WO1998040957A1

WO1998040957A1 - Electric machine

Info

Publication number: WO1998040957A1
Application number: PCT/GB1998/000540
Authority: WO
Inventors: Seamus Dominic Garvey
Original assignee: Insight-M Limited
Priority date: 1997-03-11
Filing date: 1998-03-11
Publication date: 1998-09-17
Also published as: AU6628198A; CN1252181A; GB9705020D0; EP0966787A1

Abstract

A new design for electrical machines and generators involves introducing additional windings in the stator of a machine which drive flux in complete loops around the back of the stator core drawing the stator core into use as an inductor or transformer as well as a conductor of flux for the main working flux of the machine. The stator core may be divided into several different lengths each of which behaves as an independent flux carrier. The inductor or transformer so produced has numerous possible applications including filtering the current in the DC link of a drive to suppress zero-sequence components of voltage at the terminals of the machine, suppressing certain combinations of phase currents in the machine and enabling the machine to present several different voltage-to-current ratios to its supply.

Description

Electric Machine

Field of the Invention.

This invention is a new class of electromagnetic designs of AC electrical machines - both motors and generators. The invention forms a class of designs because the novel aspect of the invention can be introduced into any one of several different existing designs to advantage - with the same effects in each case.

The invention has strong relevance to all AC machines subjected to a voltage spectrum at the machine terminals which may have substantial content in a range of frequencies well above the fundamental operating frequency of the machine. All electrical motors which are driven by PWM (pulse-width modulated) and other switched-mode electronic drives are subject to such a voltage spectrum and all generators supplying an electronic frequency-changer or rectifier are also likely to experience such a spectrum. The invention has additional or different relevance in a large proportion of circumstances where an electrical machine is to be driven from a power-electronic drive which has a DC link.

The invention also has relevance in circumstances where an electrical machine can be best utilised if it can present any one of several different voltage-to-current ratios to its supply (in the same way, for example, that changing from star to delta connection does).

The category of machines to which the distinguishing feature of this new design is most easily applied is the common category of cylindrical-airgap machines having an external stator. However, the distinguishing feature can also be applied to other machine configurations producing new designs from these also. Background to the Invention.

The background to this invention is presented in four distinct parts :

(A) Power Electronic Drives Operating with Electrical Machines.

(B) Spatial Components of Voltages and Currents ... 3 phase machines. (C) Spatial Components of Voltages and Currents ... multi-phase machines.

(D) Zero-sequence phase currents and current ripple in the DC link.

Background_A. Power Electronic Drives operating with. Machines.

Substantial power losses can occur in an electrical machine as a direct result of the presence of high-frequency currents in the machine windings. These losses exist through numerous mechanisms. Chief amongst these are eddy-current and hysteresis losses in the magnetised iron and eddy-current losses in the copper conductors when flux passes transversely through them¹. The special feature of the new design described here can have the effect of suppressing some components of high-frequency currents in some machines with the result that losses and electromagnetic emissions are reduced. The high-frequency currents come about as a result of high-frequency content in the voltage spectrum at the machine terminals. Electric motors driven from power electronic drives are invariably subject to such a spectrum - unless a filter has been fitted into the drive. In many circumstances, this invention reduces or eliminates the need for such a filter. Any power electronic drive can be idealised as Fig. 1 shows.

In Fig. 1 , the connections represented by heavy lines denote groups of conductors and the voltage source symbols represent groups of voltage sources. Similarly, the machine terminal represents a group of terminals. This idealisation has the same form for every

¹ . Dielectric losses can also be significant at certain parts of the frequency range but these are related primarily to voltages and the effect of suppressing certain patterns of current in the machine windings does not reduce these directly. combination of motor speed and load but it would have different parameters in each case.

Each group of voltage sources in Fig. 1 produces a different frequency component. The set of voltages, v₀, represents the fundamental voltage wave which produces the main working currents in the machine (typically 10Hz - 100Hz). The other sets of voltages, v, - v_x, represent other frequency components (typically between 1.5kHz and 100kHz). In the case of a PWM (pulse-width modulated) drive, there is always a strong component of carrier frequency with side-bands (spaced in frequency at multiples of fundamental main frequency) as well as harmonics of carrier frequency and side-bands on these harmonics. Other types of power electronic drive produce different voltage spectra but all have a rich spectrum of voltages at high frequencies. In the case of an induction machine, some frequency components other than v₀ can produce small amounts of net positive torque but at the expense of a disproportionately high contribution to losses and it is generally true that the performance of any motor in terms of both maximum mechanical power out or maximum efficiency would be increased if these frequency components were not present.

Fig. 1 shows an impedance, Z, in series with the voltage sources in the drive. This impedance is a matrix quantity since several currents pass through it and, correspondingly, several voltages are dropped across it. This impedance is different for each frequency component but it is normal for the voltages dropped across Z to be much smaller in magnitude than the corresponding voltages dropped across the motor for most of the frequency components in the spectrum. Filters can be fitted to drives to increase Z for certain frequency components hence reducing some of the undesirable voltages appearing at the machine terminals. The perfect drive would have a filter fitted such that Z was very large (compared with motor characteristics) for all frequencies except low frequencies in the region of the fundamental machine operating frequency. Such filters are often not practicable because of the cost, size and mass of the components which would be necessary. The invention presented in this document is a type of machine design which differs from a standard design in the fact that it contains an additional feature whose effect can be almost exactly the same as increasing Z in a particular way to reduce some of the voltages appearing at the machine terminals.

The effect can also be different depending on how the additional design feature is used. The other possible effects are more easily understood and no additional background is thought necessary on these. Hence discussion on these is reserved for the sections dealing with Generic and Specific Embodiments.

In order to understand and use this invention in the context of suppressing certain undesirable combinations of currents, it is necessary to recognise that the set of voltages and currents at the terminals of a machine can be decomposed in 2 ways:

temporally :- where the voltage (current) at each terminal is seen to be composed of an infinite number of frequency components

spatially :- where the set of voltages (currents) at the terminals at a in time given instant is seen to be composed of a finite number of combinations of voltage.

The following sub-section clarifies the meaning of decomposing a set of voltages or currents spatially. It will become evident that the invention is aimed at producing an increased impedance to certain undesirable spatial components of voltage without affecting the impedance presented to the desirable spatial components.

Background _B. Spatial Components of Voltage and Current ... 3-Phase Machines.

Almost all industrial AC electrical machines are 3-phase. Of these, a significant proportion are designed to have 6 terminals so that each end of each machine phase can be connected independently. With 6 terminals, there can be 6 different instantaneous voltages on a machine. Similarly, there can be 6 different instantaneous currents passing through the terminals. This section is devoted to explaining that it is possible to express the set of 6 voltages (or 6 currents) using linear combinations of voltages (or currents) in such a way that only two of the voltage (current) combinations are important in producing machine torque. The other combinations of voltages (currents) serve only to increase losses and are best kept as low as possible. Another term for a linear combination of voltages (currents) is a spatial component of voltages (currents).

The 6 different instantaneous terminal voltages on a machine can be expressed in any number of different ways. A number of examples are given below to illustrate this point. For the purposes of these examples, the machine terminals are labelled LI, L2, L3, Nl, N2, N3 with the numbers indicating which phase is involved with a terminal and the letter L or N indicating which end of a phase the terminal is at. The 6 voltages v_L„ v_L2, v_L3, v_N„ v_N2, v_N3 (or the corresponding currents { i_L„ i_L2, i_L3, i_N„ i_N2, i_N3} - all of which are defined as positive when current is going inward) can be expressed uniquely in any of the following alternative ways : (reference to currents is dropped for brevity in the examples below but these expressions work perfectly well for currents also)

• Three instantaneous mean phase voltages and three instantaneous differential phase voltages ...

{ (v_Lι+v_Nι)/2, (V_L2+V_N2)/2, (v_L3+v_N3)/2, (v_L,-v_N1) , (v_L2-v_N2) , (v_L3-v_N3) }

• One zero-sequence and two "cyclic" voltage terms for the "L" voltages and similarly for the "N" voltages ...

{ (v ι+v_L2+v_L3)/3, (v -(v_L2+v_L3)/2), (v_L2-v_L3) (v_N1+v_N2+v_N3)/3, (v_N1-(v_N2+v_N3)/2), (v_N2-v_N3) }

• One zero-sequence and two "cyclic" voltage terms for the mean phase voltages on individual machine phases and similarly for the voltages across individual machine phases : {(v_Lι+v_L2+v_L3+v_N1+v_N2+v_N3)/6, (v_L1+v_N1-(v_L2+v_L3+v_N2+v_N3)/2), (v_L2+v_N2-(v_L3+v_N3)) (V_LΓV_L2+V_L3-V_N1+V_N2-V_N3)/6, (V_LΓV_N1 -(v_L2-v_L3+v_N2-v_N3)/2), (v_L2-v_N2 -(v_L3-v_N3)) }

In the operation of a normal 3-phase AC machine, the mean-voltages {(v_L1+v_N1)/2, (v_L2+v_N2)/2, (v_L3+v _N3V2} on individual phases are usually of virtually no benefit whatsoever in generating mechanical torque. Their primary effect is to cause capacitive currents to flow between each individual machine phase and the machine iron as well as between different machine phases. A major application of the invention contained here is the suppression of certain combinations of currents passing through the through machine coils. The invention can also be applied to reducing the high-frequency net capacitive currents flowing into earth. This latter application is more straightforward and requires no additional background other than that given in subsection D of this Background section and in the example embodiments.

The instantaneous mean-voltage on a machine phase (like (v_L1+v_N1)/2) normally has very little tendency to drive current through that phase. For simplicity in the explanation of this invention, the mean instantaneous voltages on the machine phases are disregarded from this point on as are the instantaneous net currents passing into or out of the machine phases. For a full understanding of the behaviour of a machine subjected to high frequency voltages at its terminals, it is vital to take account of these mean voltages on phases and net currents into/from phases but they cloud the exposition contained hereafter. Hence, it is no longer necessary to refer to v_LI, v_L2, v_L3, v_N1, v_N2, v_N3 or i_L„ i_L2, i_L3, i_N1, i_N2, i_N3 and we define the following new quantities for future use :

i₂ = i_L2 - _N3 v₂ = v_L2- v_N2 ₃ = i_L3 - i_N3 v₃ = v_L3- v_N3

Now, it is shown that it is sensible to express the voltages across phases {v„ v₂, v₃} and the currents through phases {i„ i₂, i₃} in terms of the following three spatial components (for-voltages) : (v, + v₂ + v₃)/3, (2v, - (v₂ + v₃))/3 , Λ/3(V₂ - v₃) /3 (for currents) : (i, + i₂ + i₃)/3 , (2i, - (i₂ + i₃))/3 , V3(i₂ - i₃) /3

The reasoning is simple. For the normal 3-phase machine, the "zero-sequence" component of current, (iy i₂ + i₃), does no good in producing torque. The other two spatial components of current can be useful in producing torque. The above spatial components of voltage and current have been scaled to be consistent with the spatial components for multi-phase machines defined in the next subsection.

The invention described in this patent specification applies to machines having 3 or more phases. In the context of 3-phase machines, this invention has the effect of substantially reducing the zero-sequence component of current, ((i- + i₂ + i₃)/3), without having any significant effect on the properties of the machine with respect to the other spatial components of voltage and current.

Any 3-phase machines which are "delta-connected" or "star-connected" with a floating star-point already have a built-in constraint that - at low frequencies - the instantaneous sum of three currents must be zero at all times. In these machines, zero-sequence currents are prohibited automatically at low frequencies but they can occur at high frequencies when the capacitive paths provide a route to earth. Other 3-phase machines which are star connected with a connected star point or which are excited from an electronic drive which can drive each phase independently can have zero-sequence currents even at relatively low frequencies.

In machines having more than 3 phases, the design feature described here can be used to suppress more than one unproductive combination of currents. The following subsection outlines this point.

Before leaving this section on the spatial components of currents in the machine, it should be noted that the full set of currents in any machine can be decomposed according to phase currents (in the connected machine) or according to coil currents (in the unconnected machine). The remainder of this document assumes implicitly that the decomposition of interest is decomposition according to the phase currents.

Background ^. Spatial Components of Voltage and Current...Multi-Phase Machines.

Consider a machine having N phases where two terminals are brought out to the terminal box for each phase. The voltages across phases 1 to N are denoted v,, v-_j, v₃ ... v_Ν as before and currents through each of the phases are denoted i,, i₂, i₃ ... i_N.

These voltages and currents can be decomposed into spatial components using a discrete Fourier transform as follows :

v, = Σ a, cos(2π //N) + Σ b, sin(2π/ϊ/N) ... where summations done forj=0 toy=N72

Whέn Nis odd, the summations are done for 7=0 toy^'=(N-l)/2

The coefficients a, and b_j can be determined as follows :

ao = Σ v, IN b₀ = 0

a_Ara = Σ (-l)⁽-^,)v₁ /JV^f b_M2 = 0

a, = Σ v, cos(2πjϊ/N)/(N/2) b, = Σ v, sin(2π/^'t/N)/(N/2) for 0<j<N/2

Some multi-phase machines only ever use a single pair of spatial components of current to produce the bulk of the torque and all other spatial components are unproductive. That is to say, a,, b_j could both equal zero for all values of/^' but one and the machine would still operate well. It is possible for other multi-phase machines (especially multi-phase induction machines) to use different pairs of spatial components in different circumstances. In both cases, there are always certain some spatial components of current which are undesirable and these can be suppressed by the invention described here.

The effect of this invention in terms of the suppression of undesired spatial components of phase current may be stated as below :

For a 3-phase or multi-phase electrical machine, those spatial components ofthrough- phase currents which are not directly useful in producing torque can be reduced by increasing the effective machine impedance to these currents.

Background ^. Zero sequence spatial component of phase currents and the current in the DC link.

Many forms of power electronic drive convert (usually 3-phase) AC supply power into DC power before converting it back again to AC power of arbitrary variable frequency. The form of such drives is shown schematically in Fig. 2.

Depending on the machine connected to the inverter output, significant zero-sequence current can sometimes be drawn from the inverter. In the case of zero-sequence components of current, the sum of all currents is non-zero and therefore, a non-zero current must pass through the DC link. By fitting a large inductor into the DC link, the amount of oscillatory current passing through the DC link can be minimised and hence the amount of zero-sequence current available from the output of the inverter can be dramatically reduced. (The inductor in this case acts to increase the output impedance of the inverter to zero-sequence currents). One of the implications of this invention is that a large value inductance capable of passing substantial power can be made available for connection in series with the DC link as part of a filter circuit.

Accordingly, the present invention provides a rotational alternating current electrical machine comprising a rotor, a stator and a gap therebetween, the stator having a stator core comprising a front of core region and a back of core region, a set of conductors in the front of core region operative to draw magnetic flux across the gap and a further set of conductors operative to drive complete loops of magnetic flux in the back of core region of the stator core, encircling the machine axis and generally parallel with the gap such that the back of core region is operable as the magnetic circuit of an inductor or transformer.

The present invention is further described, hereinafter, by way of example, with reference to the accompanying drawings, in which:

Figure 1 is an idealisation of a power electronic drive;

Figure 2 is a schematic diagram of a power-electronic drive with a DC link;

Figure 3 is a schematic diagram of part of a preferred form of an alternating current machine according to the present invention;

Figure 4 is a schematic diagram of part of a preferred form of an alternating current machine according to the present invention showing different lengths of a stator linked differently by one circumferential flux coil (CFC); and

Figure 5 is an example of a closed slot in a stator tooth which could accommodate one turn of a CFC. GENERIC EMBODIMENT.

In its most general form, this invention provides for the quite general use of the back-of- core iron as a single core or a set of cores for a transformer or inductor with external connections or with some or all turns in series with the machine windings.

The following subsections are present in this section :

(A) General Form of the Invention.

(B) The Increase in Impedance due to introduction of Circumferential-Flux Coils

(C) Selecting the linkages of the Circumferential-Flux Coils with the back of core.

(D) Creating a Transformer with (some) External Connections. (E) Creating an Inductor with External Connections.

Subsection (A) exposes the generic embodiment of the invention which is largely the same for all applications. Subsections (B) and (C) are related to the application of the invention in the context of raising machine impedance to certain combinations of stator currents. Subsections (D) and (E) relate to two other possible applications of the invention.

Generic Embodiment _A. General Form of the Invention.

The generic embodiment of this invention is explained in terms of cylindrical-airgap external-stator machines. It has application in other machine formats and the extension to some of these formats is quite straightforward. Some of these extensions are covered in the following section entitled "variants". The description of the invention in terms of the conventional of cylindrical-airgap external-stator machines proceeds thus :

Additional to the normal winding of the machine which tends to draw magnetic flux across the airgap, coils called "Circumferential Flux Coils" are put in place such that when current passes through these coils, a component of magneto-motive force is set up tending to drive flux in a purely circumferential direction around the complete back-of- core.

Normally, the back of stator-core serves the function of transporting the main working magnetic flux from one part of the airgap to another with a relatively low drop in MMF. At any one instant in time, half of the circumference of the back-of-core is carrying very little of the working magnetic flux and the other half may be carrying a high flux density. With the present invention, all of the stator back-of-core is pressed into service.

The generic embodiment is presented schematically on a "straightened-out" stator core below. The two symbols ζ% «β represent conductors carrying current "up" (from the page) and "down" (into the page) respectively. The small scale versions of these symbols show the "circumferential" component of the winding which tends to drive flux in a circle around the back of the stator core and the larger symbols show the "radial" component of the winding (the main turns of the coil) which tends to draw magnetic flux across the machine airgap for the normal operation of the machine.

It is evident from the description above and from Fig. 3 that this invention implicitly involves conductors passing along (at least a part of) the length of the stator core outside the back of the stator core. Collectively, the turns of conductors driving pure circumferential flux are henceforth referred to as Circumferential-Flux-Coils or CFCs.

In terms of the functioning of the machine, the circumferential and radial components of the winding (coils) may be regarded as having separate effects and they can be discussed separately. The "radial" components of the winding (coils) are deployed so as to achieve a given pattern of radial MMF about the machine. The circumferential components of the winding (coils) are deployed so as to produce a net MMF about the back of the stator core when certain undesired combinations of current come to exist. The design of radial and circumferential components of the coils is connected primarily through the fact that both components may share space in the slots.

From this point forward, the text discusses the circumferential components of the winding almost exclusively and for brevity, these will be referred to as Circumferential Flux Coils (CFCs). Two important aspects should be noted with respect to the threading of the CFCs around the back-of-core :

(a) The stator may be subdivided into two or more axial lengths where each such axial length of the stator may be linked by different numbers of turns of at least 1 of the CFCs.

(b) For a given axial length of stator core, different CFCs will link this length by different amounts.

Each different axial length of stator back-of-core acts as an independent inductor/transformer core. The specific embodiments illustrate such case cases. Fig. 4 shows a section through the side of a machine stator which is divided into 3 lengths for the purposes of the CFCs in order to provide 3 independent cores.

The "breaks" between different lengths of stator back-of-core may simply be ducts which commonly exist in cylindrical airgap stators anyway for cooling purposes or they may be made deliberately longer (axially) and they may comprise non-metallic low permeability material to minimise losses and leakage of flux axially.

Generic Embodiment B. Increase in Impedance due to Introduction of the Circumferential Flux Coils (CFCs)

One of the main applications of the invention is the increase of machine impedance to certain combinations of machine currents. In this context, the CFCs are connected in series with the coils of the machine. The electrical connection of the CFCs together with the "magnetic connection" of the CFCs with each of the axial lengths of the stator core are chosen deliberately in such a way that for certain combinations of machine currents, a substantial net MMF comes to exist tending to driving flux around (one length of) the back of the stator core. The MMF drives flux which in turn generates a voltage opposing the current in every coil which contributed to creating the MMF. In short, each axial section of the back of core becomes useful as a toroidal inductor as well as a path for carrying the main working radial flux from one part of the airgap to another.

As an illustration of the principal of this invention in the context of selectively increasing inductance, consider an 8-coil machine where each coil has 2 terminals brought out to the terminal box. This is a sort of 8-phase machine in which each phase has only 1 coil within the machine. Suppose that a particular spatial combination of coil currents has been predicted to cause high losses in the machine when the machine will be operated from a drive and suppose that this combination of currents is {-2, 1, -2, 1, -2, 1, -2, 1} in coils 1-8 respectively. The combination of currents can be described without units because it can be scaled arbitrarily and still represent the same proportions of coil currents. For a given frequency and a given proportion of coil-currents, losses are proportional to the square of the magnitude of any one coil current.

To suppress the undesired combination of currents, each coil is "linked" circumferentially with the stator core in proportion to the participation of that coil current in the undesired combination. In the case above, therefore ...

coil 1 ... has 2 "negative" turns around the back of core.

(+1 Amp in this coil produces -2 Amp turns of clockwise MMF). coil 2 ... has 1 "positive" turn around the back of core. (+1 Amp in this coil produces +1 Amp turns of clockwise MMF). coil 3 ... has 2 "negative" turns around the back of core.

(+1 Amp in this coil produces -2 Amp turns of clockwise MMF). coil 4 ... has 1 "positive" turn around the back of core.

(+1 Amp in this coil produces +1 Amp turns of clockwise MMF). coil 5 ... has 2 "negative" turns around the back of core.

(+1 Amp in this coil produces -2 Amp turns of clockwise MMF). coil 6 ... has 1 "positive" turn around the back of core.

(+1 Amp in this coil produces +1 Amp turns of clockwise MMF). coil 7 ... has 2 "negative" turns around the back of core.

(+1 Amp in this coil produces -2 Amp turns of clockwise MMF). coil 8 ... has 1 "positive" turn around the back of core. (+1 Amp in this coil produces +1 Amp turns of clockwise MMF).

Then, one linear combination of coil currents will give rise to a substantial circulating flux in the back of the machine core (and hence a substantial opposing voltage will come to exist) whereas the other 7 linearly independent combinations of coil currents should be unaffected by the presence of the CFCs. The other 7 linear combinations are given below in Table #1.

TABLE #1. Example of 7 independent combinations of coil currents which create net OMMF on the back of core.

Generic Embodiment jB. The Increase in Machine Impedance due to a single axial length of stator core linked by a set of CFCs.

In general, the inductance of the machine is increased by the presence of the CFCs when they are connected in series with the main windings. The capacitance is also increased slightly but in most cases the increase in capacitance will not be significant compared with the capacitance already present in the machine. This section briefly states how the increase in inductance can be computed.

We must recognise, before beginning, that the extra inductance introduced by the CFCs will be a matrix quantity. Initially, we are interested in the extra inductance matrix for the full set of individual unconnected machine coils. The fact that the coils are connected together to form phases of the machine is dealt with later. The matrix, L_CFC, is defined implicitly by the equation below in which :

-'CFC The matrix of additional inductance contributed by the presence of the CFCs.

^■ no CFC : vector of voltages across individual coils (with all CFCs in series with their respective coils but not linking any of the back-of-core).

'CFC vector of voltages across individual coils (with all CFCs in series with their respective coils and linking the back-of-core as intended). vector of currents passing through individual coils

(VCFC - v_no_cFc) = LCFC α7dt(i)

Here is how L_CFC can be derived. It comprises the algebraic matrix sum of contributions from each of the individual axial lengths comprising the stator core. (Different axial lengths are distinguished by the fact that they have different linkages with the CFCs). For the present, it is assumed that the entire core length is used together as a single length.

Let L be the total axial length of the stator core, let H be its radial depth and let D be the effective mean diameter of the core. If the absolute permeability of the material of the core is μ, then the reluctance of the complete back of core is R = πD/(LH). A net unit magneto-motive force (MMF) will cause (1/R) units of flux to circulate in the back of core. Note that μ will be a complex quantity which is frequency-dependent because at different frequencies the skin-depth in the back of core laminations will be different.

Let k be the vector with N entries in which the ith entry is k_t - the number of positive series-turns of the z^'th CFC around the back-of-core. Note that we are implicitly assuming here that there is one CFC for each main coil of the machine. The extra inductance matrix, L_CFC, is then derived as k. (1/R). k^τ.

The derivation is simple. The net MMF acting on the back of core is k^τi. The corresponding flux is (1/R) k^τi, and the voltages acting on individual coils due to this flux is k. (1/R). k^τi.

Now, it must be observed that if the machine is working at its full flux levels, then at any one -instant in time, one-half of the back of core will be at least partially saturated. The effective permeability computed for the back of core iron must be adjusted to cater for this. When effective permeability for the back-of-core iron is computed, it is done taking account of the fact that flux will flow predominantly in the outer skins of each lamination. If the outer skin is saturated, then the flux tends to spread into each lamination more so that at higher frequencies, the effect of saturation of the back of core can be minor.

The matrix L_CFC which represents the additional inductance present due to the CFCs is applicable to the unconnected coils of the machine and the number of rows (and columns) in L_CFC is the same as the number of coils in the machine. In general, when the coils of a machine are connected into phases, there can be substantially fewer current degrees of freedom in the machine. At low frequencies, the number of independent currents is necessarily equal to the number of phases. Though this is not the case at higher frequencies (since some current starts to pass through capacitive paths) it is generally true that if i is the vector of individual coil currents, there is some transformation matrix, T, and a vector of allowable connected currents, i_c, which are related by ... i ^•= T^τi_c. Then the effect of the CFCs is to contribute an additional inductance matrix to the connected machine equal to T^τ L_CFC T.

Generic Embodiment ^. Designing the CFC linkages.

Note, firstly, that the core must be divided into axial lengths with each length being responsible for adding inductance to a particular spatial combination of stator currents. The- design process outlined here applies to an single length of stator core. Suppose, now, that a length of core is desired to suppress a certain' linear combination of coil currents which is represented by the vector g. That length of core will be linked by the CFCs in such a way that the vector k (describing the linkage of coils) is close to being a multiple of g. Mathematically, this can be expressed as (k^τ.g)² « (k^τ.k) (g^τ.g). The accuracy of the match between k and g depends, to a large extent, on the maximum number of CFC turns which will be allowed per main coil (i.e. per slot) of the machine and this number, k_max, is one of the first parameters set in the design process. Note that it is implicitly assumed in this subsection that there is one CFC for each main coil of the machine - as was assumed in the last subsection. The starting point in determining k_max is the cross-sectional area of copper needed to carry phase current. The main coils are sized in exactly the same way so that a compromise is made between machine size and cost on the one hand and copper losses through resistance on the other hand. The turns of the CFCs do not have to have the same cross-section as the turns of the main coils but the cross-sectional area will be similar. It will be desirable in many cases that those lengths of the CFCs which must ran inside the stator back-of-core should sit at the bottoms of slots.

Once k_max is chosen, a first guess at the vector k can be made as follows :

(a) Scale g so that the largest entry is equal to (k_max + 0.5)

(b) Round each entry of the result of (a) above up or down to the nearest integer.

In general it is impossible to obtain a perfect match between k and g and in such cases, a process of making certain trade-offs must begin. At the root of this process is the recognition that there will be at least two combinations of currents which are fundamental to the successful operation of the machine and it is highly desirable that these desirable combinations of current should not drive any significant flux in a Complete loop through the back of core. If the two "useful" components of current are h, and h₂, then we would wish to achieve (h,^τ.k) « 0 « (h₂ ^T.k). It is beyond the scope of this document to attempt to explain more about this design process. A machine designer will readily come to grips with it after a small number of attempts. Having chosen the vector of coil linkages, k, we can now examine whether the inductance added is sufficient and whether the maximum voltage which can be opposed (governed by saturation of the back of core) is sufficient. If either the inductance or the maximum opposing voltage are insufficient, the value of k^ would normally be increased or the depth of back-of-core could be increased to meet a small shortfall.

Generic Embodiment _D. Creating a Transformer with (Some) External Connections.

The stator core is divided axially into equal lengths whose number is the same as the number of phases in the machine. Each of these lengths is wound with two sets of CFCs in separate series-connected groups. None of the CFCs should span more than a single length of the back-of-core. For this reason, a scheme of fitting the CFCs such as that shown in Fig. 3 could be employed where the bottom of every slot was at least partly occupied by a CFC. In the context of the transformer application where the machine had N slots and M phases, the core would be divided axially into M different sections and each of these sections could be fitted with N full CFCs (one per slot) because there would be no need for any of the CFCs to span more than a single axial length.

Generic Embodiment _E. Creating a Single Inductor with the CFCs.

This application is the simplest. The stator back-of-core would be would with a number of CFCs and these would all be connected together to two terminals such that when a voltage difference appeared across the terminals, all of the CFCs would carry similar current and all would produce components of MMF driving flux about the back of core in the same direction.

The CFCs would not necessarily be connected in a single series pattern. The magnitude of current expected to be passed through the inductor would determine how many similar parallel groups of series-connected CFCs should be connected.

VARIANTS ON THE GENERIC EMBODIMENT.

In the bulk of the above section entitled "GENERIC EMBODIMENT", the text was based on the implicit assumption that the CFCs were connected 1 coil each in series with 1 of the main (radial-flux) coils and with one side of each CFC at the bottom of a slot. While this is likely to be the most common configuration of this invention, the invention also provides other possibilities.

(A) Some or all of the CFCs might be threaded through a hollow in the centre of a the stator teeth instead of through the slot. Since slots tend to be parallel, stator teeth (of cylindrical airgap, external stator machines) tend to be wider at the base of the tooth than at the top. Slots have been deliberately introduced into the teeth of some machines already for cooling purposes. Fig. 5 below shows a closed radial slot inside a stator tooth which could be used to accommodate one turn of a CFC.

(B) When a single turn of CFC is made up from multiple parallel strands of conductor, it is possible for the vector k to have non-integer entries by splitting some turns and directing part of the turn inside the back-of-core and part outside. Care must obviously be taken in this case not to provide an easy path for currents to circulate freely around the core damping down the swings in flux.

(C) When the CFCs are to be connected in series with the machine phases, they may be connected in groups at the low- voltage ends of the machine phases (where such ends exist) rather than each one being associated with in series with a single main-coil of the machine. This would reduce the insulation requirements on the CFCs. In machines which. For machines whose phases will be symmetrically excited, the groups of CFCs could be connected at the centre of the phase where the voltage (with respect to earth) was likely to be lowest.

(D) Some cylindrical-airgap machines have external rotors. The concept of the CFCs is equally applicable in the stators of these machines.

(E) The invention can be applied to some machines having non-cylindrical airgaps. Adapting the invention for any such machines is possible if there is a full magnetic loop which carries the main flux of the machine between different locations in the airgap.

SPECIFIC EMBODIMENTS.

Five specific embodiments of the invention are included.

Specific embodiment #1 is presented in 3 subsections :

(A) Outline of case #1 to which the invention is to be applied.

(B) Design of CFCs suppressing the zero-sequence current components in case #1 (C) Design of CFC for suppressing the spatial 7^th-order current components in case

#1

Specific embodiment #2 is presented in a single subsection :

(D) Use of the CFCs on a motor as a 3 -phase transformer enabling motor to run from 2 different levels of supply voltage.

Specific embodiment #3 is presented in a single subsection :

(E) Use of the CFCs on a motor as a single large inductor for smoothing the DC link current in a drive.

Specific embodiment #4 is presented in a single subsection: (F) Use of CFCs in multi phase magnetic bearings.

Specific embodiment #5 is presented in a single subsection:

(G) Use of the CFCs in conjunction with secondary inverters.

Specific Embodiment A. Outline of case #1.

Consider a machine having 24 phases with 2 ends brought out for each phase. Suppose that a calculation has been made which shows that for the anticipated spectrum of voltages at the machine terminals, 3 different spatial combinations of currents are particularly bad for producing losses in the machine and that these spatial combinations are zero-sequence (all phases carrying the same currents) and the two different "seventh- spatial harmonics" (phased carrying a current proportional to cos(14π /24) or phase j carrying current proportional to sin(14π/^'/24)).

Suppose that the machine is designed for 10-pole operation and has 240 coils. Coils 1, 25 , 49, 73 .... 217 belong to phase # 1. Coils 2, 26, 74 ... 218 belong to phase #2 and so on. Alternate coils in a given phase carry currents in the opposite directions (so as to produce North Pole, South pole, North Pole South Pole etc. . Suppose that there are 8 turns per coil.

Substantial levels of zero-sequence excitation are expected at 3000 Hz and above (3000 Hz being carrier frequency for the PWM waveform from the drive). A target voltage of 1500N (peak) per phase is required to be opposed by the flux in the relevant section of back-of-core. The zero-sequence voltages are the same on all phases at any instant. A zero-sequence current of 0.2 A (peak in each phase) is considered acceptable in terms of harmonic losses.

The other two spatial components are expected to have substantial voltages also around 3000 Hz and above. A target voltage of 800N (peak) is foreseen as the largest voltage across any phase at any instant due to the seventh order spatial harmonic. A seventh-order spatial harmonic of current is considered acceptable for losses for this particular machine if the largest peak current over all of the phases is 0.5 A.

We require to design a set of CFCs to achieve the above. The guideline stator back-of- core dimensions are as follows :

total core length L 2.6m. effective radial thickness H 0.3m effective mean diameter D 1.4m thickness of laminations t 0.3mm

It has been determined from the machine dimensions that up to two CFC turns can be accommodated per main coil of the machine.

Specific Embodiment _B. Opposing the zero-sequence voltages.

The CFCs for suppressing the zero-sequence current components are designed first. A length, L,, of 1.2m of the stator core is devoted to this task.

To determine the reluctance of the section of core devoted to suppressing the zero- sequence component of current, we first require an effective permeability for the back-of- core laminations. This permeability is a function of frequency, the low-frequency relative permeability of the core iron and the resistivity of the core iron. For f=3000Hz, μ_r = 1200 and p = 0.22E-6 Ohms/m, the effective relative permeability for the back-of-core laminations is computed as μ_{r err} = (632.7 - 496. 5/^'). Skin effect on the laminations causes this value to be complex and to be smaller in magnitude than the low-frequency value of 1200. No allowance has been made here for the saturation of the back of core due to the main machine flux. The reluctance of the magnetic circuit is determined as R = πD / (H L_! μ₀ μ_{r err} ) which has a value of 19021 + 14925/ Amps/Weber. The reluctance is complex because the relative permeability was complex.

Assuming that two CFC turns are present for each coil in the machine and that these CFCs are all connected such that when zero sequence current flows, each one acts to drive flux in the same circumferential direction about the back of core, then each phase is linked with the back-of-core flux (in Lj) by 20 turns. With peak voltages reaching 1500 N per phase for a frequency of 3000 Hz, the peak flux passing circumferentially through the back of core must be 3.98 mWeber. This corresponds to an effective flux density of 0.0088 Tesla which is obviously very small and contributes insignificantly to the saturation of the back of core.

The MMF required to drive this flux is the product of the flux and the reluctance and this MMF transpires to be (75.7 + 59.4 ) Amp turns. The magnitude of this MMF is 96.2 Amp turns. Each of 24 phases contributes 20 times its current to this MMF so the current in each phase needs to be only 0.2 Amps. Thus, the design objective has been achieved for the zero-sequence currents.

Specific Embodiment _C Opposing the seventh harmonic (spatial) voltages.

The CFCs for suppressing the seventh-order spatial current components are now discussed. Table 2, below, shows the variation in coil currents for the two such spatial components. For simplicity coil-numbering starts at 0.

TABLE #2. The 7^th spatial harmonic combinations of current in the 10-poIe. 24-phase machine.

We have conceded that the maximum number of CFC turns per coil is to be 2. Then the linkage of the first 24 coils is found (by simple rounding in the first instance) to be as Table 3 shows. The second 24 coils is identical to the first except that the linkages are reversed. Subsequent groups of 48 coils are identical to the first group of 48.

TABLE #3. Linkages for the 7^th f spatial) order set of CFCs

Table 3 above defines a proposed vector k for each of two sets of CFCs. In each case, we can compute the ratio [(k^τ. g,)² / ((k^τ.k) (g,^τ. g,)] which indicates how closely the linkage vector matches the component of current which we want to suppress. The above arrangement produces a value of 0.9846 indicating that very little has been sacrificed by rounding the linkages to the nearest integer to a maximum of 2.

Now, having used 1.2m of core for the zero-sequence currents suppression, we have 1.2m left for each of the two 7^th spatial harmonics. The reluctance is the same as was calculated earlier (in the section dealing with suppressing the zero-sequence currents) for 1.2m of back-of-core at 3000 Hz .. as R = (19021 + 14925 ) Amps/Weber.

When 1 unit of g* is flowing in the machine, we have 1 Amp in coil #0, 0.6088 Amps in coil #1 etc. (from Table 2) and combining tables 1 and 2 together, we can find that the total MMF acting on the associated section of back of core is 277.1 Amp turns. Note also that in this case, the total MMF acting on the sections of back of core associated with zero-sequence currents and combination vector g₂ are both zero.

An MMF of 277.1 Amp turns would drive a flux of (9.02 - 7.07/^') mWeber around that section of back-of-core. This flux would induce a voltage of magnitude 432 V at a frequency of 3000Hz in those coils which were linked to the back of core flux by two turns. The average linkage is less than this and a net reaction voltage on each phase would be around 2700V.

Clearly, the flux needed to oppose even 2700V per phase causes no concern about influencing saturation. Also if a maximum current of 1 A in any phase produces 2700V of opposing voltage in the same phase, then substantially less han 1A is needed to oppose 800V.

Specific Embodiment _D. Use of the CFCs on a motor as a 3-phase transformer.

Consider the same machine as described in Specific Embodiment _A except that it is now wound as a 3 -phase machine. Let the core be divided into 3 equal axial lengths and suppose that each length is linked by 240 circumferential flux coils (one per slot). Of these 240 CFCs, suppose that 140 are connected in series to form a "primary" winding and the other 100 are connected in series to form a secondary winding. Both ends of both windings are brought out to the surface of the machine with the terminals of the main winding.

The transformer thus formed, enables any one of three voltage/current ratios to be applied to the machine, normal supply ratio, supply ratio multiplied by 1.4² or supply ratio divided by 1.4² without even thinking about connecting the primary in "star" and the secondary in "delta" etc.. With the star-delta options included, the number of voltage to current ratios possible is very substantial. The inductance of the 100-coil winding on a given phase would be of the order of 10,000/(16204) Henrys = 617 mHenrys. When this is multiplied by the machine supply frequency of, say, 20 Hz, the magnitude of the impedance of the 100-turns transformer winding is 77 Ω. Clearly, this impedance should be substantially higher than the voltage-to-current ratio of a main machine phase at rated frequency and load if the transformer action is to work successfully but this is not unlikely. The voltage-to-current ratio of one phase might be of the order of 8Ω.

It would be recognised that because the flux circulating in the back of core in this machine has the same frequency as the main flux across the airgap, some parts of the back of core would have higher oscillatory flux levels than others and consideration would be given to increasing the radial depth of the core in these areas.

Specific Embodiment _E. Use of the CFCs on a motor as one single inductor.

Consider the same machine as described in Specific Embodimeήt_A. Now, one turn of CFC is made for each coil and, initially, the design calculations consider the implications of connecting all of the CFCs in series to form a single large inductor from the back of core. The ends of this inductor are brought out. The inductor thus formed has 240 series turns around a core whose (complex) reluctance is a function of frequency. However, we can say that at 3000 Hz, this reluctance is 6340 + 4975/^' Amps/Weber. At frequencies below this, the reluctance would be lower. Taking a real reluctance of 5000 for the magnetic circuit and 240 turns leads to a calculated inductance of 11.5 H. This inductance would present an impedance of more than 200 kΩ to current at 3000Hz.

This would probably be an unnecessarily high impedance acting to suppress the 3000Hz frequency component of current in the DC link of a drive. The impedance of the machine to zero-sequence currents of this frequency might only be of the order of 500Ω. With all CFCs in series, the price paid is that each CFC must have sufficient cross-section to carry the complete DC link current. A better option might be to divide the CFCs into 10 parallel groups of series-connected CFCs. Then the impedance presented would be lOkΩ. and the cross-sections of the CFCs might be allowed to have a cross-section similar to a single turn of one of the main machine coils.

Specific Embodiment _F. Use of the CFCs in magnetic bearings.

The stators of magnetic bearings sometimes resemble the stators of electrical machines for producing torque. In particular there is frequently a continuous "back-of-core". Magnetic bearings typically have at least four independent windings although only two spatial components of flux are very significant in generating the lateral forces which are intended to occur in these bearings. There are multiple reasons why it is desirable that the windings of magnetic bearings are independent. A major reason is reliability. The independence of the windings makes it possible that the bearing windings can pass spatial components of current which serve no significant useful purpose and may cause troublesome losses. The CFCs can be used in conjunction with magnetic bearings in exactly the same way that they can be used in more conventional machines. Specific Embodiment _G. Use of the CFCs with secondary inverters.

It has already been noted that the CFCs can be used to form a substantial inductance which might be used to smooth out pollution of the supply arising from the inverter switching. This is a passive measure. Active measures for cleaning up the supply can also be considered and the CFCs may play a role here also.

It is known that the current harmonics caused in a supply by a large high-power inverter can be cancelled by the addition of compensatory harmonic currents using a small secondary inverter. The secondary inverter might typically be a current-source inverter which was transformer-coupled to the main supply lines powering the main inverter. The transformer-coupling in this case could be achieved through the use of the CFCs.

Claims

1. A rotational alternating current electrical machine comprising a rotor, a stator and a gap therebetween, the stator having a stator core comprising a front of core region and a back of core region, a set of conductors in the front of core region operative to draw magnetic flux across the gap and a further set of conductors operative to drive complete loops of magnetic flux in the back of core region of the stator core, encircling the machine axis and generally parallel with the gap such that the back of core region is operable as the magnetic circuit of an inductor or transformer.

2. A machine in accordance with claim 1 wherein the stator core is composed of two or more subsections each having a front of core region and a back of core region, the back of core region of at least one of said subsections being operable as the magnetic circuit of an inductor or transformer.

3. A machine in accordance with claim 2 wherein each subsection is operable separately such that collectively a multiphase inductor or transformer can be formed in the machine.

4. A machine in accordance with claim 2 or claim 3 wherein the subsections are separated by material of relatively low magnetic permeability such that magnetic flux is generally inhibited from transferring from one subsection to another subsection.

5. A machine in accordance with any one of claims 2 to 4 wherein the further set of conductors are connected in subsets, the net effect of the further set of conductors being dependent on the relative magnitude of currents in the individual subsets, such that certain combinations of currents are operative to produce substantially zero net MMF in the back of core region of all subsections of the stator core and other combinations of currents in the subsets result in substantial MMF in the back of core region of at least one subsection of the stator core.

6. A machine in accordance with any preceding claim wherein the machine has three or more main electrical phases, each main electrical phase being in series with at least a portion of the further set of conductors, such that the impedance of the machine with respect to certain combinations of phase currents can be substantially raised.

7. A machine in accordance with any one of claims 1 to 5 wherein the machine has three or more main electrical phases, and the further set of conductors in combination with the back of core region of the stator core comprise a transformer, each of the main electrical phases being selectably connected in series with a respective winding of the transformer so as to allow the voltage to current ratio of the machine to be determined by selecting a particular connection of main phase to said transformer.

8. A machine in accordance with any one of claims 1 to 5 wherein the further set of conductors is connected such that it forms part of the circuit of a power electronic converter supplying the main phases of the machine.

9. ' A machine in accordance with any one of claims 1 to 5 in which the further set of conductors is arranged to form primary and secondary windings of a transformer, the primary winding being connected to the main supply of a primary inverter and the secondary winding being connected in series with a secondary inverter operative to cancel conducted electrical noise in the supply to the primary inverter.

10. A machine in accordance with any preceding claim wherein the stator core is generally cylindrical, and the further set of windings is operative to drive magnetic flux in a generally circumferential direction of the stator core.

11. A machine in accordance with any preceding claim wherein the stator core is generally cylindrical, and the rotor is mounted for rotation within the stator.

12. A machine in accordance with claim 11 wherein the machine includes a magnetic bearing, the conductors of the further set of conductors further being arranged to exert a lateral force on the rotor.

13. A machine in accordance with any one of claims 1 to 9 wherein the gap is substantially conical.

14. A machine in accordance with any one of claims 1 to 9 wherein the gap is substantially annular.

15. A machine in accordance with any preceding claim wherein the stator has a plurality of teeth with slots defined therein, the further set of conductors being accommodated in said slots.