EP2559159A2

EP2559159A2 - Electric machine; control device for controlling said electric machine; electric propulsion system comprising said electric machine and said control device; and method for controlling said electric machine

Info

Publication number: EP2559159A2
Application number: EP11725797A
Authority: EP
Inventors: Daniela Baratta; Massimo Caneparo; Adolfo Martino
Original assignee: Ansaldo Energia Holding SpA
Current assignee: Ansaldo Energia SpA
Priority date: 2010-04-15
Filing date: 2011-04-15
Publication date: 2013-02-20
Also published as: WO2011128770A3; WO2011128770A2; ITMI20100642A1; IT1402368B1

Abstract

An electric machine comprises a rotor (10) and a stator (6) which includes a stator pack (7) made of ferromagnetic material having a plurality of slots (8), and stator windings (9), for defining a magnetic flux (Φ) having a maximum magnetic flux value (Φ₁) defined on the basis of a first torque value (T₁), associated with a nominal frequency (f_n); the electric machine (2) being configured to supply a maximum torque (T_max) equal to a first torque value (T₁) when fed with a nominal voltage (U_n) at a frequency lower than or equal to a nominal frequency (f_n); the electric machine (2) being configured to supply, in continuous operation, a maximum torque (T_max) equal to a second torque value (T₂) when fed with a maximum voltage (U_max), higher than the nominal voltage (U_n), at the maximum frequency ( f_max ).

Description

ELECTRIC MACHINE, CONTROL DEVICE FOR CONTROLLING SAID ELECTRIC MACHINE, ELECTRIC PROPULSION SYSTEM COMPRISING SAID ELECTRIC MACHINE AND SAID CONTROL DEVICE, AND METHOD FOR CONTROLLING SAID ELECTRIC MACHINE

TECHNICAL FIELD

The present invention relates to an electric machine, to a control device for controlling said electric machine, to an electric propulsion system comprising said electric machine and said control device, and to a method for controlling said electric machine .

In particular, the present invention relates to an electric machine, which comprises a stator comprising a stator pack made of ferromagnetic material having a circular crown shape in which slots are made, and stator windings partially arranged in the slots, and a rotor.

BACKGROUND ART

Such an electric machine is generally coupled to a control device, in particular an inverter, arranged between the electric machine and a supply source. The control device adjusts voltage and frequency at the terminals of the stator windings of the electric machine. The torque delivered by the electric machine at a given rpm is a function of the supply voltage and frequency.

The maximum torque is a function of the frequency and a feature of the electric machine. The maximum torque at each frequency further depends on the magnetic stator flux defined by the stator windings.

In particular, by feeding the electric machine with scalar control, directly acting on frequency and voltage at the terminals of the electric machine, the maximum torque is constant in a range of frequencies from zero to a nominal frequency, and quadratically decreases as the frequency of the nominal frequency increases to a maximum frequency. This limits the application of said asynchronous, multiphase electric machine when a given maximum torque value at the maximum frequency is required, and in particular in most cases in which the ratio between maximum frequency and nominal frequency needs to be higher than 2.

A known solution consists in sizing the electric machine so as to increase the maximum torque value at the nominal frequency, because the maximum torque value is thereby also increased at the maximum frequency.

However, this solution increases the size and weight of the electric machine and limits its use flexibility.

According to another solution, the electric machine is sized and fed so as to increase the nominal frequency value. Thereby, indeed, the maximum torque value at maximum frequency also increases since the maximum torque remains constant in a wider range of frequencies (i.e. to the new nominal frequency) and quadratically decreases in all cases as the frequency increases beyond the new nominal frequency.

However, this solution increases the current in the windings of the electric machine and therefore requires control devices having larger size and higher costs.

DISCLOSURE OF THE INVENTION

It is an object of the present invention to provide an electric machine which limits the drawbacks of the prior art.

Another object of the present invention is to provide an electric machine which provides a given maximum torque value at the maximum frequency, thus reducing size and/or weight and/or complexity as compared to the prior art.

Another object of the present invention is to provide an electric machine which has a higher ratio between maximum frequency and nominal frequency than the prior art without increasing size and/or weight and/or complexity as compared to the prior art.

According to the present invention, an electric machine is provided, comprising a rotor and a stator which includes a stator pack made of ferromagnetic material and having a plurality of slots and stator windings, for defining a magnetic flux having a maximum magnetic flux value defined on the basis of a first torque value, associated with a nominal frequency; the electric machine being configured to supply a maximum torque equal to a first torque value when fed with a nominal voltage at a frequency lower than or equal to the nominal frequency; the electric machine being configured to supply, in continuous operation, a maximum torque equal to a second torque value when fed with a maximum voltage, higher than the nominal voltage, at the maximum frequency.

In the electric machine provided according to the present invention, the maximum torque value at the maximum frequency is higher than the prior art, the weight and/or size and/or complexity being equal.

Another object of the present invention is to provide a control device for controlling an electric machine which reduces the drawbacks of the prior art.

According to the present invention, a control device for controlling an electric machine is provided having a nominal frequency, a nominal voltage, a maximum frequency, and a maximum voltage in continuous operation; the control device being configured to control a frequency and a voltage of the electric machine, in a first frequency range lower than or equal to the nominal frequency, according to a first control mode wherein the variation of the voltage is proportional to the variation of the frequency; and, in a second frequency range higher than the nominal frequency and lower than or equal to the maximum frequency, according to a second control mode wherein the voltage is calculated on the basis of the frequency according to a function; said function defining voltage values higher than the nominal voltage and lower than or equal to the maximum voltage.

Another object of the present invention is to provide an electric propulsion system which reduces the drawbacks of the prior art.

According to the present invention, an electric propulsion system is provided, comprising an electric machine according to any one of the claims 1 to 8, and a control device according to any one of the claims 9 to 14 coupled to the electric machine.

Another object of the present invention is to provide a control device for controlling an electric machine which obviates the drawbacks of the prior art.

According to the present invention, a method for controlling an electric machine is provided, comprising the steps of:

in a first frequency range lower than a nominal frequency of the electric machine, controlling a frequency and a voltage of the electric machine according to a first control mode, wherein the variation of the voltage of the electric machine is proportional to the variation of the frequency of the electric machine, and wherein the voltage is lower or equal to a nominal voltage of the electric machine; and

in a second frequency range higher than the nominal frequency, controlling the frequency and voltage of the electric machine according to a second control mode, wherein the voltage is calculated on the basis of the frequency according to a function increasing at least in a range; said function taking voltage values higher than the nominal voltage and lower than or equal to a maximum voltage of the electric machine,

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will be apparent from the following description of a non-limitative embodiment thereof, with reference to the figures in the accompanying drawings, in which:

- figure 1 is a diagrammatic view, with parts removed for clarity, of an electric propulsion system provided according to the present invention;

- figure 2 is a side elevation view, in section and with parts removed for clarity, of an electric machine of the electric propulsion system in figure 1;

figure 3 is a diagram representing a maximum torque according to the variation of a frequency of the electric machine in figure 2;

- figure 4 is a diagram representing a voltage according to the variation of the frequency of the electric machine in figure 2; and

- figure 5 is a diagram representing a magnetic flux according to the variation of the frequency of the electric machine in figure 2.

BEST MODE FOR CARRYING OUT THE INVENTION

In figure 1, reference numeral 1 diagrammatically indicates an electric propulsion system as a whole, in particular a motor vehicle, comprising an asynchronous, multiphase electric machine 2; a control device 3, e.g. an inverter, for controlling electric machine 2; and a rechargeable supply source 4, e.g. a secondary battery, for feeding the electric machine by means of control device 3.

Supply source 4 supplies a maximum continuous supply voltage V_A at its terminals.

With reference to figure 2, electric machine 2 comprises a stator 6 including a circular crown-shaped stator pack 7 made of ferromagnetic material in which a plurality of slots 8 are made, and stator windings 9 partially arranged in slots 8; and a squirrel cage-like rotor 10 comprising rotor conducting bars 11, two rotor rings 12 (only one rotor ring 12 is shown in figure 2) made of conducting material which short-circuit the conducting bars 11 at the ends and a shaft (not shown in the accompanying figures) for transmitting the rotation outwards from electric machine 2.

In a variant of the present invention (not shown in the accompanying figures) , the rotor bars and the two rotor rings are replaced by rotor windings; therefore the rotor is a wound rotor.

Each stator winding 9 has a terminal (not shown in the accompanying figures) and is associated with a phase of electric machines 2. Each stator winding 9 comprises a number N of active, series-connected conductors 15 to define a magnetic flux Φ. In other words, electric machine 2 has a number N of conductors 15 in series per phase which, in turn, define a number of conductors 15 in series per slot 8.

Electric machine 2, in use, has voltages U and frequency f at the terminals of the stator windings 9. Voltages U are the effective voltages concatenated at the terminals of stator windings 9.

With reference to figure 3, electric machine 2 is characterized by a maximum torque T_max, which varies on the basis of the frequency f of the electric machine 2 and, through the shift frequency, is related to a speed SP of rotor 10.

The maximum torque T_max is constant and equal to a first torque value Ti from a zero frequency to a nominal frequency f_n, and has values which decrease as the frequency f increases from nominal frequency f_n to a maximum frequency f_max. The first torque value Ti thus represents the maximum value of maximum torque T_max of electric machine 2.

The maximum frequency f_max is defined according to a maximum speed value SP_max of rotor 10, which is typically established as a specification during the step of designing according to the desired use of electric machine 2. The nominal frequency f_n is defined as the maximum value of frequency f, so that the maximum torque T_max is equal to the first torque value Ti. In other words, the nominal frequency f_n establishes the value of frequency f up to which electric machine 2 exhibits a maximum torque T_max equal to the first torque value Ti . Both the first torque value ΊΊ and the nominal frequency f_n are typically established as design specifications according to the desired use of electric machine 2.

The stator windings 9 of electric machine 2, when fed with voltage U, determine the magnetic flux Φ, shown in figure 5. Such a magnetic flux Φ defines the maximum torque T_max. Stator pack 7 comprises foils made of ferromagnetic material, and is structured on the basis of a maximum magnetic flux value Φχ . Therefore, the structure of stator pack 7 is defined by the first torque value Ti .

Magnetic flux Φ is, inter alia, a function of voltage U, frequency f and number N of conductors 15 in series .

Electric machine 2 has a nominal voltage U_n which corresponds to the value of voltage U to be applied with nominal frequency f_n to the electric machine 2, for the maximum torque T_max of electric machine 2 to be equal to the first torque value Ti.

With reference to figure 2, stator 8 is structured to support a maximum voltage U_max higher than the nominal voltage U_n in continuous operation.

Continuous operation in a condition of use means that the condition of use is compatible with the operation of electric machine 2 over an extended time without the electric machine 2 being damaged due to said condition of use. On the contrary, limited operation in a condition of use means the condition of use compatible with the operation of electric machine 2 only over a limited time, beyond which electric machine 2 is damaged as a result of said condition of use.

The maximum voltage U_max is defined according to the supply voltage V_A of supply source 4, in particular maximum voltage U_max is equal to supply voltage V_A.

The number N of conductors 15 in series is defined on the basis of the maximum voltage U_max, the maximum magnetic flux value Φι, the nominal frequency f_n and the maximum frequency f_max.

The nominal voltage U_n is a function of the maximum magnetic flux value Φχ, the number N of conductors 15 in series, and the nominal frequency f_n.

Electric machine 2 is configured according to the following design requirements :

a) Nominal frequency f_n and first torque value

Ti;

b) Maximum frequency f_max and second torque value T₂ defined by the desired maximum toque value T_max at the maximum frequency f_max.

The nominal voltage U_n and the number N of conductors 15 in series per phase are defined according to the design requirements a) and b) .

The requirements a) and b) are met by using the following formula :

where N is the number of conductors in series per phase. In particular, to meet requirement b) , voltage U is set equal to maximum voltage U_max, which is equal to voltage V_A, frequency f equal to maximum frequency f_max and T_max equal to the second torque value T₂.

According to the above description, a number N of conductors 15 in series, parameterized as a function of the maximum frequency t_maxi of the second torque value T₂ and of the maximum voltage U_max is obtained.

For meeting requirement a) , formula [1] is used, in which f = f_n, T_max = Ti , and the newly found parameterized number N of conductors 15 in series is used. The parameterized nominal voltage U_n is obtained according to T_x, T₂, f_n, f_max and V_max.

Since the maximum frequency fmax, the second torque value T₂, the maximum frequency f_max_/ the nominal frequency f_nom_/ and the first torque value Ti are all known values defined beforehand on the basis of the desired use of electric machine 2, the nominal voltage U_n of electric machine 2 is obtained. Once the nominal voltage U_n has been obtained, the number N of conductors 15 in series of electric machine 2 is obtained from the parameterized number N of conductors 15 in series.

In other words, a nominal voltage U_n lower than the maximum voltage U_max and a number N of conductors 15 in series are chosen during the step of designing, so as to obtain the maximum magnetic flux value ι . Indeed, magnetic flux Φ is proportional to voltage U and reversely proportional to the number N of conductors 15 in series. Thus, the maximum magnetic flux value 4>i also be obtained with nominal voltage U_n lower than the maximum voltage U_max, providing that a number N of conductors 15 in series lower than that required to have the maximum magnetic flux value Φι with the maximum voltage U_max is chosen.

The number N of conductors 15 in series and the nominal voltage U_n are defined so that electric machine 2 has a maximum torque T_max equal to the second torque value T₂ by applying the maximum voltage U_max at the maximum frequency f_max. Furthermore, electric machine 2 has the first torque value Ti when fed with nominal voltage value U_n and nominal frequency f_n. Requirements a) and b) are met without increasing the size of electric machine 2 through an appropriate scalar control which will be illustrated below.

Said electric machine 2 may thus be fed in continuous operation with a voltage U higher than the nominal voltage U_n, as long as it is not higher than the maximum voltage U_max_# a a frequency f higher than nominal frequency f_n and lower than or equal to maximum frequency f_max.

Electric machine 2 comprises a cooling system (not shown in the accompanying figures) sized for a thermal cooling power P_t equal to a nominal power P_n defined according to the nominal voltage U_n at the nominal current consumed at nominal voltage U_n and to the efficiency of electric machine 2. With reference to figure 1, electric propulsion system 1 comprises a user interface 18 coupled to control device 3 to provide a desired speed SP_d, and a speed sensor (not shown in the accompanying figures) coupled to rotor 10 for detecting the rotor speed SP.

Control device 3 regulates voltage U and frequency f with a scalar control, according to the desired speed SPd and to the detected rotor speed SP. Hereinafter, scalar control means a control method for an asynchronous electric machine which acts on the effective frequency and voltage at the terminals of the electric machine, and in which the direct component and the quadrature component of the electric magnitude (voltage or current) used for controlling the electric machine 2 are not calculated.

With reference to figure 4, control device 3 operates according to a first control mode when frequency f is lower than or equal to nominal frequency f_n, and according to a second control mode, when frequency f is higher than nominal frequency f_n and lower than or equal to the maximum frequency f_max.

In the first control mode, the variation of voltage U is proportional to the variation of frequency f, as shown in figure 4. In other words, control device 3 proportionally increases the voltage value U to the frequency f itself as frequency f increases. With reference to figures 3 and 5, when control device 3 operates in the first control mode, electric machine 2 has a maximum torque T_max equal to the first torque value i and a magnetic flux Φ equal to the maximum magnetic flux value Φχ .

In the second control mode, voltage U is calculated on the basis of frequency f according to a function Ui(f) and takes voltage values U higher than the nominal voltage U_n and either lower than or equal to the maximum voltage U_max. In a frequency-voltage diagram, function ui(f) is a curve which joins a point defined by nominal voltage U_n and nominal frequency f_n to another point defined by maximum voltage U_max and maximum frequency fmax. The values of voltage U defined by the function ui(f) increase, at least within a range, as frequency f increases. Furthermore, at least in a range, the function ui(f)) has a positive derivative which decreases as frequency f increases .

In an alternative embodiment of the present invention (not shown in the accompanying figures) the function ui(f) is a broken line.

In a further embodiment of the present invention (not shown in the accompanying figures) , the function ui(f) is a rectilinear line which joins the point defined by nominal voltage U_n and nominal frequency f_n to the point defined by maximum frequency U_max and maximum frequency f_max-

The values of the function ui(f) are defined on the basis of the maximum desired torque values T_max and/or on the desired magnetic flux values Φ. With reference to figure 5, when control devices 3 acts according to the second control mode, magnetic flux Φ from nominal frequency f_n to maximum frequency f_max at least in a range, less quickly decreases than a function k/f as the frequency f increases. In other words, the magnetic flux Φ from the nominal frequency f_n to the maximum frequency f_max has, with the frequency being equal, values higher than a curve A', which is obtained by feeding electric machine 2 with the nominal voltage U_n at frequencies higher than the nominal frequency f_n.

Therefore, since the maximum torque T_max is proportional to the square of magnetic flux Φ, from frequency f_n to maximum frequency fmax the maximum torque T_max decreases to a lower extent than a quadratic decreases as frequency f increases. In other words, the maximum torque T_max from the nominal frequency to the maximum frequency has, with the frequency being equal, values higher than a curve A' which is obtained by feeding electric machine 2 with the nominal voltage U_n at frequencies higher than nominal frequency f_n.

Furthermore, in a non-limiting embodiment, control device 3 is configured to set voltage U equal to the maximum voltage U_max only in the surrounding of the maximum frequency f_max, and to set the voltage U equal to the nominal voltage U_n only in the surrounding of the nominal frequency f_n.

In essence, control device 3 defines a scalar control method because it directly regulates voltage U and frequency f at the terminals of electric machine 2 , without calculating the direct component and the quadrature component of the voltage. Therefore, it does not increase the complexity of the control system.

The present invention is particularly advantageous because it allows to obtain a relatively high ratio between the maximum frequency and the nominal frequency without increasing the size of the electric machine. Furthermore, the described method defines an innovative scalar control which offers better performance than the scalar control of the prior art, without increasing indeed the control complexity. Moreover, the propulsion system provided according to the present invention is relatively light and less cumbersome than the prior art.

Electric machine 2 is mainly used as an electric motor, and therefore control device 3 feeds electric machine 2 from the supply source 4 as described above. The present invention may also be applied when electric machine 2 is used as a generator, and therefore control device 3 recharges supply source 4 by similarly acting as described above.

It is finally apparent that changes and variations may be made to electric machine 1 described herein without departing from the scope of the appended claims.

Claims

1. Electric machine comprising a rotor (10) and a stator (6) which includes a stator pack (7) made of ferromagnetic material and having a plurality of slots (8) , and stator windings (9) for defining a magnetic flux (Φ) , having a maximum magnetic flux value (4>i) defined on the basis of a first torque value (Ti) , associated with a nominal frequency (f_n) ; the electric machine (2) being configured to supply a maximum torque (Tmax) equal to a first torque value (Ti) when fed with a nominal voltage (U_n) at a frequency lower than or equal to a nominal frequency (f_n) ; the electric machine (2) being configured to supply, in continuous operation, a maximum torque (T_max) equal to a second torque value (T₂) when fed with a maximum voltage (U_max) , higher than the nominal voltage (U_n) , at the maximum frequency (f_max) ·

2. Electric machine according to claim 1, wherein each stator winding (9) comprises a number (N) of series-connected conductors (15) and wherein the nominal voltage (U_n) and the number (N) of series-connected conductors (15) are defined on the basis of the maximum voltage (U_max) .

3. Electric machine according to claim 2, wherein the nominal voltage (U_n) and the number (N) of series- connected conductors (15) are defined on the basis of the second torque value (T₂) .

4. Electric machine according to claim 2 or 3 , wherein the nominal voltage (U_n) and the number (N) of series-connected conductors (15) are defined on the basis of the maximum frequency (f_max ) .

5. Electric machine according to anyone of claims 2 to 4, wherein the nominal voltage (U_n) and the number (N) of series-connected conductors (15) are defined on the basis of the nominal frequency (f_n) .

6. Electric machine according to anyone of the claims from 2 to 5, wherein the nominal voltage (U_n) and the number (N) of series-connected conductors (15) are defined on the basis of the first torque value (Τχ) .

7. Electric machine according to the anyone of the foregoing claims, comprising a cooling system sized for a thermal power (P_t) equal to a nominal power (P_n) defined on the basis of the nominal voltage (U_n) .

8. Electric machine according to the anyone of the foregoing claims, wherein the stator pack (7) is configured on the basis of the first torque value (Τχ) .

9. Control device for controlling an electric machine (2) having a nominal frequency (f_n) , a nominal voltage (U_n) , a maximum frequency (f_max ) and a maximum voltage (U_max) in continuous operation; the control device (3) being configured to control a frequency (f) and a voltage (U) of the electric machine (2), in a first frequency range lower than or equal to the nominal frequency (f_n) , according to a first control mode wherein the variation of the voltage (U) is proportional to the variation of the frequency (f) ; and, in a second frequency range higher than the nominal frequency (f_n) and lower than or equal to the maximum frequency (f_max) according to a second control mode wherein the voltage (U) is calculated on the basis of the frequency (f) according to a function (ui(f)); said function (ui(f)) defining values of the voltage (U) higher than the nominal voltage (U_n) and lower than or equal to the maximum voltage (U_max) .

10. Control device according to claim 9, wherein the function (ui(f)) has, at least in an interval, a derivative which is positive and decreases as the frequency (f) increases.

11. Control device according to claim 9 or 10, wherein the function (ui(f)) defines a line which connects a point defined by the nominal voltage (U_n) and by the nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by the maximum frequency (fmax) ; said line (ui(f)) being preferably curve or broken or rectilinear.

12. Control device according to the anyone of claims from 9 to 11, configured so that the function

(ui(f)) comprises a point defined by the nominal voltage (U_n) and by a nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by a maximum frequency (fmax) ; and configured to vary the voltage (U) and the frequency (f) according the function (ui(f)) so that, at each frequency from the nominal frequency (f_n) to the maximum frequency (f_max), a value of a magnetic flux (Φ) of the electric machine (2) , is higher than a first curve (A' ) obtained feeding the electric machine (2) with the nominal voltage (U_n) at frequencies higher than the nominal frequency (f_n) .

13. Control device according to anyone of the claims from 9 to 12, configured so that the function

(ui(f)) comprises a point defined by the nominal voltage (U_n) and by the nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by the maximum frequency (f_max) ; and configured to vary the voltage (U) and the frequency (f) according the function (ui(f)), so that, at each frequency value from the nominal frequency (f_n) to the maximum frequency ( fmax ) a value of the maximum torque (T_max) is higher than a second curve (A") which is obtained feeding the electric machine (2) with a nominal voltage (U_n) at frequencies higher than a nominal frequency (f_n) .

14. Control device according to anyone of claims 10 to 13, configured to set the voltage (U) equal to the maximum voltage (U_max) only around the maximum frequency ( fmax ) / and to set the voltage (U) equal to the nominal voltage (U_n) only around the nominal frequency (f_n) .

15. Electric propulsion system comprising an electric machine (2) according to anyone of claims 1 to 8, and a control device (4) according to anyone of claims 9 to 14 coupled to the electric machine (2) .

16. Electric propulsion system according to claim 15 comprising a supply source (4) , for providing a supply voltage (V_A) ; the electric machine (2) being coupled to the supply source (4) through the control device (4) ; and wherein the maximum voltage (U_max) of the electric machine (2) is defined on the basis of the supply voltage (V_A) of the supply source (4), preferably the maximum voltage (U_max) is substantially equal to the supply voltage (V_A) .

17. Electric propulsion system according to claim 16, wherein a ratio between the nominal voltage (U_n) and the maximum voltage (U_max) is defined on the basis of the first torque value (ΊΊ) , of the second torque value (T₂) , of the nominal frequency (f_n) , and of the maximum frequency (f_max) .

18. Method for controlling an electric machine (2) , comprising the steps of:

in a first frequency range lower than a nominal frequency (f_n) of the electric machine (2), controlling a frequency (f) and a voltage (U) of the electric machine (2) according to a first control mode, wherein the variation of the voltage (U) of the electric machine (2) is proportional to the variation of the frequency (f) of the electric machine (2), and wherein the voltage (U) is lower or equal to a nominal voltage (U_n) of the electric machine (2); and

in a second frequency range higher than the nominal frequency (f_n) , controlling the frequency (f ) and the voltage (U) of the electric machine (2) according to a second control mode, wherein the voltage (U) is calculated on the basis of the frequency (f) according to a function (ui(f)) increasing at least in an interval; said function (ui(f)) having voltage value higher than the nominal voltage (U_n) and lower than or equal to a maximum voltage (U_max) of the electric machine (2) .

19. Method according to claim 18, wherein the function (ui(f)) has, at least in an interval, a derivative which is positive and decreases as the frequency (f) increases.

20. Method according to claim 18 or 19, wherein the function (ui(f)) defines a line which connects a point defined by the nominal voltage (U_n) and by the nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by the maximum frequency (fmax) ; said line (ui(f)) being preferably curve or broken or rectilinear.

21. Method according to anyone of claims from 18 to 20, wherein the function (ui(f)) comprises a point defined by the nominal voltage (U_n) and by the nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by the maximum frequency (f_max) ; the method comprising the step of varying the voltage (U) and the frequency (f) according the function (ui(f)) so that, at each frequency from the nominal frequency (f_n) to the maximum frequency (fmax) , the electric machine (2) has a value of a magnetic flux (Φ) higher than a first curve (A' ) which is obtained feeding the electric machine (2) with the nominal voltage (U_n) at a frequencies higher than the nominal frequency (f_n) .

22. Method according anyone of claims 18 to 21, wherein the function (ui(f)) comprises a point defined by the nominal voltage (U_n) and by the nominal frequency (f_n) and a point defined by the maximum voltage (U_max) and by the maximum frequency (f_max) ; the method comprising the step of varying the voltage (U) and the frequency (f) according to the function (ui(f)) so that, at each frequency from the nominal frequency (f_n) to the maximum frequency (f_max) _/ a value of the maximum torque (Tmax) is higher of a second curve (A") which is obtained feeding the electric machine (2) with the nominal frequency (U_n) at frequency higher than the nominal frequency (f_n) .

23. Method according anyone of claims 18 to 22, wherein the maximum voltage (U_max) is applied only around to the maximum frequency (f_max) _/ and wherein the nominal voltage (U_n) is applied only around to the nominal frequency (f_n) .

24. Method according anyone of claims from 18 to

23, wherein the electric machine (2) is sized for a thermal power (P_t) equal to a nominal power (P_n) defined by the nominal voltage (U_n) .

25. Method according anyone of claims 18 to 24, wherein the electric machine (2) is fed with a supply source (4) providing a supply voltage (V_A) through a control device (3); the maximum voltage (U_max) being substantially equal to the source voltage (V_A) of the supply source (4) .

26. Scalar control method according to anyone of the claims 18 to 25, preferably the scalar control method controlling directly only the voltage (U) and the frequency (f) at terminals of the electric machine (2).