System and method for determining misalignment of coils

Abstract

A misalignment of the centres C1, C2 of primary 23 and secondary 33 coils of an inductive charging system (29, figure 1) is determined. A plurality of auxiliary coils 43-n are in predefined positions relative to the secondary coil. The primary coil is energized to generate a magnetic field and induce a voltage in the auxiliary coils. An induced voltage in each auxiliary coil is measured, the voltage being indicative of a candidate auxiliary coil horizontal offset between a centre of the corresponding auxiliary coil and the primary coil. A first set of candidate horizontal offsets are determined for each of a plurality of predefined vertical offsets. A second set of candidate secondary coil horizontal offsets is determined, each comprising at least one of a longitudinal offset and a transverse offset. An error parameter is calculated for each second set of horizontal offsets. The first set of horizontal offsets corresponding to the second set which results in the smallest error parameter is identified and used to determine misalignment of the coils.

Description

TECHNICAL FIELD The present disclosure relates to a system and method for determining misalignment of coils. The system and method have particular application in determining the misalignmentof primary and secondary coils for performing inductive charging. Aspects of the invention relate to a method, a control system, a vehicle and computer readable instructions. BACKGROUND It is known to provide a wireless charging system comprising a primary coil and a secondary coil. In use, an input current is supplied to the primary coil to induce a current in the secondary coil which may be used to charge a battery. The wireless charging system may be provided in a vehicle to perform wireless charging of an on-board battery, such as a traction battery. A physical misalignment of the primary and secondary coils may occur which causes variations in system parameters. Misalignment between the primary and secondary coils could potentially result in low efficiency in power transfer. It would be desirable to detect a misalignment between the primary and secondary coils. It is an aim of the present invention to address one or more of the disadvantages associated with the prior art. SUMMARY OF THE INVENTION Aspects and embodiments of the invention provide a method of determining a misalignment of primary and secondary coils; a control system for determining a misalignment of primary and secondary coils; a vehicle and computer readable instructions as claimed in the appended claims. According to an aspect of the present invention there is provided a method of determining a misalignment of a centre of a primary coil and a centre of a secondary coil of an inductive charging system, each of a plurality of auxiliary coils being in a predefined position relative to the secondary coil; the method comprising: energizing the primary coil to generate a magnetic field to induce a voltage in each of the plurality of auxiliary coils; measuring an induced voltage in each of the auxiliary coils, the measured induced voltage for each of the plurality of auxiliary coils being indicative of one or more candidate auxiliary coil horizontal offset between a centre of the corresponding auxiliary coil and the centre of the primary coil; for each of a plurality of predefined vertical offsets, determining a plurality of first sets of the candidate auxiliary coil horizontal offsets, each first set comprising one or more candidate auxiliary coil horizontal offset for each of the plurality of auxiliary coils, each candidate auxiliary coil horizontal offset being determined in dependence on the respective measured induced voltage; and, for each first set of the candidate auxiliary coil horizontal offsets, determining a second set of candidate secondary coil horizontal offsets, each second set of the candidate secondary coil horizontal offsets comprising at least one of a longitudinal offset and a transverse offset between the centre of the secondary coil and the centre of the primary coil; calculating an error parameter for each second set of the candidate secondary coil horizontal offsets; identifying the first set of candidate auxiliary coil horizontal offsets which corresponds to the second set which results in the smallest error parameter; and determining the misalignment of the primary coil and the secondary coil in dependence on the first set of candidate auxiliary coil horizontal offsets identified as resulting in the smallest error parameter. Wireless charging misalignment detection aligns with the vision of autonomous cars. It requires minimal user interference with the charging process thus increasing the safety and convenience for the passengers. At least in certain embodiments, the method enables determination of a magnitude and a direction of the misalignment between the primary coil and the secondary coil. The method may determine the misalignment of the secondary coil with respect to the primary coil in two-dimensions or three-dimensions. At least in certain embodiments, the method may be implemented in a control system requiring accurate determination of the misalignment at high speeds. The method may comprise outputting the secondary coil horizontal offset indicating the misalignment of the primary coil and the secondary coil along at least one of a first axis and a second axis. At least in certain embodiments, the misalignment is determined with respect to the geometric centres of the primary and secondary coils. The method has particular application in a vehicle having a wireless charging capability. The method maybe used to facilitate alignment of the primary coil and the secondary coil for inductive charging of a traction battery on a vehicle. At least in certain embodiments, determination of the misalignment facilitates control of the vehicle to reduce any misalignment between the primary and secondary coils, thereby reducing losses during charging. The vehicle may be controlled directly in dependence on the determined misalignment, for example to provide autonomous or semi-autonomous control of the vehicle. The method may comprise generating control signals to control the dynamic operation of the vehicle to align the primary and secondary coils. Alternatively, the method may comprise outputting the determined misalignment to enable a driver to control the vehicle to align the primary and secondary coils. The determined misalignment of the primary coil and the secondary coil may be output to facilitate alignment of the primary and secondary coils. For example, the determined misalignment of the primary coil and the secondary coil may be output to enable positioning of a vehicle to reduce any misalignment of the primary and secondary coils. The determined misalignment may be output as one or more of: a visible output, for example to a display or a screen; an audio output; and a haptic output. Alternatively, or in addition, the determined misalignment of the primary coil and the secondary coil may be used to provide autonomous or semi-autonomous control of a vehicle. The method may comprise controlling the vehicle in dependence on the determined misalignment. The method may comprise outputting a torque request and / or a steering request to control the vehicle to reduce the misalignment. By aligning the primary and second coils, losses may be reduced during charging of the traction battery. One of the primary coil and the secondary coil is provided on the vehicle; and the other one of the primary coil and the secondary coil is external to the vehicle, for example in a charging station. The secondary coil and the plurality of auxiliary coils may be disposed on a vehicle. Alternatively, the primary coil may be external to the vehicle. The method may comprise calculating a plurality of third sets of candidate auxiliary coil three-dimensional offsets between a centre of each of the auxiliary coils and the centre of the primary coil. Each third set of the candidate auxiliary coil three-dimensional offsets may be calculated in dependence on a corresponding one of the first sets of candidate auxiliary coil horizontal offsets and the respective predefined vertical offsets. The candidate auxiliary coil three-dimensional offset may be calculated for each of the horizontal offsets. This may be repeated for each of the plurality of predefined vertical offsets. A plurality of first sets of auxiliary coil horizontal offsets being calculated for the plurality of predefined vertical offsets. In respect of each third set, an estimated vertical offset may be calculated in dependence on the respective third set of the auxiliary coil three-dimensional offsets and the longitudinal and transverse offsets defined in the corresponding second set of the candidate secondary coil horizontal offsets. The or each error parameter may comprise an absolute value of a difference between the estimated vertical offset and the predefined vertical offset for the corresponding second set of the candidate secondary coil horizontal offsets. Each of the third sets of candidate auxiliary coil three-dimensional offset may be calculated using the following equation: Rn = J r„ + z2 wherein: Rn is the auxiliary coil three-dimensional offset; rn is the candidate auxiliary coil horizontal offset; z is the predefined vertical offset; and n identifies the auxiliary coil. The longitudinal offset and the transverse offset in each second set of the candidate secondary coil horizontal offsets may be determined by the following equations: x = a / 2 + Ri*cos(0i) y = a / 2 + R2*cos(02) wherein: x is the longitudinal offset; y is the transverse offset; a / 2 is the horizontal distance from the centre of the secondary coil to the centre of the auxiliary coil; 01 is a first included angle in a plane extending through the centre of the primary coil and a longitudinal axis of the secondary coil; and 02 is a second included angle in a plane extending through the centre of the primary coil and a transverse axis of the secondary coil. The first included angle and the second included angle may be defined by the following equations: cos(18O°-0i) = (R2 + a2 - R2) I (2* Va) cos(18O°-02) = (Rl + a2- R^ I (2* R2*a) The method may comprise accessing a look-up table to determine the first sets of the candidate auxiliary coil horizontal offsets in dependence on the induced voltages measured in each of the auxiliary coils for each of the plurality of predefined vertical offsets. An interpolation algorithm may be executed to interpolate between discrete values stored in the look-up table. The interpolation algorithm may reduce the computational overhead and / or storage requirements. The method may comprise performing linear interpolation of the stored values. Alternatively, the candidate auxiliary coil horizontal offsets may be calculated in dependence on the induced voltages. The plurality of auxiliary coils may comprise at least one auxiliary coil disposed on a first axis of the secondary coil, and at least one auxiliary coil disposed on a second axis of the secondary coil. The first and second axis extend radially from a geometric centre of the secondary coil. The first axis and the second axis are typically perpendicular to each other. The plurality of auxiliary coils may comprise two auxiliary coils disposed on the first axis; and two auxiliary coils disposed on the second axis. The first axis and the second axis may have a predetermined orientation in relation to a vehicle. One of the first axis and the second axis may be disposed on a longitudinal axis of the vehicle; and the other one of the first axis and the second axis may be disposed on a transverse axis of the vehicle. The first axis may be disposed on a longitudinal axis of the vehicle; and the second axis may be disposed on a transverse axis of the vehicle. The arrangement of the first and second axes may be reversed. One or more of the auxiliary coils may be disposed on the first axis; and one or more of the auxiliary coils may be disposed on the second axis. Two of the auxiliary coils may be disposed on the first axis; and two of the auxiliary coils may be disposed on the second axis. The auxiliary coils disposed on the first axis and the second axis may be equidistant from a geometric centre of the secondary coil. The auxiliary coils on the first axis may be disposed on opposing sides of the geometric centre of the secondary coil. The method may comprise determining a misalignment distance along a first dimension in dependence on an induced voltage measured in the opposing auxiliary coils on the first axis. The auxiliary coils on the second axis may be disposed on opposing sides of the geometric centre of the secondary coil. The method may comprise determining a misalignment distance along a second dimension in dependence on an induced voltage measured in the opposing auxiliary coils on the second axis. The plurality of auxiliary coils may comprise three, four, five or more auxiliary coils. According to a further aspect of the present invention there is provided a control system for determining a misalignment of a centre of a primary coil and a centre of a secondary coil of an inductive charging system, wherein one of the primary coil and the secondary coil is provided on a vehicle each of a plurality of auxiliary coils being in a predefined position relative to the secondary coil; the control system comprising one or more processors collectively configured to perform a method as described herein. According to a further aspect of the present invention there is provided a further aspect of the invention provides a control system for determining a misalignment of a centre of a primary coil and a centre of a secondary coil of an inductive charging system, wherein one of the primary coil and the secondary coil is provided on a vehicle, each of a plurality of auxiliary coils being in a predefined position relative to the secondary coil; the control system comprising one or more processors collectively configured to: receive a plurality of induced voltage signals indicating an induced voltage measured in each of the plurality of auxiliary coils, the measured induced voltage for each of the plurality of auxiliary coils being indicative of one or more candidate auxiliary coil horizontal offset between a centre of the corresponding auxiliary coil and the centre of the primary coil; for each of a plurality of predefined vertical offsets determine a plurality of first sets of the candidate auxiliary coil horizontal offsets, each first set comprising one or more candidate auxiliary coil horizontal offset for each of the plurality of auxiliary coils, each candidate auxiliary coil horizontal offset being determined in dependence on the respective measured induced voltage ; and, for each first set of the candidate auxiliary coil horizontal offsets, determine a second set of candidate secondary coil horizontal offsets, each second set of the candidate secondary coil horizontal offsets comprising at least one of a longitudinal offset and a transverse offset between the centre of the secondary coil and the centre of the primary coil; calculate an error parameter for each second set of the candidate secondary coil horizontal offsets; identify the first set of candidate auxiliary coil horizontal offsets which corresponds to the second set which results in the smallest error parameter; determine the misalignment of the primary coil and the secondary coil in dependence on the first set of candidate auxiliary coil horizontal offsets identified as resulting in the smallest error parameter; and output the corresponding secondary coil horizontal offset indicating the misalignment of the centre of the primary coil and the centre of the secondary coil along at least one of a longitudinal axis and a transverse axis. The control system may be used to determine misalignment of the primary coil and the secondary coil for inductive charging of a traction battery on a vehicle. The determined misalignment may facilitate positioning of the vehicle to reduce any misalignment between the primary and secondary coils, thereby reducing losses during charging. The control system is configured to output the secondary coil horizontal offset indicating the misalignment of the primary coil and the secondary coil. The secondary coil horizontal offset may be along at least one of a longitudinal axis and a transverse axis. At least in certain embodiments, the misalignment is determined with respect to the geometric centres of the primary and secondary coils. The control system described herein may be configured to calculate a plurality of third sets of candidate auxiliary coil three-dimensional offsets between a centre of each of the auxiliary coils and the centre of the primary coil, each third set of the candidate auxiliary coil three-dimensional offsets being calculated in dependence on a corresponding one of the first sets of candidate auxiliary coil horizontal offsets and the respective predefined vertical offsets. In respect of each third set, the control system may be configured to calculate an estimated vertical offset in dependence on the respective third set of the auxiliary coil three-dimensional offsets and the longitudinal and transverse offsets defined in the corresponding second set of the candidate secondary coil horizontal offsets. Each error parameter may, for example, comprise an absolute value of a difference between the estimated vertical offset and the predefined vertical offset for the corresponding second set of the candidate secondary coil horizontal offsets. Each of the third sets of candidate auxiliary coil three-dimensional offset may be calculated using the following equation: Rn= J + z2 wherein: Rn is the auxiliary coil three-dimensional offset; rn is the candidate auxiliary coil horizontal offset; z is the predefined vertical offset; and n identifies the auxiliary coil, (same language as claim 5) The longitudinal offset and the transverse offset in each second set of the candidate secondary coil horizontal offsets may be determined by the following equations: x = a / 2 + Ri*cos(8i) y = a / 2 * R3*cos(02) wherein: x is the longitudinal offset; y is the transverse offset; a / 2 is the horizontal distance from the centre of the secondary coil to the centre of the auxiliary coil; 01 is a first included angle in a plane extending through the centre of the primary coil and a longitudinal axis of the secondary coil; and 02 is a second included angle in a plane extending through the centre of the primary coil and a transverse axis of the secondary coil. The first included angle and the second included angle may be defined by the following equations: cos(18O°-0i) = (Rf + a2 - Rj) I (2* R^a) cos(18O°-02) = (Rj + a2 - R%) I (2* / ?2*a) The control system may be configured to access a look-up table to determine the first sets of the candidate auxiliary coil horizontal offsets in dependence on the induced voltages measured in each of the auxiliary coils for each of the plurality of predefined vertical offsets. The control system may be configured to interpolate between values stored in the look-up table. An interpolation algorithm may be executed to interpolate between the values stored in the look-up table. The control system may perform linear interpolation of the stored values. Alternatively, the candidate auxiliary coil horizontal offsets may be calculated in dependence on the induced voltages. The plurality of auxiliary coils may comprise at least one auxiliary coil disposed on a first axis of the secondary coil, and at least one auxiliary coil disposed on a second axis of the secondary coil. The first and second axis extend radially from a geometric centre of the secondary coil. The first axis and the second axis may be perpendicular to each other. The first axis may be aligned with a longitudinal axis of a vehicle; and the second axis may be aligned with a transverse axis of the vehicle. One or more of the auxiliary coils may be disposed on the first axis; and one or more of the auxiliary coils may be disposed on the second axis. Two of the auxiliary coils may be disposed on the first axis; and two of the auxiliary coils may be disposed on the second axis. The secondary coil horizontal offset indicating the misalignment of the centre of the primary coil and the centre of the secondary coil may be output to a screen or a display. A graphical representation of the secondary coil horizontal offset may be output, for example representing at least one of the longitudinal offset and the transverse offset between the centres of the primary and secondary coils. According to a further aspect of the present invention there is provided a vehicle comprising the control system as described herein. The vehicle may comprise one of the following: (a) the primary coil; and (b) the secondary coil and the plurality of auxiliary coils. According to a further aspect of the present invention there is provided a vehicle comprising a secondary coil and plurality of auxiliary coils for determining a misalignment of the secondary coil with a primary coil. The plurality of auxiliary coils may be provided on the vehicle. The plurality of auxiliary coils may comprise three, four, five or more auxiliary coils. The auxiliary coils may be equidistant from a geometric centre of the secondary coil. The auxiliary coils may be arranged in a symmetrical configuration about a longitudinal axis and / or a transverse axis of the vehicle. The longitudinal axis may be aligned with a central longitudinal axis of the vehicle. The plurality of auxiliary coils may be disposed at the apexes of a geometric shape having three or more sides. The geometric shape may be a regular geometric shape. The plurality of auxiliary coils may comprise at least one auxiliary coil disposed on a first axis of the secondary coil, and at least one auxiliary coil disposed on a second axis of the secondary coil. The first and second axis extend radially from a geometric centre of the secondary coil. The first axis and the second axis may be perpendicular to each other. The first axis may be aligned with a longitudinal axis of the vehicle; and the second axis may be aligned with a transverse axis of the vehicle. One or more of the auxiliary coils may be disposed on the first axis; and one or more of the auxiliary coils may be disposed on the second axis. Two of the auxiliary coils may be disposed on the first axis; and two of the auxiliary coils may be disposed on the second axis. The auxiliary coils disposed on each of the first axis and the second axis may be equidistant from a geometric centre of the secondary coil. The auxiliary coils on the first axis may be disposed on opposing sides of the geometric centre of the secondary coil. In use, the induced voltage measured in the opposing auxiliary coils on the first axis may be used to determine a misalignment distance along a first dimension. The auxiliary coils on the second axis may be disposed on opposing sides of the geometric centre of the secondary coil. In use, the induced voltage measured in the opposing auxiliary coils on the second axis may be used to determine a misalignment distance along a second dimension. At least in certain embodiments, two of the auxiliary coils may be disposed the longitudinal axis of the vehicle (, i.e., the x-axis) and two of the auxiliary coils may be disposed on the transverse (lateral) axis of the vehicle (i.e., the y-axis). The auxiliary coils disposed on each of the longitudinal axis and the transverse axis may be equidistant from a geometric centre of the secondary coil. This arrangement may simplify determination of the misalignment. In particular, the misalignment may be determined in dependence on the relationship between two variables (rather than three or more variables). This may reduce the computational overheads and / or storage requirements. The relationship between the variables may, for example, be defined in a look-up table. The vehicle may comprise a display for displaying a graphical representation of the secondary coil horizontal offset. In use, the graphical representation of the secondary coil horizontal offset may comprise at least one of the longitudinal offset and the transverse offset between the centres of the primary and secondary coils. According to a further aspect of the present invention there is provided a computer readable instructions which, when executed by a computer, cause the computer to perform the method described herein. The term “misalignment” used herein refers to the relative position of the primary coil and the secondary coil. The misalignment may be defined along at least one of a longitudinal axis, a transverse axis and a vertical axis. Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives first set out in the preceding paragraphs, in the claims and / or in the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and / or features of any embodiment can be combined in any way and / or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and / or incorporate any feature of any other claim although not originally claimed in that manner. BRIEF DESCRIPTION OF THE DRAWINGS One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which: Figure 1 shows a schematic representation of a vehicle comprising a charging coil alignment system in accordance with an embodiment of the present invention; Figure 2 shows a plan view of the vehicle shown in Figure 1; Figure 3 is a schematic representation of a primary coil of a wireless charging station offset from a secondary coil provided in the vehicle shown in Figure 1; Figure 4 illustrates the electrical connection of the auxiliary coils to a voltage sensor more measuring an induced voltage; Figure 5 is a schematic representation of a control system for the charging coil alignment system; Figure 6 shows a schematic representation of a primary coil and an auxiliary coil for calculating a mutual inductance; Figure 7A is a graph representing an estimated mutual inductance for a variable offset between the primary coil and an auxiliary coil at a fixed vertical height; Figure 7B is a graph representing the induced voltage in one of the auxiliary coils with respect to a horizontal offset from a centre of the primary coil; Figure 8 shows a model of the relationship between the primary coil and the auxiliary coils associated with the secondary coil; Figures 9A and 9B illustrate the calculation of the auxiliary coil three-dimensional offsets of each of the auxiliary coils relative to the primary coil geometric centre; Figure 10 is a block diagram representing a method of determining a misalignment of the primary and second coils in accordance with an embodiment of the present invention; Figure 11 is a schematic representation of a display for providing a graphical driver aid representing the misalignment of the primary and secondary coils; Figure 12 is a schematic representation of a further embodiment of the charging coil alignment system utilising three auxiliary coils to determine a misalignment of the primary and secondary coils; Figure 13 shows a model of the relationship between the primary coil and the auxiliary coils in the embodiment illustrated in Figure 12; Figure 14 shows a schematic representation of a further embodiment of the charging coil alignment system utilising six auxiliary coils to determine a misalignment of the primary and secondary coils; and Figure 15 shows a schematic representation of a further embodiment of the charging coil alignment system utilising eight auxiliary coils to determine a misalignment of the primary and secondary coils. DETAILED DESCRIPTION A charging coil alignment system 1 in accordance with an embodiment of the present invention is described herein with reference to the accompanying Figures. The charging coil alignment system 1 comprises a control system 3. The charging coil alignment system 1 is provided in a vehicle 5 in the present embodiment. The vehicle 5 is a road vehicle comprising a plurality of wheels W1 to W4. As shown in Figures 1 and 2, the vehicle 5 is an automobile in the present embodiment. It will be understood that the charging coil alignment system 1 maybe implemented in other types of vehicles 5. The vehicle 5 is described herein using a reference frame comprising a longitudinal axis X, a transverse axis Y and a vertical axis Z. References herein to a longitudinal direction, a transverse direction and a vertical direction refer to directions along, or parallel to the corresponding axis of the reference frame, the vehicle standing on the horizontal X-Y plane and facing in the direction parallel the X axis. The vehicle 5 is a battery electric vehicle (BEV) comprising at least one electric drive unit 7 and a traction battery 9. The vehicle 5 could be a plug-in hybrid electric vehicle (PHEV). The or each electric drive unit 7 comprises an electric traction motor 11 for propelling the vehicle 5. The vehicle 5 comprises a body 13 having a cabin 15 for occupants. The body 13 has a floor 17 in which the traction battery 9 is housed. The body 13 is suspended by a suspension system (denoted generally by the reference numeral 19) comprising suspension units SP-1 to SP-4 associated with respective wheels W1 to W4 of the vehicle 5. A height of the suspension system 19 may be modified control lably to adjust a height of the body 13. The suspension system 19 may, for example, be an air suspension system 19 comprising a plurality of inflatable bladders for adjusting the height of the suspension units SP-1 to SP-4. The vehicle 5 is configured to enable wireless charging of the traction battery 9 from an inductive (wireless) charging station 21. The inductive charging station 21 is separate from the vehicle 5 and may, for example, be disposed in a parking bay or a parking space. The inductive charging station 21 comprises a primary coil 23 and a power supply 25. The primary coil 23 comprises a first winding having a first geometric centre C1. The first winding is formed by an elongated electrical conductor wound in a spiral about the first geometric centre C1. The primary coil 23 is in the form of a first plate in the present embodiment. The power supply 25 may, for example, be connected to a mains electrical supply. The power supply 25 is electrically connected to the primary coil 23. The power supply 25 is operable to energize the primary coil 23 to generate an alternating electromagnetic field (EMF). The vehicle 5 comprises a secondary coil 33 for charging the traction battery 9. The secondary coil 33 comprises a second winding having a 7 second geometric centre C2 The second winding is formed by an elongated electrical conductor wound in a spiral about the second geometric centre C2. The secondary coil 33 is in the form of a second plate in the present embodiment. The secondary coil 33 in the present embodiment is disposed under the floor 17 of the body 13. The secondary coil 33 may, for example, be located beneath the traction battery 9. The primary coil 23 and the secondary coil 33 collectively form an inductive charging system 29. The primary coil 23 is supplied with an input current, for example from a mains (grid) electrical supply. A current is induced in the secondary coil 33 which is used to charge the traction battery 9 in the vehicle 5. In use, the alternating electromagnetic field (EMF) generated by the primary coil 23 induces a voltage in the secondary coil 33 for charging the traction battery 9. The primary and secondary coils 23, 33 thereby enable wireless charging of the traction battery 9. The primary and secondary coils 23, 33 are preferably aligned with each other to perform charging. In particular, the first and second geometric centres C1, C2 are preferably aligned with each other along a vertical axis Z1. A misalignment of the primary and secondary coils 23, 33 may result in variation in the system operating parameters, for example increasing losses and affecting power transfer from the primary coil 23 to the secondary coil 33. A schematic representation of a misalignment of the primary and secondary coils 23, 33 is shown in Figure 3. The charging coil alignment system 1 according to the present embodiment is provided to determine a misalignment of the primary and secondary coils 23, 33 in three dimensions (3D). The misalignment between the primary and secondary coils 23,33 is determined as a vector having direction and magnitude. By determining any such misalignment, the charging coil alignment system 1 facilitates positioning (or re-positioning) of the vehicle 5 to reduce any misalignment between the primary and secondary coils 23, 33. At least in certain embodiments, this may reduce losses during charging of the traction battery 9. The charging coil alignment system 1 comprises a plurality of auxiliary coils 43-n. The auxiliary coils 43-n each comprise a winding having an auxiliary coil geometric centre AC1 to AC4. Each of the auxiliary coils 43-n is formed by an elongated electrical conductor wound in a spiral about the respective auxiliary coil geometric centre AC1 to AC4. The auxiliary coils 43-n can be coincident with the secondary coil 33, for example in an overlapping arrangement. The secondary coil 33 is electrically isolated from the auxiliary coils 43-n. The auxiliary coils 43-n are electrically isolated from each other. As described herein, the auxiliary coils 43-n are provided to determine any misalignment between the primary and secondary coils 23, 33. The auxiliary coils 43-n are smaller than the secondary coil 33. An electrical switch 45-n is associated with each of the plurality of auxiliary coils 43-n. As shown in Figure 4, a capacitor C(n) is connected in parallel to each of the auxiliary coils 43-n. In the present embodiment, the vehicle 5 comprises four of the auxiliary coils 43-1 to 43-4. As described herein, the vehicle 5 may comprise less than or more than four auxiliary coils 43-n. Each of the plurality of auxiliary coils 43-1 to 43-4 is disposed in a predetermined location relative to the second geometric centre C2 of the secondary coil 33. In the present embodiment, first and third auxiliary coils 43-1, 43-3 are diametrically opposed from each other along the longitudinal axis X; and the second and fourth auxiliary coils 43-2,43-4 are diametrically opposed from each other along the transverse axis Y. The longitudinal axis X is coincident with a longitudinal centreline of the vehicle 5 in the present embodiment. The first and third auxiliary coils 43-1, 43-3 are symmetrical about the transverse axis Y; and the second and fourth auxiliary coils 43-2, 43-4 are symmetrical about the longitudinal axis X. The auxiliary coils 43-1 to 43-4 are equidistant from each other along the longitudinal axis X and the transverse axis Y. The distance between each of the auxiliary coils 43-1 to 43-4 and the second geometric centre C1 is known. In the present embodiment, four electrical switches 45-n are provided selectively to connect each of the auxiliary coils 43-1 to 43-4 to at least one voltage sensor 47. The charging coil alignment system 1 comprises four capacitors C(1) to C(4) connected in parallel with the respective auxiliary coils 43-1 to 43-4. In the present embodiment, the primary coil 23 and the secondary coil 33 each have a radius of 24cm. It will be understood that the radius of each of the primary coil 23 and the secondary coil 33 may be less than or greater than 24cm. The secondary coil 33 and the auxiliary coils 43-1 to 43-4 are disposed in a horizontal plane. The auxiliary coils 43-1 to 43-4 each have a radius of 6cm. The radius of the auxiliary coils 43-1 to 43-4 may be less than or greater than 6cm. The centres AC1 to AC4 of the auxiliary coils 43-1 to 43-4 in the present embodiment are disposed at a distance of 16cm from the second geometric centre C2, but may be less than or greater than 16cm. In use, the primary coil 23 is energized to generate a magnetic field which induces a voltage in the auxiliary coils 43-1 to 43-4. In the present embodiment, the primary coil 23 is energized in a low power mode to establish a weak EMF when determining the alignment of the primary and secondary coils 23, 33. The EMF generated by the primary coil 23 induces a voltage in the auxiliary coils 43-1 to 43-4. The electrical switches 45-1 to 45-4 are closed to connect the at least one voltage sensor 47 to the auxiliary coils 43-1 to 43-4. The induced voltage is measured by the at least one voltage sensor 47. The capacitors C(1) to C(4) are provided to establish resonance in the auxiliary coils 43-1 to 43-4 at a frequency at or near a 8 multiple of the exciting (power transfer) frequency of the EMF generated by the primary coil 23. Resonance with the EMF induces a larger voltage in the auxiliary coils 43-1 to 43-4. The induced voltage in each of the auxiliary coils 43-1 to 43-4 is measured by the at least one voltage sensor 47. Signal conditioning may be performed on the electrical signals received from each of the auxiliary coils 43-n. The measured induced voltages V1 to V4 are acquired as induced voltage data for processing. The measured induced voltages V1 to V4 for each of the auxiliary coils 43-1 to 43-4 is used to estimate the position of the secondary coil 33 relative to the primary coil 23 in three dimensions (3D). The charging coil alignment system 1 in the present embodiment comprises one voltage sensor 47. The switches 45-1 to 45-4 are closed in sequence to connect each of the auxiliary coils 43-1 to 43-4 to the voltage sensor 47 in turn. The process is repeated to measure the induced voltage in each of the auxiliary coils 43-1 to 43-4. A separate voltage sensor 47 may be associated with each of the auxiliary coils 43-1 to 43-4. The separate voltage sensors 47 can measure the induced voltages V1 to V4 of each of the auxiliary coils 43-1 to 43-4 without requiring that the switches 45-1 to 45-4 are operated selectively to connect the auxiliary coils 43-1 to 43-4. The switches 45-1 to 45-4 could be omitted in this arrangement. The control system 3 as illustrated in Figure 5 comprises one controller 105, although it will be appreciated that this is merely illustrative. The controller 105 comprises processing means 107 and memory means 109. The processing means 107 may be one or more electronic processing device 107 which operably executes computer-readable instructions. The memory means 109 may be one or more memory device 109. The memory means 109 is electrically coupled to the processing means 107. The memory means 109 is configured to store instructions, and the processing means 107 is configured to access the memory means 109 and execute the instructions stored thereon. The controller 105 comprises an input means 111 and an output means 113. The input means 111 may comprise an electrical input 111 of the controller 105. The output means 113 may comprise an electrical output 113 of the controller 105. The input 111 is arranged to receive a plurality of induced voltage signals SVn from the voltage sensor 47. The induced voltage signals SVn are electrical signals which are indicative of the induced voltage measured in each of the auxiliary coils 43-n. In the present embodiment, the input 111 receives four induced voltage signals SV1 to SV4 indicative of the measured induced voltages V1 to V4 in each of the auxiliary coils 43-1 to 43-4. The output 113 is arranged to output a misalignment control signal SAL which is indicative of the alignment or misalignment of the primary and secondary coils 23. 33. The output 113 may optionally output a vehicle control signal SVC for controlling the vehicle 5 to reduce the misalignment of the primary and secondary coils 23, 33. The vehicle control signal SVC may provide autonomous or semi-autonomous control of the vehicle 5, for example to control a steering angle and the or each electric drive unit 7. Alternatively, the vehicle control signal SVC may generate a driver prompt or instruction to facilitate positioning of the vehicle 5 to reduce or minimise a misalignment of the primary and secondary coils 23, 33. The processing means 107 receives the induced voltage signals SV1 to SV4 indicating the induced voltage measured in each of the auxiliary coils 43-1 to 43-4. The induced voltages from each of the auxiliary coils 43-1 to 43-4 are used to estimate the position of the secondary coil 33 with respect to the primary coil 23. The processing means 107 implements an estimation algorithm to estimate the position of the secondary coil 33. The estimation algorithm will now be described in more detail. A look-up table 205 defines expected induced voltages VINC for each of the auxiliary coils 43-1 to 43-4 and is stored in the memory 109 (or a storage device). The expected induced voltage VINC is defined across a first range of lateral radial misalignments r; and a second range of vertical offsets Az(i). The lateral radial misalignments r(n) each represent an offset between the first geometric centre C1 and one of the auxiliary coil geometric centres AC1 to AC4 in a horizontal plane XY. The lateral radial misalignment r(n) is referred to herein as an auxiliary coil horizontal offset r(n). The auxiliary coil horizontal offset r(n) occurs along at least one of the longitudinal axis X and the transverse axis Y. The vertical misalignment Az(i) represents a height differential between the first and second geometric centres C1, C2. The vertical misalignment Az(i) is referred to herein as a vertical offset Az(i). The vertical offset corresponds to the difference in height of the first and second centres C1, C2 and occurs along the vertical axis Z. The lookup table 205 is predefined. The expected induced voltages VINC may be determined in dependence on empirical data. In the present embodiment, the expected induced voltages VINC are calculated in dependence on the mutual inductance between the primary coil 23 and the auxiliary coil 43-n according to Neumann’s formula (e = - N.d$ / dt where, e is the induced voltage, N is the number of turns in the coil, deb is the magnetic flux, dt is the time taken). The expected induced voltage VINC is directly proportional to a calculated mutual inductance M. The calculation of the mutual inductance M will now be described with reference to Figure 6. In the illustrated arrangement, the primary coil 23 has a primary coil centre P having coordinates (0, 0, 0); and the auxiliary coil 43-n has an auxiliary coil centre A having coordinates (x, y, z). The primary coil 23 has a radius rP and the secondary coil 43-n has a radius ra. The mutual inductance for an offset r between the primary coil 23 and the secondary coil 43-n is calculated using Neumann’s formula: The formula is modified to define the offset r in terms of the x, y, z coordinates of the secondary coil 43-n relative to the primary coil 23. In the present embodiment, the mutual inductance M is calculated for a fixed vertical height z. The modified formula defines a relationship between the mutual inductance M and the offset r for the fixed vertical height z (corresponding to a fixed vertical misalignment Az(i)). The resulting equation is as follows: .... w / f Jvf ™ -—- f J —......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... / ? -> A .v t x : .-.......................................................^11.. ,. - "F "F ""2^,,¾ ) -2.^-- -¼ £«$) A graph 250 illustrating a mutual inductance M calculated for a variable offset r (at a fixed vertical height z) is shown in Figure 7A. It will be understood that the calculated mutual inductance varies depending on the vertical height z. The expected induced voltage VINC is directly proportional to the calculated mutual inductance M. An absolute value of the mutual inductance M is taken to determine the expected induced voltage VINC. A graph 300 shown in Figure 7B represents the expected induced voltage VINC in one of the auxiliary coils 43-n for different auxiliary coil horizontal offsets r(n) between the first and second geometric centres C1, C2 at a particular value of vertical misalignment Az(i). The graph 300 has been separated into three sub-sections 310,320, 330 for formulation of the lookup table 205. The sub-sections 310, 320, 330 are discrete from each other to avoid any overlap of the lateral auxiliary coil horizontal offsets r(n) for any given measured induced voltage V1 to V4. The division of the graph 300 into the discrete sub-sections 310, 320, 330 also removes the need to sense a phase of the induced voltage in the auxiliary coil 43-n. However, as is evident from the graph in Figure 7, any particular voltage below a certain value could be derived from any of three different offsets. The lookup table 205 also comprises the expected induced voltage VINC over a first (horizontal) range of the auxiliary coil horizontal offsets r(n) at a second range of vertical offsets Az(i). The lookup table 205 may, for example, comprise a multi-dimensional table defining the expected induced voltage VINC for the first and second (horizontal and vertical) ranges. The first (horizontal) range in the present embodiment extends from 0cm to 100cm, inclusive. The second (vertical) range is defined so as to correspond to a typical, real-world vertical offset between the primary and secondary coils 23, 33. The second (vertical) range may, for example, reflect changes in the height of the suspension system 19 or variations in the height of the body 13 due to loading. The second (vertical) range in the present embodiment extends from 11cm to 23cm, inclusive. The second (vertical) range may be modified in other applications, for example to increase or decrease one or both of the limits. The expected induced voltage VINC are calculated at predetermined intervals in the horizontal and second (vertical) ranges. The intervals in the present embodiment are 0.125cm, but larger or smaller intervals may be used. The processor 107 can determine intermediate values by interpolating between the defined values, for example using linear interpolation. The lookup table 205 is stored in the memory device 109 (or a storage device). The processing means 107 receives the induced voltage signals SV1 to SV4 indicating the measured induced voltages V1 to V4. The processing means 107 accesses the lookup table 205 to determine a candidate auxiliary coil horizontal offset r(n) between the first geometric centre C1 and each of the auxiliary coil centres AC1 to AC4. The processing means 107 accesses the lookup table 205 to estimate the auxiliary coil horizontal offset r(n) in dependence on the measured induced voltages V1 to V4. The auxiliary coil horizontal offset r(n) is estimated for each of the plurality of the vertical offsets Az(i) defined in the second (vertical) range. In the present embodiment, the auxiliary coil horizontal offset r(n) is estimated for each vertical offset Az(i) in the range 11cm to 23cm. Other values may be defined for the upper and / or lower limits of the second (vertical) range. Three candidate values of the auxiliary coil horizontal offsets r(n) are determined for each measured induced voltage V1 to V4 at each discrete vertical offset Az(i). In the present embodiment, the three possible values of the auxiliary coil horizontal offsets r(n) are calculated by linear interpolation of the values of the expected induced voltage VINO stored in the lookup table 205 for each value of the vertical offset Az(i). The process is repeated in respect of each of the auxiliary coils 43-1 to 43-4 using the measured induced voltages V1 to V4. The auxiliary coil horizontal offset r(1) to r(4) of each of the auxiliary coils 43-1 to 43-4 can be represented as follows: r(1) = {r(1)[1], r(1)[2], r(1)[3]} r(2) = {r(2)[1], r(2)[2], r(2)[3]} r(3) = {r(3)[1], r(3)[2], r(3)[3]} r(4) = {r(4)[1], r(4)[2], r(4)[3]} The three candidate values [1], [2], [3] of the auxiliary coil horizontal offset r(n) correspond to the auxiliary coil horizontal offset r(n) identified in each of the sub-sections 310, 320, 330 of the graph 300 for a measured induced voltage VINC. This is performed in respect of each of the auxiliary coils 43-1 to 43-4. For each set of measured induced voltages V1 to V4 for the auxiliary coils 43-1 to 43-4, there are three different candidate values of the auxiliary coil horizontal offset r(n) at each discrete vertical offset Az(i). The candidate auxiliary coil horizontal offsets r(n) are determined in dependence on the respective measured induced voltages V1 to V4. A plurality of first sets of the candidate auxiliary coil horizontal offsets {r(1), r(2), r(3), r(4)} are determined at each of the plurality of the vertical offsets Az(i). Each of the plurality of first sets comprises the candidate auxiliary coil horizontal offset r(n) of each of the auxiliary coil centres AC1 to AC4 from the first geometric centre C1. A second set comprising candidate secondary coil horizontal offsets (Ax, Ay) is determined in respect of each first set of the candidate auxiliary coil horizontal offsets r(n). The candidate secondary coil horizontal offsets (Ax, Ay) are determined at each of the plurality of vertical offsets Az(i). The candidate secondary coil horizontal offsets (Ax, Ay) each comprise at least one of a longitudinal offset (x) and a transverse offset (y) between the first centre C1 and the second centre C2. The longitudinal and transverse offsets (x, y) are defined in a horizontal plane XY. The longitudinal and transverse offsets (x, y) in each candidate secondary coil horizontal offset (Ax, Ay) represent a viable offset for the measured induced voltages V1 to V4. The second set of candidate secondary coil horizontal offsets (Ax, Ay) is calculated for all possible combinations of the auxiliary coil horizontal offsets {r(1), r(2), r(3), r(4)} at each vertical offset Az(i). The auxiliary coil horizontal offsets r(1), r(2), r(3) and r(4) are estimated values of the lateral (horizontal) misalignment of the auxiliary coil geometric centres AC1 to AC4 with respect to the first geometric centre C1 . A third set comprising candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] is calculated. Each of the candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] represents the three-dimensional distance between the auxiliary coil geometric centres AC1 to AC4 and the first geometric centre C1 of the primary coil 23. The candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] are projection lengths defined in three-dimensions which are not constrained to the horizontal plane XY. The candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] are each calculated in dependence on a corresponding one of the candidate auxiliary coil horizontal offsets r(n) in the first set and the corresponding predefined vertical offset Az(i). The candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] are calculated at each of the vertical offsets Az(i) using the following equations: R2=V'Y^ + Z2 Ra= V'W + z2 R4=V?42 + z2 Where: R1 to R4 are the distances between each of the auxiliary coil geometric centres AC1 to AC4 and the first geometric centre C1 of the primary coil 23; r(1) to r(4) are the horizontal offsets of each of the auxiliary coil geometric centres AC1 to AC4 in a horizontal plane XY with respect to the first geometric centre C1; and z is a predefined vertical offset between the primary and secondary coils 23, 33. A three-dimensional model 400 of the primary coil 23, the secondary coil 33 and the auxiliary coils 43-1 to 43-4 is shown in Figure 8. The calculation of the secondary coil horizontal offsets (Ax, Ay) is described herein with reference to Figures 9A and 9B. The three-dimensional model 400 uses the reference frame of the vehicle 5 comprising the longitudinal axis X, the transverse axis Y and the vertical axis Z. The first geometric centre C1 of the primary coil 23 has the coordinates x, y, z. The second geometric centre C2 of the secondary coil 33 is located at an origin O of the reference frame (i.e„ having coordinates 0, 0, 0). The auxiliary coils 43-1 to 43-4 are located in the XY plane in which the origin O is disposed. The first and third auxiliary coils 41-1, 43-3 are spaced apart from each other along the longitudinal axis X by a known distance (a). The second and fourth auxiliary coils 41-2, 43-4 are spaced apart from each other along the longitudinal axis Y by a known distance, also being (a). The angles 0i and 02 are calculated by application of the cosine rule for the triangles defined by the first geometric centre C1, the first auxiliary coil geometric centre AC1 and the third auxiliary coil geometric centre AC3; and by the first geometric centre C1, the second auxiliary coil geometric centre AC2 and the fourth auxiliary coil geometric centre AC4. The equations are as follows: cos(18O°-0i) = (ftl + a2 - Rj) I (2* R^a) cos(18O°-02) = (R^ + a2 - Rl) I (2* R2*a) The longitudinal offset (Ax) and the transverse offset (Ay) in each second set of the candidate secondary coil horizontal offsets (Ax, Ay) is calculated at each of the vertical offsets Az(i) using the following equations: x = a / 2 + Ri*cos(0i) y = a / 2 + R2*cos(02) The processor 107 is configured to calculate an error parameter for each second set of the candidate secondary coil horizontal offsets (Ax, Ay). The calculation of the error parameter comprises calculating an estimated vertical offset (zest) in dependence on each third set of the candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] and the longitudinal and transverse offsets (Ax, Ay) defined in a corresponding one of the second sets of the candidate secondary coil horizontal offsets (Ax, Ay). The estimated vertical offset (zest) can be calculated by using a distance formula in respect of one or more of the candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4]. By way of example, a formula for calculating the estimated vertical offset (zest) with respect to the first candidate auxiliary coil three-dimensional offset R1 is as follows: 2 x _ (7) j ~ y2 There is a particular vertical offset Az(i) associated with each candidate secondary coil horizontal offsets (Ax, Ay) calculated for the set of measured induced voltages V1 to V 4 {V1, V2, V3, V4}. The estimated vertical offset (zest) is calculated in dependence on the candidate secondary coil horizontal offsets (Ax, Ay) and the associated candidate auxiliary coil three-dimensional offset [R1, R2, R3, R4], The error parameter is the absolute value of a difference between the estimated vertical offset (zest) and the vertical offset Az(i) used in the calculation of the candidate secondary coil horizontal offset (Ax, Ay). The error parameter (error) is calculated using the following equation: error = |zest — z| The error parameter is calculated for all possible combinations of the candidate auxiliary coil horizontal offsets r(n) for each of the auxiliary coils 43-1 to 43-4. The first set of candidate auxiliary coil horizontal offsets r(n) which results in the smallest error parameter is identified. The second set of the candidate secondary coil horizontal offsets (Ax, Ay) corresponding to the identified one of the first set of candidate auxiliary coil horizontal offsets r(n) is selected. The longitudinal and transverse offsets (x, y) in the selected second set of the candidate secondary coil horizontal offsets (Ax, Ay) which most closely represent the relative position of the first and second geometric centres C1, C2 is determined. The processor 107 is configured to determine the misalignment of the primary coil 23 and the secondary coil 33 in dependence on the selected second set of the candidate secondary 12 coil horizontal offsets (Ax, Ay). At least in certain embodiments, the secondary coil horizontal offsets (Ax, Ay) may be calculated in real-time. The secondary coil horizontal offsets (Ax, Ay) may be output to a display 115, such as a liquid crystal display (LCD), to display alignment information to facilitate control of the vehicle 5. This facilitates control of the vehicle 5 to align the primary and secondary coils 23, 33. The secondary coil horizontal offsets (Ax, Ay) could be output to other types of display, such as a heads-up display (HUD). The display of the alignment information on the display 115 is shown in Figure 11 by way of example. In figure 11, numeral 1111 is used to represent “Real time relative position update; - (x, y, z)”. The vertical offset Az(i) which results in the smallest error parameter may be defined as a secondary coil vertical offset A(z) which represents the height differential between the primary and secondary geometric centres 01, C2. The processor 107 may thereby determine the secondary coil vertical offset A(z). The vertical offset A(z) may be output to enable the vehicle wireless charging system to be tuned to reduce losses, thereby improving efficiency. The processor 107 may optionally determine vehicle control signals SVC for controlling the dynamic operation of the vehicle to reduce any misalignment between the primary and secondary coils 23, 33. The vehicle control signals SVC may, for example, control a steering control unit 117 of the vehicle 5 and / or the at least one electric drive unit 7 to position the vehicle 5 such that the primary coil 23 and the secondary coil 33 are at least substantially aligned along a vertical axis. The accuracy with which the processor 107 can determine a misalignment of the primary coil 23 and the secondary coil 33 is dependent on an analogue to digital converter (ADC) which converts the measured induced voltages V1 to V4 from an analogue to digital signal. Signal conditioning may be performed to facilitate processing. The maximum error is proportional to the interval of the auxiliary coil horizontal offset r(n) taken for generation of the lookup table 2O5.The maximum errors may be calculated using the following equation: Maximum error = 4^2‘AR The maximum error for the present embodiment for different ADCs are calculated as follows: 8-bit ADC - Maximum error (including Algorithm)- 2.71*4a / 2 = 15.32 cm (up to approximately 50 cm of horizontal offset range) 10-bit ADC -Maximum error (including Algorithm) - 0.84*4^2 = 4.75 cm (up to approximately 55 cm of horizontal offset range) 12-bit ADC - Maximum error (including Algorithm) - 0.45*472 = 2.54 cm (up to approximately 70 cm of horizontal offset range) To reduce the maximum error, a 12-bit ADC is used in the present embodiment. The implementation of linear interpolation of the values stored in the lookup table 205 may enable the magnitude of the error to be reduced. The maximum error may be reduced, potentially to approximately zero, by reducing the interval size (i.e., less than 0.125cm) and / or using a better interpolation technique. A method 500 according to an embodiment of the invention is illustrated in Figure 10. The method 500 is a method of determining a misalignment of a primary coil 23 and a secondary coil 33. The primary coil 23 and the secondary coil 33 form an inductive charging system 29. One of the primary coil 23 and the secondary coil 33 may, for example, be provided in a vehicle 5, such as a road vehicle; and the other one of the primary coil 23 and the secondary coil 33 may be provided in an inductive charging station 21. A plurality of auxiliary coils are associated with one of the primary and secondary coils 23, 33 to facilitate determination of the alignment of the primary and secondary coils 23,33. The method 500 may be performed by the control system 3 described herein. In particular, the memory 109 may comprise computer-readable instructions which, when executed by the processor 107, perform the method 500 according to an embodiment of the invention. The method 500 starts (BLOCK 505). The primary coil 23 is energized to generate a fluctuating EMF. The EMF induces a voltage in the auxiliary coils 43-1 to 43-4. The voltage induced in the auxiliary coils 43-1 to 43-4 is measured one at a time (BLOCK 510). The measured induced voltages V1 to V4 in the auxiliary coils 43-1 to 43-4 are input (BLOCK 515). The analysis is initiated at a starting value of the vertical offset Az(i) and a minimum error parameter is set equal to a maximum error parameter (BLOCK 520). The lookup table 205 is accessed to determine the three possible values of the auxiliary coil horizontal offset r(n) for each of the auxiliary coils 43-1 to 43-4 in dependence on the measured induced voltages V1 to V4 (BLOCK 525). Linear interpolation of the values stored in the lookup table 205 enables determination of the auxiliary coil horizontal offset r(n) for the measured 13 induced voltages V1 to V4. The candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] are calculated at each of the vertical offsets Az(i) (BLOCK 530). Only positive values of the candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] are used. All possible combinations of the distance of the auxiliary coils 43-1 to 43-4 to the primary coil 23 are determined from the set of candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] (BLOCK 535). The secondary coil horizontal offset (Ax, Ay) comprising the longitudinal offset (Ax) and the transverse offset (Ay) are calculated in dependence on the particular candidate auxiliary coil three-dimensional offsets [R1, R2, R3, R4] (BLOCK 540). The estimated vertical offset (zest) and the error parameter (error) are calculated for each set of the secondary coil horizontal offset (Ax, Ay). A check is performed to determine if the error parameter (error) is less than the minimum error parameter (BLOCK 545). If the error parameter (error) is less than the minimum error parameter (YES), the vertical offset A(z) and the horizontal offset A (x, y) are defined as the coordinates of the first geometric centre C1 of the primary coil 23, and the minimum error parameter is set equal to the error parameter (error) (BLOCK 550). If the error parameter (error) is not less than the minimum error parameter (NO), the process proceeds. The vertical offset Az(i) is incremented by one (BLOCK 555). A check is performed to determine if the incremented vertical offset Az(i) is equal to a vertical offset stop (z_stop) (BLOCK 560). If the vertical offset stop (z_stop) is less than the upper limit of the second (vertical) range of the vertical offsets Az(i) (NO), the process is repeated and the horizontal offset r(n) for each of the auxiliary coils 43-1 to 43-4 is calculated for the incremented vertical offset Az(i) in dependence on the measured induced voltages V1 to V4 (BLOCK 525). If the vertical offset stop (z stop) is equal to the upper limit of the second (vertical) range of the vertical offsets Az(i) (YES), the coordinates of the secondary coil horizontal offset (Ax, Ay) and the vertical offset Az(i) identified as having the minimum error parameter (BLOCK 550) are output as the coordinates of the first geometric centre C1 of the primary coil 23 (BLOCK 565). The method ends (BLOCK 570). The secondary coil horizontal offset (Ax, Ay) can be output to a vehicle control system to control the dynamic operation of the vehicle 5 to reduce any misalignment between the primary and secondary coils 23, 33. In the present embodiment, the secondary coil 33 is positioned such that the second geometric centre C2 is located on the longitudinal centreline of the vehicle 5. The first and third auxiliary coils 43-1, 43-3 are also located on the longitudinal axis X; and the second and fourth auxiliary coils 43-2, 43-4 are located on the transverse axis Y. The auxiliary coils 41-1 to 41-4 are equidistant from the second geometric centre C2. The misalignment of the primary and secondary coils 23, 33 is determined in dependence on the measured induced voltages V1 to V4 in each of the auxiliary coils 43-1 to 43-4. The lookup table 205 is referenced to determine candidate secondary coil horizontal offsets (Ax, Ay) corresponding to the measured induced voltages V1 to V4. The candidate secondary coil horizontal offsets (Ax, Ay) are determined across a range of vertical offsets Az(i) and an error parameter (error) is calculated for each set of candidate secondary coil horizontal offsets (Ax, Ay). By determining which of the candidate secondary coil horizontal offsets (Ax, Ay) results in the smallest error parameter, the secondary coil horizontal offset (Ax, Ay) and the vertical offset Az(i) can be determined. A magnitude and direction of the misalignment between the primary and secondary coils 23, 33 can be determined. The lookup table 205 relates the measured induced voltages V1 to V4 to two variables, namely the horizontal offset r(n) and the vertical offset Az(i). The identification of the secondary coil horizontal offset (Ax, Ay) can be performed using only the horizontal offset r(n) and the vertical offset Az(i) corresponding to the measured induced voltages V1 to V4. This reduces the memory requirements and the computational overhead and, at least in certain embodiments, facilitates determination of the misalignment in real-time. Interpolation can be performed between the values stored in the lookup table 205. For example, linear interpolation within the lookup table 205 may help to improve accuracy and / or response time. The charging coil alignment system 1 and the method 500 in the above embodiment utilise four auxiliary coils 43-1 to 43-4. The charging coil alignment system 1 may utilise less than or more than four auxiliary coils 43-1 to 43-4. Alternate embodiments will now be described. Like reference numerals are used for like components. A further embodiment of the charging coil alignment system 1 in accordance with the present invention is shown in Figure 12. The charging coil alignment system 1 utilises three auxiliary coils 43-1 to 43-3 to determine the misalignment of the primary and secondary coils 23, 33. The auxiliary coils 43-1 to 43-3 are disposed at the vertices of an equilateral triangle having a centroid coincident with the second geometric centre C2. One of the auxiliary coils 43-1 to 43-3 is disposed on the x-axis. The relationship between the primary coil 23 and the auxiliary coils 43-n is illustrated in a model 400 shown in Figure 13. The algorithm to determine the misalignment in this arrangement will now be described. There will be twenty-seven sets of the candidate auxiliary coil three-dimensional offsets [R1, R2, R3] possible for each vertical offset Az(i). As in the above embodiment, there are a possible three values of the candidate auxiliary coil three-dimensional offsets R1, R2 and R3 for each set of the 14 measured induced voltages V1 to V3. For each set of candidate auxiliary coil three-dimensional offsets [R1, R2, R3], the projection length and projection coordinate from the first geometric centre C1 the auxiliary coil geometric centre AC-n of each of the auxiliary coils 43-n is calculated. This is represented in Figure 13 by a line AB which is projected along a d-axis, i.e. (g, h, 0), and a q-axis, i.e. (j, k, 0). The calculation is similar to the technique used in the above embodiment. Equations of lines perpendicular to the d-axis and q-axis, passing through (g, h, 0) and (j, k, 0) respectively, can be computed in the horizontal XY plane in which the second geometric centre C2 is disposed, i.e., where the vertical offset Az(i) is zero. The intersection of the perpendicular lines are the coordinates (x, y, 0). The estimated vertical offset (zest) can be calculated using the distance formula for the line AB, where point A has coordinate (a / 2, -^ / (3) / 2, 0) and B has coordinate (x, y, Az(i)). The error parameter is the absolute value of a difference between the estimated vertical offset (zest) and the vertical offset Az(i). The same minimum error algorithm can be used to find the optimized (x, y) coordinates. The coordinates of the secondary coil horizontal offset (x, y) associated with the vertical offset Az(i) which has the minimum error parameter are output as the coordinates of the first geometric centre C1 of the primary coil 23. A further embodiment of the charging coil alignment system 1 in accordance with the present invention is shown in Figure 14. The charging coil alignment system 1 utilises six auxiliary coils 43-1 to 43-6 to determine the misalignment of the primary and secondary coils 23, 33. The auxiliary coils 43-1 to 43-6 are disposed at the vertices of a regular hexagon having a centroid coincident with the second geometric centre C2. The auxiliary coils 43-1 to 43-6 are symmetrical about the longitudinal axis X. Opposing first and fourth auxiliary coils 43-1 and 43-4 are disposed on the transverse axis Y. The algorithm to determine the misalignment in this arrangement will now be described. The algorithm outlined above in respect of the embodiment consisting of three auxiliary coils 43-1 to 43-3 can be used in respect of a first equilateral triangle formed by the first, third and fifth auxiliary coils 43-1,43-3, 43-5; and a second equilateral triangle formed by the second, fourth and sixth auxiliary coils 43-2,43-4,43-6. An average of both position estimations can also be used as a final output misalignment coordinate of the primary coil 23 relative to the secondary coil 33. A further embodiment of the charging coil alignment system 1 in accordance with the present invention is shown in Figure 15. The charging coil alignment system 1 utilises eight auxiliary coils 43-1 to 43-8 to determine the misalignment of the primary and secondary coils 23, 33. The auxiliary coils 43-1 to 43-8 are disposed at the vertices of a regular octagon having a centroid coincident with the second geometric centre C2. The auxiliary coils 43-1 to 43-8 are symmetrical about the longitudinal axis X and the transverse axis Y. Opposing third and seventh auxiliary coils 43-1 and 43-5 are disposed on the x-axis; and opposing first and fifth auxiliary coils 43-1 and 43-5 are disposed on the y-axis. The algorithm to determine the misalignment in this arrangement will now be described. The measured induced voltages V1, V3, V5, V7 from the auxiliary coils 43-1, 43- 3, 43-5 and 43-7 can be used to implement the algorithm described above in respect of the embodiment utilising four auxiliary coils 43-1 to 43-4. Similarly, the algorithm can use the measured induced voltages V2, V4, V6, V8 from the auxiliary coils 43-2, 43-4, 43-6 and 43-8 to also determine the misalignment of the secondary coil 33. The misalignment can be verified by duplicating the calculation. An average of both position estimations can also be used as a final output coordinate of the position of the primary coil 23 relative to the secondary coil 33. It will be appreciated that various changes and modifications can be made to the present invention without departing from the scope of the present application.

Claims

1. A method of determining a misalignment of a centre of a primary coil and a centre of a secondary coil of an inductive charging system, each of a plurality of auxiliary coils being in a predefined position relative to the secondary coil; the method comprising:energizing the primary coil to generate a magnetic field to induce a voltage in each of the plurality of auxiliary coils;measuring an induced voltage in each of the auxiliary coils, the measured induced voltage for each of the plurality of auxiliary coils being indicative of one or more candidate auxiliary coil horizontal offsets between a centre of the corresponding auxiliary coil and the centre of the primary coil;for each of a plurality of predefined vertical offsets, determining a plurality of first sets of the candidate auxiliary coil horizontal offsets, each first set comprising one or more candidate auxiliary coil horizontal offset for each of the plurality of auxiliary coils, each candidate auxiliary coil horizontal offset being determined in dependence on the respective measured induced voltage; and, for each first set of the candidate auxiliary coil horizontal offsets, determining a second set of candidate secondary coil horizontal offsets, each second set of the candidate secondary coil horizontal offsets comprising at least one of a longitudinal offset and a transverse offset between the centre of the secondary coil and the centre of the primary coil;calculating an error parameter for each second set of the candidate secondary coil horizontal offsets;identifying the first set of candidate auxiliary coil horizontal offsets which corresponds to the second set which results in the smallest error parameter; anddetermining the misalignment of the primary coil and the secondary coil in dependence on the first set of candidate auxiliary coil horizontal offsets identified as resulting in the smallest error parameter.

2. A method as claimed in claim 1, comprising calculating a plurality of third sets of candidate auxiliary coil three-dimensional offsets between a centre of each of the auxiliary coils and the centre of the primary coil, each third set of the candidate auxiliary coil three-dimensional offsets being calculated in dependence on a corresponding one of the first sets of candidate auxiliary coil horizontal offsets and the respective predefined vertical offsets.

3. A method as claimed in claim 2, comprising, for each third set, calculating an estimated vertical offset in dependence on the respective third set of the auxiliary coil three-dimensional offsets and the longitudinal and transverse offsets defined in the corresponding second set of the candidate secondary coil horizontal offsets.

4. A method as claimed in claim 3, wherein each error parameter comprises an absolute value of a difference between the estimated vertical offset and the predefined vertical offset for the corresponding second set of the candidate secondary coil horizontal offsets.

5. A method as claimed in any one of claims 2, 3 or 4, wherein each of the third sets of candidate auxiliary coil three-dimensional offset is calculated using the following equation:Rn = J + z2wherein: Rn is the auxiliary coil three-dimensional offset;rn is the candidate auxiliary coil horizontal offset;z is the predefined vertical offset; andn identifies the auxiliary coil.

6. A method as claimed in claim 5, wherein the longitudinal offset and the transverse offset in each second set of the candidate secondary coil horizontal offsets is determined by the following equations:x = a / 2 + Ri*cos(0i)y = a / 2 + R2*cos(02)16wherein: x is the longitudinal offset;y is the transverse offset;a / 2 is the horizontal distance from the centre of the secondary coil to the centre of the auxiliary coil;01 is a first included angle in a plane extending through the centre of the primary coil and a longitudinal axis of the secondary coil; and02 is a second included angle in a plane extending through the centre of the primary coil and a transverse axis of the secondary coil.

7. A method as claimed in claim 6, wherein the first included angle 01 and the second included angle 02 are defined by the following equations:cos(18O°-0i) = (R2 + a2 - R2) I (2* R^a) cos(18O°-02) = (Rl + a2 - R2^ / (2* R2*a)8. A method as claimed in any one of the preceding claims, wherein the method comprises accessing a look-up table to determine the first sets of the candidate auxiliary coil horizontal offsets in dependence on the induced voltages measured in each of the auxiliary coils for each of the plurality of predefined vertical offsets.

9. A method as claimed in any one of the preceding claims, wherein the plurality of auxiliary coils comprises at least one auxiliary coil disposed on a first axis of the secondary coil, and at least one auxiliary coil disposed on a second axis of the secondary coil; wherein the first axis and the second axis are perpendicular to each other.

10. A method as claimed in claim 9, wherein the plurality of auxiliary coils comprises two auxiliary coils disposed on the first axis, and two auxiliary coils disposed on the second axis.

11. A method as claimed in claim 9 or claim 10, wherein the first axis is aligned with a longitudinal axis of a vehicle; and the second axis is aligned with a transverse axis of the vehicle.

12. A control system for determining a misalignment of a centre of a primary coil and a centre of a secondary coil of an inductive charging system, wherein one of the primary coil and the secondary coil is provided on a vehicle each of a plurality of auxiliary coils being in a predefined position relative to the secondary coil; the control system comprising one or more processors collectively configured to perform a method according to any preceding claim.

13. A control system as claimed in claim 12, wherein the control system is configured to:calculate a plurality of third sets of candidate auxiliary coil three-dimensional offsets between a centre of each of the auxiliary coils and the centre of the primary coil, each third set of the candidate auxiliary coil three-dimensional offsets being calculated in dependence on a corresponding one of the first sets of candidate auxiliary coil horizontal offsets and the respective predefined vertical offsets.

14. A vehicle comprising the control system as claimed in claim 12 or claim 13.

15. A vehicle according to claim 14, the vehicle comprising eitherthe primary coil; orthe secondary coil and the plurality of auxiliary coils.18

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