METHOD, COMPUTER PROGRAM, AND CONTROLLER FOR CONTROLLING AN ELECTRICAL CONVERTER, ELECTRICAL CONVERTER, AND COMPUTER-READABLE MEDIUM

Abstract

A method for controlling an electrical converter for driving an electrical machine comprises the steps of: estimating a stator flux vector depending on at least one measurement in the electrical converter; receiving a rotor speed of the electrical machine; determining an optimized pulse pattern for the electrical converter depending on the rotor speed; determining a rotor angle of a rotor flux vector depending on the rotor speed; determining a reference stator angle of the stator flux vector depending on the rotor angle; determining a reference stator flux vector depending on the optimized pulse pattern and the reference stator angle; determining a difference between the reference stator flux vector and the estimated stator flux vector; modifying switching instants of the optimized pulse pattern, such that the difference is minimized; and applying at least a part of the modified optimized pulse pattern to the electrical converter.

Claims

1. A method for controlling an electrical converter for driving an electrical machine, the method comprising: estimating a stator flux vector based on on at least one measurement in the electrical converter; receiving a rotor speed of the electrical machine; determining an optimized pulse pattern for the electrical converter based on the rotor speed; determining a rotor angle of a rotor flux vector based on on the rotor speed; determining a reference stator angle of the stator flux vector based on the rotor angle; determining a reference stator flux vector based on the optimized pulse pattern and the reference stator angle; determining a difference between the reference stator flux vector and the estimated stator flux vector; modifying switching instants of the optimized pulse pattern, such that the difference is minimized; and applying at least a part of the modified optimized pulse pattern to the electrical converter.

2. The method of claim 1, wherein: the reference stator angle is determined based on an angle difference between the rotor angle and a stator angle of the stator flux vector.

3. The method of claim 2, further comprising: estimating an electromagnetic torque based on the at least one measurement in the electrical converter; and determining a reference electromagnetic torque based on the rotor speed, wherein the angle difference is determined based on the estimated electromagnetic torque and the determined reference electromagnetic torque.

4. The method of claim 3, wherein: the angle difference is estimated from a torque error, wherein the torque error comprises a difference between the determined reference electromagnetic torque and the estimated electromagnetic torque.

5. The method of claim 4, wherein: the angle difference is determined with a proportional-integral controller from the torque error.

6. The method of claim 1, wherein: the rotor speed is measured with an encoder or estimated based on the integral of the stator voltage and/or the stator current.

7. The method of claim 1, wherein: the rotor angle is determined by integrating the angular rotor speed.

8. The method of claim 1, wherein: the optimized pulse pattern is determined based on a modulation index and/or a maximum allowed switching frequency, the modulation index is determined based on a reference stator flux magnitude.

9. The method of claim 1, wherein: the reference electromagnetic torque is determined from a rotor speed error, wherein the rotor speed error comprises the difference between a reference angular rotor speed and the angular rotor speed.

10. The method of claim 1, wherein: the at least one measurement in the electrical converter comprises measuring a stator voltage and/or a stator current of the electrical converter; and the stator flux vector is estimated based on the stator voltage and/or a stator current; and/or the electromagnetic torque is estimated based on the stator voltage and/or a stator current.

11. The method of claim 8, wherein: the optimized pulse pattern comprises a sequence of switching transitions at switching instants between different switching states of the converter, the optimized pulse pattern is loaded from a table of optimized pulse patterns stored in a controller performing the method, the table of optimized pulse patterns is indexed with respect to the modulation index, and for each optimized pulse pattern in the table, switching transitions at switching instants are stored.

12. A computer program, which when being executed by a processor, the processor is configured to execute the steps of the method of claim 1.

13. A non-transitory computer-readable medium in which a computer program according to claim 10 is stored.

14. A controller for controlling an electrical converter configured to implement the steps of the method of claim 1.

15. An electrical converter, comprising: a plurality of semiconductor switches; and the controller according to claim 14 configured to control the semiconductor switches of the electrical converter.

16. An electrical machine, comprising: an electrical converter configured to drive the electrical machine; and a controller configured to: estimate a stator flux vector based on at least one measurement in the electrical converter; receive a rotor speed of the electrical machine; determine an optimized pulse pattern for the electrical converter based on the rotor speed; determine a rotor angle of a rotor flux vector based on the rotor speed; determine a reference stator angle of the stator flux vector based on the rotor angle; determine a reference stator flux vector based on the optimized pulse pattern and the reference stator angle; determine a difference between the reference stator flux vector and the estimated stator flux vector; modify switching instants of the optimized pulse pattern, such that the difference is minimized; and apply at least a part of the modified optimized pulse pattern to the electrical converter.

17. The electrical machine of claim 16, wherein: the controller is further configured to determine the reference stator angle based on an angle difference between the rotor angle and a stator angle of the stator flux vector.

18. The electrical machine of claim 17, wherein the controller is further configured to: estimate an electromagnetic torque based on the at least one measurement in the electrical converter; and determine a reference electromagnetic torque based on the rotor speed, wherein the angle difference is determined based on the estimated electromagnetic torque and the determined reference electromagnetic torque.

19. The electrical machine of claim 18, wherein: the controller is further configured to estimate the angle difference based on a torque error, wherein the torque error comprises a difference between the determined reference electromagnetic torque and the estimated electromagnetic torque.

20. The electrical machine of claim 19, wherein: the controller is further configured to determine the angle difference based on the torque error utilizing a proportional-integral controller.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The subject-matter of the present disclosure will be explained in more detail in the following text, with reference to exemplary embodiments which are illustrated in the attached drawings.

[0038] FIG. 1 shows a circuit representation of an induction machine model in a rotating dq-reference frame for a d-axis.

[0039] FIG. 2 shows a circuit representation of an induction machine model in the rotating dq-reference frame of FIG. 1 for a q-axis.

[0040] FIG. 3 illustrates a definition of the rotating dq-reference frame of FIGS. 1 and 2.

[0041] FIG. 4 shows a circuit representation of a permanent-magnet synchronous machine in the rotating dq-reference frame of FIG. 3 for a d-axis.

[0042] FIG. 5 shows a circuit representation of a permanent-magnet synchronous machine in the rotating dq-reference frame of FIG. 3 for a q-axis.

[0043] FIG. 6 shows an example of a switching pattern modification by MP.sup.3C.

[0044] FIG. 7 schematically shows an electrical system with a converter according to an embodiment of the disclosure.

[0045] FIG. 8 schematically shows a torque controller module according to an embodiment of the disclosure.

[0046] FIG. 9 shows a flow diagram of an exemplary embodiment of a method for controlling an electrical converter for driving an electrical machine.

[0047] The reference symbols used in the drawings and their meanings are listed in the summary form in the list of reference symbols. In principle, identical parts are provided with the same reference symbols in the figures.

DETAILED DESCRIPTION

[0048] FIG. 1 shows a circuit representation of an induction machine model in a rotating dq-reference frame for a d-axis.

[0049] FIG. 2 shows a circuit representation of an induction machine model in the rotating dq-reference frame of FIG. 1 for a q-axis.

[0050] FIG. 3 illustrates a definition of the rotating dq-reference frame of FIGS. 1 and 2.

[0051] The dq-reference frame rotates with the angular stator frequency .sub.s, with its d-axis position denoted by .sub.s. An electrical angular rotor speed is .sub.rp.sub.m, where p is a number of pole pairs of an electrical machine 18 (see FIG. 7) and .sub.m is a mechanical angular speed of the rotor and shaft of the electrical machine 18. By principle of operation, .sub.r.sub.s due to a slip of the electrical machine 18. A stator voltage vs is given by .sub.s=[.sub.sd, .sub.sq].sup.T, a stator (rotor) current i.sub.s (i.sub.r) is given by i.sub.s=[i.sub.sd, i.sub.sq].sup.T (i.sub.r=[i.sub.rd, i.sub.rq].sup.T), and a stator (rotor) flux vector .sub.s (.sub.r) is given by .sub.s=[.sub.sd, .sub.sq].sup.T (.sub.r=[.sub.rd, .sub.rq].sup.T). The stator (rotor) flux vector .sub.s (.sub.r) may be referred to as stator (rotor) flux linkage vector. A stator (rotor) winding resistance R.sub.s(R.sub.r) is denoted by R.sub.s=diag(r.sub.s,r.sub.s) (R.sub.r=diag(r.sub.r,r.sub.r)), a magnetizing reactance X.sub.m is denoted by X.sub.m=diag(x.sub.m,x.sub.m) and a stator (rotor) leakage reactance X.sub.is(X.sub.ir) is denoted by X.sub.is=diag(x.sub.is,x.sub.is) (X.sub.lr=diag(x.sub.lr,x.sub.lr)). All quantities, including time t, are normalized in a per unit (p.u.) system.

[0052] Using Kirchoff's voltage law, the stator (rotor) voltage .sub.s(.sub.r) is given by

[00001]$\begin{array}{cc}\begin{array}{c}{v}_s=R_s{i}_s+\frac{d{}_s}{\mathrm{dt}}+{}_s\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]{}_s,\\ v_s=R_r{i}_r+\frac{d{}_r}{\mathrm{dt}}+\left({}_s-{}_r\right)\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],\end{array}& \left(1\right)\end{array}$

[0053] Here, the inverter voltage applied to the stator is given by

[00002]$\begin{array}{cc}{v}_a=\left[\begin{array}{c}{v}_{\mathrm{sd}}\\ v_{\mathrm{sq}}\end{array}\right]=P\left({}_s\right)v_{\mathrm{abc}}& \left(1\right)\end{array}$$\mathrm{and}$$\begin{array}{cc}P\left({}_s\right)=\left[\begin{array}{ccc}\cos \left({}_s\right)& \cos \left({}_s-\frac{2m}{3}\right)& \cos \left({}_s+\frac{2}{3}\right)\\ -\sin \left({}_s\right)& -\sin \left({}_s-\frac{2}{3}\right)& -\sin \left({}_s+\frac{2}{3}\right)\end{array}\right]& \left(3\right)\end{array}$ [0054] is the matrix used to transform quantities from an abc-reference frame into the dq-reference frame. The stator and rotor flux vectors .sub.s, .sub.r are given by

[00003]$\begin{array}{cc}\begin{array}{c}{}_s=X_s{i}_s+X_m{i}_r\\ {}_r=X_r{i}_r+X_m{i}_a\end{array}& \left(4\right)\end{array}$ [0055] where X.sub.s=X.sub.ls+X.sub.m and X.sub.r=X.sub.lr+X.sub.m are the stator and, respectively, rotor linkage reactances X.sub.s, X.sub.r. An electromagnetic torque T.sub.e of the electrical machine 18 is given by

[00004]$\begin{array}{cc}{T}_e=\frac{1}{\mathrm{pf}}{}_s{i}_s& \left(5\right)\end{array}$ [0056] where pf is a power factor. Using formula (4), formula (5) may be written as

[00005]$\begin{array}{cc}\begin{array}{c}{T}_e=\frac{1}{\mathrm{pf}}\frac{\mathrm{xm}}{x_s{x}_r-x_m^2}{}_r{}_s\\ =\frac{1}{\mathrm{pf}}\frac{x_m}{x_s{x}_r-x_m^2}.Math.{}_s.Math..Math.{}_r.Math.\sin \left(\right)\end{array}& \left(6\right)\end{array}$ [0057] where is an angle between stator and rotor flux linkage vectors .sub.s, .sub.r.

[0058] FIG. 4 shows a circuit representation of a permanent-magnet synchronous machine in the rotating dq-reference frame of FIG. 3 for a d-axis.

[0059] FIG. 5 shows a circuit representation of a permanent-magnet synchronous machine (PMSM) in the rotating dq-reference frame of FIG. 3 for a q-axis.

[0060] The dq-reference frame rotates with the angular stator speed .sub.s. By principle of operation, .sub.s=.sub.r. It may be assumed that the d-axis is aligned with the orientation of the permanent magnet mounted on the rotor of the PMSM. Hence, the rotor flux vector .sub.r is given by

[00006]$\begin{array}{cc}{}_r=\left[\begin{array}{c}{}_{\mathrm{rd}}\\ {}_{\mathrm{rq}}\end{array}\right]=\left[\begin{array}{c}{x}_{\mathrm{md}}{i}_m\\ 0\end{array}\right]=\left[\begin{array}{c}{}_{\mathrm{PM}}\\ 0\end{array}\right]& \left(7\right)\end{array}$ [0061] where i.sub.m is a hypothetical constant magnetization current flowing through the magnetizing inductance x.sub.md. A constant magnetic flux linkage is denoted by .sub.PM and is generated by a permanent magnet of the electrical machine 18. The stator flux vector .sub.s is given by

[00007]$\begin{array}{cc}{}_s=X_s{i}_s+{}_r.& \left(8\right)\end{array}$

[0062] Applying Kirchoff's voltage law, the dynamics of the stator voltage .sub.s are given by

[00008]$\begin{array}{cc}{v}_s=R_s{i}_s+\frac{d{}_s}{\mathrm{dt}}+{}_s\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]{}_s.& \left(9\right)\end{array}$

[0063] The electromagnetic torque T.sub.e is given by

[00009]$\begin{array}{cc}\begin{array}{c}{T}_e=\frac{1}{\mathrm{pf}}{}_s{i}_s\\ =\frac{1}{\mathrm{pf}}{}_s{X}_s^{-1}\left({}_s-{}_r\right)\\ =\frac{1}{\mathrm{pf}}\frac{1}{x_{\mathrm{sd}}}\left(\frac{x_{\mathrm{sd}}-x_{\mathrm{sq}}}{x_{\mathrm{sq}}}{}_{\mathrm{sd}}+{}_{\mathrm{rd}}\right){}_{\mathrm{sq}}\end{array}& \left(10\right)\end{array}$

[0064] Note that due to the saliency of the electrical machine 18, the electromagnetic torque T.sub.e is also a function of the d-component of the stator flux. Recalling that the d-axis of the rotating dq-reference frame is aligned with the rotor flux vector .sub.r, the stator flux vector .sub.s may be expressed by .sub.s=[.sub.s cos(), .sub.s sin()].sup.T.

[0065] Then, formula (10) may be written as

[00010]$\begin{array}{cc}{T}_e=\frac{1}{\mathrm{pf}}\frac{1}{x_{\mathrm{sd}}}\left(\frac{1}{2}\frac{x_{\mathrm{sd}}-x_{\mathrm{sq}}}{x_{\mathrm{sq}}}{.Math.{}_s.Math.}^2\sin \left(2\right)+{}_{\mathrm{PM}}.Math.{}_s.Math.\sin \left(\right)\right)& \left(11\right)\end{array}$ [0066] where is the angle between stator and rotor flux vectors .sub.s, .sub.r.

[0067] Optimized pulse patterns (OPPs) relate to a specific pulse width modulation (PWM) method which enables minimization of the harmonic current distortions for a given switching frequency and are well known in the art. Compared with carrier-based PWM, the use of OPPs results in a lower switching frequency of semiconductor devices of an electrical converter for a given current total harmonic distortion (THD), in a lower current THD for a given switching frequency which implies lower machine losses of the electrical machine, and in lower machine inductances or smaller LC filters during the system design phase as an effect of the ability of OPPs to shape the current harmonic spectrum.

[0068] Hence, it can be inferred that the use of OPPs lifts the artificial and unnecessary constraint of a fixed modulation interval imposed in carrier-based PWM when optimizing the system during design and operation.

[0069] To enable the use of OPPs in electrical drive systems, the concept of model predictive pulse pattern control (MP.sup.3C) has been described in EP 2 469 692 A1. MP.sup.3C controls the position of the stator flux vector .sub.s of the electrical machine 18 along an optimal flux trajectory, which is the integral of the OPP voltage waveform overtime. It achieves this by manipulating in real time the switching instants of the offline computed OPP, as described in EP 2 891 241 B1.

[0070] A control objective of a drive system may be to achieve a regulation of the electrical angular rotor speed .sub.r to the desired reference value *.sub.r. This may be achieved by appropriately adjusting the angle between stator and rotor flux vector .sub.s, .sub.r which may be computed by solving a nonlinear trigonometric equation (c.f., (6) and (11)) that depends on the type of the electrical machine 18, machine parameters, and/or the rotor flux vector .sub.r, e.g. on its orientation and/or magnitude. The electrical machine 18 may for example be an induction machine or permanent magnet machine. The machine parameters may for example be magnetizing and leakage inductances. However, acquiring knowledge of these quantities is a hard task in several applications, while robustness of the system is hindered by a false estimation of them.

[0071] FIG. 6 shows an example of a switching pattern modification by a MP.sup.3C as described in the above-mentioned prior art. An inner feedback loop of MP.sup.3C is responsible for driving the stator flux vector .sub.s towards the reference stator flux vector *.sub.s. This task may be achieved by a pattern controller module 36 (see FIG. 7), which may modify switching instants of the OPP to compensate for the difference between the stator flux vector .sub.s and the reference stator flux vector *.sub.s. A resulting pulse pattern may be encoded in a switching signal u.sub.abc (see FIG. 7) and may be used for driving the semiconductor switches of the electrical converter 12 (see FIG. 7). To illustrate this control principle, a two-level converter with stator flux vector .sub.s in phase a may be given by

[00011]$\begin{array}{cc}{}_{\mathrm{sa}}\left(t\right)={}_{\mathrm{sa}}\left(0\right)+\underset{0}{\stackrel{t}{}}{v}_a\left(r\right)\mathrm{dr},& \left(12\right)\end{array}$ [0072] where .sub.a(t) {V.sub.dc/2, V.sub.dc/2}, with V.sub.dc denoting the voltage of a dc-link 16 (see FIG. 7). Here, it is implicitly assumed that the stator resistance is negligible. It is noted that formula (12) may be used by an observer module 22 to compute the actual stator flux vector .sub.s. Let .sub.a(0) {V.sub.dc/2, V.sub.dc/2} be the voltage output at t.sub.a=0 and assume that a switching transition .sub.a={.sub.dc, V.sub.dc} may occur at time t.sub.a(0, t). So, the reference stator flux vector *.sub.s may be given by

[00012]$\begin{array}{cc}\begin{array}{c}{}_{\mathrm{sa}}^{*}\left(t\right)={}_{\mathrm{sa}}\left(0\right)+\underset{0}{\stackrel{t_a}{}}{v}_a\left(0\right)\mathrm{dr}+\underset{t_a}{\stackrel{t}{}}\left(v_a\left(0\right)+r_a\right)\mathrm{dr}\\ ={}_{\mathrm{sa}}\left(0\right)+v_a\left(0\right)t_a+\left(v_a\left(0\right)+v_a\right)\left(t-t_a\right).\end{array}& \left(13\right)\end{array}$

[0073] If this switching instant is delayed or forwarded by a time interval Ata, i.e. the switching instant occurs at time t.sub.a+t.sub.a, this results in

[00013]$\begin{array}{cc}\begin{array}{c}{}_{\mathrm{sa}}\left(t\right)={}_{\mathrm{sa}}\left(0\right)+\underset{0}{\stackrel{t_a+t_a}{}}{v}_a\left(0\right)\mathrm{dr}+\underset{t_a+t_s}{\stackrel{t}{}}\left(v_a\left(0\right)+v_a\right)\mathrm{dr}\\ ={}_{\mathrm{sa}}\left(0\right)+v_a\left(0\right)\left(t_a+v_a\right)+\left(v_a\left(0\right)+v_a\right)(\left(t-t_a-t_a\right)\\ ={}_{\mathrm{sa}}^{*}\left(t\right)+v_a{t}_a.\end{array}& \left(14\right)\end{array}$

[0074] This implies that

[00014]$\begin{array}{cc}{}_{\mathrm{sa}}\left(t\right)=v_a{t}_a.& \left(15\right)\end{array}$

[0075] Hence, based on the difference between the measured stator flux vector .sub.s and the reference stator flux vector *.sub.s the pattern controller 36 may decide whether there is a need to delay or advance the OPP switching instants. Although this section illustrates the basic principle of operation of the pattern controller, the actual implementation may be more complicated, including functionalities such as pulse insertion which may allow for fast control of the stator flux during transients and to achieve disturbance rejection.

[0076] FIG. 7 shows an electrical system 10 comprising an electrical converter 12, a DC link, an electrical machine 18, and a controller 20. The electrical converter 12 comprises several semiconductor switches (not shown) and interconnects the DC link 16 with the electrical machine 18. The electrical converter 12 may be controlled by the controller 20. The electrical converter 12 may be an inverter. It may be a voltage source or a current source converter 12. In particular, the converter 12 may be a high-power converter adapted for converting current with more than 100 A and/or 1000 V. The electrical machine 18 may be an electric motor or a generator, or may be operated as an electric motor in a first operation mode and as a generator in a second operation mode.

[0077] As explained in the following, the controller 20 embodies a Model-Free Vector Pulse Pattern Control (MF-VPPC) scheme based on OPPs that operates without the use of any information regarding the machine type, machine parameters or rotor flux vector of the electrical machine 18. The MF-VPPC scheme provides a regulation of the electrical angular rotor speed .sub.r to its reference value *.sub.r. Unlike its MP.sup.3C counterpart, MF-VPPC achieves this task without relying on any information regarding the machine type and its parameters. The control diagram of the proposed MF-VPPC scheme is described below and depicted in FIG. 8.

[0078] The controller 20 comprises an observer module 22 that may receive an output current i.sub.s and/or an output voltage .sub.s of the electrical converter 12. The output current i.sub.s and/or an output voltage .sub.s may be inputs to the electrical motor 18 and/or may be measured at corresponding outputs of the electrical converter 12. The observer module 22 may also receive a DC-link voltage of the DC-link 16 and/or a switching signal u.sub.abc, in which three-phase switch positions are encoded, to reconstruct the output voltage .sub.s applied to input terminals of the electrical machine 18, instead of receiving the measured output voltage .sub.s.

[0079] A rotor speed .sub.r of the electrical machine 18 may be measured by an encoder 23. Alternatively, the rotor speed may be estimated, e.g. by the integral of the stator voltage and/or the stator current.

[0080] The rotor speed .sub.r may also be used by the observer module 22. Based on these quantities, the observer module 22 may estimate a stator flux vector .sub.s and an electromagnetic torque T.sub.e of the electrical machine 18.

[0081] A speed controller module 24 of the controller 20 may receive a difference between a reference speed or *.sub.r and the rotor speed co, and it may determine a reference electromagnetic torque T*.sub.e therefrom, which may be an input to a torque controller module 26 of the controller. A task of the speed controller module 24 may be to regulate the rotor speed .sub.r to its reference speed *.sub.r by modifying the reference electromagnetic torque T*.sub.e. The speed controller module 24 may comprise or may be a proportional-integral (PI) controller.

[0082] The torque controller module 26 may determine a reference stator angle *.sub.s depending on the reference electromagnetic torque T*.sub.e and the electromagnetic torque T.sub.e as explained with respect to FIG. 8.

[0083] A flux reference module 28 may determine a reference stator flux vector *.sub.s, which lies on an optimal flux trajectory, and may have a desired angle and a desired magnitude. In particular, the optimal flux trajectory may be obtained by integrating a pre-calculated optimized pulse pattern OPP that is selected by a pattern loader module 32 of the controller 20 based on a modulation index m provided by a modulation index module 30 of the controller 20 and a maximum allowed switching frequency {circumflex over (f)}.sub.sw of the electrical converter 12. The maximum allowed switching frequency {circumflex over (f)}.sub.sw of the electrical converter 12 may be determined in advance and may be stored on a memory (not shown) of the controller 20.

[0084] The modulation index module 30 may provide at its output the desired modulation index m. The modulation index module 30 may determine the modulation index m depending on the rotor speed .sub.r. In case of the electrical machine 18 being an induction machine for which .sub.r.sub.s, there will be a difference, which may be referred to as steady state error, between the estimated stator flux vector .sub.s and the reference stator flux vector *.sub.s. To compensate for this steady state error, the modulation index module 30 may be augmented with an integral term as well.

[0085] The pattern controller module 36 may be a conventional pattern controller module 36, e.g. as described in the above-mentioned prior art. The pattern controller module 36 may provide one, two or more functionalities as described above with respect to FIG. 6. The pattern controller module 36 may generate the vector of switch positions encoded in the switching signal u.sub.abc that may be applied to the converter 12.

[0086] FIG. 8 schematically shows the above torque controller module 26 according to an embodiment of the disclosure. The torque controller module 26 enables the model-free pulse pattern control scheme based on OPPs to operate without the use of any information regarding the machine type, machine parameters or rotor flux vector of the electrical machine 18. The torque controller module 26 comprises an integration module 38 and a controller 40, which may be a proportional-integral (PI) controller.

[0087] The estimated electromagnetic torque T.sub.e may be compared to its reference value T*.sub.e, and the error may be passed to a proportional-integral controller which may generate an angle difference . In particular, the torque controller module 26 may calculate a difference between the determined reference electromagnetic torque T*.sub.e and the estimated electromagnetic torque T.sub.e. The difference may be referred to as torque error. The PI controller 40 may determine the angle difference depending on the torque error. The angle difference may correspond to an angle between the reference stator flux vector *.sub.s and a rotor flux vector.

[0088] A rotor angle .sub.r of the rotor flux vector may be determined by integrating the rotor speed .sub.r, e.g. by the integrator 38. A reference stator angle *.sub.s of the reference stator flux vector *.sub.s may be obtained by adding the angle difference to the rotor angle .sub.r of the rotor flux vector.

[0089] FIG. 9 shows a flow diagram of an exemplary embodiment of a method for controlling the electrical converter 12 for driving the electrical machine 18. The method may be carried out by the controller 20.

[0090] In the following, normalized quantities are used and it is focused on a three-phase inverter 12 connected to an electrical machine 18. However, it has to be understood that the following embodiments also may be applied to an inverter connected to a general p-phase load or to a grid-connected converter connected to a power grid, in which the converter may be grid forming by setting the amplitude and frequency of the grid voltage. Additional passive elements, such as filters, transformers and/or cables may be added.

[0091] In a step S2, the stator flux vector .sub.s may be estimated depending on at least one measurement in the electrical converter 12, e.g. by the observer 22. The at least one measurement in the electrical converter 12 may comprise measuring the stator voltage .sub.s and/or the stator current is of the electrical converter 12. Then, the stator flux vector .sub.s may be estimated depending on the stator voltage .sub.s and/or the stator current is, e.g. by the above formulas (1) or (9).

[0092] In a step S3, the rotor speed .sub.r of the electrical machine 18 may be received. For example, the rotor speed .sub.r may be measured by the encoder 23 and transferred to the controller 20.

[0093] In a step S4, the optimized pulse pattern OPP for the electrical converter 12 may be determined depending on the rotor speed .sub.r, e.g. as described in EP 2 469 692 A1. For example, the optimized pulse pattern OPP may be determined depending on the modulation index m and/or the maximum allowed switching frequency {circumflex over (f)}.sub.sw, e.g. by the pattern loader module 32, wherein the modulation index m may be determined depending on a reference stator flux magnitude *.sub.s. The optimized pulse pattern OPP may comprise a sequence of switching transitions 42 at switching instants between different switching states of the converter 12. The determined optimized pulse pattern OPP may be loaded from a table of optimized pulse patterns. The table of optimized pulse patterns may be stored in a memory of the controller 20. The table of optimized pulse patterns may be indexed with respect to the modulation index m, and optionally with respect to the maximum allowed switching frequency {circumflex over (f)}.sub.sw. For each optimized pulse pattern OPP in the table, switching transitions at switching instants may be stored.

[0094] In a step S6, the rotor angle .sub.r of the rotor flux vector may be determined depending on the rotor speed .sub.r, e.g. by the integrator 38.

[0095] In a step S8 the reference stator angle *.sub.s of the stator flux vector .sub.s may be determined depending on the rotor angle .sub.r, e.g. by the torque controller module 26. For example, the reference stator angle *.sub.s may be determined depending on the angle difference between the rotor angle .sub.r and a stator angle .sub.s of the stator flux vector .sub.s. The angle difference may be determined depending on the estimated electromagnetic torque T.sub.e and the determined reference electromagnetic torque T*.sub.e, e.g. by the PI controller 40. The angle difference may be determined from the difference between the determined reference electromagnetic torque T*.sub.e and the estimated electromagnetic torque T.sub.e. The difference between the determined reference electromagnetic torque T*.sub.e and the estimated electromagnetic torque T.sub.e may be referred to as torque error. The angle difference may be determined with the PI controller 40 from the torque error. The electromagnetic torque T.sub.e may be estimated depending on the at least one measurement in the electrical converter 12, e.g. depending on the stator current is and/or the stator voltage .sub.s, e.g. by the observer 22, e.g. by the formulas (5) or (10). The reference electromagnetic torque T*.sub.e may be determined depending on the rotor speed .sub.r, e.g. by the speed controller module 24. For example, the reference electromagnetic torque T*.sub.e may be determined from a difference between the reference angular rotor speed or *.sub.r and the angular rotor speed .sub.r. The difference between the reference angular rotor speed *.sub.r and the angular rotor speed .sub.r may be referred to as rotor speed error.

[0096] In a step S10, the reference flux vector *.sub.p may be determined depending on the optimized pulse pattern OPP and the reference stator angle *.sub.s, e.g. by the flux reference module 28.

[0097] In a step S12, the difference between the reference stator flux vector *.sub.s and the estimated stator flux vector .sub.s, i.e. the stator flux error, may be determined, e.g. by the controller 20.

[0098] In a step S14, the switching instants of the optimized pulse pattern OPP may be modified, e.g. by the pattern controller module 36, e.g. such that the stator flux error is minimized, e.g. as explained above and/or described in EP 2 891 241 B1.

[0099] In a step S16, at least a part of the modified optimized pulse pattern OPP, e.g. by the switching signal u.sub.abc, may be applied to the electrical converter 12, e.g. by the pattern controller module 36.

[0100] The functional modules may be implemented as programmed software modules or procedures, respectively; however, someone skilled in the art will understand that the functional modules may be implemented fully or partially in hardware.

[0101] While the disclosure has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the disclosure is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed disclosure, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality. A single processor or controller or other unit may fulfil the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.