DE102016224374A1 - Method and arrangement for controlling an at least 6-phase PSM machine - Google Patents

Abstract

Provided are a method and an arrangement for driving an at least 6-phase PSM machine with associated six windings, which is operated by means of a field-oriented control, the calculation of the set current values of the q-axes (Isq1 Ref, Isq2Ref) depending on a limited torque setpoint (MRefLimit; M1 Ref, M2Ref), filtered nominal currents (Isd1 Ref, Isd2Ref) divided between the windings of the PSM machine, determined from reference currents of the d axes from the previous sampling step (Isd1 Ref (k-1), Isd2Ref (k-1)), and set current values of the q-axes (Isq1 Ref (k-1), Isq2Ref (k-1)) from the previous sampling step, and calculating the target current values of the d-axes (Isd1 Ref, Isd2Ref) as a function of the maximum voltages of the two windings (Us1max, Us2max), the electrical angular velocity (ωs), the nominal current values of the q-axes (Isq1 Ref (k-1), Isq2Ref (k-1 )) from the previous scanning step, and the filtered current setpoints (Isd1 Ref, Isd2Ref).

Description

The present invention relates to a method for controlling an at least 6-phase PSM machine according to the preamble of patent claim 1 and a corresponding arrangement.

Permanent-magnet synchronous machines, also called PSM machines, are used e.g. used on board a motor vehicle for different purposes, e.g. for steering power assistance, for a traction drive or other drives. A PSM machine is an induction machine with a permanent magnet arranged on or in the rotor. The at least one stator comprises windings of three or more phases and forms from the phases distributed at an angle of 120 degrees. The coils of the phases are distributed on a circumference about an axis of rotation, against which the rotor is rotatably mounted with respect to the stator. In the previously used 3-phase PSM machines, the state variables such as current, voltage, flux, etc. can be in a three-coordinate system (u, v, w) or in a (d, q) or (α, β) coordinate system or displayed. By the electrification of more and more aggregates in the industry, e.g. In vehicles, airplanes, etc. and the associated demand for more safety in electric motors, redundancy in the electric drive has become an important factor. In the event that the power supply or a part of the drive fails, there must be no danger. In the automotive industry, induction machines, e.g. used for power steering and functions in electric vehicles, etc., to produce the desired power. Some faults in the drive such as a winding short circuit, power supply failure, etc. can lead to a shutdown of the (electric) machine and in the worst case to a safety-critical state.

For these reasons, increasingly multi-phase machines have been used with redundant power supply in recent times. An example of this is the six-phase permanent magnet synchronous machine with mounted or buried magnets. There are two three-phase windings in the stator, in 1 labeled U, V, W and X, Y, Z. Each three-phase winding consists of three coils distributed at 120 °. The two three-phase windings can be either in phase or offset with a mechanical angle 1 shown. The rotor is constructed similar to a 3-phase machine. Its magnetic field (from the permanent magnet 102) flows through the coils of the three-phase windings. The machine behaves like two three-phase PSM machines, which have the same rotor, but two different ones, with a winding offset by the mechanical angle.

1 shows the coordinate systems in the six-phase synchronous machine 100. There are two three-phase windings which are offset by the mechanical angle. The individual coils of a winding are also offset by 120 ° to each other. The coils U, V, W belong to the first winding. The coils X, Y, Z to the second winding. The salient pole rotor 101 is shown in the center. For the control of the machine 100, the state variables of the machine are transformed into a coordinate system (d, q) rotating with the rotor 101, whose d-components are rectified with the magnetic flux Ψ _{PM of} the permanent magnet 102. The q-components are perpendicular to the d-components. An angle between the d-axis and the a1 or U-axis corresponds to an electrical rotation angle Θel of the rotating field machine 100 between the rotor 101 and the stator. An electrical rotation angle Θel corresponds to the mechanical rotation angle Θmech multiplied by the number of pole pairs Zp. The α1β1 system is the fixed two-coordinate system of the first coils (U, V, W) of the stator. The α2β2 system is the fixed two-coordinate system of the second coils (X, Y, Z) of the stator. The two coordinate systems (α1β1 and α2β2) of the two windings U, V, W and X, Y, Z are offset by an electrical angle * * Zp, where Zp is the pole pair number of the machine.

With the transformation of the state variables of the two machine parts into the d, q coordinate system, the differential equations of the machine are simplified, since the d1 q1 coordinates for the first machine part with the three-phase winding U, V, W and the d2q2 coordinates for the second one Machine part with the three-phase winding X, Y, Z lie one above the other. Thus, each machine part can be controlled like a DC machine, i. for each part of the machine a field-oriented control (FOR) is used as for a 3-phase PSM.

2 shows a simplified representation of a FOR for a 6-phase PSM 100 in overview. The two inverters WR1 and WR2 can be supplied with the same or different power supplies Udc1, Udc2. 2 shows an example of the two machine parts with two different, independent power supplies Udc1, Udc2. In order to compensate each other for the mutual effects of the two currents Isd1,2 and Isq1,2 for each three-phase winding and the mutual effects of the two three-phase windings, decouplings are introduced.

• wel: die elektrische Winkelgeschwindigkeit,
• ωmech: die elektrische Winkelgeschwindigkeit,
• θmech: der mechanische Winkel,
• θel: der elektrische Winkel,
• Zp: die Polpaarzahl der Maschine,
• Isuvw, Isxyz: Phasenströme der ersten bzw. der zweiten dreiphasigen Wicklung (uvw) bzw. (xyz) der 6-phasigen Maschine,
• Udc1, Udc2: die Zwischenkreisspannung, welche in manchen Anwendungen in der Automobilindustrie der Batteriespannung entspricht, zur Versorgung der ersten bzw. der zweiten dreiphasigen Wicklung (uvw) bzw. (xyz) der 6-phasigen Maschine, PWM123: die PWM-Werte zur Ansteuerung des Wechselrichters.

Here are:

• wel: the electrical angular velocity,
• ωmech: the electrical angular velocity,
• θmech: the mechanical angle,
• θel: the electrical angle,
• Zp: the number of pole pairs of the machine,
• Isuvw, Isxyz: phase currents of the first and the second three-phase winding (uvw) or (xyz) of the 6-phase machine,
• Udc1, Udc2: the DC link voltage, which in some applications in the automotive industry corresponds to the battery voltage, for supplying the first and the second three-phase winding (uvw) and (xyz) of the 6-phase machine, PWM123: the PWM values for driving of the inverter.

In order to carry out the FOR, in addition to the position of the rotor 101 and the intermediate circuit voltages Udc1, Udc2, information about the phase currents Isuvw, Isxyz is required in order to ensure the feedback of the control loop. This means that current measuring sensors are needed to measure the currents. Usually, for cost reasons, only two phase currents are measured for each three-phase winding and the third current is calculated by node rule (e.g., Isw = -Isu -Isv).

Different concepts for the calculation of the current setpoints in the field-oriented control (FOR) for a 3-phase PSM are known, e.g. from the literature (for example P. Mutschler: "Control of Drives", lecture notes, Institute of power converter technology and drive control, TU Darmstadt 2004, or D. Schröder: "Electric drives - control of drive systems", Springer-Verlag Berlin Heidelberg 2009). Here, an attempt is made to calculate the optimum d, q desired currents in the two axes d and q from a torque and a rotational speed, in order to achieve optimum efficiency and to increase the accuracy of the torque.

For the 6-phase PSM, in addition to the interactions between the two axes d and q of the individual three-phase windings, the interactions between the two three-phase windings of the machine must be taken into account. This leads to increased complexity in the control of the machine. The calculation of the d, q current setpoints should not only take into account the currents of the own winding, since the currents of the adjacent winding influence the d, q currents of each winding. A calculation of the d, q set currents, which takes into account all mutual interactions in a 6-phase machine (PSM), is not yet known.

Therefore, it is an object of this invention to provide a method and arrangement for driving an at least 6-phase PSM machine. This object is achieved by the features of the independent claims. Advantageous embodiments are the subject of the dependent claims.

More specifically, the proposed method provides for optimizing the calculation of the d, q desired torque for the desired torque in as many as possible operating points of the machine in driving the 6-phase PSM machine. The optimal calculation of the d, q set currents in the FOR leads to better efficiency, more accuracy of the torque and the maximum power exploitation of the machine.

A method is proposed for driving an at least 6-phase PSM machine with associated six windings, which is operated by means of a field-oriented control, wherein the calculation of the setpoint current values of the q-axes in dependence on a limited and on the windings of the PSM Machine split torque setpoint, filtered setpoint currents, determined from target currents of the d axes from the previous sampling step, and set current values of the q axes from the previous sampling step, and wherein the calculation of the target current values of the d axes as a function of the maximum Voltages of the two windings, the electrical angular velocity, the desired current values of the q-axes from the previous sampling step, and the filtered current setpoints takes place.

In one embodiment, the desired torque is determined and limited to a limited torque setpoint, wherein the limited torque setpoint is equally divided between the at least two windings of the PSM machine.

In one embodiment, a filter time constant for filtering the d-axis current command values from the previous sampling step is selected between 2 * TA and 6 * TA, where TA is the control sampling time.

In one embodiment, depending on the difference between the calculated desired current values and measured current values of the q-axes and the d-axes, an adjusted d or q set point is generated, which is applied to a decoupling network for generating output signals for driving the PSM Machine is transferred, wherein in the decoupling network, a compensation of the dependencies of the coordinate axes for each of the windings of the PSM machine and each of the windings from each other.

In one embodiment, a transformation of the determined output signals in coordinates for driving the PSM machine via the electrical angle and the offset angle of the at least two windings takes place.

In one embodiment, the PSM machine is a 6-phase PSM machine, and the desired current values of the q-axes are determined according to equations 31 and 32 for the first winding and for the second winding of the PSM machine.

In one embodiment, the PSM machine is a 6-phase PSM machine and the target current values of the d-axes for the first winding and for the second winding of the PSM machine are calculated according to Equations 27-30.

In the context of the present invention, provision is further made for an arrangement for controlling an at least 6-phase PSM machine with associated six windings, which is operated by means of a field-oriented control and the at least d1 q1 coordinates for a first machine part with a first three-phase winding and having the d2q2 coordinates for a second machine part having a second three-phase winding, at least comprising at least one setpoint generator configured to generate desired current values of the q-axes and the d-axes as inputs according to the described method , Furthermore, it has a comparison device for providing PI output signals from at least one difference between the input variables generated by the setpoint value generation device and corresponding measured actual values, as well as a decoupling device which is set up to output the output signals of the comparison device into d and q -Output quantities to control the PSM machine to be calculated, whereby the mutual dependencies between d- and q-axis are compensated.

In one embodiment, the at least one desired value generating device has at least one first desired current generating device for generating the desired current values of the q-axes for at least the first winding and the second winding of the PSM machine, wherein at least one limited torque reference value is used as input variables , which is equally divided among the windings of the PSM machine, received by each at least one filter means filtered target current values of the d axes from a previous sampling step and set current values of the q axes from a previous sampling step for the calculation.

In one embodiment, the at least one desired value generating device further comprises at least one second desired current generating device for generating the desired current values of the d-axes for at least the first winding and the second winding of the PSM machine, wherein at least the electrical Angular velocity of the PSM machine, each one adjustable for the first and for the second winding maximum voltage, by means of at least one filter means filtered target current values of the d-axes from a previous sampling step, and target current values of the q-axes from a previous sampling step to the calculation.

Further features and advantages of the invention will become apparent from the following description of embodiments of the invention, with reference to the figures of the drawing, the inventive details shows, and from the claims. The individual features can be realized individually for themselves or for several in any combination in a variant of the invention.

• 1 zeigt eine Darstellung der unterschiedlichen Koordinatensysteme für die 6-phasige permanenterregte Synchronmaschine PSM nach Stand der Technik.
• 2 zeigt ein Strukturbild der Feldorientierten Reglung (FOR) der Permanenterregten Synchronmaschine (PSM) nach Stand der Technik.
• 3 zeigt einen prinzipiellen Aufbau einer 6-phasigen PSM-Maschine mit versetzten dreiphasigen Wicklungen.
• 4 zeigt ein Strukturbild der Ansteuerung einer 6-phasigen PSM-Maschine mittels FOR gemäß einer Ausführung der vorliegenden Erfindung.
• 5 zeigt ein Strukturbild des d, q-Sollwerte-Generators bei Ansteuerung der in 4 gezeigten sechsphasigen PSM-Maschine mittels FOR gemäß einer Ausführung der vorliegenden Erfindung.

Preferred embodiments of the invention are explained below with reference to the accompanying drawings.

• 1 shows a representation of the different coordinate systems for the 6-phase permanent magnet synchronous machine PSM according to the prior art.
• 2 shows a structure diagram of the field-oriented control (FOR) of the permanent magnet synchronous machine (PSM) according to the prior art.
• 3 shows a basic structure of a 6-phase PSM machine with offset three-phase windings.
• 4 shows a structural diagram of the driving of a 6-phase PSM machine by means of FOR according to an embodiment of the present invention.
• 5 shows a structure diagram of the d, q setpoint generator when controlling the in 4 shown six-phase PSM machine by means of FOR according to an embodiment of the present invention.

In the following description of the figures, the same elements or functions are provided with the same reference numerals.

A concept for optimizing or developing a calculation algorithm for the current setpoint values Isd1 Ref, Isq1 Ref, Isd2Ref and Isq2Ref in a d, q coordinate system in the case of the FOR for a 6-phase PSM machine is shown below. In addition to interactions between the two axes d and q of the individual three-phase windings, the concept also takes into account the interactions between the two three-phase windings u, v, w and x, y, z of the machine itself. The aim is optimum efficiency, greater accuracy of the machine Torque and a maximum power output of the machine to achieve, so that a smooth transition is achieved with each parameter set change and the risk of high phase currents or current peaks is prevented.

1. 1. LIs: Streuinduktivität einer Spule
2. 2. La: Konstante Hauptinduktivität einer Spule
3. 3. Lb: winkelabhängige Induktivität des Rotors

3 shows a basic structure of a six-phase salient pole permanent-magnet synchronous machine with three-phase windings u, v, w and x, y, z, which are offset to each other with an arbitrary angle. If the angle is equal to zero, the two windings are in phase. The inductance of an axis is composed of three parts, which will be described in more detail below.

1. 1. LIs: leakage inductance of a coil
2. 2. La: Constant main inductance of a coil
3. 3. Lb: angle-dependent inductance of the rotor

Accordingly, the matrix of inductances [Lss] results in: $$\left[\text{lss}\right]=\left[\text{LIs}\right]+\left[\text{La}\right]+\left[\text{lb}\right]$$

The leakage inductance [LIs] is very small compared to the main inductance [La], so the influence on adjacent coils is neglected. The leakage inductance only affects the own coil, resulting in: $$\left[\text{LIs}\right]=\text{LIs}{\left[\text{I}\right]}_{6\times 6}\to \left[L_{ls}\right]=L_{ls}\left(\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right)$$

The main inductance of a coil has the largest share of the magnetic flux of one phase and has a significant effect on adjacent coils. For this reason, the interactions are considered by converting the main inductance of the causing coil to the considered coil: $$\begin{array}{l}\left[L_a\right]=\\ {\text{L}}_{\text{a}}\left(\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& \text{cos}\left(\gamma \right)& \text{cos}\left(\gamma +\frac{2\pi }{3}\right)& \text{cos}\left(\gamma +\frac{4\pi }{3}\right)\\ -\frac{1}{2}& 1& -\frac{1}{2}& \text{cos}\left(\gamma +\frac{4\pi }{3}\right)& cOs\left(\gamma \right)& \text{cos}\left(\gamma +\frac{2\pi }{3}\right)\\ -\frac{1}{2}& -\frac{1}{2}& 1& \text{cos}\left(\gamma +\frac{2\pi }{3}\right)& \text{cos}\left(\gamma +\frac{4\pi }{3}\right)& \text{cos}\left(\gamma \right)\\ \text{cos}\left(\gamma \right)& \text{cos}\left(\gamma -\frac{2\pi }{3}\right)& \text{cos}\left(\gamma -\frac{4\pi }{3}\right)& 1& -\frac{1}{2}& -\frac{1}{2}\\ \text{cos}\left(\gamma -\frac{4\pi }{3}\right)& cOs\left(\gamma \right)& \text{cos}\left(\gamma -\frac{2\pi }{3}\right)& -\frac{1}{2}& 1& -\frac{1}{2}\\ \text{cos}\left(\gamma -\frac{2\pi }{3}\right)& \text{cos}\left(\gamma -\frac{4\pi }{3}\right)& \text{cos}\left(\gamma \right)& -\frac{1}{2}& -\frac{1}{2}& 1\end{array}\right)\end{array}$$

The magnetic conductivity in the direction of a coil depends on the position of the rotor, because the flow passes through the stator and the rotor. The smaller the air gap, the higher the magnetic conductivity. The inductance is minimal at θ = 0 ° in the direction of coil u and at θ = 90 ° maximum. Accordingly, the amplitude Lb is minimal at θ = 0 ° and maximum at θ = 90 °. The matrix for Lb is obtained: $$\left[L_b\right]=-L_b(\begin{array}{ccc}\text{cos}\left(2\theta \right)& \text{cos}\left(2\theta -\frac{2\mathrm{\pi }}{3}\right)& \text{cos}\left(2\theta -\frac{4\mathrm{\pi }}{3}\right)\\ \text{cos}\left(2\theta -\frac{2\mathrm{\pi }}{3}\right)& \text{cos}\left(2\theta -\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(2\theta \right)\\ \text{cos}\left(2\theta -\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(2\theta \right)& \text{cos}\left(2\theta -\frac{2\mathrm{\pi }}{3}\right)\\ \text{cos}\left(\gamma -2\theta \right)& \text{cos}\left(\gamma -2\theta +\frac{2\mathrm{\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)\\ \text{cos}\left(\gamma -2\theta +\frac{2\mathrm{\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta \right)\\ \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta \right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)\end{array}\begin{array}{ccc}\text{cos}\left(\gamma -2\theta \right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)\\ \text{cos}\left(\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta \right)\\ \text{cos}\left(\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(\gamma -2\theta \right)& \text{cos}\left(\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)\\ \text{cos}\left(2\gamma -2\theta \right)& \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)& \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)\\ \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)& \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(2\gamma -2\theta \right)\\ \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{4\pi }}{3}\right)& \text{cos}\left(2\gamma -2\theta \right)& \text{cos}\left(2\gamma -2\theta +\frac{\mathrm{2\pi }}{3}\right)\end{array})$$

The inductors can be converted in a d, q coordinate system to the new following quantities. The main inductors in d1 and d2 axes: $$L_{d11}=L_{d22}=\left(\frac{3L_a}{2}-\frac{3{\mathrm{<figure-callout\; id="2"\; label="L\; b"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_b}{2}+L_{ls}\right)$$

The inductances representing the influence of the d1 axis on the d2 axis, ie Ld21 and vice versa Ld12, are: $$L_{d12}=L_{d21}=\left(\frac{3L_a}{2}-\frac{3L_b}{2}\right)$$

The main inductances in q1 and q2 axes: $$L_{q11}=L_{q22}=\left(\frac{3L_a}{2}+\frac{3{\mathrm{<figure-callout\; id="2"\; label="L\; b"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">L\; </figure-callout>}}_b}{2}+L_{ls}\right)$$

The inductances representing the influence of the q1 axis on the q2 axis, ie Lq21 and vice versa Lq12, are: $$L_{q12}=L_{q21}=\left(\frac{3L_a}{2}+\frac{3L_b}{2}\right)$$

Für die q1-Achse gilt : $$U_{sd2}=R_s\cdot {{\rm I}}_{sd2}+L_{d22}\cdot \frac{d{{\rm I}}_{sd2}}{dt}+L_{sd21}\cdot \frac{d{{\rm I}}_{sd1}}{dt}-L_{q22}\cdot {\omega }_s\cdot {{\rm I}}_{sq2}-L_{q21}\cdot {\omega }_s\cdot {{\rm I}}_{sq1}$$

Für die d2-Achse gilt : $$U_{sq2}=R_s\cdot {{\rm I}}_{sq2}+L_{q22}\cdot \frac{d{{\rm I}}_{sq2}}{dt}+L_{q21}\cdot \frac{d{{\rm I}}_{sq1}}{dt}+L_{d22}\cdot {\omega }_s\cdot {{\rm I}}_{sd2}+L_{d21}\cdot {\omega }_s\cdot {{\rm I}}_{sd1}+{\mathrm{\Psi }}_{PM}\cdot {\omega }_s$$

Für die q2-Achse gilt : $$U_{sq2}=R_s\cdot {{\rm I}}_{sq2}+L_{q22}\cdot \frac{d{{\rm I}}_{sq2}}{dt}+L_{q21}\cdot \frac{d{{\rm I}}_{sq1}}{dt}+L_{d22}\cdot {\omega }_s\cdot {{\rm I}}_{sd2}+L_{d21}\cdot {\omega }_s\cdot {{\rm I}}_{sd1}+{\mathrm{\Psi }}_{PM}\cdot {\omega }_s$$

By employing the inductors, a new notation of the machine's differential equations in the d, q coordinate system is achieved. For the d1 axis: $$U_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}=R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+L_{d11}\cdot \frac{d{{\rm I}}_{sd1}}{dt}+L_{sd12}\cdot \frac{d{{\rm I}}_{sd2}}{dt}-L_{q11}\cdot {\omega }_s\cdot {{\rm I}}_{sq1}-L_{q12}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}$$

For the q1 axis: $$U_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}=R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+L_{d22}\cdot \frac{d{{\rm I}}_{sd2}}{dt}+L_{sd21}\cdot \frac{d{{\rm I}}_{sd1}}{dt}-L_{q22}\cdot {\omega }_s\cdot {{\rm I}}_{sq2}-L_{q21}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}$$

For the d2 axis: $$U_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}=R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}+L_{q22}\cdot \frac{d{{\rm I}}_{sq2}}{dt}+L_{q21}\cdot \frac{d{{\rm I}}_{sq1}}{dt}+L_{d22}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+L_{d21}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+{\mathrm{\Psi }}_{PM}\cdot {\omega }_s$$

For the q2 axis: $$U_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}=R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}+L_{q22}\cdot \frac{d{{\rm I}}_{sq2}}{dt}+L_{q21}\cdot \frac{d{{\rm I}}_{sq1}}{dt}+L_{d22}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+L_{d21}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+{\mathrm{\Psi }}_{PM}\cdot {\omega }_s$$

4 shows the structure of the FOR for a 6-phase PSM machine 100 , In this case, for each of the three-phase windings u, v, w and x, y, z of the PSM machine 100 two comparison devices, here PI Controllers PI for the two streams d and q (Isd1 and Isq1 for u, v, w; Isd2 and Isq2 for x, y, z). The FOR is performed by taking the difference between the setpoint and the actual value of the current as the input of the respective PI knob PI is used.

Depending on this difference, a current or a voltage Y, in turn depending on the decoupling device used 300 , as PI output signals Yd1; yd 2; YQ1; Yq2 of the regulator PI generated. Of the PI -Controller serves to compensate for the difference. The outputs of the PI Controllers Yd1, Yq1, Yd2 and Yq1 become a decoupling device 300 pass to the desired voltages Usd1k, Usq1k, Usd2k and Usq2k as respectively d and q outputs for driving the PSM machine 100 to calculate. The decoupling device 300 has the task to compensate for the mutual dependence of the two axes d and q for each three-phase winding and the dependence of the two three-phase windings with each other. For the calculation of the current setpoints Isd1 Ref, Isq1 Ref, Isd2Ref and Isq2Ref off 4 becomes 5 used. Here you can see how these individual nominal currents are determined. This is explained below:

$$U_{s2\text{max}}=\sqrt{{\left(R_s\cdot {{\rm I}}_{sq2}+{\omega }_s\cdot \left(L_{d22}\cdot {{\rm I}}_{sd2}+L_{d21}\cdot {{\rm I}}_{sd1}+{\mathrm{\Psi }}_{PM}\right)\right)}^2+{\left(R_s\cdot {{\rm I}}_{sd2}-{\omega }_s\cdot \left(L_{q22}\cdot {{\rm I}}_{sq2}+L_{q21}\cdot {{\rm I}}_{sq1}\right)\right)}^2}$$

From the desired torque and the current speed at a given intermediate circuit voltage, the setpoint currents in d, q axes are determined for both windings. Taking into account the maximum voltage limit of the machine, the two voltages of the GL. 9 and GL. 10 in the steady state (dls / dt = 0) the voltage equation for the first winding u, v, w in GL. 13 determined. From the two tensions of the GL. 11 and GL. 12 in the stationary state (dls / dt = 0), the voltage equation for the second winding x, y, z in GL. 14 determined: $$U_{s1\text{Max}}=\sqrt{{\left(R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}+{\omega }_s\cdot \left(L_{d11}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+L_{d12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+{\mathrm{\Psi }}_{PM}\right)\right)}^2+{\left(R_s\cdot {{\rm I}}_{sd1}-{\omega }_s\cdot \left(L_{q11}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}+L_{q12}\cdot {{\rm I}}_{sq2}\right)\right)}^2}$$

$$U_{s2\text{Max}}=\sqrt{{\left(R_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}+{\omega }_s\cdot \left(L_{d22}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+L_{d21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+{\mathrm{\Psi }}_{PM}\right)\right)}^2+{\left(R_s\cdot {{\rm I}}_{sd2}-{\omega }_s\cdot \left(L_{q22}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}+L_{q21}\cdot {{\rm I}}_{sq1}\right)\right)}^2}$$

If the two equations are solved for Isd1 and Isd2, four solutions result, from which the two negative solutions for Isd1 and Isd2 can be calculated. After simplifications, the following equations result in the calculation of the two currents Isd1 and Isd2 for the d1 and d2 axes.

mit $$\begin{array}{l}Q1=(-{{\rm I}}_{sq1}^2\cdot L_{d11}^2\cdot L_{q11}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}^2\cdot L_{d11}\cdot L_{q11}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq1}^2\cdot R_s^4+U_{s1max}^2\cdot \left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot L_{d11}\cdot L_{q11}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd2}^2\cdot L_{d12}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d11}\cdot L_{d12}\cdot L_{q11}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d12}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd2}\cdot L_{d11}\cdot L_{d12}\cdot L_{q12}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd2}\cdot L_{d12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d11}^2\cdot L_{q11}\cdot L_{q12}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sq2}\cdot L_{d11}\cdot L_{q12}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq2}}^2\cdot L_{d11}^2\cdot L_{q12}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}\cdot L_{d11}\cdot L_{q12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

und: $$N1=\left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)$$

woraus resultiert: $$I_{sd1}=\frac{\left(A_1+\sqrt{Q_1}\right)}{N1}$$

For the d1-axis results: $$A1=-R_s\cdot {\omega }_s\cdot \left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{sq1}-L_{d11}\cdot {\omega }_s^2\cdot {\mathrm{\Psi }}_{PM}-L_{d11}\cdot L_{d12}\cdot {\omega }_s^2\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+R_s\cdot L_{q12}\cdot {\omega }_s\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}$$

With $$\begin{array}{l}Q1=(-{{\rm I}}_{sq1}^2\cdot L_{d11}^2\cdot L_{q11}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}^2\cdot L_{d11}\cdot L_{q11}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq1}^2\cdot R_s^4+U_{s1max}^2\cdot \left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot L_{d11}\cdot L_{q11}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd2}^2\cdot L_{d12}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d11}\cdot L_{d12}\cdot L_{q11}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d12}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd2}\cdot L_{d11}\cdot L_{d12}\cdot L_{q12}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd2}\cdot L_{d12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd2}\cdot L_{d11}^2\cdot L_{q11}\cdot L_{q12}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sq2}\cdot L_{d11}\cdot L_{q12}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq2}}^2\cdot L_{d11}^2\cdot L_{q12}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}\cdot L_{d11}\cdot L_{q12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

and: $$\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">N</figure-callout>}1=\left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)$$

as a result: $$I_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}=\frac{\left(A_1+\sqrt{Q_1}\right)}{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">N</figure-callout>}1}$$

mit : $$\begin{array}{l}Q2=(-{{\rm I}}_{sq2}^2\cdot L_{d22}^2\cdot L_{q22}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}^2\cdot L_{d22}\cdot L_{q22}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq2}^2\cdot R_s^4+U_{s2max}^2\cdot \left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot L_{d22}\cdot L_{q22}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd1}^2\cdot L_{d21}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d22}\cdot L_{d21}\cdot L_{q22}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d21}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd1}\cdot L_{d22}\cdot L_{d21}\cdot L_{q21}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd1}\cdot L_{d21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d22}^2\cdot L_{q22}\cdot L_{q21}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sq1}\cdot L_{d22}\cdot L_{q21}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq1}}^2\cdot L_{d22}^2\cdot L_{q21}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}\cdot L_{d22}\cdot L_{q21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

und: $$N2=\left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)$$

woraus resultiert: $$I_{sd2}=\frac{\left(A_2+\sqrt{Q_2}\right)}{N2}$$

For the d2 axis results: $$A2=-R_s\cdot {\omega }_s\cdot I_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2}\cdot \left(L_{d22}-L_{q22}\right)-L_{d22}\cdot {\mathrm{\Psi }}_{PM}\cdot {\omega }_s^2-L_{d22}\cdot L_{d21}\cdot {\omega }_s^2\cdot I_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+R_s\cdot {\omega }_s\cdot I_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}\cdot L_{q21}$$

With : $$\begin{array}{l}Q2=(-{{\rm I}}_{sq2}^2\cdot L_{d22}^2\cdot L_{q22}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}^2\cdot L_{d22}\cdot L_{q22}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq2}^2\cdot R_s^4+U_{s2max}^2\cdot \left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot L_{d22}\cdot L_{q22}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd1}^2\cdot L_{d21}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d22}\cdot L_{d21}\cdot L_{q22}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d21}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq1}\cdot {{\rm I}}_{sd1}\cdot L_{d22}\cdot L_{d21}\cdot L_{q21}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd1}\cdot L_{d21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sd1}\cdot L_{d22}^2\cdot L_{q22}\cdot L_{q21}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2}\cdot {{\rm I}}_{sq1}\cdot L_{d22}\cdot L_{q21}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq1}}^2\cdot L_{d22}^2\cdot L_{q21}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1}\cdot L_{d22}\cdot L_{q21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

and: $$\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">N</figure-callout>}2=\left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)$$

as a result: $$I_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}=\frac{\left(A_2+\sqrt{Q_2}\right)}{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">N</figure-callout>}2}$$

gezeigt. Unter dieser Annahme können die beiden gleichen Teildrehmomente der beiden Wicklung der 6-phasigen PSM-Maschine in GL. 23 und GL. 24 ausgedrückt werden. Dabei zeigen sich die gegenseitigen Wirkungen der beiden Wicklungen im Ausdruck der GL. 23 und GL. 24: $$M_{1\text{Re}f}=\frac{3}{2}\cdot \mathfrak{z}p\cdot \left(\left(L_{d11}\cdot {{\rm I}}_{sd1}+L_{d12}\cdot {{\rm I}}_{sd2}+{\mathrm{\Psi }}_{PM}\right)\cdot {{\rm I}}_{sq1}-\left(L_{q11}\cdot {{\rm I}}_{sq1}+L_{q12}\cdot {{\rm I}}_{sq2}\right)\cdot {{\rm I}}_{sd1}\right)$$

$$M_{\text{2Re}f}=\frac{3}{2}\cdot \mathfrak{z}p\cdot \left(\left(L_{d21}\cdot {{\rm I}}_{sd1}+L_{d22}\cdot {{\rm I}}_{sd2}+{\mathrm{\Psi }}_{PM}\right)\cdot {{\rm I}}_{sq2}-\left(L_{q21}\cdot {{\rm I}}_{sq1}+L_{q22}\cdot {{\rm I}}_{sq2}\right)\cdot {{\rm I}}_{sd2}\right)$$

For the calculation of the optimum q-set currents IsqRefl and IsqRef2 of the two windings for setting the desired torque, first the entire setpoint torque MRef is limited over a characteristic curve. In this case, depending on the speed, the maximum torque Mmax is determined, to which the desired torque MRefLimit is limited. The characteristic Mn can be calculated offline and stored, for example, as a code or characteristic curve. To load the two windings symmetrically, the limited torque MRefLimit is equally divided between the two windings, as in 4 with the halving element $\frac{1}{2}$

shown. Under this assumption, the two equal partial torques of the two windings of the 6-phase PSM machine in GL. 23 and GL. 24 expressed. This shows the mutual effects of the two windings in the expression of GL. 23 and GL. 24: $$M_{1\text{re}f}=\frac{3}{2}\cdot \mathfrak{z}p\cdot \left(\left(L_{d11}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+L_{d12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+{\mathrm{\Psi }}_{PM}\right)\cdot {{\rm I}}_{sq1}-\left(L_{q11}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}+L_{q12}\cdot {{\rm I}}_{sq2}\right)\cdot {{\rm I}}_{sd1}\right)$$

$$M_{\text{2re}f}=\frac{3}{2}\cdot \mathfrak{z}p\cdot \left(\left(L_{d21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+L_{d22}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+{\mathrm{\Psi }}_{PM}\right)\cdot {{\rm I}}_{sq2}-\left(L_{q21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1}+L_{q22}\cdot {{\rm I}}_{sq2}\right)\cdot {{\rm I}}_{sd2}\right)$$

$${{\rm I}}_{sq\text{Re}f2}=\frac{\left(\frac{M_{\text{2Re}f}}{\left(3\text{/}2\right)\cdot \mathfrak{z}p}+L_{q21}\cdot {{\rm I}}_{sd2}\cdot {{\rm I}}_{sq1}\right)}{\left(\left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{sd2}+L_{d21}\cdot {{\rm I}}_{sd1}+{\mathrm{\Psi }}_{PM}\right)}$$

From the two partial torques of the two windings, the two q-current setpoints IsqRefl and IsqRef2 can be determined. After forming, the two setpoints of the q-current for both windings result as a function of the d-currents and the torque setpoints GL. 25 and GL.26: $${{\rm I}}_{sq\text{re}\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">f</figure-callout>}1}=\frac{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1\text{re}f}}{\left(3\text{/}2\right)\cdot \mathfrak{z}p}+L_{q12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}\cdot {{\rm I}}_{sq2}\right)}{\left(\left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+L_{d12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+{\mathrm{\Psi }}_{PM}\right)}$$

$${{\rm I}}_{sq\text{re}\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">f</figure-callout>}2}=\frac{\left(\frac{M_{\text{2re}f}}{\left(3\text{/}2\right)\cdot \mathfrak{z}p}+L_{q21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}\cdot {{\rm I}}_{sq1}\right)}{\left(\left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2}+L_{d21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1}+{\mathrm{\Psi }}_{PM}\right)}$$

As from GL.15 to GL. 22 for the d-set currents and from the GL. 25 and 26 can be seen for the q-set currents, the four currents to be determined are interdependent. The currents to be calculated for the d1-axis and d2-axis are additionally directly dependent on each other. The d1 current that is calculated depends on d2 current, which is also calculated at the same time. The same applies to the two q1 and q2 streams. To avoid algebraic loops and simultaneous feedback of the calculations, measures are introduced. In the calculation of the current Isq1 Ref in GL. 25 the current Isq2Ref (k-1) from the previous calculation step, and in the calculation of the current Isq2Ref in GL. 26, the current Isq1 Ref (k-1) from the previous calculation step is used. Additionally, in GL. 25 and GL.26 the filtered d-set currents Isd1 RefFilt, Isd2RefFilt used to achieve a certain decoupling between the two axes for each winding. Thus, a stable system can be achieved. The filters for the two d-currents can be selected as delay elements of the first order. For the time constants of the two d-current filters, a value between 2 * TA to 6 * TA can be selected, where TA is the regulation sampling step of the control. Analogously, for the calculation of Isd1 Ref in GL.15 to GL.18, the two currents Isq1 Ref (k-1) and Isq2Ref (k-1) from the preceding calculation step and the filtered setpoint current Isd2RefFilt are used. For the calculation of the setpoint current Isd2Ref in GL.19 to GL.22, the two currents Isq1 Ref (k-1) and Isq2Ref (k-1) from the preceding calculation step and the filtered setpoint current Isd1 RefFilt are used.

mit: $$\begin{array}{l}Q1=(-{{\rm I}}_{sq1\text{Re}f\left(k-1\right)}^2\cdot L_{d11}^2\cdot L_{q11}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d11}\cdot L_{q11}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq1\text{Re}f\left(k-1\right)}^2\cdot R_s^4+U_{s1max}^2\cdot \left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq1\text{Re}f\left(k-1\right)}\cdot L_{d11}\cdot L_{q11}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{Re}f\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd2\text{Re}fFilt}^2\cdot L_{d12}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq1\text{Re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q11}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{Re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q12}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2Ref\left(k-1\right)}\cdot L_{d11}^2\cdot L_{q11}\cdot L_{q12}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq2\text{Re}f\left(k-1\right)}}^2\cdot L_{d11}^2\cdot L_{q12}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

For the d-current setpoint of the first winding u, v, w GL.27 and GL apply. 28: $$\begin{array}{l}{{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1\text{re}f}=(-R_s\cdot {\omega }_s\cdot \left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}-L_{d11}\cdot {\omega }_s^2\cdot {\mathrm{\Psi }}_{PM}\\ -L_{d11}\cdot L_{d12}\cdot {\omega }_s^2\cdot {{\rm I}}_{sd2RefFilt}+R_s\cdot L_{q12}\cdot {\omega }_s\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}+\sqrt{Q1})\mathfrak{/}\left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\end{array}$$

With: $$\begin{array}{l}Q1=(-{{\rm I}}_{sq1\text{re}f\left(k-1\right)}^2\cdot L_{d11}^2\cdot L_{q11}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d11}\cdot L_{q11}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq1\text{re}f\left(k-1\right)}^2\cdot R_s^4+U_{s1max}^2\cdot \left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot L_{d11}\cdot L_{q11}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd2\text{re}fFilt}^2\cdot L_{d12}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q11}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q12}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2Ref\left(k-1\right)}\cdot L_{d11}^2\cdot L_{q11}\cdot L_{q12}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq2\text{re}f\left(k-1\right)}}^2\cdot L_{d11}^2\cdot L_{q12}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

If Q1 is negative, the value can be set to zero. Wherein the switching between 0 (zero) and a positive value should be performed by hysteresis with a minimum value Qmin.

mit: $$\begin{array}{l}Q2=(-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}^2\cdot L_{q22}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}\cdot L_{q22}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot R_s^4+U_{s2max}^2\cdot \left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q22}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd1RefFilt}^2\cdot L_{d21}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q22}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q21}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1Ref\left(k-1\right)}\cdot L_{d22}^2\cdot L_{q22}\cdot L_{q21}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq1Ref\left(k-1\right)}}^2\cdot L_{d22}^2\cdot L_{q21}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

For the d-current setpoint value of the second winding x, y, z, GL.29 and GL apply. 30: $$\begin{array}{l}{{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2\text{re}f}=(-R_s\cdot {\omega }_s\cdot \left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2\text{re}f\left(k-1\right)}-L_{d22}\cdot {\omega }_s^2\cdot {\mathrm{\Psi }}_{PM}\\ -L_{d22}\cdot L_{d21}\cdot {\omega }_s^2\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1\text{re}fFilt}+R_s\cdot {\omega }_s\cdot L_{q21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1\text{re}f\left(k-1\right)}+\sqrt{Q2})\mathfrak{/}\left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\end{array}$$

With: $$\begin{array}{l}Q2=(-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}^2\cdot L_{q22}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}\cdot L_{q22}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot R_s^4+U_{s2max}^2\cdot \left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q22}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd1RefFilt}^2\cdot L_{d21}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q22}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q21}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1Ref\left(k-1\right)}\cdot L_{d22}^2\cdot L_{q22}\cdot L_{q21}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq1Ref\left(k-1\right)}}^2\cdot L_{d22}^2\cdot L_{q21}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

If Q2 is negative, the value can be set to 0 (zero). Wherein the switching between 0 (zero) and a positive value should be performed by hysteresis with a minimum value Q2min.

For the q-current setpoint in first winding u, v, w, the following applies: $${{\rm I}}_{sq\text{re}\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">f</figure-callout>}1}=\frac{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1\text{re}f}}{\left(3\text{/}2\right)\cdot zp}+L_{q12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1\text{re}fFilt}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">q</figure-callout>}2\text{re}f\left(k-1\right)}\right)}{\left(\left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1\text{re}fFilt}+L_{d12}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2\text{re}fFilt}+{\mathrm{\Psi }}_{PM}\right)}$$

For the q-current setpoint in the second winding x, y, z, the following applies: $${{\rm I}}_{sq\text{re}\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">f</figure-callout>}2}=\frac{\left(\frac{M_{\text{2re}f}}{\left(3\text{/}2\right)\cdot zp}+L_{q21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2\text{re}fFilt}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">q</figure-callout>}1\text{re}f\left(k-1\right)}\right)}{\left(\left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102016224374A1\_0041.png,DE102016224374A1\_0043.png"\; state="\{\{state\}\}">d</figure-callout>}2\text{re}fFilt}+L_{d21}\cdot {{\rm I}}_{s\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="DE102016224374A1\_0040.png,DE102016224374A1\_0042.png"\; state="\{\{state\}\}">d</figure-callout>}1\text{re}fFilt}+{\mathrm{\Psi }}_{PM}\right)}$$

• Rs: Statorwiderstand der PSM-Maschine
• Zp: Polpaarzahl der PSM-Maschine
• ΨPM: Fluss des Permanentmagneten der PSM-Maschine
• Ld11: Hauptinduktivität in d1-Achse (GL. 5)
• Lq11: Hauptinduktivität in q1-Achse (GL. 6)
• Ld22: Hauptinduktivität in d2-Achse (GL. 7)
• Lq22: Hauptinduktivität in q1-Achse (GL. 8)
• Ld12: Induktivität entsprechend des Einflusses d2-Achse auf d1-Achse (GL. 13)
• Lq12: Induktivität entsprechend des Einflusses q2-Achse auf q1-Achse (GL. 15)
• Ld21: Induktivität entsprechend des Einflusses d1-Achse auf d2-Achse (GL. 13)
• Lq21: Induktivität entsprechend des Einflusses q1-Achse auf q2-Achse (GL. 15)
• ω3: (=wel) die elektrische Winkelgeschwindigkeit der Maschine (= η*Zρ*2*π/60)
• n: Drehzahl der Maschine
• TA: verwendeter Regel-Abtastschritt
• M1Ref: Solldrehmoment für die erste Wicklung uvw der PSM-Maschine
• M2Ref: Solldrehmoment für die zweite Wicklung xyz der PSM-Maschine
• Id1Ref(k), Iq1Ref(k): (bzw. Id1Ref, Iq1Ref): Sollströme der ersten Wicklung in d1- und q1-Achse (aktuell)
• Id1 Ref(k-1), Iq1 Ref(k-1): Sollströme der ersten Wicklung in d1- und q1-Achse (ein Abtastschritt zuvor)
• Id2Ref(k), Iq2Ref(k): (bzw. Id2Ref, Iq2Ref ) Sollströme der zweiten Wicklung in d2- und q2-Achse (aktuell)
• Id2Ref(k-1), Iq2Ref(k-1): Sollströme der zweiten Wicklung in d2- und q2-Achse (ein Abtastschritt zuvor)
• Id1 RefFilt: gefilterter Sollstrom in d1 -Ache für die erste Wicklung uvw PSM-Maschine Isd2RefFilt: gefilterter Sollstrom in d2-Ache für die zweite Wicklung xyz PSM-Maschine
• Udc1: Zwischenkreisspannung des Wechselrichters zur Versorgung der ersten Wicklung uvw der PSM-Maschine
• Udc2: Zwischenkreisspannung des Wechselrichters zur Versorgung der zweiten Wicklung xyz der PSM-Maschine
• Us1max: maximal einstellbare Eingangsspannung für die erste Wicklung uvw der PSM-Maschine
• Us2max: maximal einstellbare Eingangsspannung für die zweite Wicklung xyz der PSM-Maschine.

With:

• Rs: Stator resistance of the PSM machine
• Zp: pole pair number of the PSM machine
• ΨPM: Flow of the permanent magnet of the PSM machine
• Ld11: Main inductance in d1-axis (GL 5)
• Lq11: Main inductance in q1 axis (GL 6)
• Ld22: Main inductance in d2 axis (GL 7)
• Lq22: Main inductance in q1 axis (GL 8)
• Ld12: Inductance according to the influence d2-axis on d1-axis (GL 13)
• Lq12: Inductance according to influence q2-axis on q1-axis (GL.15)
• Ld21: Inductance according to the influence d1-axis on d2-axis (GL 13)
• Lq21: Inductance according to influence q1-axis on q2-axis (GL.15)
• ω3: (= wel) the electrical angular velocity of the machine (= η * Zρ * 2 * π / 60)
• n: speed of the machine
• TA: used rule scanning step
• M1Ref: Target torque for the first winding uvw of the PSM machine
• M2Ref: Target torque for the second winding xyz of the PSM machine
• Id1Ref (k), Iq1Ref (k): (or Id1Ref, Iq1Ref): Set currents of the first winding in the d1 and q1 axes (current)
• Id1 Ref (k-1), Iq1 Ref (k-1): Set currents of the first winding in the d1 and q1 axes (one sampling step before)
• Id2Ref (k), Iq2Ref (k): (or Id2Ref, Iq2Ref) Set currents of the second winding in the d2 and q2 axes (current)
• Id2Ref (k-1), Iq2Ref (k-1): Set currents of the second winding in the d2 and q2 axes (one sampling step before)
• Id1 RefFilt: filtered nominal current in d1 -axis for the first winding uvw PSM-machine Isd2RefFilt: filtered nominal current in d2-axis for the second winding xyz PSM-machine
• Udc1: DC link voltage of the inverter to supply the first winding uvw of the PSM machine
• Udc2: DC link voltage of the inverter to supply the second winding xyz of the PSM machine
• Us1max: maximum adjustable input voltage for the first winding uvw of the PSM machine
• Us2max: maximum adjustable input voltage for the second winding xyz of the PSM machine.

The entire control of a 6-phase machine 100 According to an embodiment of the present invention with the calculation of the current setpoints is in 4 and 5 shown.

In 5 is the set value generation means 200 shown adapted to generate target current values of the q-axis Isq1 Ref, Isq2Ref and the d-axis Isd1 Ref, Isd2Ref as inputs to the FOR. For this purpose, each setpoint torque MRef is converted into optimal d and q setpoint currents as a function of the speed and the intermediate circuit voltages of the two inverters for feeding in the two windings u, v, w and x, y, z of the 6-phase machine.

First, the q-set currents for both windings u, v, w and x, y, z are determined. The total setpoint torque MRef is limited by a characteristic curve. As a result, the maximum torque Mmax is determined in each operating point as a function of the rotational speed. The target torque MRef is limited to the maximum torque, the limited torque command value MRefLimit. The maximum speed-torque characteristic, also referred to as M-n characteristic, can be calculated off-line and e.g. be stored as a table or code. The maximum value of the limited torque setpoint MRefLimit is preferably set below a maximum value of the speed-torque characteristic. In order to load the two windings u, v, w and x, y, z symmetrically, the limited torque MRefLimit is divided equally on both windings, half in this embodiment (M1 Ref, M2Ref). Taking into account the reluctance component of the torque, the two d-currents in both windings u, v, w and x, y, z are taken into account in the calculation of Isq1 Ref and Isq2Ref.

To avoid mutual couplings and algebraic loops, filtered current setpoints of the d-axes (or d-current setpoints) Isd1 RefFilt and Isd2RefFilt are used for this calculation. These filtered current command values result from a filtering of target currents of the d axes from a previous sampling step k-1. The filter time constant of the two filters Filter1 and Filter2 of the filter device, which e.g. First order delay elements can be selected between 2 * TA and 6 * TA, where TA is the control sampling time.

One receives from GL. 31 and GL. 32 the two setpoints of the current setpoints of the q-axes (or q-current setpoints) in both windings. In this case, the dependence of the two q-current setpoint values on one another is weakened by the use of the q-current setpoint values calculated from the previous sampling step k-1 in the respective equation.

When calculating the two d current setpoint values Isd1 Ref and Isd2Ref for the two windings u, v, w and x, y, z, the maximum voltages Us1 max and Us2max of the two windings u, v, w and x, y, z, the q-current setpoint values from the preceding sampling step Isq1 Ref (k-1) and Isq2Ref (k-1), and the electrical angular velocity ωs (= ωel), as well as the nominal current values of the d- filtered by means of at least one filter device Filter1 and Filter2. Axes from a previous sampling step Isd1 RefFilt (k-1) and Isd2RefFilt (k-1) are required.

The maximum voltage Us1 max is the maximum voltage that can be set by the inverter for the first winding u, v, w. The maximum voltage Us2max is the maximum voltage that can be set by the inverter for the second winding x, y, z. By setting the factor Kdc, the maximum voltage can be set arbitrarily. For a value Kdc = 1, the maximum voltage is the inner circle of the voltage hexagon of the inverter, smaller Kdc values mean smaller maximum Tensions. The maximum possible voltage is achieved at a value of Kdc = (2/3) / (1 / Sqrt (3)), where the voltage is limited to the length of the individual voltage vectors of the hexagon.

The electrical angular velocity ωs (= wel) becomes the rotational speed n and the pole pair number of the PSM machine 100 is obtained via the calculation ωs (= wel) = n * Zp * 2 * π / 60, as in 5 shown.

For a decoupling of the two axes d and q for each winding u, v, w and x, y, z, the q-set values calculated from the preceding (scanning) step k-1 are used. This feedback is prevented, which make the control system susceptible to vibration. By GL. 27 and GL. 28, the d-current setpoint for the first winding u, v, w and by GL. 29 and GL. 30, the d-current setpoint for the second winding x, y, z is determined.

4 shows the setting of the calculated dq set currents 5 using the FOR for a 6-phase PSM machine. First, the differences between the determined setpoints, as in 4 and measured actual values of the currents d1, q1, d2 and q2 are determined and the inputs of the comparison devices, in this embodiment of the PI Controllers PI , to hand over. The PI Controllers calculate the corresponding setpoints and output them as PI Output signals Yd1, Yd2, Yq1 and Yq2 off. In order to compensate for the mutual interactions between the axes d, q of the windings u, v, w and x, y, z and between the two windings, the PI Controller outputs to a decoupling device 300 forwarded.

This decoupling device 300 For example, by means of an algorithm, the drive voltages Usd1k, Usq1k, Usd2k, Usq2k for the PSM machine 100 to calculate. This achieves better dynamics. The PI Regulators are greatly relieved and serve mainly to compensate for the remaining deviations to reach a steady state. Each part of the machine, that is each of the three-phase windings u, v, w and x, y, z, is driven similarly to a normal FOR for three-phase machines.

The d and q components Usd1k, Usq1k, Usd2k, Usq2k are respectively converted or transformed by means of at least one converter dq / αβ from the d, q coordinate system into an aß coordinate system. For the transformation of state variables such as voltages, currents, flows, etc., of the winding u, v, w into d1q1 coordinates and vice versa, only the electrical angle θel is used. Due to the offset of the windings u, v, w and x, y, z to each other with the angle .mu., All transformations and backtransformations of x, y, z into d2, q2 coordinates with the electrical angle .theta.el and the angle (Zp * ). The voltages Usd1, Usq1 are transformed into x, y, z only via the electrical angle θel in the u, v, w system and the voltages Usd2, Usq2 in the x, y, z system via θel and (Zp * ү), as in 4 shown.

From the voltages Ua and Uß obtained by transformation together with the stator voltages, for each part of the machine, the respective PWM values PWM 1, PWM 2, PWM 3 are determined by means of a respective vector modulator 400 determined. The changes in the individual battery voltages, if the two windings have a different voltage supply, have no influence on the desired d, q currents for both machine parts. These determined PWM values PWM 1, PWM 2, PWM 3 are then converted via corresponding inverters WR1 and WR2 into corresponding signals u, v, w and x, y, z and the PSM machine 100 supplied as drive signals. In this case, the phase currents Isu, Isv, Isw and Isx, Isy, Isz of the first and the second three-phase winding (u, v, w) and (x, y, z) of the 6-phase PSM machine can be tapped and used further ,

The effectiveness of the method described can be substantiated by simulations. In simulations carried out, the two three-phase windings of the machine were driven under the same boundary conditions, namely with Udc1 = 12V and Udc2 = 12V. Further, the following sizes were chosen: Isd1Ref, Isd1ist; Isq1Ref, Isq1ist; Isd2Ref, Isd2ist; Isq2Ref, Isq2is [A]; Speed [rpm]; MGRef, MGIst, M1Ist, M2Ist [Nm]; Isu, Isv, Isw [A]; Isx, Isy, Isz [A] (motor and alternatively generator). The machine was accelerated to a speed of 4000rpm. In one simulation (Isu, Isv, Isw [A], Isx, Isy, Isz [A] (motor)) the torque is positive and in the other simulation (Isu, Isv, Isw [A], Isx, Isy, Isz [ A] (regenerative)) the torque is negative.

The result is that the currents Isd1 Ref, IsqRef1, Isd2Ref and Isq2Ref are set and show a smooth progression. The interactions with each other are through the decoupling device 300 and the concept designed to determine d, q-set currents 4 and 5 optimally compensated. The phase currents Isu, Isv, Isw and Isx, Isy, Isz of the two windings are sinusoidal and have the same amplitude. For this purpose, the required total torque MGRef is set, set the two windings through their optimally calculated setpoint values Isd1 Ref, IsqRef1, Isd2Ref and Isq2Ref the two torque parts M1Ist and M21st of the windings u, v, w and x, y, z. These together form the total torque MGIst.

By the designed measures 5 the mutual dependence of the two axes d and q for each three-phase winding as well as the dependence of each three-phase winding on the other three-phase winding can be optimally compensated for the calculation of the nominal currents for the motor and generator operation. For each speed and each DC link voltage of the inverter can be set by the optimal calculation of the setpoints a desired torque of the machine more accurate than before. The setpoint currents Isd1 Ref and Isd2Ref are calculated so that the maximum voltage of the inverter is utilized and smaller currents are then set for the same torque. Thus, a good accuracy of the torque and high efficiency of the 6-phase PSM machine can be achieved from the example shown.

The following is a summary of the advantages of the described invention.

With the six-phase machine, the failure of the entire electric drive can occur with certain errors, such as a failure of a power supply or a short circuit of the windings to be avoided. For a redundant drive, the cost of a six-phase machine is much smaller than for two three-phase PSM machines, since only a single rotor with the expensive magnet and a single stator with a similar iron content as a single three-phase PSM machine must be used.

Further, in case of a possible failure of a power supply or a fault in one of the two three-phase windings, the machine can continue to be operated at least with half of the total power.

Due to the developed concept of the control, the six-phase machine can be better controlled than before. In addition, the interactions between the two three-phase windings of the six-phase machine in the controller and d, q setpoint generator can be optimally compensated.

In an application e.g. in the automotive industry, traction drives such as hybrid vehicles or electric vehicles, or actuators such as e.g. Used steering systems, more safety and more redundancy for the user.

In addition, both space and cost of the drive can be reduced because instead of two machines a single, e.g. 6-phase PSM machine is used. The improved control of the PSM machines avoids power fluctuations and superimpositions of the magnetic harmonics in the machine, which cause noise problems in some current and speed ranges.

The optimum calculation of the d, q current setpoints of the two windings as a function of the speed, the DC link voltage and the required torque enables the machine to be optimally utilized. The efficiency is increased and losses minimized, whereby the cooling effort of the machine can be reduced, which in turn saves effort and costs.

Furthermore, a maximum possible torque is achieved, so that the machine can be optimally designed (not oversized), which in turn saves costs and volume or space. By taking into account the mutual influences of the windings, a high accuracy of the torque is achieved at each operating point.

LIST OF REFERENCE NUMBERS

100

PSM machine

101

rotor

102

permanent magnet

200

Setpoint generation device

300

decoupling device

400

vector modulator

PI

Comparison device ( PI Regulators)

Claims (10)

Method for controlling an at least 6-phase PSM machine with associated six windings, which is operated by means of a field-oriented control, wherein - the calculation of the set current values of the q-axes (Isq1 Ref, Isq2Ref) depending on a limited torque setpoint (MRefLimit; M1Ref, M2Ref) divided between the windings of the PSM machine, - filtered nominal currents (Isd1 Ref, Isd2Ref), determined from reference currents of the d axes from the previous sampling step (Isd1 Ref (k-1), Isd2Ref (k-1)), and - Is set current values of the q-axes (Isq1 Ref (k-1), Isq2Ref (k-1)) from the previous sampling step, and wherein - the calculation of the nominal current values of the d-axes (Isd1 Ref, Isd2Ref) as a function of the maximum voltages of the two windings (Us1max, Us2max), the electrical angular velocity (ωs), the target current values of the q-axes (Isq1 Ref (k-1), Isq2Ref (k-1)) from the previous sampling step, and - the filtered nominal currents (Isd1 Ref, Isd2Ref) takes place. Method according to Claim 1 in which the setpoint torque (MRef) is determined and limited to a limited torque setpoint (MRefLimit), the limited torque setpoint (MRefLimit) is divided equally (M1Ref, M2Ref) over the at least two windings of the PSM machine. Method according to one of the preceding claims, wherein a filter time constant for filtering the current setpoint values of the d-axes from the preceding sampling step (Isd1 Ref (k-1), Isd2Ref (k-1)) is selected between 2 * TA us 6 * TA, wherein TA is the rule sampling time. Method according to one of the preceding claims, wherein depending on the difference between the calculated desired current values (Isq1 Ref, Isq2ref, Isd1Ref, Isd2Ref) and measured current values (Isq1, Isq2, Isd1, Isd2) of the q-axes and the d-axes adjusted d or q set point (Yd1, Yd2, Yq1, Yq2) is generated, which is passed to a decoupling network for generating output signals (Usd1, Usq1, Usd2, Usq2) for driving the PSM machine, wherein in the decoupling network compensation is made for the dependencies of the coordinate axes (d, q) for each of the windings of the PSM machine and each of the windings from each other. Method according to Claim 4 in which a transformation of the determined output signals (Usd1, Usq1, Usd2, Usq2) into coordinates (d, q) for driving the PSM machine via the electrical angle (Θ _el ) and the offset angle ()) of the at least two windings (uvw; xyz). Method according to one of the preceding claims, wherein the PSM machine is a 6-phase PSM machine and the desired current values of the q-axes (Isq1 Ref; Isq2Ref) for the first winding (uvw) and for the second winding ( xyz) of the PSM machine are calculated as follows: $${{\rm I}}_{sq\text{re}f1}=\frac{\left(\frac{M_{1\text{re}f}}{\left(3\text{/}2\right)\cdot zp}+L_{q12}\cdot {{\rm I}}_{sd1\text{re}fFilt}\cdot {{\rm I}}_{sq2\text{re}f\left(k-1\right)}\right)}{\left(\left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{sd1\text{re}fFilt}+L_{d12}\cdot {{\rm I}}_{sd2\text{re}fFilt}+{\mathrm{\Psi }}_{PM}\right)}$$

$${{\rm I}}_{sq\text{re}f2}=\frac{\left(\frac{M_{\text{2re}f}}{\left(3\text{/}2\right)\cdot zp}+L_{q21}\cdot {{\rm I}}_{sd2\text{re}fFilt}\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\right)}{\left(\left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{sd2\text{re}fFilt}+L_{d21}\cdot {{\rm I}}_{sd1\text{re}fFilt}+{\mathrm{\Psi }}_{PM}\right)}$$

With: Zp: number of pole pairs of the machine, ΨPM: flux of the permanent magnet of the PSM machine, Ld11: main inductance in d1 -axis, Lq11: main inductance in q1 -axis, Ld22: main inductance in d2-axis, Lq22: main inductance in q1-axis, Ld12: Inductance according to the influence d2-axis on d1-axis, Lq12: inductance corresponding to the influence q2-axis on q1-axis, Ld21: inductance corresponding to the influence d1-axis on d2-axis, Lq21: inductance corresponding to the influence q1-axis on q2-axis, M1Ref: setpoint torque for the first winding uvw of the PSM machine M2Ref: setpoint torque for the second winding xyz of the PSM machine Isd1 RefFilt: filtered setpoint current in d1 -axis for the first winding uvw of the PSM machine, Isd2RefFilt: filtered Target current in d2 axis for the second winding xyz of the PSM machine, Isq1 RefFilt: filtered nominal current in q1 -axis for the first winding uvw of the PSM machine, Isq2RefFilt: filtered nominal current in q2-axis for the second e winding xyz of PSM machine, Isq1Ref (k-1): Isq1Ref one sampling step before, Isq2Ref (k-1): Isq2Ref one sampling step before. Method according to one of the preceding claims, wherein the PSM machine is a 6-phase PSM machine and the desired current values of the d-axes (Isd1 Ref; Isd2Ref) for the first winding (uvw) and for the second winding (xyz) the PSM machine can be calculated as follows: $$\begin{array}{l}{{\rm I}}_{sd1\text{re}f}=(-R_s\cdot {\omega }_s\cdot \left(L_{d11}-L_{q11}\right)\cdot {{\rm I}}_{sq1\text{RE}f\left(k-1\right)}-L_{d11}\cdot {\omega }_s^2\cdot {\mathrm{\Psi }}_{PM}\\ -L_{d11}\cdot L_{d12}\cdot {\omega }_s^2\cdot {{\rm I}}_{sd2\text{re}fFilt}+R_s\cdot L_{q12}\cdot {\omega }_s\cdot {{\rm I}}_{sq2\text{re}f\left(k-1\right)}+\sqrt{Q1})\mathfrak{/}\left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\end{array}$$

With: $$\begin{array}{l}Q1=(-{{\rm I}}_{sq1\text{re}f\left(k-1\right)}^2\cdot L_{d11}^2\cdot L_{q11}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d11}\cdot L_{q11}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq1\text{re}f\left(k-1\right)}^2\cdot R_s^4+U_{s1max}^2\cdot \left(L_{d11}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot L_{d11}\cdot L_{q11}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd2\text{re}fFilt}^2\cdot L_{d12}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q11}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d11}\cdot L_{d12}\cdot L_{q12}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd2RefFilt}\cdot L_{d12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd2Ref\left(k-1\right)}\cdot L_{d11}^2\cdot L_{q11}\cdot L_{q12}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq2\text{re}f\left(k-1\right)}}^2\cdot L_{d11}^2\cdot L_{q12}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d11}\cdot L_{q12}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

$$\begin{array}{l}{{\rm I}}_{sd2\text{re}f}=(-R_s\cdot {\omega }_s\cdot \left(L_{d22}-L_{q22}\right)\cdot {{\rm I}}_{sq2\text{re}f\left(k-1\right)}-L_{d22}\cdot {\omega }_s^2\cdot {\mathrm{\Psi }}_{PM}\\ -L_{d22}\cdot L_{d21}\cdot {\omega }_s^2\cdot {{\rm I}}_{sd1\text{re}fFilt}+R_s\cdot {\omega }_s\cdot L_{q21}\cdot {{\rm I}}_{sq1\text{re}f\left(k-1\right)}+\sqrt{Q2})\end{array}$$

With: $$\begin{array}{l}Q2=(-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}^2\cdot L_{q22}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot L_{d22}\cdot L_{q22}\cdot R_s^2\cdot {\omega }_s^2-{{\rm I}}_{sq2Ref\left(k-1\right)}^2\cdot R_s^4+U_{s2max}^2\cdot \left(L_{d22}^2\cdot {\omega }_s^2+R_s^2\right)\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q22}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^3\cdot {\omega }_s-{\mathrm{\Psi }}_{PM}^2\cdot R_s^2\cdot {\omega }_s^2)\hfill \\ -{{\rm I}}_{sd1RefFilt}^2\cdot L_{d21}^2\cdot {\omega }_s^2\cdot R_s^2-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q22}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\omega }_s\cdot R_s^3\hfill \\ -2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d22}\cdot L_{d21}\cdot L_{q21}\cdot R_s\cdot {\omega }_s^3-2\cdot {{\rm I}}_{sd1RefFilt}\cdot L_{d21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sd1Ref\left(k-1\right)}\cdot L_{d22}^2\cdot L_{q22}\cdot L_{q21}\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq2Ref\left(k-1\right)}\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot R_s^2\cdot {\omega }_s^2\hfill \\ -{{\rm I}}_{{}_{sq1Ref\left(k-1\right)}}^2\cdot L_{d22}^2\cdot L_{q21}^2\cdot {\omega }_s^4-2\cdot {{\rm I}}_{sq1Ref\left(k-1\right)}\cdot L_{d22}\cdot L_{q21}\cdot {\mathrm{\Psi }}_{PM}\cdot R_s\cdot {\omega }_s^3\hfill \end{array}$$

With: Rs: stator resistance of the PSM machine, Zp: number of pole pairs of the PSM machine, ΨPM: flux of the permanent magnet of the PSM machine, Ld11: main inductance in d1-axis, Lq11: main inductance in q1-axis, Ld22: main inductance in d2-axis, Lq22: main inductance in q1-axis, Ld12: inductance according to influence d2-axis on d1-axis, Lq12: inductance according to influence q2-axis on q1-axis, Ld21: inductance according to influence d1-axis on d2-axis, Lq21: inductance corresponding to the influence q1-axis on q2-axis, ωs: (= wel) electric angular velocity of the PSM-machine, (= n * Zp * 2 * π / 60) n: speed of the PSM-machine, TA: used Control sampling step, M1Ref: setpoint torque for the first winding uvw of the PSM machine, M2Ref: setpoint torque for the second winding xyz of the PSM machine, Id1Ref (k), Iq1Ref (k): (or Id1Ref, Iq1Ref) the setpoint currents of first winding in d1 and q1 axis (current), Id1 Ref (k-1), Iq1 Ref (k-1): the target flow e of the first winding in the d1 and q1 axes (one sample before), Id2Ref (k), Iq2Ref (k): (resp. Id2Ref, Iq2Ref) the nominal currents of the first winding in the d2 and q2 axes (current), Id2Ref (k-1), Iq2Ref (k-1): the nominal currents of the first winding in the d2 and q2 axes (one sampling step previously ), Id1 RefFilt: filtered nominal current in d1-axis for the first winding uvw of the PSM machine, Isd2RefFilt: filtered nominal current in d2-axis for the second winding xyz of the PSM machine, Udc1: the DC link voltage of the inverter to supply the first winding uvw of the 6-phase PSM machine, Udc2: the DC link voltage of the inverter to supply the second winding xyz of the 6-phase PSM machine, Us1max: maximum adjustable input voltage for the first winding uvw of the PSM machine, Us2max: maximum adjustable input voltage for the second winding xyz of the PSM machine. Arrangement for controlling an at least 6-phase PSM machine (100) with associated six windings (u, v, w, x, y, z), which is operated by means of a field-oriented control and the at least d1q1 coordinates for a first machine part with a first three-phase winding (u, v, w) and the d2q2 coordinates for a second machine part having a second three-phase winding (x, y, z), comprising at least - At least one set value generating means (200), which is adapted to set current values of the q-axes (Isq1 Ref, Isq2Ref) and the d-axes (Isd1 Ref, Isd2Ref) as inputs according to the method of any one of the preceding To create claims; a comparison means (PI) for providing PI output signals (Yd1, Yd2, Yq1, Yq2) from at least one difference between the input quantities (Isq1Ref, Isq2Ref, Isd1Ref, Isd2Ref) generated by the setpoint generating means (200) and corresponding ones measured (Isd1, Isq1, Isd2, Isq2) actual values; a decoupling device (300) which is set up to output the output signals (Yd1; Yd2; Yq1; Yq2) of the comparison device (PI) into d and q output variables (Usq1k; Usd1k; Usq2k; Usd2k) for driving the PSM machine (100), compensating the mutual dependencies between the d and q axes. Arrangement according to Claim 8 wherein the at least one target value generating means (200) comprises at least a first target current generating means (IsqRef) for generating the target current values of the q-axes (Isq1 Ref; Isq2Ref) for at least the first winding (u, v, w) and the second winding (x, y, z) of the PSM machine (100), wherein as inputs at least - a limited torque setpoint (MRefLimit), the equal parts (MRef1, MRef2) on the windings of the PSM machine (100 ), - by means of at least one filter device (Filter1, Filter2), filtered target current values of the d axes from a preceding sampling step (Isd1 RefFilt (k-1); Isd2RefFilt (k-1)) and target current values of the q axes from a preceding one Sampling step (Isq1 Ref (k-1); Isq2Ref (k-1)) for calculation. Arrangement according to Claim 9 wherein the at least one target value generating means (200) further comprises at least one second target current generating means (IsdRef) for generating the target current values of the d axes (Isd1 Ref; Isd2Ref) for at least the first winding (uvw) and the second Winding (xyz) of the PSM machine (100), wherein as input variables at least - the electrical angular velocity (ωs) of the PSM machine (100), - one for the first and for the second winding (u, v, w; x, y, z) adjustable maximum voltage (Us1max; Us2max); - Target current values of the d axes filtered by means of at least one filter device (Filter1, Filter2) from a preceding sampling step (Isd1 RefFilt (k-1); Isd2RefFilt (k-1)), and - Target current values of the q axes a previous sampling step (Isq1 Ref (k-1); Isq2Ref (k-1)) for the calculation.

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