Patent Publication Number: US-2022229096-A1

Title: Power measurement apparatus and power measurement method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. National stage application claims priority under 35 U.S.C. § 119(a) to Japanese Patent Application No. 2019-101927, filed in Japan on May 31, 2019, the entire contents of which are hereby incorporated herein by reference. 
     BACKGROUND 
     Field of the Invention 
     A power measurement apparatus and a power measurement method for measuring power supplied from an AC power source through a conductive path in such a manner as not to come into contact with the conductive path. 
     Background Information 
     For example, as described in Japanese Unexamined Patent Application Publication No. 2006-343109, there has been known a power measurement apparatus in which a detection electrode is arranged in a contactless manner near an electric wire to which a power supply voltage is applied to detect a voltage waveform of the electric wire and measure power. The power measurement apparatus described in Japanese Unexamined Patent Application Publication No. 2006-343109 has a configuration in which the electric wire and a probe are connected by capacitive coupling to enable measurement of the voltage waveform even in a contactless way. 
     SUMMARY 
     In the power measurement apparatus described in Japanese Unexamined Patent Application Publication No. 2006-343109, however, a distortion of a voltage or a current of the conductive path, which is the measurement target, causes a reduction in the measurement accuracy of power to be measured. In addition, there is a case where fluctuations in the relationship between the voltage generated in the electric wire and the voltage generated in the probe with fluctuations In coupling between the electric wire and the probe cause a reduction in the measurement accuracy of power in the power measurement apparatus in Japanese Unexamined Patent Application Publication No. 2006-343109. 
     A power measurement apparatus for measuring power supplied through a conductive path in such a manner as not to come into contact with the conductive path has to address improving measurement accuracy. 
     A power measurement apparatus according to a first aspect includes a voltage detector, a current detector, and a power calculator. The voltage detector detects in a contactless manner an  AC voltage of a conductive path to which power is supplied from an AC power source whose magnitude of AC voltage is regulated to be a predetermined value, and outputs first data signal regarding a voltage waveform of the AC voltage of the conductive path. The current detector detects in a contactless manner an AC current flowing through the conductive path, and outputs second data signal regarding a current waveform of the AC current of the conductive path. The power calculator receives the first data signal and the second data signal and calculates active power of the conductive path from a product of a second instantaneous voltage and an instantaneous current of the current waveform indicated by the second data signal, the second instantaneous voltage being generated by converting a first instantaneous voltage of the voltage waveform indicated by the first data signal on the basis of the predetermined value. 
     In the power measurement apparatus according to the first aspect, with the use of a regulated predetermined value, the influence of contactless detection of an AC voltage on power calculation can be suppressed, and, in addition, calculating the active power from the product of the second instantaneous voltage and the instantaneous current can take the influence of the harmonics into account. Thus, power measurement accuracy is improved. 
     A power measurement apparatus according to a second aspect is the power measurement apparatus according to the first aspect, in which the predetermined value is an effective value or a peak value of the AC voltage of the AC power source, and, in calculation of the active power of the conductive path, the power calculator converts the first instantaneous voltage into the second instantaneous voltage on the basis of a ratio of an effective value or a peak value indicated by the voltage waveform to the predetermined value. 
     In the power measurement apparatus according to the second aspect, a change in the ratio of the effective value or the peak value indicated by the voltage waveform to the predetermined value, which is caused by an environmental change around the conductive path, can be reflected in the harmonics, and power measurement accuracy can be improved. 
     A power measurement apparatus according to a third aspect includes a voltage detector, a current detector, and a power calculator. The voltage detector detects in a contactless manner an AC voltage of a conductive path to which power is supplied from an AC power source whose magnitude of the AC voltage is regulated to be a predetermined value, and outputs first data signal regarding a voltage waveform of the voltage of the conductive path. The current detector detects in a contactless manner an AC current flowing through the conductive path and outputs second data signal regarding a current waveform of the current of the conductive path. The power calculator receives the first data signal and the second data signal and calculates active power of  the conductive path from a magnitude of an AC current of the current waveform indicated by the second data signal, the predetermined value, and a phase difference between a fundamental of the voltage waveform obtained from the first data signal and a fundamental of the current waveform obtained from the second data signal. 
     In the power measurement apparatus according to the third aspect, with the use of a regulated predetermined value, even if harmonics are superimposed on a voltage, the influence of the harmonics on power calculation can be suppressed. In addition, with the use of the fundamental of the current waveform for the phase difference, an error of the phase difference due to noise can be suppressed. Thus, power measurement accuracy is improved. 
     A power measurement apparatus according to a fourth aspect is the power measurement apparatus according to any of the first aspect to the third aspect, in which the voltage detector includes a probe, an input part, a differential amplifier, and a regulator. The probe includes an electrode arranged so as not to come into contact with the conductive path, and generates an impedance including a capacitive component between the conductive path and the electrode. The input part is connected to the probe and produces an input signal corresponding to a waveform of an AC voltage of the conductive path on the basis of a potential of the electrode. The differential amplifier amplifies the input signal produced by the input part and outputs an output signal, the output signal being the first data signal. The regulator regulates at least one of a gain of the differential amplifier and a magnitude of the input signal produced by the input part on the basis of a magnitude of the output signal of the differential amplifier, and keeps the magnitude of the output signal of the differential amplifier within a predetermined range. 
     In the power measurement apparatus according to the fourth aspect, even if the impedance greatly changes with a change in surrounding environment and the potential of the electrode greatly changes, the regulator can keep the magnitude of the output signal of the differential amplifier within a predetermined range. As a result, a decrease in the resolution of the voltage waveform of the AC power supply voltage to be measured by a contactless voltage measurement circuit is suppressed. 
     A power measurement apparatus according to a fifth aspect is the power measurement apparatus according to the fourth aspect, in which the conductive path includes a first electric wire and a second electric wire. The probe includes, as the electrode, a first electrode arranged so as not to come into contact with the first electric wire and a second electrode arranged so as not to come into contact with the second electric wire, generates a first impedance including a capacitive component between the first electric wire and the first electrode, and generates a  second impedance including a capacitive component between the second electric wire and the second electrode. The input part produces an input signal corresponding to a waveform of a potential difference between the first electrode and the second electrode. 
     In the power measurement apparatus according to the fifth aspect, even if the impedance greatly changes with a change in surrounding environment and the potential difference generated between the first electrode and the second electrode greatly changes, the regulator can keep the magnitude of the output signal of the differential amplifier within a predetermined range. 
     A power measurement apparatus according to a sixth aspect is the power measurement apparatus according to the fourth aspect or the fifth aspect, in which the regulator is configured such that a magnitude of the output signal of the differential amplifier obtained when the gain is regulated to a minimum is allowed to be smaller than one half of a magnitude of the output signal of the differential amplifier obtained when the gain is regulated to a maximum. 
     In the power measurement apparatus according to the sixth aspect, even in a case where the input signal of the differential amplifier greatly changes by a factor of two or more in response to a change in surrounding environment, the regulator can keep the magnitude of the output signal of the differential amplifier within a predetermined range. 
     A power measurement apparatus according to a seventh aspect is the power measurement apparatus according to any of the fourth aspect to the sixth aspect, in which the regulator is a programmable resistor that changes a resistance value determining the gain of the differential amplifier on the basis of the magnitude of the output signal of the differential amplifier. 
     In the power measurement apparatus according to the seventh aspect, the programmable resistor makes it easy to perform control to keep the magnitude of the output signal of the differential amplifier within a predetermined range. 
     A power measurement apparatus according to an eighth aspect is the power measurement apparatus according to any of the fourth aspect to the sixth aspect, in which the input part includes a voltage divider circuit connected to the electrode to divide an AC power supply voltage of the conductive path. The voltage divider circuit includes at least one of a variable capacitor and a variable resistor that are regulated by the regulator to change the magnitude of the input signal. 
     In the power measurement apparatus according to the eighth aspect, at least one of the variable capacitor and the variable resistor makes it easy to perform control to keep the magnitude of the output signal of the differential amplifier within a predetermined range. 
     A power measurement apparatus according to a ninth aspect is the power measurement apparatus according to any of the fourth aspect to the sixth aspect, in which the input part includes  a voltage divider circuit connected to the electrode to divide an AC power supply voltage of the conductive path. The voltage divider circuit includes at least one of a variable capacitor and a variable resistor that are regulated by the regulator to change the magnitude of the input signal. The regulator includes a programmable resistor that changes a resistance value determining the gain of the differential amplifier on the basis of the magnitude of the output signal of the differential amplifier. The regulator is configured to change the resistance value of the programmable resistor and a value of the at least one of the variable capacitor and the variable resistor on the basis of the magnitude of the output signal of the differential amplifier. 
     In the power measurement apparatus according to the ninth aspect, the programmable resistor and at least one of the variable capacitor and the variable resistor make it easy to perform control to keep the magnitude of the output signal of the differential amplifier within a predetermined range. 
     A power measurement method according to a tenth aspect includes detecting in a contactless manner a voltage waveform of an AC voltage of a conductive path to which power is supplied from an AC power source whose magnitude of the AC voltage is regulated to be a predetermined value, detecting in a contactless manner a current waveform of an AC current flowing through the conductive path, converting a first instantaneous voltage indicated by the voltage waveform on the basis of the predetermined value to generate a second instantaneous voltage, and calculating active power of the conductive path from a product of the second instantaneous voltage and an instantaneous current indicated by the current waveform. 
     A power measurement method according to an eleventh aspect includes detecting in a contactless manner a voltage waveform of an AC voltage of a conductive path to which power is supplied from an AC power source whose magnitude of the AC voltage is regulated to be a predetermined value, detecting in a contactless manner a current waveform of an AC current flowing through the conductive path, calculating a magnitude of the AC current from the current waveform, calculating a phase difference between a fundamental of the current waveform and a fundamental of the voltage waveform, and calculating active power of the conductive path from the predetermined value, the magnitude of the AC current of the current waveform, and the phase difference between the fundamental of the current waveform and the fundamental of the voltage waveform. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic diagram illustrating an overview of the configuration of a power measurement apparatus according to a first embodiment and a relationship between the power  measurement apparatus according to the first embodiment and a conductive path. 
         FIG. 2  is a circuit diagram illustrating an example of the configuration of the power measurement apparatus according to the first embodiment. 
         FIG. 3  includes cross-sectional views of three probes attached to the conductive path. 
         FIG. 4  is a plan view of a probe attached to a first electric wire. 
         FIG. 5  is a side view of the probe attached to the first electric wire. 
         FIG. 6  is a circuit diagram for describing the configuration of an input part. 
         FIG. 7  is a graph for describing the magnitudes of AC voltages detected by the probes. 
         FIG. 8  is a flowchart illustrating how a power measurement method according to the first embodiment is performed. 
         FIG. 9  is a circuit diagram illustrating an example of the configuration of a power measurement apparatus according to a second embodiment. 
         FIG. 10  is a flowchart illustrating how a power measurement method according to the second embodiment is performed. 
         FIG. 11  is a block diagram illustrating an overview of the configuration of a power measurement apparatus. 
         FIG 12  is a schematic cross-sectional view for describing a relationship between the probes and electric wires. 
         FIG. 13  is a circuit diagram illustrating the configuration of a power measurement apparatus according to a third embodiment. 
         FIG. 14  is a conceptual diagram for describing an overview of the configuration of a contactless voltage measurement circuit in  FIG. 11 . 
         FIG. 15  is a circuit diagram illustrating the configuration of a power measurement apparatus according to Modification 3A. 
         FIG. 16  is a circuit diagram illustrating the configuration of a power measurement apparatus according to a fourth embodiment. 
         FIG. 17  is a circuit diagram illustrating the configuration of a power measurement apparatus according to Modification 4B. 
         FIG. 18  is a circuit diagram illustrating the configuration of a power measurement apparatus according to a fifth embodiment. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENT(S) 
     First Embodiment 
     (1) Overall Configuration  
       FIG. 1  illustrates a power measurement apparatus  1 . The power measurement apparatus  1  is connected to a breaker  901  of an AC power source  900 . The magnitude of the AC voltage of the AC power source  900  is regulated to be a predetermined value. The predetermined value is, for example, an effective value of 200 V. While a description will be given here using an effective value, the magnitude of the AC voltage is not limited to the effective value. The predetermined value may be regulated by, for example, a peak value. For example, the magnitude of the AC voltage of the AC power source  900  may be regulated to be a peak value of 282 V In a first embodiment, a case where the alternating current of the AC power source  900  is a three-phase alternating current will be described as an example. However, the AC power source  900  may be configured to supply power by any other alternating current such as a two-phase alternating current. 
     The AC power source  900  is connected to a conductive path  100 . The AC power source  900  supplies power to an air conditioner  800  through the conductive path  100 . To be more specific, the conductive path  100  is connected to an outdoor unit of the air conditioner  800 , and power is supplied to the outdoor unit through the conductive path  100 . 
     The power measurement apparatus  1  measures the active power of the conductive path  100 . For the power measurement of the conductive path  100 , the power measurement apparatus  1  includes a voltage detector  3 , a current detector  4 , and a power calculator  2 . 
     The voltage detector  3  detects in a contactless manner an AC voltage of the conductive path  100  to which power is supplied from the AC power source  900  whose magnitude of the AC voltage is regulated to be a predetermined value, and outputs first data signal da 1  regarding the voltage waveform of the voltage of the conductive path  100 . The voltage detector  3  includes probes  5  that detect in a contactless manner AC voltages of the conductive path  100 . A voltage measurer  38  receives the AC voltages output from the probes  5  and outputs the first data signal da 1  corresponding to the AC voltage of the conductive path  100 . The current detector  4  detects in a contactless manner an AC current flowing through the conductive path  100 , and outputs second data signal da 2  regarding a current waveform. The current detector  4  includes a current transformer  6  that detects in a contactless manner an AC current flowing through the conductive path  100 . A current measurer  48  receives the AC current, which has been transformed by the current transformer  6 , and outputs the second data signal da 2  corresponding to the AC current flowing in the conductive path  100 . 
     The power calculator  2  receives the first data signal da 1  output from the voltage detector  3 , and receives the second data signal da 2  output from the current detector  4 . The power  calculator  2  may not only directly receive the first data signal da 1  and the second data signal da 2  but also indirectly receive the content of the first data signal da 1  and the second data signal da 2 . Examples of the case where the power calculator  2  indirectly receives the content of the first data signal da 1  and the second data signal da 2  include the following case. The first data signal da 1  and the second data signal da 2 , which are output as analog signals, are converted into digital signals by an AD converter, and the AD converter directly outputs the first data signal da 1  and the second data signal da 2  as the digital signals to the power calculator  2 . The power calculator  2  according to the first embodiment has an AD converter  25  incorporated therein. The power calculator  2  having such a configuration directly receives the analog first data signal da 1  and the analog second data signal da 2  output from the voltage detector  3  and the current detector  4 , and the analog data signal is converted into digital data signal in the power calculator  2 . 
     The power calculator  2  calculates the active power from the magnitude of the AC current, the magnitude of the AC voltage, and the phase difference between the AC current and the AC voltage. The power calculator  2  uses the magnitude indicated by the second data signal da 2  as the magnitude of the AC current of the current waveform. The power calculator  2  uses the predetermined value of the AC power source  900  as the magnitude of the AC voltage. The power calculator  2  uses, as the phase difference, the phase difference between the fundamental of the voltage waveform obtained from the first data signal da 1  and the fundamental of the current waveform obtained from the second data signal da 2 . 
     The power measurement apparatus  1  outputs the active power, which is calculated by the power calculator  2 , as the active power of the conductive path  100 . 
     (2) Detailed Configuration 
     The conductive path  100  includes a first electric wire  101 , a second electric wire  102 , and a third electric wire  103 . The first electric wire  101  corresponds to the R phase of the AC power source  900 , the second electric wire  102  corresponds to the S phase, and the third electric wire  103  corresponds to the phase. 
     (2-1) Voltage Detector  3   
     As illustrated in  FIG. 2 , the voltage detector  3  includes three probes  5   r ,  5   s , and  5   t  and the voltage measurer  38 . The voltage measurer  38  includes an input part  31  and a gain-adjustable amplifier unit  35 . To clarify the correspondence relationships between the three probes illustrated in  FIG. 1  and the R,  5 , and T phases, the probes  5  are given suffixes, like the probes  5   r ,  5   s , and  5   t  illustrated in  FIG. 2 , to distinguish them. 
     As illustrated in  FIG. 3 , the probe  5   r  is attached to the first electric wire  101  so that the  first electric wire  101  with an insulating coating  121  is surrounded from above. Also, the probe  5   s  is attached to the second electric wire  102  so that the second electric wire  102  with an insulating coating  122  is surrounded from above, and the probe  5   t  is attached to the third electric wire  103  so that the third electric wire  103  with an insulating coating  123  is surrounded from above. A first electrode  51  of the probe  5   r , a second electrode  52  of the probe  5   s , and a third electrode  53  of the probe  5   t  are arranged on the outer periphery of the insulating coatings  121 ,  122 , and  123 , respectively. The insulating coatings  121 ,  122 , and  123  are made of, for example, plastic or rubber. 
       FIG. 4  and  FIG. 5  illustrate the shapes of the probe  5   r  as viewed from above and as viewed from a side. Like the probe  5   r , the shapes of the probes  5   s  and  5   t  are substantially rectangular when viewed from above and when viewed from a side. The probe  5   r  extends in a direction in which the insulating coating  121  extends. A wiring line  55  connected to the first electrode  51  is drawn out from the probe  5   r . Wiring lines  56  and  57  illustrated in  FIG. 1  and  FIG. 2  are also connected to the second electrode  52  and the third electrode  53 , respectively. The first electrode  51 , the second electrode  52 , and the third electrode  53  are included in an electrode  50  arranged so as not to come into contact with an electric wire to which an AC power supply voltage is applied. 
     The probes  5   r ,  5   s , and  5   t  include the first electrode  51 , the second electrode  52 , and the third electrode  53  arranged so as not to come into contact with the first electric wire  101 , the second electric wire  102 , and the third electric wire  103  of the conductive path  100 , respectively. The probes  5   r ,  5   s , and  5   t  generate an impedance including a capacitive component between the conductive path  100  and the first electric wire  101 , between the conductive path  100  and the second electric wire  102 , and between the conductive path  100  and the third electric wire  103 , respectively. 
     As illustrated in  FIG. 2 , the probes  5   r ,  5   s , and  5   t  are connected to the input part  31  by the wiring lines  55  to  57 , respectively. The input part  31  is configured to include, for example, capacitors Cr and Ct. An AC voltage corresponding to a phase-to-phase voltage generated between the first electric wire  101  and the second electric wire  102  is produced across the capacitor Cr. Likewise, an AC voltage corresponding to a phase-to-phase voltage generated between the third electric wire  103  and the second electric wire  102  is produced across the capacitor Ct. 
       FIG. 6  illustrates an overview of another configuration of the input part  31 . The input part  31  illustrated in  FIG. 6  includes a first circuit RC 1  and a second circuit RC 2 , each including a  resistor and a capacitor, and unity gain operational amplifiers UA 1  to UA 4 . The unity gain operational amplifier UA 1  has input terminals  311  and  312  to which an AC voltage Vr generated between an analog ground AGND and the wiring line  55  of the probe  5   r  is input. The AC voltage Vr generated between the analog ground AGND and the wiring line  55  of the probe  5   r  is applied between the input terminals  311  and  312  of the unity gain operational amplifier UA 1 , The unity gain operational amplifiers UA 2  and UA 3  have input terminals  313  and  314  to which an AC voltage Vs generated between the analog ground AGND and the wiring line  57  of the probe  5   s  is applied. The unity gain operational amplifier UA 4  has input terminals  315  and  316  to which an AC voltage Vt generated between the analog ground AGND and the wiring line  56  of the probe  5   t  is applied. The first circuit RC 1  produces an AC voltage Vrs having a voltage waveform similar to that of the phase-to-phase voltage of the first electric wire  101  and the second electric wire  102  from the voltage Vr of the probe  5   r  output from the unity gain operational amplifier UA 1  and the voltage Vs of the probe  5   s  output from the unity gain operational amplifier UA 2 , and outputs the AC voltage Vrs from output terminals  317  and  318 . The second circuit RC 2  produces an AC voltage Vts having a voltage waveform similar to that of the phase-to-phase voltage of the third electric wire  103  and the second electric wire  102  from the voltage Vt of the probe  5   t  output from the unity gain operational amplifier UA 4  and the voltage Vs of the probe  5   s  output from the unity gain operational amplifier UA 3 , and outputs the AC voltage Vts from output terminals  319  and  320 . Since the first circuit RC 1  and the second circuit RC 2  having such configurations can be implemented by a known circuit that is conventionally known, the description of the circuit configurations of the first circuit RC 1  and the second circuit RC 2  will be omitted here. 
     The amplitudes of the voltage waveforms of the AC voltages Vrs and Vts output from the input part  31  are affected by the surface areas of the probes  5   r ,  5   s , and  5   t , the thicknesses of the insulating coatings  121 ,  122 , and  123 , the thicknesses of the core wires of the first electric wire  101  to the third electric wire  103 , dirt on the surfaces of the electric wires, the degree of adhesion of the probes  5   r ,  5   s , and  5   t , the ambient temperatures and humidities of the probes  5   r ,  5   s , and  5   t , and so on. 
     A voltage detection circuit constituting the input part  31  is capable of outputting a voltage waveform without distortion, but is incapable of detecting the absolute value of a voltage waveform. Accordingly, the amplitudes of the voltage waveforms of the AC voltages Vrs and Vts output from the input part  31  of the power measurement apparatus  1  are handled as specified values (for example, an effective value of 200 V).  
       FIG. 7  illustrates various voltage waveforms Vrs 1 , Vrs 2 , and Vrs 3  as AC voltages Vrs output from the input part  31 , and a voltage waveform VRS having the same magnitude as a reference value (for example, AC 200 V). As illustrated in  FIG. 7 , even if the voltage waveform VRS is distorted due to superimposition of harmonics, the voltage waveforms Vrs 1 , Vrs 2 , and Vrs 3  output from the input part  31  are similar to the distorted voltage waveform VRS. 
     The voltage waveforms of the AC voltages Vrs and Vts output from the input part  31  are amplified by amplifiers  37   a  and  37   b  whose gains can be changed, respectively. The amplifiers  37   a  and  37   b  are, for example, programmable gain amplifiers. Since the AD conversion error is large if the voltage waveforms output from the input part  31  are excessively small, the amplifiers  37   a  and  37   b  amplify the voltage waveforms output from the input part  31  to appropriate magnitudes to expand the voltage waveforms. The amplifiers  37   a  and  37   b  select the factor of amplification from among, for example, 2, 4, 8, 16, 32, and so on. If the voltage waveforms output from the input part  31  are excessively large, it is not possible to correctly convert the waveforms. Thus, the amplifiers  37   a  and  37   b  amplify the waveforms to appropriate magnitudes to compress the waveforms. The amplifiers  37   a  and  37   b  select the factor for amplification from among, for example, ½, ¼, ⅛, 1/16, 1/32, and so on. The outputs of the amplifiers  37   a  and  37   b  are input to AD converters  23   a  and  23   b.    
     (2-2) Current Detector  4   
     The current detector  4  illustrated in  FIG. 2  includes current transformers  6   a  and  6   b  and the current measurer  48 . The current measurer  48  includes resistors R 11  and R 12  and amplifiers  61  and  62 . The current transformer  6   a  is arranged so as not to come into contact with the first electric wire  101 . The current transformer  6   a  transforms an AC current flowing in the first electric wire  101  and outputs an AC current having a different magnitude from that of the AC current of the first electric wire  101 . The resistor R 11  is connected to the current transformer  6   a , and the AC current output from the current transformer  6   a  flows through the resistor R 11 . A voltage waveform having the same shape as that of the current waveform of the AC current output from the current transformer  6   a  is produced across the resistor R 11 . The amplifier  61  amplifies the voltage waveform across the resistor R 11  to a magnitude such that the voltage waveform can be handled as the AC current of the first electric wire  101 . 
     The current transformer  6   b  is arranged so as not to come into contact with the third electric wire  103 . The current transformer  6   b  transforms an AC current flowing in the third electric wire  103  and outputs an AC current having a different magnitude from that of the AC current of the third electric wire  103 . The resistor R 12  is connected to the current transformer  6   b , and the AC  current output from the current transformer  6   b  flows through the resistor R 12 . A voltage waveform having the same shape as that of the current waveform of the AC current output from the current transformer  6   b  is produced across the resistor R 12 . The amplifier  62  amplifies the voltage waveform across the resistor R 12  to a magnitude such that the voltage waveform can be handled as the AC current of the third electric wire  103 . 
     (2-3) Power Calculator  2   
     The power calculator  2  includes AD converters  22   a ,  22   b ,  23   a , and  23   b  and a power computation unit  21 . The power calculator  2  can be implemented by, for example, a computer including an AD converter. For example, the computer executes a program to form the power computation unit  21  in a CPU of the computer. The AD converter  22   a  is connected to the amplifier  61 , and the AD converter  22   b  is connected to the amplifier  62 . The AD converter  22   a , converts an instantaneous value of an analog signal indicating an AC current Ir output from the amplifier  61  into digital data signal. The AD converter  22   b  converts an instantaneous value of an analog signal indicating an AC current It output from the amplifier  62  into digital data signal. The magnitudes of the AC currents Ir and It indicated by the analog signals output from the amplifiers  61  and  62  are equal to the magnitudes of the AC currents output from the current transformers  6   a  and  6   b , respectively. The analog signals output from the amplifiers  61  and  62  are the second data signal output from the current detector  4 . The digital data signal regarding the magnitudes and the current waveforms of the AC currents output the current transformers  6   a  and  6   b  is output to a memory  211  of the power computation unit  21  through the AD converters  22   a  and  22   b.    
     The AD converter  23   a  is connected to the amplifier  37   a , and the AD converter  23   b  is connected to the amplifier  37   b . The AD converters  23   a  and  23   b  convert instantaneous values of analog signals indicating the AC voltages Vrs and Vts output from the amplifiers  37   a  and  37   b  into digital data signal, respectively. The analog signals output from the amplifiers  37   a  and  37   b  are the first data signal output from the voltage detector  3 . The digital data signal regarding the voltage waveform of the voltage generated between the first electric wire  101  and the second electric wire  102  and the voltage waveform of the voltage generated between the third electric wire  103  and the second electric wire  102  is output to the memory  211  of the power computation unit  21  through the AD converters  23   a  and  23   b.    
     Ratio determiners  212  and  213  of the power computation unit  21  of the power calculator  2  determine ratios α and β of effective values or peak values indicated by the voltage waveforms of the AC voltages Vrs and Vts to the predetermined value. For example, it is assumed that there  are n pieces of digital data corresponding to two cycles of the AC voltage Vrs, namely; {Vrs( 1 ), Vrs( 2 ), Vrs( 3 ), . . . , Vrs(n- 1 ), and Vrs(n)}. The root mean square of these n pieces of data is computed to determine an effective value Vrs rms  of the AC voltage Vrs. Likewise, an effective value Vts rms  of the AC voltage Vts is determined from n pieces of digital data {Vts( 1 ), Vts( 2 ), Vts( 3 ), . . . , Vts(n- 1 ), Vts(n)} corresponding to two cycles of the AC voltage Vts. For example, if the predetermined value is an effective value of 200 V the predetermined value is divided by the effective value Vrs rms  of the AC voltage Vrs to determine α (α= 200 /Vrs rms ), and the predetermined value is divided by the effective value Vts rms  of the AC voltage Vts to determine β(β=200/Vts ms ). 
     Further, using a current conversion coefficient γ determined by the current transformers  6   a  and  6   b , if instantaneous values of the AC current flowing through the first electric wire  101  are n pieces of data {γIr( 1 ), γIr( 2 ), . . . , γIr(n)} and instantaneous values of the AC current flowing through the third electric wire  103  are n pieces of data {γIt( 1 ), γIt( 2 ), . . . , γIt(n)}, active power P is determined by the sum of P 1  and P 2  expressed by equation (1) and equation (2). 
     
       
         
           
             
               
                 
                   
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     While the effective value is used in the computation of the active power P described above, a peak value (for example, 282 V) of the predetermined value may be used instead of the effective value (for example, 200 V) of the predetermined value. For example, α is determined by 282/(the peak value of the AC voltage Vts). 
     A multiplier  214  illustrated in  FIG. 2  multiplies an instantaneous value of the AC voltage Vrs stored in the memory  211  by the ratio α output from the ratio determiner  212 . The multiplier  214  receives a value of a first instantaneous voltage and outputs a value of a second instantaneous voltage. A multiplier  215  multiplies an instantaneous value of the AC voltage Vts stored in the memory  211  by the ratio β output from the ratio determiner  213 . The multiplier  215  receives a value of a first instantaneous voltage and outputs a value of a second instantaneous voltage. A coefficient output unit  216  outputs the current conversion coefficient γ stored in the memory  211 . A multiplier  217  multiplies an instantaneous value of the AC current Ir stored in the memory  211  by the current conversion coefficient γ output from the coefficient output unit  216 . A multiplier  218  multiplies an instantaneous value of the AC current It stored in the memory  211  by the current conversion coefficient γ output from the coefficient output unit  216 . A multiplier  219  multiplies the value of the second instantaneous voltage output from the multiplier  214  by the value of the instantaneous current output from the multiplier  217 . For example, the multiplier  219  performs  computation of αVr(n)×γIr(n). A multiplier  220  multiplies the value of the second instantaneous voltage output from the multiplier  215  by the value of the instantaneous current output from the multiplier  218 . For example, the multiplier  220  performs computation of βVt(n)×γIt(n). An accumulator  221  accumulates the n pieces of data output from the multiplier  219  and the n pieces of data output from the multiplier  220 . A multiplier  223  multiplies the output of the accumulator  221  by a value of 1/n output from a coefficient output unit  222 , and the value of the active power P(=P1+P2) is output from the multiplier  223 . 
     (3) Overview of Power Measurement Method 
     An overview of a power measurement method will be described with reference to  FIG. 8 . First, the power measurement apparatus  1  detects in a contactless manner a voltage waveform of an AC voltage of the conductive path  100  to which power is supplied from the AC power source  900  whose magnitude of the AC voltage is regulated to be a predetermined value (step ST 1 ). As described above, the voltage detector  3  detects the voltage waveform of the AC voltage in a contactless manner by using the probes  5   r ,  5   s , and  5   t , attached to the first electric wire  101 , the second electric wire  102 , and the third electric wire  103 . 
     At the same time as the detection of the voltage waveform (step ST 1 ), the power measurement apparatus  1  detects in a contactless manner a current waveform of an AC current flowing through the conductive path  100  (step ST 2 ). As described above, the current detector  4  detects the current waveform of the AC current in a contactless manner by using the current transformers  6   a  and  6   b  attached to the first electric wire  101  and the third electric wire  103 . 
     The power measurement apparatus  1  converts a first instantaneous voltage indicated by the voltage waveform on the basis of the predetermined value and generates a second instantaneous voltage (step ST 3 ). As described above, in the first embodiment, the value provided to the multipliers  214 ,  215  is the value of the first instantaneous voltage. The value of the first instantaneous voltage is multiplied by the ratios α and β to calculate the value of the second instantaneous voltage, α and β are the ratios of effective values or peak values indicated by the voltage waveforms of the AC voltages Vrs and Vts to the predetermined value (effective value or peak value) of the AC voltage of the AC power source  900 , respectively. 
     The power computation unit  21  calculates the active power of the conductive path  100  by using the product of the second instantaneous voltage and the instantaneous current (step ST 4 ), The power measurement apparatus  1  outputs the active power of the conductive path  100  calculated by the power computation unit  21  (step ST 5 ). 
     (4) Features  
     (4-1) 
     In the power measurement apparatus  1  or the power measurement method according to the first embodiment, with the use of a predetermined value regulated for the AC power source  900 , the influence of contactless detection of an AC voltage using the probes  5   r ,  5   s , and  5   t , on power calculation can be suppressed. In the power measurement apparatus  1  according to the first embodiment, furthermore, since the active power is calculated using the product of the second instantaneous voltage and the instantaneous current, the influence of the harmonics can be taken into account. Thus, power measurement accuracy is improved. 
     (4-2) 
     In the power measurement apparatus  1  or the power measurement method according to the first embodiment, an environmental change around the conductive path  100  causes a change in the ratios α and β of the effective values or peak values indicated by the voltage waveforms to the predetermined value. For example, the magnitudes of the AC voltages output from the probes  5   r ,  5   s , and  5   t , change due to the ambient temperatures and humidities of the probes  5   r ,  5   s , and  5   t , or the like. Since the ratios α and β can be reflected even in the harmonics of the AC current, it is possible to improve the measurement accuracy of the active power output from the power measurement apparatus  1 . 
     (5) Modifications 
     (5-1) Modification 1A 
     In the first embodiment, a description has been given of a case where the AC power source  900  is configured to supply a three-phase alternating current. However, the application of the technique described in the first embodiment is not limited to an AC power source configured to supply a three-phase alternating current. For example, the technique described in the first embodiment is also applicable to an AC power source configured to supply a two-phase alternating current. 
     (5-2) Modification 1B 
     In the first embodiment, a method for determining the magnitude of an AC voltage by computation using digital data signal has been described. However, the method for determining the magnitude of an AC voltage is not limited to such a method. For example, a rectifier voltmeter may be used to detect the magnitude of an AC voltage. Alternatively, simply, the magnitude of the fundamental of an AC voltage including harmonics may be determined by FFT analysis, and the magnitude of the fundamental may be regarded as the magnitude of the AC voltage. FFT is an abbreviation for fast Fourier transform.  
     Second Embodiment 
     (6) Overview of Power Measurement Apparatus 
     In the first embodiment, a description has been given of a case where the power calculator  2  calculates the active power P by using the product of an instantaneous voltage and an instantaneous current. However, the configuration of the power calculator  2  can be modified as in a second embodiment described below. As illustrated in  FIG. 9 , the power calculator  2  of the power measurement apparatus  1  includes filters  231  to  234 , AD converters  235  to  238 , phase difference calculators  239  and  240 , current amplitude calculators  241  and  242 , and an arithmetic unit  243 . The power calculator  2  can be implemented by, for example, a computer including a filter and an AD converter. For example, the computer executes a program to form the power computation unit  21  in a CPU of the computer. 
     The voltage detector  3  and the current detector  4  according to the second embodiment are similar to those of the first embodiment. The voltage detector  3  detects in a contactless manner an AC voltage of the conductive path  100  to which power is supplied from an AC power source whose magnitude of the AC voltage is regulated to be a predetermined value. The voltage detector  3  outputs voltage waveforms of the AC voltages Vrs and Vts, which are first data signal regarding the voltage waveform of the voltage of the conductive path  100 . The current detector  4  detects in a contactless manner an AC current flowing through the conductive path  100 . The current detector  4  outputs analog signals indicating the AC currents Ir and It output from the current transformers  6   a  and  6   b , which are second data signal regarding the current waveform. 
     The filters  231  and  232  filter the analog signals indicating the voltage waveforms of the AC voltages Vrs and Vts output from the amplifiers  37   a  and  37   b  of the voltage detector  3 , respectively. For example, if the AC voltage of the AC power source  900  has a frequency of 60 Hz, the filters  231  and  232  attenuate voltage waveforms having frequencies other than 60 Hz. In other words, the filters  231  and  232  output analog signals indicating the voltage waveforms of the fundamentals of the AC voltages. 
     The filters  233  and  234  filter output signals of the amplifiers  61  and  62  of the current detector  4  indicating the output currents Ir and It of the current transformers  6   a  and  6   b , respectively. The filters  233  and  234  attenuate current waveforms having frequencies other than a frequency of 60 Hz of the AC power source  900 . In other words, the filters  233  and  234  output analog signals indicating the current waveforms of the fundamentals of the AC currents and the magnitude of the currents. 
     The AD converters  235 ,  236 ,  237 , and  238  convert the analog signals output from the  filters  231 ,  232 ,  233 , and  234  into digital signals. 
     The current amplitude calculators  241  and  242  detect the amplitudes of the AC currents from the output signals of the AD converters  237  and  238 , respectively. The current amplitude calculators  241  and  242  output signals indicating, for example, the magnitudes of the effective values Ir rms and It rms  of the AC currents to the arithmetic unit  243 , respectively, 
     The phase difference calculator  239  detects a phase difference Φ1 between the fundamental of the AC voltage Vrs indicated by the output signal of the AD converter  235  and the fundamental of the AC current Ir indicated by the output signal of the AD converter  237 . The phase difference calculator  240  detects a phase difference Φ2 between the fundamental of the AC voltage Vts indicated by the output signal of the AD converter  236  and the fundamental of the AC current It indicated by the output signal of the AD converter  238 . Since the fundamentals of the AC voltages Vrs and Vts and the fundamentals of the AC currents Ir and It are simple sine waves, the detection of the phase differences Φ1 and Φ2 can be easily calculated using a conventionally known method, and thus a detailed description of the phase difference calculators  239  and  240  will be omitted here. 
     The arithmetic unit  243  calculates the active power P using the magnitudes Ir rms  and It rms  of the fundamentals of the AC currents Ir and It output from the filters  233  and  234 , the specified value (here, an effective value of 200 V) of the magnitude of the voltage of the AC power source  900 , and the phase differences Φ1 and Φ2 between the fundamentals of the AC voltages Vrs and Vts and the fundamentals of the AC currents Ir and It. Specifically, the arithmetic unit  243  computes the sum of P 1  and P 2  given by equation (3) and equation (4) below. Note that denotes a current conversion coefficient determined by the current transformers  6   a  and  6   b.    
     
       
         
           
             
               
                 
                   
                     P 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   = 
                   
                     200 
                     × 
                     
                       ( 
                       
                         γ 
                         × 
                         
                           Ir 
                           rms 
                         
                       
                       ) 
                     
                     × 
                     
                       cos 
                       ⁢ 
                       Φ 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     200 
                     × 
                     
                       ( 
                       
                         γ 
                         × 
                         
                           It 
                           rms 
                         
                       
                       ) 
                     
                     × 
                     
                       cos 
                       ⁢ 
                       Φ 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     (7) Overview of Power Measurement Method 
     An overview of a power measurement method will be described with reference to  FIG. 10 , First, the power measurement apparatus  1  detects in a contactless manner a voltage waveform of an AC voltage of the conductive path  100  to which power is supplied from the AC power source  900  whose magnitude of the AC voltage is regulated to be a predetermined value (step ST 11 ). As described above, the voltage detector  3  detects the voltage waveform of the AC voltage in a contactless manner by using the probes  5   r ,  5   s , and  5   t  attached to the first electric wire  101 , the second electric wire  102 , and the third electric wire  103 . 
     At the same time as the detection of the voltage waveform (step ST 11 ), the power  measurement apparatus  1  detects in a contactless manner a current waveform of an AC current flowing through the conductive path  100  (step ST 12 ). As described above, the current detector  4  detects the current waveform of the AC current in a contactless manner by using the current transformers  6   a  and  6   b  attached to the first electric wire  101  and the third electric wire  103 . The power measurement apparatus  1  calculates the magnitude of the AC current from the current waveform (step ST 13 ). As described above, in the second embodiment, for example, the current amplitude calculators  241  and  242  calculate the magnitudes of the effective value Ir rms  and It rms  of the AC currents, respectively. Further, the power measurement apparatus  1  calculates a phase difference between the fundamental of the current waveform and the fundamental of the voltage waveform (step ST 14 ). In the power measurement apparatus  1 , the power computation unit  21  calculates the active power of the conductive path  100  from the predetermined value defining the magnitude of the voltage of the AC power source  900 , the magnitude of the AC current of the current waveform, and the phase difference between the fundamental of the current waveform and the fundamental of the voltage waveform (step ST 15 ). The power measurement apparatus  1  outputs the active power of the conductive path  100  calculated by the power computation unit  21  (step ST 16 ). 
     (8) Features 
     (8-1) 
     In the power measurement apparatus  1  or the power measurement method according to the second embodiment, with the use of a predetermined value regulated as the magnitude of the voltage of the AC power source  900 , the influence of contactless detection of an AC voltage using the probes  5   r ,  5   s , and  5   t  on power calculation can be suppressed. Thus, power measurement accuracy is improved. 
     (9) Modifications 
     (9-1) Modification 2A 
     In the second embodiment, a description has been given of a case where the AC power source  900  is configured to supply a three-phase alternating current. However, the application of the technique described in the second embodiment is not limited to an AC power source configured to supply a three-phase alternating current. For example, the technique described in the second embodiment is also applicable to an AC power source configured to supply a two-phase alternating current. 
     (9-2) Modification 2B 
     A description has been given of a case where in the power measurement apparatus  1   according to the second embodiment, the filters  231  to  234  are used to detect the fundamentals of the current waveforms and the voltage waveforms. However, the method for detecting the fundamentals of the current waveforms and the voltage waveforms is not limited to the method using the filters  231  to  234 . For example, the power measurement apparatus  1  may be configured to use FFT analysis to detect the fundamentals of the current waveforms and the voltage waveforms. 
     Third Embodiment 
     (10) Overall Configuration 
     As illustrated in  FIG. 11 , the power measurement apparatus  1  is an apparatus for measuring power supplied through the conductive path  100 . In a third embodiment, a description will be given of a case where the conductive path  100  is constituted by a first electric wire  101  and a second electric wire  102 . In the present disclosure, the term “electric wire” refers to a portion formed of only a conductor and does not include an insulating coating arranged around the conductor for insulation. An AC power supply voltage is applied to the conductive path  100 . When power is consumed by a device connected to the conductive path  100 , an AC current flows through the conductive path  100 . 
     As illustrated in  FIG. 11 , the power measurement apparatus  1  includes a power computation circuit  20  corresponding to the power calculator  2  according to the first embodiment and the second embodiment, a contactless current measurement circuit  10  corresponding to the current detector  4  according to the first embodiment and the second embodiment, and a contactless voltage measurement circuit  30  corresponding to the voltage detector  3  according to the first embodiment and the second embodiment. 
     (10-1) Contactless Current Measurement Circuit  10   
     As illustrated in  FIG. 11 , the contactless current measurement circuit  10  includes a current transformer  6  and a current measurer  48 . The current transformer  6  is arranged so as not to come into contact with the first electric wire  101 . The current transformer  6  transforms an AC current flowing in the first electric wire  101  and outputs an AC current having a different current magnitude from that of the AC current flowing in the first electric wire  101 . The current measurer  48  is connected to the current transformer  6 . The current measurer  48  receives the AC current, which has been transformed by the current transformer  6 , and outputs an analog signal I 1  corresponding to the AC current flowing in the first electric wire  101 . 
     (10-2) Contactless Voltage Measurement Circuit  30   
     The contactless voltage measurement circuit  30  includes a probe  5  and a voltage measurer   38 . The probe  5  is arranged so as not to come into contact with the conductive path  100 . The probe  5  is capacitively coupled to the conductive path  100 . The voltage measurer  38  includes an input part.  31 , a differential amplifier  32 , and a regulator  33 , as illustrated in  FIG. 13 . 
     (10-2-1) Probe  5   
       FIG. 12  schematically illustrates a relationship between the conductive path  100  and the probe  5 . The probe  5  has an electrode  50 . The electrode  50  is arranged so as not to come into contact with the conductive path  100 . The electrode  50  includes a first electrode  51  arranged so as not to come into contact with the first electric wire  101 , and a second electrode  52  arranged so as not to come into contact with the second electric wire  102 . 
     An insulating coating  120  is disposed around the conductive path  100  for insulation. A first insulating coating  121  made of, for example, plastic or rubber is provided around the first electric wire  101 . A second insulating coating  122  made of, for example, plastic or rubber is provided around the second electric wire  102 . Accordingly, the case where the electrode  50  of the probe  5  is arranged so as not to come into contact with the conductive path  100  includes a case where the electrode  50  comes into contact with the insulating coating  120  around the conductive path  100  composed of a conductor. More specifically, the case where the first electrode  51  is arranged so as not to come into contact with the first electric wire  101  includes a case where the first electrode  51  comes into contact with the first insulating coating  121 . The case where the second electrode  52  is arranged so as not to come into contact with the second electric wire  102  includes a case where the second electrode  52  comes into contact with the second insulating coating  122 . 
       FIG. 13  illustrates the configuration of the power measurement apparatus  1  in more detail, A capacitor C 1  illustrated in  FIG. 13  is a capacitor formed by the first electric wire  101 , the first electrode  51 , and the first insulating coating  121 . The insulating coating  121  serves as a dielectric. In other words, the first electric wire  101  and the first electrode  51  are capacitively coupled to each other. While only the capacitor C 1  is illustrated, actually, not only a capacitive component but also, for example, a resistance component is generated between the first electric wire  101  and the first electrode  51 . in another point of view, as illustrated in  FIG. 14 , the probe  5  generates an impedance Za including a capacitive component between the first electric wire  101  and the first electrode  51 . 
     A capacitor C 2  illustrated in  FIG. 13  is a capacitor formed by the second electric wire  102 , the second electrode  52 , and the second insulating coating  122 . The insulating coating  122  serves as a dielectric, in other words, the second electric wire  102  and the second electrode  52  are  capacitively coupled to each other. While only the capacitor C 2  is illustrated, actually, not only a capacitive component but also, for example, a resistance component is generated between the second electric wire  102  and the second electrode  52 . In another point of view, as illustrated in  FIG. 14 , the probe  5  generates an impedance Zb including a capacitive component between the second electric wire  102  and the second electrode  52 . 
     (10-2-2) Input Part  31   
     The input part  31  is connected to the probe  5 . The input part  31  produces an input signal SI corresponding to the waveform of the AC power supply voltage on the basis of the potential of the electrode  50 . In the contactless voltage measurement circuit  30  illustrated in  FIG. 13 , the potential difference between the first electrode  51  and the second electrode  52  is the input signal SI. 
     (10-2-3) Differential Amplifier  32   
     The input signal SI produced by the input part  31  is input to the differential amplifier  32 , The differential amplifier  32  amplifies the input signal SI and outputs an output signal SO. The differential amplifier  32  outputs the output signal SO to the power computation circuit  20 . 
     (10-2-4) Regulator  33   
     The regulator  33  regulates at least one of the gain of the differential amplifier  32  and the magnitude of the input signal SI produced by the input part  31  on the basis of the magnitude of the output signal SO of the differential amplifier  32  to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. The differential amplifier  32  according to the third embodiment is a differential amplifier whose gain can be changed by the regulator  33 . The regulator  33  according to the third embodiment has a function of regulating the gain of the differential amplifier  32 . The regulation of the magnitude of the input signal SI produced by the input part  31  will be described in another embodiment. 
     The predetermined mange is set in advance to a range that is smaller than the full scale output of the differential amplifier  32  and that allows an appropriate resolution to be maintained, The predetermined range is a range in which the magnitude of the output signal SO of the differential amplifier  32  is a specific proportion of the full scale output of the differential amplifier  32 . The predetermined range is, for example, a range in which the effective value of the output signal SO of the differential amplifier  32  is a specific proportion of the full scale output of the effective value of the differential amplifier  32 . The specific proportion is determined such that, for example, the effective value of the output signal SO is in the range of 60%±5% or the range of 60% to 50% of the fill scale output of the differential amplifier  32 . Alternatively, the  predetermined range is, for example, a range in which the absolute value of the peak value of the output signal SO is a specific proportion of the full scale output of the absolute value of the peak value of the differential amplifier  32 . 
     The regulator  33  is preferably configured such that the magnitude of the output signal SO of the differential amplifier  32  obtained when the gain of the differential amplifier  32  is regulated to the minimum is allowed to be smaller than one half of the magnitude of the output signal SO of the differential amplifier  32  obtained when the gain is regulated to the maximum. This is because an example in which the magnitude of the input signal SI changes about twice in one day due to a change in environment (such as humidity or temperature) even when the magnitude of the AC power supply voltage is constant has been observed in an experiment. 
     (10-3) Power Measurement by Power Measurement Apparatus  1   
     The power measurement apparatus  1  feeds back a signal indicating the magnitude of the output signal SO of the differential amplifier  32  of the contactless voltage measurement circuit  30  to the regulator  33  to regulate the magnitude of the voltage waveform to be measured by the contactless voltage measurement circuit  30 . The power measurement apparatus  1  determines that the effective value of the AC power supply voltage applied to the conductive path  100  is the predetermined value, and measures the power supplied through the conductive path  100  on the basis of the measurement results of the contactless voltage measurement circuit  30  and the contactless current measurement circuit  10 . For example, in the case of a commercial AC power supply voltage of 100 V, the predetermined value of the effective value is 100 V. 
     (11) Detailed Configuration 
     (11-1) Power Computation Circuit  20   
     The power computation circuit  20  includes a power computation unit  21  and AD converters  22  and  23 . The power computation unit  21  is implemented by a CPU (central processing unit)  90 . The CPU  90  executes a program stored in a memory (not illustrated) to form the power computation unit  21 . The power computation circuit  20  calculates a power value using a current value output from the AD converter  22  and a voltage value output from the AD converter  23 . 
     The AD converter  22  is connected to the current measurer  48 . The AD converter  22  converts an instantaneous value of the analog signal I 1  into a digital signal. The number of digits of the digital signal output from the AD converter  22  is the number of digits that can be input to the CPU  90  in the subsequent stage. For example, if the CPU  90  can input a 16-bit digital signal, 1 bit is used to indicate positive or negative, and the remaining 15 bits (15 digits) are used to  represent the magnitude of the instantaneous value. 
     The AD converter  23  receives the output signal SO of the differential amplifier  32 . The AD converter  23  converts an instantaneous value of the output signal SO, which is an analog signal, into a digital signal and outputs the digital signal to the CPU  90 . The number of digits of the digital signal output from the AD converter  23  is the number of digits that can be input to the CPU  90  in the subsequent stage. For example, if the CPU  90  can input a 16-bit digital signal, 1 bit is used to indicate positive or negative, and the remaining 15 bits (15 digits) are used to represent the magnitude of the instantaneous value. 
     (11-2) Input Part  31   
     As illustrated in  FIG. 13 , the input part  31  according to the third embodiment includes a capacitor C 3  and resistors R 1  and R 2 . One end of the capacitor C 3  is connected to the first electrode  51  of the probe  5 , and the other end of the capacitor C 3  is connected to the second electrode  52  of the probe  5 . One end of the resistor R 1  is connected to the first electrode  51 , and the other end is grounded. One end of the resistor R 2  is connected to the second electrode  52 , and the other end is grounded. Further, the one end of the resistor R 1  is connected to one input terminal of the differential amplifier  32 , and the one end of the resistor R 2  is connected to the other input terminal of the differential amplifier  32 . The potential difference between the potential at the one end of the resistor R 1  and the potential at the one end of the resistor R 2  is amplified by the differential amplifier  32 . The potential difference between the potential at the one end of the resistor  1  and the potential at the one end of the resistor R 2  is the input signal SI. 
     As illustrated in  FIG. 14 , the input part  31  can be regarded as generating an impedance Zi between the first electrode  51  and the second electrode  52  of the probe  5 . As can be seen from  FIG. 14 , the duce impedances Za, Zi, and Zb are connected in series between the first electric wire  101  and the second electric wire  102 . Accordingly, the voltage (potential difference) produced across the impedance Zi is a voltage obtained by dividing the AC power supply voltage applied between the first electric wire  101  and the second electric wire  102 . 
     Since Za≈the capacitance value of the capacitor C 1 , Zb≈the capacitance value of the capacitor C 2 , and Zi≈the capacitance value of the capacitor C 3 , the voltage is substantially a voltage that is divided by the capacitors C 1 , C 21 , and C 3  connected in series. In other words, the input part  31  according to the third embodiment includes a voltage divider circuit. 
     (11-3) Regulator  33   
     The regulator  33  includes a programmable resistor R 3 . The programmable resistor R 3  functions as again resistor that changes the gain of the differential amplifier  32 .  FIG. 13  illustrates  a case where the programmable resistor R 3  is externally attached to the differential amplifier  32 . However, the programmable resistor R 3  functioning as a gain resistor may be incorporated in the differential amplifier  32 . The programmable resistor R 3  has a resistance value that changes in accordance with a fed back signal indicating the magnitude of the output signal SO. 
     (11-4) Feedback Circuit  40   
     The power measurement apparatus  1  includes a feedback circuit  40  that feeds back a signal indicating the magnitude of the output signal SO of the differential amplifier  32  to the regulator  33 . The feedback circuit  40  according to the third embodiment includes a switch  41  and a voltage signal determiner  42 . 
     The switch  41  selectively switches to which of the power computation unit  21  and the voltage signal determiner  42  to provide the digital signal provided from the AD converter  23 . The switch  41  is implemented by the CPU  90 . The CPU  90  executes a program stored in the memory (not illustrated) to form the switch  41 . While a case where the switch  41  is implemented by the CPU  90  is described here as an example, the switch  41  may be disposed as one physical component. 
     The voltage signal determiner  42  is implemented by the CPU  90 . The CPU  90  executes a program stored in the memory (not illustrated) to form the voltage signal determiner  42 . While a case where the voltage signal determiner  42  is implemented by the CPU  90  is described here as an example, the voltage signal determiner  42  may be disposed as one physical component. 
     The voltage signal determiner  42  determines the magnitude of the output signal SO of the differential amplifier  32  before the power computation unit  21  performs power computation. Accordingly, the switch  41  is switched before power computation to provide the digital signal provided from the AD converter  23  to the voltage signal determiner  42 . The voltage signal determiner  42  outputs a signal indicating the magnitude of the output signal SO to the regulator  33  so that the magnitude of the output signal SO can be kept within a predetermined range. When the magnitude of the output signal SO is kept within the predetermined range, the voltage signal determiner  42  switches the switch  41  so that the digital signal provided from the AD converter  23  can be provided to the power computation unit  21 . 
     If the output signal SO is large, the voltage signal determiner  42  outputs a feedback signal for decreasing the gain of the differential amplifier  32  to the programmable resistor R 3 . In other words, the feedback signal for decreasing the gain of the differential amplifier  32  is a signal indicating that the output signal SO is large. If the output signal SO is small, the voltage signal determiner  42  outputs a feedback signal for increasing the gain of the differential amplifier  32  to  the programmable resistor R 3 . In other words, the feedback signal for increasing the gain of the differential amplifier  32  is a signal indicating that the output signal SO is small. 
     (12) Overall Operation 
     For example, when a device such as an air conditioner is connected to the conductive path  100  and is in operation, power is consumed by the device connected to the conductive path  100 . At this time, a current flows through the conductive path  100  in accordance with the power supplied to the device. Since the AC power supply voltage is applied to the conductive path  100 , computation of the power requires not only the values of the voltage and current supplied through the conductive path  100  but also a voltage waveform and a current waveform to compute the power factor. 
     Since the process related to the current by using the contactless current measurement circuit  10  and the power computation circuit  20  is performed by a known method that is conventionally known, a description of the process related to the current will be omitted here. 
     A case where the conductive path  100  is connected to a commercial AC power source of 100 V will be described as an example. In this case, for example, the power computation circuit  20  stores information indicating that the commercial AC power source is 100 V in the memory (not illustrated). The power computation unit  21  determines that the effective value of the AC voltage related to the AC power to be computed is 100 V (an example of the predetermined value) from the storage of the memory. 
     The power computation unit  21  computes the effective value of the AC current from the digital signal related to the AC current provided from the AD converter  22 . 
     The power computation unit  21  computes the power factor from the digital signals related to the AC current and the AC voltage provided from the AD converter  22  and the AD converter  23  by using the AC current waveform and the AC voltage waveform. In this computation, the power computation unit  21  can use an AC voltage waveform obtained from the output signal SO of the differential amplifier  32  whose magnitude is regulated to fall within the predetermined range by the regulator  33 . 
     The power computation unit  21  computes power consumption using the effective value of the AC current and the power factor, which are computed in the way described above, and the stored effective value of the AC voltage. While a description has been given of a case where the power computation unit  21  computes power consumption using the effective value of the AC current, the effective value of the AC voltage, and the power factor, the method for computing power consumption is not limited to such a method. For example, the power computation unit  21   may be configured to compute power consumption from the average of the product of an instantaneous value of the AC current and an instantaneous value of the AC voltage. For example, the configuration of the power computation circuit  20  according to the third embodiment may be the same as the configuration of the power calculator  2  according to the first embodiment. For example, the configuration of the power computation circuit  20  according to the third embodiment may be the same as the configuration of the power calculator  2  according to the second embodiment. 
     (13) Modifications 
     (13-1) Modification 3A 
     In the third embodiment, a description has been given of a case where the power measurement apparatus  1  has a configuration in which a period during which the feedback circuit  40  generates a signal to be fed back and a period during which the power computation unit  21  computes power are separate. However, as illustrated in  FIG. 15 , the power measurement apparatus  1  may be configured such that the power computation unit  21  computes power while the feedback circuit  40  generates a signal to be fed back. 
     The feedback circuit  40  illustrated in  FIG. 15  includes, for example, a microprocessing unit (MPU)  43 . The MPU  43  receives a digital signal indicating an AC voltage output from the AD converter  23 . The MPU  43  calculates the magnitude of the output signal SO of the differential amplifier  32  from the digital signal of the AD converter  23 , and determines a gain resistance that can keep the output signal SO within a predetermined range. The MPU  43  outputs a control signal for changing the gain resistance to a determined value to the programmable resistor R 3 . 
     (13-2) Modification 3B 
     In the third embodiment, a description has been given of a case where the regulator  33  that regulates the gain of the differential amplifier  32  is the programmable resistor R 3 . However, the method for regulating the gain of the differential amplifier  32  is not limited to changing a resistance value determining the gain. For example, a programmable gain amplifier having an integration of the functions of a regulator and a differential amplifier may be used. Further, the differential amplifier having an integration of the functions of a regulator and a differential amplifier may be, for example, a differential amplifier whose gain is changed in accordance with the magnitude of a voltage provided from the outside. 
     Fourth Embodiment 
     (14) Overall Configuration 
     A power measurement apparatus  1  according to a fourth embodiment is different from the  power measurement apparatus  1  according to the third embodiment in the configuration of the contactless voltage measurement circuit  30  and the regulator  33 . Thus, the power measurement apparatus  1  and the contactless voltage measurement circuit  30  according to the fourth embodiment will be described focusing on the modified points of the contactless voltage measurement circuit  30  and the regulator  33 , whereas the description of the other portions will be omitted. 
     The regulator  33  according to the fourth embodiment illustrated in  FIG. 16  regulates the magnitude of the input signal SI produced by the input part  31  on the basis of the magnitude of the output signal SO of the differential amplifier  32  to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     (15) Detailed Configuration 
     (15-1) Input Part  31   
     As illustrated in  FIG. 16 , the input part  31  according to the fourth embodiment includes a programmable capacitor C 4  and resistors R 1  and R 2 . One end of the programmable capacitor C 4  is connected to the first electrode  51  of the probe  5 , and the other end of the programmable capacitor C 4  is connected to the second electrode  52  of the probe  5 . One end of the resistor R 1  is connected to the first electrode  51 , and the other end is grounded. One end of the resistor R 2  is connected to the second electrode  52 , and the other end is grounded. Further, the one end of the resistor R 1  is connected to one input terminal of the differential amplifier  32 , and the one end of the resistor R 2  is connected to the other input terminal of the differential amplifier  32 . The potential difference between the potential at the one end of the resistor R 1  and the potential at the one end of the resistor R 2  is amplified by the differential amplifier  32 . The potential difference between the potential at the one end of the resistor RI and the potential at the one end of the resistor R 2  is the input signal SI. 
     As illustrated in  FIG. 14 , the input part  31  can be regarded as generating an impedance Zi between the first electrode  51  and the second electrode  52  of the probe  5 . As can be seen from  FIG. 14 , the three impedances Za, Zi, and Zb are connected in series between the first electric wire  101  and the second electric wire  102 . Accordingly, the voltage (potential difference) produced across the impedance Zi is a voltage obtained by dividing the AC power supply voltage applied between the first electric wire  101  and the second electric wire  102 . 
     Since Za≈the capacitance value of the capacitor C 1 , Zb≈the capacitance value of the capacitor C 2 , and Zi≈the capacitance value of the programmable capacitor C 4 , the voltage is substantially a voltage that is divided by these three capacitors connected in series. In other words,  the input part  31  according to the fourth embodiment includes a voltage divider circuit. 
     (15-2) Differential Amplifier  32   
     A resistor R 4  that determines the gain of the differential amplifier  32  according to the fourth embodiment is a fixed resistor whose resistance value is not changeable. 
     (15-3) Regulator  33   
     As illustrated in  FIG. 16 , the regulator  33  according to the fourth embodiment includes the programmable capacitor C 4 . The programmable capacitor C 4  is a variable capacitor. The programmable capacitor C 4  functions as a variable capacitor that regulates the magnitude of the input signal SI produced by the input part  31 . The programmable capacitor C 4  has a capacitance value that changes in accordance with a fed back signal indicating the magnitude of the output signal SO. 
     The programmable capacitor C 4  is preferably configured such that the magnitude of the output signal SO of the differential amplifier  32  obtained when the capacitance is regulated to the minimum is allowed to be smaller than one half of the magnitude of the output signal SO of the differential amplifier obtained when the capacitance is regulated to the maximum. 
     (15-4) Feedback Circuit  40   
     The voltage signal determiner  42  outputs a signal indicating the magnitude of the output signal SO to the regulator  33  so that the magnitude of the output signal SO can be kept within a predetermined range. If the output signal SO is large, the voltage signal determiner  42  outputs a feedback signal for decreasing the input signal SI of the differential amplifier  32  to the programmable capacitor C 4 . In other words, the feedback signal for decreasing the input signal SI is a signal indicating that the output signal SO is large. If the output signal SO is small, the voltage signal determiner  42  outputs a feedback signal for increasing the input signal SI to the programmable capacitor C 4 . In other words, the feedback signal for increasing the input signal SI is a signal indicating that the output signal SO is small. 
     (16) Modifications 
     (16-1) Modification 4A 
     Also in the power measurement apparatus  1  according to the fourth embodiment, as in the power measurement apparatus  1  according to Modification 3A, the feedback circuit  40  can be modified such that the MPU  43  illustrated in  FIG. 15  is used. 
     (16-2) Modification 4B 
     In the power measurement apparatus  1  and the contactless voltage measurement circuit  30  according to the fourth embodiment, the regulator  33  is configured using the programmable  capacitor C 4 . However, the regulator  33  for controlling the magnitude of the input signal SI produced by the input part  31  is not limited to that having a configuration using a variable capacitor (the programmable capacitor C 4 ). 
     For example, as illustrated in  FIG. 17 , a variable resistor R 5  may be used in place of the variable capacitor C 4  in  FIG. 16 . One end of the variable resistor R 5  is connected to the first electrode  51  of the probe  5 , and the other end of the variable resistor R 5  is connected to the second electrode  52  of the probe  5 , The variable resistor R 5  is, for example, a programmable resistor. The regulator  33  can regulate the magnitude of the input signal SI produced by the input part  31  by changing the resistance value of the variable resistor R 5 . 
     Fifth Embodiment 
     (17) Overall Configuration 
     A power measurement apparatus  1  according to a fifth embodiment is different from the power measurement apparatus  1  according to the third embodiment in the configuration of the contactless voltage measurement circuit  30  and the regulator  33 . Thus, the power measurement apparatus  1  and the contactless voltage measurement circuit  30  according to the fifth embodiment will be described focusing on the modified points of the contactless voltage measurement circuit  30  and the regulator  33 . whereas the description of the other portions will be omitted. 
     The regulator  33  according to the fifth embodiment illustrated in  FIG. 18  regulates the gain of the differential amplifier  32  and the magnitude of the input signal SI produced by the input part  31  on the basis of the magnitude of the output signal SO of the differential amplifier  32  to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     (18) Detailed Configuration 
     (18-1) Input Part  31   
     As illustrated in  FIG. 18 , like the input part  31  according to the fourth embodiment, the input part  31  according to the fifth embodiment includes a programmable capacitor C 4  and resistors R 1  and R 2 . 
     (18-2) Differential Amplifier  32   
     As in the third embodiment, the differential amplifier  32  according to the fifth embodiment is configured such that the gain can be changed by the programmable resistor R 3 , The input signal SI produced by the input part  31  is input to the differential amplifier  32 . The differential amplifier  32  amplifies the input signal SI and outputs an output signal SO. The differential amplifier  32  outputs the output signal SO to the power computation circuit  20 .  
     (18-3) Regulator  33   
     As illustrated in  FIG. 18 , the regulator  33  according to the fifth embodiment is constituted by the programmable resistor R 3  and the programmable capacitor C 4 . 
     The programmable resistor R 3  and the programmable capacitor C 4  are preferably configured such that the magnitude of the output signal SO of the differential amplifier  32  obtained when the resistance value and the capacitance are regulated to the minimum is allowed to be smaller than one half of the magnitude of the output signal SO of the differential amplifier obtained when the resistance value and the capacitance are regulated to the maximum. 
     (18-4) Feedback Circuit  40   
     The voltage signal determiner  42  outputs a signal indicating the magnitude of the output signal SO to the regulator  33  so that the magnitude of the output signal SO can be kept within a predetermined range. If the output signal SO is lame, the voltage signal determiner  42  outputs a feedback signal to the programmable resistor R 3  and the programmable capacitor C 4  to decrease the input signal SI of the differential amplifier  32 . If the output signal SO is small, the voltage signal determiner  42  outputs a feedback signal to the programmable resistor R 3  and the programmable capacitor C 4  to increase the input signal SI. 
     (19) Modifications 
     (19-1) Modification 5A 
     Also in the power measurement apparatus  1  according to the fifth embodiment, as in the power measurement apparatus  1  according to Modification 3A, the feedback circuit  40  can be modified such that the MPU  43  illustrated in  FIG. 15  is used. 
     (19-2) Modification 5B 
     In the power measurement apparatus  1  and the contactless voltage measurement circuit  30  according to the fifth embodiment, the regulator  33  is configured using the programmable resistor R 3  and the programmable capacitor C 4 . However, the regulator  33  for controlling the magnitude of the input signal SI produced by the input part  31  is not limited to that having a configuration using the programmable resistor R 3  and the programmable capacitor C 4 . 
     For example, as in the power measurement apparatus  1  according to Modification 4B, as illustrated in  FIG. 17 , the regulator  33  may be configured by using the variable resistor R 5  as a resistor of the input part  31  according to the fifth embodiment. 
     (20) Features 
     (20-1) 
     In the contactless voltage measurement circuit  30  according to the embodiments and the  modifications described above, the impedance generated between the electrode  50  of the probe  5  and the conductive path  100  may greatly change with a change in surrounding environment. More specifically, the impedance Za (an example of a first impedance) between the first electrode  51  and the first electric wire  101  and the impedance Zb (an example of a second impedance) between the second electrode  52  and the second electric wire  102 , illustrated in  FIG. 14 , may greatly change with a change in surrounding environment. 
     If the impedance generated between the electrode  50  and the conductive path  100  greatly changes, the input signal SI to be input to the differential amplifier  32  greatly changes. However, the regulator  33  can regulate the gain of the differential amplifier  32  to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range, for example, within the range of 80%+5%. As a result, the resolution of the voltage waveform obtained by the power computation unit  21  from the differential amplifier  32  can be maintained within an appropriate range. As described above, even if the impedance between the electrode  50  of the probe  5  and the conductive path  100  changes depending on the surrounding environment, the contactless voltage measurement circuit  30  can suppress a decrease in the resolution of the voltage waveform of the AC power supply voltage to be measured. In this manner, since a decrease in the resolution of the voltage waveform of the AC power supply voltage to be measured by the contactless voltage measurement circuit  30  is suppressed, the power measurement apparatus  1  can accurately measure power. 
     (20-2) 
     The regulator  33  is preferably configured such that the magnitude of the output signal SO of the differential amplifier  32  obtained when the gain is regulated to the minimum is allowed to be smaller than one half of the magnitude of the output signal SO of the differential amplifier  32  obtained when the gain is regulated to the maximum. With such a configuration, even in a case where the input signal SI of the differential amplifier  32  greatly changes by a factor of two or more in response to a change in surrounding environment, the regulator  33  can keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     (20-3) 
     In the contactless voltage measurement circuit  30  according to the third embodiment, the regulator  33  is constituted by the programmable resistor R 3 . The programmable resistor R 3  changes a resistance value determining the gain of the differential amplifier  32  on the basis of the magnitude of the output signal SO of the differential amplifier  32 . Accordingly, the programmable resistor R 3  is configured such that a signal relating to the magnitude of the output  signal SO is fed back to the programmable resistor R 3  from the feedback circuit  40 . With the use of the programmable resistor R 3 , the contactless voltage measurement circuit  30  can easily perform control to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     (20-4) 
     In the contactless voltage measurement circuit  30  according to the fourth embodiment, the regulator  33  is constituted by the programmable capacitor C 4 . The programmable capacitor C 4  is a variable capacitor that changes a capacitance value determining the magnitude of the input signal SI of the input part  31  on the basis of the magnitude of the output signal SO of the differential amplifier  32 . Accordingly, the programmable capacitor C 4  is configured such that a signal relating to the magnitude of the output signal SO is fed back to the programmable capacitor C 4  from the feedback circuit  40 . With the use of the programmable capacitor C 4 . the contactless voltage measurement circuit  30  can easily perform control to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     (20-5) 
     In the contactless voltage measurement circuit  30  according to the fifth embodiment, the regulator  33  is constituted by the programmable resistor R 3  and the programmable capacitor C 4 , The programmable resistor R 3  and the programmable capacitor C 4  are a variable resistor and a variable capacitor that change a resistance value determining the gain of the differential amplifier  32  and a capacitance value determining the magnitude of the input signal SI of the input part  31  on the basis of the magnitude of the output signal SO of the differential amplifier  32 . Accordingly, the programmable resistor R 3  and the programmable capacitor C 4  are configured such that a signal relating to the magnitude of the output signal SO is fed back to the programmable resistor R 3  and the programmable capacitor C 4  from the feedback circuit  40 . With the use of the programmable resistor R 3  and the programmable capacitor C 4 , the contactless voltage measurement circuit  30  can easily perform control to keep the magnitude of the output signal SO of the differential amplifier  32  within a predetermined range. 
     While embodiments of the present disclosure have been described, it will be understood that forms and details can be changed in various ways without departing from the spirit and scope of the present disclosure as recited in the claims.