Patent Description:
Self-commissioning is a functionality of a power electronic converter that enables faster commissioning of an electric drive and reduces a risk of user errors. In self-commissioning, a power electronic converter performs a predefined set of measurements to estimate parameters of an electric machine. The estimated parameters are relevant to control of the electric machine, and the parameters may comprise for example inductance parameters and resistance parameters. In conjunction with an electric machine having a salient-pole rotor, the inductance parameters comprise direct-axis inductance and quadrature-axis inductance related to the stator windings of the electric machine. In a case where an electric machine has windings also in its rotor, the inductance parameters may further comprise inductances related to the rotor and mutual inductances between the stator windings and the rotor windings.

In many cases, there is a need to model the effect of magnetic saturation in the inductances of an electric machine. Thus, a process for estimating the inductances of an electric machine should be suitable for estimating the inductances as functions of currents. The situation is further complicated by the cross-saturation effect where the direct-axis inductance is dependent not only on direct-axis currents but also on quadrature-axis currents and, correspondingly, the quadrature-axis inductance is dependent not only on the quadrature-axis currents but also on the direct-axis currents.

In many cases, there is a requirement that the rotor of an electric machine does not need to be disconnected from a mechanical load during the estimation of the inductances. Thus, the inductances need to be estimated when the rotor is stationary i.e. non-rotating. On the other hand, currents injected to the electric machine when estimating the inductances should not cause excessive torques on the rotor so as to avoid a need to lock the rotor to be stationary during the estimation process. Estimation of inductances of a stationary electric machine requires typically information indicative of rotational position of a rotor with respect to stator windings. Thus, the process for estimating the inductances comprises advantageously a subprocess for estimating the rotational position of the rotor.

<CIT> discloses a method of estimating inductances and flux linkages of an electrical machine operated in standstill or quasi standstill condition, which electrical machine is supplied with drive currents via current regulators and actual values of the drive currents are measured and fed back to the current regulators such that closed-loop control is provided. The method comprises the steps of providing one of the current regulators with an alternating current (AC) value either for a direct axis current reference i*d or for a quadrature axis current reference i*q of the machine current vector, while providing another one of the current regulators with a predetermined direct current (DC) value for the remaining one of the two current references i*d and i*q.

In accordance with the invention, there is provided a device for estimating inductances of an electric machine when the rotor of the electric machine is stationary. The electric machine can be for example a synchronous reluctance machine, a permanent magnet machine having saliency, a permanent magnet assisted synchronous reluctance motor, or a salient-pole electrically excited synchronous machine.

A device according to the invention comprises a processing system configured to:.

The ratio of the amplitude of the balanced multi-phase alternating voltage and the frequency of the balanced multi-phase alternating voltage, i.e. the U/f-ratio, is advantageously selected to be so low that the resulting rotating magnetic flux is not able to accelerate the rotor to rotate together with the magnetic flux, but the rotor is substantially stationary. Thus, due to the saliency of the rotor, the reluctance encountered by the rotating magnetic flux varies depending on a varying angle between the direct-axis of the rotor and the rotating magnetic flux and therefore the negative sequence component of the stator currents is formed. The above-mentioned balanced multi-phase alternating voltage needs to be however so strong that the negative sequence component is sufficient for reliable detection. The trajectory of the space-vector of the stator currents deviates from a circle due to the negative sequence component, and the orientation of the non-circular trajectory with respect to magnetic-axes of the stator phases is indicative of the rotational position of the rotor.

The direct-axis DC-current which is supplied to the electric machine during the estimation of the quadrature-axis inductance provides two advantages. Firstly, the direct-axis DC-current keeps the rotor substantially stationary and thus prevents the position of the rotor from drifting away from its desired position. For example, in a case where a rotor of a synchronous reluctance machine is not locked to be stationary and there is no direct-axis current, a slight error in the orientation between the rotor and the quadrature-axis current for inductance estimation might result in small torque that might drift the rotor away from its desired rotational position. Secondly, the direct-axis DC-current can be varied for obtaining estimates of the quadrature-axis inductance corresponding to various levels of magnetic saturation.

In accordance with the invention, there is provided also a power electronic converter that comprises:.

In accordance with the invention, there is provided also a method for estimating inductances of an electric machine when the rotor of the electric machine is stationary. A method according to the invention comprises:.

In accordance with the invention, there is provided also a computer program for estimating inductances of an electric machine when the rotor of the electric machine is stationary. A computer program according to the invention comprises computer executable instructions for controlling a programmable processor to:.

In accordance with the invention, there is provided also a computer program product. The computer program product comprises a non-volatile computer readable medium, e.g. a compact disc "CD", encoded with a computer program according to the invention.

Various exemplifying and non-limiting embodiments of the invention are described in accompanied dependent claims.

Exemplifying and non-limiting embodiments of the invention both as to constructions and to methods of operation, together with additional objects and advantages thereof, are best understood from the following description of specific exemplifying embodiments when read in conjunction with the accompanying drawings.

The verbs "to comprise" and "to include" are used in this document as open limitations that neither exclude nor require the existence of un-recited features.

Exemplifying and non-limiting embodiments of the invention and their advantages are explained in greater detail below with reference to the accompanying drawings, in which:.

The specific examples provided in the description below should not be construed as limiting the scope and/or the applicability of the accompanied claims. Lists and groups of examples provided in the description below are not exhaustive unless otherwise explicitly stated.

<FIG> illustrates a power electronic converter <NUM> according to an exemplifying and non-limiting embodiment. The power electronic converter <NUM> comprises a converter stage <NUM> for forming stator voltages for an electric machine <NUM>. In <FIG>, the stator phase voltages are denoted as uu, uv, and uw. In the exemplifying case shown in <FIG>, the input voltage of the power electronic converter <NUM> is direct "DC" voltage UDC. It is also possible that the input voltage is e.g. three-phase alternating "AC" voltage. In this exemplifying case, the power electronic converter may comprise for example a rectifier and a DC-voltage intermediate circuit between the rectifier and the converter stage <NUM>. The converter stage <NUM> can be configured to employ e.g. pulse width modulation "PWM" for converting the DC-voltage UDC into the stator voltages uu, uv, and uw. It is however also possible that the converter stage <NUM> is a matrix converter stage for carrying out a direct conversion from e.g. three-phase input AC-voltage to the stator voltages uu, uv, and uw of the electric machine <NUM>. The power electronic converter <NUM> further comprises a controller <NUM> for controlling the stator voltages uu, uv, and uw of the electric machine <NUM>. In <FIG>, a set of switch control values delivered by the controller <NUM> to the converter stage <NUM> is denoted with s. The controller <NUM> may comprise means for implementing different control modes such as one or more vector control modes and a scalar control mode. In a vector control mode, the controller <NUM> may control the stator voltages uu, uv, and uw at least partly based on stator currents iu and iv of the electric machine <NUM> and on estimates of the direct-axis, i.e. d-axis, inductance Ld and the quadrature-axis, i.e. q-axis, inductance Lq of the electric machine <NUM>. In the exemplifying situation shown in <FIG>, it is assumed that the sum of stator currents iu, iv, and iw is zero and thus the controller <NUM> needs only two stator currents iu and iv since iw = - iu - iv.

The power electronic converter <NUM> further comprises a device <NUM> according to an exemplifying and non-limiting embodiment for estimating the d-axis inductance Ld and the q-axis inductance Lq of the electric machine <NUM> when the rotor <NUM> of the electric machine is stationary. In many cases, the d-axis and the q-axis are selected so that the d-axis is parallel with the minimum reluctance path and the q-axis is parallel with the maximum reluctance path of a rotor. However, in case of an interior permanent magnet machine "IPM", or "IPMSM", or a permanent magnet assisted synchronous reluctance machine "PMaSynRM", the reluctance of a path perpendicular to the direction of a permanent magnet "PM" flux can be smaller than that of a path parallel with the PM-flux and the selection of the d- and q-axes can be such that the d-axis is parallel with the PM-flux, i.e. parallel with the maximum reluctance path, and the q-axis is parallel with the minimum reluctance path. In the exemplifying situation shown in <FIG>, the rotor <NUM> is assumed to be stationary and the rotational position of the rotor <NUM> is denoted with θr. The electric machine <NUM> is a two-pole electric machine for demonstration purposes, but the pole number can be any positive even number. The number of phases of the electric machine <NUM> is three for demonstration purposes, but a different number of phases is also possible.

The rotational position θr of the rotor <NUM> is assumed to be unknown, and it may have any value from a range from -<NUM> electrical degrees to +<NUM> electrical degrees. The device <NUM> is configured to estimate the rotational position θr of the rotor <NUM> as a preparatory action for the determination of the d-and q-axis inductances Ld and Lq. <FIG> shows an exemplifying functional block-diagram corresponding to a processing system <NUM> of the device <NUM> when the processing system <NUM> is estimating the rotational position θr of the rotor <NUM>. The processing system <NUM> is configured to control the stator voltages uu, uv, and uw of the electric machine <NUM> to constitute a balanced multi-phase AC-voltage. In <FIG>, this is illustrated so that d-axis voltage is UACcos(2πfit) and q-axis voltage is UACsin(2πfit), where UAC is the amplitude of the phase voltages of the balanced multi-phase AC-voltage i.e. the length of the space-vector of the balanced multi-phase AC-voltage, 2πfi is the angular frequency of the balanced multi-phase AC-voltage i.e. the angular speed of the space-vector of the balanced multi-phase AC-voltage, and t is time. A functional block <NUM> converts the above-mentioned d- and q-axis voltages from a dq-coordinate system fixed to the rotor <NUM> to a xy-coordinate system fixed to the stator. It is worth noting that the coordinate system conversion is carried out as if the rotational angle of the rotor <NUM> were zero, or some other predetermined constant. As mentioned above, the actual rotational position θr of the rotor <NUM> is assumed to be unknown. Thus, in this operational phase, the dq-coordinate system related to the functional block <NUM> does not necessarily correspond to the real dq-coordinate system defined by the d- and q-axes of the rotor <NUM>. The functional block <NUM> produces references values uxref and uyref for the x- and y-axis voltages, and a functional block <NUM> converts the references values uxref and uyref into a set s of switch control values that are delivered to the converter stage <NUM>. In the exemplifying case shown in <FIG> where the rotational angle of the dq-coordinate system related to the functional block <NUM> is chosen to be zero, the dq-coordinate system related to the functional block <NUM> coincides with the xy-coordinate system, i.e. uxref = UACcos(2πfit) and uyref = UACsin(2πfit).

The balanced multi-phase AC-voltage creates a rotating magnetic flux whose rotational speed is the above-mentioned fi and thereby the angular speed is 2πfi. When stator resistances are neglected, the length of the space vector of the rotating magnetic flux is UAC/2πfi. When the rotor <NUM> is at standstill and the balanced multi-phase AC-voltage is supplied to the stator windings, the reluctance encountered by the rotating magnetic flux is different depending on the direction of the rotating magnetic flux with respect to the rotor <NUM> because of the saliency of the rotor <NUM>, i.e. the difference between the d- and q-axis inductances Ld and Lq. As an effect, the impedance of the stator windings is different at different time instants. Therefore, the stator currents iu, iv, and iw constitute an unbalanced multi-phase alternating current. The unbalance is manifested by a negative sequence component of the stator currents iu, iv, and iw. The trajectory of the space-vector of the stator currents iu, iv, and iw deviates from a circle due to the negative sequence component, and the orientation of the non-circular trajectory with respect the stator phases is indicative of the rotational position θr of the rotor <NUM> in the xy-coordinate system fixed to the stator. In an exemplifying and non-limiting embodiment, the processing system <NUM> is configured to determine, in the xy-coordinate system, a direction in which the length of the space-vector of the stator currents iu, iv, and iw reaches a minimum or a maximum and to determine the rotational position θr of the rotor <NUM> based on the determined direction of the minimum or the maximum. The space-vector of the stator currents iu, iv, and iw in the xy-coordinate system can be computed at each moment of time e.g. as <NUM>(iu + aiv - a<NUM>(iu + iv))/<NUM>, where a = (<NUM> + j√<NUM>)/<NUM>, j being an imaginary unit. In cases where the d-axis inductance Ld is greater than the q-axis inductance Lq, the direction of the minimum length of the space-vector of the stator currents iu, iv, and iw is parallel with the d-axis and the direction of the maximum length of the space-vector of the stator currents iu, iv, and iw is parallel with the q-axis. Correspondingly, in cases where the d-axis inductance Ld is smaller than the q-axis inductance Lq, the direction of the maximum length of the space-vector of the stator currents iu, iv, and iw is parallel with the d-axis and the direction of the minimum length of the space-vector of the stator currents iu, iv, and iw is parallel with the q-axis.

The above-mentioned negative sequence component of the stator currents iu, iv, and iw can be understood as a space-vector whose rotation speed is the opposite number of the rotation speed of a space-vector representing the positive sequence component of the stator currents iu, iv, and iw. In an exemplifying and non-limiting embodiment, a functional block <NUM> converts the stator currents iu, iv, and iw into x-axis current ix and y-axis current iy. In the exemplifying case shown in <FIG>, the functional block <NUM> computes the current iw as -iu - iv. A functional block <NUM> converts the x-axis and y-axis currents ix and iy from the xy-coordinate system to the dq-coordinate system using the same rotational angle, e.g. zero, that was used by the functional block <NUM>. In the exemplifying case shown in <FIG> where the rotational angle of the dq-coordinate system related to the functional blocks <NUM> and <NUM> is chosen to be zero, the dq-coordinate system related to the functional blocks <NUM> and <NUM> coincides with the xy-coordinate system, i.e. id = ix and iq = iy. The functional block <NUM> converts the dq-representation of the space-vector of the stator currents iu, iv, and iw into a coordinate system that rotates at angular speed -2πfi with respect to the stator i.e. to the xy-coordinate system. After this coordinate system transformation, the negative sequence component appears as a direct "DC" quantity and the positive sequence component appears as a double-frequency quantity that can be removed with suitable low-pass filtering such as e.g. moving average filtering. The functional block <NUM> is configured to carry out the above-mentioned low-pass filtering and to extract the direction angle of the low-pass filtered space-vector. The direction angle of the low-pass filtered space-vector is indicative of the rotational position θr of the rotor <NUM>.

The rotating magnetic flux produced by the above-mentioned balanced multi-phase AC-voltage is advantageously selected to be so small that the rotating magnetic flux is not able to accelerate the rotor <NUM> to rotate together with the rotating magnetic flux, but the rotor <NUM> is substantially stationary. The balanced multi-phase AC-voltage needs to be however so strong that the negative sequence component is sufficient for reliable detection of the rotational position θr. In the invention, the processing system <NUM> is configured to set the UAC/fi-ratio to be in a range from <NUM>% to <NUM>%, e.g. <NUM>%, of the UN/fN-ratio, where UN is the amplitude of the nominal i.e. nameplate phase voltage the electric machine <NUM> and fN is the nominal i.e. nameplate supply frequency the electric machine <NUM>. In the invention, the rotating magnetic flux produced by the balanced multi-phase AC-voltage is from <NUM>% to <NUM>% of the nominal magnetic flux of the electric machine <NUM>. For example, in an exemplifying case where the nominal supply frequency fN is e.g. <NUM> and the frequency fi of the above-mentioned balanced multi-phase AC-voltage is e.g. <NUM>, UAC which produces <NUM>% of the nominal magnetic flux is <NUM>× <NUM> × UN/(<NUM>) i.e. <NUM>% of UN. In many cases, to facilitate compensation for delays in a measurement system, the frequency fi of the balanced multi-phase AC-voltage is advantageously smaller than the nominal supply frequency fN.

<FIG> shows an exemplifying functional block-diagram corresponding to the processing system <NUM> of the device <NUM> when the processing system <NUM> is estimating the q-axis inductance Lq as a function of the d-axis current id i.e. Lq = Lq(id, iq ≈ <NUM>). The processing system <NUM> is configured to control the d-axis current id to be DC-current and the q-axis voltage of the electric machine to be AC-voltage uq = UACqcos(2πfqt), where UACq is the amplitude of the q-axis AC-voltage and fq is the frequency of the q-axis AC-voltage. A functional control block <NUM> drives the d-axis current id to a refence value IDC,dref by controlling d-axis DC-voltage UDC,d based on the difference IDC,dref - id. The functional control block <NUM> may comprise for example a proportional and integrating "PI" controller or a two-level hysteresis controller i.e. a bang-bang-controller. The functional block <NUM> converts the above-mentioned d- and q-axis voltages from the dq-coordinate system fixed to the rotor <NUM> to the xy-coordinate system fixed to the stator. The conversion is carried out according to the estimated rotational position θr of the rotor <NUM>. The functional block <NUM> produces the references values uxref and uyref for the x- and y-axis voltages, and the functional block <NUM> converts the references values uxref and uyref into the set s of switch control values that are delivered to the converter stage <NUM>. The functional block <NUM> converts the stator currents iu, iv, and iw into x-axis current ix and y-axis current iy. In the exemplifying case shown in <FIG>, the functional block <NUM> computes the current iw as -iu - iv. A functional block <NUM> converts the x-axis and y-axis currents ix and iy from the xy-coordinate system to the dq-coordinate system using the estimated rotational position θr of the rotor <NUM>. The functional block <NUM> produces the estimate of the q-axis inductance Lq as the function of the d-axis current id based on: i) the q-axis AC-voltage uq, ii) the frequency fq of the q-axis AC-voltage, and iii) the q-axis current iq that is AC-current caused by the q-axis AC voltage. <FIG> shows the waveforms of the q-axis AC-voltage uq and the d-axis voltage ud in an exemplifying case where the refence value IDC,dref of the d-axis DC-current is increased so that IDC,dref has a first value during a first time interval t<NUM>. t<NUM>, IDC,dref is increased to a second value during a second time interval t<NUM>. t<NUM>, IDC,dref is increased to a third value during a third time interval t<NUM>. t<NUM>, and IDC,dref is increased to a fourth value during a fourth time interval t<NUM>. Thus, multiple points of the saturation curve of the q-axis inductance Lq are obtained as the function of the d-axis current id.

In an exemplifying and non-limiting embodiment, the processing system <NUM> is configured to set the ratio of the amplitude of the q-axis AC-voltage and the frequency of the q-axis AC-voltage, i.e. the UACq/fq-ratio, to be in a range from <NUM>% to <NUM>%, e.g. <NUM>%, of the UN/fN-ratio, where UN is the amplitude of the nominal phase voltage the electric machine <NUM> and fN is the nominal supply frequency the electric machine <NUM>. In this exemplifying case, the amplitude of the alternating q-axis flux linkage produced by the q-axis AC-voltage is in the range from <NUM>% to <NUM>% of the nominal flux linkage of the electric machine <NUM>. For example, in a case where the UACq is <NUM> % of UN and fq is <NUM> × fN, the amplitude of the alternating q-axis flux linkage produced by the q-axis AC-voltage is <NUM>% of the nominal flux linkage of the electric machine. With this exemplifying selection, the alternating q-axis flux linkage is sufficiently low to satisfy the iq ≈ <NUM> approximation.

<FIG> shows an exemplifying functional block-diagram corresponding to the processing system <NUM> of the device <NUM> when the processing system <NUM> is estimating the d-axis inductance Lq as a function of the d-axis current id i.e. Ld = Ld(id, iq ≈ <NUM>). The processing system <NUM> is configured to control the d-axis current id to be AC-current and the q-axis voltage of the electric machine to be substantially zero, i.e. uq = <NUM>. Thus, the processing system <NUM> is configured control the d-axis voltage ud to be AC-voltage. The q-axis current iq is substantially zero since uq = <NUM>. A functional control block <NUM> drives the amplitude IAC,d of the d-axis AC-current to a refence value IAC,dref by controlling the amplitude UAC,d of the d-axis AC-voltage ud = UAC,dcos(2πfdt) based on the difference IAC,dref - IAC,d, where fd is the frequency of the d-axis AC-voltage. The functional control block <NUM> may comprise for example a two-level hysteresis controller i.e. a bang-bang-controller, or a PI-controller. The functional block <NUM> converts the d- and q-axis voltages from the dq-coordinate system fixed to the rotor <NUM> to the xy-coordinate system fixed to the stator. The conversion is carried out according to the estimated rotational position θr of the rotor <NUM>. The functional block <NUM> produces the references values uxref and uyref for the x- and y-axis voltages, and the functional block <NUM> converts the references values uxref and uyref into the set s of switch control values that are delivered to the converter stage <NUM>. The functional block <NUM> converts the stator currents iu, iv, and iw into x-axis current ix and y-axis current iy. In the exemplifying case shown in <FIG>, the functional block <NUM> computes the current iw as -iu - iv. A functional block <NUM> converts the x-axis and y-axis currents ix and iy from the xy-coordinate system to the dq-coordinate system using the estimated rotational position θr of the rotor <NUM>. The functional block <NUM> produces the estimate of the d-axis inductance Ld as the function of the d-axis current id based on: i) the amplitude of the d-axis AC-voltage UAC,d, ii) the frequency fd of the d-axis AC-voltage, and iii) the amplitude IAC,d of the d-axis AC-current. <FIG> shows the waveform of the d-axis AC-voltage ud in an exemplifying case where the refence value IAC,dref of the d-axis AC-current is increased so that IAC,dref has a first value during a first time interval t<NUM>. t<NUM>, IAC,dref is increased to a second value during a second time interval t<NUM>. t<NUM>, IAC,dref is increased to a third value during a third time interval t<NUM>. t<NUM>, and IAC,dref is increased to a fourth value during a fourth time interval t<NUM>. Thus, multiple points of the saturation curve of the d-axis inductance Ld are obtained as the function of the amplitude IAC,d of the d-axis AC-current.

In an exemplifying and non-limiting embodiment, the processing system <NUM> is configured to set the frequency fd of the d-axis AC-voltage to be less than the nominal supply frequency fN of the electric machine <NUM>. When the frequency fd is less than fN, the amplitude of the alternating d-axis flux linkage can be raised above the nominal flux linkage level of the electric machine without a need to exceed the nominal voltage level of the electric machine. Thus, a sufficiently high-reaching saturation curve for the d-axis inductance Ld can be obtained. The frequency fd can be for example about <NUM>% of fN.

In the above-described procedures for estimating the inductances Ld and Lq and their saturation curves, the amplitude of appropriate AC-current is extracted based on measured currents and the extracted amplitude value is filtered to obtain an average amplitude value. Then, each inductance value is calculated as a ratio of the amplitude of the corresponding AC-voltage and the average amplitude value divided by the angular frequency of the AC-voltage. In many cases, the effect of stator resistance can be neglected in the inductance calculation. It is however also possible to arrange a mathematical compensation for the stator resistance in the inductance calculation. The estimated inductance values can be stored for example in a look-up table for later use.

The processing system <NUM> shown in <FIG> can be implemented with one or more processor circuits, each of which can be a programmable processor circuit provided with appropriate software, a dedicated hardware processor such as for example an application specific integrated circuit "ASIC", or a configurable hardware processor such as for example a field programmable gate array "FPGA". Furthermore, the processing system may comprise one or more memory devices each of which can be for example a Random-Access-Memory "RAM" circuit. In many power electronic converters, a device according to an exemplifying and non-limiting embodiment for estimating inductances can be implemented using the hardware of the control system of the power electronic converter.

The above-described control device <NUM> is an example of a device that comprises:.

Claim 1:
A device (<NUM>) for estimating inductances (Ld, Lq) of an electric machine (<NUM>) when a rotor (<NUM>) of the electric machine (<NUM>) is stationary, the device (<NUM>) comprising a processing system (<NUM>) configured to:
- control stator voltages (uu, uv, uw) of the electric machine (<NUM>) to constitute a balanced multi-phase alternating voltage, and
estimate rotational position (θr) of the rotor (<NUM>) based on a negative sequence component of stator currents (iu, iv, iw) of the electric machine (<NUM>), the negative sequence component being caused by saliency of the rotor (<NUM>),
- control direct-axis current of the electric machine (<NUM>) to be direct current and quadrature-axis voltage of the electric machine (<NUM>) to be alternating voltage,
- estimate quadrature-axis inductance (Lq) of the electric machine (<NUM>) based on the quadrature-axis alternating voltage and on quadrature-axis alternating current caused by the quadrature-axis alternating voltage,
- control direct-axis voltage of the electric machine (<NUM>) to be alternating voltage and the quadrature-axis voltage of the electric machine (<NUM>) to be substantially zero, and
- estimate direct-axis inductance (Ld) of the electric machine (<NUM>) based on the direct-axis alternating voltage and on direct-axis alternating current caused by the direct-axis alternating voltage
wherein the processing system (<NUM>) is further configured to:
- set a ratio of amplitude of phase-voltages of the balanced multi-phase alternating voltage and frequency of the balanced multi-phase alternating voltage to be in a range from <NUM>% to <NUM>% of a ratio of amplitude of a nominal phase voltage of the electric machine and a nominal supply frequency of the electric machine (<NUM>) so as to produce a rotating magnetic flux whose amplitude is in a range from <NUM>% to <NUM>% of a nominal magnetic flux of the electric machine (<NUM>).