Patent Publication Number: US-11646579-B2

Title: Electrical systems

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This specification is based upon and claims the benefit of priority from UK Patent Application Number 1913015.2 filed on 10 Sep. 2019, the entire contents of which are incorporated herein by reference. 
     TECHNICAL FIELD 
     This disclosure concerns electrical systems for connecting rotary electric machines with rotating machinery such as gas turbine spools. 
     BACKGROUND 
     In aerospace, the more electric engine (MEE) and more electric aircraft (MEA) concepts have been advocated for the substantial reduction in fuel consumption and complexity they bring. For example, one known aircraft configuration includes in its engines electric machines operable as both motors and generators so as to facilitate both generation of electrical power during flight but also starting of the engine and removal of the air-turbine starter. One engine configuration for this known aircraft includes such electric machines coupled to the high-pressure spool of a twin-spool turbofan. Another includes such electric machines coupled to the intermediate-pressure spool of a triple-spool turbofan. 
     Service experience has shown however that the means of electrical generation in such configurations can and do fail from time to time. In addition, the electrical aspects of the devices are considered complex systems and so a rate approach to certification is not possible. This imposes a requirement for fault-tolerant designs. It is accepted practice to provide single fault-tolerance, on the basis that the mean time before failure for the surviving system is sufficiently long. 
     Increasingly, it is seen as desirable to facilitate power transfer between spools of a gas turbine engine. Studies have shown that improvements in component life and specific fuel consumption are possible, which can be substantial on short-haul missions. Other studies have shown that augmentation of the core gas turbine using the electrical system allows reduction in the size of the turbomachinery. 
     Clearly, however, if the extreme position is taken to the extent that the safe flight of the vehicle relies on such an electrical power augmentation system, said system must have the requisite fault-tolerance to facilitate continued operation in the presence of a fault. Such a requirement may be summarised by saying that the engine is dispatchable in the presence of a single fault, i.e. even with a single fault having occurred, the electrical system may still tolerate another fault which will not cause a hazardous or catastrophic event. 
     Alongside developments in turbofans for airliners, vehicles such as electric vertical take-off and landing (EVTOL) aircraft are being developed which require a similar approach to guarantee operational safety. Near term proposals are configured with redundant turboelectric generators for powering electric propellers. For the purposes of weight management, the turboelectric generators are likely to be single-spool gas turbines. In a similar way to multi-spool turbofan engines benefiting from shaft power transfer, it is beneficial in such installations to facilitate fault-tolerant transfer of power between the turboelectric generators, for example to allow in-flight relight. 
     Thus, it is an object of the invention to provide an electrical system for connecting rotary electric machines to gas turbine spools. It will be appreciated in view of the foregoing discussion that the gas turbine spools may form part of the same engine, or different engines. 
     In this specification, the following mathematical notation is assigned to objects for the purposes of clarity and conciseness. A collection of objects having an ordered relationship therebetween may be represented as a sequence of members. For a finite sequence—of length N, each member has an associated index n identifying its position in the sequence. 
     As used herein, the length of a sequence is denoted by an uppercase letter, with the variable representing the indices of the members of the sequence denoted by the equivalent lowercase letter. In this way it is possible herein to concisely define properties of each member of a sequence. 
     For example, let a sequence α have length N=8 such that the members each have an associated index n. It is possible to state that for all n≡0 (mod 2), the nth member has property X. In this way a particular property is defined over the even-indexed members. 
     This is in contrast to having to set out that each of the second member, the fourth member, the sixth member, and the eighth member has property X. 
     Thus it may be seen that great improvements in conciseness are possible for sequences of large length with properties shared over a mathematically-defined sub-sequence. 
     Furthermore, say we wish to describe links between the members of a multiplicity of sequences. For example, let a sequence β have a length P=3, and let a sequence γ also have a length P=3. The members of both sequences therefore have an index p associated therewith. 
     Given these definitions, we may concisely state that for all p=(1 . . . P), the pth member of sequence β is linked to the pth member of sequence γ. 
     This is in contrast to having to set out that the first member of sequence β is linked to the first member of sequence γ, the second member of sequence β is linked to the second member of set γ, and the third member of sequence β is linked to the third member of sequence γ. 
     Whilst the statements are equivalent, it will be appreciated that by using the notation explained heretofore significant improvements in conciseness are achieved. 
     SUMMARY 
     The invention is directed towards electrical systems for connecting rotary electric machines with rotating machinery, which rotating machinery may comprise, for example, gas turbine spools. Thus, the invention is also directed towards a gas turbine comprising such electrical systems, and arrangements comprising two gas turbines and such electrical systems. 
     In an aspect, an electrical systems comprises: 
     a first rotary electric machine mechanically coupled with a first gas turbine spool and a second rotary electric machine mechanically coupled with a second gas turbine spool, each said electric machine having an identical even number N≥4 of phases, each phase having a respective index n=(1, . . . , N), and each phase comprising an identical number P≥1 of coils wound in a P-plex configuration in which adjacent phases are radially separated by 2π/NP mechanical radians; 
     a first set of N bidirectional converter circuits for conversion of alternating current (ac) to and from direct current (dc), each converter circuit having a respective index n and being connected with the P coils in the nth phase of the first rotary electric machine; 
     a second set of N bidirectional converter circuits for conversion of ac to and from dc, each converter circuit having a respective index n and being connected with the P coils in the nth phase of the second rotary electric machine; 
     a number 1≤R≤N/2 of dc outputs for connection with an R-channel electrical network, wherein each dc output has respective index r=(1, . . . , R); 
     wherein for all r, the rth dc output is connected with the dc side of the nth converter circuits in both the first set and second set, for which n(mod R)≡r is satisfied. 
     In an embodiment, N=4. 
     In an embodiment, P=2 such that the coils are wound in a duplex configuration. 
     In an embodiment, R=2. 
     In an embodiment, for all n, a dc side of the nth converter circuit in said first set is connected with a dc side of the nth converter circuit in said second set to facilitate dc power transfer between the first gas turbine spool and the second gas turbine spool. 
     In an embodiment, the electrical system further comprises N switch arrays each having a respective index n, wherein for all n, the nth switch array is configured to connect the nth converter circuits in the first and second sets to the corresponding dc output. 
     In an embodiment, each switch array comprises: 
     a first input connected with one of the converter circuits; 
     a second input connected with another of the converter circuits; 
     an output for connection to the dc output, and to which the first input and the second input are connected; 
     a first switch between the first input and the output; 
     a second switch between the second input and the output; 
     a bus tie across the first input and the second input, the bus tie comprising a third switch. 
     In an embodiment, the switch arrays are configured to operate in: 
     a non-fault condition in which the first switch and the second switch are closed, and the third switch is open; 
     a first fault condition in which the first switch is closed and the second and third switches are open; 
     a second fault condition in which the second switch is closed and the first and third switches are open; 
     a third fault condition in which the third switch is closed and the first and second switches are open. 
     In an embodiment, the first, second, and third switches all have the same electrical rating. 
     In an embodiment, each switch array comprises: 
     a first input connected with one of the converter circuits; 
     a second input connected with another of the converter circuits; 
     an output for connection with the dc output; 
     a node with which the first input, the second input and the output are connected; 
     a first switch between the first input and the node; 
     a second switch between the node and the output. 
     In an embodiment, the switch arrays are configured to operate in: 
     a non-fault condition in which the first switch and the second switch are closed; 
     a first fault condition in which the first switch is closed and the second switch is open; 
     a second fault condition in which the first and second switches are open. 
     In an embodiment, the first switch has half the electrical rating of the second switch. 
     In an embodiment, the switches are dc contactors. 
     In another aspect, there is provided a gas turbine engine having a low-pressure spool and a high-pressure spool, and further comprising the electrical system of the aforesaid type, in which the first gas turbine spool is the low-pressure spool and the second gas turbine spool is the high-pressure spool. 
     In another aspect, there is provided an arrangement comprising: 
     a first gas turbine engine having a spool; 
     a second gas turbine engine having a spool; and 
     the electrical system of the aforesaid type, in which the first gas turbine spool is the spool in the first gas turbine engine, and the second gas turbine spool is the spool in the second gas turbine engine. 
     In another aspect, there is provided an aircraft having an R-channel electrical network and comprising the aforesaid gas turbine or the aforesaid arrangement. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will now be described by way of example only with reference to the accompanying drawings, which are purely schematic and not to scale, and in which: 
         FIG.  1    shows a general arrangement of a turbofan engine for an aircraft, including a rotary electric machine on each spool thereof; 
         FIG.  2    shows an electrical system for connecting the electric machines of  FIG.  1   ; 
         FIG.  3    shows the winding configuration of one of the electric machines of  FIG.  1   ; 
         FIG.  4    shows a first embodiment of the electrical system of  FIG.  2   , in which the switching arrangement comprises two switch arrays; 
         FIG.  5    shows one of the switch arrays of  FIG.  4   ; 
         FIG.  6    shows a second embodiment of the electrical system of  FIG.  2   , in which the switching arrangement comprises two switch arrays; 
         FIG.  7    shows one embodiment of one of the switch arrays of  FIG.  6   ; 
         FIG.  8    shows another embodiment of one of the switch arrays of  FIG.  6   ; 
         FIG.  9    shows a third embodiment of the electrical system of  FIG.  2   ; 
         FIG.  10    shows a fourth embodiment of the electrical system of  FIG.  2   ; 
         FIG.  11    shows a fifth embodiment of the electrical system of  FIG.  2   , in which the switching arrangement comprises two switch arrays for connecting the electric machines with two output busses and four engine busses; and 
         FIG.  12    shows one of the switch arrays of  FIG.  11   . 
     
    
    
     DETAILED DESCRIPTION 
     
       FIG.  1   
     
     A general arrangement of an engine  101  for an aircraft is shown in  FIG.  1   . In the present embodiment, the engine  101  is of turbofan configuration, and thus comprises a ducted fan  102  that receives intake air A and generates two pressurised airflows: a bypass flow B which passes axially through a bypass duct  103  and a core flow C which enters a core gas turbine. 
     The core gas turbine comprises, in axial flow series, a low-pressure compressor  104 , a high-pressure compressor  105 , a combustor  106 , a high-pressure turbine  107 , and a low-pressure turbine  108 . 
     In operation, the core flow C is compressed by the low-pressure compressor  104  and is then directed into the high-pressure compressor  105  where further compression takes place. The compressed air exhausted from the high-pressure compressor  105  is directed into the combustor  106  where it is mixed with fuel and the mixture is combusted. The resultant hot combustion products then expand through, and thereby drive, the high-pressure turbine  107  and in turn the low-pressure turbine  108  before being exhausted to provide a small proportion of the overall thrust. 
     The high-pressure turbine  107  drives the high-pressure compressor  105  via an interconnecting shaft. The low-pressure turbine  108  drives the low-pressure compressor  104  via another interconnecting shaft. Together, the high-pressure compressor  105 , high-pressure turbine  107 , and associated interconnecting shaft form part of a high-pressure spool of the engine  101 . Similarly, the low-pressure compressor  104 , low-pressure turbine  108 , and associated interconnecting shaft form part of a low-pressure spool of the engine  101 . Such nomenclature will be familiar to those skilled in the art. 
     The fan  102  is driven by the low-pressure turbine  108  via a reduction gearbox in the form of a planetary-configuration epicyclic gearbox  109 . Thus in this configuration, the low-pressure turbine  108  is connected with a sun gear of the gearbox  109 . The sun gear is meshed with a plurality of planet gears located in a rotating carrier, which planet gears are in turn are meshed with a static ring gear. The rotating carrier drives the fan  102  via a fan shaft  110 . 
     It will be appreciated that in alternative embodiments a star-configuration epicyclic gearbox (in which the planet carrier is static and the ring gear rotates and provides the output) may be used instead. 
     In order to facilitate electrical generation by the engine  101 , a first rotary electric machine  111  capable of operating both as a motor and generator is mechanically coupled with the high-pressure spool. In the present embodiment, the first electric machine  111  is coupled to the high-pressure spool via a high-pressure spool driven, core-mounted accessory gearbox  112  of conventional drive configuration. Thus, as well as operation as a generator to supply an aircraft on which the engine  101  is installed with electrical power, the first electric machine  111  may drive the high-pressure spool to facilitate starting of the engine  101  in place of an air turbine starter, and may also drive it in certain flight phases to improve operability, fuel consumption, etc. 
     In alternative embodiments, the first electric machine  111  may be mounted coaxially with the turbomachinery in the engine  101 . For example, the first electric machine  111  may be mounted axially in line with the duct between the low- and high-pressure compressors  104  and  105 . 
     Similarly, a second rotary electric machine  113  capable of operating both as a motor and generator is mechanically coupled with the low-pressure spool. In the present embodiment, the second electric machine  113  is mounted in the tail cone  114  of the engine  101  coaxially with the turbomachinery and is coupled to the low-pressure turbine  108 . In alternative embodiments, the second rotary electric machine  113  may be located axially in line with low-pressure compressor  104 , which may adopt a bladed disc or bladed drum configuration to provide space for the second rotary electric machine  113 . 
     It will of course be appreciated by those skilled in the art that any other suitable location for the first and second electric machines may be adopted. 
     In the present embodiment, the first and second electric machines are connected with power electronics. Extraction of power from, or application of power to the electric machines is performed by a power electronics module (PEM)  115 . In the present embodiment, the PEM  115  is mounted on the fan case  116  of the engine  101 , but it will be appreciated that it may be mounted elsewhere such as on the core of the gas turbine, or in the vehicle to which the engine  101  is attached, for example. 
     Control of the PEM  115  and of the first and second electric machines  111  and  113  is in the present example performed by an engine electronic controller (EEC)  117 . In the present embodiment the EEC  117  is a full-authority digital engine controller (FADEC), the configuration of which will be known and understood by those skilled in the art. It therefore controls all aspects of the engine  101 , i.e. both of the core gas turbine and the first and second electric machines  111  and  113 . In this way, the EEC  117  may holistically respond to both thrust demand and electrical power demand. 
     The internal configuration of PEM  115  guarantees fault-tolerant transfer of electric power between the first electric machine  111  and second electric machine  113 . In this way, the turbomachinery may be designed to exploit the attendant advantages conferred by transfer of power between the high-pressure spool and the low-pressure spool. For example, transfer of power from the low-pressure spool to the high-pressure spool during the approach phase reduces the effective thrust of the engine  101  whilst maintaining sufficient high-pressure spool rotational speed to safely initiate a go-around manoeuvre. Further, in engine  101 , transfer of power from the high-pressure spool to the low-pressure spool during a deceleration manoeuvre reduces the risk of weak extinction, therefore enabling a more optimal combustor design. 
     In an implementation contemplated herein, the PEM  115  is configured such that it may output to or receive electrical power from two dc busses—a configuration contemplated for future more electric aircraft platforms. The configuration of this electrical system will be described with reference to  FIG.  2   . 
     Various embodiments of the engine  101  may include one or more of the following features. 
     It will be appreciated that instead of being a turbofan having a ducted fan arrangement, the engine  101  may instead be a turboprop comprising a propeller for producing thrust. 
     The low- and high-pressure compressors  104  and  105  may comprise any number of stages, for example multiple stages. Each stage may comprise a row of rotor blades and a row of stator vanes, which may be variable stator vanes (in that their angle of incidence may be variable). In addition to, or in place of, axial stages, the low- or high-pressure compressors  104  and  105  may comprise centrifugal compression stages. 
     The low- and high-pressure turbines  107  and  108  may also comprise any number of stages. 
     The fan  102  may have any desired number of fan blades, for example 16, 18, 20, or 22 fan blades. 
     Each fan blade may be defined as having a radial span extending from a root (or hub) at a radially inner gas-washed location, or 0 percent span position, to a tip at a 100 percent span position. The ratio of the radius of the fan blade at the hub to the radius of the fan blade at the tip—the hub-tip ratio—may be less than (or on the order of) any of: 0.4, 0.39, 0.38 0.37, 0.36, 0.35, 0.34, 0.33, 0.32, 0.31, 0.3, 0.29, 0.28, 0.27, 0.26, or 0.25. The hub-tip ratio may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). The hub-tip ratio may both be measured at the leading edge (or axially forwardmost) part of the blade. The hub-tip ratio refers, of course, to the gas-washed portion of the fan blade, i.e. the portion radially outside any platform. 
     The radius of the fan  102  may be measured between the engine centreline and the tip of a fan blade at its leading edge. The fan diameter may be greater than (or on the order of) any of: 2.5 metres, 2.6 metres, 2.7 metres, 2.8 metres, 2.9 metres, 3 metres, 3.1 metres, 3.2 metres, 3.3 metres, 3.4 metres, 3.5 metres, 3.6 metres, 3.7 metres, 3.8 metres or 3.9 metres. The fan diameter may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). 
     The rotational speed of the fan  102  may vary in use. Generally, the rotational speed is lower for fans with a higher diameter. Purely by way of non-limitative example, the rotational speed of the fan at cruise conditions may be less than 2500 rpm, for example 2300 rpm. Purely by way of further non-limitative example, the rotational speed of the fan  102  at cruise conditions for an engine having a fan diameter in the range of from 2.5 metres to 3 metres (for example 2.5 metres to 2.8 metres) may be in the range of from 1700 rpm to 2500 rpm, for example in the range of from 1800 rpm to 2300 rpm, or, for example in the range of from 1900 rpm to 2100 rpm. Purely by way of further non-limitative example, the rotational speed of the fan at cruise conditions for an engine having a fan diameter in the range of from 3.2 metres to 3.8 metres may be in the range of from 1200 rpm to 2000 rpm, for example in the range of from 1300 rpm to 1800 rpm, for example in the range of from 1400 rpm to 1600 rpm. 
     In use of the engine  101 , the fan  102  (with its associated fan blades) rotates about a rotational axis. This rotation results in the tip of the fan blade moving with a velocity U tip . The work done by the fan blades on the flow results in an enthalpy rise dH of the flow. A fan tip loading may be defined as dH/U tip   2 , where dH is the enthalpy rise (for example the one-dimensional average enthalpy rise) across the fan and U tip  is the (translational) velocity of the fan tip, for example at the leading edge of the tip (which may be defined as fan tip radius at leading edge multiplied by angular speed). The fan tip loading at cruise conditions may be greater than (or on the order of) any of: 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39 or 0.4. The fan tip loading may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds). 
     The engine  101  may have any desired bypass ratio, where the bypass ratio is defined as the ratio of the mass flow rate of the flow B through the bypass duct to the mass flow rate of the flow C through the core at cruise conditions. Depending upon the selected configuration, the bypass ratio may be greater than (or on the order of) any of the following: 10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, or 17. The bypass ratio may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). The bypass duct may be substantially annular. The bypass duct may be radially outside the core engine. The radially outer surface of the bypass duct may be defined by a nacelle and/or a fan case. 
     The overall pressure ratio of the engine  101  may be defined as the ratio of the stagnation pressure upstream of the fan  102  to the stagnation pressure at the exit of the high-pressure compressor  105  (before entry into the combustor). By way of non-limitative example, the overall pressure ratio of the engine  101  at cruise may be greater than (or on the order of) any of the following: 35, 40, 45, 50, 55, 60, 65, 70, 75. The overall pressure ratio may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). 
     Specific thrust of the engine  101  may be defined as the net thrust of the engine divided by the total mass flow through the engine  101 . At cruise conditions, the specific thrust of the engine  101  may be less than (or on the order of) any of the following: 110 Nkg −1 s, 105 Nkg −1 s, 100 Nkg −1 s, 95 Nkg −1 s, 90 Nkg −1 s, 85 Nkg −1 s, or 80 Nkg −1 s. The specific thrust may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds). Such engines may be particularly efficient in comparison with conventional gas turbine engines. 
     The engine  101  may have any desired maximum thrust. For example, the engine  101  may be capable of producing a maximum thrust of at least (or on the order of) any of the following: 160 kilonewtons, 170 kilonewtons, 180 kilonewtons, 190 kilonewtons, 200 kilonewtons, 250 kilonewtons, 300 kilonewtons, 350 kilonewtons, 400 kilonewtons, 450 kilonewtons, 500 kilonewtons, or 550 kilonewtons. The maximum thrust may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). The thrust referred to above may be the maximum net thrust at standard atmospheric conditions at sea level plus 15 degrees Celsius (ambient pressure 101.3 kilopascals, temperature 30 degrees Celsius), with the engine  101  being static. 
     In use, the temperature of the flow at the entry to the high-pressure turbine  107  may be particularly high. This temperature, which may be referred to as turbine entry temperature or TET, may be measured at the exit to the combustor  106 , for example immediately upstream of the first turbine vane, which itself may be referred to as a nozzle guide vane. At cruise, the TET may be at least (or on the order of) any of the following: 1400 kelvin, 1450 kelvin, 1500 kelvin, 1550 kelvin, 1600 kelvin or 1650 kelvin. The TET at cruise may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). The maximum TET in use of the engine  101  may be, for example, at least (or on the order of) any of the following: 1700 kelvin, 1750 kelvin, 1800 kelvin, 1850 kelvin, 1900 kelvin, 1950 kelvin or 2000 kelvin. The maximum TET may be in an inclusive range bounded by any two of the aforesaid values (i.e. the values may form upper or lower bounds). The maximum TET may occur, for example, at a high thrust condition, for example at a maximum take-off (MTO) condition. 
     A fan blade and/or aerofoil portion of a fan blade described and/or claimed herein may be manufactured from any suitable material or combination of materials. For example, at least a part of the fan blade and/or aerofoil may be manufactured at least in part from a composite, for example a metal matrix composite and/or an organic matrix composite, such as carbon fibre. By way of further example at least a part of the fan blade and/or aerofoil may be manufactured at least in part from a metal, such as a titanium-based metal or an aluminium based material (such as an aluminium-lithium alloy) or a steel-based material. The fan blade may comprise at least two regions manufactured using different materials. For example, the fan blade may have a protective leading edge, which may be manufactured using a material that is better able to resist impact (for example from birds, ice or other material) than the rest of the blade. Such a leading edge may, for example, be manufactured using titanium or a titanium-based alloy. Thus, purely by way of example, the fan blade may have a carbon-fibre or aluminium-based body with a titanium leading edge. 
     The fan  102  may comprise a central hub portion, from which the fan blades may extend, for example in a radial direction. The fan blades may be attached to the central portion in any desired manner. For example, each fan blade may comprise a fixture which may engage a corresponding slot in the hub. Purely by way of example, such a fixture may be in the form of a dovetail that may slot into and/or engage a corresponding slot in the hub/disc in order to fix the fan blade to the hub. By way of further example, the fan blades maybe formed integrally with a central hub portion. Such an arrangement may be a bladed disc or a bladed ring. Any suitable method may be used to manufacture such a bladed disc or bladed ring. For example, at least a part of the fan blades may be machined from a billet and/or at least part of the fan blades may be attached to the hub/disc by welding, such as linear friction welding. 
     The engine  101  may be provided with a variable area nozzle (VAN). Such a variable area nozzle may allow the exit area of the bypass duct to be varied in use. The general principles of the present disclosure may apply to engines with or without a VAN. 
     As used herein, cruise conditions have the conventional meaning and would be readily understood by those skilled in the art. 
     Such cruise conditions may be conventionally defined as the conditions at mid-cruise, for example the conditions experienced by the aircraft and/or engine at the midpoint (in terms of time and/or distance) between top of climb and start of descent. Cruise conditions thus define an operating point of the gas turbine engine which provides a thrust that would ensure steady state operation (i.e. maintaining a constant altitude and constant Mach number) at mid-cruise of an aircraft to which it is designed to be attached, taking into account the number of engines provided to that aircraft. For example, where an engine is designed to be attached to an aircraft that has two engines of the same type, at cruise conditions the engine provides half of the total thrust that would be required for steady state operation of that aircraft at mid-cruise. 
     In other words, for a given gas turbine engine for an aircraft, cruise conditions are defined as the operating point of the engine that provides a specified thrust (required to provide—in combination with any other engines on the aircraft—steady state operation of the aircraft to which it is designed to be attached at a given mid-cruise Mach number) at the mid-cruise atmospheric conditions (defined by the International Standard Atmosphere according to ISO 2533 at the mid-cruise altitude). For any given gas turbine engine for an aircraft, the mid-cruise thrust, atmospheric conditions and Mach number are known, and thus the operating point of the engine at cruise conditions is clearly defined. 
     The cruise conditions may correspond to ISA standard atmospheric conditions at an altitude that is in the range of from 10000 to 15000 metres, such as from 10000 to 12000 metres, or from 10400 to 11600 metres (around 38000 feet), or from 10500 to 11500 metres, or from 10600 to 11400 metres, or from 10700 metres (around 35000 feet) to 11300 metres, or from 10800 to 11200 metres, or from 10900 to 11100 metres, or 11000 metres. The cruise conditions may correspond to standard atmospheric conditions at any given altitude in these ranges. 
     The forward speed at the cruise condition may be any point in the range of from Mach 0.7 to 0.9, for example one of Mach 0.75 to 0.85, Mach 0.76 to 0.84, Mach 0.77 to 0.83, Mach 0.78 to 0.82, Mach 0.79 to 0.81, Mach 0.8, Mach 0.85, or in the range of from Mach 0.8 to 0.85. Any single speed within these ranges may be the cruise condition. For some aircraft, the cruise conditions may be outside these ranges, for example below Mach 0.7 or above Mach 0.9. 
     Thus, for example, the cruise conditions may correspond specifically to a pressure of 23 kilopascals, a temperature of minus 55 degrees Celsius, and a forward Mach number of 0.8. 
     It will of course be appreciated, however, that the principles of the invention claimed herein may still be applied to engines having suitable design features falling outside of the aforesaid parameter ranges. 
     
       FIG.  2   
     
     An electrical system  201  for connecting the first and second electric machines  111  and  113  to the high- and low-pressure spools is shown in  FIG.  2   . The electrical system  201  is shown in the form of a single line diagram, the conventions of which will be familiar to those skilled in the art. Thus for alternating current (ac) a single line replaces a plurality of polyphase lines, and for direct current (dc) a single line replaces the +V and −V lines. 
     In the illustrated configuration, the ac output of the electric machines is provided to the PEM  115 . The configuration of the electric machines will be described further with reference to  FIG.  3   . 
     A controller  202  for the PEM  115  is provided in the EEC  117 . In the present example, the controller  202  is a functional module implemented in software running on the EEC  117 . It will be appreciated that in alternative embodiments the controller  202  may be implemented in hardware in the EEC  117 . It will also be appreciated that the controller  202  may be a separate module in addition to the EEC  117 . 
     As shown in  FIG.  2   , a first set of bidirectional converter circuits  203  is connected with the first electric machine  111 , and a second set of bidirectional converter circuits  204  is connected with the second electric machine  113 . 
     The controller  202  is configured to control the operation of the first and second sets of bidirectional converter circuits  203  and  204  so as to control the operation of the electric machines  111  and  113 . 
     In operation, the bidirectional converter circuits are configured to convert alternating current to and from direct current by either rectification or inversion under the control of the controller  202 . 
     The direct current output of the converter circuits is provided to a switching arrangement  205 , which is configured to interface with an electrical network  206 , such as the electrical network on an aircraft. 
     In general terms, the electrical system  201  is an N-phase system. 
     Each one of the electric machines  111  and  113  has an identical even number N≥4 of phases, which defines the number of phases in the electrical system  201 . Embodiments in which N=4 will be described with reference to  FIGS.  3  to  8   . An embodiment in which N=6 will be described with reference to  FIG.  9   . 
     Each phase in each electric machine comprises P≥1 coils wound in a P-plex configuration. For example, for P=2, the coils are wound in a duplex configuration. This configuration will be described further with reference to  FIG.  3   . The P-plex winding configuration results in each phase being separated by 2π/NP radians. 
     Each set of bidirectional converter circuits  203  and  204  comprises N individual converter circuits, each connected with the P coils in an equivalent phase in each electric machine. 
     In this way, the N phases in the electrical system  201  are isolated and independent as each machine phase has its own dedicated converter circuit, which improves fault tolerance. 
     The electrical network may be an R-channel network, 1≤R≤N/2. The switching arrangement  205  therefore comprises R dc outputs for connection to the R-channel network. Embodiments in which R=2 will be described with reference to  FIGS.  3  to  9   . An embodiment in which R=3 will be described with reference to  FIG.  10   . 
     In an embodiment, the switching arrangement  205  is configured to also connect equivalent phase bidirectional converter circuits to each other to facilitate power transfer between the first electric machine  111  and the second electric machine  113  without requiring connection to the electrical network  206 . 
     In this way, various faults may be managed, whilst maintaining the capability to transfer power between the gas turbine spools and to and from an external electrical network. 
     
       FIG.  3   
     
     In this first example, the electrical system  201  is an N=4 phase system, with each phase having an associated index n=(1, . . . , 4). The winding configuration of the first electric machine  111  for this example is shown in schematic form in  FIG.  3   . In the present embodiment, the configuration—so far as described herein—of the second electric machine  113  is the same. 
     A primary advantage of an N=4 phase system is that the first electric machine  111  only needs to be over-rated by 33 percent in order to deliver the requisite drive or generating power in the presence of a fault with one of the phases. This is in contrast to dual-wound three-phase machines which are typically over-rated by 100 percent. 
     The first electric machine  111  comprises a stator  301 . In the present embodiment, the stator  301  is configured as an alternate-wound stator. This means that the coils are evenly spaced on alternate teeth such that there is one coil side per slot—this arrangement may also be referred to as a modular winding. This provides physical, thermal, electrical, and magnetic isolation between the coils which provides fault tolerance. 
     In the present embodiment, P=2 thus each phase comprises two coils separated by r radians, i.e. in a duplex configuration. Adjacent phases are separated by 2π/NP=π/4 radians. Pairing coils together in a duplex arrangement means that the machine is mechanically balanced, in particular during a fault condition when one or more phases may be disabled. It will be appreciated that a triplex or greater winding is possible and may be used to further improve rotordynamics, hence the parameterisation of the number of coils to the number P. Indeed, as set out herein it is also possible to utilise a single coil per phase, i.e. P=1, as this has advantages in terms of simplicity and in normal operation does not suffer from any imbalances. It is only during a fault condition that imbalance may occur, however this may be mitigated through implementation of sophisticated control algorithms in the controller  202 —such approaches will be familiar to those skilled in the art and indeed have been implemented by the present applicant in aircraft fuel pump systems. 
     In the present embodiment, the stator  301  comprises teeth  302  defining slots therebetween. NP=8 coils (identified in the Figure as  303  through  310 ) each having an associated index np=(1, . . . , 8) are wound on the requisite sixteen teeth to achieve the alternate-wound configuration. In the present example, for all np, the (np)th coil forms part of the nth phase for which np (mod N)≡n is satisfied. Thus, the first coil  303  and fifth coil  307  form part of the first phase as both 1 and 5 are congruent modulo 4. Similarly, the second coil  304  and sixth coil  308  form part of the second phase as both 2 and 6 are also congruent modulo 4, and so on. 
     In the present embodiment, the first electric machine  111  is a permanent magnet electric machine. Thus, in operation as a motor, magnetic fields generated by the coils  303  to  310  interact with permanent magnets on a rotor  311  which generates torque. In operation as a generator, the magnetic field of the rotor  311  interacts with the coils  303  to  310  to generate a voltage. In the present embodiment, the magnets on the rotor  311  are samarium cobalt magnets, which material is selected due to its relatively high temperature capability. It is envisaged that if sufficient cooling capacity can be guaranteed, then neodymium magnets may be used instead. It will be appreciated that other known suitable permanent magnet materials may be substituted. 
     In a specific embodiment, short circuits are accommodated by configuring each coil to have a per-unit inductance of about unity. In an embodiment, the per-unit inductance is from 1.1 to 1.4. In a specific embodiment, the per-unit inductance is 1.25. In this way, the short circuit current is limited to from 1.1 to 1.4, and optionally 1.25, times normal operational values, which may be accommodated by providing appropriate insulation and cooling capacity, without imposing as high losses during normal operation as with a strict one-per-unit inductance design. In addition, this higher per-unit inductance provides sufficient margin for the controller  202  to differentiate between normal operating conditions and fault conditions. 
     In a specific embodiment a non-overlapping winding approach is adopted which results in smaller end-windings which improves efficiency. 
     It will be appreciated that a different machine types may be used, such as an induction machine or a switched-reluctance machine. 
     
       FIG.  4   
     
     A first embodiment of electric system  201  where N=4, P=2, and R=2 is shown in  FIG.  4    in the form of a single line diagram. 
     As described previously with reference to  FIG.  2   , in general the first electric machine  111  is connected with the first set of bidirectional converter circuits  203 , and the second electric machine  113  is connected with the second set of bidirectional converter circuits  204 . 
     In the present example, both the first set of bidirectional converter circuits  203  and the second set of bidirectional converter circuits  204  comprise N=4 individual bidirectional converter circuits. In each set, each converter circuit has a respective index n and is connected with, in this embodiment, the P=2 coils in the nth phase of the associated electric machine. 
     In practice, therefore, and as shown in the Figure, the first set of bidirectional converter circuits  203  comprises four converter circuits  401 ,  402 ,  403 , and  404  connected with the first electric machine  111 . In the present example, converter circuit  401  is connected with coils  303  and  307 , converter circuit  402  is connected with coils  304  and  308 , converter circuit  403  is connected with coils  305  and  309 , and converter circuit  401  is connected with coils  306  and  310 . 
     A similar configuration exists for the second set of bidirectional converter circuits  204 , which comprises four converter circuits  405 ,  406 ,  407 , and  408  connected with the second electric machine  113  in the same manner. 
     In the present embodiment, the coils forming part of the same phase (i.e. coils  303  and  307 , and so on) are connected to the respective bidirectional converter circuit in parallel, although it is envisaged that they may also be connected in series utilising internal connections between the coils. The choice may be made upon, for example, the ability to run cables and/or the installation space envelope for terminations, etc. 
     In the present embodiment, the bidirectional converter circuits  401  to  408  are H-bridges accompanied by appropriate filters. However, it will be appreciated that other suitable bidirectional converter topologies may be used, such as neutral-point clamped topologies. 
     In the present embodiment, the functionality of the switching arrangement  205  is implemented by R=2 switching arrays, each having an associated index r. Thus in the Figure they are identified as first switching array  411  and second switching array  412 . The first switching array  411  interfaces with a first dc output  413  for connection with a first channel of the aircraft electrical system, and the second switching array  412  interfaces with a second dc output  414  for connection with a second channel of the aircraft electrical system. 
     In order to provide fault tolerant connection of the two electric machines with the aircraft electrical system, the bidirectional converter circuits  401  to  408  are connected by the first switching array  411  and second switching array in a specific configuration with the first and second dc outputs. 
     In general terms it is possible to say that, for all r, the rth dc output is connected with the dc side of the nth converter circuits in both first set  203  and the second set  204 , for which n (mod R)≡r is satisfied. 
     Applying this general principle to the example of  FIG.  4   , and initially considering the first dc output  413 , the dc side of the first converter circuit  401  and the third converter circuit  403  in the first set  203 , and the dc side of the first converter circuit  405  and the third converter circuit  407  in the second set  204 , are connected to the first dc output  413  via the first switch array  411 . 
     Now considering the second dc output  414 , the dc side of the second converter circuit  402  and the fourth converter circuit  404  in the first set  203 , and the dc side of the second converter circuit  406  and the fourth converter circuit  408  in the second set  204 , are connected to the second dc output  414  via the second switch array  412 . 
     It will therefore be appreciated that in this embodiment, each dc output is connected with a pair of phases in each electric machine that are separated by π/2 radians. Given the alternate-wound stator and duplex winding of this embodiment, and independent phase drive arrangement, this means that the entire electrical circuit connected with one dc output can fail but power can still be provided to and drawn from the wider electrical network on, for example, an aircraft. 
     
       FIG.  5   
     
     Detail of the first switch array  411  is shown in the form of single line diagram in  FIG.  5   . Second switch array  413  is similarly configured. 
     The switch array  411  comprises four inputs  501 ,  502 ,  503 ,  504  for connection with the dc sides of the bidirectional converter circuits as previously described, and an output  505  for connection with the first dc output  413 . Each input  501  to  504  is connected with the output  505  via a respective switch  506 ,  507 ,  508 , and  509 . 
     In a specific embodiment, the switches  506  to  509  are dc contactors, which as will be familiar to those skilled in the art are electrically-controlled switch used for switching an electrical power circuit, where the control circuit has a lower power level than the switched circuit. This is advantageous as in the contemplated implementations of the electrical system  201 , the power levels may be in excess of 500 kilowatts at 540 volts dc. 
     In the present embodiment, the switches  506  to  509  operate under the control of controller  202 , which provides respective control signals Q 1 , Q 2 , Q 3 , and Q 4  to the switches. In this way, it is possible to isolate any one of the inputs and output during a fault condition and to continue to operate the rest of the electrical system  201 . The fault may be any type of fault which risks the safe operation of the system, for example a short circuit or an earth fault. Such faults may be sensed by the controller  202  on the basis of a measurement of any of current flow or voltage of each phase. For example, the fault may be sensed using one or more of overcurrent protection, ground (earth) fault protection, unit (or differential) protection and negative phase sequence protection. The fault may be sensed by one or more of a current transformer and a voltage transformer, or digital equivalents. 
     Recalling that switch array  411  and switch array  413  are of the same configuration, it will therefore be appreciated that, for all n, the dc side of the nth converter circuit in the first set  203  is connected with the dc side of the nth converter circuit in the second set  204 . In this way, power transfer between the spools of the engine  101  may be achieved by way of dc power. 
     In the present embodiment, given R=2, converter circuits with odd ordinals are connected to each other via the first switch array  411 , and converter circuits with even ordinals are connected to each other via the second switch array  412 . It will be appreciated that for greater values of N and greater values of R, more switch arrays will be provided for connection with the R-channel aircraft electrical system 
     
       FIG.  6   
     
     A second embodiment of the electrical system is shown in  FIG.  6   , again in the form of a single line diagram. The electrical system is identified as  201 ′, and N=4, P=2, and R=2. 
     In this embodiment, features in common with the first embodiment described with reference to  FIG.  4    are identified with like numerals. 
     The primary difference in this second embodiment concerns the switch arrays. In this embodiment, four switch arrays are provided to implement the functionality of the switching arrangement  205 : first switch array  601 , second switch array  602 , third switch array  603 , and fourth switch array  604 . 
     Thus, it will be seen that, in general terms, N switch arrays are provided, each having a respective index n. In this implementation, for all n, the nth switch array is configured to connect the dc side of the nth converter circuit in the first set  203  to the dc side of the nth converter circuit in the second set  204 . In this way, power transfer between the spools of the engine  101  may be achieved by way of dc power. 
     It will be appreciated that this arrangement is of the same functionality as that of the first embodiment, however the separation out of the switch arrays means such that power transfer only occurs between equivalent phases in each electric machine ensures that a single faulted phase has no effect on the power transfer function. Two possible embodiments of the switch arrays  601  to  604  will be described with reference to  FIGS.  7  and  8   . 
     In the embodiment of  FIG.  6   , it will be noted that the nth switch array further provides for connection of the nth converter circuits to the dc output determined by the relation previously described with reference to  FIG.  4   . Thus, the first switch array  601  connects the converter circuit  401  and the converter circuit  405  together for power transfer, and also to the first dc output  413 . Similarly, the second switch array  602  connects the converter circuit  403  and the converter circuit  407  together for power transfer, and also to the first dc output  413 . The same principle applies for the converter circuit  603  and converter circuit  604  connected with the second dc output  414 . 
     
       FIG.  7   
     
     Detail of one embodiment of the first switch array  601  is shown in the form of single line diagram in  FIG.  7   . Switch array  602  to  604  would be similarly configured in a practical implementation of the electrical system of  FIG.  6   . 
     The switch array  601  comprises a first input  701  for connection with one of the converter circuits, a second input  702  for connection with another one of the converter circuits, and an output  703  for connection with a dc output. In the present example, the first input  701  is connected with the first bidirectional converter circuit  401  in the first set  203 , and the second input  702  is connected with the first bidirectional converter circuit  405  in the second set  204 . The output  703  is connected with the first dc output  413 . Both the first input  701  and the second input  702  are connected to the output  703  via a node  704 . 
     In order to facilitate connection of inputs and output, a first switch  705  is provided between the first input  501  and the node  504 , and a second switch  706  is provided between the node  504  and the output  503 . 
     One advantage of this arrangement is that the number of switches is minimised, reducing complexity and likelihood of failure. Further, the first switch  705  only requires half the rating of switch  706  in terms of current carrying capacity. In a specific embodiment, the switches  705  and  706  are dc contactors. 
     In the present embodiment, the switches  705  and  706  operate under the control of controller  202 , which provides respective control signals Q 1  and Q 2  to the switches. In this way, it is possible to isolate the inputs from the output and vice versa during fault conditions and to continue to operate the rest of the electrical system  201 . 
     In operation, there are three possible states with associated switching states for the first switch array  601 : one no-fault condition and two fault conditions. 
     The primary mode of operation is the no-fault condition. The first fault condition is the existence of a fault at the dc output  413 , for example on the wider electrical network. The second fault condition is either the existence of a fault between the first electric machine  111  and the first bidirectional converter circuit  401  in the first set  203 , or between the second electric machine  113  and the first bidirectional converter circuit  405  in the second set  204 . 
     Control signals Qn associated with these fault conditions are set out in Table 1 below, in which a “0” indicates an open switch, and a “1” indicates a closed switch: 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Fault Condition 
                 Q1 
                 Q2 
               
               
                   
                   
               
             
            
               
                   
                 No-fault 
                 1 
                 1 
               
               
                   
                 First 
                 1 
                 0 
               
               
                   
                 Second 
                 0 
                 0 
               
               
                   
                   
               
            
           
         
       
     
     Thus, in the no-fault condition, the first switch  705  and the second switch  706  are closed allowing current to flow as normal between the bidirectional converter circuits  401  and  405  and the first dc output  413 . 
     Should a fault occur outwith the electrical system  201 ′, first switch  705  may be opened to isolate the bidirectional converter circuits  401  and  405  from the first dc output  413 , thereby allowing power transfer to continue between the spools of the engine  101 . 
     If a fault occurs between either electric machine and the respective sets of bidirectional converter circuits, both the first switch  705  and the second switch  706  may be opened so as to isolate the fault both as between the electric machines and sets of bidirectional converter circuits, and also from the first dc output  413 . 
     
       FIG.  8   
     
     Detail of another embodiment of the first switch array, identified as  601 ′, is shown in the form of single line diagram in  FIG.  8   . Switch arrays  602  to  604  would be similarly configured in a practical implementation of the electrical system of  FIG.  6   . 
     The switch array  601 ′ comprises a first input  801  for connection with one of the converter circuits, a second input  802  for connection with another one of the converter circuits, and an output  803  for connection with a dc output. In the present example, the first input  801  is connected with the first bidirectional converter circuit  401  in the first set  203 , and the second input  802  is connected with the first bidirectional converter circuit  405  in the second set  204 . The output  803  is connected with the first dc output  413 . Both the first input  801  and the second input  802  are connected to the output  803 . 
     In order to facilitate connection and disconnection of inputs and output, a first switch  804  is provided between the first input  801  and the output  803 , a second switch  805  is provided between the second input  802  and the output  803 , and a third switch  806  is provided in a bus tie across the first input  801  and second input  802 . 
     One advantage of this arrangement is that each switch  804  to  806  may be configured with the same voltage and current rating, and thus may be provided as identical parts. In a specific embodiment, the switches  804  to  806  are dc contactors. 
     In the present embodiment, the switches  804  to  806  operate under the control of controller  202 , which provides respective control signals Q 1 , Q 2 , and Q 3  to the switches. In this way, it is possible to isolate any one of the inputs and output during a fault condition and to continue to operate the rest of the electrical system  201 ′. 
     In operation, the controller  202  is configured to respond to four possible operating conditions with appropriate switching states for the first switch array  406 : one no-fault condition and three fault conditions. The fault may be any type of fault which risks the safe operation of the system, for example a short circuit or an earth fault. Such faults may be sensed by the controller  202  on the basis of a measurement of any of current flow or voltage of each phase. For example, the fault may be sensed using one or more of overcurrent protection, ground (earth) fault protection, unit (or differential) protection and negative phase sequence protection. The fault may be sensed by one or more of a current transformer and a voltage transformer, or digital equivalents. 
     The primary mode of operation is the no-fault condition. The first fault condition is the existence of a fault between the first electric machine  111  and the first bidirectional converter circuit  401  in the first set  203 . The second fault condition is the existence of a fault between the second electric machine  113  and the first bidirectional converter circuit  405  in the second set  204 . The third fault condition is the existence of a fault at the dc output  413 , for example on the wider electrical network. 
     Control signals Qn associated with these fault conditions are set out in Table 2 below, in which a “0” indicates an open switch, and a “1” indicates a closed switch: 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Fault Condition 
                 Q1 
                 Q2 
                 Q3 
               
               
                   
                   
               
             
            
               
                   
                 No-fault 
                 1 
                 1 
                 0 
               
               
                   
                 First 
                 0 
                 1 
                 0 
               
               
                   
                 Second 
                 1 
                 0 
                 0 
               
               
                   
                 Third 
                 0 
                 0 
                 1 
               
               
                   
                   
               
            
           
         
       
     
     Thus, in the no-fault condition the first switch  804  and the second switch  805  are closed, whilst the third switch  806  in the bus tie across the first input  801  and the second input  802  is open. In this way, current flows as normal between the bidirectional converter circuits  401  and  405  and the first dc output  413 . 
     For each of the other fault conditions as defined previously, the switches  804  to  806  are configured to isolate the faulted part of the electrical system  201 ′ from the remaining, operational parts. Power transfer between the gas turbine spools is possible in the presence of a fault outwith the electrical system  201 ′ by provision of switch  806  in the bus tie across the first input  801  and second input  802 , which is closed by the controller in the third fault condition. Supply of power to and from a non-faulted phase is possible even in the presence of a fault between one of the electric machines and the associated bidirectional converter circuit by the provision of switches  804  and  805 , which can isolate the faulty phase and maintain connection of the non-faulted phase with the dc output. 
     
       FIG.  9   
     
     Another example of the electrical system is shown in  FIG.  9    in the form of a single line diagram. The electrical system is identified as  201 ″ and N=6, P=4, and R=2. Features in common with the first embodiment of the electrical system  201  are identified with like numerals. 
     As illustrated in the Figure, the first set of bidirectional converter circuits  203  comprises N converter circuits  901  through  906 . Similarly, the second set of bidirectional converter circuits  204  comprises N converter circuits  907  through  912 , each also having an associated index n. 
     The electrical system  201 ″ further comprises R dc outputs: first dc output  413  and second dc output  414 , each having an associated index r. Furthermore, as shown, for all r, the rth dc output is connected with the dc side of the nth converter circuits in both the first set  203  and the second set  204 , for which n (mod R)=r is satisfied. This is achieved in the present embodiment via a first switch array  913  and a second switch array  914 . 
     It is contemplated that either the connection topology of the first embodiment of the electrical system  201  or of the second embodiment of the electrical system  201 ′ could be used depending upon the level of fault tolerance required. 
     
       FIG.  10   
     
     A further example of the electrical system is shown in  FIG.  10    in the form of a single line diagram. The electrical system is identified as  201 ′″ and N=6, P=2, and R=3. Features in common with the first embodiment of the electrical system  201  are identified with like numerals. 
     As illustrated in the Figure, the first set of bidirectional converter circuits  203  comprises N converter circuits  1001  through  1006 . Similarly, the second set of bidirectional converter circuits  204  comprises N converter circuits  1007  through  1012 , each also having an associated index n. 
     In this embodiment, the electrical system  201 ′″ further comprises R dc outputs: first dc output  1013 , second dc output  1014 , and third dc output  1015 , each having an associated index r. Thus, this electrical system may be utilised in electrical networks having three dc channels. 
     As shown, for all r, the rth dc output is connected with the dc side of the nth converter circuits in both the first set  203  and the second set  204 , for which n (mod R)=r is satisfied. This is achieved in the present embodiment via a first switch array  1015 , a second switch array  1016 , and a third switch array  1017 . 
     Again, it is contemplated that either the connection topology of the first embodiment of the electrical system  201  or of the second embodiment of the electrical system  201 ′ could be used depending upon the level of fault tolerance required. 
     
       FIG.  11   
     
     It is envisaged that the principles of the present invention may also be extended to support fault-tolerant engine accessories, such as a fuel pump or an oil pump. Such an arrangement is shown in  FIG.  11   , which is based upon the second embodiment of the electrical system  201 ′, and thus like numerals are used to identify the same features. Furthermore, in this example, N=4, P=2, and R=2 
     In addition to the first dc output  413  and the second dc output  414 , N engine dc busses are provided, each having an associated index n. In particular, a first switch array  1101  connects the first converter circuits  401  and  405  and the third converter circuits  403  and  407  to the first dc output  413  and also to a first engine dc bus  1111  and a third engine dc bus  1113 . A second switch array  1102  connects the second converter circuits  402  and  406  and the fourth converter circuits  404  and  408  to the second dc output  414  and also to a second engine dc bus  1112  and a fourth engine dc bus  1114 . 
     An electric machine  1103 , which for example may electrically drive a fuel pump or an oil pump, is driven via four converter circuits  1104 ,  1105 ,  1106 , and  1107 . The electric machine  1103  comprises the same number of phases N as the electric machines  111  and  113 . In a specific embodiment, the number of coils per phase in the electric machine  1105  is 1. Alternatively, it may be 2. It may be identical with the electric machines  111  and  113 , i.e. equal to P. Further, in a specific embodiment, given the electric machine  1105  is only required to drive an engine accessory and not to generate any power, the converter circuits  1104  through  1107  are configured as inverters for converting dc to ac. Alternatively, however, the converter circuits may be bidirectional converters depending upon the nature of the accessory being driven. 
     
       FIG.  12   
     
     A single line diagram of the connection between the first switch array  1101 , the dc output  413  and the engine dc busses  1111  and  1113  is shown in  FIG.  12   . 
     The second switch array  1102  and the connections to the dc output  414  and the engine dc busses  1112  and  1114  are equivalent. 
     The switch array  1101  comprises four inputs  1201 ,  1202 ,  1203 ,  1204  for connection with the dc sides of the bidirectional converter circuits  401 ,  405 ,  403  and  407  respectively. The switch array further comprises an output  1205  for connection with the first dc output  413 . Each input  1201  to  1204  is connected with the output  1205  via a respective switch  1206 ,  1207 ,  1208 , and  1209 . 
     The first engine dc bus  1111  is connected between the first input  1201  and the switch  1206  via a switch  1210 , and is further connected between the second input  1202  and the switch  1207  via a switch  1211 . 
     The third engine dc bus  1113  is connected between the third input  1203  and the switch  1208  via a switch  1212 , and is further connected between the fourth input  1204  and the switch  1209  via a switch  1213 . 
     Thus, in general terms, the nth engine dc bus is connected with the nth bidirectional converter circuit in each of the first set  203  and the second set  204 . In this way, fault tolerant supply of the engine dc busses is achieved. In an embodiment, this fault tolerant supply allows removal of the permanent magnet alternator from the engine  101 , as each engine dc bus is supplied from two independent coil pairs in each electric machine  111  and  113 . In operation, this arrangement retains full fault tolerance vis-à-vis the loads connected with the engine dc busses, even in the presence of a single fault elsewhere in the system. In this way, dispatch of an aircraft with said fault is still permitted. 
     As described previously, whilst the present embodiments have been described in the context of transferring power between spools within a gas turbine engine, it will be appreciated by those skilled in the art that the principles of the invention may be applied to arrangements comprising two separate gas turbine engines, each with a respective spool. 
     Furthermore, it is contemplated that the electrical system configuration described herein may be extended to facilitate connection of rotary electric machines with other types of rotating machinery. For example, the rotary electric machines may be connected with other types of heat engines, for example internal combustion engines such as reciprocating or Wankel-type engines. Other types of heat engines such as steam turbines operating according to the Rankine cycle may be connected. Combinations of different types of rotating machinery may be connected. 
     Thus it will be appreciated that the invention described herein may be expressed as an electrical system for connecting rotary electric machines with other rotating machines, the system having the properties and attributes heretofore described. 
     It should also be noted that whilst the present embodiments have been described with reference to a turbofan engine  101  for an aircraft, it will be understood that the principles of the described electrical systems may be applied to other installations, for example in a marine environment such as on a naval vessel powered by gas turbines, or in an energy production environment such as in a power station utilising natural gas fired gas turbines, or any other suitable application. 
     Various examples have been described, each of which feature various combinations of features. It will be appreciated by those skilled in the art that, except where clearly mutually exclusive, any of the features may be employed separately or in combination with any other features and the invention extends to and includes all combinations and sub-combinations of one or more features described herein.