TECHNICAL FIELD

The present disclosure relates to a filter apparatus and method. Aspects of the invention relate to a filter for modulating signals applied to a multi-phase electrical machine; a power supply apparatus for supplying drive signals; an electric machine; and a vehicle.

BACKGROUND

At high power, alternating current electrical machines (due to their limited voltage) the power can be increased by machine current per phases. This leads to high current levels per phase in a three (3) phase electrical machine. These high current levels per phase can be reduced by increasing of the number of phases. This may be implemented in an asymmetrical six (6) phase electrical machine.

If the six (6) phase electrical machine is powered by a conventional generator (which outputs sinusoidal currents), then the machine voltage will contain significant voltage harmonics, which will increase significantly the machine voltage demand. If the machine is powered with a voltage generator (sinusoidal voltage), then the machine current will contain current high harmonics (higher current demand and increased losses in the coils). In both cases, the most significant harmonics are the 5th and 7th (current and voltages). This problem also occurs in synchronous (wound rotor and permanent magnet) machines and asynchronous (induction) machines.

These voltage and current harmonics generate additional losses in the electrical machines as well as in the system which power them. It would be desirable to reduce these harmonics, for example in the systems as well as in electrical vehicles (HEV, PHEV or any other drives with high power demands asymmetrical six-phase systems).

It is an aim of the present invention to address one or more of the disadvantages associated with the prior art.

SUMMARY OF THE INVENTION

Aspects and embodiments of the invention provide a filter; a power supply apparatus; an electric machine; and a vehicle as claimed in the appended claims.

According to an aspect of the present invention there is provided a filter for modulating drive signals applied to a six-phase electrical machine comprising first and second three-phase winding systems, the filter comprising: at least one magnetic loop; and a plurality of windings for supplying drive signals to respective phases of the six-phase electrical machine, the windings being wound on the at least one magnetic loop; the windings comprising: at least one first winding, the or each first winding having a first number of turns; and at least one second winding, the or each second winding having a second number of turns; wherein the first number of turns is different from the second number of turns to modulate the drive signals.

The ratio of the first and second numbers of turns may modulate the drive signals applied to the electrical machine. At least in certain embodiments, the filter may be configured to modulate the drive signals to reduce or minimise harmonic content (i.e. current and voltage) of the electrical machine. Voltage harmonics may be generated by base harmonic currents in a magnetic circuit, such as the electrical machine. The first number of turns and the second number of turns may be selected at least partially to reduce harmonics. If the machine current is sinusoidal, the filter may reduce or inhibit harmonics at the inverter. A serial connection of the filter and electrical machine (whereby the same current flows through the filter and electrical machine) may reduce or eliminate voltage harmonics. The first number of turns and the second number of turns may, for example, be selected to reduce or cancel at least the 5 ^th voltage harmonic in the electrical machine. Alternatively, or in addition, the winding arrangement may reduce or cancel the 7 ^th voltage high harmonics of the electrical machine. At least in certain embodiments, when applying drive signals comprising a sinusoidal voltage, the electrical machine current harmonic content may be lower than a comparable system comprising an electrical machine connected directly to an inverter to supply sinusoidal voltage.

The at least one first winding may be configured to apply drive signals to the one of the three-phase winding systems in the electrical machine. The at least one second winding may be configured to apply drive signals to the second three-phase winding system in the electrical machine.

The filter may be incorporated into the electrical machine. Alternatively, the filter may be separate from the electrical machine. The filter and the electrical machine may be disposed in an electric drive unit for a vehicle, such as an automobile.

The filter may be disposed between the electrical machine and a drive signal generator. The filter, the electrical machine and the drive signal generator may be connected in series. The drive signal generator may, for example, comprise an inverter. The inverter may be a three-phase inverter or a six-phase inverter. The inverter may be a six-phase inverter which may be controlled selectively to operate as a three-phase inverter.

The filter may be connected in series to the inverter and the electrical machine. The windings in the filter may be connected in series to the inverter. The configuration of the first and second windings establishes additional voltage harmonic components, which have opposite sign compared to the corresponding machine harmonics. In this way, at the sinusoidal inverter voltage, the filter may reduce a current harmonic content in the electrical machine.

The first number of turns may be less than the second number of turns. Alternatively, the first number of turns may be greater than the second number of turns.

The or each magnetic loop may comprise or consist of a ferromagnetic ring. The ferromagnetic ring may have a unitary construction or may be formed from a plurality of components.

The at least one magnetic loop may comprise or consist of a first magnetic loop. The at least one first winding and the at least one second winding may be wound around the first magnetic loop. The filter may have one of the first winding and two of the second windings. The first winding and the second windings may be wound around the first magnetic loop. The first winding and one of the second windings may have a first winding orientation (i.e. they are both wound in a first direction). The other one of the second windings may have a second winding orientation (i.e. it is wound in a second direction). The first and second winding orientations oppose each other. The first and second directions may be opposite to each other.

The filter may comprise two or more of the magnetic loops. The magnetic loops may be disposed adjacent to each other. The magnetic loops may be arranged in a non-overlapping array. ^JLRI WO 2023/066983 PCT/EP2022/079072

The filter may comprise a plurality of each of the following: the magnetic loops, the first windings and the second windings. The filter may comprise two or more of the magnetic loops; two or more of the first windings; and two or more of the second windings.

The plurality of magnetic loops may comprise or consist of a first magnetic loop and a second magnetic loop. One of the first windings may be wound on each of the first and second magnetic loops. The first windings on each of the first and second magnetic loops may have like winding orientations. The first windings on each of the first and second magnetic loops may be wound in the same direction. The current flow in the first windings on the first and second magnetic loops may be in the same reference direction.

The filter may comprise two (2) of the first windings and four (4) of the second windings.

The second windings may be wound on the first and second magnetic loops. Two of the second windings may be wound on each of the first and second magnetic loops. The second windings on the first magnetic loop may have opposing winding orientations. The second windings on the first magnetic loop may be wound in opposing directions. The current flow in the second windings on the first magnetic loop may have opposing reference directions. The second windings on the second magnetic loop may have opposing winding orientations. The second windings on the second magnetic loop may be wound in opposing directions. The current flow in the second windings on the second magnetic loop may be in opposing reference directions.

The ratio of the number of turns in the or each first winding to the number of turns in the or each second winding on the first magnetic loop may be defined by the following equation:

Where:

N1 is the first number of turns of the first winding(s) of the filter;

N2 is the second number of turns in the second winding(s) of the filter;

N _lf is the effective turn number of the phase windings of the first three-phase winding system; and

N _2f is the effective turn number of phase winding of the second three-phase winding system.

In the above equation the effective turn ratio of the first and second three-phase winding systems are multiplied by a constant (referred to herein as a modulation constant) to determine the ratio of the number of turns. The modulation constant has a value of 7/4 in the above embodiment. In a variant, the equation may utilise a different modulation constant. The modulation constant may be selected from the range 1.2 to 2.33 inclusive (corresponding to a range from 6/5 to 8/3 inclusive); or from the range 1.4 to 2 inclusive (corresponding to a range from 7/5 to 8/4 inclusive). The modulation constant may, for example, be 13/8 or 15/8.

The ratio of the number of turns in the or each first winding to the number of turns in the or each second winding on the second magnetic loop may be defined by the following equation:

Where:

SUBSTITUTE SHEET (RULE 26) ^JLRI WO 2023/066983 PCT/EP2022/079072

N1 is the first number of turns in the filter;

N2 is the second number of turns in the filter;

N _1f is the effective turn number of the phase windings of the first three-phase winding system; and

N _2f is the effective turn number of phase winding of the second three-phase winding system.

In the above equation the effective turn ratio of the first and second three-phase winding systems are multiplied by a constant (referred to herein as a modulation constant) to determine the ratio of the number of turns. The modulation constant has a value of 7/4 in the above embodiment. In a variant, the equation may utilise a different modulation constant. The modulation constant may be selected from the range 1.2 to 2.33 inclusive (corresponding to a range from 6/5 to 8/3 inclusive); or from the range 1.4 to 2 inclusive (corresponding to a range from 7/5 to 8/4 inclusive). The modulation constant may, for example, be 13/8 or 15/8.

The plurality of magnetic loops may comprise or consist of a first magnetic loop, a second magnetic loop and a third magnetic loop.

One of the first windings may be wound on each of the first, second and third magnetic loops. The first windings on the first, second and third magnetic loops may have like winding orientations. The first windings on the first, second and third magnetic loops may be wound in the same direction. The current flow in the first windings on each of the first, second and third magnetic loops may be in the same reference direction. .

The second windings may each be wound around a pair of the first, second and third magnetic loops. Each second winding may be wound around a different pair of the first, second and third magnetic loops.

The filter may comprise two of the second windings on the first magnetic loop. The second windings on the first magnetic loop may have opposing winding orientations. The second windings on the first magnetic loop may be wound in opposing directions. The current flow in the second windings on the first magnetic loop may be in opposing reference directions.

The filter may comprise two of the second windings on the second magnetic loop. The second windings on the second magnetic loop may have opposing winding orientations. The second windings on the second magnetic loop may be wound in opposing directions. The current flow in the second windings on the second magnetic loop may be in opposing reference directions.

The filter may comprise two of the second windings on the third magnetic loop. The second windings on the third magnetic loop may have opposing winding orientations. The second windings on the third magnetic loop may be wound in opposing directions. The current flow in the second windings on the third magnetic loop may be in opposing reference directions.

The ratio of the number of turns in the or each first winding to the number of turns in the or each second winding on the third magnetic loop may be defined by the following equation:

Where:

N1 is the first number of turns in the filter;

N2 is the second number of turns in the filter;

SUBSTITUTE SHEET (RULE 26) ^JLRI WO 2023/066983 PCT/EP2022/079072

N _1f is the effective turn number of the phase windings of the first three-phase winding system; and N _2f is the effective turn number of phase winding of the second three-phase winding system.

In the above equation the effective turn ratio of the first and second three-phase winding systems are multiplied by a constant (referred to herein as a modulation constant) to determine the ratio of the number of turns. The modulation constant has a value of 7/4 in the above embodiment. In a variant, the equation may utilise a different modulation constant. The modulation constant may be selected from the range 1.2 to 2.33 inclusive (corresponding to a range from 6/5 to 8/3 inclusive); or from the range 1.4 to 2 inclusive (corresponding to a range from 7/5 to 8/4 inclusive). The modulation constant may, for example, be 13/8 or 15/8.

The filter may comprise three (3) of the first windings and three (3) of the second windings. Each of the first and second windings may be associated with a respective phase of the six-phase electrical machine. The first windings may be configured to supply drive signals to a first three-phase winding system in the six-phase electrical machine. The second windings may be configured to supply drive signals to a second three-phase winding system in the six-phase electrical machine.

The first number of turns may be six (6), seven (7) or eight (8) or a whole number multiple thereof. The second number of turns may be three (3), four (4) or five (5) or a whole number multiple thereof. The ratio of the number of turns on the first and second windings may, for example, be one of the following set: 6/3; 6/4; 7/3; 7/5; 8/4 and 8/5.

The first number of turns may be seven (7) or a whole number multiple of seven (7). The second number of turns may be four (4) or a whole number multiple of four (4).

The filter may comprise a plurality of first electrical connectors for connecting a first end of each first winding to an inverter. The filter may comprise a plurality of second electrical connectors for connecting a first end of each second winding to the inverter. The inverter may be a six-phase inverter or a three-phase inverter.

The second windings may be connected to each other at a first end. By connecting the second windings to each other, a short circuit connection may be established between the windings in the second winding set. In this arrangement, the second windings may not be connected to the inverter.

According to a further aspect of the present invention there is provided a power supply apparatus for supplying drive signals to a six-phase electrical machine, the power supply apparatus comprising a filter as described herein. The filter may be connected to an inverter. The inverter may be a three-phase inverter; or a six-phase inverter.

According to a further aspect of the present invention there is provided an electric machine comprising a filter as described herein.

According to a further aspect of the present invention there is provided a vehicle comprising at least one filter as described herein.

According to a further aspect of the present invention there is provided a method of operating an inverter for supplying drive signals to an electrical machine, the electrical machine being a six-phase electrical machine having first and second three-phase winding systems, the inverter having a first outputs for outputting drive signals to the first three-phase winding system and second outputs for outputting drive signals to the second three-phase winding system, the method comprising selectively inhibiting the first outputs or the second outputs.

SUBSTITUTE SHEET (RULE 26) Inhibiting the first outputs or the second outputs may comprise controllably short-circuiting those outputs.

The current flow in the windings is described herein as having a reference direction. The reference direction of the current flow through two or more windings is described herein. For example, the current flow in two or more windings may be described as being in the same reference direction or in opposing reference directions. It will be understood that the reference direction refers to the current flow in the two or more windings at the same time (i.e. the current direction in the windings at a particular time). Furthermore, the reference direction of the current flow is specified in respect of corresponding sections of the two or more windings. For example, the reference direction may define the current flow along the longitudinal sections of the or each winding disposed within an interior of the corresponding magnetic loop.

Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, in the claims and/or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and/or features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 shows a first circuit diagram of a filter for modulating drive signals to an electrical machine in accordance with an embodiment of the present invention;

Figures 2A and 2B show the voltage orthogonal components and the voltage spectrum for an electrical machine having a sinusoidal current source;

Figures 3A and 3B show the phase currents and the current spectrum for an electrical machine having a sinusoidal voltage source;

Figure 4A shows the voltage phasors of a three-phase winding system;

Figure 4B shows the phase shift of the phase windings in the three-phase winding system;

Figure 4C shows the distribution of the phase windings in the stator of the three-phase winding system;

Figure 5A shows the voltage phasors of an asymmetric six-phase winding system;

Figure 5B shows the phase shift of the phase windings in the asymmetric six-phase winding system;

Figure 5C shows the distribution of the phase windings in the stator of the asymmetric six-phase winding system;

Figure 6 shows the “αβ” stator coordinate system and phase coils;

Figure 7 shows an electromagnetic circuit comprising a single magnetic loop having first and second windings;

Figure 8A shows a first equivalent circuit for a base harmonic;

Figure 8B shows a second equivalent circuit for a higher order harmonic;

Figure 9 shows a filter in accordance with an embodiment of the present invention comprising a single magnetic loop having first and second windings, the first winding being split into two components;

Figure 10 shows a filter in accordance with an embodiment of the present invention comprising first and second magnetic loops having first and second windings;

Figure 11 shows a circuit diagram including a filter for modulating drive signals generated by a six-phase inverter in accordance with a further embodiment of the present invention; Figure 12 shows a filter in accordance with an embodiment of the present invention comprising first and second magnetic loops having first and second windings;

Figure 13 shows a circuit diagram including a filter for modulating drive signals generated by a six-phase inverter in accordance with a further embodiment of the present invention;

Figure 14 shows a filter in accordance with an embodiment of the present invention comprising three magnetic loops having first and second windings;

Figure 15 shows the flux linkage vectors of the filter shown in Figure 14;

Figure 16 shows a filter in accordance with an embodiment of the present invention comprising two magnetic loops having first and second windings;

Figure 17A shows the phasors of the flux linkages of the windings in the filter shown in Figure 16;

Figure 17B shows the phasors of the voltages of the filter shown in Figure 16;

Figure 18 shows the coil and line voltages phasors of first and second three-phase winding systems;

Figure 19 shows the line and phase voltage phasors of first and second three-phase winding systems in a filter;

Figure 20 shows a first variant of the filter described herein having a first core profile;

Figure 21 shows a second variant of the filter described herein having a second core profile;

Figure 22 shows a second circuit diagram including a filter for modulating drive signals generated by a three-phase inverter in accordance with a further embodiment of the present invention;

Figure 23A shows simulated phase currents for the arrangement shown in Figure 22 utilising a filter having two magnetic loops;

Figure 23B shows the torque spectrum for the electrical machine electrically connected to the filter having two magnetic loops;

Figure 23C shows the torque harmonics for the electrical machine electrically connected to the filter having two magnetic loops;

Figure 23D shows the current spectrum in the arrangement comprising the filter having two magnetic loops;

Figure 23E shows the high harmonics for the current spectrum in the arrangement comprising the filter having two magnetic loops;

Figure 24A shows simulated phase currents for the arrangement shown in Figure 22 utilising a filter having three magnetic loops;

Figure 24B shows the torque spectrum for the electrical machine electrically connected to the filter having three magnetic loops;

Figure 24C shows the torque harmonics for the electrical machine electrically connected to the filter having three magnetic loops;

Figure 24D shows the current spectrum in the arrangement comprising the filter having three magnetic loops;

Figure 24E shows the high harmonics for the current spectrum in the arrangement comprising the filter having three magnetic loops;

Figure 25 shows line voltage characteristics; and

Figure 26 shows a vehicle comprising a filter in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

A filter 1 for modulating drive signals applied to an electrical machine 2 in accordance with an embodiment of the present invention is described herein with reference to the accompanying Figures. The filter 1 is a selective filter. The filter 1 has an input (inverter) side for receiving inverter outputs; and an output (machine) side for outputting drive signals to the electrical machine 2. As described herein, the filter 1 is suitable for modulating the drive signals applied to the electrical machine 2. The electrical machine 2 has particular application in a road vehicle 3 (shown in Figure 26), such as an automobile, a utility vehicle, a sports utility vehicle or a tractor. The electrical machine 2 may be provided in an electric drive unit (EDU) for propelling the vehicle 3.

The vehicle 3 is a battery electric vehicle (BEV) in the present embodiment, but the filter 1 could be employed in a hybrid electric vehicle (HEV) or a plug-in hybrid electric vehicle (PH EV). The vehicle 3 comprises a battery 4 and an inverter 5. The inverter 5 is connected to the battery 4 and, in use, converts direct current (DC) supplied by the battery 4 into alternating current (AC). The alternating current (AC) is applied as drive signals to the electrical machine 2. The electrical machine 2 in the present embodiment comprises a six-phase electrical machine. The inverter 5 is a six-phase inverter and, in use, generates six (6) drive signals. As described herein, the drive signals are applied to respective phases of the electrical machine 2. The filter 1 is connected to the inverter 5 and modulates the drive signals which are output to the electrical machine 2.

A connection diagram of the filter 1 , the electrical machine 2 and the inverter 5 is shown in Figure 1. The connection diagram includes the following nomenclature:

A, B, C, D, E, F (upper case) denote the phases of the six-phase winding system; a, b, c, d, e, f (lower case) denote the phase voltages and currents in the six-phase winding system;

V _DC is the DC link voltage (for example battery voltage of the vehicle 3),

X1 are the connections of the inverter 5; are the connections of the filter 1 on the input (inverter) side, these connections are connected to the corresponding inverter outputs. These are beginning ends of coil windings, they enter to the coil sides denoted by “0” (as described herein with reference to the winding arrangement of the filter 1);

X ₂ are the connections of the filter 1 on the output (machine) side, these connections are connected to the corresponding inputs of the electrical machine 2. These are finishing ends of coils, they come out from coil sides denoted by (as described herein with reference to the winding arrangement of the filter 1);

V _1x are phase voltages provided by the inverter 5, they are determined by the modulation strategy of inverter (for example sinusoidal, six step or any other modulation strategy);

I _1x are the inverter currents (equivalent to the currents in the electrical machine 2);

V _Mx are the phase voltages of the electrical machine 2, these voltages are very similar to the voltages of the electrical machine 2 with sinusoidal currents (these voltages usually contain significant 5 ^th and 7 ^th harmonic components); and

I _Mx M are the currents of the electrical machine 2 (equivalent to the currents of the inverter 5).

The harmonic contents of the electrical machine 2 will now be described. For a sinusoidal current source, the current in the electrical machine 2 is sinusoidal and the voltages contain significant 5 ^th and 7 ^th harmonics. The voltage orthogonal components and their spectrums are shown in Figures 2A and 2B. As shown in Figure 2B, the 5 ^th harmonic is the most significant harmonic. In the illustrated example, the 5 ^th harmonic is approximately 5% of the base harmonic. The phase currents and the current spectrum are shown in Figures 3A and 3B. For a sinusoidal voltage source, the machine voltage is sinusoidal until its currents contain significant 5 ^th and 7 ^th harmonics components, as shown in Figure 3A. As shown in Figure 3B, the 5 ^th harmonic is the most significant harmonic. In the illustrated example, the 5 ^th harmonic is more than 20% of the base harmonic. The electrical machine 2 comprises a rotor and a stator. A winding system comprising a plurality of coils is provided on the stator. The winding system of the six-phase electrical machine 2 in the present embodiment comprises six (6) windings. As described herein, these windings are effectively formed as first and second three-phase winding systems which are angularly offset from each other. The configuration of a three-phase winding system and a six-phase winding system will now be described.

Three-phase Winding System

The coils in a three-phase winding system are evenly distributed in slots formed in the stator, typically on an inner circumferential surface of the stator. The coil system consists of three (3) windings which are at least substantially electro-magnetically identical to each other. A small difference between the windings of different phases may be acceptable in certain applications. The voltage phasors of the three-phase winding system are shown in Figure 4A. A projection of the voltage phasors onto the horizontal axis determines their instantaneous values. The symmetrical axes of the phase windings are shifted by 120 electrical degrees, as shown in Figure 4B. This winding configuration will generate rotating magnetic field if the currents in coils are shifted in time by 120 electrical degree. This rotating magnetic field is important for operation of rotating electrical machines. The currents are developed in the coils by voltages which have a similar phase shift as the phase currents. The coil sides each cover 60 electrical degree in the stator inner surface. As shown in Figure 4B, the phase shift between the coils is 120 electrical degree. The distribution of phase windings in the stator is shown in Figure 4C for a two-pole topology. If the coils of the three-phase winding system are divided into two, this will result in an asymmetrical six-phase winding system.

Asymmetrical Six-phase Winding System

The coils in the asymmetric six-phase winding system are evenly distributed in slots formed in the stator, typically on an inner circumferential surface of the stator. The coil system consists of six (6) windings having at least substantially electro-magnetically identical windings. A small difference between the windings of different phases may be acceptable in certain applications. Three coils are arranged in first and second three-phase winding systems (referred to herein as first and second three-phase winding systems). The voltage phasors of the asymmetrical six-phase winding system are shown in Figure 5A. The projection of the voltage phasors on the horizontal axis determines their instantaneous values. The phase shift between the axes of the phase coils is 120 electrical degree. As shown in Figure 5B, the phase shift between the first and second three-phase winding systems is 30 electrical degrees. The phase shifts between the voltages are identical to the shifts between the phase windings. The phase coils in the six- phase winding system are arranged in the stator slots. In this arrangement, each coil covers 30 electrical degrees, as illustrated in Figure 5C. The phase shift between the coils in the stator is 30 electrical degree; and the shift between the first and second three- phase winding systems is 30 electrical degree. The distribution of the phase windings in the stator is illustrated in Figure 5C. Each coil side covers 30 electrical degree.

The windings of the first and second three-phase winding systems are connected in star. The star points (centres) of the first and second phase winding systems are electrically separated. Due to the differences of winding systems, the six-phase winding system has significantly higher harmonic content compared to the three-phase winding system.

Space Vectors of Asymmetrical Six-phase Winding System The asymmetrical six-phase winding system is divided into first and second three-phase winding systems. The phase voltages of the first three-phase winding system are denoted by letters “a”, “c” and “e”, as shown in Figures 5A and 5B. The phase voltages of the second three-phase winding system are denoted by “b”, “d” and “f”. The coils of the second three-phase winding system are shifted by 30 electrical degrees compared to the first three-phase winding system. The instantaneous values of phase currents and voltages of each phase winding system determine the corresponding so-called space vectors in a “αβ” “stator” coordinate system, as shown in Figure 6.

The components of the space vectors of three-phase winding system can be determined by the following equations:

Where: x _α1 , x _β1 are the components of space vector in the “αβ” “stator” coordinate system, determined by phase quantities of phases “a”, “c’ and “e”; x _α2 , xβ ₂ are the components of space vector in the “αβ” “stator” coordinate system, determined by phase quantities of phases “b”, “d”and “f; and

“x” can be the voltage or current.

The instantaneous values of phase voltages and currents are the sum of voltage harmonics. These are harmonics with odd harmonic order numbers (1 , 3, 5, 7, ...). The phase shift between the harmonics of different phases is equivalent to the phase shift between the base harmonics of voltage vectors (shown in Figure 5a) multiplied by their order number. The shift between the space vectors of different phase winding systems is shown in Table 1 for different harmonics. As can see, the phase shifts between the harmonics which order number are determined by expressions “12(k-1)+1” or “12(k-1)-1” (where “k” is an integer) is ZERO, until the phase shift between the components determined by expressions “12(k- 1 )+1 +6” or “12(k-1 )-1 +6” (where “k” is an integer) is 180 electrical degree. The sum of “a” and “β” component of the first and second three-phase winding systems will contain the harmonics “12(k-1 )+1” or “12(k-1 )-1”, until the difference of “a” and “β” component will contain the harmonics “12(k-1 )+1 +6” or “12(k-1 )-1 +6”. As described herein, the phase shift difference between the harmonics of the first and second three-phase winding system making up the six-phase winding system is used to separate the base harmonic from the 5 ^th and 7 ^th harmonic components.

By way of background, the basic electromagnetic formulas used in relation to a magnetic circuit will now be described. The Maxwell- Ampere equation states: Where the integral of the magnetic field strength (H) for a closed contour (C) is equivalent to the movement of charges (current J _f ) and change of electric displacement through a surface (S) surrounded/determined by the contour (C).

In the present case, the electric displacement (D) can be ignored, and the integral is equivalent to the sum of the current passing through the inner surface surrounded by the magnetic core. This analogy can be applied to a first electromagnetic circuit having a plurality of windings W1 -1 , W2-2, W2-1 each wound on a first magnetic loop 10-1, as shown in Figure 7. The first magnetic loop 10-1 comprises a ferromagnetic core. The ferromagnetic core could have a unitary composition. Alternatively, the ferromagnetic core may be formed from a plurality of components, for example two or more segments. The core or the segments may each be formed by a plurality of laminations. Each winding comprises an elongate electrical conductor which is wound around the first magnetic loop 10-1. The elongate electrical conductor in the present embodiment comprises a wire which may have a single core, or may have a plurality of strands (i.e. a multistrand wire) such as a Litz wire. The electrical conductor has an exterior which is electrically insulated, for example by application of an electrically insulating film or coating.

Each winding comprises a plurality of turns (N) on the first magnetic loop 10-1. In the present embodiment, the windings have either a first number (N1) of turns or a second number (N2) of turns. The windings having the first number (N1) of turns are referred to herein as first windings; and the windings having the second number (N2) of turns are referred to herein as second windings. The first electromagnetic circuit shown in Figure 7 comprises one first winding and two second windings. In the present embodiment, the first winding has seven (7) turns (i.e. W ₁ =7); and the second windings each have four (4) turns (i.e. W ₂ = 4).

A reference direction of current flow through each of the windings in the first electromagnetic circuit is represented in Figure 7. A first symbol indicates a first reference direction of current flow; and a second symbol indicates a second reference direction of current flow. In the illustrated arrangement, the first reference direction of current flow (represented by the first symbol is out of the page; and the second reference direction of current flow (represented by the second symbol is into the page. The current flowing into the page is assumed to be positive. This format is used throughout the present application to indicate the reference direction of current flow in the windings at a given time. In practice, the reference direction of current flow through each of the windings is determined by the winding direction of the turns formed around the first magnetic loop (referred to herein as the winding orientation). A first winding direction results in a first reference direction of the current flow; and a second winding direction results in a second reference direction of current flow. The reference direction of current flow is described herein in respect of a longitudinal section of each winding disposed within an interior of the magnetic loop. It will be understood that the reference direction of current flow is reversed (i.e. in the opposite direction) in the longitudinal section of each winding disposed on an exterior of the magnetic loop. The first and second reference directions of current flow are opposite to each other. As shown in Figure 7, the current flow in the windings is in opposing first and second reference directions. The first winding direction may be clockwise (about a central axis); and the second winding direction may be anticlockwise (about the central axis). It will be understood that the first and second winding directions may be reversed. In the first electromagnetic circuit shown in Figure 7, the first winding and one of the second windings have a first winding direction (the reference direction of current flow being directed out of the page in Figure 7); and the other one of the second windings has a second winding direction (the reference direction of current flow being directed into the page in Figure 7).

The first magnetic loop in the first electromagnetic circuit comprises a first ferromagnetic core in the form of an annulus. The annulus is circular in plan form and is circular in transverse cross-section (A), as illustrated in Figure 7. The first ferromagnetic core has a symmetrical configuration which results in a constant tangential magnetic field along a centreline (denoted by a dashed line in Figure 7), having a length equivalent to the mid length (I) of the magnetic circuit. The following equation is valid for this configuration:

Only the coil sides in the inner circle of magnetic circuit are taken into the formula. The coil sides around the magnetic circuit do not have a significant influence on the magnetic field strength (H) and, therefore, can be ignored.

The flux density (B) in the magnetic circuit is determined by the magnetic field strength (H) and the magnetic permeability of magnetic circuit (μ ):

Where μ ₀ is the magnetic permeability of the air/vacuum and μ _r is the relative magnetic permeability which depends on the saturation and material of ferromagnetic circuit. For a given material, the relative magnetic permeability μ _r is a function of the flux density In some simplified cases, the relative magnetic permeability μ _r may have a constant value.

The magnetic flux (Φ) is calculated by as follows:

Where Φ _A is the flux through the surface A. The expression can be simplified for magnetic circuit shows in Figure 7 as follows:

Where B is the flux density perpendicular to the surface A.

The number of turns and the flux which pass through the coils defines the flux linkage (ip) as follows:

Where N is the number of turns of corresponding coil, and the Φ is the flux through the surface surrounded by the coil.

The change of flux linkage results in a voltage in the coil (Faraday law), which is calculated by the following expression:

These formulas together define the theoretical background of the flux density (B), flux (Φ), flux linkage (ψ) and the induced voltage (e) in the electromagnetic system consists a magnetic circuit and coil(s).

Synchronous Machine Models The induced voltage in the coils of a synchronous electrical machine contain high harmonic components (beside the base harmonic). These harmonic components are a result of the saturation of the magnetic field. The superposition of voltage harmonics enables representation of each harmonics with an ideal synchronous machine model. A first electrical circuit for a base harmonic is shown in Figure 8A; and a second electrical circuit for a higher order harmonic (i.e. harmonics having a higher order than the base harmonic) is shown in Figure 8B. (The machine resistance is not considered in this model as it is not relevant for the present analysis)

The electrical machine is powered by the voltage inverter which provides base harmonic voltage on the connections of electrical machine. The inverter behaves as a short circuit for the rest of the harmonics. The currents of harmonics are limited by the inductance L _x . The inductance L _x is relatively low and this results in a high short-circuit current I _x . The short circuit current I _x could be reduced with additional inductance in series with L _x , but simple inductances in serial with the electrical machine 2 may increase the base harmonic voltage demand, and this may require filtering of the harmonics.

Filtering of the 5 ^th and 7 ^th harmonics can be implemented by subtracting corresponding orthogonal components of space vectors of the first and second three-phase winding systems of the six-phase winding (x _α1 - x _α2 and x _β1 - x _β2 ). This difference will contain the harmonics where the phase shift is 180 degree. The phase shift between the voltage, current and flux linkage harmonic components of the first and second three-phase winding systems in the six-phase electrical machine are shown in Table 1.

Table 1. Phase shift between the harmonics of the first and second three-phase winding systems in the electrical machine.

The phase shifts between the flux linkages and induced voltages in the filter 1 will now be described. The phase shift of 180 degrees means that the corresponding harmonics of the first and second three-phase winding systems are in the opposite phase and, therefore, partially or completely cancel each other. The voltage of these harmonics is at least substantially zero. The flux linkage and voltage is not zero for components where the phase shift is zero between the corresponding harmonics of the first and second three-phase winding systems. At least in certain embodiments, these voltages will balance (or reduce) the voltage difference between the electrical machine and the inverter. The phase shifts detailed in Table 2 (see below) are also valid. The phase shift between the excitations developed by current harmonics of first and second three-phase winding systems in the magnetic circuits (in the ferromagnetic cores) of the filter 1 is shown in Table 2. The excitation components (magneto motive forces -> Nl ), resulting from the current harmonics of the first and second three-phase winding systems, which order numbers are 1 (base), 11, 13, 23, 25 etc., will be in opposite phases, and will at least partially cancel each other. The fluxes in the magnetic circuits will not contain these harmonic components. The partial or complete cancelation of these harmonics will result in induced voltages in the coils of the filter 1, which do not contain these harmonics (1, 11, 13, 23, 25 etc).

The excitation components (magneto motive forces -> Nl), resulting from the current harmonics of the first and second three-phase winding systems, which order numbers are 5, 6, 17, 19 etc., will be in the phase. These components are added and the fluxes in the magnetic circuits will contain these harmonic components. This will result in induced voltages in the coils of the filter 1 containing harmonics 5, 7, 17, 19 etc.

Table 2. The phase shift between the harmonic components of two three-phase winding system in the filter

The phase shifts between the excitations developed by harmonics of the first and second three-phase winding systems in the magnetic circuits of filter.

The excitation produced by the winding topology of the electromagnetic circuit shown in Figure 7 is proportional to the difference between the components of the space vector of the first and second three-phase windings of the six-phase winding (x _α1 - x _a2 ). This approach may electrically separate the first and second three-phase winding systems and may at least partially cancel the base harmonic component in the resultant excitation. The harmonics where the phase shift between the corresponding harmonic of first and second three-phase winding system is 180 electrical degree (see Table 1) are separated from another harmonic components of system.

Expression of excitation is proportional to the difference of the orthogonal components "α” of the first and second three-phase winding systems. The difference in the corresponding orthogonal components eliminates the harmonics which are in the phase at the first and second three-phase winding systems, until harmonics are added/doubled which are in the opposite phase. The determined expression of excitation at least substantially corresponds to the or each first winding having seven (7) turns (i.e. N ₁ = 7) a 4nd the or each second winding having four (4) turns (i.e. N ₂ = 4). The error made in applying a correction from 4.04 to 4 is approximately 1%.

The initial expression for current components in the six (6) phase system are:

The six (6) phase system forms two (2) electrically isolated three (3) phase systems, which are connected in star. In the star points the arithmetical sums of currents are zero, so the two (2) three (3) phase systems determine the following relationships between the phase currents:

The expressions (11) for components x _α1 and x _α2 can be modified considered the relationships:

The I _α1 is expressed in two different way; and I _α2 is determined in three different ways (the first forms are used in the initial configuration described herein with reference to Figure 7). The different combinations of the expressions defining I _α1 and I _α2 correspond to six (6) possible configurations. The first configuration is described above. The second expression of I _al how two (2) current components, resulting in some topologies consisting of four (4) coils per magnetic loop. A topology consisting of four (4) coils on a single magnetic loop 10-1 is shown in Figure 9.

These further coil configurations (number of coils and the number of turns in a magnetic loop) are detailed in Table 3. These coil configurations are developments of the initial topology of the filter 1 described herein (corresponding to Topology 1 in Table 3). A general configuration of the coils in a single magnetic loop 10-1 is shown in Figure 9. The negative sign of turn numbers in Table 3 indicates that the coils have the opposite reference direction compared to the arrangement illustrated in Figure 9. The currents are denoted by letters “a”, “b”, “c”, “d”, “e” and“f'. The denotation of the currents and the phase shifts between the currents is used to determine the phase shifts between the currents in a magnetic loop where the indexes of currents are different form indexes in Table 3. These topologies have two (2) magnetic loops or three (3) magnetic loops.

Table 3. The number of turn and the currents

The base harmonics of currents denoted by indexes “b”, “c”, “d”, “e” and “f” are delayed compared to the current denoted by index “a”. The delays of corresponding phase currents in Table 3 compared to phase current with index “a” are as follows:

"l_b” is delayed by 30° electrical degree;

“l_c” is delayed by 120° electrical degree;

“l_d” is delayed by 150° electrical degree;

“l_e” is delayed by 240° electrical degree; and

“l _f ” is delayed by 270° electrical degree.

A schematic filter 1 having a coil configuration according to Topology 2 of Table 3 is shown in Figure X10. The filter 1 is a two (2) loop arrangement comprising a first magnetic loop 10-1, and a second magnetic loop 10-2. The coil N1 is divided into two components, having first and second turns N _{1 1 :} N _{1 2} . The filter 1 has the following configuration N _{1 1} = 3, N _{1 2} = N ₄ = 4, N ₃ = 8. A connection diagram for the filter 1 , electrical machine 2 and the inverter 5 is shown in Figure X11.

The expressions of fluxes in the first and second magnetic loops 10-1, 10-2 are as follows:

The expressions of flux linkages of phases based on fluxes in the first and second magnetic loops 10-1, 10-2 are as follows:

A schematic filter 1 having a coil configuration according to Topology 3 of Table 3 is shown in Figure X12. The filter 1 is a two (2) loop arrangement comprising a first magnetic loop 10-1, and a second magnetic loop 10-2. The coil N1 is divided into two components, having first and second turns N _{1 _1} N _{1 _2} . The filter 1 has the following configuration N _{1 _1} = 3, N _{1 _2} = N ₄ = 4, N ₃ = 8. A connection diagram for the filter 1, electrical machine 2 and the inverter 5 is shown in Figure X13.

The expressions of fluxes in the first and second magnetic loops 10-1, 10-2 are as follows:

The expressions of flux linkages of phases based on fluxes in the first and second magnetic loops 10-1, 10-2 are as follows:

A filter 1 in accordance with a further embodiment of the present invention will now be described with reference to Figure 14 The filter 1 has a core comprising first, second and third magnetic loops 10-1, 10-2, 10-3 (i.e. a triple core arrangement). The first, second and third magnetic loops 10-1, 10-2, 10-3 are in the form of respective ferromagnetic cores. The first, second and third magnetic loops 10-1, 10-2, 10-3 are disposed adjacent to each other in a non-overlapping arrangement. The filter has six (6) windings for supplying drive signals to respective phases of the six-phase electrical machine 2. The windings are wound on the first, second and third magnetic loops 10-1, 10-2, 10-3. The filter has a winding topology derived from the arrangement of the filter shown in Figure 7. A first symbol indicates a first reference direction of current flow; and a second symbol ® indicates a second reference direction of current flow. In the illustrated arrangement, the first reference direction of current flow (represented by the first symbol is out of the page; and the second reference direction of current flow (represented by the second symbol ®) is into the page. The current flowing into the page is assumed to be positive.

The filter 1 comprises three (3) of the first windings W1-n; and three (3) of the second windings W2-n. As outlined above, the first windings W1-n have a first number of turns N1; and the second windings W2-n have a second number of turns N2. The first and second numbers are different from each other. In the present embodiment, the first windings each have seven (7) turns (i.e. N ₁ =7) and the second windings each have four (4) turns (i.e. N ₂ = 4).

One of the first windings W1-n is wound on each of the first, second and third magnetic loops 10-1, 10-2, 10-3. The first windings W1-n have like winding orientations (i.e. are all wound in the same direction). As shown in Figure 14, the reference direction of the current flow in each of the first windings W1-n within an interior of the respective magnetic loops is directed out of the page. The second windings W2-n are each wound around a pair of the first, second and third magnetic loops 10-1, 10-2, 10-3. The second windings W2-n are each wound around a different pair of the first, second and third magnetic loops 10-1, 10-2, 10-3. As shown in Figure 14, the second windings W2-n are configured such that the reference direction of the current flow in the second windings W2-n within an interior of the respective magnetic loops 10-1, 10-2, 10-3 are in opposite directions. Thus, within each of the magnetic loops 10-1, 10-2, 10-3, the reference direction of the current flow in one of the second windings W2-n within each magnetic loop is directed in a first direction (out of the page in the illustrated arrangement), and the reference direction of the current flow in the other one of the second windings W2-n within the same magnetic loop is directed in a second direction (into the page in the illustrated arrangement). This is achieved by winding the second windings W2-n within each of the first, second and third magnetic loops 10-1, 10-2, 10-3 in opposite directions. Thus, the two second windings W2-n on the first magnetic loop having opposing winding orientations (i.e. are wound in opposite directions); the two second windings W2-n on the second magnetic loop have opposing winding orientations (i.e. are wound in opposite directions); and the two second windings W2-n on the third magnetic loop have opposing winding orientations (i.e. are wound in opposite directions).

The filter 1 is configured to maintain the symmetry in the two three-phase winding systems. The filter 1 keeps the symmetry between the phases of the three-phase winding systems. This helps to avoid indirect components in the phase winding systems. The flux linkages can be determined on the basis of fluxes of separated magnetic circuits. These fluxes are:

The flux linkages of individual coils are equivalent to the product of flux passing through the surface surrounded by the coil and by the number of turns.

The flux linkage space vectors are illustrated in Figure 15. The resultant flux linkage components and the voltages generated by the change of these flux linkages of two different phase winding systems are in the opposite phase winding systems in the filter 1. The base harmonics of these voltages are neglected, since the excitation of the base current harmonics are cancelled by the winding system.

The generated voltages in the two three-phase winding systems are in the opposite phase compared to those voltage harmonics, which resulted in the corresponding currents in the coils of the filter. This effect will reduce the current harmonics of the electrical machine.

The magnetic circuit comprises a core having first, second and third magnetic loops 10-1, 10-2, 10-3 which are made from a ferromagnetic material (having a high magnetic permeability). The first, second and third magnetic loops 10-1, 10-2, 10-3 generally comprise a ring (torus). Other shapes can be used to form the first, second and third magnetic loops 10-1, 10-2, 10-3. For example, the first, second and third magnetic loops 10-1, 10-2, 10-3 may each comprise a polygon, such as a square or a rectangle. The first, second and third magnetic loops 10-1, 10-2, 10-3 may each be formed from a plurality of laminations. This winding configuration provides the appropriate operating characteristics of the filter 1 and the proper induced voltages in the corresponding phases of an asymmetrical six-phase winding system. A filter in accordance with a further embodiment of the present invention will now be described with reference to Figure 16. The filter comprises a core having first and second magnetic loops 10-1, 10-2 (i.e. a double core arrangement). Each of the magnetic loops is in the form of a ferromagnetic core. The first and second magnetic loops 10-1, 10-2 are disposed adjacent to each other in a non-overlapping arrangement. The filter has six (6) windings for supplying drive signals to respective phases of the six-phase electrical machine. The windings are wound on the first and second magnetic loops 10-1, 10-2. The filter has a winding topology derived from the arrangement of the filter shown in Figure 7. A first symbol indicates a first reference direction of current flow; and a second symbol indicates a second reference direction of current flow. In the illustrated arrangement, the first reference direction of current flow (represented by the first symbol is out of the page; and the second reference direction of current flow (represented by the second symbol is into the page. The current flowing into the page is assumed to be positive. The first and second reference directions of the current flow are dependent on the winding orientation of the coils. For example, the current flow in coils having opposing winding orientations will be in opposing reference directions. A coil having a first winding orientation will have current flow in a first reference direction; and a coil having a second winding orientation will have current flow in a second reference direction. The first and second reference directions being opposite to each other.

The filter 1 comprises two (2) of the first windings W1-n; and four (4) of the second windings W2-n. The first windings W1-n have a first number of turns N1; and the second windings W2-n have a second number of turns N2. The first and second numbers are different from each other. In the present embodiment, the first windings each have seven (7) turns (i.e. N ₁ =7) and the second windings each have four (4) turns (i.e. N ₂ = 4).

One of the first windings W1-n is wound on each of the first and second magnetic loops 10-1, 10-2. The first windings W1-n have like winding orientations (i.e. the first windings W1-n have the same winding direction). As shown in Figure 16, the current flow in each of the first windings W1-n is in a first reference direction (directed out of the page). The second windings W2-n are each wound around one of the first and second magnetic loops 10-1, 10-2. In the present embodiment, the second windings W2-n are not wound around a pair of the magnetic loops. As shown in Figure 16, the second windings W2-n are configured such that the current flow in the second windings W2-n are in opposing first and second reference directions. Thus, within each magnetic loop 10-1, 10-2, the current flow in one of the second windings W2-n within each magnetic loop 10-1, 10-2 has a first reference direction (out of the page in the illustrated arrangement), and the current flow in the other one of the second windings W2-n within the same magnetic loop 10-1, 10-2 has a second reference direction (into the page in the illustrated arrangement). This is achieved by ensuring that the second windings W2-n within each of the first and second magnetic loops 10-1, 10-2 having opposing winding orientations (i.e. are wound in opposite directions). Thus, the two second windings W2-n on the first magnetic loop have opposing winding orientations (i.e. are wound in opposite directions); and the two second windings W2-n on the second magnetic loop have opposing winding orientations (i.e. are wound in opposite directions).

The fluxes are expressed as follows:

And the flux linkages on the basis of fluxes:

As the excitation N ₁ I _α + N ₂ (I _d - / _b ) is proportional to the difference of “α” components of current space vectors of two three- phase winding systems in the expression of Φ ₁ , and the excitation N ₁ I _f + N ₂ (I _C - I _e ) is proportional by the difference of “β” components of current space vectors of two three-phase winding systems in the expression of </> ₂ , and components “a” and “β” are shifted by 90 degree in the time, then Φ ₁ and Φ ₂ will be shifted with 90 degree in the time. This phase shift will be valid for coil voltages as well, because the induced voltages in the coils are the first derivative of the flux linkage by time.

The phasors of the flux linkages of the windings of a first and second three-phase system are shown in Figure 17A; and the phasors of the voltages of the first and second three-phase system are shown in Figure 17B. The line voltages of two three-phase winding systems (ace) and (bdf) forms triangles, which relative lengths are 8, These triangles are very similar to the triangle of line voltages in the three-phase winding systems, and a good approximation (ace) and (bdf) could be considered as two three-phase winding systems.

The coil and line voltages phasors of two three-phase systems are illustrated in Figure 18. The line voltage can be determined on the basis of following expressions:

The line and phase voltage phasors of the two three-phase winding systems in the filter 1 are illustrated in Figure 18. The line voltages determine the phase voltages of the three-phase winding systems. The relationships between the line and phase voltages are defined as follows: It can be determined that the filter 1 composed of first and second magnetic loops 10-1, 10-2 results in two three-phases systems similar to the filter 1 having first, second and third magnetic loops 10-1, 10-2, 10-3. Thus, the filter 1 with two magnetic loops 10- 1, 10-2 behaves in a similar manner to the filter 1 with first, second and third magnetic loops 10-1, 10-2, 10-3. The differences are described below.

Simulations

Filter 1 comprising a core with three (3) magnetic loops 10-1, 10-2, 10-3: This filter 1 maintains symmetry in a three-phase winding system, such that the peak values of base harmonics of “a” and “β” components in a three-phase winding system are equivalent difference can be observed between the peak currents of two different two phase winding systems, The difference is less than 1% of corresponding currents, which is acceptable (currents with index “1” are determined by phases “ace” and currents with index “2” are determined by phases “bdf”).

Filter with two (2) magnetic loops 10-1, 10-2: At this system the peak values of “a” and “β” components are different in a three- phase winding system (at both three-phase winding system it can be observed) the difference is approximately lower than 1 % of the corresponding values, but the orthogonal components of different three-phase winding system are approximately equivalent (currents with index “1” are determined by phases “ace” and currents with index “2” are determined by phases “bdf’).

Turn Ratio

The ratio of the number of turns on the filter 1 and the electrical machine 2 will now be considered. The initial turn ratio of coils of the filter 1 is 4n the simulation of system which consists of filter 1 and six-phase electrical machine. This turn ratio is suitable for machine topologies where the turn ratio of the phase windings of the first and second three-phase winding systems of the asymmetrical six-phase machine 2 is In the presented expressions N ₁ and N ₂ are the turn numbers in the filter 1. N _1f is the effective turn number of phase winding of the first three-phase system; and N _2f is the effective turn number of the phase winding of the second three-phase winding system. The effective turn number of the phase windings are calculated by the following equations:

Where:

N _x _conductors the number of conductors in the stator slots belonging to the phase system “x”, a _x the number of parallel paths in the phase system “x”, k is a coefficient.

The coefficient k is set as one (1) when the phase system “x” is connected in a star configuration; and is set as the square root of three when the phase system “x” is connected in a delta configuration.

SUBSTITUTE SHEET (RULE 26) The ratio of the first number of turns (N1) in the or each first windings to the second number of turns (N2) in the second windings in a symmetrical filter 1 (having three (3) magnetic loops) for an asymmetrical six-phase system will now be described. The turn ratio (N 1 :N2) of the first and second windings in the filter 1 is determined as follows:

Where the current in the first three-phase winding systems flows through coils having index “1”; and the current in the second three-phase winding systems flows through coils having index “2”. In this case only one turn number ratio can be defined, because the currents of the phase system “1” flow in the first windings (having turn number N ₁ ) of the filter 1 ; and currents of phase system “2” flow in the second windings (having turn number W ₂ ) of the filter 1.

The ratio of the turns of an asymmetrical filter 1 (having two (2) magnetic loops) will now be described. The turn ratio of the first and second windings on the first magnetic loop is defined by the following equation:

Where the current of phase system “1” flows through the coil N ₁ .

The turn ratio of the first and second windings on the second magnetic loop is determined as follows:

Where the current of the other one of the two three-phase winding systems flows through the coil N ₁ . This means the turn ratios at asymmetrical filter 1 are different at the two magnetic loop, because the currents of coils with index “1” belong to different three- phase winding systems.

In this example, the ratio of the effective number of turns of the first and second three-phase winding systems are multiplied by a constant (referred to herein as a modulation constant). The modulation constant has a value of 7/4 in the above embodiment. Different modulation constants may also be employed. For example, the modulation constant may be selected from the range 1.2 to 2.33 inclusive (corresponding to a range from 6/5 to 8/3 inclusive); or from the range 1.4 to 2 inclusive (corresponding to a range from 7/5 to 8/4 inclusive). In a variant, the modulation constant may, for example, be 13/8 or 15/8.

Core Topology

The filter 1 has been described herein as comprising a core having one or more magnetic loops 10-n. The magnetic loops 10-n have been described as being annular or toroidal in shape. The magnetic loops 10-n may have different shapes. A variant of the filter 1 described herein with reference to Figure 14 is shown in Figure 20. In this variant, each of the first, second and third magnetic loops 10-1, 10-2, 10-3 form a sector of a circle (bounded by two radii and an arc). In particular, the first, second and third magnetic loops 10-1, 10-2, 10-3 each comprise an outer wall 17 and first and second sidewalls 18-1, 18-2. An aperture 19-1, 19-2, 19-3 is

SUBSTITUTE SHEET (RULE 26) formed in each of the first, second and third magnetic loops 10-1, 10-2, 10-3. The outer wall 17 comprises a circular arc; and the sidewalls 18-1, 18-2 each comprise a radial wall. The first, second and third magnetic loops 10-1, 10-2, 10-3 form sectors of a circle and can be assembled to form a core 15 having a circular profile. Each sector in this arrangement has an internal angle of 120°. The arrangement of the core in the reduces the overall dimensions of the filter 1. The magnetic loops 10-n are formed by separate components in this arrangement. One or more fasteners may be used to fasten the magnetic loops 10-n. The configuration of the first and second windings in the filter 1 is unchanged from the arrangement shown in Figure 14. Other interlocking shapes are contemplated for the first, second and third magnetic loops 10-1, 10-2, 10-3.

A further variant of the filter 1 is shown in Figure 21. The filter 1 is similar to the arrangement shown in Figure 20. In particular, the first, second and third magnetic loops 10-1, 10-2, 10-3 each comprise a sector having an internal angle of 120°. In the present arrangement, the first, second and third magnetic loops 10-1, 10-2, 10-3 are formed integrally in a core 15. The core 15 comprises an outer wall 17 and three internal walls 18-1, 18-2, 18-3. The core 15 comprises three internal apertures 19-1, 19-2, 19-3 formed between the internal walls 18-1, 18-2, 18-3. The outer wall 17 in the present embodiment comprise a circular cylinder, but other profiles are also contemplated. The internal walls 18-1, 18-2, 18-3 have an angular spacing of 120° and define the sectors of the filter 1. The first and second windings are wound around the outer wall 17 and the internal walls 18-1, 18-2, 18-3. The configuration of the first and second windings in the filter 1 is unchanged from the arrangement shown in Figure 14.

Magnetic Loops

The reference directions of the current flow in the coils forming the first and second windings are the same in each of the topologies described herein. The coils and magnetic loops determine mutual connections, which may be referred to as linkage. A coil is linked with a magnetic loop if the amper-turn (Nl) is taken into account in the expression of the magneto-motive force (excitation Nl). The flux in the loop is taken into account in the flux linkage (ψ = N Φ ) of the winding. By way of example, a winding with l_a current is linked with a first magnetic loop, until the coil with l_b current is linked with the first magnetic loop and the third magnetic loop

By appropriate design of the magnetic circuits described herein (for example comprising selection of appropriate cross sections of the magnetic loops), it is possible to implement a filter 1 having different topologies but exhibiting at least substantially equivalent electromagnetic characteristics. Despite the different shapes of the magnetic loops, the electromagnetic coupling of the windings and the magnetic loops are at least substantially equivalent in the topologies described herein. These topologies are effectively electromagnetically equivalent to each other and implement the same filter 1 function.

Three-phase Inverter

In the arrangement illustrated in Figure 1, the inverter 5 is a six-phase inverter configured to generate six (6) drive signals which are applied to respective phases of the six-phase electrical machine 2. The filter 1 is connected to the six-phase inverter 5 and modulates the drive signals applied to the electrical machine 2. In a variant, the filter 1 may be configured to enable the six-phase electrical machine 2 to receive drive signals generated by a 3-phase inverter.

As described herein, the electrical machine 2 comprises first and second three-phase winding systems. As shown in Figure 22, one of the first and second three-phase winding systems may be short-circuited. In this arrangement, the filter 1 may be configured to receive a three-phase signal from the inverter 5. The short circuit of one of the three-phase winding systems can be implemented

SUBSTITUTE SHEET (RULE 26) between the inverter and filter 1. The short-circuit may be implemented by controlling the inverter 5, for example in hardware or software. The currents of three-phase winding system which is powered by three-phase inverter will have a slightly higher current, because it has to provide the magnetising current of magnetic circuit in the filter 1.

The different topologies of the filter 1 described herein, for example comprising two (2) or three (3) magnetic loops, can be used in conjunction with a three-phase inverter 5 to apply drive signals to a six-phase electrical machine 2. The simplified filter with two cores (magnetic circuits) results in a slightly higher asymmetry in the currents. The current harmonics content of machine current are relatively low. In the two core filter, the torque ripple may increase by approximately 1-2% of the machine torque.

The simulation results of a filter 1 having first and second magnetic loops 10-1, 10-2 for the three-phase inverter 5 configuration shown in Figure 22 are shown in Figures 23A-E. The six phase currents are shown in Figure 23A. The torque spectrum is shown in Figure 23B; and the torque harmonics are shown in Figure 23C. The highest torque harmonic in this simulation is approximately 0.06 Nm which is less than 2% of the average torque. The simulated torque spectrum and torque harmonics show that machine torque ripples are similar or unchanged when the six-phase electrical machine 2 is powered by the three-phase inverter. Figure 23D shows the current spectrum. A first plot (system “a”) represents the base harmonics provided by the inverter; and a second plot (system “b”) represents the base harmonics of the current in the short-circuited coils. It will be noted that the high harmonics are lower than the base harmonics. Figure 23E shows the high harmonics and illustrates that the high harmonics are less than 1 % of the base harmonics. A first plot (system “a”) represents the high harmonics provided by the inverter; and a second plot (system “b”) represents the high harmonics of the current in the short-circuited coils.

The simulation results of a filter 1 having first, second and third magnetic loops 10-1, 10-2, 10-3 for the three-phase inverter 5 configuration shown in Figure 22 are shown in Figures 24A-E. The six phase currents are shown in Figure 24A. The torque spectrum is shown in Figure 24B; and the torque harmonics are shown in Figure 24C. Figure 24D shows the current spectrum and illustrates that the high harmonics are lower than the base harmonics. A first plot (system “a”) represents the base harmonics provided by the inverter; and a second plot (system “b”) represents the base harmonics of the current in the short-circuited coils. Figure 24E represents the high harmonics. A first plot (system “a”) represents the high harmonics provided by the inverter; and a second plot (system “b”) represents the high harmonics of the current in the short-circuited coils.

The line voltages of the inverter 5 are illustrated in Figure 25.

The filter 1 offers certain advantages over prior art arrangements. For example, the filter 1 may enable the six-phase electrical machine 2 to be driven by either a six-phase inverter or a three-phase inverter without modification. This may be desirable as three-phase inverters are typically less expensive since it contains fewer high-power semiconductor components (approximately half the number of components).

The filter 1 enables operation of the six-phase electrical machine 2 with either a three-phase inverter 5 or a six-phase inverter 5. The three-phase inverter 5 or the six-phase inverter 5 can be used without modifying the electrical machine 2. This enables dynamic switching of the electrical supply to the filter 1, for example to switch from a six-phase supply to a three-phase supply and vice versa. When used in conjunction with the filter 1 described herein, the six-phase inverter 5 may be dynamically controlled to operate either as a three-phase inverter or as a six-phase inverter. To operate as a three-phase inverter 5, a short circuit may be implemented, for example using appropriate software control. The six-phase inverter 5 may be dynamically switched between three-phase and six-phase operation in dependence on the operating conditions of the electrical machine 2. For example, when

SUBSTITUTE SHEET (RULE 26) the electrical machine 2 is operating at low speed (where the machine power is low at high current values), a short circuit may be implemented (using appropriate software or hardware control) to operate as a three-phase inverter. As a result, fewer high-power components in the inverter have to perform switching and this may result in improved efficiency. For example, switching of the high-power components may be reduced to one turn-off and one turn-on per electrical cycle of base harmonic, compared to more than one hundred until at the non-short circuited three-phase winding system. This may lead to lower overall losses in the inverter

5 at the same power, thereby improving the inverter efficiency.

It will be appreciated that various changes and modifications can be made to the present invention without departing from the scope of the present application.

SUBSTITUTE SHEET (RULE 26)