Patent Publication Number: US-11022630-B2

Title: Measurement of current within a conductor

Description:
FIELD OF INVENTION 
     This invention relates to an electrical interface for connection to a Rogowski coil that is arranged around a primary conductor. 
     BACKGROUND OF THE DISCLOSURE 
     A Rogowski coil  10  is an electrical device for measuring alternating current (AC). As shown in  FIG. 1 , it consists of a helical coil  12  of wire  14  which is wrapped around a primary conductor  16  whose current, i.e. primary current i p , is to be measured. The coil  12  is mutually coupled with the primary conductor  16  via air, and so the absence of an iron core means that no saturation of the coil  12  will occur, irrespective of the level of current flowing through the primary conductor  16 . 
     The voltage induced in the coil  12  is proportional to the rate of change, i.e. the derivative, of the primary current i p  flowing through the primary conductor  16 . The output of the Rogowski coil  10  can therefore be connected to an electrical or electronic integrator to provide an output signal that is proportional to the primary current i p . 
     BRIEF SUMMARY 
     According to an aspect of the invention there is provided an electrical interface, for connection to a Rogowski coil arranged around a primary conductor, including: 
     a. an input configured to sample an input voltage signal from the Rogowski coil; and 
     b. an integrator circuit including an integrator module configured to integrate the sampled input voltage signal to provide an output voltage signal from which can be derived a primary current flowing through the primary conductor, the integrator module employing a transfer function that includes an attenuation factor. 
     The inclusion within the integrator circuit of an integrator module which employs a transfer function that includes an attenuation factor desirably maintains stability of the operation of the integrator module without unduly impacting on its accuracy, particularly at very high sampling frequencies, e.g. many tens of thousands of samples per second. 
     The attenuation factor gives rise to an error in the derived primary current flowing through the primary conductor that is not greater than a predetermined percentage selected according to the nature of the primary current (i p ) flowing through the primary conductor ( 16 ). 
     The percentage error in the derived primary current (i p (n)) may be selected to be:
         not greater than 10% when the primary current (i p ) is decaying; and   not greater than 0.3% when the primary current (i p ) is in steady state.       

     Such features limit the size of the attenuation factor to a level which provides for an acceptable overall degree of accuracy for the integrator circuit, particularly at very high sampling frequencies (i.e. typically many thousands of samples per second), without sacrificing the stability of operation of the integrator module therein. 
     Optionally the integrator module employs a transfer function which additionally down-samples a previous output voltage signal. 
     Down-sampling only a previous output voltage signal, i.e. a feedback output voltage signal, helps to reduce distortion in a subsequent output voltage signal (which might otherwise arise because of the integrator module becoming saturated) without affecting the sampling frequency at which the input operates, which as indicated above may be many tens of thousands of samples per second. 
     The integrator module may be or include one or more of:
         a first rectangular integrator embodying a transfer function in the discrete time domain of the form       

     
       
         
           
             
               
                 H 
                 ⁡ 
                 
                   ( 
                   z 
                   ) 
                 
               
               = 
               
                 1 
                 
                   1 
                   - 
                   
                     
                       e 
                       
                         
                           - 
                           
                             AT 
                             s 
                           
                         
                         ⁢ 
                         
                           N 
                           d 
                         
                       
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         
                           N 
                           d 
                         
                       
                     
                   
                 
               
             
             ; 
           
         
       
         
         
           
             a second rectangular integrator embodying a transfer function in the discrete time domain of the form 
           
         
       
    
     
       
         
           
             
               
                 H 
                 ⁡ 
                 
                   ( 
                   z 
                   ) 
                 
               
               = 
               
                 
                   1 
                   
                     N 
                     d 
                   
                 
                 ⁢ 
                 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       
                         N 
                         d 
                       
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         k 
                       
                     
                   
                   
                     1 
                     - 
                     
                       
                         e 
                         
                           
                             - 
                             
                               AT 
                               s 
                             
                           
                           ⁢ 
                           
                             N 
                             d 
                           
                         
                       
                       ⁢ 
                       
                         z 
                         
                           - 
                           
                             N 
                             d 
                           
                         
                       
                     
                   
                 
               
             
             ; 
           
         
       
         
         
           
             a trapezoidal integrator embodying a transfer function in the discrete time domain of the form 
           
         
       
    
                 H   ⁡     (   z   )       =       1     N   d       ⁢           ∑     k   =   0       N   d       ⁢     z     -   k         -     1   2     -       1   2     ⁢     z     -     N   d               1   -       e       -     AT   s       ⁢     N   d         ⁢     z     -     N   d                   ;         
and
         a Taylor&#39;s approximation integrator embodying a transfer function in the discrete time domain of the form       

                 H   ⁡     (   z   )       =       1   6     ⁢     {       1   +     4   ⁢     z       -     N   d       /   2         +     z     -     N   d             1   -       e       -     AT   s       ⁢     N   d         ⁢     z     -     N   d               }         ,         
where,
 
     a. A is the attenuation factor; 
     b. T s  is a sampling period of the input voltage signal; and 
     c. N d  is a down-sampling scale. 
     Each of the foregoing integrators provides a desired degree of accuracy, particularly at high sampling frequencies, e.g. typically of many thousands per second, while maintaining their operational stability. 
     In an embodiment of the invention the integrator circuit additionally includes at least one averaging module arranged in communication with the output of the integrator module, the or each averaging module being configured to calculate an average output voltage signal over one or more operating cycles of an electrical system of which the primary conductor forms a part and to subtract the said calculated average output voltage from the output voltage signal provided by the integrator module to establish a corrected output voltage signal. 
     The inclusion of one or more such averaging modules removes low frequency noise from the output voltage signal provided by the integrator module as well as any inherent DC voltage offset in the input voltage signal when sampling begins. 
     In an embodiment of the invention the integrator circuit further includes a disturbance detector configured to detect a disturbance in the current flowing through the primary conductor and thereafter suspend operation of the or each averaging module while the disturbance remains. 
     The inclusion of a disturbance detector, and more particularly suspending operation of the or each averaging module if there is a disturbance in the primary conductor, helps to ensure that the previous output voltage signal from the integrator module is maintained and so the accuracy with which any DC voltage offset is removed from the output voltage signal is unaffected by the disturbance and so is similarly maintained. 
     Optionally the disturbance detector is configured to determine the absolute value of the sampled input voltage signal and to detect a disturbance in the current flowing through the primary conductor when the absolute value of the sampled input voltage signal exceeds a predetermined threshold. 
     Such an arrangement readily and reliably implements the detection of a rise in the current flowing in the primary conductor, and hence facilitates the desired detection of a disturbance in the primary conductor. 
     The integrator circuit still further includes a reconstruction module which is configured to derive the primary current flowing through the primary conductor by multiplying the corrected output voltage signal by a gain factor. 
     The inclusion of such a reconstruction module desirably permits the integrator circuit to output a primary current value corresponding to the level of current flowing through the primary conductor that can be used, e.g. in other control or monitoring operations associated with the primary conductor. 
     The reconstruction module may also be configured to modify the corrected output voltage signal to compensate for errors arising from the attenuation factor. 
     Optionally the reconstruction module carries out one or more of phase compensation and steady state input signal compensation. 
     The foregoing features help to further maintain the accuracy of the derived primary current. 
     In a still further embodiment of the invention the reconstruction module is also configured to modify the gain factor according to a measured temperature of the electrical interface. 
     Such a reconstruction module usefully helps the integrator circuit to indicate actual changes in the derived primary current which might otherwise be masked by temperature changes in or adjacent to the electrical interface. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       There now follows a brief description of embodiments of the invention, by way of non-limiting example, with reference being made to the following figures in which: 
         FIG. 1  shows a schematic view of a conventional Rogowski coil arranged around a primary conductor; and 
         FIG. 2  shows a schematic view of an electrical interface according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     An electrical interface according to a first embodiment of the invention is designated generally by reference numeral  30 , as shown in  FIG. 2 . 
     The electrical interface  30  includes an input  32  which is configured to sample an input voltage signal u s (n) from a Rogowski coil  10  that is arranged around a primary conductor  16 . 
     The input  32  operates at a very high sampling frequency, which is typically many tens of thousands of samples per second and may, for example, be 64,800 Hz which gives a sampling period T s  of 1/64800 seconds, i.e. 0.0000155 seconds. 
     The electrical interface  30  also includes an integrator circuit  34  which, in turn, includes an integrator module  36  that in the embodiment shown is a digital integrator module  36 , i.e. is an integrator module which operates in the discrete time, or digital domain. 
     The integrator module  36  is configured to integrate the sampled input voltage signal u s (n) to provide an output signal u INT (n) from which can be derived the primary current i p (n) flowing through a primary conductor  16  around which an associated Rogowski coil  10  is, in use, arranged. 
     The integrator module  36  employs a transfer function that includes an attenuation factor A. The attenuation factor A is chosen such that the error in the derived primary current i p (n) flowing through the primary conductor  16  is not greater than a predetermined percentage which is selected according to the nature of the primary current i p  flowing through the primary conductor  16 . 
     For example, in circumstances when the primary current i p  is decaying then the percentage error is selected to be not more than 10%. When the primary current i p  is in steady state, i.e. neither increasing nor decreasing, then the percentage error in the derived primary current i p (n) is selected to be not more than 0.3%. 
     The integrator module  36  also employs a transfer function which additionally down-samples a previous output voltage signal u INT (n), i.e. a feedback output voltage signal as part of its operation. 
     More particularly, in the embodiment shown the integrator module  36  adopts a rectangular approximation of the required integration as set out in the following frequency expression:
 
 u   INT ( n )= K   1   u   INT ( n−N   d )+ u   s ( n )
 
     where, 
     u INT (n) is the output voltage signal generated by the integrator module  36 ; 
     u s (n) is the sampled input voltage signal from the associated Rogowski coil  10 ; 
     N d  is the down-sampling scale which, by way of example, is 16; 
     T s  is the sampling period of the input voltage signal u s (n) which, for an exemplary sampling frequency of 64,800 Hz is given by 1/64,800, i.e. 0.00000155 seconds; and 
     K 1  is given by
 
 K   1   =e   −AN     d     T     s    
 
     with, 
     A being the attenuation factor which, by way of example, is 0.5. 
     Other values for the down-sampling scale N d , sampling period T s , and attenuation factor A, may be used in other embodiments of the invention. 
     In view of the above-mentioned frequency expression, the integrator module  36  can be said to define a rectangular integrator that embodies a transfer function in the discrete time domain of the form 
     
       
         
           
             
               H 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               1 
               
                 1 
                 - 
                 
                   
                     e 
                     
                       
                         - 
                         
                           AT 
                           s 
                         
                       
                       ⁢ 
                       
                         N 
                         d 
                       
                     
                   
                   ⁢ 
                   
                     z 
                     
                       - 
                       
                         N 
                         d 
                       
                     
                   
                 
               
             
           
         
       
     
     Accordingly, utilising the example values indicated above, the maximum output of the transfer function will be 
     
       
         
           
             
               1 
               
                 1 
                 - 
                 
                   e 
                   
                     
                       - 
                       0.5 
                     
                     * 
                     16 
                     * 
                     0.0000155 
                   
                 
               
             
             = 
             
               8 
               , 
               100 
             
           
         
       
     
     This compares to a maximum output of 129,600 for a conventional integrator which omits both an attenuation factor and the down-sampling of a previous output voltage signal. Such a large potential maximum output, which is an order of magnitude greater than that achieved by the first embodiment of the invention, means that the conventional integrator will very quickly magnify any error in the sampled input voltage signal, particularly at very high sampling frequencies (i.e. many tens of thousands of samples per second), and will therefore become saturated. As a consequence the accuracy of the output of such a conventional integrator is also lost. 
     In the meantime, an attenuation factor of 0.5 means that a DC offset in the sampled input voltage signal u s (n) with a decaying time constant of 275 milliseconds results in an error in the derived primary current i p (n) that is less than 10%. 
     In other embodiments of the invention (not shown) the integrator module  36  may adopt a more accurate trapezoidal approximation of the required integration, e.g. as set out in the following frequency expression: 
     
       
         
           
             
               
                 u 
                 INT 
               
               ⁡ 
               
                 ( 
                 n 
                 ) 
               
             
             = 
             
               
                 
                   K 
                   I 
                 
                 ⁢ 
                 
                   
                     u 
                     INT 
                   
                   ⁡ 
                   
                     ( 
                     
                       n 
                       - 
                       
                         N 
                         d 
                       
                     
                     ) 
                   
                 
               
               + 
               
                 
                   { 
                   
                     
                       
                         
                           u 
                           s 
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       2 
                     
                     + 
                     
                       
                         
                           u 
                           s 
                         
                         ⁡ 
                         
                           ( 
                           
                             n 
                             - 
                             
                               N 
                               d 
                             
                           
                           ) 
                         
                       
                       2 
                     
                     + 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             n 
                             - 
                             
                               N 
                               d 
                             
                           
                         
                         n 
                       
                       ⁢ 
                       
                         
                           u 
                           s 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   } 
                 
                 / 
                 
                   N 
                   d 
                 
               
             
           
         
       
     
     Such an integrator module  36  therefore defines a trapezoidal integrator which embodies a transfer function in the discrete time domain of the form 
     
       
         
           
             
               H 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   N 
                   d 
                 
               
               ⁢ 
               
                 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       
                         N 
                         d 
                       
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         k 
                       
                     
                   
                   - 
                   
                     1 
                     2 
                   
                   - 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         
                           N 
                           d 
                         
                       
                     
                   
                 
                 
                   1 
                   - 
                   
                     
                       e 
                       
                         
                           - 
                           
                             AT 
                             s 
                           
                         
                         ⁢ 
                         
                           N 
                           d 
                         
                       
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         
                           N 
                           d 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The integrator module  36  may also adopt a Taylor&#39;s approximation of the required integration, e.g. as set out in the following frequency expression:
 
 u   INT ( n )= K   1   u   INT ( n−N   d )+{ u   S ( n )+ 4   u   S ( n−N   d /2)+ u   S ( n−N   d )}/6
 
     Such an integrator module  36  therefore defines a Taylor&#39;s approximation integrator which embodies a transfer function in the discrete time domain of the form 
     
       
         
           
             
               H 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               
                 1 
                 6 
               
               ⁢ 
               
                 { 
                 
                   
                     1 
                     + 
                     
                       4 
                       ⁢ 
                       
                         z 
                         
                           
                             - 
                             
                               N 
                               d 
                             
                           
                           / 
                           2 
                         
                       
                     
                     + 
                     
                       z 
                       
                         - 
                         
                           N 
                           d 
                         
                       
                     
                   
                   
                     1 
                     - 
                     
                       
                         e 
                         
                           
                             - 
                             
                               AT 
                               s 
                             
                           
                           ⁢ 
                           
                             N 
                             d 
                           
                         
                       
                       ⁢ 
                       
                         z 
                         
                           - 
                           
                             N 
                             d 
                           
                         
                       
                     
                   
                 
                 } 
               
             
           
         
       
     
     In still further embodiments of the invention the integrator module could define a second rectangular integrator (which is more accurate than the first rectangular integrator mentioned hereinabove) that embodies a transfer function in the discrete time domain of the form 
     
       
         
           
             
               H 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   N 
                   d 
                 
               
               ⁢ 
               
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       0 
                     
                     
                       N 
                       d 
                     
                   
                   ⁢ 
                   
                     z 
                     
                       - 
                       k 
                     
                   
                 
                 
                   1 
                   - 
                   
                     
                       e 
                       
                         
                           - 
                           
                             AT 
                             s 
                           
                         
                         ⁢ 
                         
                           N 
                           d 
                         
                       
                     
                     ⁢ 
                     
                       z 
                       
                         - 
                         
                           N 
                           d 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     Returning to the embodiment shown in  FIG. 2 , the integrator circuit  34  also includes first and second averaging modules  38 ,  40 . The first averaging module  38  is arranged in direct communication with the output of the integrator module  36 , and the second averaging module  40  is arranged in communication with the integrator module  36  via the first averaging module  38 . 
     Each averaging module  38 ,  40  is configured to calculate an average output voltage signal over one operating cycle of an electrical system of which the primary conductor  16  forms a part, and to subtract the calculated average output voltage from the output voltage signal u INT (n) provided by the integrator module  36  to establish a corrected output voltage signal u pp (n). 
     More particularly, the first averaging module  38  subtracts the calculated average output voltage directly from the output voltage signal u INT (n) provided by the integrator module  36  and the second averaging module  40  subtracts the calculated average voltage from the modified output of the first averaging module  38  to establish the corrected output voltage signal u pp (n). 
     In other embodiments of the invention the integrator circuit may include fewer than or more than two series-connected averaging modules. One or more of the averaging modules may also calculate an average output voltage over more than one operating cycle of the electrical system of which the primary conductor forms a part. 
     By way of example one or more of the averaging modules  38 ,  40  may employ a first method of calculating the average output voltage according to 
     
       
         
           
             
               y 
               ⁡ 
               
                 ( 
                 n 
                 ) 
               
             
             = 
             
               
                 1 
                 N 
               
               ⁢ 
               
                 
                   ∑ 
                   
                     k 
                     = 
                     
                       n 
                       - 
                       N 
                       + 
                       1 
                     
                   
                   n 
                 
                 ⁢ 
                 
                   x 
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
               
             
           
         
       
     
     where, 
     y(n) is the calculated average voltage; and 
     N is the number of samples per cycle of fundamental frequency f 0  of the electrical system of which the primary conductor  16  forms a part, with N being given by 
     
       
         
           
             N 
             = 
             
               1 
               
                 
                   T 
                   s 
                 
                 × 
                 
                   f 
                   0 
                 
               
             
           
         
       
     
     which, using the example values set out above and a fundamental frequency f 0  of 50 Hz, gives 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     = 
                       
                     ⁢ 
                     
                       64800 
                       50 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   1296 
                 
               
             
           
         
       
     
     One or more of the averaging modules  38 ,  40  may also employ a second method of calculating the average output voltage according to 
     
       
         
           
             
               y 
               ⁡ 
               
                 ( 
                 n 
                 ) 
               
             
             = 
             
               
                 y 
                 ⁡ 
                 
                   ( 
                   
                     n 
                     - 
                     1 
                   
                   ) 
                 
               
               + 
               
                 
                   x 
                   ⁡ 
                   
                     ( 
                     n 
                     ) 
                   
                 
                 N 
               
               - 
               
                 
                   x 
                   ⁡ 
                   
                     ( 
                     
                       n 
                       - 
                       N 
                     
                     ) 
                   
                 
                 N 
               
             
           
         
       
     
     where N is again given by 
     
       
         
           
             N 
             = 
             
               1 
               
                 
                   T 
                   s 
                 
                 × 
                 
                   f 
                   0 
                 
               
             
           
         
       
     
     One or more of the averaging modules  38 ,  40  might still further employ a third method of calculating the average output voltage according to 
     
       
         
           
             
               y 
               ⁡ 
               
                 ( 
                 n 
                 ) 
               
             
             = 
             
               
                 
                   h 
                   ⁡ 
                   
                     ( 
                     n 
                     ) 
                   
                 
                 - 
                 
                   h 
                   ⁡ 
                   
                     ( 
                     
                       n 
                       - 
                       N 
                     
                     ) 
                   
                 
               
               N 
             
           
         
       
     
     where,
 
 h ( n )= h ( n− 1)+ x ( n ); and
 
     N is given by 
     
       
         
           
             
               
                 
                   N 
                   = 
                     
                   ⁢ 
                   
                     1 
                     
                       
                         T 
                         s 
                       
                       × 
                       
                         f 
                         0 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   1296 
                 
               
             
           
         
       
     
     In addition to the foregoing the integrator circuit  34  also includes a disturbance detector  42  that is configured to detect a disturbance in the current flowing through the primary conductor  16  and thereafter suspend operation of the first and second averaging modules  38 ,  40  while the disturbance remains. 
     Such suspension of the operation of the first and second averaging modules  38 ,  40  means that neither subtracts the calculated average voltage signal from the output voltage signal u INT (n) generated by the integrator module  36 , and so the extent to which any DC voltage offset is removed from the output voltage signal u INT (n) is frozen, and thereby is unaffected by the disturbance. 
     The disturbance detector  42  detects a disturbance in the current flowing through the primary conductor  16  by determining the absolute value of the sampled input voltage signal u s (n), e.g. the maximum absolute value of the sampled input voltage signal u s (n) over the previous operating cycle of the electrical system of which the primary conductor  16  forms a part, and establishing that a rise in current has occurred (which is indicative of there being a disturbance in the current flowing in the primary conductor  16 ) when the absolute value of the sample input voltage exceeds a predetermined threshold. 
     The integrator circuit  34  also includes a reconstruction module  44  which is configured to derive the primary current i p (n) flowing in the primary conductor  16  by multiplying the corrected output voltage signal u pp (n), i.e. as output by the second averaging module  40 , by a gain factor K L (T c ). 
     The reconstruction module  44  also, first of all, modifies the corrected output voltage u pp (n) to compensate for errors arising from the attenuation factor A. 
     More particularly, the reconstruction module  44  carries out phase compensation N comp  and steady state input signal compensation A comp  to produce a modified corrected output voltage signal i pp (n) according to
 
 i   PP ( n )= A   comp   u   PP ( n−N   comp )
 
     where, 
     N comp  is the number of samples for phase compensation and is given by 
                 N   comp     =     floor   ⁡     (         π   /   2     -     arctan   ⁡     (       ω   0     /   A     )             ω   0     ⁢     T   s         )         ;         
and
 
     A comp  is the compensation value for the steady state input signal which is given by 
               A   comp     =       N   d     ⁢     ω   0     ⁢     T   s     ⁢       1   +       (     A     ω   0       )     2                 
with,
 
     ω 0  being the angular frequency of the associated electrical system of which the primary conductor  16  is a part, which is given by ω 0 =2πf 0  (with f 0  being the fundamental frequency of the associated electrical system which, as given above by way of example is 50 Hz, but might also be 60 Hz). 
     Thereafter the reconstruction module  44  derives the primary current i p (n) flowing in the primary conductor  16  by multiplying the modified corrected output voltage signal i pp (n) according to the following
 
 i   P ( n )= K   L ( T   c ) i   PP ( n )
 
     where, 
     K L (T c ) is the gain factor which is given by
 
 K   L ( T   c )= K   0 +α( T−T   0 )+β( T−T   0 ) 2  
 
with,
 
     K 0  being 1/L Rogow  which is a characteristic of the Rogowski coil  10  that is determined under laboratory conditions at a standard temperature T 0  of 20° C.; 
     α and β being temperature dependent coefficients; and 
     T being a measured temperature of the electrical interface  30 .