Technical Field

1. The present technology relates generally to multiphase electrical machines and systems and methods for their design and control. Certain embodiments find par ticularly effective application in Permanent Magnet Synchronous machines

(PMSMs) and reluctance machines.

Background

2. Permanent magnet synchronous machines (PMSMs) have been found to be more useful for many applications than conventional induction machines, switched reluc tance machines, and field-excited synchronous machines because of their superior performance, compact size, high torque density, and higher efficiency. PMSMs are now widely deployed in applications ranging from home appliances to electric ve hicles and safety critical applications such as drones and aircrafts. The basics for understanding the most common types of PMSMs, fundamentals of their opera tion, and their electromagnetic mechanism are set out below.

3. A PMSM comprises a stationary stator and a rotating rotor separated by an airgap.

The stator comprises a set of rectangular coils, each placed in a slot. The coils are connected in series to make a set of windings in a way that injection of current creates a rotating magnetic field in the air gap, the magnetic field having a plurality of magnetic poles. The stator can be three or more phases (multi-phase). The permanent magnet (PM) rotor comprises PMs either placed on the rotor surface, or buried inside the rotor iron such that the PM flux density in the airgap maintains the same number of magnetic poles as the stator. In a PMSM, mechanical motion is generated by locking of the rotor magnetic poles on to the magnetic poles of the stator rotating magnetic field, causing the rotor to be dragged along and rotate.

Stator winding in a PMSM

4. The stator winding configuration in a PMSM affects energy transfer phenomena and the strength and number of poles of the rotating magnetic field. A winding con figuration is identified by the simplest form of its slots-per-pole-per-phase ratio, de noted by ^S PP’ and given by: where Q is the number of slots, P is the number of poles, m is the number of phases, x is the numerator for the simplest possible fraction in (1), and c is the de nominator. Throughout this document, ^S PP is referred to as the“class” of a PMSM.

In order to facilitate a symmetrical distribution of all the phase windings in the sta tor, the number of slots associated with each phase winding must be the same; therefore, the number of stator slots, Q, must be an integer multiple of the number of phases, m.

Equation (1) is indivisible as ^S PP indicates the simplest form of a fraction. There fore, the number of poles for a PMSM of a certain class is a multiple of the denom inator of its ^S PP’ e.g. for a three-phase PMSM of class 3/7 where the stator has 18 slots, the number of poles is equal to 14. Note that in any PMSM, the number of poles is always an even number to maintain a balance between the north-poles and south-poles of the magnetic field; i.e. the number of north-poles is equal to the number of south-poles.

PMSMs are commonly categorized with respect to their rotor and stator types. The stator utilized in a PMSM is usually from one of the two following families:

• Distributed-wound (DW) stators

• Fractional-slot concentrated-wound (FSCW) stators, commonly single layer or double-layer.

Among these two stator families, DW stators are the major stator type convention ally used in PMSMs because of the following major reasons:

a. They have a history of more than a century through which they have not changed much;

b. Their theory is well developed through years of utilization and trial and error;

c. They have a near-sinusoidal magneto-motive force (MMF);

d. They have a high main harmonic winding factor, resulting in a high average torque density.

However, from a performance point of view, DW PMSMs suffer from a high torque ripple that can sometimes exceed 30% of the average torque. Moreover, they don’t perform well under an electrical fault.

It was not until recently that it was disclosed that FSCW stators with the right com bination of slots and poles can also produce a high main harmonic winding factor which facilitates a high average torque. This prompted investigations into FSCW PMSMs in the last decade showing they are superior to DW PMSMs in some as pects, including: a. Torque ripple in a PMSM that utilizes a FSCW stator is several times lower in magnitude compared with the conventional DW PMSMs;

b. Cogging torque in FSCW stators is much less than DW stators; c. FSCW stators require less copper compared with the convention al DW stators, which makes them cheaper, lighter in weight, more compact, higher in torque density, and more efficient when it comes to ohmic losses. This feature is brought about because of shorter end-windings in FSCW stators compared with DW stators;

d. FSCW stators are easier to manufacture compared with their DW counterparts;

e. FSCW stators have a wider field-weakening region due to the higher self- inductance;

f. Certain topologies of FSCW stators feature a very low mutual in ductance compared with their self-inductance, which brings about a better fault tolerant capability.

There are drawbacks in FSCW machines including as associated complexity of electromagnetic analysis of FSCW stators; immature theory, higher eddy current losses, as well as complicated thermal management.

Various slot and pole combinations for FSCW machines and design considerations for obtaining an optimal design have been investigated.

Different FSCW PMSMs having different winding types are used in different applications, some having been found to have been more useful in some applications than others.

Electromagnetic principles and analysis of FSCW stators

FSCW stators are generally found to be grouped as set out below:

Single-Layer FSCW stators;

Double-Layer FSCW stators. Each of the above groups is generally divided into two sub-categories:

Sub-category 1 : Winding configurations that have a zero net mag netic pull;

Sub-category 2: Winding configurations that have a non-zero net magnetic pull. The various FSCW stator categories have similar working principles and electro magnetic analysis. Performance characteristics of electric machines are depen dent on their stator magnetomotive force (MMF) which is determined by the stator winding configuration. These will be discussed in the following.

Principles of MMF in a FSCW Stator

In an FSCW stator, each coil is wound around a single tooth, resulting in a winding span of 2 tt/Q. The magnetic field intensity, H, and the flux density, B, inside a ma terial with permeability m have the following relationship:

where and is the relative permeability.

We turn now to considering a single-coil FSCW stator. The direction of the cur rent in a typical coil is such that the field is projected out of the stator tooth into the air-gap. The air-gap MMF due to the single coil can be found from Ampere’s law in combination with Gauss’ law. From Ampere’s law, the line integral of the magnetic field intensity along a closed path called“Ampere’ s path" is equal to the net cur rent, /, enclosed within the path: where r is the Ampere’s path.

In a (/-slot FSCW stator each coil is wound around a single tooth, for which the spatial MMF distribution is a square pulse with its width equal to 2 ixJQ mechanical radians. Thus, the spatial MMF distribution of a single coil is a function of time and space and can be expressed by

where/is the MMF in Ampere-turns, 0 _V is the stator peripheral angle in mechanical radians, N _c is the number of turns in the coil, and i _j is the instanta- neous current in Amperes that flows through phase j winding in which the coil ex ists.

19. The present technology seeks to provide a machine controller, a method of ma chine control, a multi-phase electric machine drive system and a method for its de sign, that is configured to operate under one or more electrical fault conditions with reduced torque ripple or at least not introducing any new sources of torque ripple or at least an optimised torque response.

Summary

20. Broadly, the present technology provides a new class of multiphase electric ma chine drive system that is configured to inhibit an increase in torque ripple under post-fault operating conditions of

a. single or multiple open-phase faults, and/or b. single or multiple semiconductor failures, such as for example in an open ended winding configuration a switch fails in an inverter leg connected to a winding.

21. Broadly, the present technology also provides a robust multi-phase electric ma chine drive system which is configured to tolerate fault conditions of one or more open-phases or one or more semiconductor switch failures.

22. Broadly, the present technology yet further provides a method of remediating MMF in post-fault multi-phase machines, where the fault is caused by one or more open- phases or one or more semiconductor switch failures. The type of remediation de ployed depends on the fault diagnosed, which is then is used to control the ma chine, post-fault.

23. The present technology, in one aspect, provides a multi-phase electric machine system which is tolerant to one or more types of open-phase or semiconductor faults which includes:

a controller configured to inject a resultant current waveform, including one or more selected types of zero-sequence current and one or more pre-fault cur rents, into a multiphase electric machine during an open-phase or semiconductor fault; and

a multiphase electric machine configured to interact with the injected resul tant current, such that one or more harmonic winding factors that interact in the machine with the one or more zero sequence currents are zero. In operation, the advantage of the structural feature of the electric machine is that it is resistant to injection of zero-sequence current. In other words, injection of zero-sequence cur rents does not contribute to an increase in torque ripple.

In accordance with one aspect of the technology, there is provided a multi-phase UWF electric machine, which is one which has a Unidirectional Winding Function. The UWF arrangement of the multi-phase electric machine is one wherein a wind ing function, associated with a single phase of a stator winding, obtained by adding individual winding functions associated with each coil in that phase, has the condition set out below:

a plurality of coils in a phase winding are arranged such that they have the same polarity. In operation of preferred embodiments, the winding function under the tooth associated with each coil (which is resulted from that coil only) for all the winding coils are all either positive, or negative.

Advantageously, the multi-phase UWF electric machine is tolerant to various kinds of electrical faults, including one or more open-phase faults and one or more semi conductor switch failures.

In one embodiment there is provided a stator with a high main harmonic winding factor. In one embodiment, the high main harmonic winding factor is between about 0.65 and 1 and could be 0.7, 0.75, 0.8, 0.85, 0.9, 0.95 or values therebe tween.

In one embodiment there is provided a UWF machine which is tolerant to electrical faults such that, during a fault, one or more phases is injected with currents such that there is about the same, or lower, or at least substantially no more torque rip ple than existed before the fault. In one embodiment the currents injected are zero- sequence currents, superposed on pre-fault waveforms. In one embodiment the current the zero sequence current could be square wave, triangular waves, half sine wave, sine wave, DC currents, rectangular or suitable waveforms. Any one or combination of harmonic currents that can be injected to heal the MMF are con templated to be useful.

In some embodiments, the machine includes a stator which exhibits a zero net magnetic pull and includes an even number of pole pairs.

In some embodiments, the machine includes a stator which includes FSCW stators with a non-zero net magnetic pull and includes either an even or an odd number of pole pairs.

In operation, embodiments of the present technology inhibit, minimise, or provide substantially no increase in torque ripple caused by the fault.

Embodiments of the present technology in operation provide zero-sequence injec tion to remediate the MMF such that the MMF will adopt a shape similar to that during the pre-fault condition, in other words, with the same or substantially similar spatial harmonic content. In some embodiments that spatial harmonic content is at a relatively lower amplitude.

Embodiments of the present technology seek to manipulate the post-fault MMF in a rotor-stator air gap of an electric machine using zero-sequence current injection so that the MMF maintains a similar shape to the pre-fault condition, thus similar spatial MMF harmonics. In some embodiments the harmonics and/or average torque are at lower amplitudes. In selected applications such as FSCW stators, the method takes advantage of a magnetic coupling between the stator teeth that al lows manipulation of the MMF under one tooth by manipulation of the MMF under adjacent or other more distal teeth.

Thus, the technology provides, in a broad aspect, a method of manipulation of MMF in a multi-phase electric machine by superimposed injection of selected zero- sequence currents into the faulted and/or non-faulted phases in accordance with one or more diagnosed faults. The arrangement is such that when an electrical fault is diagnosed, an algorithm is solved to identify appropriate zero-sequence current for the remediation of that kind of fault, and that zero-sequence current is then superimposed on the pre-fault current to the faulted and/or non-faulted phas es.

In accordance with an aspect of the present technology there is provided a system for manipulation of MMF in a multi-phase electric machine, the system including: a computer processing system including:

a diagnostic engine configured to be wirelessly or otherwise con nected to the multi-phase electric machine, for identifying and/or recording a type of fault in the electric machine and selecting data relating to an appropriate zero- sequence current waveform to inject that zero-sequence current waveform (to gether with one or more pre-fault current waveforms) into one or more faulted and/ or healthy phases of the electric machine based on a machine fault type;

a modulation engine for arithmetically resolving a resultant current waveform being a pre-fault waveform and the zero-sequence waveform so that the injected waveform can be utilised in a controller connected to an inverter drive unit. In an embodiment the system includes a monitor wirelessly or otherwise connected to the multi-phase electric machine for monitoring one or more machine para meters and sending data to the diagnostic engine.

In accordance with one aspect of the technology there is provided a method for manipulation of post-fault MMF in a multi-phase electric machine, the method in cluding the steps of:

identifying and/or recording, in a computer processing system, one or more pre-fault current waveforms in the multi-phase electric machine; and, after a fault, selecting, by a computer processing system, an appropriate zero-sequence waveform to inject, together with the pre-fault current, into one or more faulted and/ or healthy phases of the electric machine based on a machine fault type;

resolving, in a computer processing system, a resultant current waveform being a resultant of the pre-fault waveform and the zero-sequence current wave form so that the resultant injected waveform can be utilised in a controller connect ed to an inverter drive unit.

In one embodiment the method includes the step of generating data relating to a suitable winding configuration of the electric machine by an optimisation engine. In one embodiment the optimisation engine provides winding configuration data in accordance with an algorithm, which selects for the highest main harmonic winding factors in a selected winding topology of phases, slots and poles.

In one embodiment the optimisation engine provides FSCW winding configuration data which include unidirectional winding functions.

In one embodiment the method includes the step of injection of currents from an inverter drive into the electric machine according to the resultant current waveform generated.

In one embodiment the optimisation engine includes a computer system which im plements an optimisation method including the steps of:

generates data relating to a plurality of possible winding topologies based on a selected plurality of phases, slots, and poles;

identifying topologies with a UWF characteristic;

calculating a plurality of harmonic winding factors for one or more of the possible winding topologies;

categorising the generated topology data based on their associated har monic winding factors; and

selecting a winding topology configuration with the highest main harmonic winding factor.

In one embodiment, lower main harmonic winding factors are assigned a higher weight to influence the selection of a winding topology configuration.

In one embodiment the weight depends on the PM flux density.

In one embodiment a winding performance index (WPI) is utilised to provide a small number of eligible winding configurations. In one embodiment a winding de sign engine selects the best-performing winding configuration (in other words, the highest). The winding design engine in one embodiment processes the WPI and then compares the harmonic winding factors of the winding configurations and se lects the highest or higher.

The winding performance index is:

is the per unit value of and dependent on rotor structure.

In one embodiment the optimisation engine generates the winding topology data based on an algorithm described herein.

In one embodiment the categorising step involves ranking the harmonic winding factors according to a torque waveform harmonic.

In one embodiment the categorising step involves assigning a weighting factor to one or more of the harmonic winding factors in accordance with an algorithm. In one embodiment there is also provided a step of differentiating between eligible winding topologies on the basis of a Winding Performance Index which weights the main harmonic winding factors and generates an index for recognising the winding topology with the highest average torque.

In one embodiment the injected zero-sequence current is the current required to be added to the pre-fault currents such that a state similar to the faulty condition is maintained.

In one embodiment the injected zero-sequence currents is the inverse of the pre fault currents flowing through one or more open-phases.

In one embodiment the injected zero-sequence current waveform is a positive or negative dc-offset wave.

In one embodiment the injected zero-sequence dc offset current has an amplitude substantially equal to or higher than the amplitude of one or more post-fault healthy-phase currents. In one embodiment the injected zero-sequence current is a positive or negative half-wave of the pre-fault current flowing in the one or more post-fault phases. In one embodiment the RMS values of the combined currents are calculated and then the injected post-fault currents are moderated so that the current flowing in the machine does not exceed the rated RMS.

In one embodiment the multiphase electric machine is a FSCW PMSM.

In one embodiment the multiphase electric machine is open ended or star con nected wherein the centre of the star is connected to an inverter leg.

In one aspect of the present invention there is provided a method of control of mul ti-phase electric machines under fault conditions of one or more open phases, the method including the step of manipulating MMF in a computer processing system by:

identifying, in a computer processing system, one or more post-fault current waveforms resulting from a fault in the multi-phase electric machine;

selecting, by a computer processing system, an appropriate zero-sequence waveform to inject into one or more fault or non-fault phases of the electric ma chine based on the machine fault type;

resolving, in a computer processing system, a current waveform being a resultant of the pre-fault waveform and the zero-sequence waveform so that the injected waveform can be utilised in a controller connected to an inverter drive unit; and

injection of currents from an inverter drive into the electric machine accord ing to the resultant current generated.

In one embodiment there is provided a closed-loop current PI control system for receiving resolved waveform data and providing phase voltage reference data to an inverter drive unit for controlling the multi-phase electric machine.

In one embodiment, an optimisation engine receives data from sensors monitoring back-EMF and one or more phase currents.

In one embodiment an optimisation engine operates offline during the fault condi tion. In one embodiment the optimisation engine operates online during the fault condition.

In one embodiment there is provided an online database or lookup table config ured to be consulted by the controller during the fault condition.

In one embodiment the controller consults the lookup table to retrieve the current phasor references for use in online development of a post-fault FOC transforma tion matrix. Further aspects of the technology summarised

64. Broadly, the present technology also provides a method of optimising the design of elements of a new electrical machine wherein a winding topology includes high main harmonic winding factors close to unity. The method is advantageous be cause high main harmonic winding factors facilitate a high average developed torque, thus a higher torque density.

65. Broadly the present technology still further provides a method of optimising a multi phase electric machine drive design which is tolerant to fault conditions of one or more open-phases or one or more semiconductor switch failures.

66. In accordance with one aspect of the present invention there is provided a method of optimising the design of elements of an electrical machine for fault tolerance, the method including the steps of,

generating, in a computing processor, data relating to a plurality of possible winding topologies that feature unidirectional winding functions for a selected plu rality of phases, slots, and poles;

calculating in a computing processor a plurality of harmonic winding factors for one or more of the possible winding topologies;

categorising, in a computing processor, the generated topologies based on their main harmonic winding factors,

selecting in a computing processor, the winding topology with the highest main harmonic winding factor associated with the average output torque.

Definitions

67. Throughout the specification and the claims that follow, the following phrases and terms are to be understood as follows:

Harmonic winding factors

68. Harmonic winding factors are used to determine the weight of each spatial MMF harmonic in generating the back-EMFs, PM flux linkages and consequently the electromagnetic torque. Regardless of the ^S PP value, harmonic winding factors of an m-phase machine can be calculated by dividing the amplitude of their respec tive spatial winding function harmonic by a scaling factor: where is the scaling factor for the spatial winding function harmonic. This

scaling factor is considered as the amplitude of the spatial winding function harmonic

associated to a hypothetical single-coil phase winding with Q/m turns that spans p radians around the stator circumference, obtained using the Fourier series as:

Main harmonic winding factor

66. Stator topologies are evaluated based on their main harmonic winding factors which are associated with the main spatial harmonics of their winding function. A main harmonic winding factor of order hP/2 is referred to as the main harmonic winding factor. Maximum possible value of a winding factor is equal to unity. High main harmonic winding factors are desirable as they indicate a better utilization of the stator and hence higher main harmonic back-EMFs, PM flux linkages, and av erage electromagnetic torque. These performance characteristics are directly pro portional to their harmonic winding factors. Main harmonic winding factors of a smaller order are less important than higher order ones.

67. A 5-phase 48-pole 50-slot PMSM will be studied for better understanding of the theory explained in previous sections. This slot/pole combination is associated with the base winding configuration for stator class as they result in a peri

odicity of 2.

68. The standard winding configuration (benchmark) for one phase of the 5-phase 48- pole 50- slot FSCW stator obtained using standard approaches is shown below at (a) together with an alternative design for this slot/pole combination at (b).

The winding layout associated to the remaining phases are obtained by shifting the winding configurations of (a) and (b) by kn/m radians. The winding functions asso ciated to the base winding configurations of (a) and (b) are obtained as shown be low in (a) and (b), respectively.

The associated harmonic winding factors for the spatial harmonics of the wave forms shown in (a) and (b) above are obtained using the explained methodology as shown overleaf in (a) and (b), respectively.

71. The values for the main harmonic winding factors of (a) and (b) above, are shown below in the table. It can be seen that both Design A and Design B feature close to unity main harmonic winding factors, indicating that these winding configurations will have a desirably high torque density. Among the two main harmonic winding factors listed in the table below, the first main harmonic winding factor is more im portant and carries a higher weight in torque production.

Not every winding configuration will produce high main harmonic winding factors. For a 50-slot double layer FSCW stator, 2000 distinct valid winding configurations can be generated that yield 48 poles in the airgap. The first and third main harmon ic winding factors for these 2000 valid 50-slot 48-pole winding configurations are shown in (a) and (b), below. Only a few of the valid winding configurations feature a high main harmonic winding factor, out of which two of them with the highest main harmonic winding factors are coloured in red. Optimal winding configuration in a machine can provide high performance and torque density.

Zero sequence current

73. Sequence networks are used to represent an unbalanced multiphase system, which occurs during asymmetrical machine faults. Essentially, each phase of a zero sequence current waveform is in phase with the other phases and are of the same amplitude.

Winding function

74. The winding function describes polarity of the winding coils, as well as the number of times that a winding links the airgap flux density at different positions in the sta tor.

Unidirectional winding function

75. A unidirectional winding function (UWF), as the phrase is deployed in this docu ment, is a winding function associated with a single phase of a stator winding ob tained from adding the individual winding functions associated with each coil in that phase, which have the following condition:

All coils in a phase winding being arranged such that they have the same polarity.

76. That means that the winding function under the tooth associated with each coil (which is resulted from that coil only) for all the winding coils are all either positive, or negative.

Advantages

77. Advantageously, the arrangement of embodiments of the technology are that the electric machine drive system facilitates remedial MMF manipulation. Embodi ments of the technology advantageously have this feature also when used in com bination with zero-sequence current injection. In other words, when one phase or a number of phase windings in a machine of some embodiments are opened, or when embodiments of the drive system are subject to certain semiconductor switch failures, the machine can maintain substantially its original form of MMF and spatial MMF harmonics (at relatively lower amplitudes in some embodiments) us ing the zero-sequence injection scheme described herein.

78. In operation, the injected zero-sequence currents can be considered to imperson ate, or stand in for, the missing currents or current harmonics in the faulty phases and have substantially zero contribution toward torque pulsation. Hence, an aver age torque can be maintained in the machine of one embodiment without introduc ing substantially any additional torque ripple. 79. These are significant improvements over known technology, in part shown in the examples and results obtained in testing.

Clarifications

80. In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date:

(a) part of common general knowledge; or

(b) known to be relevant to an attempt to solve any problem with which this specification is concerned.

81. It is to be noted that, throughout the description and claims of this specification, the word 'comprise' and variations of the word, such as 'comprising' and 'comprises', is not intended to exclude other variants or additional components, integers or steps.

Brief Description of the drawings

82. In order to enable a clearer understanding, a preferred embodiment of the technol ogy will now be further explained and illustrated by reference to the accompanying drawings, in which:

83. Figure 1 is a flowchart of a method of an embodiment of the technology;

84. Figure 2 is a schematic drawing of a computer processor which may implement one or more steps of embodiments of the technology;

85. Figure 3 shows injected current waveforms for fault type 1 (Open-phase fault in phase a) showing the fundamental, zero-sequence, and the final current. These waveforms are calculated by a computer processor in one step of the method of an embodiment;

86. Figure 4 shows injected current waveforms for fault type 2 - Case 1 (a semicon ductor switch failure in in phase a) showing the fundamental, DC zero-sequence, and the final currents These waveforms are calculated by a computer processor in one step of the method of an embodiment;

87. Figure 5 shows injected current waveforms for fault type 2 - Case 2 (a semicon ductor switch failure in in phase a) showing the fundamental, half-wave zero-se quence, and the final currents, calculated and selected by the computer processor in one step of the method of an embodiment; Figure 6 shows single-phase MMFs and the total MMF obtained by injecting the balanced three-phase current set (33) into the conventional three-phase 18-slot 16-pole FSCW PMSM at time t = Os (healthy condition);

Figure 7 shows single-phase MMFs and the total MMF obtained by injecting the zero-sequence currents (45) into the conventional three-phase 18-slot 16-pole FSCW PMSM at time t = Os under an open-phase fault (Phase a open-phase fault condition. These MMFs are injected by a controller during operation of an embod iment of the invention;

Figure 8 is a comparison between the winding function of the conventional 18-slot 16-pole FSCW machine and the invented UWF configuration (a) Conventional topology (b) topology of an embodiment of the present invention;

Figure 9 is a comparison between the harmonic winding factors unction of the conventional 18-slot 16- pole FSCW machine and the invented UWF configuration.

Main harmonic winding factor is of 8 ^th order (a) Conventional topology (b) topolo gy of an embodiment of the present invention;

Figure 10 shows Single-phase MMFs and the total MMF obtained by injecting the balanced three-phase current set (33) into the embodiment of the invention in a three-phase 18-slot 16-pole UWF FSCW PMSM at time t = Os (healthy condition); Figure 11 shows Single-phase MMFs and the total MMF obtained by injecting the zero-sequence currents (45) into an embodiment of three-phase 18-slot 16-pole UWF FSCW PMSM at time t = Os under an open-phase fault (Phase a open-phase fault condition);

Figure 12 shows an FEA model for an embodiment of the technology, being a three-phase UWF FSCW 18-slot 16-pole FSCW PMSM;

Figure 13 shows injected balanced current set into a conventional known stan dard three-phase 18-slot 16-pole FSCW PMSM. (Healthy condition);

Figure 14 shows electromagnetic torque for an embodiment of the invention be ing a three-phase 18-slot 16-pole UWF FSCW PMSM when supplied with a bal anced sinusoidal current set of amplitude 2 A _rms; Figure 15 shows injected currents (45) containing zero-sequence according to an embodiment of the proposed invention into an embodiment of the invention being a three-phase 18-slot 16-pole UWF FSCW PMSM under an open-phase fault condition (Phase a open-phase fault condition); 98. Figure 16 shows electromagnetic torque for the conventional known three-phase 18-slot 16-pole FSCW PMSM under phase a open-phase fault condition, supplied with zero-sequence currents. A current amplitude of 2 A _rms is maintained;

99. Figure 17 shows injected currents containing zero-sequence according to an embodiment of the present invention, being resolutions of equations (47) -(49), for a scenario of switch failure in phase a which will only allow flow of positive current amplitudes in phase a. Maximum current RMS value is set to 2 A _rm .

100. Figure 18 shows electromagnetic torque for the conventional/standard three- phase 18-slot 16-pole FSCW PMSM under a switch failure with the currents (47)- (49);

101. Figure 19 shows electromagnetic torque for an embodiment of the invention being a three-phase 18-slot 16-pole UWF FSCW PMSM under a switch failure with the currents (47)-(49);

102. Figure 20 is a schematic of a system of an embodiment of the present invention showing electric machine, controller and various engines contributing to various elements of the technology;

103. Figure 21 is a method for finding an optimal winding configuration for an m-phase FSCW PMSM with Q slots and P poles;

104. Figure 22 is a system schematic showing an arrangement of a diagnostic engine and inverter for injecting zero sequence current into an electric machine; and

105. Figure 23 is a system schematic showing elements of a machine design system.

Detailed description of an example embodiment

106. Referring to the drawings (at least Figure 20) there is shown a control system gen erally indicated at 10. The control system 10 is in communication, wirelessly or otherwise, with a multi-phase electric machine 99. The control system 10 includes an electronic system 100 as described below.

107. The control system 10 is configured to deploy a control method in accordance with at least Figure 1 in the event of an electrical fault which may be in the form of an open-phase fault or a semiconductor failure in an inverter leg associated with one or more phases.

108. In operation the control system 10 identifies and/or receives notification of a fault, at step 500 in Figure 1. The control system 10 then selects from a database or lookup table a suitable zero-sequence waveform at step 510. The control system 10 then adds the selected zero-sequence waveform to add (in step 520) to the post-fault phases to obtain a resultant waveform which is then sent to the controller to be injected into the phases of the multiphase machine.

Other embodiments of the invention are implemented by the control system 10.

The control system 10 calculates various intermediate steps xxx

It can be seen that Figure 2 portrays a schematic diagram of an embodiment of an electronic system 100, the system 100 comprises several key components, includ ing a user computer 102; an application server 104; interface modules 106; and a data network 108. The system 100 also includes various data links 110 that con nect the user computer 102, the application server 104 and the interface modules 106 to the data network 108 so that data can be exchanged between the user computer 102, the application server 104 and the interface modules 106.

The user computer 102 may be any type of computing system and may include any sort of suitable computing device, including but not limited to a desktop com puting system, a portable computing system such as a laptop, a smartphone, a tablet computing system, or any other type of computing system including a pro prietary device.

For the purpose of clarity of understanding, the embodiment of the system 100 will be described with reference to an Intel based computer such as those available from, for example, Lenovo, Dell or HP. The user computer 102 has a hard disk (not shown in the diagrams) that contains a range of software and data. In particular, the software typically includes the Windows or OSX operating system. The hard disk also contains a web browser application such as, although not limited to, Google Chrome.

Like all desktop computers, the user computer 102 also comprised a keyboard, mouse and visual display device (monitor).

The application server 104 is in the form of an Internet-connected computer server and is an Intel based server such as that available from IBM, Dell or HP. The appli cation server 104 has a hard disk (not shown in the figures) that contains a range of software and data. In particular, the software on the hard disk of the application server 104 includes the Linux operating system. In addition to providing the usual operating system functions, the Linux operating system also provides web server functionality. As described in more detail in subsequent paragraphs of this descrip tion, the web server functionality of the Linux operating system allows the user computer 102 to interact with the application server 104.

In addition to the Linux operating system software, the hard disk of the application server 104 is also loaded with an electronic document test application. While sub sequent paragraphs of this description provide a detailed description of the elec- tronic document test application, the electronic document test application is in the form of a web based application that the user of the user computer 102 can access to test various aspects of webpages (or other electronic documents) that are ac cessible via any one of the modules 106. It is envisaged that in alternative embod iments of the system 100 different forms of the application server 104 can be used. The modules 106 are not dissimilar to the application server 104 insofar as the modules 106 are capable of transmitting and receiving data. One or more of the modules 106 is connected to a multi-phase electric machine (not shown in Figure 2) that is partially or wholly monitored and/or controlled by the modules 106. That is, the electronic system 100 provides the controller, optimisation engines, other engines and like control elements for making decisions on various control strate gies under fault conditions.

The data network 108 is in the form of an open TCP/IP based packet network and in this embodiment of the system 100 the data network 108 is equivalent to the protocols and systems utilised on the Internet. The primary purpose of the data network 108 is to allow the user computer 102, the application server 104 and the modules 106 to exchange data with each other. To further facilitate the exchange of data between the user computer 102, the application server 104 and the mod ules 106, each of those components are in data communication with the data net work 108 by virtue of the data links 110. The data links 110 are in the form of broadband connections. In alternative embodiments of the system 100 different forms of the data network 108 can be used.

An optimisation engine (not shown) can be engaged by the electronic system 100 to be caused to design or optimise a stator winding topology as described herein, utilising the steps in the method described.

EXAMPLE ONE

Zero sequence current injection

Machine equations imply that average torque is generated by the current harmon ics associated with the main harmonic winding factors of the stator. Thus, zero-se quence currents are expected to have no effect on the average torque. Surprising ly, however, the present inventors have identified and hereindisclosed that, judi ciously deployed, they can have an effect on the stability of a system in a post-fault environment.

In an embodiment of the proposed method shown in Figure 22, a monitor module 197 wirelessly or otherwise connected to the multi-phase machine 99 monitors the current flow therein and then sends fault data to a diagnostic engine 199. That data is sent to a diagnostic engine 199, which selects zero-sequence waveform data appropriate to the fault data, to be injected into the machine 99. The diagnos tic engine 199 is connected wirelessly or otherwise to the multi-phase electric ma chine 99 and disposed in or otherwise connected to the computing processing sys tem 100.

So, for each faulty phase, data relating to an appropriate zero sequence current is calculated in the diagnostic engine 199 as set out below, and that current data is then numerically added in a modulation engine 195 to data relating to pre-fault cur rent equations of the machine 99. If there is more than one post-fault phase, for each faulty phase, data relating to a separate zero-sequence current is obtained in the diagnostic engine 199, and sent to the modulation engine 195, and all the re sultant zero-sequence currents are added in the modulation engine 195 into the pre-fault current set. This results in a final current set to be injected into the multi phase electric machine 99 via a PI controller and inverter drive 193. This method facilitates the maintenance of an MMF shape and spatial MMF harmonics similar to the pre-fault condition. As discussed, the torque may be slightly lower, but the harmonic shape is substantially the same, such that the torque ripple is not in creased.

For each fault, whether faulty phase or semiconductor fault, the zero sequence current data is the current waveform required to be added to the pre-fault current of that phase such that a current shape similar to the post-fault current of that phase is obtained.

Accordingly, examples are provided and set out below for the zero-sequence cur rent calculation for different types of faults in three-phase machines which is calcu lated in the modulation engine 195. This approach is extendable to higher number of phases (four, five, six, seven, eight, nine, etc) in multi-phase FSCW PMSMs. Assume the below healthy fundamental three-phase current set:

Fault Type 1: open phase fault in phase a of a three-phase FSCW PMSM

124. The zero-sequence current for this condition is:

125. The currents to be caused to be injected into the machine 99 by PI controller and inverter drive 193 are now calculated by summing (33) and (34) in the modulation engine 195:

In this example, these currents were caused to be injected into a conventional 18-slot 16-pole PMSM by the PI controller and inverter drive 193. The RMS values of the currents in (36) is caused to be adjusted, also by the modulation engine 195, such that they will not exceed the rated RMS current of the machine thus its ther mal capability. RMS value of the currents in (36) are:

The output currents from the modulation engine 195 and injected by the PI controller and inverter drive 193 are shown in Fig 3.

Fault type 2: Single semiconductor failure in an inverter leg associated with phase a of a three-phase FSCW PMSM

In this scenario, only positive currents can flow in a winding of phase a. Once the current data has been conveyed from the monitor 197 through the modulation en gine 195 with or without modulation, or even directly, to the diagnostic engine 199, one of at least two types of zero sequence current are caused to be summed in the modulation engine 195 with (33) to realize this condition:

Case 1 : A positive DC current with an amplitude equal to the healthy sinusoidal current set can be numerically obtained by the diagnostic engine 199, (and modu lated by the modulation engine 195 and then injected by the PI controller and in verter drive 193 into all phases) such that the resultant phase a current is shifted up and is always positive:

With the above zero-sequence currents, the injected currents are caused to be in jected into the machine by the PI controller and inverter drive 193, can be numeri cally obtained in the diagnostic engine 199 as follows:

RMS values of the above currents, monitored by the monitor 197 and/or calculated by the modulation engine 195, are:

From (40), the RMS values of the injected currents should be readjusted in the modulation engine 195 such that they will not exceed the rated RMS current of the machine thus its thermal capability.

An example of the resultant currents caused to be output from the engines 199, 195, in this case is shown in Fig. 4, where all the healthy-state currents are shifted up by a positive DC offset.

Case 2: In this scenario only the positive half-sine wave of the current can flow in the faulty winding. The zero sequence current selected by the diagnostic engine 199 for this scenario is caused by the computer control system 100 to be added to (33) by the modulation engine 195 such that only the positive half-sine wave is left in phase a:

When the above zero-sequence currents have been provided by the diagnosis en gine 199 and resolved by the modulation engine 195, the injected currents into the machine are:

RMS values of the above currents are:

The maximum RMS value of the injected currents is modulated in the modulation engine 195 using numerical solutions to equations (43) such that it will substantial ly not exceed the rated RMS current of the machine. These efforts are directed to wards not exceeding the thermal capability of the machine 99.

An example of the currents in this case is shown in Fig. 5, where a zero sequence current is added by the modulation engine 195 to all the healthy-state currents and injected by the PI controller and inverter drive 193 such that no negative current is passing through phase a and the faulty switch.

Remedial Magnetic Field Manipulation with Zero-Sequence Current Injection

Now, we disclose the effect of zero sequence injection by the PI controller and in verter drive 193 on the generated magnetic field/MMF in the following FSCW ma chines:

a. conventional FSCW PMSMs with an even number of pole-pairs belonging to Sub-category 1 which feature a zero net magnetic pull; b. UWF FSCW PMSMs with an even number of pole-pairs belonging to Sub-category 1 which have a zero net magnetic pull. The response of conventional FSCW designs to zero-sequence injection by the PI controller and inverter drive 193 will be first set out. Then, set out below will be the response to zero-sequence injection of a unidirectional winding function (UWF) FSCW PMSM which, as the inventors have identified and disclosed herein, have MMF manipulation capability for remediation.

Known 18-Slot 16-Pole Three-Phase FSCW PMSM

Operational response to fault, and zero-sequence injection of a known 18-slot 16- pole FSCW machine 99 is discussed and disclosed hereinbelow. This machine 99 has an even number of pole-pairs and belongs to Sub-category 1 and thus fea tures a zero net magnetic pull.

Assuming injection by PI controller and inverter drive 193 of the balanced current set (33) into the conventional 18-slot 16-pole FSCW PMSM (pre-fault or healthy condition), the generated MMF by each phase at time t = Os and the total MMF ob tained by summing all the single-phase MMFs is illustrated in Fig. 6.

When an open-phase fault occurs, in this kind of machine, in (say) phase a, the relevant faulty part of the stator teeth will stop contributing toward building the MMF in the airgap. For this type of fault, the injection of the zero- sequence cur rents (36) as discussed above - Fault Type 1 - will result in the MMF profile shown in Fig. 7. The amplitude of the injected currents under the zero- sequence injection for this case is scaled by the modulation engine 195 to result in the same RMS current rating as the pre- fault condition. Accordingly, from (35)-(37), the amplitude l’ _m for the post-fault injected currents are:

A comparison between (healthy or pre-fault) Fig. 6 and (faulted) Fig. 7 presents the result that zero-sequence injection to an electric machine after a fault according to the method described earlier leads to an MMF which is fundamentally different from the pre-fault MMF. The generated torque by injection of healthy currents when the injected current amplitude was maintained at 2 A _rms can be calculated. Thus, an average electromagnetic torque of 16.18 N.m with a considerable torque ripple of 5.5 N.m (34%) was observed.

An embodiment: optimisation of an 18-Slot 16-Pole Three-Phase UWF FSCW PMSM

144. As explained earlier, the present technology seeks to manipulate the post-fault MMF in the airgap of the electric machine 99 such that it maintains a similar har monic shape to the pre-fault condition. In other words, the present technology seeks to restore similar main spatial MMF harmonics in the post-fault environment. For the two types of FSCW stators mentioned herein, the inventors have surpris ingly identified that this can be achieved, since they have identified that a magnetic coupling exists between the stator teeth that allow manipulation of the MMF under teeth other than themselves.

145. The improvement is to be achieved by injecting a zero-sequence current with the properties as explained in this specification into the machine windings. The inject ed post-fault currents desirably realize the following:

* The resultant post-fault MMF shape underneath the healthy teeth desirably remain about the same as that of the pre-fault condition;

* A post-fault MMF harmonic shape similar to that of the pre-fault condition should be generated under the faulty teeth.

*The post-fault currents should maintain the same RMS value with in the machine’s rating and thermal capability.

146. In order to facilitate an improvement to the known conditions and/or meeting of the above conditions, in certain embodiments in addition to the zero-sequence injec tion, the winding configuration is desirably also altered. Investigation into the generation mechanism of the MMF (using Ampere’s law and Gauss’s law) by the inventors has identified the surprising phenomenon that if the winding configuration maintains a unidirectional winding function, the above results using zero-sequence injection can be improved. However, the inventors have iden tified constraints in the design of such unidirectional winding function (UWF) multi phase PMSMs which can be used to affect performance, and are discussed as set out below.

A computer-implemented optimisation engine 299 is deployed as part of a computer processing system 100 described above, to implement a method where in winding topologies of an electric machine are optimised. In an embodiment of the method, shown in Figure 21 , FSCW windings with unidirectional winding func tions are optimised.

Inputs to the optimisation engine 299 are provided at step 610, and are the num ber of phases, number of slots and number of poles.

Not every slot/pole combination can yield a UWF FSCW PMSM with acceptable characteristics. The inventors have identified that one desirable factor in making a winding topology acceptable is to have high main harmonic winding factors close to unity. High main harmonic winding factors facilitate a high amplitude for the as sociated back-EMF harmonics and average developed torque, thus a higher torque density.

The optimisation engine 299, by causing (in one embodiment) the steps in Figure 21 , generates data relating to one or more possible winding topologies for a given number of phases, slots, and poles. In those steps, the optimisation engine 299 categorizes the generated topologies based on their main harmonic winding fac tors, and those with the proposed UWF characteristic (if any available) which have high main harmonic winding factors are selected as being suitable.

Based on the output of the optimisation engine 299, lookup tables can be generat ed that show one or more eligible slot/pole combinations with UWF characteristics for a given number of phases, and a selector 285 selects the optimal design. An example follows that illustrates how this method of utilising optimised UWF topolo gy of one embodiment can facilitate obtaining of desired properties.

The optimisation engine 299 utilises a Winding Performance Index (WPI). A design method is disclosed for obtaining optimal winding configurations for multi phase FSCW stators with high torque density. In the embodiment disclosed, a method called the CHI method is deployed. Average torque in a multiphase ma chine is a function of its main harmonic winding factors which are in turn charac terised by the winding design. Accordingly, a method for obtaining a WPI is dis- closed that quantifies the torque production ability of a winding configuration. The disclosed WPI is utilized in a further method for determining an optimal multiphase winding configuration for a given slot/pole combination.

154. The main spatial MMF harmonics of a multiphase winding can be used in the CHI method to enhance the average torque production of the machine. In the CH I method, in addition to the fundamental current, odd current harmonics are injected into the multiphase machine 99 by a PI controller and inverter drive 193 to produce higher order main spatial MMF harmonics that interact with their associated PM flux density harmonics in the air gap to produce an additional average torque. The number of the injected current harmonics is proportional to the number of machine phases. In particular all current harmonics with an order smaller than the number of the machine phases produce spatial MMF harmonics that can participate in av erage torque production. The weight of each main spatial MMF harmonic in aver age torque production is evaluated by its associated main harmonic winding factor.

155. For a multiphase stator with a given slot/pole combination, numerous valid winding configurations can be generated by the optimisation engine 299. In the method shown and disclosed herein with reference to Figures 21 and 23, the optimal wind ing configuration is caused by the optimisation engine 299 to be selected from this batch by considering all the main harmonic winding factors. Accordingly, a WPI is disclosed in the following as an indicator of the average torque density in a multi phase winding design that considers all the main harmonic winding factors.

156. First, some theory. The average torque in an m-phase symmetrical machine run ning under the CHI method is given by

where iq,k is the injected g-axis current harmonic of /cth order, which is associated to the main spatial MMF harmonic of order kP! 2 (Mb main harmonic winding factor).

157. The nth flux linkage harmonic is directly proportional to

158. In the CHI method , the amplitude ratio of the Mi injected current har monic to the fundamental is the same as that of its respective back-EMF harmonic [23]. From (11), amplitude of the 2th hack-EMF harmonic is directly proportional to 59. From the equation in para 158 the generated average torque is proportion al with the PM flux linkage and current harmonics. Therefore, based on (13) and (14), the proposed WPI for evaluating the torque production ability of an FSCW stator is defined as

61 . where the per-unit value of and i s stri ctl y depen dent on the rotor structure. 62. For a given slot/pole combination many possible multiphase winding con figurations exist, among which the winding configuration with the highest WPi as defined in para 161 will result in the highest torque density. 63. A flowchart of an embodiment of a new and inventive method for obtain ing the optimal winding configuration is shown in Fig 21. In summary, the proposed method first, in a winding configuration engine 297, gener ates substantially all the valid multiphase winding configurations for a given slot/ pole combination. Then, their harmonic winding factors and WPIs are calculated in the winding configuration engine 297. The winding configurations caused to be output by the winding configura tion engine 297 with the highest WPIs are then selected by a selection en gine 295 as the optimal configurations. The procedure shown in Fig. 21 which is merely one embodiment of the new method can be broken down into the following steps: In more detail, as shown in Figures 21 and 23, first, the number of phases, slots, and poles are input to the winding configuration engine 297 at step 610, either manually or are automatically detected by some automatic de tector which detects resistance, inductance, reluctance, and other relevant factors by rotating the machine and monitoring the response by measur ing those factors. The number of slots should be a multiple of 2m to satis fy the criteria of Section II-A. Second, S _pp , the number of slots Qbase and poles P _base for the base winding configuration are calculated in the winding configuration engine 297 at step 620. Periodicity of the base winding configuration is equal to 2, thus, one coil of each coil pair is located in the first half of the stator. There fore, T _| , ₂ which is equal to half of the teeth count is calculated in the winding configuration engine 297, among which, a total number of T _pli teeth are allocated to each phase winding. In a distribution engine, 293 , and at step 630, all possible distributions of T _ph coils among T _{j /2} teeth are found and grouped in a set Hi of arrays that are of lengthT _1/2 . Each array of the set Pi is one possible distribution of the coils in the stator for the phase winding with code name“1.” Since the stator is symmetrical, data relating to array sets Il _{k ,} k 2,

3, . . . , m are created in the distribution engine 293 at step 640 by circular shifting the arrays of the set Il _{k -l} by T _{p h} . These sets contain all the pos sible distribution of coils among the stator teeth for their respective phase

“r. In a FSCW stator each tooth is allocated to a single coil. Therefore, the arrays in the set Pi are caused to be compared in an elimination engine 291 at step 650 with their respective arrays in Il _k , k = 2, 3 ,..., m and those arrays in which more than one coil is allocated to a single tooth are elimi nated from the set. Moreover, the arrays that result in the same winding configuration, but physically shifted, are eliminated. At step 660, the assumption that the stator is symmetrical is stored in a coil generator 289 and array set Pi is recorded in the coil generator 289 as reference and data relating to all possible unique coil polarities are generated in the coil generator 289, each of which indicating half of a phase winding in a valid w- phase base winding configuration. A complete base winding configuration is obtained by duplicating the arrays in TTi. Polarities of the coils are caused to be determined in the coil generator 289 based on the number of pole pairs in the base winding configuration as discussed in Section II-B. In particular, for an even number of P _{h a s e} /2 the polarities in the second half of the base winding configuration is the same as that of the first half, whereas, if P _{h a s e} /2 is an odd number the coils in the second half of the base winding configuration will have an opposite polarity compared with the first half. At step 670, for each array in XI j which indicates a valid base winding con figuration, the main spatial SWF harmonic amplitudes of order k=l 3,5,

... ,(k<m) are calculated. This is performed by arithmetic summation of the main harmonics of all coil pairs obtained from

The main harmonic winding factors of order for each

array of Pi are then caused to be found using:

At step 680, the processor 100 causes WPIs to be calculated by using the above equation for WPI for all the base winding configurations of I I i . At step 690, the processor 100 causes the base winding configurations in Hi with the highest WPIs to be selected as candidates for the optimal base winding configuration. At step 700, the processor 100 causes complete winding designs for the Q- slot P-poie m-phase FSCW PMSM to be established by repeating the op timal base winding configurations for Pile times. Depending on the slot/pole combination, the disclosed method may gen erate a small number of optimal winding configurations, out of which, the optimal winding design can be selected by a selector 285, which takes into account the average torque under the CHI method, torque ripple, and losses.

EXAMPLE THREE

An 18-slot 16-pole FSCW PMSM with a conventional/known topology that was in vestigated earlier in this example, is selected. The optimisation engine 299 is de ployed to investigate the possibility of an eligible UWF topology and, if it exists, its winding configuration and winding factors.

Accordingly, a UWF topology (in this case) is obtained as an output from the opti misation engine 299, with its winding function as shown in Fig. 8 and compared against the conventional topology ((a) is conventional topology, and (b) is UWF topology). A comparison between the generated harmonic winding factors is also shown in Fig. 9 ((a) being conventional topology and (b) being UWF topology). The t _h

first main harmonic winding factor is of 8 order. Thus, for the drive’s slot/pole combination the main harmonic winding factor for the UWF topology is 12% lower which would mean around 12% reduction in the average torque. This might look like a drawback, however, the UWF machine has fault-tolerance capabilities which compensate for this loss in the average torque as discussed herein.

The MMF manipulation of one embodiment of the present invention, which uses zero-sequence current injection in UWF FSCW topology, is now set out. From the winding function shown in Fig. 8(b), the generated MMF by each phase using the balanced current set (33) and the total MMF for the UWF FSCW PMSM is ob tained at t = 0s as shown in Fig. 10.

Now assume phase a is subject to an open-phase fault. The MMF generated by each current component at t = 0s when injecting the zero-sequence currents (45) in the 18-slot 16- pole UWF FSCW is obtained based on the winding function shown in Fig. 8(b) as illustrated in Fig. 11. In this figure, the generated MMF by phase a is zero. The MMFs generated by the fundamental and the zero-sequence currents are separately illustrated in Fig. 11. Summing these separate MMF com ponents yields the total MMF generated by the UWF FSCW stator. 181. A comparison between the total MMF under the healthy and open-phase fault con ditions in Fig. 10 and 11 (respectively) for the UWF topology shows that the same spatial harmonic MMF waveform (at a lower amplitude) is generated under both of these conditions. Therefore, the same spatial MMF harmonics are expected to ex ist in both conditions. This means that the proposed zero-sequence injection method and system of one embodiment of the present invention, in UWF FSCW PMSMs, results in remedial magnetic field manipulation such that both the pre fault and the post-fault MMFs have the same spatial waveforms and same spatial harmonics, albeit with lower amplitudes. Consequently, the generated electromag netic torque in the post-fault condition is expected to have a lower average torque with no additional torque ripple compared with the pre-fault condition.

182. An FEA model of the 18-slot 16-pole UWF FSCW PMSM is shown in Fig. 12. This model is used to evaluate the performance characteristics and remedial magnetic field properties of the 18-slot 16-pole UWF FSCW PMSM under both the healthy and faulty condition with zero- sequence injection.

183. In order to evaulate the performance of the UWF FSCW PMSM, the balanced three-phase current set with an amplitude of 2 A _rms is injected into the FEA model as shown in Fig. 13. The generated torque under this condition is shown in Fig. 14 and summarized in the table below. The average torque can be seen to be 23.6N.m with a 0.5 N.m (2.12%) torque ripple.

It can be seen that the average torque is 13.72 N.m with a negligible torque ripple of 0.37Nm (2.7%). This demonstrates the effectiveness of one embodiment of the invention, which is a remedial magnetic field manipulation method using zero-se quence injection in UWF FSCW PMSMs.

In order to further disclose the performance of remedial magnetic field manipula tion technique using zero-sequence injection in the UWF FSCW PMSMs of one embodiment, a switch fault in one leg of phase a winding is considered next.

This switch fault is assumed to block injection of negative current magnitudes into phase a. The associated zero-sequence for this condition is expressed in (41). Ac cordingly, the injected currents are as expressed in (42). From (43), in order to keep the RMS value of the proposed post-fault currents similar to the pre-fault condition, the amplitude of the currents should be down-rated to:

Therefore the post-fault injected currents into the machine are shown over- leaf at (47), (48) and (49).

These currents are simulated using FEA and injected into the machine as shown in Fig. 17. Performance of the conventional/standard FSCW PMSM and a UWF FSCW PMSM of one embodiment of the present invention under this condition are obtained using FEA as shown in Fig. 18 and 19, respectively

From Fig. 18 and 19 it is clear that the proposed UWF FSCW stator under the pro posed zero-sequence injection is capable of remedial magnetic field manipulation such that the post- fault torque maintains low torque ripple similar to the pre-fault condition, albeit at a slightly lower average torque. A comparison between the con ventional 18-slot 16-pole FSCW PMSM and the UWF FSCW topology of one em bodiment of the present invention with the same number of slots and poles is summarised in the table below.

and

A Mathematical Insight into Multi-Phase UWF FSCW PMSM with Remedial Magnetic Field Manipulation Capability Using Zero-Sequence Injection Technique of one example embodiment

191. The remedial magnetic field manipulation capability of the UWF PMSM of one em bodiment of the present invention requires injection of high-amplitude zero-se quence currents into the machine. In a conventional / standard PMSM these cur rents would interact with their respective PM flux linkage harmonics and generate high torque pulsations which could render the machine non- operational. However, this is not the case in the UWF PMSM of one embodiment of the present invention as explained in the following.

192. The PM flux linkages, back-EMFs and generated torque in a multiphase PMSM are directly proportional to the harmonic winding factors of the machine:

Harmonic winding factors are a direct result of the spatial harmonics of the winding function in a PMSM. In brief, the zero-sequence currents interact with the zero-se quence back-EMF (or the zero-sequence PM flux linkages) and contribute toward the excessive torque pulsation. In the machine topology of one embodiment of the present invention, the harmonic winding factors associated with the zero-sequence back-EMFs (zero-sequence PM flux linkages) are physically zero as shown in Fig. 9(b) for the three-phase 18-slot 16-pole PMSM case-study. This structural feature of the topology of the embodiment inhibits or substantially eliminates the contribu tion of zero-sequence currents toward torque pulsation.

The Eligible Slot/Pole Combinations for the Multi-Phase UWF FSCW PMSM with Remedial Magnetic Field Manipulation Capability Using Zero-Sequence Injection Technique of one embodiment of the present invention

The UWF FSCW design of an embodiment of the present invention and method of remedial magnetic field manipulation capability using zero-sequence injection is applicable to three-phase and multiphase machines with eligible combination of slots and poles.

Not every slot/pole combination can yield a UWF topology with a high average torque. A software package is developed for obtaining the eligible slot/pole combi nation that can yield a UWF topology. The winding configuration and the associat ed harmonic winding factors are also the output of this software.

A table detailing a list of the eligible slot/pole combinations with their characteristics is generated and stored as a lookup table in a storage element of the computer processing system 100 for access by the controller or is calculated online.