WO2019227179A1

WO2019227179A1 - A method and system for facilitating control of electric machines

Info

Publication number: WO2019227179A1
Application number: PCT/AU2019/050569
Authority: WO
Inventors: Matthew PRIESTLEY
Original assignee: Newsouth Innovations Pty Limited
Priority date: 2018-05-31
Filing date: 2019-05-31
Publication date: 2019-12-05
Also published as: AU2019277274A1

Abstract

A method of facilitating control of a multi-phase electric machine under fault conditions of one or more open phases, the method including the steps of receiving unbalanced current data from an optimisation engine into a stationary transformation engine and a rotational transformation engine, in a computing processor; transforming the unbalanced current data using selected machine algorithms in the stationary transformation engine to identify a locus of unbalanced current data on two phase-referenced axes; transforming the unbalanced current data using selected machine algorithms in the rotational transformation engine, to identify dc reference current data; multiplying the transformed locus data and transformed dc reference data together to provide transformed dc-reference error data to one or more PI current controllers in an FOC architecture to control the electric motor.

Description

A METHOD AND SYSTEM FOR FACILITATING CONTROL OF ELECTRIC MACHINES

Technical Field

1. The present technology relates generally to control of multi-phase electric ma chines under faulted conditions. Embodiments of the technology are effective in permanent magnet synchronous machines (PMSM), and in that application, for inverter topologies which allow for zero-sequence current flow such as open-end winding topology. Some embodiments of the technology find particularly effective application in control of five-phase machines, when one or two phases in the ma chine are open-circuited.

Background

2. There are a range of safety, cost, and mission-critical applications which utilise electric machines. Any operational disturbance for such applications can have costly or dangerous consequences.

3. Therefore, an electric drive system which can continue to operate after a fault has occurred is valuable for these applications. Although there are other machines which can be useful, the permanent-magnet synchronous machine (PMSM) is be- ing considered for many critical applications including wind turbine generation, naval propulsion systems, electric vehicle traction drives and aircraft drive and control systems, including UAVs. Consequently, a control technique which allows for post-fault operation in a PMSM system is beneficial.

4. There are known post-fault techniques for open-phase faults in a three-phase PMSM system. In one method, two non-faulted phase currents are wave-shaped to avoid portions of the machine rotational cycle experiencing opposite torque po larity and to increase average torque. However, the existence of a neutral point in a standard three-phase wye connected system considerably limits the degrees of freedom for optimisation, resulting in high post-fault current harmonic solutions and high torque pulsation. Consequently, a five phase PMSM system is also being considered as an option, since it offers more degrees of freedom for post-fault op- timisation.

5. There are documented post-fault strategies for a single open-phase fault in a five- phase system. These strategies establish the non-faulted phase currents to opti mise the post-fault machine output torque. Some known optimisation strategies produce high post-fault current harmonic solutions which are difficult to implement. Consequently, most optimisation strategies only consider fundamental, and some-

Substitute Sheet

(Rule 26) RO/AU times, include third harmonic phase current solutions. Some optimisation tech niques consider the machine stator winding temperature and flux-weakening con ditions. The abovementioned methods assume that the machine stator windings are star-connected.

The existence of a neutral point in the star-configuration constrains the system in that the phase currents must sum to zero (i.e. zero zero-sequence current). Anoth er single open-phase fault constraint requires that the post-fault current phasors be symmetrical about the faulted phase to minimise torque pulsation. Still another constraint, which maximises the post-fault average torque per ampere, requires that the amplitude of the post-fault currents be equal to avoid derating the post fault torque to the highest phase current. These constraints have limitations in that they cause the post-fault current phasors to be locked into the arrangement shown in Fig. 1 during a single open-circuit. This post-fault current phasor arrangement produces considerable torque pulsation.

There are some reported post-fault techniques which consider different five-phase winding configurations. Some consider the star, pentagon and pentacle configura tions. One possible configuration which can remove the zero zero-sequence con straint is the single dc supply open-end winding configuration shown in Fig. 2. However, there are not many known post-fault techniques for this topology.

The open-end winding topology applies the full dc bus voltage across each phase and hence provides three-level voltage output and increased dc bus utilisation.

This topology also allows for zero-sequence current flow which can be used to ob tain better post-fault current optimisation. Therefore, optimised unbalanced phase currents can be injected in this topology to further optimise the machine output torque during a single/dual open-phase fault while maximising average torque per ampere. However, this solution requires a closed-loop method for controlling these unbalanced phase currents.

A strategy for suppressing the low-frequency zero-sequence current, which is caused by zero-sequence back-EMF components and by deadtime distortion, uses a zero-sequence PI current controller to actively suppress the zero-sequence cur rent to zero, whilst using a modulation strategy which provides independent control of the CMV. However, this strategy cannot be adopted for a varying non-null zero- sequence current reference without obtaining a significant undesired tracking error in the PI controller output. Another strategy for controlling post-fault currents is to use phase current hysteresis controllers.

Another method uses hysteresis controllers to drive analytically-determined unbal anced post-fault phase currents in the open-end winding topology. However, prac tical experimental testing with phase current hysteresis controllers has found that

Substitute Sheet

(Rule 26) RO/AU these controllers become unstable when used in an open-end winding topology inverter and are therefore unsuitable for this application. This instability is caused by zero-sequence voltage cross-coupling between each phase due to the low zero-sequence impedance in this topology. For example, a phase current hystere- sis controller may demand a certain voltage, however this demand changes the phase winding zero sequence voltage and hence indirectly changes the voltages of the other phases. This cross-coupling causes high harmonic current production and can cause instability. Note that phase current hysteresis controllers can be used during a single open phase fault to a three-phase open-end winding system as there are only two non-faulted currents and hence no zero-sequence compo nent. Consequently, phase current hysteresis controllers cannot be used to drive more than two currents in an open-end winding system.

11. The post-fault control strategies mentioned so far use phase current hysteresis controllers to control the currents. Not only do these controllers present harmonic and stability issues for the open-end winding topology, they also inherently create higher current harmonics and a wide frequency range of electromagnetic interfer ence. The field-oriented control (FOC) architecture, when combined with PI current controllers, produces fast dynamic response times and does not cause these is sues.

12. Therefore, known methods for controlling unbalanced post-fault currents in a multi phase open-end winding system provide high current harmonics, instability or a large tracking error during open-phase faults.

13. The present technology seeks to provide a method and system for post-fault con trol of a multi-phase electric machine which ameliorates one or more of the abovementioned disadvantages, or provides a new controller for a multi-phase electric machine under open-phase fault conditions.

Summary

14. Broadly, the present technology provides a new decoupled field-oriented control method for controlling multiple unbalanced post-fault currents in an electric ma- chine. In one embodiment the electric machine is a PMSM but it could be any oth- er machine including any kind of synchronous machine. The method advanta geously allows the machine to be controlled to provide an improved proportion, over what is known, of the average (pre-fault) rated torque together with, or in the alternative, a lower torque ripple.

Substitute Sheet

(Rule 26) RO/AU Broadly, the present technology also provides a method of facilitating control of a multi-phase electric motor under open-phase fault conditions, in which an optimisa tion engine determines characteristics of current phasors for the injected phase current refined by data from back EMF and current sensors on the electric ma chine. In one embodiment the electric motor is a permanent magnet synchronous machine (PMSM). In one embodiment the optimisation engine conducts optimisa tion offline but provides output to other control engines during operation.

During operation of one embodiment, under open-phase fault conditions, a trans formation engine receives data relating to unbalanced currents from an optimisa tion engine and then outputs dc reference current data under steady state opera tion. The output data is then processed and delivered to PI current controllers in an FOC architecture to control the electric motor. Advantageously, with this embodi- ment, the current control waveforms have negligible current harmonics as there is no tracking error and cross-coupling between the transformation axes is min- imised. Output results of an embodiment of an optimisation engine, such as those shown in Fig. 4, are used to control the post-fault currents and optimise the ma- chine output torque waveform.

Thus, in accordance with one aspect of the present technology there is provided a method of facilitating control of a multi-phase electric machine under fault condi tions of one or more open phases, the method including the steps of:

receiving, in a computer processor, current data relating to unbalanced fault currents from a post-fault current optimisation engine;

building, in a computer processor, a post-fault stationary matrix transforma tion engine using the unbalanced sinusoidal current data from the post-fault cur rent optimisation engine and selected machine algorithms, the stationary transfor- mation engine being configured to identify stationary locus data of the currents when plotted on a plurality of orthogonal phase-referenced axes;

building, in a computer processor, a post-fault rotational matrix transforma- tion engine which, using the stationary locus data from the stationary transforma tion engine, is configured to identify planar current locus data, when plotted on two orthogonal phase-referenced axes; and

providing the planar current locus data to a PI controller as dc current ref erences.

Substitute Sheet

(Rule 26) RO/AU In accordance with another aspect of the present technology there is provided a method of facilitating control of a multi-phase electric machine under fault condi tions of one or more open phases, the method including the steps of:

building, in a computer processor, a post-fault stationary matrix transforma tion engine using the unbalanced sinusoidal current data from the post-fault cur rent optimisation engine and selected machine algorithms, the post-fault stationary transformation engine being configured to identify stationary locus data of the si nusoidal current if it were plotted on a plurality of orthogonal phase-referenced axes;

building, in a computer processor, a post-fault rotational matrix transforma- tion engine which, using the stationary locus data from the post-fault stationary transformation engine, is configured to rotate one or more locus axes which are perpendicular to the stationary locus, so as to identify planar current locus data, if it were plotted on two orthogonal phase-referenced axes;

generating matrices in the post-fault stationary and rotational transforma tion engines and combining them to provide dc current references; and

providing the combined matrix data to a PI controller.

Substitute Sheet

(Rule 26) RO/AU % In one embodiment, one of the selected machine algorithms is in the form:

In one embodiment, one of the selected machine algorithms is in the form:

In one embodiment, the matrix that is generated in the stationary and rotational matrix transformation engines is in the form

W cos( )t— C) — w sin(i t— C)

^3

In one embodiment, the method includes a decoupling step to reduce coupling be tween orthogonal axes.

In one embodiment the decoupling step includes a feed-forwarding step wherein the phase back-EMFs of the motor are fed-forward such that the PI current con trollers do not compensate for the back-EMF terms.

In one embodiment, the decoupling step includes estimating, in a computer pro cessor, the phase back-EMF for the respective rotor position.

Substitute Sheet

(Rule 26) RO/AU In one embodiment, the decoupling step includes estimating, in a computer pro cessor, the phase self- and mutual- inductances of the electric machine for the re- spective rotor position.

In one embodiment the decoupling step includes the step of transforming the esti- mated phase-referenced inductances onto the transformed domain using the post fault transformation data.

In one embodiment the decoupling step includes the step of calculating, in a com- puter processor, optimized feedforward voltage references to minimize cross-cou- pling between the post-fault transformed axes using the transformed inductances, machine rotational speed and phase back-EMFs.

In one embodiment the decoupling step includes the step of summing the voltage error references with the feedforward voltage references to obtain the final refer ence voltages.

In accordance with one aspect of the present technology there is provided a method of facilitating control of a multi-phase electric machine under fault condi tions of one or more open-phases, the method including the steps of:

optimising, in a computing processor, the characteristics of one or more non-faulted injected current phasors for the multi-phase electric machine to provide optimised current phasor data;

transforming, in a computing processor, reference current data which is ob tained via a torque reference and the optimised post-fault phase current data to provide reference phase current data for use in one or more PI current controllers; adjusting phase voltage signals which are outputted from the PI controller environment, using the reference phase current data.

The arrangement is such that the adjusted phase voltage signals are transmitted from the PI controller to an inverter drive unit configured to be connected to the multi-phase electric machine to control the phase currents and hence control the output torque of the machine.

In one embodiment the transformed reference current data is dc reference current data.

In one embodiment the method includes the step of receiving in the PI controller environment, measured phase current data so as to compare with reference phase current data.

In one embodiment the method includes the step of calculating in the PI controller environment, reference phase voltage data from compared phase current data.

Substitute Sheet

(Rule 26) RO/AU In one embodiment there is provided a feedforward step, which includes receiving, in a computing processor, data relating to measured back EMF and current from a plurality of PMSM phases for input into the back-EMF feed forward block and PI current controller environment respectively. It may be that in some embodiments the measured back EMF is calculated from some measurement of one or more motor characteristics, for example, a measurement of motor speed and position and current in one or more phases.

In accordance with one aspect of the present invention there is provided a method of control of a multi-phase electric machine under fault conditions of one or more open-phases, the method including the steps of:

retrieving in a computing processor reference current data which is ob- tained via a torque reference and the optimised post-fault phase current data from an optimisation engine database in accordance with a selected fault condition in the electric machine;

transforming, in the computing processor, a torque matrix using the opti- mised current phasor data to provide reference phase current data for use in one or more PI current controllers;

receiving, from the PI current controller environment, the reference phase voltages so as to provide control over adjusted phase current signals which have been sent to an inverter drive unit configured to be connected to the multi-phase PMSM.

In accordance with one aspect of the present invention there is provided an optimi sation method for facilitating control of a multi-phase electric machine under fault conditions of one or more open-phases, the method including the steps of:

receiving, in a computing processor, data relating to measured back EMF and current from a plurality of non-faulted electric machine phases;

optimising, in a computing processor, characteristics of one or more non- faulted injected current phasors for the multi-phase electric machine under select- ed fault conditions;

refining the injected current phasor characteristics by comparing the opti mised current phasor characteristics with data obtained from the receiving step. The optimisation method is configured to provide output data suitable for input into a transformation engine which provides phase reference current data for PI con trollers in an FOC environment during fault conditions.

Substitute Sheet

(Rule 26) RO/AU In accordance with a further aspect of the present invention there is provided a control system for controlling a multi-phase electric machine under fault conditions of one or more open-phases, the controller including:

an optimisation engine for optimising characteristics of one or more injected current phasors for the multi-phase electric machine under selected fault condi- tions;

a transformation engine for transforming the one or more optimised current phasors to provide reference current data for the electric machine;

a closed-loop current PI control system for receiving compared current phasor data and providing phase voltage reference data to an inverter drive unit. In accordance with still another aspect of the present invention there is provided a system for controlling a multi-phase electric machine under fault conditions of one or more open-phases, the system including a computing system which includes: an optimisation engine for providing optimised characteristics of one or more injected current phasors for the multi-phase electric machine under selected fault conditions;

a transformation engine for transforming the one or more optimised current phasor characteristics to provide reference current data for the electric machine; a closed-loop current PI control system configured to receive compared current phasor data and configured to provide phase voltage reference data to an inverter drive unit.

In accordance with a third aspect, the present invention provides a computing pro gram that includes at least one instruction, which, when executed on a computing system, performs the method steps in accordance with one or more aspects of the invention.

In accordance with a fourth aspect, the present invention provides a computer readable medium incorporating a computer program in accordance with one or more aspects of the invention.

In accordance with a fifth aspect of the present invention there is provided a drive system including an electric machine and a controller substantially as hereinde- scribed.

In one embodiment the transformation engine assigns an equal magnitude to each one of three optimized currents so as in use to avoid de-rating some of the phase windings.

In one embodiment the magnitude of the three optimised currents is selected to be the largest phase current.

Substitute Sheet

(Rule 26) RO/AU In one embodiment, the optimisation engine iteratively solves an algorithm to opti mise the post-fault current angles a, b, and y phase-shift angle data to obtain the desired machine output torque characteristics.

In one embodiment, the optimisation engine receives data from sensors monitoring back-EMF and non-faulted phase currents.

In one embodiment the 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 transformation engine during the fault condition.

In one embodiment the transformation engine consults the lookup table to retrieve the current phasor references for use in the online development of the post-fault FOC transformation matrix.

In one embodiment, the optimisation engine facilitates calculation of theoretical torque waveforms by iteratively calculating all phase angle combinations until the desired torque characteristics are obtained.

In one embodiment the transformation engine graphically generates a standard operation surface and a post-fault current surface, plotted on orthogonal three-di mensional axes.

In one embodiment the transformation engine rotates the axes of the plotted sur- faces such that one of the axes is perpendicular to the post-fault operating surface and the other two axes lie parallel to the standard surface.

In one embodiment, the phase back-EMFs of the motor are fed-forward such that the PI current controllers no longer compensate for the PM flux-linkage terms and now only compensate for the transformed inductive and resistive terms

In one embodiment, there is provided a fault-tolerant motor which includes sub- stantially constant phase self-inductance and low mutual-inductance

In one embodiment, the optimisation engine constrains the post-fault current pha- sors to be symmetrical about the faulted phase to minimize torque pulsation. In one embodiment, the transformation engine constrains post-fault current data to give zero t_2f - axis current. In one embodiment, the transformation engine constrains the unit vector length of the t - axis current component so that it is equal to one.

Substitute Sheet

(Rule 26) RO/AU In one embodiment, the transformation engine constrains the t_if - axis to be or- thogonal to the t_2f axis. In one embodiment the transformation engine constrains the post-fault phase cur- rents to provide zero t_2f - axis current. In one embodiment the PI current controller is relieved of responsibility for com pensation for permanent motor flux-leakage terms.

In accordance with still another aspect of the present invention, there is provided a method of controlling a multi-phase electrical machine in a post-fault condition of one or more faulted phases, the method including the steps of:

receiving, in a computer processing system, current data from post-fault current optimisation engine;

building a post-fault stationary transformation engine;

building a post-fault rotational transformation engine;

multiplying the post-fault stationary and rotational transformations to pro vide transformation data; and

transmitting the transformation data to a PI control architecture.

In one embodiment the method includes the step of generating three post-fault sta- tionary axes that are specific to the three unbalanced sinusoidal phase currents which are to be controlled.

In one embodiment the method includes the step of aligning one of the post-fault stationary axes to be perpendicular to the post-fault plane of operation, wherein the post-fault plane of operation is the plane that is parallel to a locus generated by plotting three unbalanced sinusoidal phase currents, which are to be controlled, on a phase-referenced set of orthogonal axes. This alignment ensures that the other two post-fault stationary axes are parallel to the post-fault plane of operation. In one embodiment the method includes the step of configuring the post-fault axes that are parallel to the post-fault plane of operation such that the stationary trans formation outputs a circular locus in these two axes when three unbalanced sinu soidal phase currents are the input references.

In one embodiment the method includes the step of configuring the post-fault axes that are parallel to the post-fault plane of operation such that the stationary trans formation outputs an elliptical locus in these two axes when three unbalanced si- nusoidal phase currents are the input references.

Substitute Sheet

(Rule 26) RO/AU In one embodiment the method includes the step of generating four post-fault sta- tionary axes that are specific to the four unbalanced sinusoidal phase currents which are to be controlled.

In one embodiment the method includes the step of configuring two of the post fault stationary axes such that the stationary transformation outputs zero in these two axes when four unbalanced sinusoidal phase currents are the input refer ences.

In one embodiment the method includes the step of configuring the other two post fault axes such that the stationary transformation outputs a circular locus in these axes when four unbalanced sinusoidal phase currents are the input references. In one embodiment the method includes the step of configuring the other two post fault axes such that the stationary transformation outputs an elliptical locus in these axes when four unbalanced sinusoidal phase currents are the input refer- ences.

In one embodiment, the method includes the step of analytically solving the sta tionary transformation for a generic set of sinusoidal phase currents to yield simple linear equations to calculate each element in the stationary transformation matrix. Advantageously, these equations minimize processing requirements and hence allow for the online generation of the transformation each iteration of the control system.

In accordance with a still further aspect of the present invention there is provided a method of decoupling between transformed axes in machine equations, the method including the steps of:

receiving voltage error reference data, post-fault transformation data, ma chine rotor position data and machine rotational speed data into a computer pro- cessing system;

estimating the phase back-EMF for the respective rotor position;

estimating the phase self- and mutual- inductances of the electric machine for the respective rotor position;

transforming the estimated phase-referenced inductances onto the trans- formed domain using the post-fault transformation data;

calculating the feedforward voltage references to minimize cross-coupling between the post-fault transformed axes using the transformed inductances, ma chine rotational speed and phase back-EMFs;

providing a summing junction to sum the voltage error references with the feedforward voltage references to obtain final reference voltages.

Substitute Sheet

(Rule 26) RO/AU In accordance with another aspect of the present invention there is provided a method of facilitating control of a multi-phase electric machine under fault condi tions of one or more open phases, the method including the steps of:

receiving unbalanced current data from an optimisation engine into a sta- tionary transformation engine and a rotational transformation engine, in a comput- ing processor;

transforming the unbalanced current data using selected machine algo rithms in the stationary transformation engine to identify a locus of unbalanced cur rent data on two phase-referenced axes;

transforming the unbalanced current data using selected machine algo rithms in the rotational transformation engine, to identify dc reference current data; multiplying the transformed locus data and transformed dc reference data together to provide transformed dc-reference error data to one or more PI current controllers in an FOC architecture to control the electric motor.

In one embodiment there is provided the additional step of:

generating three post-fault stationary axes that relate to three unbalanced sinusoidal phase currents;

aligning one of the post-fault stationary axes to be perpendicular to the post-fault plane of operation, being the place that is parallel to the locus generated by plotting the three unbalanced sinusoidal phase currents on the phase-refer enced set of orthogonal axes.

In one embodiment there is provided the additional step of configuring the post fault stationary axes such that the stationary transformation engine outputs a circu lar locus in these two axes when three unbalanced sinusoidal phase currents are the input references.

In one embodiment there is provided the additional step of configuring the post fault axes such that the stationary transformation outputs an elliptical locus in these two axes when three unbalanced sinusoidal phase currents are the input references.

In one embodiment there is provided the additional step of providing a diagnostic locus selector which selects a general locus form based on the presence of healthy currents, faulted currents, or harmonic content.

In one embodiment the PI current controllers are transformed onto the rotational post-fault axes.

Substitute Sheet

(Rule 26) RO/AU Advantages

78. Advantageously, the arrangement of embodiments of the technology are that the post-fault machine output torque can be optimised to produce lower torque ripple while operating to the maximum possible post-fault average torque per ampere when compared with known methods.

79. For example, in an experiment with a five-phase PMSM machine, under fault con- ditions of single open-phase, the post-fault torque achieved with an embodiment of the present method and system was 77.2% of average rated torque, with a torque ripple of 5.7% of the average torque. By way of comparison, the best known alter- native method of post-fault control garnered results of 73.5% of rated torque, with a 16.67% torque ripple.

80. In another experiment conducted with the present technology, the fault condition was dual open phase in a PMSM. The control method and system of an embodi- ment of the present technology provided 50% of the average rated torque with a peak to peak torque ripple of 14%. In comparison, the best known alternative con- trol method provided an average torque of 60.7% with 91.21 % peak to peak torque ripple.

81. These are significant improvements over known technology.

Clarifications

82. 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.

83. 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

84. 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:

85. Figure 1 is an example three-dimensional current plot, during a dual open-phase fault, showing the planes created by the locus of the post-fault currents and the

Substitute Sheet

(Rule 26) RO/AU locus of the conventional _^ -pnase phase currents when plotted. This is the output of a stationary transformation engine which is a component of an embodi- ment of the present invention;

Figure 2 is a three-dimensional current plot detailing the loci generated by the ex ample post-fault phase currents of the form disclosed herein, and the example post-fault phase currents from Figure 1. This is the output of a stationary transfor mation engine which is a component of an embodiment of the present invention; Figure 3 is a schematic view of a substantial portion of a post-fault control architec- ture as disclosed herein;

Figure 4 is a schematic view of an FOC post-fault transformation building engine, at least showing the overall form of a first parallel transformation calculation;

Figure 5 is a schematic view of a multiplication junction of the FOC post-fault trans- formation building engine;

Figure 6 is a schematic view of a novel decoupling module which interfaces with the FOC transformation building engine;

Figures 7 to 13 show results of the proposed post-fault FOC strategy for a dual non-adjacent open-phase fault to a five-phase open-end winding PMSM system; Figure 14 is a schematic view of architecture of the proposed post-fault FOC strat egy for a dual open-phase fault to a five-phase open-end winding PMSM system; Figure 15 is a schematic of architecture of the post-fault flux-oriented control strat egy for a dual open-phase fault to a five-phase open-end winding PMSM system; Figure 16 is a schematic of the architecture of the proposed post-fault FOC strate gy for a single open-phase fault to a five-phase open- end winding PMSM system; Figure 17 is a flowchart showing steps in a method of an embodiment of the present invention;

Figure 18 is another flowchart showing steps in a method of an embodiment of the present invention;

Figure 19 is a generalised computer system architecture of an embodiment of the present invention which can provide an optimisation engine and a transformation engine for input to PI architecture, and for receiving input from motor sensors; Figure 20, 21 and 22 are graphical results of a new post-fault FOC strategy for a faulted motor using third harmonics;

Figure 24 is a flowchart of an optimisation engine.

Substitute Sheet

(Rule 26) RO/AU 1i6c

Detailed description of an example embodiment

100. Referring to the drawings there is shown a control system generally indicated at 10 for facilitating control of a multi-phase PMSM 60 under faulted conditions of at least one open phase fault.

101. The control system 10 includes an optimisation engine 20, an FOC transformation building engine 30, a PI control architecture 40 and an inverter drive 50.

102. A PMSM is indicated at 60, which is the subject motor in (at least one) open-phase fault condition.

103. In more detail, and with reference to Figure 23, there is shown a schematic dia- gram of an embodiment of an electronic computing system 100, the system 100 comprises several key components, including a user computer 102; an application server 104; interface engines 106 which interface with comparator engines and other elements of PI control architecture 40; and a data network 108. The system

100 also includes various data links 110 that connect the user computer 102, the application server 104 and the interface engines 106 to the data network 108 so that data can be exchanged between the user computer 102, the application server 104 and the interface engines 106.

104. The electronic computer system 100 interfaces with the control system 10 and in cludes optimisation engine 20 and transformation engine 30. The electronic com puter system 100 could also include PI elements and other control elements, as suits practical considerations. Various networked servers could hold and calculate selected portions of the control algorithm in real time or offline as required. Those portions could be, for example, some initial elements of the optimisation algorithm.

105. 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 PLC, Raspberry PI, Arduino, or any kind of proprietary device.

106. For the purpose of clarity only, the embodiment of the system 100 will be described with reference to an Intel-based computer such as those available from, for exam ple, Lenovo, Dell or HP. The user computer 102 has a data and/or memory store, say, on a drive, being solid state or virtual or otherwise (not shown in the diagrams) that contains a range of software and data. In particular, the software typically in cludes the Windows or OSX operating system. The memory store also contains a web browser application such as, although not limited to, Google Chrome.

107. Like all desktop computers 102, the user computer 102 also comprises a key

board, mouse and visual display device (monitor).

Substitute Sheet

(Rule 26) RO/AU The application server 104 is in the form of an Internet computer server and is an Intel based server such as that available from IBM, Dell or HP. The application server 104 has a data and/or memory store (not shown in the figures) that contains a range of software and data, and could be in the form of a solid state device, hard disk, or virtual store. In particular, the software on the memory store of the applica tion 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 description, 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 one or more matrix transformation applications. While subsequent paragraphs of this description provide a detailed description of the transformation application, the transformation application may be in the form of a web based application that the user of the user computer 102 can access to transform matrices available via any one of the interface engines 106. It is envis- aged that in alternative embodiments of the system 100, different forms of the ap plication server 104 can be used.

The interface engines 106 are not dissimilar to the application server 104 insofar as the interface engines 106 are capable of transmitting and receiving data. Each interface engine 106 is connected to a comparator or other PI control element that is partially or wholly monitored and/or controlled by the interface engines 106. To provide some context regarding the PI control architecture, which is shown in Figures 14, 15, and 16, the interface engines 106 can be considered to connect at least, in those Figures, to comparator unit 75.

The data network 108 may be in the form of an open TCP/IP based packet net work 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 interface engines 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 interface engines 106, each of those components are in data communication with the data network 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.

It can be seen that the optimisation engine 20 and the transformation engine 30 can be connected wirelessly or via electrical cabling to the PI control architecture

Substitute Sheet

(Rule 26) RO/AU 40 to provide input to the PI control architecture 40 via the summing/comparator circuitry 75, and also to receive information from motor control sensors 70.

All these connections could be made wirelessly so that the PI control architecture could be on board a vehicle such as a UAV, UMV, or other vehicle driven by motor 60, or indeed any other application for the motor 60. The PI control architecture 40 could be remote from the vehicle (not shown) and wirelessly input data to the in verter drive 50, but practically speaking, in embodiments, the algorithms and/or control transformations are simplified so that computations are kept simple and therefore fast, so they can be done with small and light computer processing hardware. Therefore, it is likely that the PI control architecture 40 will be on board, together with the optimisation engine 20 and transformation engine 30, as de scribed in the examples in this specification.

Shown in Figure 20 is a schematic diagram of the control system 10, which inter faces with the inverters 50 for controlling the PMSM 60. The fault diagnosis engine 90 outputs fault data to the current optimisation engine 20. The fault diagnosis en- gine 90 is in the form of a voltage sensor 92 measuring the voltage in between in verter 50 output phase terminal and the motor 60 input terminal. During non-fault- ed conditions, this voltage sensor 92 will only measure the copper losses for the cable connection between the inverter phase terminal and the machine terminal. This voltage drop will be small, i.e. less than 5V. During faulted conditions, the fault detection voltage sensor 92 will measure a much larger voltage (depending on the switching state and phase back-EMF). Therefore, the fault diagnosis engine 90 registers an open-phase fault if the measured voltage, using this sensor 92, in creases to a value greater than 5V. That voltage is high enough to avoid spurious tripping from inrush currents when starting the machine. This fault detection tech nique is crude but is suitable for the purposes of testing the control system of the present invention.

The current optimisation engine 20 is shown in Figure 20 to be configured to re ceive fault data from the fault diagnosis engine 90. Then the current optimisation engine 20 is caused to resolve the proposed optimization algorithm in a manner outlined in Fig. 24. The optimization algorithm can be seen in that Figure to first generate a set of initial phase currents over one electrical cycle. These currents and the offline recorded flux-linkages are then used to calculate a theoretical in stantaneous torque array for one electrical cycle using the equation set out below.

Substitute Sheet

(Rule 26) RO/AU The above torque array is then used in the objective function below to optimize both the post-fault torque ripple and the average developed torque.

OF = abs(T_WV - T_r ) + /f suppress X abs(r/ - T_r )

A differential evolution algorithm is then used to select a new set of post-fault phase currents, of the form set out below, which provide improved compliance with the objective function.

This process is performed offline for a certain number of iterations, N, in the cur rent optimisation engine 20 until the phase currents which give the desired torque characteristics are obtained. As mentioned, this process is outlined in the flowchart in Fig. 24. This optimization algorithm is used to determine the optimal post-fault phase currents which are input into the transformation engine 30.

Turning to Figures 3, and 14 to 16, it can be seen that the current optimisation en- gine 20 is connected to the transformation building engine 30. The transformation building engine 30 is connected to a stationary transformation engine 32 and a ro- tational transformation engine 34, which tend to run their operations in parallel in a first stage, while each of the transformation engines 32 and 34 has outputs which are connected to a current summing or current multiplication engine 36 so that they can send data thereto for a second stage of calculation. An input of the sta tionary transformation engine 32 is configured to receive encoder data on rotor po sition of the motor shaft of the PMSM 60, as well as current references in the phase domain, and transformation equations from the transformation building en gine 30. An input of the rotational transformation engine 34 is configured to receive encoder data on motor shaft angular position, receive measured current in the phase domain from the current sensors disposed on the PMSM 60, as well as transformation equations and data from the transformation building engine 30. The current summing or multiplication engine 36 is connected at its output via a data manifold to one or more PI current controllers 40 so it can send data to one or more PI current controllers. The output of the one or more PI current controllers 40 is connected to a decoupling module 95 which is configured to transform the trans- formed-domain voltage error reference data which is in use output from the PI cur-

Substitute Sheet

(Rule 26) RO/AU ¾

rent controllers, back to the phase domain for use by the inverter topology 50 which is connected to the PMSM 60.

122. In the Figures, decoupling module 95, is disposed at an output of the PI current controller architecture 40, and is also connected to an output of the transformation building engine 30. A decoupling block 96 is provided as part of the decoupling module 95, and arranged such that the input of the decoupling block can receive transformed voltage error data from the PI controller, and decoupling data from the transformation building engine 30, while another output of the FOC transformation building engine 30 is connected to a stationary transformation engine 132 which is disposed downstream from the decoupling block 96. An output of the stationary transformation engine 132 is connected to a duty cycle generator 97 so that it can receive phase-referenced voltage reference data.

123. A detail schematic view of the transformation building engine 30 can be seen in Figures 4 and 5. It can be seen there, that the transformation building engine 30 includes a stationary transformation engine 32 and a rotational transformation en gine 34 working in parallel for a first stage of calculation and then it can be seen that a multiplication engine 36 is deployed to combine the outputs from the two transformation engines 32 and 34.

124. The output from the multiplication engine 36 is a transformed current error refer ences which can be output to the PI controllers which are in the phase domain.

OPERATION

125. Turning to Figures 3 and 14 to 16, as well as 25, it can be seen that in the event of a faulted condition, the optimization engine 20 receives fault data regarding fault type from a diagnostic engine 90 (Step 900), as well as torque reference data from a speed controller 69, and outputs optimized current phasor reference data to the transformation engine 30. The optimisation algorithm is discussed in the para graphs above in this specification.

126. A current magnitude reference or torque reference is then obtained from either a PI speed controller architecture 40 or current reference generator 67 and is sent to the FOC transformation building engine 30. The measured current data is ob tained from the current sensors 80 and is sent to the transformation building en gine 30. Rotor position data of the PMSM 60 is obtained from the encoder 65 and is also sent to the transformation building engine 30.

127. The FOC transformation building engine 30 in operation receives post-fault current data from the current optimisation engine 20. The FOC transformation building en gine 30 (Step 910) generates three or four post-fault stationary axes that are spe-

Substitute Sheet

(Rule 26) RO/AU cific to the three unbalanced sinusoidal phase currents which are to be controlled. The unbalanced sinusoidal phase currents are plotted on the axes such as those shown in Figures 1 and 2, and then solved mathematically. The stationary trans formation engine 32 receives the current references in the phase domain from the current optimisation engine 20 and rotor position data from the encoder and out puts current reference data in the form of a locus in 2-dimensions to the input of a current multiplication/summing engine 36. The selected equations that are used in the stationary transformation engine 32 to plot the locus and output the data are as set out below, which are selected depending on the input from a transform selector 98, which is connected to the speed calculation engine and forms part of the diag- nostic engine 90. The transformation building engine 30 resolves the equations mathematically at step 920. The multiplication junction 36 combines the outputs of the stationary and rotational transformations at step 930 and then provides them to the PI controllers at step 940 as detailed below.

TWO FAULTED PHASES - low speed

128. First, the transform selector 98 identifies the number of faulted phases and, if there is more than one, whether they are adjacent or spaced apart from one another.

129. Secondly the transform selector 98 identifies the speed of the rotor of the PMSM 60 and, if the rotor is below about 500rpm, a stationary transformation is used, which is set out below in this paragraph. This stationary transformation matrix con verts three phase currents, which each contain fundamental and third harmonic components, into stationary frame input references.

130. Also below about 500rpm, the stationary transformation above may be used to- gether with a rotational transformation set out below, which converts the stationary frame references into dc input references. os (cot— 6f ) + p_x cos(3 cot— 35^) sin(cot— S_f ) + sin(3cot— 36_f )

sin(a t— + p_x sin(3c t— 3<5 ) cos(o )t— — p cos(3cot— 3 )

Substitute Sheet

(Rule 26) RO/AU The dc input references are of the form set out below.

131. The outputs of these two stationary and rotational transformations are then com- bined in the multiplication junction 36 to provide an FOC transformation matrix, which can convert three phase currents, which each contain a fundamental and third harmonic component, into dc references. The FOC transformation matrix is set out below.

rot. f ¹ stat.3rd_Hami,/

132. Advantageously, the final FOC transformation matrix above yields dc references and avoids obtaining tracking errors in the PI current controllers. The proposed method is utilized for the event of a dual open-phase fault occurring in a five-phase open-end winding PMSM system. All other known techniques send non-dc input references to the PI current controllers when controlling three unbalanced phase currents with fundamental and third harmonic components. These techniques suf- fer from PI controller tracking errors, which generate undesired torque and current ripple and make accurately tuning the PI controllers difficult. Advantageously, the method of embodiments of the present technology inhibits PI controller tracking error issues, when injecting the currents.

133. The transform selector 98 may identify that the rotor speed of the PMSM 60 is high, in the region of somewhere above 500, to 1500rpm. In that case, the trans- form selector 98 deploys a different stationary transform as set out below. Flowev- er, it is to be understood that this speed-dependent selection of transforms is just one embodiment, and the transforms set out below may be used at any speed. It is to be understood that sometimes the other transform set out above can improve the results, so the transform selector makes an assessment as to which one to de ploy, depending on the projected or actual results at desired rotor speeds..

Substitute Sheet

(Rule 26) RO/AU TWO FAULTED PHASES - high speed

134. First, this proposed method uses simplified linear equations set out below, which in real-time generates the transformation for any set of three sinusoidal currents of the form set out below.

v cos(o )t— B ) w cos (cut— C)

T/,30( —v sin(cut— B )

n₂

where

sin («-c)

n·, = -n.

sinter-//)

sin(//- )

n = n_> -

¹ ’ sin(«-/i)

sin(2(<r-/f ))

sin(2(tr— y )) +sin(2(//— y ) )

sin(2(«- ))

V =—iv

sin(2 («-/ ))

sin(2(/y— y))

U = W

sin(2(«-/ )

135. The proposed transformation matrix is implemented in the adapted FOC architec ture, which is shown at Figure 14 to 16. This architecture uses three PI controllers to control the currents, which are transformed onto the new proposed df, qf and tf post-fault axes. These axes have been designed such that the tf- axis is perpen dicular to the new post-fault current surface of operation, Fig 2. Note that these axes are not perpendicular to the conventional three- dimensional d-q-0 axes, which are used in conventional FOC with three-phase PMSM drives. The trans formed back-EMF term in the transformed machine equation possesses harmonic components which couple the transformed axes.

136. Therefore, the proposed FOC architecture also can be seen in the Figure 14 to include a back-EMF feed-forward block which means that the PI current controllers no longer compensate for this term in the transformed machine equation. This re duces the cross-coupling between the transformed axes. The proposed method will yield the least amount of undesired current harmonic generation when a

Substitute Sheet

(Rule 26) RO/AU PMSM with negligible mutual inductance and relatively constant self-inductance is used. Therefore, this technique is well-suited to surface-mount PMSMs with no saliency.

137. This transformation’s major advantage is yielding dc reference inputs for the PI current controllers to avoid obtaining tracking errors, which produce undesired harmonics in the phase currents. This means that this method provides a simple solution for obtaining the desired dynamic torque characteristics at all machine op erating points when controlling three unbalanced sinusoidal phase currents. This technique is a significant contribution to the field of post-fault control of five-phase PMSMs, in an open-end winding configuration, after a dual open-phase fault has occurred.

ONE FAULTED PHASE

138. When there is shown to be only one faulted phase, the transform selector 98 se lects the following strategy.

139. A four-dimensional post-fault transformation strategy is deployed, using the equa tions set out below.

sin²( a)

t2 ^~ , 2 (sin² (a) +sin² (/?) )

Substitute Sheet

(Rule 26) RO/AU This transformation converts a set of four unbalanced sinusoidal phase currents into dc input references for the PI current controllers. The technique has been pro posed for the event of a single open-phase fault occurring in a five- phase PMSM system with an open-end winding configuration. Other known techniques send non-dc references to the PI current controllers when controlling four unbalanced sinusoidal phase currents. Therefore these techniques suffer from PI controller tracking errors, which generate undesired torque and current ripple when control ling these currents. This embodiment of the FOC transformation does not suffer from PI controller tracking error issues when controlling four unbalanced sinusoidal phase currents.

The proposed transformation matrix is implemented in the FOC architecture in Fig. 16. This architecture uses four PI controllers to control the currents, which are transformed onto the novel d_f, q_f, t and t₂f post-fault axes. Results are discussed hereinbelow, using an example transformation, in an experimental setup with an open-phase fault to phase‘a’. The results from this test show that the proposed control technique can accurately control the unbalanced post-fault sinusoidal cur rents with negligible distortion and harmonics. The results also show that the pro posed technique can produce approximately 77.2% of the average rated torque with a peak-to-peak torque ripple approximately equal to 5.7% of the average torque during a single open-phase fault.

From the Figures it can be seen that once the transformation matrices have been resolved, the transformed reference and transformed measured current data is output from the FOC transformation engine 32 and 34, and sent to the summing engine 36, which calculates the error signal data.

The PI current controller architecture 40 receives this error signal data and outputs transformed reference voltage data. The FOC transformation building engine 30, receives this transformed voltage data and outputs reference phase voltage data. The back-EMF feed-forward block 70, receives machine speed and rotor position information from the encoder 65 and outputs estimated phase back-EMF voltage data. The summing engine 36 receives the reference phase voltage data and es timated phase back-EMF voltage data and outputs the resultant voltage data to the inverter 50 via the decoupling block. While there is no fault, the optimization engine 20 will send standard healthy current phasor data to the FOC transformation build ing engine 30 and the system will act just as known FOC architecture.

Substitute Sheet

(Rule 26) RO/AU The optimisation engine 20 and FOC transformation building engine 30 or some other speed control module (not shown) may provide speed control for the motor 60 to facilitate calculations of the phase angles and other quantities. In one em bodiment the speed controller sets the speed to a single speed.

It can be seen that the method in operation is as shown in Figures 17 and 18. The steps of the embodiments shown are as set out in the Figures.

Substitute Sheet

(Rule 26) RO/AU 2

EXPERIMENTAL RESULTS

146. The example post-fault transformations T f,3_{Phase, bde}(0) and T f, 3_{Phase, cde} ( Q ) have been implemented in separate experimental tests to show that the proposed method will yield post-fault transformations which can be used to accurately control three unbalanced post-fault currents. The experimental setup consists of a dSPACE DS1006 processor operating with a 20kHz control algorithm cycle time and a DS5203 FPGA which generates the gate-drive signals at a carrier frequency of 20 kHz with 1 ps of deadtime. Two five-phase two-level inverters have been configured in an open-end winding topology with a single 140 V dc bus voltage. A five-phase prototype surface-mount PMSM was used for this test. This machine has been shaft driven to an induction generator to provide variable load torque.

The appropriate phases have been disconnected from the machine and inverter output terminals to create a dual open-phase fault. The novel post-fault control technique has then been implemented for the PMSM whilst operating at a low speed, 300 rpm, and high speed, 1500rpm, with a load torque which demands rat ed current. These speeds have been chosen as low and high speeds for the sur- face-mount PMSM. Torque has been calculated, together with the offline recorded back-EMF profile.

Case 1 : Dual Non-adjacent open phase fault experimental results

147. The results for the dual non-adjacent open-phase fault when using T _/,3_0,Me(0) are shown in Figs. 7 to 13. Fig. 7 shows that there is approximately 40 mA of peak-to- peak ripple in the id q and i_t current responses at 300 rpm, which is approx imately 2% of the phase current amplitude. This ripple is small and is likely due to some remnant cross-coupling between the axes.

148. Most of the cross-coupling is due to the harmonics in the non-diagonal elements in the inductance matrix L^qt - The only effective method of reducing this cross coupling is to use a machine with near constant self-inductance and negligible mu tual-inductance. Some of the cross-coupling is also due to small inaccuracies in the fed-forward back-EMF. This back-EMF that is fed-forward is dependent on ac curate speed calculation using the encoder position measurements and is depen dent on the offline measured PM flux- linkage being unchanged during all operat ing conditions. The speed calculation has been averaged across 80 control algo-

Substitute Sheet

(Rule 26) RO/AU rithm cycles to obtain a resolution of approximately 0.75 rpm at 1500 rpm. The speed calculation resolution and small variations of the PM flux-linkage from the offline measured values will introduce minor errors in the back-EMF feedforward ing.

Fig. 8 shows that there is approximately 200 mA of peak-to-peak ripple in the i^j current response, and approximately 150 mA and 500 mA of peak-to-peak ripple in the iq and i_t j current responses at 1500 rpm. Therefore, the magnitude of the transformed current peak-to-peak ripple is larger when operating at higher speeds. This validates the theory that cross-coupling between the axes will cause this rip ple. This is because the non-diagonal harmonic elements in the inductance matrix ^Ldqt ,/ ^will result in cross- coupled terms in the voltage machine equation which are multiplied by the electrical speed of the machine. Hence, the magnitude of these terms will increase as speed increases. Note that the very small ripples in the i_qj reference current are requested by the speed controller to keep the speed constant at 1500rpm.

Fig. 9 shows that the phase currents at 300 rpm and 1500 rpm are sinusoidal in shape and possess negligible distortion. This proves that the example post-fault transformation T (q) can be used in an FOC architecture to accurately generate three unbalanced f,30,bde post-fault currents with negligible distortion. An FFT of these currents, Fig. 10, shows that there are no other significant low-order current harmonics aside from the desired fundamental at 300 rpm. At higher speeds, at 1500 rpm, there are some minor low-order harmonics which can be considered negligible in comparison to the fundamental current amplitude.

The phase-shift angles of the fundamental current are computed in the frequency spectra for 300 rpm and 1500 rpm as shown in Figure 11. At 300 rpm, the phase- shift angles of the fundamental are equal to the desired reference current phase- shift angles. At 1500 rpm, the phase-shift angles have an error of approximately 2° lagging which is likely due to the increased phase current distortion at higher speeds because of cross- coupling and the positional accuracy of the encoder at higher speeds. However, the error margin in the phase-shift angles is still insignifi cant at higher speeds.

The developed torque waveforms at 300 rpm and 1500 rpm are shown in Fig. 12. At 300 rpm there is approximately 0.175 Nm of peak-to-peak torque ripple with an average torque of 1.59 Nm. At 1500 rpm there is approximately 0.24 Nm of peak-

Substitute Sheet

(Rule 26) RO/AU 2$h

to-peak torque ripple with an average torque of 1.61 Nm. There is slightly more torque ripple at higher speeds, which is due to the slightly larger current ripple and small phase-shift angle errors experienced at higher speeds. The rated torque of the machine is approximately 3.2 Nm. Therefore, approximately 50% of the aver age rated torque can be generated with a peak- to-peak torque ripple equal to ap proximately 14% of the developed average torque when the proposed post-fault transformation is used during a non-adjacent dual open-phase fault.

153. The torque transient performance has been shown in Fig. 13. The speed of the machine has been stepped from 300 rpm to 1500 rpm for this test. Fig. 13 shows that the integral terms of the PI current controller gains can be chosen to achieve zero steady-state error, within a user defined time, during a torque reference change.

Case 2: Dual adjacent open-phase fault experimental results

154. The results for the dual non-adjacent open-phase fault when using T _f,z _,cde{e) are shown in Fig 17 to 19. The peak-to-peak current ripple in id jq and i_t is ap proximately 50 mA at 300 rpm. In comparison to the dual non-adjacent trans- formed current responses, Fig. 7, which have approximately 40 mA of peak-to- peak current ripple, the dual adjacent transformed current responses have slightly more ripple. This is due to the fact that the transformed inductances, Ldj and Lqj, for the dual adjacent transformation have a higher peak-to-peak ripple than the dual non-adjacent transformed inductances. These variances in the transformed inductances will cause some minor cross-coupling between the transformed axes, which leads to increased current harmonic generation.

155. The peak-to-peak current ripple in i_j j , i_q and i_t is approximately 250 mA, 225 mA and 190 mA at 1500 rpm, Fig. 18. The dual adjacent idj and iqj current re sponses have larger peak-to-peak current ripple values when compared to the dual non-adjacent idj and iqj current responses, in Figure 8. Flowever, the dual adjacent ///current response has a smaller peak-to-peak current ripple value when compared to the dual non-adjacent itj current response. This is because the dual adjacent transformation yields Ldj and Lqj waveforms with a higher peak-to-peak ripple and an /./ waveform with a smaller peak-to-peak ripple when compared to the dual adjacent transformation transformed inductance waveforms.

156. This shows that smaller ripples in the transformed inductances will yield less unde sired current harmonic generation. Therefore, the proposed post-fault FOC method

Substitute Sheet

(Rule 26) RO/AU will produce the least amount of undesired current harmonic generation when used with PMSMs that possess negligible mutual inductance and a constant self-induc- tance. However, the proposed post-fault FOC method can still be successfully im plemented to accurately control the post-fault phase currents with PMSMs that have self- and mutual- inductance harmonics.

Fig. 19 shows that the phase current responses at 300 rpm and 1500 rpm are si- nusoidal in shape and possess negligible distortion. This proves that the example post- fault transformation T _f,30,ei/e(0) can be used in an FOC architecture to accu rately generate three unbalanced post-fault currents with negligible distortion dur ing a dual adjacent open-phase fault.

The developed torque waveforms at 300 rpm and 1500 rpm are now discussed for the dual adjacent transformation. At 300 rpm there is approximately 0.14 Nm of peak-to- peak torque ripple with an average torque of 1.57 Nm. At 1500 rpm there is approximately 0.20 Nm of peak-to-peak torque ripple with an average torque of

1.61 Nm. There is slightly more torque ripple with the dual non-adjacent transfor- mation method as compared to the dual adjacent transformation method. This is likely because the dual non- adjacent ifJ current response possesses a higher cur rent ripple value compared to the dual adjacent itJ current response.

The torque transient performance was measured. The speed of the machine has been stepped from 300 rpm to 1500 rpm for this test. The results showed that the integral terms of the PI current controller gains can be chosen to achieve zero steady-state error, within a user defined time, during a torque reference change. A speed reversal test was performed For this test, the reference speed is a square wave at 1 Hz and is stepped from 100 rpm to -100 rpm. This result is the final vali dation that the proposed transformation technique provides accurate current con trol.

This embodiment shows a novel method for developing a new post-fault transfor mation matrix, which obtains dc PI current controller input references when control- ling three unbalanced currents in a dual-faulted five-phase PMSM machine. It is the only known technique which substantially does not suffer from PI controller tracking error when controlling unbalanced sinusoidal post-fault currents during a dual open-phase fault to a five-phase PMSM machine. The proposed method uses simplified linear equations which real-time generates the transformation for any set of three sinusoidal currents of the form discussed and disclosed herein.

Substitute Sheet

(Rule 26) RO/AU Results - single faulted phase

162. An experimental test has been conducted to show that the proposed four-dimen sional post-fault transformation can be used with PI current controllers in an FOC architecture to accurately control four unbalanced optimized post-fault currents. This test has been conducted with a testbed like that outlined above. In this test, phase‘a’ has been disconnected from the inverter to create an open-phase fault. As with the dual-fault test, the proposed post-fault current control technique with the example transformation matrix, has been implemented with the machine oper ating at speeds of 300 rpm and 1500 rpm. A load torque was then applied to the machine such that the rated current is achieved. The results from these tests are shown in Figs. 20 to 22.

163. At 300 rpm, Fig. 20, the measured i_q waveform accurately tracks the i_qj refer ence waveform with approximately 40 mA of peak-to-peak ripple. Also, the i^ , i_t and i_t2 waveforms have an average of 0 A with peak-to-peak current ripples of 60 mA, 60 mA and 75 mA respectively.

164. At 1500 rpm, as shown in Fig. 21 , the measured i_qj waveform accurately tracks the i_qj reference waveform but displays an increased peak-to-peak ripple of ap proximately 100 mA. Also, the i^ , i_t† and z;2,/^wavef°^{rms have} increased peak-to-peak ripples of approximately 240 mA, 120 mA and 300 mA. Therefore, the current ripple increases as the speed increases. This speed/current ripple rela tionship is due to the cross-coupling terms in the post- fault transformation ma chine equations. The transformed inductance matrix Jdqt^ tl ’ possesses small harmonic components in each element of the matrix which will provide cross-cou pling between the axes. Also, the final terms of the transformed machine equations contain L^j and L_q j. Therefore, the harmonics in these two transformed induc tance terms will cause rotor-position variant and hence speed-variant cross-cou pling. This cross-coupling will cause undesired current harmonics (i.e. current rip ple) as the PI current controllers can no longer independently control each trans formed reference frame. Note that this cross-coupling will increase as speed in creases.

165. There will be some current harmonic generation from small inaccuracies in the back- EMF value that is fed-forward. This feed-forward term is dependent on the

Substitute Sheet

(Rule 26) RO/AU measured PM flux-linkage being constant for all operating conditions. Note that small variations in the PM flux-linkage may occur across all operating points. The back-EMF feed-forwarding is also dependent on the speed calculation using the encoder position measurements. This calculation measures the change in rotor position across 80 control algorithm cycles which gives a resolution of approxi mately 0.75 rpm when operating at 1500 rpm. These two small inaccuracies in the fed-forward back-EMF will produce some cross-coupling between axes which cause small speed-dependent current harmonics.

The phase currents at 300 rpm and 1500 rpm, Fig 22, have minimal distortion and are sinusoidal in shape. This proves that the small magnitude current harmonics in the transformed axes responses produce negligible current harmonics in the phase domain.

The torque responses at both 300 rpm and 1500 rpm have an average torque of 2.47 Nm with 0.14 Nm peak-to-peak ripple. Note that the rated torque of the ma chine is 3.2 Nm. Therefore, the proposed post-fault transformation in an FOC ar- chitecture can produce approximately 77.2% of the average rated torque with a peak-to-peak torque ripple approximately equal to 5.7% of the average torque dur ing a single open-phase fault at rated current.

The transformed currents and output torque have also been recorded during a torque transient. The transient has been performed by step-changing the speed from 300 rpm to 1500 rpm. The result was that the integral terms of the PI current controller gains can be chosen to achieve zero steady-state error during a torque reference change. Therefore, this result validates that proposed method does not obtain a tracking error during a torque reference change.

Also, the transformed currents and output torque have been recorded transitioning from healthy conditions to faulted conditions. During this test, the machine is initial ly controlled at 1500 rpm using the conventional five-phase transformation matrix in an FOC architecture. A load torque is applied such that rated current will be achieved after the open-phase fault occurs. This avoids over-currenting the ma chine after the fault occurs. An open-phase fault is then triggered on phase‘a’. A fault diagnosis system has been designed to immediately detect the fault for this test, which would be the case in a practical system. This diagnosis system com prises of a voltage sensor measuring the voltage in between the inverter output phase terminal and the motor input terminal. During non-faulted conditions, this voltage sensor will only measure the copper losses for the cable connection be tween the inverter phase terminal and the machine terminal. This voltage drop will be small, i.e. less than 5 V.

Substitute Sheet

(Rule 26) RO/AU 170. During faulted conditions, the fault detection voltage sensor will measure a much larger voltage (depending on the switching state and phase back-EMF). Therefore, the fault detection algorithm registers an open-phase fault if the measured voltage, using this sensor, increases to a value greater than 5 V. Note that 5 V is high enough to avoid spurious tripping from inrush currents when starting the machine. This fault detection technique is crude but is suitable for the purposes of these tests.

171. The results show that the proposed post-fault technique can be engaged, once an open- phase fault has been detected, to successfully keep the machine operating safely. This occurs without any major disruption to the output torque and the con trollers all remain stable during the transition from the non-faulted to faulted mode. There is a small dip in the output torque when the fault occurs, but the desired av- erage torque reference is quickly obtained when the proposed post-fault technique engages. The peak-to-peak current ripple in the i<jJ and if 1 responses increases by a factor of two when compared to the non-faulted id 1 and id2 responses.

Whereas, the peak-to-peak current ripple in the iqJ and if2J responses increases from 60 mA to 185 mA and from 80 mA to 280 mA when compared to the non- faulted /gi and iq2 responses respectively. Also, the torque ripple increases from 0.108 Nm to 0.260 Nm during the transition from non-faulted to faulted operation. However, the torque ripple is still small post-fault and there is no audible noise in dicating the presence of undesired machine vibration.

172. The transformed currents and output torque have been recorded transitioning from healthy conditions to faulted conditions with a small fault diagnosis delay time of approximately 0.3 s.

173. These results demonstrate that the four-dimensional post-fault transformation of an embodiment of the present technology can be used with PI current controllers and a back-EMF feed-forward controller to accurately control four unbalanced post fault phase currents with minimal harmonics or distortion in a five-phase open-end winding PMSM system. The only limitation of this method is that the back-EMF must be determined to be fed-forward in the FOC architecture. This is not a major disadvantage as measuring these waveforms is simple.

Control with first and third harmonics after a dual Open-phase fault

174. The proposed transformation has been validated by experimentally testing three different example post-fault transformations. These transformations are created on-line for three different y and pi combinations discussed above un- der the heading“two faulted phases - low speed” and shown in the Table be-

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(Rule 26) RO/AU low. The specific y and p 1 combinations have been selected to minimize torque ripple for three different maximum torque per ampere values. The y and pi combinations in Transformations 1-2 are for a dual non-adjacent fault to phases ‘b’ and‘e’ and Transformation 3 is for a dual adjacent fault to phases‘b’ and‘c’. Note that these combinations were obtained from the optimization algorithm outlined hereinabove.

The average transformed inductances for these example transformations are

Table 6. 1

The g and p _\ combinations for the experimental tests in this section.

Trans Peak current ( u I )

shown in Table 6.2.

Table 6.2

_ The average transformed inductances for each example transfonnation.

The three example transformation tests have been implemented in the experi mental test setup outlined above. As with the other dual-faulted tests, the three tests have been conducted at a low speed of 300 rpm and a higher speed of

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(Rule 26) RO/AU 1500 rpm. A constant load torque has been applied such that the rated rms phase current is achieved in the phase with the largest amplitude phase current reference. The peak-peak current and torque ripple values from these results have been presented below in Table 6.3.

Table 6.3

Peak-to-peak current and torque ripple for the three example transformations.

Pcak-to-pcak Peak-to-peak current ripple

Example

Speed (rpm) torque ripple (mA)

Transformation

Trans. #1 300 0.1 200 160 45 Trans. #2 300 0.175 200 200 45 Trans. #3 300 0.125 200 200 30 Trans. #1 1500 0.3 1 125 1200 30 Trans. #2 1500 0.425 750 2500 40 Trans. #3 1500 0.21 750 600 150 The peak-to-peak ripple of the transformed currents at 300 rpm are larger than the peak-to-peak current ripple values of the corresponding transformed cur rents obtained with the dual post-fault transformation detailed above, in Figure 7. This transformation has been developed to obtain dc input references when injecting purely sinusoidal post-fault phase currents during a dual open-phase fault. The increase in the peak-to-peak current ripple, for the proposed tech- nique, is due to the extra rotor position dependent components in the Tcoup term, which occur with the new adapted rotational transformation. The harmon ics in the transformed inductances are not compensated for with the feed-for- ward block and hence will cause instantaneous cross- coupling between the axes. This instantaneous cross-coupling will increase the oscillation in the phase currents. The peak-to-peak ripple of the transformed currents at 1500 rpm are larger than the peak-to-peak ripple of the corresponding transformed currents at 300 rpm. This is because the harmonics in the transformed inductances are multi- plied by the electrical frequency in the Tcoup term in and will hence generate more cross- coupling between the transformed axes as the electrical frequency increases. Also, the non-diagonal harmonic elements in the inductance matrix

^Ldqt,f ^w'll result in cross coupled terms in the voltage machine equations

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(Rule 26) RO/AU which are multiplied by the electrical speed of the machine. Hence, the magni tude of these terms will also increase as speed increases. This relationship be tween the peak-to-peak ripple in the transformed currents and the electrical frequency also explains why the peak-to-peak torque ripple is larger at 1500 rpm, when compared to the torque ripple at 300 rpm. The peak-to-peak torque ripple at 300 rpm, when using the proposed technique with example transformation 1 , is 0.1 Nm. Whereas, the peak-to-peak ripple at 300 rpm, when using the technique outlined above, is 0.175 Nm. Therefore, example transformation #1 reduces the torque ripple by 0.075 Nm, as com pared to the technique outlined first above, when operating at 300 rpm. The peak-to-peak torque ripple at 1500 rpm, when using the proposed tech nique with example transformation #1 , is 0.3 Nm. Whereas, the peak-to-peak ripple at 1500 rpm, when using the other technique outlined above, is 0.24 Nm. Therefore, example transformation #1 increases the torque ripple by 0.06 Nm, as compared to the technique outlined above when operating at 1500 rpm. Consequently, example transformation #1 obtains smaller torque ripple at lower speeds but produces larger torque ripple at higher speeds when compared to the technique outlined first in this specification. This is due to the extra rotor position dependent components in the Tcoup term in which occur with the pro posed technique and produce speed dependent current oscillation. In the mea sured phase currents, with Transformation #1 , there is more distortion in the phase currents at 1500 rpm when compared to those at 300 rpm. This is due to the relationship between the peak-to-peak ripple in the transformed currents and the electrical frequency. The transformed currents and output torque have also been recorded during a torque transient using transformation #1. The transient has been performed by step-changing the speed from 300 rpm to 1500 rpm. The result shows that the integral terms of the PI current controller gains can be chosen to achieve zero steady-state error during a torque reference change when using transformation #1. Therefore, this result validates that the proposed method does not obtain a tracking error during a torque reference change. Also, the peak-to-peak ripple in the transformed currents and torque increases as the speed change occurs. These results demonstrate that the proposed three-dimensional post-fault transformation can be used with PI current controllers and a back-EMF and Tcoup feed- forward block to accurately control three unbalanced phase cur rents with fundamental and third harmonic components. These currents are

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(Rule 26) RO/AU controlled with minimal harmonics or distortion at lower speeds and significantly reduce the developed torque ripple when compared to injecting purely sinu soidal phase currents in a five-phase open-end winding PMSM system. At higher speeds, the cross-coupling between the axes, due to the additional Tcoup term in the transformed machine equations, generates oscillations in the phase currents which increase the developed torque ripple. Therefore, the pro posed technique is best-suited to operating at or below 300 rpm during a dual open-phase fault to a five-phase open-end winding PMSM system. When oper ating at higher speeds, 1500 rpm, the first-discussed technique will generate a torque waveform with smaller torque ripple and hence should be used. In summary, the novel method for developing three- phase post-fault transforma tions can be combined with a back- EMF feed-forward controller in an FOC archi tecture. This combination gives the only known documented successful method for injecting optimized post-fault currents during a non-adjacent dual open-phase fault in a five-phase single dc supply open-end winding PMSM system.

Modifications and improvements to the invention will be readily apparent to those skilled in the art. Such modifications and improvements are intended to be within the scope of this invention.

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(Rule 26) RO/AU

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A method of facilitating control of a multi-phase electric machine under fault condi tions of one or more open phases, the method including the steps of:

receiving unbalanced current data from an optimisation engine into a station ary transformation engine and a rotational transformation engine, in a computing pro cessor;

transforming the unbalanced current data using selected machine algorithms in the stationary transformation engine to identify a locus of unbalanced current data on two phase-referenced axes;

transforming the unbalanced current data using selected machine algorithms in the rotational transformation engine, to identify dc reference current data;

multiplying the transformed locus data and transformed dc reference data to gether to provide transformed dc-reference error data to one or more PI current con trollers in an FOC architecture to control the electric motor.

2. The method in accordance with claim 1 further including the step of:

generating three post-fault stationary axes that relate to three unbalanced si nusoidal phase currents;

aligning one of the post-fault stationary axes to be perpendicular to the post fault plane of operation, being the place that is parallel to the locus generated by plot ting the three unbalanced sinusoidal phase currents on the phase-referenced set of orthogonal axes.

3. The method in accordance with claim 2 further including the step of configuring the post-fault stationary axes such that the stationary transformation engine outputs a circular locus in these two axes when three unbalanced sinusoidal phase currents are the input references.

4. The method in accordance with claim 2 or 3 further including the step of configuring the post-fault axes such that the stationary transformation outputs an elliptical locus in these two axes when three unbalanced sinusoidal phase currents are the input refer- ences.

5. The method in accordance with claim 1 further including a diagnostic locus selector which selects a general locus form based on the presence of healthy currents, faulted currents, or harmonic content.

6. The method in accordance with claim 1 or 2 wherein the PI current controllers are transformed onto the rotational post-fault axes.

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(Rule 26) RO/AU

7. The method in accordance with claim 3 wherein the rotational post-fault axes are per pendicular to the current locus data plane.

8. The method in accordance with any one of claims 1 to 4 further including the step of feed-forwarding the back-EMF to the PI current controllers.

9. The method in accordance with any one of claims 1 to 5 wherein one of the selected machine algorithms is in the form:

10. The method in accordance with any one of claims 1 to 6 wherein one of the selected machine algorithms is in the form:

i i = / [sin(i t— d ) + p₁ sin(3a>t— 3 )]

1₂ = /_m [sin

1₃ = / [sin

11. The method in accordance with any one of the previous claims wherein the matrix that is generated in the stationary and rotational matrix transformation engines is in the form

which are solved by using

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(Rule 26) RO/AU

12. The method in accordance with any one of the previous claims further including a de coupling step to reduce coupling between orthogonal axes.

13. The method in accordance with claim 9 wherein the decoupling step includes a feed forwarding step wherein the phase back-EMFs of the motor are fed-forward such that the PI current controllers do not compensate for the back-EMF terms.

14. The method in accordance with claim 9 or 10 wherein the decoupling step includes estimating, in a computer processor, the phase back-EMF for the respective rotor po sition.

15. The method in accordance with any one of claims 9 to 11 wherein the decoupling step includes estimating, in a computer processor, the phase self- and mutual- induc tances of the electric machine for the respective rotor position.

16. The method in accordance with any one of claims 9 to 12 wherein the decoupling step includes the step of transforming the estimated phase-referenced inductances onto the transformed domain using the post-fault transformation data.

17. The method in accordance with any one of claims 9 to 13 wherein the decoupling step includes the step of calculating, in a computer processor, optimized feedforward voltage references to minimize cross-coupling between the post-fault transformed axes using the transformed inductances, machine rotational speed and phase back- EMFs.

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(Rule 26) RO/AU

18. The method in accordance with any one of claims 9 to 14 wherein the decoupling step includes the step of summing the voltage error references with the feedforward voltage references to obtain the final reference voltages.

19. A control system for controlling a multi-phase electric machine under fault conditions of one or more open phases, the controller including:

a post-fault stationary matrix transformation engine configured to build a post fault stationary matrix transformer, using unbalanced sinusoidal current data from a post-fault current optimisation engine and selected machine algorithms, the post-fault stationary transformation engine being configured to identify stationary locus data of the sinusoidal current if it were plotted on two orthogonal phase-referenced axes; a post-fault rotational matrix transformation engine configured to build a post fault rotational matrix transformer, using the post-fault stationary transformation en gine, the post-fault rotational matrix transformation engine being configured to identify dc reference data;

the transformation engine configured to combine the outputs of the stationary and rotational transformation engines to provide transformed dc current reference data;

wherein the transformation engines are connected to a PI controller so as to provide the dc current reference data to a PI controller.

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(Rule 26) RO/AU