Abstract:
Methods and apparatus for measuring the voltage of at least one conductor ( 121, 122, 123 ) of an electrical power cable ( 10 ) comprise providing a container ( 22 ) made from a conductive material around a portion of the cable and at least one electric field sensor ( 301, 302, 303, 304 ) between the container and the cable and bringing the container to a constant potential and measuring the electric field with a sensor. The voltage is determined by comparing the measured electric field with electric fields simulated for a plurality of configurations of punctual electric charges.

Description:
The present patent application claims the benefit of International Patent Application No. PCT/FR2014/051278, filed on May 28, 2014, which claims the priority benefit of French patent application FR13/54984, filed on May 31, 2013 which is herein incorporated by reference. 
     BACKGROUND 
     The present invention relates to a voltage measurement device and method, and more specifically to a device and a method for measuring the voltage in a power cable. 
     DISCUSSION OF THE RELATED ART 
     An electric power cable generally comprises at least one conductive wire, also called conductor, for example, three conductive wires. Each conductive wire may be surrounded with an insulating sheath, and the conductive wires with their insulating sheaths are maintained together in an insulating sleeve. As a variation, the conductive wires may be embedded in a single insulating sheath. 
     As an example, in a three-phase current power cable, the conductive wires transport sinusoidal currents having the same maximum amplitude and the same frequency, the phases of the currents being shifted from one conductive wire to the other, for example by 120°. As an example, for an industrial application, the effective voltage in each conductive wire may be in the range from 300 to 400 V. 
     It may be desirable to measure the voltage in each conductor of an electric power cable, for example, to determine whether the values of the effective voltages and the phase balancing are conformable. However, current voltage measurement devices require exposing each conductor of the cable and connecting a voltmeter to each exposed conductor. 
     It would thus be desirable to be able to measure the voltages of the conductors of an electric power cable while leaving the conductors in their insulating sheath. 
     SUMMARY 
     An object of an embodiment aims at providing a voltage measurement device and method which overcomes all or part of the disadvantages of usual voltage measurement devices. 
     According to another object of an embodiment, the measurements of the voltages of the conductors of the power cable may be performed without removing the insulating sheaths surrounding the conductors. 
     According to another object of an embodiment, the voltage measurement method may be implemented without knowing the number of conductors of the cable. 
     According to another object of an embodiment, the structure of the voltage measurement device is simple. 
     Thus, an embodiment of the present invention provides a method of measuring the voltage of at least one conductor of an electric power cable comprising the steps of: 
     arranging an enclosure of a conductive material around a portion of the cable and at least one electric field sensor between the enclosure and the cable; 
     taking the enclosure to a constant potential and measuring the electric field with the sensor; and 
     determining said voltage based on the comparison of the measured electric field with simulated electric fields for a plurality of configurations of point electric charges. 
     According to an embodiment, the method further comprises the steps of: 
     determining by simulation the electric field obtained at the location of said sensor for a plurality of configurations of point electric charges corresponding to different positions of the point electric charges; 
     determining a criterion of comparison between the measured electric field and the simulated electric field for each configuration; and 
     storing the configuration for which the comparison criterion is at an extremum. 
     According to an embodiment, the method comprises determining by simulation the electric field obtained at the location of said sensor for each configuration of a first set of configurations having a first number of point electric charges and for each configuration of a second set of configurations having a second number of point electric charges different from the first number. 
     According to an embodiment, the method comprises the steps of: 
     selecting at least one parameter from the group comprising the position of the center of the conductor with respect to the center of the cable, the mean radius of the conductor, the angular position of the conductor with respect to a reference axis, the phase of the voltage of the conductor, and the maximum amplitude of the voltage of the conductor; 
     varying the parameter between an initial value and a final value with a step; and 
     determining the electric field obtained at the location of said sensor for each configuration of point electric charges associated with each value of the parameter. 
     According to an embodiment, the method comprises the steps of:
         (a) determining the number of conductors of the cable based on the comparison of the measured electric field with the simulated electric fields for configurations of point electric charges comprising different numbers of point electric charges; and   (b) determining said voltage based on the comparison of the measured electric field with the simulated electric fields for a plurality of configurations having the same number of point electric charges.       

     According to an embodiment, step (a) is carried out by varying, simultaneously for each conductor, at least one first parameter from said group and step (b) is carried out by varying, independently for each conductor, at least one second parameter from said group. 
     An embodiment also provides a device for measuring the voltage of at least one conductor of an electric power cable comprising:
         an enclosure of a conductive material intended to be arranged around a portion of the cable and at least one electric field sensor intended to be arranged between the enclosure and the cable;   a source of a constant potential connected to the enclosure; and   a processing unit capable of determining said voltage based on the comparison of the measured electric field with the simulated electric fields for a plurality of configurations of point electric charges.       

     According to an embodiment, the device comprises a plurality of electric field sensors. 
     According to an embodiment, the sensors are maintained in a tubular support of a dielectric material. 
     According to an embodiment, the device comprises at least one optical sensor measuring the electric field comprising an isotropic electro-optical crystal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other features and advantages of the present invention will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings, among which: 
         FIG. 1  is a cutaway view of an electric power cable; 
         FIGS. 2 and 3  are cross-sections in two orthogonal planes of an embodiment of a device for measuring the voltage of a power cable; 
         FIG. 4  illustrates parameters determined by the voltage measurement device; 
         FIG. 5  shows in the form of a block diagram an embodiment of a voltage measurement method; 
         FIG. 6  shows an example of measurements of electric fields by the voltage measurement device according to the embodiment of  FIGS. 2 and 3 ; 
         FIGS. 7 to 10  show different structures of electric power cables and the equivalent electrical models implemented by the embodiment of the voltage measurement method illustrated in  FIG. 5 ; and 
         FIG. 11  shows an example of simulations of electric fields implemented by the embodiment of the voltage measurement method illustrated in  FIG. 5 . 
     
    
    
     DETAILED DESCRIPTION 
     For clarity, the same elements have been designated with the same reference numerals in the various drawings and, further, the various drawings are not to scale. In the following description, unless otherwise indicated, terms “substantially”, “about”, “approximately”, and “in the order of” mean “to within 10%”. 
       FIG. 1  shows an example of a power cable  10  of axis Δ. Cable  10  comprises N conductors  12   i , N being an integer greater than or equal to 1, for example varying from 1 to 10, preferably from 1 to 5, and i being an integer varying from 1 to N. In the example shown in  FIG. 1 , N is equal to three. Each conductor  12   i , made of a metallic material, particularly based on copper or on aluminum, may correspond to a single wire or to an assembly of strands. Each conductor  12   i  is surrounded with a sheath  14   i  of a dielectric material. The three conductors  12  are maintained in an insulating sleeve  16 , where the space between sleeve  16  and sheaths  14   i  may be filled with an insulating filling material  18 . The insulating materials forming sheaths  14   i , sleeve  16 , or filling material  18  may be identical or different. 
     As an example, each conductor  12   i  has a circular or elliptic cross-section. However, each conductor  12   i  may have a cross section of more complex shape, for example, an angular sector shape or an initially circular shape which has been more or less crushed. The cross-sections of conductors  12   i  may be identical or different. 
       FIGS. 2 and 3  show an embodiment of a device  20  for measuring the voltages in conductors  12   i  of power cable  10 . 
     Device  20  comprises an enclosure  22 , made of a conductive material, for example, nickel silver, and comprising a cylindrical portion  24  of axis Δ closed at its ends by ring-shaped portions  26 . The internal wall of cylindrical portion  24  corresponds to a cylinder of axis Δ and of radius R. Length L measured along axis Δ is preferably strictly greater than R. Each ring-shaped portion  26  comprises a cylindrical opening  28  of axis Δ for the passing of cable  10 . 
     Device  20  comprises M electric field sensors  30   k  where M is an integer greater than or equal to 1, for example, varying from 1 to 8, and k is an integer varying from 1 to M. As an example, in  FIG. 2 , M is equal to four. Preferably, sensors  30   k  are arranged in a plane perpendicular to axis Δ. As an example, sensors  30   k  are arranged on a circle of axis Δ. Sensors  30   k  are maintained by a support  32 , made of a dielectric material. As an example, support  32  corresponds to a tube of axis Δ, attached to enclosure  20  at its ends and having sensors  30   k  attached to its wall. 
     Device  20  further comprises a processing unit  34 , only shown in  FIG. 2 , which is connected to each sensor  30   k . Processing unit  34  for example comprises a processor and may correspond to a computer. Processing unit  34  may further comprise a non-volatile memory having a sequence of instructions which control the operation of processing unit  34  stored therein. As a variation, processing unit  34  may be formed by a dedicated electronic circuit. 
     Processing unit  34  is connected to each sensor  30   k , with k varying from 1 to M, by one electric wire or more and/or by one optical fiber  35   k  or more. Processing unit  34  is connected to an interface unit  36 , for example comprising a display screen, a keyboard, a mouse, etc. 
     Device  20  enables to maintain cable  10  in position with respect to sensors  30   k  and with respect to cylindrical portion  24 . According to a variation, an intermediate part may be arranged inside of support  32  and between openings  28  to adapt to power cables  10  having different diameters. According to another variation, the holding of cable  10  is not ensured by enclosure  20 , but by additional means which, when device  20  is installed on cable  10 , enables to maintain constant the distance between cable  10  and sensors  30   k  and between cable  10  and cylindrical portion  24 . 
     Enclosure  22  may be formed of two half-enclosures mobile with respect to each other and support  32  may be formed of two half-supports, each half-support being connected to one of the half-enclosures. The two half-enclosures are for example connected to each other by a hinge connection. The mounting of measurement device  20  on cable  10  may then be performed by sandwiching cable  10  between the two half-enclosures which are temporarily attached to each other. 
     According to an embodiment, at least one of sensors  30   k  comprises an optical sensor such as described in patent application U.S. Pat. No. 8,264,685. 
     According to another embodiment, at least one of sensors  30   k  comprises a microelectromechanical system such as described in the publication entitled “Electric field sensor using electrostatic force deflection of a micro-spring supported membrane” by A. Roncin, C. Shafai, and D. R. Swatek or in the publication entitled “A Self-Resonant MEMS-based Electrostatic Field Sensor with 4V/m/√Hz Sensitivity” by T. Denison, J. Kuang, J. Shafran, M. Judy, and K. Lundberg. 
     According to an embodiment, sensor  30   k  is an optical sensor comprising an electro-optical crystal. The thickness of the electro-optical crystal, measured along a direction parallel to axis Δ, may vary from 0.2 to 10 millimeters, preferably from 1 to 5 millimeters. As an example, the crystal is an isotropic electro-optical crystal. An isotropic electro-optical crystal is a crystal having isotropic optical properties in the absence of an electric field and having anisotropic optical properties in the presence of an electric field. The crystal may be zinc tellurium (ZnTe), cadmium tellurium (CdTe), cadmium zinc tellurium (Cd 1-x Zn x Te) (x being capable of varying from 0.01 to 0.15), bismuth silicon oxide (BSO), gallium arsenide (AsGa), or indium phosphide (InP). 
     The thickness of support  32  may be substantially equal to the thickness of sensor  30   k . As a variation, the thickness of support  32  may be greater than the thickness of sensor  30   k , sensor  30   k  being then embedded in support  32 . The relative permittivity of the material forming support  32  is substantially equal to the relative permittivity of sensor  30   k . As an example, when sensor  30   k  corresponds to an electro-optical crystal, the electro-optical crystal and material  32  have a relative permittivity which may vary from 4 to 60, preferably from 7 to 15. The material forming support  32  may be a resin comprising a filler enabling to adjust the relative permittivity of support  32 . 
     When sensor  30   k  corresponds to an optical sensor comprising an electro-optical crystal, processing unit  34  may comprise a system for emitting a light beam towards the electro-optical crystal and a system for analyzing the light beam originating from the electro-optical crystal. The light beams may be transported between the crystal and the processing unit by optical fibers  35   k . 
     When sensor  30   k  corresponds to an optical sensor, its operating principle may be the following. The electric field present at the level of the electro-optical crystal varies certain optical properties of the crystal. The light beam crossing the crystal is thus modified. The modification of the light beam is detected by processing unit  34  which supplies signals representative of the amplitudes of the measured electric field components. 
     As an example, the dimensions of measurement device  20  are:
         inner diameter of cylindrical portion  24  of enclosure  20 : 69 mm;   thickness of cylindrical portion  24 : 0.5 mm;   diameter of opening  28 : 30 mm;   axial length of cylindrical portion  24 : 100 mm;   inner diameter of support  20 : 30 mm; and   outer diameter of support  20 : 70 mm.       

     In the present embodiment, sensors  30   k  are fixed with respect to enclosure  22 . As a variation, it is possible for device  20  to comprise a single electric field sensor, or a decreased number of electric field sensors and to further comprise a system for displacing the electric field sensors with respect to cable  10  and/or to enclosure  22 . It may be a system for pivoting the electric field sensor around cable  10  according to a circle of axis Δ. 
       FIG. 4  is a cross-section view in a plane perpendicular to axis Δ of cable  10  and illustrates certain parameters taken into account to implement an embodiment of the voltage measurement method. The cross-section plane of  FIG. 4  is called measurement plane in the following description. 
     Point O corresponds to the intersection point between axis Δ of cable  10  and the cross-section plane of  FIG. 4 . Point O may correspond to the geometric center of the cross-section of cable  10 , particularly to the center of symmetry of the cross-section when cable  10  has a circular, elliptic, rectangular cross-section, etc. Axis (Ox) corresponds to a reference axis. In the measurement plane, each conductor  12   i  comprises a center O i . Center O i  corresponds to the geometric center of conductor  12   i , particularly to the center of symmetry of the cross-section when conductor  12   i  has a circular, elliptic, rectangular, etc. cross-section. Further, in the measurement plane, the cross-section of each conductor  12   i  occupies a surface S i . In the case where conductor  12   i  has a circular cross-section, surface S i  is a disk and point O i  corresponds to the center of the disk. Call {right arrow over (r)} 1  the vector connecting point O to point O i  and Ψ 2  the angle, measured clockwise, between axis (Ox) and vector {right arrow over (r)} 2 . Further, call δr i  the mean radius of conductor  12   i . Mean radius δr i  corresponds to the radius of conductor  12   i  in the case where conductor  12   i  has a circular cross-section and corresponds to the radius of the disk having the same surface area as conductor  12   i  when conductor  12   i  has a non-circular cross-section. 
     When voltages are applied to conductors  12   i  of power cable  10 , this translates as the occurrence of an electric field {right arrow over (E)} at any point in space around cable  10 , this electric field being time-variable in the case of variable voltages. Each sensor  30   k  is capable of measuring the amplitude of electric field vector {right arrow over (E)} k  at the location of sensor  30   k  schematically designated by point C k . The measurement plane comprises all the points C k , k varying from 1 to M, a single point C k  being shown in  FIG. 4 . 
     More specifically, each sensor  30   k  is capable of measuring the amplitude of radial component {right arrow over (E)} rk  of the electric field at the location of sensor  30   k  and the amplitude of tangential component {right arrow over (E)} θk  of the electric field at the location of sensor  30   k . Radial component {right arrow over (E)} rk  is the component of the electric field directed along line (OC k ). Tangential component {right arrow over (E)} θk  is the electric field component directed along the line perpendicular to line (OC k ) in the cross-section plane of  FIG. 4  and crossing point C k . In the following description, the component of electric field {right arrow over (E)} k  along Δ is neglected, since this component can be neglected as soon as the twist of the internal conductors has a pitch which is large as compared with the mean distance between point O and the center of conductors O i . 
     According to an embodiment, to determine the voltage in each conductor  12   i  with no contact with conductors  12   i , processing unit  34  should determine voltage V i  in each conductor  12   i  from the measurements of electric field {right arrow over (E)} k . 
     Voltages V i  in conductors  12   i , with i varying from 1 to N, cannot be directly determined Electric charge Q i  in each conductor  12   i  first has to be determined in the measurement plane, after which voltages V i  have to be determined based on charges Q i . 
     The determination of charges Q i  based on electric fields {right arrow over (E)} k  may theoretically be performed by using Gauss&#39;s theorem which can be written according to the following relation (1): 
                       ∯   S     ⁢           ⁢       E   →     ·         d   2     ⁢   S     →         =       Q   int         ɛ   0     ⁢     ɛ   r                 (   1   )               
where S is a closed surface, Q int  is the electric charge inside of surface S, ∈ 0  is the permittivity of vacuum, and ∈ r  is the relative permittivity of the medium at the level of surface S.
 
     Further, the superposition principle provides that electric field {right arrow over (E)} k  at point C k  is equal to the sum of the electric fields due to each charge Q i  considered separately and distributed on surface S i  of each conductor  12   i . 
     For an electric power cable, voltage V i  may be searched for according to the following relation (2):
 
 V   i   =A   i  cos(ω t+φ   i )  (2)
 
where A i  is the amplitude of voltage V i , ω is the pulse of voltage V i , and φ i  is the phase of voltage V i . In the following description, call T the period of voltage V i . Period T is equal to 2π/ω.
 
     It can then be considered that linear charge Q i  in conductor  12   i  is proportional to voltage V i  according to a proportionality factor F i  which especially depends on the shapes of conductors  12   i , on the relative positions between conductors  12   i , and on the permittivity of the dielectric materials present in cable  10 . When conductors  12   i  are substantially identical and regularly distributed, proportionality factors F i  may be identical and equal to a proportionality factor F. 
     In practice, the resolution of the previously-indicated equations Q i  cannot be simply implemented in real time by a computer since many parameters are not known. Indeed, the exact shape of surface S i  of each conductor  12   i , the position of center O i  of each conductor  12   i  and the environment of cable  10  are not known at the time of the measurement. Now, the environment of cable  10 , due to the presence of other conductors or of equipotential surfaces having any shape, may significantly modify the distribution of the electric field at the level of sensors  30   k . Further, number N of conductors  12   i  cannot be known at the time of the measurement. 
     The inventors have shown that, when a cylindrical enclosure is coaxially arranged around the power cable and when this enclosure is set to a reference potential, for example, the ground, electric field {right arrow over (E)} present between the enclosure and conductors of the cable is substantially identical to the electric field due to positive and negative point electric charges, the positions and the values of these point charges especially depend on the number of conductors, on their positions, and on their shapes. Further, the distribution of the electric field at the level of sensors  30   k  no longer depends on the environment external to device  20 . A method of determining positions and values of point electric charges based on the previously-indicated equations may be implemented in real time by a computer or by means of a simple embarked calculator. 
       FIG. 5  shows in the form of a block diagram an embodiment of a voltage measurement method. The method comprises successive steps  40 ,  42 ,  44 , and  46 . 
     At step  40 , measurement device  20  is arranged around cable  10  and enclosure  22  of measurement device  20  is taken to a reference potential, for example, the ground. 
     At step  42 , processing unit  34  measures the amplitude of radial component {right arrow over (E)} rk  and the amplitude of tangential component {right arrow over (E)} θk  of electric field {right arrow over (E)} k  at the location of each sensor  30   k , with k varying from 1 to M. A plurality of measurements, for example, more than twenty measurements, are performed over a period T of oscillation of voltages V i . 
       FIG. 6  shows an example of measurements of electric field by four sensors for a power cable comprising three conductors  12   1 ,  12   2 , and  12   3 .  FIG. 6  shows the centers C 1 , C 2 , C 3  and C 4  of the sensors and the positions of the end of electric field vector {right arrow over (E)} k  applied to center C k  at the measurement times during a period T. Curve  52  of the variation of the position of the end of electric field vector {right arrow over (E)} k  obtained by interpolation has also been shown. As appears in  FIG. 6 , the end of each electric field {right arrow over (E)} k  follows a curve having a general shape close to an ellipse. 
     At steps  44  and  46 , processing unit  34  uses electric models equivalent to the assembly formed by conductors  12   i  and enclosure  22 . 
       FIGS. 7 to 10  show conductors  12   i  with hatched circles, respectively for a cable  10  comprising a single conductor  12   1  ( FIG. 7 ), two conductors  12   1  and  12   2  ( FIG. 8 ), three conductors  12   1 ,  12   2 , and  12   3  ( FIG. 9 ), and four conductors  12   1 ,  12   2 ,  12   3 , and  12   4  ( FIG. 10 ). Enclosure  22  of measurement  20  is further shown by a circle  54  in dotted lines of radius R in these drawings. Each of  FIGS. 7 to 10  further shows the electric model based on point electric charges, which is equivalent to the assembly comprising conductors  12   i  and enclosure  22  maintained at a reference potential. 
     In  FIG. 7 , when cable  10  comprises a single conductor  12   1 , the equivalent electric model comprises a single point electric charge P 1 , having electric charge Q 1 , placed at center O 1  of conductor  12   1 . More generally, for an electric cable  10  comprising N conductors, with N greater than 1, the electric model equivalent to the assembly comprising electric conductors  12   i  and enclosure  22  maintained at a reference potential comprises a number 2N(N−1) of point charges. More specifically, electric conductor  12   i , for i varying from 1 to N, has N−1 associated point charges P i,u  and N−1 associated point image charges P′ i,u , where u is an integer varying from 1 to N−1. Each point charge P i,u  has an electric charge equal to a fraction of Q i , the sum of electric charges P i,u  associated with a same electric conductor  12   i  being equal to Q i . Each image point charge P′ i,u  has an electric charge equal, in absolute value, to electric charge P i,u  and of opposite sign. 
     The point charges are arranged so that curve  54  corresponds to an equipotential line.  FIGS. 7 to 10  illustrate the principles for determining the positions of the point charges. In particular, certain point charges are placed on the lines connecting the centers of adjacent conductors. Further, as compared with point charge P i,u , image point charge P′ i,u  is arranged so that distance OP′ i,u  verifies the following relation (3): 
     
       
         
           
             
               
                 
                   
                     OP 
                     
                       i 
                       , 
                       u 
                     
                     ′ 
                   
                   = 
                   
                     
                       R 
                       2 
                     
                     
                       OP 
                       
                         i 
                         , 
                         u 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     At step  44 , processing unit  34  determines number N of conductors  12   i  of the cable when this number is not known. Processing unit  34  successively uses the electric model equivalent to a single conductor, the electric model equivalent to two conductors, the electric model equivalent to three conductors, etc. 
     Further, conditions linking the parameters of the equivalent electric models are used to simplify calculations. It is especially considered that:
         (i) conductors  12   i  are identical, of circular cross-section, and of same radius δr;   (ii) centers O i  of the conductors are at the same distance r from center O;   (iii) conductors  12   i  are regularly distributed around center O of cable  10 ;   (iv) amplitudes F*A i  are identical;   (v) phases φ i  are linked by a relation which depends on the number of conductors  12   i ; and   (vi) when cable  10  comprises more than four conductors  12   i , the potential of at least one of the conductors is constant and set to 0 V.       

     Condition (i) particularly means that weighting factors F i  are identical and equal to F. Condition (iii) means, particularly in the case of a cable  10  comprising two conductors  12   1  and  12   2 , that these conductors are arranged symmetrically with respect to center O and, in the case of a cable  10  comprising three conductors  12   1 ,  12   2  and  12   3 , that these conductors are arranged at 120° with respect to one another around center O and at a same distance from center O. Condition (v) for example means that in the case of a cable with three conductors  12   1 ,  12   2  and  12   3 , phases φ 1 , φ 2  and φ 3  are shifted with respect to one another by 120°. 
     For each equivalent electric model, processing unit  34  independently varies the following parameters between an initial value and a final value with an incrementation step:
         distance r;   angle Ψ 1 ; and   amplitude F*A 1 .       

     In each obtained configuration, processing unit  34  determines the curve of variation of the electric field obtained at centers C k , with k varying from 1 to M, of each sensor during a period T. Processing unit  34  then compares the simulated curve obtained for sensor  30   k  with the curve measured at step  42  for sensor  30   k  and determines a comparison criterion for the configuration. As an example, processing unit  34  determines, for each sensor  30   k , the mean square error between the measured curve and the simulated curve or other criteria such as the average absolute error, the average relative quadratic error, or also Pearson&#39;s correlation coefficient. The comparison criterion for the configuration is for example equal to the sum of the mean square errors for each sensor. 
     Processing unit  34  determines that number N of conductors of cable  10  is the number of conductors of the configuration for which the comparison criterion is minimum. It is the configuration for which the measured curves are as close as possible to the simulated curves. 
     Processing unit  34  keeps in a memory the values of parameters r, Ψ 1  and F*A 1  for which the comparison criterion is minimum. These values are respectively noted r INI , Ψ INI1  and F*A INI1 . Further, in the case shown in  FIG. 4 , value Ψ INI1  sets values Ψ INI2  and Ψ INI3 . 
     At step  44 , if number N of conductors  12   i  of cable  10  is already known, the operator performing the measurement may indicate this number N to processing unit  34  via interface unit  36 . Processing unit  34  may then independently vary parameters r, Ψ 1 , and F*A 1  only for the equivalent electric model corresponding to the known number N of conductors. 
     At step  46 , processing unit  34  uses the configuration determined at step  44  for which the comparison criterion is minimum. 
     Processing unit  34  modifies the equivalent electric model of this configuration by independently varying the following parameters, for each conductor  12   i , between an initial value and a final value with an incrementation step:
         distance r i ;   angle Ψ i ;   radius δr i ;   amplitude F*A 1 ; and   phase φ i .       

     As a variation, for some of the previously-indicated parameters, and particularly radius δr i , the parameter may be simultaneously modified, and possibly identically, for all conductors  12   i . 
     As an example, in relation with the example shown in  FIG. 4 , processing unit  34  may vary, independently for each conductor, parameters r i , F*A i , Ψ 1 , Ψ 2 , Ψ 3  respectively around values r INI , F*A INI1 , Ψ INI1 , Ψ INI2 , and Ψ INI3  determined at step  44 . 
     In each obtained configuration, processing unit  34  determined the curve of variation of the electric field obtained at centers C k , with k varying from 1 to M, of each sensor during a period T. 
       FIG. 11  shows an example of simulations of the electric fields {right arrow over (E)} k  at centers C 1 , C 2 , C 3  and C 4  of four sensors for a cable  10  comprising three conductors.  FIG. 6  shows curves  56  followed by the end of electric field vector {right arrow over (E)} k  applied to center C k  during a period T for values of parameters δr i /r i  varying from 0.1 to 0.8 for i varying from 1 to 3. 
     Processing unit  14  then compares the simulated curve obtained for sensor  30   k  with the curve measured at step  42  for sensor  30   k  and determines a comparison criterion for the configuration. As an example, processing unit  14  determines for each sensor  30   k  the mean square error between the measured curve and the simulated curve. The comparison criterion for the configuration is for example equal to the sum of the mean square errors for each sensor. 
     Processing unit  34  keeps in a memory the values, for each conductor  12   i , with i varying from 1 to N, of parameters r i , Ψ i , δr i , F*A i  and φ i  for which the comparison criterion is minimum. These values are respectively noted r FINi , Ψ FINi , δr FINi , F*A FINi , and φ FINi . Processing unit  34  may provide the operator, via interface unit  36 , with values r FINi , Ψ FINi , δr FINi , F*A FINi  and φ FINi , with i varying from 1 to N. 
     To display the time variation of voltage V i , it is necessary to have proportionality factors F i  for each conductor  12   i . Proportionality factors F i  may be obtained by a previous step of calibration of cable  10  and may be stored in a non-volatile memory of processing unit  34 . As an example, a list of weighting factors may be stored in the non-volatile memory of processing unit  34 , each weighting factor corresponding to a specific type of power cable. The operation may then select the values of proportionality factors F i  by using interface unit  36 . Even if proportionality factor F i  is not known, measurement device  20  provides for each conductor  12   i  a signal which is proportional to voltage V i . This signal may then be used to verify the proper operation of cable  10 .