often this parameter is set by the terms

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

Taking as the initial parameter the outer diameter of the stator of the electric machine simple mathematical transformations allow from expressions (10),(11), (12), (13), (14), (15), print the equations that determine the basic geometric dimensions of the magnetic circuit of the double-feed machine (see **Figure 27**):

1. Variable *fs* allows determining the diameter of the hole in the rotor (16):

ffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* þ *f* <sup>а</sup> � *fs*

, (16)

; (17)

;

,

(18)

(19)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* þ *f* <sup>а</sup> � *f er* þ *f* <sup>а</sup> � *fs*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* þ *f* <sup>а</sup> � *f er* þ *f* <sup>а</sup> � *fs*

*Din* ¼ *Dout* �

2. Variable *f <sup>а</sup>* allows determining the diameter of the rotor Da (17):

q

3. The variable *f er* allows determining the height of the groove of the rotor

�

4. The variable *f zr* allows defining the width of the groove of the rotor*bzr* (19):

þ

q

q

*Da* ¼ *Dout* �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* þ *f* <sup>а</sup> � *fs*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � *fs* þ *f* <sup>а</sup> � *fs*

where *Dout* is the outer diameter of the stator;

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

q

�

∗

q

�

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*

## **6.4 The determination of the geometry of DFIA using generalized variables**

The above six generalized variables allow us to accurately calculate the basic dimensions of the magnetic circuit of the DFIA but for the product of this calculation it is necessary to set the initial parameter from which the further calculation will be made. As this parameter, it is most convenient to take the outer diameter of the stator of the electric machine, since most often this parameter is set by the terms of reference.

Taking as the initial parameter the outer diameter of the stator of the electric machine simple mathematical transformations allow from expressions (10),(11), (12), (13), (14), (15), print the equations that determine the basic geometric dimensions of the magnetic circuit of the double-feed machine (see **Figure 27**):

1. Variable *fs* allows determining the diameter of the hole in the rotor (16):

$$\text{Dim} = \text{Dout} \times \sqrt{\mathbf{1} - f\_s},\tag{16}$$

where *Dout* is the outer diameter of the stator;

2. Variable *f <sup>а</sup>* allows determining the diameter of the rotor Da (17):

$$\text{Da} = \text{Dout} \times \sqrt{\mathbf{1} - f\_s + f\_\mathbf{a} \times f\_s};\tag{17}$$

3. The variable *f er* allows determining the height of the groove of the rotor *hzr* (18):

$$h\_{xr} = 0.5 \times \text{Dout} \times \left(\sqrt{\mathbf{1} - f\_s + f\_\mathbf{a} \times f\_s} - \sqrt{\mathbf{1} - f\_s + f\_\mathbf{a} \times f\_{cr} + f\_\mathbf{a} \times f\_s}\right) \tag{18}$$

4. The variable *f zr* allows defining the width of the groove of the rotor*bzr* (19):

$$b\_{\rm ir} = \frac{\pi \times \text{Dout} \times f\_{\rm ir}}{2 \times z\_{\rm p}} \times \left(\sqrt{1 - f\_s + f\_a \times f\_s} + \sqrt{1 - f\_s + f\_a \times f\_{\rm cr} + f\_a \times f\_s}\right) \tag{19}$$

$$= \frac{\pi \times \text{Dit}}{2}$$

$$= \frac{\pi \times \text{Dit}}{2}$$

**Figure 27.** *Cross-sectional sketch of DFIA.*

*<sup>f</sup> zs* <sup>¼</sup> *Scross section of stator slots*

Once again, we emphasize the visibility and clear physical meaning of the

introduced generalized variables.

**Figure 24.** *Variable f <sup>z</sup>.*

*Aerodynamics*

**Figure 25.** *Variable f er.*

**Figure 26.** *Variable f zr.*

**20**

*Scross section of stator slot*�*tooth layer*

; (15)

where *z<sup>р</sup>* is the number of rotor slots;

5. The variable *f es* allows determining the height of the stator slot *hzs* (20):

$$h\_{\rm x} = 0.5 \times \left( \sqrt{f\_{\rm \alpha} \times Dut^2 - (Da + 2 \times \delta)^2 \times \left(f\_{\rm \alpha} + 1\right)} - Da - 2 \times \delta, \tag{20}$$

where δ is the air gap;

6. The variable *f zs* allows determining the width of the stator groove *bzs* (21):

$$b\_{\pm} = \frac{f\_{\pm} \times f\_{\pm} \times \pi \times \left(\text{Dout}^2 - \left(\text{Da} + 2 \times \delta\right)^2\right)}{4 \times \text{z}\_{\text{t}} \times h\_{\text{zt}}},\tag{21}$$

The calculation in Maxwell Ansys can be divided into three stages:

Mass, (kg) 1200 Outline sizes (mm\*mm) 1260\*320

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

2.Analysis of the model using Maxwell2D on the basis of already created models

3.Analysis of the model using the Maxwell3D on the basis of the model created

The program Ansys Electronics Desktop has a very developed interface. This

At the first stage, when working with RMxprt, it is enough to fill in special forms. They include geometrical dimensions, winding data and nominal parameters of the machine. The mathematical model of calculation is made on the basis of a method of schemes of substitution therefore are carried out within 1 min. The

At the second stage, the program automatically creates a 2D model of the generator, splits it into finite elements, sets the boundary conditions and current loads. To simplify the calculations, the program determines the axial symmetry and solves the problem of calculating the field taking into account the periodicity condition. The resulting characteristics are obtained by multiplying the results by the number

To test the generator, the following numerical experiment was carried out: the different rotation frequency of the generator shaft (0, 10, 60 and 100) rpm was set.

program calculates all the necessary parameters and characteristics.

1.Analysis of the model using the RMxprt;

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

in RMxprt;

in RMxprt.

makes it easier to use.

of symmetric fragments.

**Figure 28.**

**23**

*The analysis of the magnetic field at frequency of rotation of 10 rpm.*

where *zs* is number of stator slots.

Thus, for a known outer diameter and given generalized variables defined by expressions (10–15), the transverse geometry of DFIA can be uniquely determined. On the basis of the accepted variables, a mathematical model of the generator was developed, which was used to optimize the geometry of a number of wind power plants based on DFIA. As a block optimizer used an algorithm that combines the method of coordinate-wise descent Gauss-Seidel with the Fibonacci method.

The main advantage of the generalized variables is their visibility, due to the fact that they have a clear physical meaning and can independently act as criteria for the quality of the electric machine. The second advantage is that the generalized variables have a fixed range of changes [0;1], which allows to apply optimization algorithms to the mathematical model [5, 18], built on the basis of these variables.

On the basis of this technique and with the use of the algorithm, DFIA with output power of 10 kV, line voltage 380 V and synchronous speed of 50 rpm with the required optimality criteria—maximum efficiency and minimum weight—was calculated . The calculation time of the program written in Delphi for six independent generalized variables was about 30 seconds, which is quite acceptable.

## **7. Analysis of the results of geometry optimization**

At the stage of DFIA synthesis the method of substitution schemes was used, which contains equations in integral form. This is due to the fact that a simplified calculation model is required for optimization. This model should allow the calculation of a large number of options to select the best option.

A thorough analysis of the results after optimization is required. This analysis should use accurate methods. The finite element method is such an accurate method [2–4, 8–18, 23].

The software package Ansys Electronics Desktop allows you to perform analysis of electromagnetic and fields in an electric machine. The application of the program for the analysis of DFIA is shown below.

The data of alternator is:


*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*


The calculation in Maxwell Ansys can be divided into three stages:

1.Analysis of the model using the RMxprt;

where *z<sup>р</sup>* is the number of rotor slots;

*bzs* ¼

where *zs* is number of stator slots.

**7. Analysis of the results of geometry optimization**

lation of a large number of options to select the best option.

for the analysis of DFIA is shown below.

The data of alternator is:

*hzs* ¼ 0*:*5 �

*Aerodynamics*

[2–4, 8–18, 23].

**22**

�

where δ is the air gap;

5. The variable *f es* allows determining the height of the stator slot *hzs* (20):

<sup>q</sup> � � � *Da* � <sup>2</sup> � *<sup>δ</sup>*,

6. The variable *f zs* allows determining the width of the stator groove *bzs* (21):

Thus, for a known outer diameter and given generalized variables defined by expressions (10–15), the transverse geometry of DFIA can be uniquely determined. On the basis of the accepted variables, a mathematical model of the generator was developed, which was used to optimize the geometry of a number of wind power plants based on DFIA. As a block optimizer used an algorithm that combines the method of coordinate-wise descent Gauss-Seidel with the Fibonacci method.

The main advantage of the generalized variables is their visibility, due to the fact that they have a clear physical meaning and can independently act as criteria for the quality of the electric machine. The second advantage is that the generalized variables have a fixed range of changes [0;1], which allows to apply optimization algorithms to the mathematical model [5, 18], built on the basis of these variables. On the basis of this technique and with the use of the algorithm, DFIA with output power of 10 kV, line voltage 380 V and synchronous speed of 50 rpm with the required optimality criteria—maximum efficiency and minimum weight—was calculated . The calculation time of the program written in Delphi for six independent generalized variables was about 30 seconds, which is quite acceptable.

At the stage of DFIA synthesis the method of substitution schemes was used, which contains equations in integral form. This is due to the fact that a simplified calculation model is required for optimization. This model should allow the calcu-

A thorough analysis of the results after optimization is required. This analysis should use accurate methods. The finite element method is such an accurate method

The software package Ansys Electronics Desktop allows you to perform analysis of electromagnetic and fields in an electric machine. The application of the program

Rated output power, (kW) 10 Rated voltage, (V) 380 Frequency, (Hz) 50 Rated speed, (RPM) 60

*<sup>f</sup> zs* � *<sup>f</sup> es* � *<sup>π</sup>* � *Dout*<sup>2</sup> � ð Þ *Da* <sup>þ</sup> <sup>2</sup> � *<sup>δ</sup>* <sup>2</sup> � � 4 � *zs* � *hzs*

(20)

, (21)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>f</sup> es* � *Dout*<sup>2</sup> � ð Þ *Da* <sup>þ</sup> <sup>2</sup> � *<sup>δ</sup>* <sup>2</sup> � *<sup>f</sup> es* <sup>þ</sup> <sup>1</sup>


The program Ansys Electronics Desktop has a very developed interface. This makes it easier to use.

At the first stage, when working with RMxprt, it is enough to fill in special forms. They include geometrical dimensions, winding data and nominal parameters of the machine. The mathematical model of calculation is made on the basis of a method of schemes of substitution therefore are carried out within 1 min. The program calculates all the necessary parameters and characteristics.

At the second stage, the program automatically creates a 2D model of the generator, splits it into finite elements, sets the boundary conditions and current loads. To simplify the calculations, the program determines the axial symmetry and solves the problem of calculating the field taking into account the periodicity condition. The resulting characteristics are obtained by multiplying the results by the number of symmetric fragments.

To test the generator, the following numerical experiment was carried out: the different rotation frequency of the generator shaft (0, 10, 60 and 100) rpm was set.

**Figure 28.** *The analysis of the magnetic field at frequency of rotation of 10 rpm.*

For these speeds, the frequency of the excitation winding supply and the current in the excitation winding were selected so that the nominal voltage was obtained at the generator output.

The results of the analysis are presented below (**Figures 28**–**31**).

**Tables 2** and **3** show the main electrical parameters of the generator obtained experimentally.

The results of the numerical experiment show that the output voltage and power have stable values when the rotation frequency of the generator shaft changes from a braked state to 10 RPM. It is very important for wind turbines.

Thus, the main problem of wind power to obtain standard parameters of electricity at different wind speeds is solved through the use of DFIA.

**Figure 29.** *EMF of anchor winding (10 rpm).*

**8. The solving of the problem of an accumulation with using the**

difficult to carry out repair work in these conditions.

Wind power plants must be highly reliable. This is due to the fact that the generator is located at high altitude, works in different climatic zones, and it is very

This requirement makes the supply of electricity to the rotor without sliding

In the proposed generator, a second built-in electric machine is used to solve this

**concept of DFIA**

*Generator p depending on speed.*

**Rotational speed, rpm**

**Figure 31.**

**Table 2.**

**Table 3.**

**Rotational speed, rpm** **Stator voltage (RMS), V**

*The voltage of the exitating winding (10 rpm).*

*DOI: http://dx.doi.org/10.5772/intechopen.89255*

*Generator voltages and currents depending on speed.*

**Output power, kW** **Load current (RMS), А**

**Excitation power, kW**

 10.65 11.67 0.00 11.54 0.912 10.54 10.78 0.55 21.03 0.93 10.05 5.81 4.55 19.72 0.97 10.20 0.267 10.03 19.41 0.99

 236 15.05 148.0 26.3 235 14.95 137.0 26.25 232 14.43 74.5 26.0 233 14.59 2.8 31.85

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium…*

**Excitation winding voltage (RMS), V**

**Mechanical power on shaft, kW**

**Excitation winding current(RMS), A**

**Total power, kW** **Efficiency**

contact.

problem.

**25**

**Figure 30.** *Anchor currents (10 rpm).*

*Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium… DOI: http://dx.doi.org/10.5772/intechopen.89255*



#### **Table 2.**

For these speeds, the frequency of the excitation winding supply and the current in the excitation winding were selected so that the nominal voltage was obtained at

**Tables 2** and **3** show the main electrical parameters of the generator obtained

Thus, the main problem of wind power to obtain standard parameters of

The results of the numerical experiment show that the output voltage and power have stable values when the rotation frequency of the generator shaft changes from

The results of the analysis are presented below (**Figures 28**–**31**).

a braked state to 10 RPM. It is very important for wind turbines.

electricity at different wind speeds is solved through the use of DFIA.

the generator output.

experimentally.

*Aerodynamics*

**Figure 29.**

**Figure 30.**

**24**

*Anchor currents (10 rpm).*

*EMF of anchor winding (10 rpm).*

*Generator voltages and currents depending on speed.*


**Table 3.**

*Generator p depending on speed.*
