Patent Publication Number: US-2022214383-A1

Title: Current measurement device

Description:
TECHNICAL FIELD 
     An aspect of the present invention relates to a current measurement device. 
     Priority is claimed on Japanese Patent Application No. 2019-091311, filed May 14, 2019, the content of which is incorporated herein by reference. 
     BACKGROUND ART 
     Conventionally, various current measurement devices capable of directly measuring a current flowing through a conductor to be measured in a non-contact mode have been developed. Representative examples of the current measurement devices include a current transformer (CT) type current measurement device, a zero-flux type current measurement device, a Rogowski-type current measurement device, a Hall element type current measurement device, and the like. 
     For example, in the CT type and zero-flux type current measurement devices, a magnetic core on which a winding is wound is provided near a conductor to be measured and a current flowing through the winding (a secondary side) is detected such that a magnetic flux generated in the magnetic core due to a current flowing through the conductor to be measured (a primary side) is canceled out. Thereby, the CT type and zero-flux type current measurement devices measure the current flowing through the conductor to be measured. 
     Also, in a Rogowski-type current measurement device, a Rogowski coil (an air-core coil) is provided near a conductor to be measured and a magnetic field generated due to an alternating current flowing through the conductor to be measured interlinks with the Rogowski coil, such that a voltage induced in the Rogowski coil is detected. Thereby, the Rogowski-type current measurement device measures the current flowing through the conductor to be measured. 
     The following Patent Literature 1 discloses an example of the zero-flux type current measurement device. Also, the following Patent Literature 2 discloses a current measurement device using a plurality of magnetic sensors. Specifically, in the current measurement device disclosed in the following Patent Literature 2, two magnetic sensors are disposed at different distances from a conductor to be measured, the distances between the magnetic sensors and the conductor to be measured are calculated from outputs of the magnetic sensors, and a magnitude of a current flowing through the conductor to be measured is calculated using the calculated distances. 
     CITATION LIST 
     Patent Literatures 
     [Patent Literature 1] 
     Japanese Unexamined Patent Application, First Publication No. 2005-55300 
     [Patent Literature 2] 
     Japanese Unexamined Patent Application, First Publication No. 2011-164019 
     SUMMARY OF INVENTION 
     Technical Problem 
     Incidentally, a plurality of conductors to be measured, which are current measurement targets, may be arranged in proximity to each other. For example, a pair of conductors to be measured through which currents flow in mutually opposite directions may be arranged in proximity and parallel to each other. In this case, there are a current path of a current flowing through one of the conductors to be measured (for example, an outward path) and a current path of a current flowing through the other conductor to be measured (for example, a return path). 
     In this case, if an attempt is made to measure the current flowing through one of the pair of current paths, the measurement accuracy may deteriorate due to an influence of the magnetic field generated due to the current flowing through the other current path. Specifically, if an attempt is made to measure the current flowing along the outward path, there is an influence of a magnetic field generated due to the current flowing along the return path. In contrast, if an attempt is made to measure the current flowing along the return path, there is an influence of a magnetic field generated due to the current flowing along the outward path. Also, in this case, a distance between the current paths is short and, for example, it may be often difficult to install the above-described magnetic core near the conductor to be measured. 
     An aspect of the present invention has been made in view of the above circumstances and an objective of the present invention is to provide a current measurement device capable of flexibly arranging current paths along which currents flow in mutually opposite directions and which are arranged in proximity to each other and accurately measuring the currents flowing along the current paths in a non-contact mode. 
     Solution to Problem 
     To solve the above-described problem, a current measurement device ( 1 ) according to one aspect of the present invention includes: four or more triaxial magnetic sensors ( 11  to  14 ) arranged to have predefined positional relationships such that magnetism-sensing directions thereof are parallel to each other; and a calculator ( 25 ) configured to calculate currents flowing through a pair of conductors (MC 1 , MC 2 ) to be measured, which are arranged in proximity to each other, based on detection results of the four or more triaxial magnetic sensors and the positional relationships between the four or more triaxial magnetic sensors, the currents flowing in mutually opposite directions. 
     In addition, in the current measurement device according to one aspect of the present invention, the calculator includes: a position estimator ( 25   b ) configured to estimate positions (VA, VB, or vA, vB) of the pair of conductors to be measured using the detection results of the four or more triaxial magnetic sensors and the positional relationships between the four or more triaxial magnetic sensors; and a current calculator ( 25   d ) configured to calculate the currents flowing through the pair of conductors to be measured based on the positions estimated by the position estimator and the detection results of the four or more triaxial magnetic sensors. 
     In addition, in the current measurement device according to one aspect of the present invention, the calculator includes a background magnetic field estimator ( 25   c ) configured to estimate a background magnetic field (ϕ or Φ) uniformly acting on the four or more triaxial magnetic sensors based on the detection results of the four or more triaxial magnetic sensors and the positional relationships between the four or more triaxial magnetic sensors, wherein the current calculator calculates the currents flowing through the pair of conductors to be measured based on the positions estimated by the position estimator, the detection results of the four or more triaxial magnetic sensors, and the background magnetic field estimated by the background magnetic field estimator. 
     In addition, in the current measurement device according to one aspect of the present invention, the calculator further includes a noise remover ( 25   a ) configured to remove noise components included in the detection results of the four or more triaxial magnetic sensors, wherein the calculator calculates the currents flowing through the pair of conductors to be measured using the detection results of the four or more triaxial magnetic sensors from which the noise components have been removed by the noise remover. 
     In addition, in the current measurement device according to one aspect of the present invention, the noise remover removes the noise components included in the detection results of the four or more triaxial magnetic sensors by separately performing an averaging process or a root sum square process on each of the detection results of the four or more triaxial magnetic sensors obtained for each predefined given period. 
     In addition, in the current measurement device according to one aspect of the present invention, the current measurement device includes: a sensor head ( 10 ) including the four or more triaxial magnetic sensors; and a circuit ( 20 ) including the calculator. 
     In addition, in the current measurement device according to one aspect of the present invention, signals indicating the detection results of the four or more triaxial magnetic sensors are digital signals. 
     In addition, in the current measurement device according to one aspect of the present invention, when magnetic fields obtained by projecting the detection results of the four or more triaxial magnetic sensors onto a complex plane are denoted by h m , the currents flowing through the pair of conductors to be measured are denoted by I, positions of the four or more triaxial magnetic sensors projected onto the complex plane are denoted by p m , the positions of the pair of conductors to be measured on the complex plane are denoted by v A  and v B , and a background magnetic field on the complex plane is denoted by φ, the calculator calculates the current I using an equation of: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                        
                       
                         2 
                         ⁢ 
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               
                                 h 
                                 m 
                               
                               - 
                               φ 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     p 
                                     m 
                                   
                                   - 
                                   
                                     ν 
                                     A 
                                   
                                 
                                 ) 
                               
                               * 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     p 
                                     m 
                                   
                                   - 
                                   
                                     v 
                                     B 
                                   
                                 
                                 ) 
                               
                               * 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   v 
                                   A 
                                 
                                 - 
                                 
                                   v 
                                   B 
                                 
                               
                               ) 
                             
                             * 
                           
                         
                       
                        
                     
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     In addition, in the current measurement device according to one aspect of the present invention, when magnetic fields, which are the detection results of the four or more triaxial magnetic sensors, are denoted by H m , the currents flowing through the pair of conductors to be measured are denoted by I, a unit vector of a direction in which the current I flows is denoted by j, a background magnetic field obtained by restoring a background magnetic field on a complex plane to an XYZ Cartesian coordinate system is denoted by Φ, and vectors parallel to perpendicular lines drawn from each of the four or more triaxial magnetic sensors to the pair of conductors to be measured are denoted by r Am  and r Bm , the calculator calculates the current I using an equation of: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     2 
                     ⁢ 
                     
                       π 
                       ⁡ 
                       
                         ( 
                         
                           
                             H 
                             m 
                           
                           - 
                           Φ 
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             
                                
                               
                                 r 
                                 
                                   A 
                                   ⁢ 
                                   m 
                                 
                               
                                
                             
                             2 
                           
                           ⁢ 
                           
                             
                                
                               
                                 r 
                                 
                                   B 
                                   ⁢ 
                                   m 
                                 
                               
                                
                             
                             2 
                           
                         
                         
                           
                             
                               
                                  
                                 
                                   r 
                                   
                                     B 
                                     ⁢ 
                                     m 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               ( 
                               
                                 j 
                                 × 
                                 
                                   r 
                                   
                                     A 
                                     ⁢ 
                                     m 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               
                                  
                                 
                                   r 
                                   
                                     A 
                                     ⁢ 
                                     m 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               ( 
                               
                                 j 
                                 × 
                                 
                                   r 
                                   
                                     B 
                                     ⁢ 
                                     m 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Advantageous Effects of Invention 
     According to one aspect of the present invention, it is possible to flexibly arrange current paths along which currents flow in mutually opposite directions and which are arranged in proximity to each other and accurately measure the currents flowing along the current paths in a non-contact mode. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram schematically showing a current measurement device according to an embodiment of the present invention. 
         FIG. 2  is a block diagram showing a main configuration of the current measurement device according to the embodiment of the present invention. 
         FIG. 3  is a diagram for describing a current measurement principle of the current measurement device according to the embodiment of the present invention. 
         FIG. 4  is a view of conductors to be measured and triaxial magnetic sensors when viewed from a direction D 1  in  FIG. 3 . 
         FIG. 5  is a flowchart showing an outline of an operation of the current measurement device according to the embodiment of the present invention. 
         FIG. 6  is a flowchart showing details of the processing of step S 14  in  FIG. 5 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, a current measurement device according to an embodiment of the present invention will be described in detail with reference to the drawings. Hereinafter, the overview of the embodiment of the present invention will be first described and then details of the embodiment of the present invention will be described. 
     [Overview] 
     The embodiment of the present invention is configured such that it is possible to flexibly arrange current paths along which currents flow in mutually opposite directions and which are arranged in proximity to each other and accurately measure the currents flowing along the current paths in a non-contact mode. Specifically, it is possible to measure currents of the same magnitude flowing along the current paths in mutually opposite directions in a non-contact mode with high accuracy in consideration of both a magnetic field generated due to the current flowing along one of the current paths (for example, an outward path) and a magnetic field generated due to the current flowing along the other one of the current paths (for example, a return path). At this time, a position or an orientation related to the current path is not limited and accurate current measurement is enabled with a flexible arrangement. 
     In recent years, in a process of developing hybrid vehicles (HVs) and electric vehicles (EVs), a current flowing through a pin of a power semiconductor such as silicon carbide (SiC) or a current flowing through an assembled bus bar has been required to be directly measured. Many power semiconductors have narrow pin pitches. A bus bar may be installed in an area where a nearby space is limited. For the above power semiconductor or bus bar and the like, a current measurement device capable of being flexibly installed at the time of current measurement is desirable. Also, in a hybrid vehicle or an electric vehicle, for example, a direct current supplied from a battery or an alternating current flowing through a motor is handled. Thus, a current measurement device capable of measuring a direct current and an alternating current of a low frequency (for example, about several hundred hertz [Hz] or less) in a non-contact mode is desirable. 
     However, in the zero-flux type current measurement device disclosed in Patent Literature 1 described above, it is necessary to provide a magnetic core having a certain size near the conductor to be measured. Thus, it is difficult to install the zero-flux type current measurement device disclosed in Patent Literature 1 in a small space. Also, the Rogowski-type current measurement device described above detects the voltage induced in the Rogowski coil. Thus, the Rogowski-type current measurement device cannot measure a direct current in principle. Also, in a low-frequency region, an output signal is weak and a phase shifts, such that the measurement accuracy is poor. Also, in the current measurement device disclosed in Patent Literature 2 described above, it is necessary to cause a magnetism-sensing direction of the magnetic sensor to match a circumferential direction of the conductor to be measured. Thus, in the current measurement device disclosed in Patent Literature 2, the arrangement of the magnetic sensor is limited and it is difficult to arrange the magnetic sensor flexibly. 
     Also, the current generally flows out from a positive electrode of a power supply and then flows into a negative electrode of the power supply via a load or the like. Thus, the current path of the current supplied from the power supply includes a path along which the current flows out from the positive electrode of the power supply (the outward path) and a path along which the current flows into the negative electrode of the power supply (the return path). Furthermore, the former path may be referred to as the return path and the latter path may be referred to as the outward path. Thus, for example, if an attempt is made to measure the current flowing along the outward path, there is an influence of a magnetic field generated due to the current flowing along the return path. In contrast, if an attempt is made to measure the current flowing along the return path, there is an influence of the magnetic field generated due to the current flowing along the outward path. Consequently, the current measurement accuracy may deteriorate. 
     In the embodiment of the present invention, there are provided four or more triaxial magnetic sensors arranged to have predefined positional relationships such that magnetism-sensing directions thereof are parallel to each other; and a calculator configured to calculate currents flowing through a pair of conductors to be measured, which are arranged in proximity to each other, based on detection results of the four or more triaxial magnetic sensors and the positional relationships between the four or more triaxial magnetic sensors, wherein the currents flow in mutually opposite directions. When the currents are calculated, positions or orientations of the triaxial magnetic sensors (i.e., the four or more triaxial magnetic sensors arranged to have the predefined positional relationships) with respect to the pair of conductors to be measured are arbitrary. Thereby, it is possible to flexibly arrange current paths along which currents flow in mutually opposite directions and which are arranged in proximity to each other and accurately measure the currents flowing along the current paths in a non-contact mode. 
     EMBODIMENT 
     &lt;Configuration of Current Measurement Device&gt; 
       FIG. 1  is a diagram schematically showing a current measurement device  1  according to an embodiment of the present invention. As shown in  FIG. 1 , the current measurement device  1  of the present embodiment includes a sensor head  10  and a circuit  20  connected by a cable CB. The above current measurement device  1  directly measures currents I flowing through a pair of conductors MC 1  and MC 2  to be measured, which are arranged in proximity and parallel to each other, in a non-contact mode, wherein the currents I flow in mutually opposite directions. 
     Here, the fact that the conductors MC 1  and MC 2  to be measured are in proximity to each other indicates a case in which a distance set between the conductors MC 1  and MC 2  to be measured is so narrow that the magnetic field generated due to the current flowing through one of the conductors MC 1  and MC 2  to be measured cannot be considered to uniformly act on a plurality of triaxial magnetic sensors (whose details will be described below) provided in the sensor head  10 . In other words, this indicates a case in which a distance set between the conductors MC 1  and MC 2  to be measured is so narrow that the magnetic field generated due to the above-described current non-uniformly acts on the above-described plurality of triaxial magnetic sensors. 
     Furthermore, for example, the conductors MC 1  and MC 2  to be measured are any conductors such as pins and bus bars of power semiconductors. Hereinafter, for simplicity of description, a case in which the conductors MC 1  and MC 2  to be measured are cylindrical conductors will be described. The currents I flowing through the conductors MC 1  and MC 2  to be measured flow in mutually opposite directions. Hereinafter, a current path of the current flowing through the conductor MC 1  to be measured may be referred to as an “outward path” and a current path of the current flowing through the conductor MC 2  to be measured may be referred to as a “return path.” 
     The sensor head  10  is a member arranged at any position in any orientation with respect to the conductors MC 1  and MC 2  to be measured so that the currents I flowing through the conductors MC 1  and MC 2  to be measured are measured in a non-contact mode. The sensor head  10  is formed of a material (for example, resin or the like) that does not block magnetic fields (for example, magnetic fields H 1 , H 2 , H 3 , and H 4  shown in  FIG. 1 ) generated due to the currents I flowing through the conductors MC 1  and MC 2  to be measured. The sensor head  10  is used as a so-called probe for measuring the currents I flowing through the conductors MC 1  and MC 2  to be measured in a non-contact mode. 
     Four triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are provided in the sensor head  10 . The triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are magnetic sensors having magnetism-sensing directions on three axes orthogonal to each other. The triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are arranged to have predefined positional relationships so that magnetism-sensing directions thereof are parallel to each other. For example, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are arranged at prescribed intervals in prescribed directions so that first axes of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are parallel to each other, second axes of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are parallel to each other, and third axes of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are parallel to each other. Hereinafter, as shown in  FIG. 1 , a case in which the triaxial magnetic sensors  13 ,  11 , and  12  are arranged at prescribed intervals in a first axis direction and the triaxial magnetic sensors  11  and  14  are arranged at a prescribed interval in a third axis direction will be described. 
     Each of signals indicating detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  may be either an analog signal or a digital signal. However, when each of the signals indicating the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  is a digital signal, the number of cables CB connecting the sensor head  10  and the circuit  20  can be reduced as compared with when each of the signals indicating the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  is an analog signal. 
     For example, when the signals indicating the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are analog signals, three cables CB are required to output triaxial detection results for each of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . Thus, a total of 12 cables CB are required. On the other hand, when the signals indicating the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are digital signals, only one cable CB is required. When the number of cables CB is small, the flexibility of the cables CB is improved, such that handling becomes easy, for example, when the sensor head  10  is arranged within a small space. 
     The circuit  20  measures the currents I flowing through the conductors MC 1  and MC 2  to be measured based on the detection results (the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 ) output from the sensor head  10 . The circuit  20  displays results of measuring the currents I or externally outputs the measurement results. Although any cable CB for connecting the sensor head  10  and the circuit  20  can be used, a cable CB, which has flexibility, is easy to handle, and is unlikely to break, is desirable. 
       FIG. 2  is a block diagram showing a main configuration of the current measurement device  1  according to the embodiment of the present invention. In  FIG. 2 , the same reference signs are given to blocks corresponding to the components shown in  FIG. 1 . Hereinafter, details of an internal configuration of the circuit  20  will be mainly described with reference to  FIG. 2 . As shown in  FIG. 2 , the circuit  20  includes an operator  21 , a display  22 , a memory  23 , and a calculator  25 . 
     The operator  21  includes various types of buttons such as a power button and a setting button and outputs signals indicating operation instructions for the various types of buttons to the calculator  25 . The display  22  includes, for example, a display device such as a 7-segment light emitting diode (LED) display or a liquid crystal display device. The display  22  displays various types of information output from the calculator  25  (for example, information indicating results of measuring the currents I flowing through the conductors MC 1  and MC 2  to be measured). Furthermore, the operator  21  and the display  22  may be separated physically. Also, the operator  21  and the display  22  may be integrated physically as in a touch panel type liquid crystal display device having both a display function and an operation function. 
     The memory  23  includes, for example, a volatile or non-volatile semiconductor memory. The memory  23  stores the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  output from the sensor head  10 , the calculation results of the calculator  25  (the results of measuring the currents I flowing through the conductors MC 1  and MC 2  to be measured), and the like. Furthermore, the memory  23  may include an auxiliary storage device such as a hard disk drive (HDD) or a solid-state drive (SSD) together with the above-described semiconductor memory (or instead of the above-described semiconductor memory). 
     The calculator  25  causes the memory  23  to store the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  output from the sensor head  10 . Also, the calculator  25  reads the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  stored in the memory  23  and performs a calculation process of calculating the currents I flowing through the conductors MC 1  and MC 2  to be measured. The calculator  25  includes a noise remover  25   a , a position estimator  25   b , a background magnetic field estimator  25   c , and a current calculator  25   d.    
     The noise remover  25   a  removes noise components included in the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . Specifically, the noise remover  25   a  separately performs an averaging process or a root sum square process on a plurality of detection results obtained from each of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  at predefined given intervals (for example, 1 second). Thereby, the noise remover  25   a  removes the noise components included in the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . The triaxial detection results are output from the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . The noise component removal by the noise remover  25   a  is performed separately for the detection result of each axis. The above noise removal is performed to improve a signal-to-noise (SN) ratio of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  to improve the accuracy of measurement of the currents I. 
     The position estimator  25   b  estimates positions of the conductors MC 1  and MC 2  to be measured (i.e., positions of the conductors MC 1  and MC 2  to be measured with respect to the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 ) using the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  and the positional relationships between the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . The above estimation is performed to measure the currents I flowing through the MC 2  with high accuracy in consideration of both the magnetic field generated due to the current I flowing through the conductor MC 1  to be measured and the magnetic field generated due to the current I flowing through the conductor MC 2  to be measured. Furthermore, details of the process performed by the position estimator  25   b  will be described below. 
     The background magnetic field estimator  25   c  estimates a background magnetic field (for example, geomagnetism) that uniformly acts on the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  based on the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  and the positional relationships of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . The above estimation is performed to measure the currents I flowing through the conductors MC 1  and MC 2  to be measured with high accuracy by eliminating an influence of the background magnetic field (for example, the geomagnetism). The background magnetic field estimator  25   c  can be omitted when it is not necessary to take into account the influence of the background magnetic field. Furthermore, details of the process performed by the background magnetic field estimator  25   c  will be described below. 
     The current calculator  25   d  calculates the currents flowing through the conductors MC 1  and MC 2  to be measured based on the positions estimated by the position estimator  25   b  and the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . Here, when it is necessary to take into account the influence of the background magnetic field, the current calculator  25   d  calculates the currents flowing through the conductors MC 1  and MC 2  to be measured based on the positions estimated by the position estimator  25   b , the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 , and the background magnetic field estimated by the background magnetic field estimator  25   c . Furthermore, details of the process performed by the current calculator  25   d  will be described below. 
     Here, as shown in  FIGS. 1 and 2 , the circuit  20  is separated from the sensor head  10  and is connected to the sensor head  10  via the cable CB. According to the above configuration, a magnetic field detection function (the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 ) and a calculation function (the calculator  25 ) can be separated. Thus, it is possible to avoid various problems (related to, for example, temperature characteristics, dielectric strength, and installation in a small space) and the like that occur when the calculator  25  is provided within the sensor head  10 . Thereby, it is possible to expand the applications of the current measurement device  1 . 
     &lt;Current Measurement Principle&gt; 
     Next, a current measurement principle in the current measurement device  1  will be described.  FIG. 3  is a diagram for describing the current measurement principle in the current measurement device  1  according to the embodiment of the present invention. In  FIG. 3 , only the triaxial magnetic sensor  11  provided on the sensor head  10  is shown in consideration of visibility and the triaxial magnetic sensors  12 ,  13 , and  14  are not shown. First, as shown in  FIG. 3 , a coordinate system (an XYZ Cartesian coordinate system) related to the sensor head  10  is set. 
     The XYZ Cartesian coordinate system is a coordinate system defined in accordance with a position and an orientation of the sensor head  10 . In the above XYZ Cartesian coordinate system, the origin is set at the position of the triaxial magnetic sensor  11 . Also, in the above XYZ Cartesian coordinate system, an X-axis is set in the first axis direction of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  (an arrangement direction of the triaxial magnetic sensors  13 ,  11 , and  12 : see  FIG. 1 ). Also, in this XYZ Cartesian coordinate system, a Y-axis is set in the second axis direction of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . Also, in the above XYZ Cartesian coordinate system, a Z-axis is set in the third axis direction of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  (an arrangement direction of the triaxial magnetic sensors  11  and  14 : see  FIG. 1 ). 
     Here, the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are denoted by P m  (m=1, 2, 3, 4). P m  is a vector. That is, the position of the triaxial magnetic sensor  11  is denoted by P 1 . Also, the position of the triaxial magnetic sensor  12  is denoted by P 2 . Also, the position of the triaxial magnetic sensor  13  is denoted by P 3 . Also, the position of the triaxial magnetic sensor  14  is denoted by P 4 . For example, assuming that distances between the triaxial magnetic sensors  13 ,  11 , and  12  in the X direction and distances between the triaxial magnetic sensors  11  and  14  in the Z direction are d [m] (see  FIG. 1 ), the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are represented as follows. 
     Position of triaxial magnetic sensor  11 : P 1 =(0, 0, 0) 
     Position of triaxial magnetic sensor  12 : P 2 =(d, 0, 0) 
     Position of triaxial magnetic sensor  13 : P 3 =(−d, 0, 0) 
     Position of triaxial magnetic sensor  14 : P 4 =(0, 0, −d) 
     Here, magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  due to the current I flowing through the conductor MC 1  to be measured are denoted by H Am  (m=1, 2, 3, 4). Furthermore, H Am  is a vector. That is, the magnetic field formed at the position of the triaxial magnetic sensor  11  due to the current I flowing through the conductor MC 1  to be measured is denoted by H A1 . Also, the magnetic field formed at the position of the triaxial magnetic sensor  12  due to the current I flowing through the conductor MC 1  to be measured is denoted by H A2 . Likewise, the magnetic field formed at the position of the triaxial magnetic sensor  13  due to the current I flowing through the conductor MC 1  to be measured is denoted by H A3 . Also, the magnetic field formed at the position of the triaxial magnetic sensor  14  due to the current I flowing through the conductor MC 1  to be measured is denoted by H A4 . 
     Further, as shown in  FIG. 3 , the magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  due to the current I flowing through the conductor MC 2  to be measured are denoted by H Bm  (m=1, 2, 3, 4). Furthermore, H Bm  is a vector. That is, the magnetic field formed at the position of the triaxial magnetic sensor  11  by the current I flowing through the conductor MC 2  to be measured is denoted by H B1 . Also, the magnetic field formed at the position of the triaxial magnetic sensor  12  due to the current I flowing through the conductor MC 2  to be measured is denoted by H B2 . Also, the magnetic field formed at the position of the triaxial magnetic sensor  13  due to the current I flowing through the conductor MC 2  to be measured is denoted by H B3 . Also, the magnetic field formed at the position of the triaxial magnetic sensor  14  due to the current I flowing through the conductor MC 2  to be measured is denoted by H B4 . 
     Also, the background magnetic field that uniformly acts on the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  is denoted by Φ. Furthermore, Φ is a vector. The magnetic fields H m  (m=1, 2, 3, 4) formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  due to the currents I flowing through the conductors MC 1  and MC 2  to be measured are expressed by the following Eq. (1). Furthermore, H m  is a vector. 
       [Math. 3] 
         H   m   =H   Am   −H   Bm +Φ  (1)
 
     Also, the magnetic fields H m  formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are expressed by the following Eq. (2) according to Ampere&#39;s law. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     H 
                     m 
                   
                   = 
                   
                     
                       
                         I 
                         ⁡ 
                         
                           ( 
                           
                             j 
                             × 
                             
                               r 
                               
                                 A 
                                 ⁢ 
                                 m 
                               
                             
                           
                           ) 
                         
                       
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                              
                             
                               r 
                               
                                 A 
                                 ⁢ 
                                 m 
                               
                             
                              
                           
                           2 
                         
                       
                     
                     - 
                     
                       
                         I 
                         ⁡ 
                         
                           ( 
                           
                             j 
                             × 
                             
                               r 
                               
                                 B 
                                 ⁢ 
                                 m 
                               
                             
                           
                           ) 
                         
                       
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                              
                             
                               r 
                               
                                 B 
                                 ⁢ 
                                 m 
                               
                             
                              
                           
                           2 
                         
                       
                     
                     + 
                     Φ 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     A first term on the right side of the above Eq. (2) represents magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  due to the current I flowing through the conductor MC 1  to be measured (i.e., H Am  in the above Eq. (1)). A second term on the right side of the above Eq. (2) represents magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  due to the current I flowing through the conductor MC 2  to be measured (i.e., H Bm  in the above Eq. (1)). A sign of the second term on the right side of the above Eqs. (1) and (2) is negative because the direction of the current I flowing through the conductor MC 2  to be measured is opposite to the direction of the current I flowing through the conductor MC 1  to be measured. 
     r Am  in the above Eq. (2) denotes a vector parallel to a perpendicular line drawn from each of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  to the conductor MC 1  to be measured. r Bm  in the above Eq. (2) denotes a vector parallel to a perpendicular line drawn from each of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  to the conductor MC 2  to be measured. Also, j in the above Eq. (2) is a unit vector in the direction of the current I. 
     Here, it is assumed that E is a unit matrix. Also, the position of the conductor MC 1  to be measured is denoted by V A . Also, the position of the conductor MC 2  to be measured is denoted by VdB. Furthermore, V A  and V B  are vectors. The vectors r Am  and r Bm  in the above Eq. (2) are expressed by the following Eqs. (3). 
       [Math. 5] 
         r   Am =( E−jj   T )( P   m   −V   A ) 
         r   Bm =( E−jj   T )( P   m   −V   B )  (3)
 
     Because the directions of the currents I flowing through the conductors MC 1  and MC 2  to be measured are orthogonal to the direction of the magnetic field, a direction of an outer product of differences between the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  matches the direction of the current I. Thus, the unit vector j in the direction of the current I is expressed by the following Eq. (4) using, for example, the detection results (the magnetic fields H 1 , H 2 , and H 3 ) of the triaxial magnetic sensors  11 ,  12 , and  13 . 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   j 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             H 
                             3 
                           
                           - 
                           
                             H 
                             1 
                           
                         
                         ) 
                       
                       × 
                       
                         ( 
                         
                           
                             H 
                             2 
                           
                           - 
                           
                             H 
                             1 
                           
                         
                         ) 
                       
                     
                     
                        
                       
                         
                           ( 
                           
                             
                               H 
                               3 
                             
                             - 
                             
                               H 
                               1 
                             
                           
                           ) 
                         
                         × 
                         
                           ( 
                           
                             
                               H 
                               2 
                             
                             - 
                             
                               H 
                               1 
                             
                           
                           ) 
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Next, a complex plane F perpendicular to the unit vector j expressed by the above Eq. (4) is taken into account. The above complex plane F is taken into account to simplify the calculation process. 
       FIG. 4  is a view of the conductors MC 1  and MC 2  to be measured and the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  when viewed from a direction D 1  in  FIG. 3 . Furthermore, j 1  and j 2  in  FIG. 4  denote unit vectors orthogonal to each other within the complex plane F. The direction D 1  in  FIG. 3  is a direction along a longitudinal direction of the conductors MC 1  and MC 2  to be measured (i.e., a direction opposite to the direction of the current I flowing through the conductor MC 1  to be measured or a direction along the direction of the current I flowing through the conductor MC 2  to be measured). Furthermore, in  FIG. 4 , the conductors MC 1  and MC 2  to be measured and the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are shown in a state in which the illustration of the sensor head  10  is omitted for ease of understanding. 
     The conductors MC 1  and MC 2  to be measured, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 , and the magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 ,  14  are projected onto the complex plane F shown in  FIG. 4 . As shown in  FIG. 4 , the magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are orthogonal to the unit vector j due to the current I flowing in a direction perpendicular to the paper surface (i.e., a direction along the unit vector j or a direction opposite to the unit vector j). Accordingly, the magnetic fields formed at the positions of the triaxial magnetic sensors  11 ,  12 , and  13  can be projected onto the complex plane Γ orthogonal to the direction in which the current I flows, without changing its magnitude. 
     Here, the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  on the complex plane Γ are denoted by p m  (in =1, 2, 3, 4). Also, the position of the conductor MC 1  to be measured on the complex plane Γ is denoted by v A . Also, the position of the conductor MC 2  to be measured on the complex plane Γ is denoted by v B . Also, the magnetic fields h m  (i=1, 2, 3, 4) projected onto the complex plane Γ is expressed by the following Eq. (5). h Am , h Bm , and ϕ in the following Eq. (5) are obtained by projecting H Am , H Bm , and Φ in the above Eq. (1) onto the complex plane F, respectively. 
       [Math. 7] 
         h   m   =h   Am   −h   Bm +φ  (5)
 
     The magnetic fields h m  at the positions of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  on the projected complex plane Γ are expressed by the following Eq. (6). Furthermore, i in the following Eq. (6) is an imaginary unit. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     h 
                     m 
                   
                   = 
                   
                     
                       iI 
                       
                         2 
                         ⁢ 
                         
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   m 
                                 
                                 - 
                                 
                                   ν 
                                   A 
                                 
                               
                               ) 
                             
                           
                           * 
                         
                       
                     
                     - 
                     
                       
                         i 
                         ⁢ 
                         I 
                       
                       
                         2 
                         ⁢ 
                         
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   m 
                                 
                                 - 
                                 
                                   v 
                                   B 
                                 
                               
                               ) 
                             
                           
                           * 
                         
                       
                     
                     + 
                     φ 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     By modifying the above Eq. (6), the following Eq. (7) can be obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   I 
                   = 
                   
                      
                     
                       2 
                       ⁢ 
                       
                         π 
                         ⁡ 
                         
                           ( 
                           
                             
                               h 
                               m 
                             
                             - 
                             φ 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   p 
                                   m 
                                 
                                 - 
                                 
                                   ν 
                                   A 
                                 
                               
                               ) 
                             
                             * 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   p 
                                   m 
                                 
                                 - 
                                 
                                   v 
                                   B 
                                 
                               
                               ) 
                             
                             * 
                           
                         
                         
                           
                             ( 
                             
                               
                                 ν 
                                 A 
                               
                               - 
                               
                                 v 
                                 B 
                               
                             
                             ) 
                           
                           * 
                         
                       
                     
                      
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The magnetic fields h m  in the above Eq. (7) are obtained by projecting the detection results (the magnetic fields H m ) of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  onto the complex plane Γ. The positions p m  are obtained by projecting the positions P m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  onto the complex plane Γ. Thus, the magnetic fields h m  and the positions p m  can be calculated in a calculation process. Consequently, the currents I flowing through the conductors MC 1  and MC 2  to be measured can be calculated using the above Eq. (7) if the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ and the background magnetic field ϕ on the complex plane Γ are obtained. 
     Thus, a process of estimating the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ and the background magnetic field ϕ on the complex plane Γ from the magnetic fields projected onto the complex plane Γ is conceivable. The following Eq. (8) can be obtained by moving the third term (ϕ) on the right side of the above Eq. (6) to the left side, multiplying both sides by the complex conjugate of the left side, and arranging the equation by canceling the denominator. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Math 
                       . 
                       
                           
                       
                       ⁢ 
                       10 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         h 
                         m 
                         * 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               ν 
                               A 
                             
                             ⁢ 
                             
                               v 
                               B 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   ν 
                                   A 
                                 
                                 + 
                                 
                                   ν 
                                   B 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               p 
                               m 
                             
                           
                           + 
                           
                             p 
                             m 
                             2 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         φ 
                         * 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   v 
                                   A 
                                 
                                 - 
                                 
                                   v 
                                   B 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               p 
                               m 
                             
                           
                           - 
                           
                             p 
                             m 
                             2 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           iI 
                           
                             2 
                             ⁢ 
                             π 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             v 
                             A 
                           
                           - 
                           
                             ν 
                             B 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         φ 
                         * 
                       
                       ⁢ 
                       
                         v 
                         A 
                       
                       ⁢ 
                       
                         ν 
                         B 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Here, the right side of the above Eq. (8) is a constant that does not depend on the subscript m. Thus, as shown in the following Eq. (9), the right side of the above Eq. (8) is set as a variable k. Also, as shown in the following Eq. (9), a sum of the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured is set as a variable v. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     k 
                     = 
                     
                       
                         
                           - 
                           
                             iI 
                             
                               2 
                               ⁢ 
                               π 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               v 
                               A 
                             
                             - 
                             
                               v 
                               B 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           φ 
                           * 
                         
                         ⁢ 
                         
                           v 
                           A 
                         
                         ⁢ 
                         
                           v 
                           B 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     v 
                     = 
                     
                       
                         v 
                         A 
                       
                       - 
                       
                         v 
                         B 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     When both sides of the above Eq. (8) are divided by h m *, the following Eq. (10) is obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         v 
                         A 
                       
                       ⁢ 
                       
                         v 
                         B 
                       
                     
                     - 
                     
                       v 
                       ⁢ 
                       
                         p 
                         m 
                       
                     
                     + 
                     
                       p 
                       m 
                       2 
                     
                     + 
                     
                       
                         
                           φ 
                           * 
                         
                         ⁢ 
                         ν 
                         ⁢ 
                         
                           p 
                           m 
                         
                       
                       
                         h 
                         m 
                         * 
                       
                     
                     - 
                     
                       
                         
                           φ 
                           * 
                         
                         ⁢ 
                         
                           p 
                           m 
                           2 
                         
                       
                       
                         h 
                         m 
                         * 
                       
                     
                     - 
                     
                       k 
                       
                         h 
                         m 
                         * 
                       
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     If the case in which m=1 in the above Eq. (8) is subtracted from the above Eq. (8) and the denominator is canceled by h m *, h 1 *, the following Eq. (11) is obtained. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Math 
                       . 
                       
                           
                       
                       ⁢ 
                       13 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               h 
                               1 
                               * 
                             
                             ⁢ 
                             
                               p 
                               m 
                             
                           
                           - 
                           
                             
                               h 
                               m 
                               * 
                             
                             ⁢ 
                             
                               p 
                               1 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       v 
                       ⁢ 
                       
                         ϕ 
                         * 
                       
                     
                     - 
                     
                       
                         h 
                         m 
                         * 
                       
                       ⁢ 
                       
                         
                           h 
                           1 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               p 
                               m 
                             
                             - 
                             
                               p 
                               1 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                       ν 
                     
                     - 
                     
                       
                         ( 
                         
                           
                             
                               h 
                               1 
                               * 
                             
                             ⁢ 
                             
                               p 
                               m 
                               2 
                             
                           
                           - 
                           
                             
                               h 
                               m 
                               * 
                             
                             ⁢ 
                             
                               p 
                               1 
                               2 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         φ 
                         * 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             h 
                             m 
                             * 
                           
                           - 
                           
                             h 
                             1 
                             * 
                           
                         
                         ) 
                       
                       ⁢ 
                       k 
                     
                     + 
                     
                       
                         h 
                         m 
                         * 
                       
                       ⁢ 
                       
                         
                           h 
                           1 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               p 
                               m 
                               2 
                             
                             - 
                             
                               p 
                               1 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Referring to the above Eq. (11), a quadratic homogeneous simultaneous equation related to the background magnetic field ϕ*, the variable v, and the variable k is given. Because the above Eq. (11) is established when m&gt;1, the background magnetic field ϕ*, the variable v (=v A +v B ), and the variable k can be calculated by solving the equation. 
     Hereinafter, an example of a method of solving the quadratic homogeneous simultaneous equations shown in the above Eq. (11) is shown. Assuming that coefficients of the above Eq. (11) are denoted by a m , b m , c m , d m , and e m , the above Eq. (11) is expressed by the following Eq. (12). 
       [Math. 14] 
         a   m   vφ*+b   m   v+c   m   φ*+d   m   k+e   m =0  (12)
 
     
       
      
       a 
       m 
       =h 
       1 
       *p 
       m 
       −h 
       m 
       *p 
       1  
      
     
         b   m   =−h   m   *h   1 *( p   m   −p   1 ) 
         c   m =−( h   1   *p   m   2   −h   m   *p   1   2 )
 
         d   m   =h   m   *−h   1 * 
         e   m   =h   m*   h   1 *( p   m   2   −p   1   2 ) 
     Using the above Eq. (11) when the subscript is in and the above Eq. (11) when the subscript is n, the following Eq. (13) can be obtained by eliminating the variable k. 
       [Math. 15] 
       ( a   m   d   n   −a   n   d   m ) v φ*+( b   m   d   n   −b   n   d   m ) v +( c   m   d   n   −c   n   d   m )φ*+( e   m   d   n   −e   n   d   m )=0  (13)
 
     Assuming that coefficients of the above Eq. (13) are denoted by A mn , B mn , C mn , and D mn , the above Eq. (13) is expressed by the following Eq. (14). 
       [Math. 16] 
         A   mn   vφ*+B   mn   v+C   mn   φ*+D   mn   k= 0  (14)
 
     
       
      
       A 
       mn 
       =a 
       m 
       d 
       n 
       −a 
       n 
       d 
       m  
      
     
     
       
      
       B 
       mn 
       =b 
       m 
       d 
       n 
       −b 
       n 
       d 
       m  
      
     
     
       
      
       C 
       mn 
       =C 
       m 
       d 
       n 
       −C 
       n 
       d 
       m  
      
     
     
       
      
       D 
       mn 
       =e 
       m 
       d 
       n 
       −e 
       n 
       d 
       m  
      
     
     From the above Eq. (14), the variable v can be expressed by the following Eq. (15) as a function of the background magnetic field ϕ*. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   v 
                   = 
                   
                     
                       
                         
                           C 
                           mn 
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         D 
                         mn 
                       
                     
                     
                       
                         
                           A 
                           mn 
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         B 
                         mn 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Now, when there are four triaxial magnetic sensors  11 ,  12 ,  13 , and  14 , the above Eq. (15) is established in the case of (m, n)=(1, 2) and the case of (m, n)=(2, 3) and the following Eq. (16) is established. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           C 
                           
                             1 
                             ⁢ 
                             2 
                           
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         D 
                         
                           1 
                           ⁢ 
                           2 
                         
                       
                     
                     
                       
                         
                           A 
                           12 
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         B 
                         
                           1 
                           ⁢ 
                           2 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         
                           C 
                           
                             2 
                             ⁢ 
                             3 
                           
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         D 
                         
                           2 
                           ⁢ 
                           3 
                         
                       
                     
                     
                       
                         
                           A 
                           
                             2 
                             ⁢ 
                             3 
                           
                         
                         ⁢ 
                         
                           φ 
                           * 
                         
                       
                       - 
                       
                         B 
                         
                           2 
                           ⁢ 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     If the denominators of the above Eq. (16) are canceled and the above Eq. (16) is summarized as the equation of ϕ*, the following Eq. (17) is given. 
       [Math. 19] 
       (− A   12   C   23   +A   23   C   12 )φ* 2 +(− A   12   D   23   A   23   D   12   −B   12   C   23   +B   23   C   12 )φ*− B   12   D   23   +B   23   D   12 =0  (17)
 
     Assuming that coefficients of the above Eq. (17) are denoted by α, β, and γ, the above Eq. (17) is expressed by the following Eq. (18). 
       [Math. 20] 
       αφ* 2 +βφ*+γ=0  (18)
 
       α=− A   12   C   23   +A   23   C   12  
 
       β=− A   12   D   23   +A   23   D   12   −B   12   C   23   +B   23   C   12  
 
       γ=− B   12   D   23   +B   23   D   12  
 
     Because the above Eq. (18) is a quadratic equation of ϕ*, the background magnetic field ϕ* can be calculated from the following Eq. (19). Furthermore, two background magnetic fields ϕ* can be obtained using the unknown variable k, but only one background magnetic field ϕ* satisfies Eq. (6). Thereby, the background magnetic field ϕ* on the complex plane Γ is estimated. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     φ 
                     * 
                   
                   = 
                   
                     
                       
                         - 
                         β 
                       
                       ± 
                       
                         
                           
                             β 
                             2 
                           
                           - 
                           
                             4 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             α 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             γ 
                           
                         
                       
                     
                     
                       2 
                       ⁢ 
                       α 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     By substituting the background magnetic field ϕ* calculated from the above Eq. (19) into the above Eq. (15), the variable v (=v A +v B ) can be calculated. Further, by substituting the calculated background magnetic field ϕ* and the calculated variable v into the above Eq. (12), the variable k can be calculated. 
     Finally, when the calculated background magnetic field ϕ*, the calculated variable v, and the calculated variable k are substituted into the above Eq. (10), a product (v A v B ) of the positions v A  and vs of the conductors MC 1  and MC 2  to be measured on the complex plane Γ can be calculated. According to the above, the sum (v=v A +v B ) and the product (v A v B ) of the positions v A  and vs of the conductors MC 1  and MC 2  to be measured on the complex plane Γ can be calculated. Consequently, the position v A  of the conductor MC 1  to be measured on the complex plane Γ and the position v B  of the conductor MC 2  to be measured on the complex plane T can be estimated. 
     As described above, the background magnetic field ϕ* on the complex plane Γ is estimated from the above Eq. (19). Also, the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ are estimated from the above Eq. (10). Consequently, by substituting the background magnetic field ϕ and the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured into the above Eq. (7), the currents I flowing through the conductors MC 1  and MC 2  to be measured can be calculated. 
     Furthermore, by modifying the above Eq. (2), the following Eq. (20) can be obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   I 
                   = 
                   
                     2 
                     ⁢ 
                     
                       π 
                       ⁡ 
                       
                         ( 
                         
                           
                             H 
                             m 
                           
                           - 
                           Φ 
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               r 
                               
                                 A 
                                 ⁢ 
                                 m 
                               
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                              
                             
                               r 
                               
                                 B 
                                 ⁢ 
                                 m 
                               
                             
                              
                           
                           2 
                         
                       
                       
                         
                           
                             
                                
                               
                                 r 
                                 
                                   B 
                                   ⁢ 
                                   m 
                                 
                               
                                
                             
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               j 
                               × 
                               
                                 r 
                                 
                                   A 
                                   ⁢ 
                                   m 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             
                                
                               
                                 r 
                                 
                                   A 
                                   ⁢ 
                                   m 
                                 
                               
                                
                             
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               j 
                               × 
                               
                                 r 
                                 
                                   B 
                                   ⁢ 
                                   m 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     The magnetic fields H m  in the above Eq. (20) are the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . In the above Eq. (20), j is a unit vector in the direction of the current I. j is calculated from the above Eq. (4) using the detection results (the magnetic fields H 1 , H 2 , and H 3 ) of the triaxial magnetic sensors  11 ,  12 , and  13 . Consequently, the currents I flowing through the conductors MC 1  and MC 2  to be measured can be calculated using the above Eq. (20) if the background magnetic field and the vectors r Am  and r Bm  parallel to the perpendicular lines drawn from each of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  to the conductors MC 1  and MC 2  to be measured are obtained. 
     The background magnetic field D can be obtained by restoring the background magnetic field ϕ on the complex plane Γ estimated from the above Eq. (19) to the XYZ Cartesian coordinate system. Also, the vectors r Am  and r Bm  can be obtained by restoring the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ to the XYZ Cartesian coordinate system, calculating the positions V A  and V B  of the conductors MC 1  and MC 2  to be measured, and substituting the calculated positions V A  and V B  into the above Eqs. (3). As described above, the currents I flowing through the conductors MC 1  and MC 2  to be measured can be measured using the above Eq. (7) or the above Eq. (20). 
     &lt;Operation of Current Measurement Device&gt; 
     Next, an operation when the currents I flowing through the conductors MC 1  and MC 2  to be measured using the current measurement device  1  are measured will be described. First, a user of the current measurement device  1  causes the sensor head  10  to be arranged in proximity to the conductors MC 1  and MC 2  to be measured so that the currents I flowing through the conductors MC 1  and MC 2  to be measured are measured. A position and an orientation of the sensor head  10  with respect to the conductor MC 1  to be measured is arbitrary. 
       FIG. 5  is a flowchart showing an overview of the operation of the current measurement device  1  according to the embodiment of the present invention. The flowchart shown in  FIG. 5  is started, for example, at given intervals (for example, 1 second). When a process of the flowchart shown in  FIG. 5  is started, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  first detect magnetic fields formed by the currents I flowing through the conductors MC 1  and MC 2  to be measured (step S 11 ). Furthermore, the magnetic fields are detected by the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 , for example, about 1000 times per second. Next, the calculator  25  in the circuit  20  performs a process of accumulating detection data representing the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  in the memory  23  (step S 12 ). 
     Next, the noise remover  25   a  performs a process of removing noise from the detection data (step S 13 ). Specifically, the noise remover  25   a  performs a process of removing noise components included in the detection data by reading the detection data stored in the memory  23  and performing an averaging process or a root sum square process on the read detection data. Furthermore, because the sign disappears when the root sum square process is performed, the sign is added separately. Here, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  output three types of detection data for outputting the detection results of the three axes. The noise components are removed by the noise remover  25   a  separately for the detection data of each axis. 
     Subsequently, the position estimator  25   b  and the background magnetic field estimator  25   c  perform a process of estimating the positions and background magnetic fields of the conductors MC 1  and MC 2  to be measured (step S 14 ). 
       FIG. 6  is a flowchart showing details of the processing of step S 14  in  FIG. 5 . When the processing of step S 14  is started, the calculator  25  first performs a process of calculating directions of the currents I flowing through the conductors MC 1  and MC 2  to be measured as shown in  FIG. 6  (step S 21 ). For example, the calculator  25  performs a process of calculating the unit vector j in the directions of the currents I flowing through the conductors MC 1  and MC 2  to be measured by performing the calculation process shown in the above Eq. (4) using the detection results of the triaxial magnetic sensors  11 ,  12 , and  13 . 
     Next, the calculator  25  performs a process of projecting the conductors MC 1  and MC 2  to be measured, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 , and the magnetic fields H m  (in =1, 2, 3, 4) detected by the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  onto the complex plane Γ perpendicular to the current I (step S 22 ). Here, the positions V A  and V B  of the conductors MC 1  and MC 2  to be measured are unknown. Thus, the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured projected onto the complex plane Γ are unknown values. Furthermore, the background magnetic field ϕ on the complex plane Γ is also unknown. 
     On the other hand, the positions P m  (m=1, 2, 3, 4) of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are known. Also, the magnetic fields H m  detected by the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are known. Thus, the positions p m  (m=1, 2, 3, 4) of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  projected onto the complex plane Γ and the magnetic fields h m  (m=1, 2, 3, 4) projected onto the complex plane Γ are known values. 
     Subsequently, the background magnetic field estimator  25   c  performs a process of estimating an unknown background magnetic field ϕ on the complex plane Γ (step S 23 ). Specifically, the background magnetic field estimator  25   c  performs the process of estimating the unknown background magnetic field ϕ using the above Eq. (19). Here, referring to the above-described Eqs. (18), (14), and (12), it can be seen that the coefficients α, β, and γ in the above Eq. (19) have the positions p m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  projected onto the complex plane Γ and the magnetic fields h m  projected onto the complex plane Γ as elements. Thus, the background magnetic field estimator  25   c  estimates the unknown background magnetic field ϕ on the complex plane Γ based on the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  and the positional relationships between the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . 
     Subsequently, the position estimator  25   b  performs a process of estimating the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured, which are unknown values (step S 24 ). Specifically, the position estimator  25   b  first performs a process of substituting the background magnetic field ϕ estimated in the processing of step S 23  into the above Eq. (15) to calculate the variable v (=v A +v B ). Furthermore, the coefficients A mn , B mn , C mn , and D mn  in Eq. (15) are calculated from the positions p m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  projected onto the complex plane Γ and the magnetic fields h m  projected onto the complex plane Γ. 
     Next, a process of calculating the variable k by substituting the background magnetic field ϕ estimated in the processing of step S 23  and the above variable v into the above Eq. (12) is performed. Furthermore, the coefficients a m , b m , c m , d m , and e m  in Eq. (12) are calculated from the positions p m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  projected onto the complex plane Γ and the magnetic fields h m  projected onto the complex plane Γ. 
     A process of calculating the product (v A v B ) of the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ by substituting the estimated background magnetic field ϕ and the calculated variables v and k into the above Eq. (10) is performed. Finally, the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ are calculated from the sum (v=v A +v B ) of the positions v A  and v B  calculated from the above Eq. (15) and the product (v A v B ) of the positions v A  and v B  calculated from the above Eq. (10). In this way, the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured are estimated. 
     When the above process is completed, the current calculator  25   d  performs a process of calculating the currents I flowing through the conductors MC 1  and MC 2  to be measured (step S 15 ). Specifically, the current calculator  25   d  calculates the currents I flowing through the conductors MC 1  and MC 2  to be measured by performing a calculation process shown in the above Eq. (7) using the positions p m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  projected onto the complex plane Γ, the magnetic fields h m  projected onto the complex plane Γ, and the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured and the background magnetic field ϕ on the complex plane Γ estimated in the processing of step S 14 . 
     Furthermore, in step S 15 , the current calculator  25   d  may calculate the currents I flowing through the conductors MC 1  and MC 2  to be measured by performing the calculation process shown in the above Eq. (20) instead of the above Eq. (7). When the currents I are calculated by performing the calculation process shown in Eq. (20), the current calculator  25   d  first performs a process of obtaining the background magnetic field ϕ by restoring the background magnetic field ϕ on the complex plane Γ to the XYZ Cartesian coordinate system. Also, the current calculator  25   d  performs a process of obtaining the positions v A  and V B  of the conductors MC 1  and MC 2  to be measured by restoring the positions v A  and v B  of the conductors MC 1  and MC 2  to be measured on the complex plane Γ to the XYZ Cartesian coordinate system. 
     Next, the current calculator  25   d  performs a process of calculating the vectors r Am  and r Bm  by substituting the obtained positions v A  and V B  of the conductors MC 1  and MC 2  to be measured and the positions P m  of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  into the above Eqs. (3). The current calculator  25   d  calculates the currents I flowing through the conductors MC 1  and MC 2  to be measured by performing the calculation process shown in the above Eq. (20) using the unit vector j calculated in step S 21  of  FIG. 6  and the magnetic fields H ill  detected by the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  in addition to the background magnetic fields Φ and the vectors r Am  and r Bm  obtained in the above process. 
     As described above, in the present embodiment, the currents I flowing through the conductors MC 1  and MC 2  to be measured are measured using the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  and the positional relationships between the triaxial magnetic sensors  11 ,  12 ,  13 , and  14 . Here, in the present embodiment, the position and the orientation of the sensor head  10  with respect to the conductors MC 1  and MC 2  to be measured may be arbitrary. Also, the detection results of the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  can be obtained regardless of whether the current I is a direct current or an alternating current. Thus, in the present embodiment, a flexible arrangement is possible, currents flow in mutually opposite directions, and a direct current and an alternating current of a low frequency (for example, several hundred hertz [Hz]) flowing through the current paths (the conductors MC 1  and MC 2  to be measured) arranged in proximity to each other can be measured accurately in a non-contact mode. 
     Also, in the present embodiment, the sensor head  10  in which the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  are provided and the circuit  20  in which the calculator  25  is provided are separated and connected by a cable CB. Thereby, because the handling of the sensor head  10  is facilitated, and for example, the sensor head  10  can be easily installed within a small space, the sensor head  10  can be arranged more flexibly. 
     Although the current measurement device according to the embodiment of the present invention has been described above, the present invention is not limited to the above embodiment and can be freely changed within the scope of the present invention. For example, in the above-described embodiment, an example in which the triaxial magnetic sensors  13 ,  11 , and  12  are separated at intervals d [m] in the first axis direction (the x-axis direction), and the triaxial magnetic sensors  11  and  14  are separated an interval d [m] in the third axis direction (the z-axis direction) has been described. However, the triaxial magnetic sensors  11 ,  12 ,  13 , and  14  have any relative positional relationship as long as magnetism-sensing directions thereof are set in parallel to each other. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  Current measurement device 
               10  Sensor head 
               11  to  14  Triaxial magnetic sensor 
               20  Circuit 
               25  Calculator 
               25   a  Noise remover 
               25   b  Position estimator 
               25   c  Background magnetic field estimator 
               25   d  Current calculator 
             I Current 
             MC 1  Conductor to be measured 
             MC 2  Conductor to be measured 
             V A , v A  Position of conductor to be measured 
             V B , v B  Position of conductor to be measured 
             ϕ, Φ Background magnetic field