DE102021202926A1 - Method for monitoring the operating mode of a variable-speed electric prime mover - Google Patents

Abstract

The invention relates to a method for monitoring the operating mode of an electric asynchronous machine with a variable speed, the asynchronous machine being used in a rail vehicle for driving and for braking. The asynchronous machine is supplied with voltage or current by an inverter, the operating mode of the asynchronous machine being set and regulated by adjusting the phase position of the voltages or currents fed in. According to the invention, a sign of the electrical slip frequency of the asynchronous machine is determined. A sign of the rotational speed of the asynchronous machine is also determined. The sign of the slip frequency is compared with the sign of the speed of the asynchronous machine. If the speed and slip frequency have the same sign, the operating mode is recognized as drive. If speed and slip frequency have different signs, braking mode is recognized. The sign of a value proportional to the slip frequency is determined from the stator currents and the speed of the asynchronous machine.

Description

The invention relates to a method for monitoring the operating mode of a variable-speed electrical drive machine, in particular an asynchronous machine.

As a drive for vehicles, in particular rail vehicles, asynchronous machines are used as variable-speed electric drive machines not only for driving but also for braking.

The asynchronous machine is typically fed by an inverter that provides current and voltage for the asynchronous machine. By adjusting the phase position of applied voltages or the corresponding currents of the asynchronous machine in relation to the magnetic field of the asynchronous machine, its "drive" or "braking" operating mode is set or regulated.

In the case of intentional braking, particularly in the case of emergency braking or emergency braking of the rail vehicle, it must be ensured that the asynchronous machine does not under any circumstances apply a driving force or force effect to the rail vehicle that would oppose the braking effect.

In the railway system, emergency braking is understood to mean braking with maximum braking force and the fastest possible effect. It is usually only initiated or used by a train driver in an emergency.

In the railway system, emergency braking is understood to mean braking that is initiated by monitoring devices or by a train control device.

Monitoring is typically provided for the above-described safeguard in the rail vehicle, which reliably brings about a safe state for the braking process in the event of a fault. The monitoring is specific to the rail vehicle and is checked as part of the approval of the rail vehicle.

In order to avoid the problems described or errors, it is customary to switch off the electric drive machine when braking.

This has the disadvantage that mechanical brake components are subject to high stress and are consequently subject to high wear. In addition, by switching off the electric drive machine, the possibility of recovering energy during the braking process is dispensed with.

Another way to avoid errors is to monitor the electrical power supplied to the asynchronous machine. The power is obtained by multiplying the voltages applied to the electric drive machine by the associated currents. The power monitoring allows conclusions to be drawn about the driving force of the asynchronous machine on the rail vehicle.

Another way of avoiding errors is to measure the current in the intermediate circuit of the feeding inverter as part of the monitoring and to analyze it as a measure of the power. This is for example in the publication WO 2016 134 964 A1 described. The power monitoring allows conclusions to be drawn about the driving force of the asynchronous machine on the rail vehicle.

The disadvantage of the two power-based monitoring described is that when the speed is reduced, measurement errors that are always present when determining the power greatly falsify the conclusion about an actually acting driving force.
It has therefore hitherto been customary, for safety reasons alone, to dispense with the possibility of electrical braking by the asynchronous machine when the rail vehicle is traveling slowly, which in turn leads to increased wear of mechanical brake components.

It is the object of the present invention to specify an improved method for monitoring the operating mode of an asynchronous machine that is used as a variable-speed electric drive machine in a rail vehicle, which method can be implemented precisely and reliably and with little effort.

This object is solved by the features of claim 1. Advantageous developments are specified in the dependent claims.

The invention relates to a method for monitoring the operating mode of a variable-speed three-phase asynchronous machine that is used in a rail vehicle both for driving and for braking.

The invention is based on the fact that meaningful monitoring in detail does not depend on an absolute level of an acting electrical braking or driving force. It is enough to even notice a difference between the "Drive" and "braking" operating modes can be recognized in the asynchronous machine.

For this distinction, the electrical slip of the asynchronous machine, also known as the slip frequency, is used, which represents the difference between the supplied stator frequency and the mechanical rotor frequency in relation to the number of pole pairs of the asynchronous machine.

According to the invention, the sign of the slip frequency is compared with the sign of the speed of the asynchronous machine.

If the speed and slip frequency have the same sign, then the asynchronous machine drives the rail vehicle or it is in the "drive" operating mode.

If the sign differs, the asynchronous machine brakes the rail vehicle or it is then in the “braking” operating mode.

The speed of the asynchronous machine, including the sign, is determined using a sensor on the shaft of the asynchronous machine.

Calculating the slip frequency from speed and stator frequency is often problematic. On the one hand, the speed of the asynchronous machine changes constantly due to the operational requirements of the rail vehicle. On the other hand, the regulation of the stator frequency generates a voltage that feeds the asynchronous machine due to ongoing changes in the setpoint torque and the speed, which voltage is not necessarily sinusoidal and/or periodic.

Therefore, in a preferred development, the slip frequency or its sign is determined by analyzing the currents in the asynchronous machine using a model that is described below.

A sign of the mechanical torque is determined with the aid of the model. The model is based on the fact that currents with the slip frequency flow in the rotor of the asynchronous machine, with the sign of the slip frequency reflecting the sign of the torque direction.

The model uses differential equations to describe the electrical and mechanical behavior of the asynchronous machine, the details of which are known from the literature - see, for example, the publication "Controlled drives with induction machines and self-commutated converters" by Felix Jenni, University of Applied Sciences Northwestern Switzerland, University of Applied Sciences, 2019 edition , Chapter 4.4.3.

The specific model used is explained in more detail below.

In a further preferred development, the inverter, which is connected upstream of the asynchronous machine for the electrical supply, is blocked in the event that the monitoring system detects the “drive” operating mode when the rail vehicle is intended to brake when the asynchronous machine is used. This is understood in terms of a "safe lock" as part of the approval of the rail vehicle.

With the present invention, reliable monitoring and detection of the “driving” and “braking” operating modes of the asynchronous machine is implemented with little effort, additional measuring transformers for current and voltage are not required.

The present invention enables reliable, electrical braking even at low (residual) speeds of the rail vehicle.

The present invention ensures, in particular, reliable emergency braking or emergency braking of the rail vehicle.

The wear of mechanical components of the rail vehicle's brake is reduced by the present invention, since the electrical braking effect of the asynchronous machine supports the braking effect of the mechanical components.

• 1 ein Ersatzschaltbild einer Asynchronmaschine,
• 2 eine prinzipielle Struktur für ein Modell der Asynchronmaschine zur Berechnung des Vorzeichens des Drehmoments, und
• 3 mit Bezug auf 2 das detaillierte Modell zur Berechnung des Vorzeichens des Drehmoments.

The present invention is explained in more detail below using a drawing using the example of a squirrel-cage asynchronous machine. It shows:

• 1 an equivalent circuit diagram of an asynchronous machine,
• 2 a basic structure for a model of the asynchronous machine for calculating the sign of the torque, and
• 3 regarding 2 the detailed model for calculating the sign of the torque.

1 shows a known T-equivalent circuit diagram of a squirrel-cage asynchronous machine.

The following, known equations for the equivalent circuit diagram of an asynchronous machine are taken from the publication "Regulated drives with rotary field machines and self-commutated converters" by Felix Jenni, University of Applied Sciences Northwestern Switzerland, University of Applied Sciences, Edition 2019, Chapter 4.4.3.

$$\underset{\_}{{\text{u}}_{\text{R}}}={\text{ R}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+\text{ d}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{dt }+\text{ j }\left({\mathrm{\omega }}_{\text{K}}-\text{ p }{\mathrm{\omega }}_{\text{me}}\right)\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}={\text{ L}}_{\text{S}}\underset{\_}{{\text{i}}_{\text{S}}}+{\text{ L}}_{\text{h}}\underset{\_}{{\text{i}}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{ L}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+{\text{ L}}_{\text{h}}\underset{\_}{{\text{i}}_{\text{S}}}$$

$${\text{M}}_{\text{me}}=\mathrm{1,5}\text{ p Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)=\mathrm{1,5}{\text{ p L}}_{\text{h}}/{\text{L}}_{\text{R}}\text{ Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)$$

mit:

uS

Spannungs-Drehzeiger (Raumzeiger, Momentanwert), Statorseite,

iS

Strom-Drehzeiger (Raumzeiger, Momentanwert), Statorseite,

RS

Widerstand, Statorseite,

LσS

Streuinduktivität, Statorseite,

Lh

Hauptinduktivität,

LS

Statorinduktivität,

ΨS

Statorfluss, Statorflussverkettung,

im

Strom (Momentanwert), Magnetisierung,

uR

Spannungs-Drehzeiger (Momentanwert), Rotorseite,

iR

Strom-Drehzeiger (Raumzeiger, Momentanwert), Rotorseite,

RR

Widerstand, Rotorseite,

LσR

Streuinduktivität, Rotorseite,

LR

Rotorinduktivität,

ΨR

Rotorfluss, Rotorflussverkettung (Raumzeiger, Momentanwert),

ωK

Kreisfrequenz des Koordinatensystems,

p

Zahl der Polpaare,

ωme

mechanische Kreisfrequenz (Welle der Drehstrommaschine),

Mme

mechanisches Drehmoment,

Im(x)

Imaginärteil von x

With reference to the T-equivalent circuit diagram of a general asynchronous machine, the following differential equations apply in space vector representation in a coordinate system rotating with an angular frequency ω _k : $$\underset{\_}{{\text{and}}_{\text{S}}}={\text{R}}_{\text{S}}\underset{\_}{{\text{i}}_{\text{S}}}+\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}/\text{German}+\text{j}{\mathrm{\omega }}_{\text{K}}\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}$$

$$\underset{\_}{{\text{and}}_{\text{R}}}={\text{R}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}+\text{j}\left({\mathrm{\omega }}_{\text{K}}-\text{p}{\mathrm{\omega }}_{\text{me}}\right)\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}={\text{L}}_{\text{S}}\underset{\_}{{\text{i}}_{\text{S}}}+{\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{L}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+{\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}$$

$${\text{M}}_{\text{me}}=1.5\text{p Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)=1.5{\text{p L}}_{\text{H}}/{\text{L}}_{\text{R}}\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)$$

With:

US

Voltage rotation vector (space vector, instantaneous value), stator side,

iS

Current rotary pointer (space vector, instantaneous value), stator side,

RS

resistance, stator side,

LσS

leakage inductance, stator side,

Lh

main inductance,

LS

stator inductance,

ΨS

stator flux, stator flux linkage,

in the

current (instantaneous value), magnetization,

uR

Voltage rotary pointer (instantaneous value), rotor side,

iR

Current rotary pointer (space vector, instantaneous value), rotor side,

RR

resistance, rotor side,

LσR

leakage inductance, rotor side,

LR

rotor inductance,

ΨR

rotor flux, rotor flux linkage (space vector, instantaneous value),

ωK

angular frequency of the coordinate system,

p

number of pole pairs,

ωme

mechanical circular frequency (shaft of the three-phase machine),

Mme

mechanical torque,

Im(x)

imaginary part of x

• - Gleichung (1) eine Stator-seitige Maschengleichung,
• - Gleichung (2) eine Rotor-seitige Maschengleichung und
• - Gleichung (5) das mechanische Drehmoment der Asynchronmaschine.

It describes:

• - Equation (1) a stator-side mesh equation,
• - Equation (2) a rotor-side mesh equation and
• - Equation (5) the mechanical torque of the asynchronous machine.

In order to calculate the mechanical torque, the rotor flux Ψ _R must be known in addition to the measurable currents i _S .

If one chooses ω _K = p*ω _me and u _R = 0 as the coordinate system, because it is a squirrel-cage asynchronous machine, equation (2) gives: $$0={\text{R}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}$$

Solving equation (6) for the rotor current i _R results in: $$\underset{\_}{{\text{i}}_{\text{R}}}=-\left(\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}\right)/{\text{R}}_{\text{R}}$$

Substituting equation (6a) into equation (4) results in the differential equation for the rotor flux: $$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}-{\text{L}}_{\text{R}}/{\text{R}}_{\text{R}}\left(\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}\right)$$

erhält man somit ein System, mit dem aus gemessenen Strömen i_S das mechanische Drehmoment Mme der Asynchronmaschine bestimmbar ist.With Equation (7) and with Equation $${\text{M}}_{\text{me}}=1.5\text{p Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)=1.5{\text{p L}}_{\text{H}}/{\text{L}}_{\text{R}}\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)$$

one thus obtains a system with which the mechanical torque Mme of the asynchronous machine can be determined from measured currents i _S .

For an exact determination of the torque Mme, the inductances and resistances used in the equations would be required as parameters. It should also be noted that the resistances also change due to changing temperatures of the asynchronous machine. An exact determination is therefore complex.

However, within the scope of the invention it is only necessary to recognize a distinction between "driving" and "braking" within the scope of the monitoring, which is not determined by the exact value but only by the sign of the mechanical torque.

This simplification is explained below in 2 taken into account in the model described there.

2 shows, with reference to the above statements, a basic structure for a model MOD or for a machine model of the rotor mesh, ie equations (5) and (7).

The measured stator currents I1, I2, I3 and the mechanical angular frequency ω _me as measured speed of the asynchronous machine are fed to the model MOD as input variables.

The MOD model supplies the sign of the torque DMVZ as an output variable.

The MOD model is designed in such a way that its stability and mode of action can be understood and validated.

Since the absolute value of the torque Mme is not important, the model is designed to be robust to parameter changes in reality. Accordingly, there is no tracking of thermal changes in parameters.

In the MOD model, an abstract, parameter-independent torque Mme is calculated, of which only the sign is evaluated.

3 shows with reference to 2 the MOD model for calculating the sign of the torque Mme.

und $$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{ L}}_{\text{h}}\underset{\_}{{\text{i}}_{\text{S}}}-{\text{ L}}_{\text{R}}/{\text{R}}_{\text{R}}\left(\text{d}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{dt}\right)$$

wie folgt modelliert, wobei die Bezeichnung „VZ(x)“ für „Vorzeichen der Größe x“ steht: $$\text{VZ }\left({\text{M}}_{\text{me}}\right)=\text{ VZ }\left(\text{Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)\right)$$

$$\text{d}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{dt }={\text{ R}}_{\text{R}}/{\text{L}}_{\text{R}}\left({\text{L}}_{\text{h}}\underset{\_}{{\text{i}}_{\text{S}}}-\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}\right)$$

In this case, in a coordinate system revolving with ω _K = p*ω _me , the equations $${\text{M}}_{\text{me}}=1.5{\text{p L}}_{\text{H}}/{\text{L}}_{\text{R}}\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)$$

and $$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}-{\text{L}}_{\text{R}}/{\text{R}}_{\text{R}}\left(\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}\right)$$

modeled as follows, where the designation "VZ(x)" stands for "sign of quantity x": $$\text{vz}\left({\text{M}}_{\text{me}}\right)=\text{vz}\left(\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)\right)$$

$$\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}={\text{R}}_{\text{R}}/{\text{L}}_{\text{R}}\left({\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}-\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}\right)$$

• Einem ersten Block B1 werden die gemessenen Ständerströme I1, I2, I3 als kombinierter Raumzeiger i_S sowie die Drehzahl ω_me als Eingangssignale zugeführt.

Equation (9) becomes in 3 implemented as a MOD model in blocks B1, B2 and B3 as follows:

• A first block B1 is supplied with the measured stator currents I1, I2, I3 as a combined space vector i _S and the speed ω _me as input signals.

The space vectors of the measured stator currents are rotated into a revolving coordinate system with ω _K = p*ω _me in order to obtain an effect on the rotor flux or on a variable proportional thereto.

For this rotation, the measured speed ω _me is subjected to an integration Integ, taking into account the number of pole pairs p, and from this an angle a is calculated, which is used for the rotation.

The angle a characterizes the position of the rotor in the revolving coordinate system.

The space vector of the measured stator currents i _s is converted into the coordinate system of the rotating rotor by a rotation operation through the negative angle -a.

This corresponds to the rotation of the stator rotating field, which is perceived from the rotor.

The stator rotating field is transferred to the rotor by induction and forms the rotor magnetic field there.

The rotor magnetic field builds up in the steady state with a rotor time constant.

This is simulated in the model in a second block B2 by a PT1 element, which corresponds to first-order smoothing of the output signals of the first block B1.

A rotor time constant of the PT1 element represents a parameter that is calculated from the machine parameters. Its exact determination is unimportant, since deviations only affect the transient but not the steady-state behavior.

The result of the second block B2 corresponds to the magnetizing current in the rotor with a pointer in the coordinate system of the rotor.

In a third block B3, the rotor magnetic field is rotated back through the angle +a into the stator coordinate system.

Finally, in a fourth block B4, the torque is calculated or the sign of the torque DMVZ is determined according to equation (8).

The torque or its sign DMVZ is determined by multiplying the results of the third block B3 with the conjugate-complex space vector of the stator currents.

The model described here is very simple and therefore easy to implement. It is not dependent on special machine parameters and does not have to be adapted during operation.

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• WO 2016134964 A1 [0011]

Claims (8)

Method for monitoring the operating mode of a variable-speed electrical asynchronous machine, - in which the asynchronous machine is used for propulsion and braking in a rail vehicle, - in which the asynchronous machine is supplied with voltage or current by an inverter, the operating mode of the asynchronous machine being set and regulated by adjusting the phase position of the voltages or currents fed in, - in which a sign of the electrical slip frequency of the asynchronous machine is determined, - at which a sign of the speed of the asynchronous machine is determined, - where the sign of the slip frequency is compared with the sign of the speed of the asynchronous machine, - in which the drive operating mode is recognized if the speed and slip frequency have the same sign, - in which the operating mode braking is recognized if speed and slip frequency have different signs. procedure after claim 1 , in which the sign of the speed is determined using a sensor on the shaft of the asynchronous machine. procedure after claim 1 or 2 , - in which a sign of the mechanical torque of the asynchronous machine is determined to determine the sign of the slip frequency, and - in which the sign of the torque is used as the sign of the slip frequency. procedure after claim 3 , in which the speed and the stator currents of the asynchronous machine are analyzed using a model to determine the sign of the mechanical torque. Method according to one of the preceding claims, in which the inverter, which is connected upstream of the asynchronous machine for the electrical supply, is blocked if the monitoring mode is “drive” and the rail vehicle is simultaneously braking. Method according to one of the preceding claims, in which a squirrel-cage asynchronous machine is used as the asynchronous machine. procedure after claim 6 , in which to determine the sign of the mechanical torque, the following differential equations are used in space vector representation in a coordinate system rotating with an angular frequency ω _k : $$\underset{\_}{{\text{and}}_{\text{S}}}={\text{R}}_{\text{S}}\underset{\_}{{\text{i}}_{\text{S}}}+\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}/\text{German}+\text{j}{\mathrm{\omega }}_{\text{K}}\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}$$

$$\underset{\_}{{\text{and}}_{\text{R}}}={\text{R}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}+\text{j}\left({\mathrm{\omega }}_{\text{K}}-\text{p}{\mathrm{\omega }}_{\text{me}}\right)\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}={\text{L}}_{\text{S}}\underset{\_}{{\text{i}}_{\text{S}}}+{\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{R}}}$$

$$\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}={\text{L}}_{\text{R}}\underset{\_}{{\text{i}}_{\text{R}}}+{\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}$$

$${\text{M}}_{\text{me}}=1.5\text{p Im}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{S}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)=1.5{\text{p L}}_{\text{H}}/{\text{L}}_{\text{R}}\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)$$

with u _s voltage rotation vector, stator side, i _s current rotation vector, stator side, R _s resistance, stator side, L _σS leakage inductance, stator side, L _h main inductance, L _S stator inductance, Ψ _S stator flux or stator flux linkage, space vector, instantaneous value, i _m Current or magnetizing current, u _R voltage rotation vector, space vector, instantaneous value, rotor side, i _R current rotation vector, space vector, instantaneous value, rotor side, R _R resistance, rotor side, L _σR leakage inductance, rotor side, L _R rotor inductance, Ψ _R rotor flux, rotor flux linkage , space vector, instantaneous value, ω _K angular frequency of the coordinate system, p number of pole pairs, ω _me mechanical angular frequency, M _me mechanical torque, and with Im(x) imaginary part of size x procedure after claim 6 and 7 , where the following equations are used to calculate the sign VZ of the mechanical torque Mme: $$\text{i.e}\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}/\text{German}={\text{R}}_{\text{R}}/{\text{L}}_{\text{R}}\left({\text{L}}_{\text{H}}\underset{\_}{{\text{i}}_{\text{S}}}-\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}\right)$$

$$\text{vz}\left({\text{M}}_{\text{me}}\right)=\text{vz}\left(\text{in the}\left(\underset{\_}{{\mathrm{\Psi }}_{\text{R}}}*\underset{\_}{{\text{i}}_{\text{S}}}\right)\right)$$

and in which parameters that are unknown or changeable during operation are neglected when determining the sign.

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