Method of controlling a multi-channel multi-phase electrical machine

The invention describes a method of controlling a multi channel multi-phase electrical machine; a control arrangement of a multi-channel multi-phase electrical machine; and a wind turbine comprising a multi-channel multi-phase generator.

A multi-phase electrical machine such as a generator or motor seldom operates ideally, and there is generally some degree of ripple in one or more of output variables. For example, a multiphase generator may exhibit torque ripple as well as ripples on its output voltage and output power. The magnetic flux distribution in the airgap is determined to a large extent by the generator design. Harmonics in the magnetic flux result in ripple in the electromagnetic torque, machine electrical power and terminal voltages, i.e. the three-phase voltages of each channel of the electrical machine.

The different kinds of ripple are problematic for various reasons. Torque ripple causes vibration of the electrical machine, and must be reduced in order to avoid material fatigue. The vibrations caused by torque ripple result in acoustic noise. Particularly in the case of wind turbines, measures must be taken to reduce torque ripple in order to comply with acoustic regulations, which are often very strict. Various control methods that are known from the prior art, for example as described in EP3223422A1 and EP2043255A2, are limited to reducing acoustic noise arising from torque ripple .

Voltage ripple results primarily from harmonics in the machine EMF and the phase currents. In the presence of voltage ripple, the voltage usage for control of such an electrical machine may have to be reduced when fed from a voltage source converter. This is because, for a typical three-phase voltage source converter, the DC link voltage places a limit on the maximum value of the terminal voltage. This effectively defines a saturation level for the

modulation depth. However, a high modulation depth is necessary to operate such a machine efficiently. Generally, to allow for current control dynamics, a margin is reserved between design value and maximum value. If there is ripple on the control voltage, the level of the average voltage must be lowered to remain below the saturation level. This amounts to a lowering of the modulation depth. In the prior art, this problem has been addressed by applying a technique of harmonic current injection to reduce torque ripple. This known approach of harmonic current injection is normally done by current injection in the q-axis. It is also possible to minimize voltage ripple and torque ripple by harmonic current injection in the d-axis.

However, ripple in the machine electrical power (or simply "power ripple") is not reduced by harmonic current injection in the d and q axes, and may even be increased instead. Power ripple will be passed on to the DC link and will generate heat in the capacitors of the DC link, thereby shortening their useful lifetime. The capacitors require cooling, which is difficult to achieve and which adds to the overall cost. A DC link may also comprise batteries, and any power ripple will also generate heat in the batteries, reducing their useful lifetime.

Power ripple should also be prevented from passing to the grid, since harmonics may violate grid regulations and may cause control instability in the grid converter. This is particularly relevant for large generators such as wind turbines that generate power in the megawatt range, since power ripple may reach an amplitude of 100 kW.

It is therefore an object of the invention to provide an improved way of controlling an electrical machine to reduce ripple while overcoming the problems outlined above. This object is achieved by the method of claim 1 of

controlling a multi-channel multi-phase electrical machine; by the control arrangement of claim 9; by the wind turbine of claim 14; and by the computer program product of claim 15.

The inventive method is provided for controlling a multi channel multi-phase electrical machine comprising a plurality of channels each with a set of phase windings connected to a converter. It will be assumed in the following that the electrical machine is designed to electromagnetically phase- shift the channels. According to the invention, the method comprises the steps of operating the converters to

electrically phase-shift the channels accordingly and then, for each channel, computing harmonic injection currents for a specific harmonic on the basis of electrical quantities in a rotating reference frame. The injection currents may also be referred to as injection current references or injection current demands in the following. The injection currents are computed on the basis of a target ripple value for the dominant harmonic, which target ripple value comprises a target power ripple component and a target voltage ripple component. Harmonic voltage references (or "harmonic voltage demands") for a specific harmonic are then calculated on the basis of the harmonic injection currents, and the AC output voltages of the channel are subsequently calculated on the basis of the harmonic voltage references and fundamental voltage references.

To simplify control of a multi-channel multi-phase machine, it is usual to perform a suitable transformation so that an AC variable which alters its value as a function of the rotating magnetic field can be treated as if it were a DC variable. This greatly simplifies calculations. For example, as will be known to the skilled person, a dqO transformation or Park transformation can be performed on the AC voltage and current values to obtain voltage and current vectors in a rotating dqO reference frame (also referred to as a dq reference frame) . In the context of the invention, the term "injection current" is to be understood as a current vector comprising a d-axis component and a q-axis component in the rotating reference frame.

In the context of the invention, the specific harmonic is the dominant harmonic. The dominant harmonic is a certain

multiple of the machine electrical frequency and depends on the number of phases in a channel. For example, in a three- phase electrical machine, the dominant harmonic is at six times the electrical frequency, i.e. the sixth harmonic appears in the frequency spectrum at six times the

fundamental frequency or machine frequency fo. This harmonic may be simply referred to as the "6f harmonic". The invention is based on the insight that, in a multi-channel multi-phase machine with an electromagnetic phase-shift between the channels, torque ripple at the dominant harmonic can be cancelled out. Although the invention can be used for

essentially any multi-channel multi-phase electrical machine, for the sake of simplicity it will be assumed in the

following that the electrical machine has two channels, each with three phases, and that there is a 30° phase-shift between the two channels. An electrical machine with two three-phase channels is generally referred to as a dual three-phase machine. In a dual three-phase machine with a 30° phase-shift between the two channels, torque ripple at the 6f harmonic is cancelled out.

An advantage of the control method according to the invention is that additional freedom of control arises from the

effective elimination of the 6f torque ripple by phase- shifting the two channels. Because the 6f torque ripple is already taken care of, the electrical machine can better tolerate the presence of 6f harmonics in the phase currents. In other words, it is not necessary to design the machine to prevent development of 6f flux linkages that are represented in the rotating reference frame. Instead, it is possible to apply a relatively straightforward control method to eliminate or at least very significantly reduce the 6f voltage ripple as well as the 6f power ripple.

When the inventive control method is used by an electrical machine such as a wind turbine generator, reducing the 6f power ripple to a favourably low level or even eliminating it entirely results in a higher bandwidth for the DC link control. Increasing the DC link bandwidth significantly improves power flow between generator and grid. A further advantage of reducing or eliminating the 6f power ripple is that the size of the DC link capacitors may be reduced, and smaller capacitors are less costly, so that the overall cost of a wind turbine can be reduced.

According to the invention, the control arrangement of a multi-channel multi-phase electrical machine comprises a voltage reference generator realised to generate fundamental voltage references for the machine frequency; a harmonic voltage reference generator (realised to generate harmonic voltage references for a selected dominant harmonic of the machine frequency; and an output voltage controller realised to control a machine output voltage on the basis of the fundamental voltage demands and the harmonic voltage demands.

The inventive control arrangement can advantageously be implemented in any controller of an already existing multi channel multi-phase electrical machine, for example a dual three-phase electrical machine with a 30° electromagnetic phase shift between channels, so that the performance of an already existing machine can be improved.

In the context of the invention, it may be assumed that the converters are controlled by pulse-width modulation (PWM) , and that the fundamental voltage references and the harmonic voltage references are input to a PWM controller that

determines the generator output voltage. The voltage

reference generator may also be referred to as the

fundamental controller since it generates voltage references for the machine frequency or fundamental frequency. According to the invention, the wind turbine comprises a multi-channel multi-phase generator, preferably a dual three- phase generator, and a controller that implements an

embodiment of the inventive control arrangement. An advantage of the inventive wind turbine is that the dynamic in power flow between the generator and the grid can be improved

(compared to a wind turbine that does not implement the inventive control method) , since the reduced 6f power ripple results in a higher bandwidth for DC link control.

Furthermore, the inventive wind turbine can be constructed at a lower cost, since the DC link capacitors can be smaller that a comparable wind turbine that does not implement the inventive control method.

According to the invention, the computer program product comprises a computer program that is directly loadable into a memory of a controller of a multi-channel multi-phase

electrical machine and which comprises program elements for computing harmonic voltage references for use in the

inventive control method when the computer program is

executed by the controller of the multi-channel multi-phase electrical machine.

The units or modules of the computer program product can be completely or partially realised as software modules running on a processor of the controller.

Particularly advantageous embodiments and features of the invention are given by the dependent claims, as revealed in the following description. Features of different claim categories may be combined as appropriate to give further embodiments not described herein.

As indicated above, the inventive method may be applied to any multi-channel multi-phase machine, for example a quad (four channel) three-phase machine with 15° phase-shift between the channels. However, for the sake of clarity, and without restricting the invention in any way, it may be assumed that the electrical machine is a dual three-phase wind turbine generator. Again, without restricting the invention in any way, it may be assumed that the generator is realised as a fractional slot concentrated windings

generator .

In the inventive control method, for each channel, the harmonic injection currents are preferably computed using a model that relates generator electrical values to generator speed. An advantage of this approach is that the generator electrical values and generator speed are quantities that can be measured with relative ease, and a wind turbine controller will generally already comprise some means of measuring these quantities .

According to the invention, the injection currents are computed for each channel on the basis of a target ripple value or target ripple reference for the dominant harmonic. For example, a target ripple value may comprise a target power reference and a target voltage reference.

Alternatively, the target ripple value may be in the form of a vector, with a target power ripple component and a target voltage ripple component. For example, the target ripple vector can comprise the sine and cosine terms of power ripple and voltage ripple.

According to the invention, the harmonic voltage reference generator comprises computation modules realised to compute a generator power value and a generator voltage value on the basis of electrical quantities in the rotating reference frame; an injection current computation module realised to compute injection current references ("injection current demands") for the dominant harmonic on the basis of the generator power value and a generator voltage value; and a harmonic current controller realised to compute the harmonic voltage references from the harmonic injection current references to obtain the final control voltages for PWM operation . The harmonic voltage reference generator of the inventive control arrangement comprises a harmonic current controller that outputs the harmonic voltage reference components, i.e. the d-axis component and the q-axis component of the harmonic voltage reference vector. The harmonic voltage reference components are then passed to the PWM controller, which adds them to the fundamental voltage reference components to determine the generator output voltage for that channel, as explained above. The generator output voltage or terminal voltage of each channel will have favourably low or

negligible voltage ripple.

There are various possible ways of computing the 6f injection current references when carrying out the inventive method. In a first approach, the harmonic injection currents are

computed using a feedforward control method. In this

approach, the injection current computation module is

realised to compute the 6f current references working

backwards from a desired or target ripple that was specified for the machine output voltage and power. A machine model is used to approximate the relationship between torque ripple, voltage ripple and power ripple.

In a second approach, the harmonic injection currents are computed using a decoupled feedback control method

implementing a harmonic power regulator and a harmonic voltage regulator. In this approach, the injection current computation module comprises a 6f power regulator and a 6f voltage regulator. The 6f power regulator receives a 6f generator power value and a 6f power ripple reference, and computes a d-axis injection current value as well as a q-axis injection current value. The 6f voltage regulator receives a 6f generator voltage value and a 6f voltage ripple reference, and computes a q-axis injection current value as well as a d- axis injection current value. The d-axis components are summed, the q-axis components are summed, and the resulting d-axis and q-axis injection current values are passed on to the harmonic current controller. In a third approach, the harmonic injection currents are computed using a multivariable feedback control method. In this approach, the injection current computation module implements a multivariable regulator that is realised to optimise a specific term, formed from the normalised voltage ripple and power ripple. As the objective is to minimise this single term, the technique of regulation used in the above feedback control can be applied, and the required I _d6* and I _q6* values can be generated and fed to harmonic current controllers to obtain the voltage demands.

Other objects and features of the present invention will become apparent from the following detailed descriptions considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for the purposes of illustration and not as a

definition of the limits of the invention.

Fig 1 shows a simplified electrical diagram of a dual three- phase electrical machine;

Fig 2 illustrates an electromagnetic phase-shift between windings of the first channel and windings of the second channel of the electrical machine of Fig 1;

Fig 3 shows an exemplary frequency spectrum of a dual three- phase electrical machine;

Fig 4 shows a simplified block diagram of the inventive control arrangement;

Fig 5 shows a block diagram of a first embodiment of an injection current computation module for the control

arrangement of Fig 4;

Fig 6 shows a block diagram of a second embodiment of an injection current computation module for the control

arrangement of Fig 4;

Fig 7 shows a block diagram of a harmonic regulator

implemented in the control arrangement of Fig 6;

Fig 8 shows a block diagram of a third embodiment of an injection current computation module for the control

arrangement of Fig 4; Fig 9 shows 6f ripple waveforms resulting from the inventive control method;

Figs 10 - 12 show 6f ripple waveforms observed in a prior art control method;

Fig 13 shows a block diagram of a prior art controller.

In the diagrams, like numbers refer to like objects

throughout. Objects in the diagrams are not necessarily drawn to scale.

Fig 1 shows a simplified electrical diagram of a dual three- phase electrical generator. The two channels Cl, C2 of the generator are indicated on the right. The terminal voltages of each channel Cl, C2 are controlled by a machine-side converter Ml, M2. A DC link capacitor Dl, D2 is arranged in the DC link between a machine-side converter Ml, M2 and a grid-side converter Gl, G2. The grid-side converters Gl, G2 are connected to a transformer T via line reactors Rl, R2.

Fig 2 illustrates a 30° phase shift between the first channel and the second channel of Fig 1, by overlaying phasor

diagrams of the channel currents on a simplified

representation of the stator. The first channel Cl is

represented by three windings WA1, WB1, WC1 and the second channel C2 is represented by three windings WA2, WB2, WC2. Here, the windings are connected in a star configuration (a delta configuration is equally possible) . The 30° phase shift between the first channel Cl and the second channel C2 has been shown to have various advantages, one of which is that 6f torque ripple is effectively cancelled out.

Fig 3 shows an exemplary frequency spectrum of a dual three- phase electrical machine controlled using a conventional control approach. The diagram indicates the fundamental fo (at the machine electrical frequency) and a number of

harmonics. In a dual three-phase electrical machine, the sixth harmonic 6f (at six times the machine electrical frequency) is the largest (dominant) and therefore also the most problematic harmonic. The amplitude of a harmonic in the frequency spectrum (relative to the amplitude of the fundamental fo) corresponds to the amplitude of the ripple component that is overlaid on the output voltage or output power .

Fig 4 shows a simplified block diagram of the inventive control arrangement 1. A transformation has been performed on the measured current to obtain vector I _dq in the rotating dqO reference frame, whilst V _dq is the voltage vector derived from an I _dq current controller (not shown) , as will be known to the skilled person. The vectors I _dq , V _dq are passed to a fundamental controller 11 that generates voltage references V _d* , V _q* for a PWM control unit 12 that determines or

regulates the output voltages Vc or terminal voltages Vc of that channel. The current vector I _dq shall be understood to comprise a d-axis component I _d and a q-axis component I _q in the rotating reference frame. The same applies for the voltage vector V _dq , which shall be understood to also

comprise a d-axis component V _d and a q-axis component V _q in the rotating reference frame. A conventional control

arrangement generally only comprises a fundamental controller and a PWM control unit that determines or regulates the terminal voltages V _q using only the fundamental voltage references V _d* , V _q* .

In the inventive control arrangement, the vectors I _dq , V _dq are also passed to a harmonic voltage reference computation module 10 that can be realised in one of several ways as will be explained below, and which comprises a 6f reference computation module that provides harmonic voltage references V _d6* , V _q6* to be added by the PWM control unit to the

fundamental voltage references V _d* , V _q* . The harmonic voltage reference computation module 10 is realised to provide 6f voltage references V _d6* , V _q6* , i.e. voltage references that will result in a minimization of the 6f ripple on the machine output voltage and output power. In the inventive control arrangement 1, the PWM control unit 12 for that channel determines the generator output voltage V not only on the basis of the fundamental voltage references V _d* , V _q* , but also by taking into consideration the harmonic voltage references V _d6* , V _q6* , so that the dominant harmonic ripple on the output power and voltage of that channel can be minimized or even eliminated .

Figs 5, 6 and 7 show various possible embodiments of the 6f reference computation module 102 of the harmonic voltage reference computation module 10. In each case, a generator power computation module 101_P computes a value of the generator power sixth harmonic P6 on the basis of the vectors I _ciq , V _dq , and a generator voltage computation module 101_V computes a value of the generator voltage sixth harmonic V6 on the basis of the vectors I _<¾ , V _dq . Each computation module 101_P, 101_V includes a speed-dependent band-pass filter to only pass the sixth harmonic frequency. Injection references I _d6* , I _q6* are computed in an injection current computation module 102 and passed to a harmonic current controller 103 which in turn generates the 6f voltage references V _d6* , V _q6* .

In Fig 5, the injection current computation module 102 implements as a ripple control module 1021 (or "ripple minimisation module") using a feedforward approach. At a given operating point with a certain speed and a certain load, the 6f power ripple Re can be expressed as

where w is the speed or electrical angular frequency of the machine; I _d , I _q , V _d and V _q are the d-axis and q-axis

components of the vectors I _dq , V _dq; and I _d6 and I _q6 are the harmonic current vectors that will be injected at the

respective phase angles of 6 _d6 and d _R6 for the injection currents. i|r _Pm o is the DC value of flux linkage from the permanent magnets, and i|r _Pm6a and i|r _pm6b are derived from the 6f harmonic values in the d and q-axis permanent magnet flux linkage according to

At that operating point, the 6f voltage ripples _Vd6 , v _q6 can be expressed as and the rms voltage 6f ripple v _rms6 can be expressed as where v _rms o is the fundamental rms (root mean square) voltage. A current injection vector Ii _nj can then be defined as:

The 6f power ripple Re and 6f rms voltage ripple v _rms6 can also be expressed as V6_5in ^Sin ( ^{6 e} ) ( ⁶ ) sin Sin(60) ( 7 ) in which the relationship between the current injection vector and the output ripple vector is expressed as:

R ₆ =A-I _inj +B (8) where the matrices A and B are related to the machine

parameters and the fundamental electrical quantities only, and can be derived by using the equations presented above. For example,

An output ripple vector R ₆ can be put together from the sine and cosine terms of the 6f power ripple Re and 6f voltage ripple V ₆ :

allowing the terms P6_ _cos , Rb_ _Xίh , V6_ _Cos , V6_ _sin to be established for equation (6) and equation (7) . For example, if the target 6f power ripple and target 6f voltage ripple are each zero, the ripple vector is a 4 x 1 vector of null entries. With the ripple vector set up, and the closed form of matrices A and B derived from the machine parameters and the fundamental electrical quantities, values for the 6f power ripple Re and the 6f rms voltage ripple V _rmS6 can be calculated.

Subsequently, using equation (1), the required harmonic currents I _d6 , I _q6 can be calculated from the target power ripple and target rms voltage ripple. Because power ripple can also be expressed in terms of voltage or current ripple, this machine parameter dependency may be removed.

Fig 6 shows a block diagram of a second embodiment of the injection current computation module 102 for the control arrangement of Fig 4. Here, the harmonic currents I _d6 , I _q6 are calculated using a pair of harmonic power and voltage

regulators 102_P, 102_V connected in a feedforward

arrangement. A harmonic power regulator 102_P receives the 6f power ripple Re from the generator power computation module 101_P, and a power reference P6_ref (e.g. zero), and computes a d-axis current reference component I _d6* and a q-axis current reference component I _q6* . Since dominant harmonic power ripple is to be minimised, the value of the power reference P6_ref may be zero.

A harmonic voltage regulator 102_V receives the 6f voltage ripple V from the generator voltage computation module

101_V, and a voltage reference V6_ref (e.g. zero), and computes a d-axis current reference component I _d6* and a q- axis current reference component I _q6* . In this case also, since dominant harmonic voltage ripple is to be minimised, the value of the voltage reference V6_ref may be zero.

The d-axis components are summed to obtain the d-axis current reference I _d6* . The q-axis components are summed to obtain the q-axis current reference I _q6* . The current references I _ci6* , I _q6* are then passed to the harmonic current controller 103 which generates the 6f voltage references V _d6* , V _q6* .

Fig 7 shows an exemplary block diagram of the harmonic power regulator 102_P of Fig 5 (the harmonic voltage regulator 102_V is constructed identically, and only the relevant signals must be substituted) . A feedback signal P6 is

subtracted from the reference signal P6_ref. The result is passed to a 90° phase-shifter 1021 and also to a frame transformation module 1022, which performs a transformation of the non-phase-shifted with the phase-shifted signals from a dq rotating reference frame to a frame rotating at the 6f frequency. The outputs of the frame transformation module 1022 are passed to two proportional-integral controllers 1023, whose outputs are in turn passed to a second phase transformation module 1024 that generates the d-axis current reference component I _d6* and the q-axis current reference component I _q6* .

Fig 8 shows a block diagram of a third embodiment of the injection current computation module 102 for the control arrangement of Fig 4. Here, a multivariable regulator 1028 receives the 6f power ripple Re from the generator power computation module 101_P and the 6f voltage ripple V from the generator voltage computation module 101_V. The

multivariable regulator 1028 is also given weighting factors l, m. The multivariable regulator 1028 is realised to

optimise the following equation:

where y is the objective signal that is derived from the feedback of power ripple and voltage ripple (P ₆ , Ve ) and from the DC values in the power and voltage (Po, Vo) . Since the objective is to minimise y, the technique of regulation shown in Fig 6 can be applied, and the required values of I _d6* and I _q6* can be generated and then passed to the HCC controllers to compute the voltage demands.

Fig 9 illustrates the simultaneous minimisation of all three 6f ripples when the inventive method is applied in the control of a dual three-phase machine in which the two channels Cl, C2 are electromagnetically phase shifted by 30°. The upper part of the diagram shows the 6f torque ripple T _6i of the first channel Cl and the 6f torque ripple ΐ b ₂ of the second channel C2. The 6f torque ripple Tei, Tb ₂ in each case lies within the range ±45 kNm. Since the two channels Cl, C2 have been phase-shifted by 30°, the 6f torque ripples Tei, Tb ₂ cancel each other out, so that the net 6f torque ripple Te is 0 Nm.

The middle part of the diagram shows the 6f power ripple Re and the lower part of the diagram shows the 6f Vrms voltage ripple V of either one of the two channels Cl, C2. With the inventive method, using any of the three approaches described above with the aid of Figs 4 - 7, the 6f power ripple Re has been reduced to a very favourable level that is significantly less than ±0.01 kW, and the 6f voltage ripple V has been reduced to a very favourable level close to zero volts.

Figs 10 - 12 show typical waveforms that result when one type of ripple is minimized by I _q harmonic current injection control, i.e. by harmonic current injection in the q-axis, as practiced in the prior art. The machine being controlled is a dual three-phase generator of a wind turbine. For either one of the two channels Cl, C2, the diagrams show the 6f ripple on each of torque, power and rms voltage against rotor electrical angle in radians. When only one type of 6f ripple is minimized, the other two 6f ripple types exhibit

significantly higher levels:

In Fig 10, only the torque ripple is minimized by I _q harmonic current injection. The 6f torque ripple Tio now lies within a favourably low range of -0.2 - 0.2 kNm. However, the 6f power ripple Pio is relatively high, reaching ±300 kW. Similarly,

6f voltage ripple Vio is also relatively high, reaching

±80 V.

In Fig 11, only power ripple is minimized by Iq harmonic current injection, and the 6f power ripple Pn lies within a _favourably low range of ±3 kW. However, 6f voltage ripple Vu is also relatively high, reaching ±18 V. The 6f torque ripple Tii is relatively high, reaching ±45 kNm.

In Fig 12, only voltage ripple is minimized by Id harmonic current injection, and the 6f voltage ripple V ₁₂ now does not exceed ±0.02 V. However, the 6f power ripple P ₁₂ is also relatively high, reaching ±80 kW. The 6f torque ripple T ₁₂ is relatively high, reaching ±50 kNm.

These diagrams illustrate that the known approaches to ripple reduction or elimination are only beneficial from the point of view of the reduced ripple, but the problems associated with the other two types of ripple may cancel out those benefits . Fig 13 shows a simple block diagram of a prior art controller for a first channel of a dual three-phase machine. An Id current controller 70d receives an Id reference Idl_ref and a measured Id value Idl, and computes a d-axis voltage

reference Vdl*. An Iq current controller 70q receives an Iq reference Iql_ref and a measured Iq value Iql, and computes a q-axis voltage reference Vql*.

A harmonic current controller 71 provides harmonic voltage references Vqhl*, Vdhl* for a specific harmonic, for example the dominant harmonic. Inputs to the harmonic current

controller 71 are received from three modules: a voltage ripple control module 710 that receives the generator Vrms value; a power ripple control module 711 that receives the generator power value; and a torque ripple control module 712 that receives the generator torque value. Each harmonic reference Vqhl*, Vdhl* is summed with the corresponding voltage reference Vql*, Vdl* and the summed signals are passed to a PWM unit 72 that uses them to control the

terminal voltages Vci of the first channel.

Although the present invention has been disclosed in the form of preferred embodiments and variations thereon, it will be understood that numerous additional modifications and

variations could be made thereto without departing from the scope of the invention. The invention may be applied to electrical machines with different numbers of channels and different numbers of phases. For example, an electrical machine may have three channels each with three phases, and a 20° phase-shift between the channels. If the electrical machine has four channels each with three phases, a 15° phase-shift between the channels is used. For a three-phase machine, it is the 6f harmonic that is dominant and needs to be dealt with using the inventive method. Similarly, an electrical machine may have two/three/four channels each with five phases, and a 18°/12°/9° phase-shift between the

channels. In this case, it is the lOf (tenth) harmonic that is dominant and needs to be dealt with using the inventive method. For an electrical machine with two/three/four

channels each with seven phases, and a 12.86 ° /8.57 ° / 6.42 ° phase-shift between the channels, it is the 14f (fourteenth) harmonic that is dominant and needs to be dealt with using the inventive method.

For the sake of clarity, it is to be understood that the use of "a" or "an" throughout this application does not exclude a plurality, and "comprising" does not exclude other steps or elements. The mention of a "unit" or a "module" does not preclude the use of more than one unit or module.