Methods for determining admittance components

Abstract

A method according to the invention for determining admittance components (YΣ, YΔa, YΔb) of a three-phase three-phase motor (2) comprises the following steps: a) Generating a first phase current (iU), a second phase current (iV) and a third phase current (iW) which flow through phase windings of the three-phase motor (2), wherein the phase currents (iU, iV, iW) are generated by an inverter (4) to which a motor voltage (uM) is supplied as a control signal, and wherein the motor voltage (uM) is generated by superimposing a fundamental frequency voltage (uf) generated by a current controller (7) and a carrier voltage (uc) generated by a carrier voltage generator (8);b) Acquiring a number (n) of measurement sets with one sampling period (TPWM), wherein each of the measurement sets comprises the first phase current (iU) as the first measurement, the second phase current (iV) as the second measurement, and the third phase current (iW) as the third measurement, and wherein the measurement values ​​of each measurement set are acquired time-synchronously; c) Combining the measurement values ​​of the acquired number (n) of measurement sets to form an input vector (E); d) Multiplying the input vector (E) by a matrix (M) to form an output vector (A); e) Determining an isotropic admittance component (YΣ), a first anisotropic admittance component (YΔa), and a second anisotropic admittance component (YΔb) from the output vector (A).

Description

The invention relates to a method for determining the admittance components of a three-phase three-phase motor. In this method, an isotropic admittance component, a first anisotropic admittance component, and a second anisotropic admittance component are determined, which represent the admittance of the three-phase three-phase motor. From EP 3 729 634 B1, a method for determining the rotor position of a rotating field machine without a encoder and a device for controlling a three-phase motor without a encoder are known. First, the admittance components of a stator of the three-phase motor are determined, and the admittance of the three-phase motor is then determined from these admittance components. From the admittance of the three-phase motor, the current rotation angle of a rotor of the three-phase motor can be determined. From DE 10 2019 210 279 A1, a method for the sensorless determination of the position of a rotor of a rotating field machine is known. In this method, unlinked strand admittances are determined, and rotor position information is derived from the determined unlinked admittances. From US 2024 / 0418780 A1, a method for measuring the magnetic saturation profile of a synchronous machine is known. From the document “FRIEDMANN, Jan; HOFFMANN, Rolf; KENNEL, Ralph: A new approach for a complete and ultrafast analysis of PMSMs using the arbitrary injection scheme. In: Symposium on Sensorless Control for Electrical Drives (SLED) - 5-6 June 2016 - Nadi, Fiji, 2016, pp. 1-6. ISBN 978-1-5090-2745-3 (E); 978-1-5090-2746-0 (P). https: / / doi.org / 10.1109 / SLED. 2016.7518803”, a method for measuring the magnetic properties of permanent magnet synchronous motors is known. Knowing the current rotation angle of the rotor of a three-phase motor is necessary for controlling the motor. However, determining the admittance components to calculate the admittance of the three-phase motor by measuring physical quantities is relatively complex and prone to errors. The invention is based on the objective of further developing a method for determining admittance components of a three-phase three-phase motor. The problem is solved according to the invention by a method for determining admittance components of a three-phase AC motor with the features specified in claim 1. Advantageous embodiments and further developments are the subject of the dependent claims. The inventive method for determining admittance components of a three-phase AC motor comprises the following steps: In step a), a first phase current, a second phase current, and a third phase current are generated, which flow through phase windings of the three-phase motor. The phase currents are generated by an inverter, to which a motor voltage is supplied as a control signal. The motor voltage is generated by superimposing a fundamental frequency voltage generated by a current controller and a carrier voltage generated by a carrier voltage generator. In step b), a number of measurement sets are recorded with one sampling period, where each measurement set includes the first phase current as the first measurement, the second phase current as the second measurement, and the third phase current as the third measurement. The measurement values ​​of each measurement set are recorded synchronously. In step c), the measured values ​​of the recorded number of measurement sets are combined to form an input vector. In step d), the input vector is multiplied by a matrix to obtain an output vector. In step e), an isotropic admittance component, a first anisotropic admittance component and a second anisotropic admittance component are determined from the initial vector. The current rotation angle of the three-phase motor's rotor is then determined from the admittance components of the three-phase motor. In the method according to the invention, the admittance components are generated with the lowest possible noise level. This enables a significant improvement in the quality of the encoderless control of the three-phase motor. The matrix in question is a Moore-Penrose pseudoinverse matrix. Applying such a Moore-Penrose pseudoinverse matrix to a vector of oversampled current values ​​allows the simultaneous determination of the complete set of rotor position-dependent admittance components and a fundamental current phasor predicted for a future time. Crucially, the matrix's content is determined by the sequence of voltage vectors defined for the carrier voltage. The content of the matrix to be inverted contains the physical model of the fundamental current in the form of two quadratic curves, each with three degrees of freedom: one constant, one linear, and one quadratic coefficient.Likewise, the matrix to be inverted contains the section-wise course of the carrier current components which are caused by the individual admittance components due to the chosen course of the carrier voltage. According to an advantageous embodiment of the invention, the determination of the admittance components of the three-phase AC motor is repeated with an injection period. The injection period is greater than or equal to the product of the number of measurement sets and the sampling period. Each time the admittance components of the three-phase three-phase motor are determined, new measured values ​​are always used. According to an advantageous embodiment of the invention, the fundamental frequency voltage is kept constant during each injection period. The injection period is greater than or equal to the product of the number of measurement sets and the sampling period. The fundamental voltage is a voltage vector generated by the current controller at its output, which is necessary for the actual operation of the three-phase motor. In steady-state operation of the three-phase motor, i.e., at constant speed and torque, the fundamental voltage is a rotational voltage that can be specified by its magnitude and frequency. The fundamental voltage is generated by the current controller according to a control formula, tailored to the current operating state of the three-phase motor. In transient cases, however, the fundamental voltage also contains additional voltage components, which are necessary, for example, to achieve a desired change in torque. These voltage components are generated by the current controller at its output, for example, in response to a step change in the setpoint of the torque-generating current. According to an advantageous embodiment of the invention, the carrier voltage is kept constant during each sampling period. The carrier voltage is changed after each sampling period, and a sequence of carrier voltages is repeated with the injection period. The carrier voltage thus follows a fixed, predetermined pattern, which is repeated after each injection period. According to an advantageous embodiment of the invention, the sequence of the carrier stress comprises the number of temporally successive stress vectors. The vector sum of the number of stress vectors results in a zero vector. The aforementioned stress pattern thus consists of a number of distinct, successive stress vectors, which were predefined. The number of distinct stress vectors is greater than or equal to the number of measurement sets. The specific choice of successive stress vectors also determines the content of the matrix. The successive stress vectors are defined in such a way that a two-dimensional surface is spanned in the stress plane. The specific definition of these stress vectors is geared towards ensuring the best possible quality for determining the admittance components. According to an advantageous embodiment of the invention, the stress vectors of the carrier stress have the same amplitude. The individual carrier stress vectors thus differ from one another only with respect to their direction. In a further advantageous embodiment, the different directions of the individual carrier stress vectors are equidistantly distributed over the entire possible 360° range. According to an advantageous embodiment of the invention, the output vector is decomposed into a plurality of output values. A predicted a-component of a fundamental wave current is determined from a first output value, and a predicted b-component of the fundamental wave current is determined from a second output value. The predicted a-component and the predicted b-component of the fundamental wave current are supplied to the current controller as actual values. The predicted a-component and the predicted b-component of the fundamental current are predicted for a future time point that lies after the last current samples used within the injection period. The simultaneous separation and prediction of the fundamental current components allows for high dynamics of the current controller and thus also high dynamics of superimposed control loops. According to an advantageous embodiment of the invention, the isotropic admittance component is determined by dividing a third output value by an output factor. The first anisotropic admittance component is determined by dividing a fourth output value by the output factor. The second anisotropic admittance component is determined by dividing a fifth output value by the output factor. The admittance components correspond to the reciprocals of the inductances of the phase windings of the three-phase motor. The isotropic admittance component represents an average value of the admittance. The anisotropic admittance components represent differences from the average value of the admittance. According to an advantageous embodiment of the invention, the output factor is equal to the product of the amplitude of the stress vectors of the carrier stress and the sampling period. According to an advantageous embodiment of the invention, when acquiring the sets of measured values, each of the phase currents is sampled by a sample-and-hold element with a sampling period of . After each subsequent sampling period, the sampled measured values ​​are fed to a chain of delay elements and, after each further sampling period, forwarded to the next delay element in the chain. The measured values ​​stored in the sample-and-hold elements and the measured values ​​stored in the delay elements are combined into the input vector after an injection period. The injection period is greater than or equal to the product of the number of measured value sets and the sampling period. The invention is not limited to the combination of features stated in the claims. For a person skilled in the art, further meaningful combinations of claims and / or individual claim features and / or features of the description and / or the figures will become apparent, in particular from the problem statement and / or the problem arising from a comparison with the prior art. The invention will now be explained in more detail with reference to the figures. The invention is not limited to the embodiments shown in the figures. The figures represent the subject matter of the invention only schematically. They show: Fig. 1: a schematic representation of a signal flow diagram for determining admittance components of a three-phase AC motor, Fig. 2: a sequence of magnetic flux through phase windings of the AC motor caused by a sequence of a carrier voltage, Fig. 3: for an exemplary sequence of the carrier voltage, the time course of the a and b components, Fig. 4: in four partial views, the course of the flux chaining, the carrier current component caused by the isotropic admittance component, the carrier current component caused by the first anisotropic admittance component, and the carrier current component caused by the second anisotropic admittance component, each in the Cartesian ab coordinate system, Fig.Fig. 5: a trajectory of the isotropic carrier current profile and the time course of the Cartesian components, Fig. 6: the trajectory of the first anisotropic carrier current profile and the time course of the Cartesian components, and Fig. 7: the trajectory of the second anisotropic carrier current profile and the time course of the Cartesian components. Fig. 1 shows a schematic representation of a signal flow diagram for determining the admittance components YΣ, YΔa, YΔ of a three-phase AC motor 2. The three-phase motor 2 comprises a stator (not shown) with three phase windings. The three-phase motor 2 also comprises a rotor (not shown) which is rotatable about an axis of rotation relative to the stator. To control the three-phase motor 2, knowledge of the current rotational position of the rotor relative to the stator of the three-phase motor 2 is required. The rotational speed of the three-phase motor 2 is approximately 100 Hz to 200 Hz during normal operation. At such a speed, the rotational position of the rotor relative to the stator of the three-phase motor 2 can be determined relatively easily using methods known from the prior art. However, in certain operating conditions, the rotational speed of the three-phase motor 2 is significantly lower, for example, between 0 Hz and 20 Hz. At such low speeds, determining the rotational position of the rotor relative to the stator of the three-phase motor 2 is more complex. In this case, the rotor position is deduced from the rotor position dependence of the admittances of the three-phase motor. For this purpose, the admittances of the three-phase motor must be continuously measured with the highest possible accuracy during operation in the lower speed range. A first phase current iU, a second phase current iV, and a third phase current iW flow through the phase windings of the three-phase motor 2. The phase currents iU, iV, and iW are generated by a three-phase inverter 4. A motor voltage uM is supplied to the inverter 4 as a control signal. The motor voltage uM corresponds to a vector with an a-component and a b-component. The motor voltage uM is generated by superimposing a fundamental frequency voltage u and a carrier voltage uc. The fundamental frequency voltage u is generated by a current controller 7 and corresponds to a vector with an a-component and a b-component. The carrier voltage uc is generated by a carrier voltage generator 8 and corresponds to a vector with an a-component and a b-component. The fundamental frequency voltage uf causes a fundamental frequency current if to flow through the phase windings of the three-phase motor 2. The fundamental frequency current if corresponds to a vector with an a-component and a b-component. The carrier voltage uc causes a carrier current ic to flow through the phase windings of the three-phase motor 2. The carrier current icent corresponds to a vector with an a-component and a b-component. A motor current iM flows through the phase windings of the three-phase motor 2, which is generated by a superposition of the fundamental wave current if and the carrier current ic. The motor current iM corresponds to a vector with an a-component and a b-component. The phase currents iU, iV, iW, which flow through the phase windings of the three-phase motor 2, correspond to the motor current iM. The phase currents iU, iV, iW generated by the inverter 4 are measured by a three-phase ammeter 6. Each of the phase currents iU, iV, iW is sampled by a separate sample-and-hold element 12 with a sampling period TPWM. The sampling period TPWM is, for example, 125 µs in this case. Thus, with each sampling period TPWM, a set of measurements is acquired, comprising the first phase current iU as the first measurement, the second phase current iV as the second measurement, and the third phase current iW as the third measurement. The measurements of each individual set are acquired synchronously. After each subsequent TPWM sampling period, the sampled measured values ​​are fed to a chain of delay elements 14. After each subsequent TPWM sampling period, the sampled measured values ​​in the chain of delay elements 14 are forwarded to the next delay element 14. A number n of measurement sets are acquired with a sampling period of TPWM. The number of delay elements 14 in a chain is always one less than the number n of acquired measurement sets. For example, the number n of acquired measurement sets is eight, i.e.: After each injection period Tinj, the measured values ​​stored in the sample-and-hold elements 12 and the measured values ​​stored in the delay elements 14 are combined by a multiplexer 16 to form an input vector E. The dimension of the input vector E corresponds to three times the number n of recorded sets of measured values, which in this embodiment is 24. The injection period Tinj is greater than or equal to the product of the number n of recorded measurement sets and the sampling period TPWM. Therefore, the injection period Tinj is 1 ms in the present embodiment. The inductances of the phase windings of the three-phase motor 2 can be represented by an inductance matrix L with an a-component and a b-component. The inductance matrix L describes the relationship between a change in the carrier current ic and the corresponding carrier voltage uc. The inductance matrix L is symmetrical and therefore contains three independent parameters. The following applies: A change in the carrier current ic as a consequence of an applied carrier voltage uc is determined by a matrix inverse to the inductance matrix L. The following holds: The inverse of the inductance matrix L is referred to below as the admittance matrix Y. The admittance matrix Y is also symmetric and determined by the three parameters Ya, Yb, and Yabb. Therefore, the relationship between the applied injection voltage uc and the differential of the carrier current ic is as follows: The admittance matrix Y can be described in polar form as follows: Here, YΣ is the isotropic admittance component, YΔ is the magnitude of the anisotropic admittance component, and αi0 is the direction of the anisotropic admittance component. The admittance matrix Y can be described in map-like representation as follows: The admittance matrix Y thus has an isotropic admittance component YΣ, a first Cartesian anisotropic admittance component YΔa and a second Cartesian anisotropic admittance component YΔbauf. For the isotropic admittance component YΣ, the following applies: For the first anisotropic admittance component YΔaglit: For the second anisotropic admittance component YΔb, the following applies: The carrier voltage uc causes a change in the magnetic flux through the phase windings of the three-phase motor 2 and thus a change in the carrier current ic. The carrier current is a superposition of several components originating from the individual admittance components. The following applies: The same imprinted carrier flux chain ΔΨc is mapped to the corresponding carrier current change for the three admittance components YΣ, YΔa, and YΔb using different mapping matrices. For the change in the isotropic carrier current component ΔicΣ, the mapping matrix is ​​an identity matrix; for the first anisotropic carrier current component ΔicΔa, the mapping matrix is ​​a reflection across the a-axis of the stator-fixed ab-coordinate system; and for the second anisotropic carrier current component ΔicΔb, the mapping matrix is ​​a reflection across the first angle bisector of the stator-fixed ab-coordinate system. Furthermore, the mapping of the carrier flux chain Δψc onto the different carrier flux components according to equations (10) to (12) includes the value of the admittance component to be determined. In the case of the isotropic carrier flux change ΔicΣ, the value of the isotropic admittance component YΣ ​​according to equation (10); in the case of the first anisotropic carrier flux change ΔicΔaden, the value of the first anisotropic admittance component YΔa according to equation (11); and in the case of the second anisotropic carrier flux change ΔicΔb, the value of the second anisotropic admittance component YΔb according to equation (12). The carrier voltage uc is kept constant during each TPWM sampling period. The carrier voltage uc is changed after each TPWM sampling period. This change in the carrier voltage uc occurs cyclically with the injection period Tinj. Thus, a sequence of the carrier voltage uc is repeated with the injection period Tinj. Fig. 2 shows an example of a sequence of magnetic flux through the phase windings of the three-phase motor 2 caused by a sequence of the carrier voltage uc. The sequence of the carrier voltage uc shown here enables a precise determination of the admittance components YΣ, YΔa, YΔb of the three-phase motor 2. However, other sequences of the carrier voltage uc are also conceivable. At the beginning and end of a sequence, the instantaneous value of the flux chain is offset from the origin. This offset depends on the specific choice of the carrier stress sequence. A sequence of the carrier stress uc comprises the number n, in this case eight, of temporally successive stress vectors. The vector sum of the number n of individual stress vectors results in a zero vector. The stress vectors of the carrier stress uc each have the same amplitude ûc. Fig. 3 shows for an exemplary sequence of the carrier voltage ucderen time course of the a- and b-components, which are each kept constant for a period of time TPWM, this sequence is repeated after the injection period Tinj, which in the present embodiment corresponds to Tinj= 8 · TPWM. Other sequences of the basic voltage pointers within a carrier voltage sequence are also possible and represent further embodiments of the method according to the invention. In further embodiments, the basic pointers from which the injection sequence is formed are not equidistantly spaced in 60° increments as in the present example, but have other equidistant or even non-equidistant directions. The method according to the invention can also be applied to such carrier stress sequences. In the selected embodiment, the carrier voltage has a direction of +60° in PWM interval no. 0, while in PWM interval no. 1 it has a direction of -60° or +300°, and so on. In each subsequent PWM interval, the carrier voltage has a different direction. Here, the directions of the individual carrier voltages are integer multiples of 60°. The Cartesian components of the carrier voltage for the exemplary injection sequence are as follows: in PWM interval no. 0: and in PWM interval no. 1: The Cartesian components of the carrier stress in the further intervals are calculated according to the respective direction and can be seen in the illustration in Fig. 3. Fig. 4 shows in part (a) the course of the flux linkage applied to the motor windings by the carrier voltage sequence in the Cartesian stator-fixed ab coordinate system. Since the individual basic carrier voltage vectors are each TPWM active for a certain period of time, the following results for the individual basic vector lengths of the carrier flux linkage: In sub-figure (b), the carrier current component caused by the isotropic admittance component YΣ ​​is shown in the Cartesian ab coordinate system. This profile results from the carrier flux chaining by linear scaling with the isotropic admittance component YΣ ​​to be determined. According to Fig. (10), the isotropic carrier flux profile ΔicΣ is obtained from the carrier flux profile ΔΨc by applying the identity matrix and the scalar scaling factor YΣ. The profile of the isotropic carrier flux is therefore neither rotated nor mirrored relative to the carrier flux profile, but merely scaled by YΣ. Figure (c) shows the carrier current component caused by the first anisotropic admittance component YΔa in the Cartesian ab-coordinate system. This profile is derived from the carrier flux chain by linear scaling with the first anisotropic admittance component YΔa to be determined, and by reflection across the a-axis. According to Eq. (11), the first anisotropic carrier flux profile ΔiΔa is obtained from the carrier flux profile ΔΨc by applying the matrix and the scalar scaling factor YΔa. The profile of the first anisotropic carrier flux is therefore reflected across the a-axis relative to the carrier flux profile and scaled with YΔa. Figure (d) shows the carrier current component caused by the second anisotropic admittance component YΔb in the Cartesian ab coordinate system. This profile results from the carrier flux chaining by linear scaling with the second anisotropic admittance component YΔb to be determined and reflection across the first bisector. According to equation (12), the second anisotropic carrier flux profile ΔiΔbaus is obtained from the carrier flux profile ΔΨc by applying the matrix and the scalar scaling factor YΔb. The profile of the second anisotropic carrier flux is therefore reflected across the first bisector relative to the carrier flux profile and scaled with YΔb. The method according to the invention allows the separate determination of the admittance components YΣ, YΔa and YΔ, which are contained as scaling factors in the individual carrier current components, taking into account the different imaging properties of the associated admittance components in the equations to be set up. Figure 5 shows the trajectory of the isotropic carrier current icΣ in sub-image (a) and the time course of the Cartesian components in sub-images (b) and (c). In the exemplary embodiment shown, the carrier voltage has the same amplitude ûc in each PWM period, which also means that the length of the carrier current changes of the isotropic component occurring within a PWM period is always the same, namely: The trajectory in sub-image (a) as well as the time-dependent profiles of the a-component in sub-image (b) and the b-component in sub-image (c) are normalized to this peak value icΣ. The rising and falling profiles within the PWM periods, during which the carrier voltage is held constant, are simplified as linear profiles in Fig. 5. In a real pulse-width modulated converter, however, the current increases occur during the drive phases. This difference, however, has no influence on the instantaneous values ​​of the current components at the beginning and end of the PWM periods. The current values ​​recorded at the beginning of the PWM intervals n = 0 ... 7 due to the isotropic admittance component are as follows for the a-component and for the b-component. Each of the 16 recorded current values ​​(8 a-components and 8 b-components) can therefore be expressed as the product of a constant kΣan or kΣbn and the top value of the isotropic carrier current: The constants kΣan and kΣbn are determined by the choice of injection sequence and the resulting course of the associated carrier flow chain and are therefore known. For the injection sequence chosen here as an example, these are: and: Since the amplitude of the carrier voltage ûc and the duration of a PWM period TPWM are also known, all recorded current values ​​contain only the value of the unknown and to be determined quantity of the isotropic admittance component YΣ ​​as a common scaling factor due to the isotropic admittance component. Figure 6 similarly shows the trajectory of the first anisotropic carrier current profile icΔa in sub-image (a) and the time course of the Cartesian components in sub-images (b) and (c). The length of the carrier current changes of the first anisotropic component, which occur within one PWM period, is now The current values ​​recorded at the beginning of the PWM intervals n = 0 ... 7 due to the first anisotropic admittance component are as follows for the a-component and for the b-component The common roof value of the first anisotropic carrier current component îcΔa now contains the first anisotropic admittance component YΔa to be determined. For the constants that describe the magnitude of the individual instantaneous values ​​of the first anisotropic carrier current profile, the following applies with respect to the a-component and for the b-component The factors of the b-component for the first anisotropic carrier current component are inverted with respect to the b-factors of the isotropic carrier current component, since the first anisotropic admittance component acts as a mirror on the a-axis according to (11), which corresponds to an inversion of the b-component, whereas the isotropic admittance component contains an identity matrix at the corresponding position. For the injection sequence chosen here as an example, the constants kΔaan and kΔabn are as follows: Figure 7 again shows the trajectory of the second anisotropic carrier current profile icΔbin in sub-image (a) and the time course of the Cartesian components in sub-images (b) and (c). The length of the carrier current changes of the second anisotropic component, which occur within one PWM period, is now The current values ​​recorded at the beginning of the PWM intervals n = 0 ... 7 due to the second anisotropic admittance component are as follows for the a-component and for the b-component. The common roof value of the second anisotropic carrier current component îcΔben now contains the second anisotropic admittance component YΔb to be determined. For the constants that describe the magnitude of the individual instantaneous values ​​of the second anisotropic carrier current profile, the following applies with respect to the a-component: and with respect to the b-component: The factors of the a- and b-components for the second anisotropic admittance component are interchanged with respect to the a- and b-factors of the isotropic carrier current component, since the second anisotropic admittance component acts reflectively at the 1st angle bisector according to (12), which corresponds to an interchange of the a- and b-components. For the injection sequence chosen here as an example, the constants kΔaan and kΔabn are as follows: During an injection period Tinj, the number n, in this case eight, of the carrier current ic are sampled. Each of these measurements consists of an a and a b component, resulting in a total of 2 · n scalar measurements of the carrier current within one injection period. The carrier current components originating from the individual admittance components are additively superimposed in the total recorded carrier current values. Thus, the vector ic messin, which summarizes all measured scalar individual values, is as follows: On the right-hand side, all quantities are known except for the 3-component vector of the admittance components to be determined, after defining the injection sequence. Once all current values ​​of the carrier current vector within an injection sequence have been recorded, the result is an overdetermined linear system of equations that could be optimally solved quadratically for the 3-component vector of the admittance components to be determined, provided that no other current components flowed in the machine besides the carrier current. Using the numerical values ​​for the injection sequence used here as an example, we thus obtain: Since the fundamental wave current required for torque generation also flows in the windings of the machine alongside the carrier currents, it must also be taken into account in the system of equations before determining the admittance components. The fundamental frequency voltage uf is kept constant during each injection period Tinj. Only after the expiry of an injection period Tinj, i.e., after a new determination of the admittance components YΣ, YΔa, YΔb of the three-phase three-phase motor 2, is the fundamental frequency voltage uf changed at the beginning of the next injection interval. The fundamental current i within each injection period Tinj is sensibly modeled as a quadratic curve. This allows for the consideration of a changing slope of the fundamental current curve due to nonlinear inductances of the phase windings of the three-phase motor 2. This more precise modeling of the fundamental current curve also results in a more accurate determination of the admittance components to be calculated. For the modeled time history of the fundamental current component if within an injection period, the following applies: where 0 ≤ t ≤ Tinj. Here, both the fundamental waveform ifals and the coefficients for the constant (αf), linear (mf) and quadratic (qf) component are 2-component vectors. For the fundamental wave current vector at the individual sampling times s, the following applies: where in the present embodiment for n = 8, the following applies: 0 ≤ s ≤ 7, or more generally: 0 ≤ s ≤ n - 1. In an injection period Tinj, the number n, in this case eight, of measured values ​​of the fundamental waveform current phasor is sampled. These measured values ​​of the fundamental waveform current phasor can be represented collectively as a vector, where each measured value is itself a two-component vector. The following holds true: The individual scalar measurements of the sampled fundamental wave current if can also be represented as a vector. The following applies: The measured total current imess, which corresponds to the motor current iMent, is the sum of the measured fundamental current if mess and the measured carrier current ic mess. The following applies to the measured total current: The system matrix S is not square and therefore not invertible. However, a Moore-Penrose pseudoinverse B of the system matrix S can be given as follows if the system matrix S has maximum column rank: This results in a quadratically optimal solution for the unknown parameters: The pseudoinverse matrix B maps the vector of the measured currents imess to the 9-component vector which, when mapped to a current vector via the system matrix S according to equation (49), has the smallest squared error to the measured current vector itself. This approach yields the lowest possible signal noise for the 9 model parameters to be determined, given the noise level of the measured current components. The nine model parameters to be determined according to equation (51) consist of a total of six parameters of the fundamental wave current, where three parameters (constant, linear, and quadratic) describe the behavior of the a- and b-current components of the fundamental wave current within the considered injection interval, as well as the three admittance parameters. The constant parameters of the fundamental wave current afa and afbs are directly included in the vector of model parameters, the linear coefficients of the fundamental wave current mfa and mfbs are scaled with the sampling period TPWM, and the quadratic coefficients qfa and qfb are scaled with the square of the sampling period TPWM. The three admittance parameters, however, are scaled with the voltage-time surface of the carrier voltage during one sampling period TPWM, i.e., with ûc·TPWM. In this way, all nine components of the vector of model parameters in equations (49) and (51) have the unit of a current. The system matrix S and the pseudoinverse matrix B therefore contain only dimensionless coefficients. The isotropic admittance component YΣ ​​can be determined using the 7th row of the pseudoinverse matrix, followed by division by the stress-time surface of the carrier stress. Similarly, the first anisotropic admittance component YΔ can be determined using the 8th row of the pseudoinverse matrix: Similarly, the second anisotropic admittance component YΔb is determined from the 9th row of the pseudoinverse matrix: The system matrix S and the Moore-Penrose pseudoinverse B depend on the chosen injection scheme, i.e., on the sequence of the carrier voltage ucab. For the current control loop of the fundamental frequency current, it is advantageous if an actual value phasor is supplied to it, which corresponds to the actual fundamental frequency current phasor at the time when the fundamental frequency voltage newly determined by the current controller 7 becomes effective. In the present embodiment, this is the beginning or the end of the injection period. A current phasor measured at this time, i.e., at t = 8 · TPWM, cannot be used for two reasons. Firstly, there would not be sufficient processing time between the sampling time of the actual value and the time at which the fundamental voltage phasor to be determined by the current controller 7 becomes effective for the execution of the current control algorithm, for example, on a microcontroller. Secondly, the measured value sampled at this time contains, in addition to the actual fundamental current, components of the carrier current, which must not be included in the actual value supplied to the current controller 7 and therefore must be eliminated beforehand. According to the invention, the problem of supplying the current controller 7 with an actual value for the fundamental frequency current, which corresponds to the actual fundamental frequency current at the future time t = 8 · TPWM, is solved as follows: A value for the fundamental frequency current ifpam at the end of the injection period Tinj is obtained according to equation (44) for t = 8 · TPWM. When decomposed into its Cartesian components, the following applies to the a-component: and to the b-component: The constant, linear and quadratic coefficients of the a-component can be calculated according to (51) using the first, third and fifth rows of the pseudoinverse matrix B as follows: Similarly, the constant, linear and quadratic coefficients of the b-component can be obtained using the second, fourth and sixth rows of the pseudoinverse matrix B: Using equations (58), (59) and (60) in equation (56), the a-component of ifpade's predicted fundamental current ifp is: For the b-component ifpb of the predicted fundamental current ifper, the following results: The row vectors of the weights, which are used to calculate the predicted fundamental wave current components, are thus summarized from three rows of the pseudoinverse matrix B: Thus, using a separation matrix M2 directly, the quantities to be determined, namely the a and b components of the predicted fundamental current vector ifps as well as the admittance components scaled with the voltage-time surface of the carrier voltage, can be determined: Using the Moore-Penrose pseudoinverse B, the quantities to be determined are calculated from the a-components and b-components of the measured currents. Therefore, the Moore-Penrose pseudoinverse B has twice the number n, in this case sixteen, columns. The same applies to the separation matrix M2, whose rows are derived from the rows of the pseudoinverse matrix B. A 2-3 transformation of the separation matrix M2 yields a matrix M, from which the quantities to be determined from the phase currents iU, iV, iW are calculated. The matrix M then has three times the number n, in this case twenty-four, columns. As shown in Fig. 1, the input vector E is multiplied by the matrix M to produce an output vector A. In this case, the dimension of the output vector A is, for example, five. The matrix M therefore has five rows. The resulting output vector A is decomposed by a demultiplexer 18 into a plurality of output values ​​A1, A2, A3, A4, A5. The number of output values ​​A1, A2, A3, A4, A5 corresponds to the dimension of the output vector A. From a first output value A1 of the output vector A, a predicted a-component ifpade of the fundamental current if is determined, and from a second output value A2 of the output vector A, a predicted b-component ifpb of the fundamental current if is determined. The predicted a-component ifpade of the fundamental current if and the predicted b-component ifpb of the fundamental current if are fed to the current controller 7 as actual values. By dividing a third output value A3 of the output vector A by an output factor FA, the isotropic admittance component YΣ ​​is determined. By dividing a fourth output value A4 of the output vector A by the output factor FA, a first anisotropic admittance component YΔa is determined. By dividing a fifth output value A5 of the output vector A by the output factor FA, a second anisotropic admittance component YΔ is obtained. The output factor FA is equal to the product of the amplitude ûc of the voltage vectors of the carrier voltage wc and the sampling period TPWM. Thus, the isotropic admittance component YΣ, the first anisotropic admittance component YΔa and the second anisotropic admittance component YΔbaus are determined from the initial vector A. From the isotropic admittance component YΣ, the first anisotropic admittance component YΔa, and the second anisotropic admittance component YΔb, the admittance of the three-phase three-phase motor 2 is then determined. The determination of the admittance components YΣ, YΔa, and YΔb of the three-phase three-phase motor 2 is repeated with the injection period Tinj. Reference symbol list 2 Three-phase motor 6 Ammeter 8 Carrier voltage generator 12 Sampling-hold element 16 Multiplexer A Output vector A1...A5 Output values ​​FA Output factor E Input vector M Matrix ic Carrier current if Fundamental current iM Motor current ifpa Predicted a-component of the fundamental current ifpb Predicted b-component of the fundamental current iU First phase current iV Second phase current iW Third phase current L Inductance matrix n Number Tinj Injection period TPWM Sampling period uc Carrier voltage uf Fundamental voltage uM Motor voltage ûc Carrier voltage amplitude YΣ Isotropic admittance component YΔa First anisotropic admittance component YΔb Second anisotropic admittance component 4 Inverter 7 Current regulator 14 Delay element 18 Demultiplexer

Claims

Method for determining admittance components (YΣ, YΔa, YΔb) of a three-phase AC motor (2), comprising the following steps: a) Generating a first phase current (iU), a second phase current (iV) and a third phase current (iW) flowing through phase windings of the three-phase motor (2), wherein the phase currents (iU, iV, iW) are generated by an inverter (4) to which a motor voltage (uM) is supplied as a control signal, and wherein the motor voltage (uM) is generated by superimposing a fundamental frequency voltage (uf) generated by a current controller (7) and a carrier voltage (uc) generated by a carrier voltage generator (8);b) Acquiring a number (n) of measurement sets with one sampling period (TPWM), wherein each of the measurement sets comprises the first phase current (iU) as the first measurement, the second phase current (iV) as the second measurement, and the third phase current (iW) as the third measurement, and wherein the measurement values ​​of each measurement set are acquired time-synchronously; c) Combining the measurement values ​​of the acquired number (n) of measurement sets to form an input vector (E); d) Multiplying the input vector (E) by a matrix (M) to form an output vector (A); e) Determining an isotropic admittance component (YΣ), a first anisotropic admittance component (YΔa), and a second anisotropic admittance component (YΔb) from the output vector (A). Method according to one of the preceding claims, characterized in that the determination of the admittance components (YΣ, YΔa, YΔb) of the three-phase three-phase motor (2) is repeated with an injection period (Tinj), wherein the injection period (Tinj) is greater than or equal to the product of the number (n) of measurement sets and the sampling period (TPWM). Method according to one of the preceding claims, characterized in that the fundamental frequency voltage (uf) is kept constant during each injection period (Tinj), wherein the injection period (Tinj) is greater than or equal to the product of the number (n) of measurement sets and the sampling period (TPWM). Method according to one of the preceding claims, characterized in that the carrier voltage (uc) is kept constant during each sampling period (TPWM), and that the carrier voltage (uc) is changed after each sampling period (TPWM), and that a sequence of the carrier voltage (uc) is repeated with the injection period (Tinj). Method according to claim 4, characterized in that the sequence of the carrier stress (uc) comprises the number (n) of temporally successive stress vectors, and that a vectorial sum of the number (n) of stress vectors yields a zero vector. Method according to claim 5, characterized in that the stress vectors of the carrier stress (uc) have the same amplitude (ûc). Method according to one of the preceding claims, characterized in that the output vector (A) is decomposed into a plurality of output values ​​(A1, A2, A3, A4, A5), and that a predicted a-component (ifpa) of a fundamental wave current (if) is determined from a first output value (A1), and that a predicted b-component (ifpb) of the fundamental wave current (if) is determined from a second output value (A2), and that the predicted a-component (ifpa) of the fundamental wave current (if) and the predicted b-component (ifpb) of the fundamental wave current (if) are supplied to the current controller (7) as actual values. The method according to claim 7, characterized in that the isotropic admittance component (YΣ) is determined by dividing a third output value (A3) by an output factor (FA), and that the first anisotropic admittance component (YΔa) is determined by dividing a fourth output value (A4) by the output factor (FA), and that the second anisotropic admittance component (YΔb) is determined by dividing a fifth output value (A5) by the output factor (FA). Method according to claim 8, characterized in that the output factor (FA) is equal to the product of an amplitude (ûc) of the voltage vectors of the carrier voltage (uc) and the sampling period (TPWM). A method according to one of the preceding claims, characterized in that, when acquiring the sets of measured values, each of the phase currents (iU, iV, iW) is sampled by a sample-hold element (12) with the sampling period (TPWM), and that after each further sampling period (TPWM), the sampled measured values ​​are fed to a chain of delay elements (14) and, after each further sampling period (TPWM), are forwarded in the chain of delay elements (14) to the next delay element (14), and that the measured values ​​stored in the sample-hold elements (12) and the measured values ​​stored in the delay elements (14) are combined after an injection period (Tinj) to form the input vector (E), wherein the injection period (Tinj) is greater than or equal to the product of the number (n) of sets of measured values ​​and the sampling period (TPWM).

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