JP4665875B2 - measuring device - Google Patents

Description

  The present invention relates to a measuring apparatus that measures voltage, current, power, and the like.

  Conventionally, measuring devices for measuring voltage, current, power, and the like have been used. For example, in an integrating wattmeter that obtains an integrated value of instantaneous power by multiplying an alternating voltage and an alternating current, an integrated power meter that obtains an integrated power value every predetermined unit time has been proposed (for example, see Patent Document 1). . In this integrating wattmeter, the data update cycle is set regardless of the cycle of the AC voltage or AC current.

FIG. 14 shows a basic configuration of a conventional measuring apparatus 100.
As shown in FIG. 14, the measuring apparatus 100 includes a voltage input terminal 111, a voltage input circuit 112, an A / D converter 113, a zero-cross data generation unit 114, a current input terminal 115, a current input circuit 116, and an A / D converter. 117, zero cross data generation unit 118, external signal input terminal 121, external signal zero cross data generation unit 122, selector 130, DSP (Digital Signal Processor) 140, CPU (Central Processing Unit) 150, display 160, data update cycle setting unit 170.

  The voltage input circuit 112 normalizes the voltage signal input from the voltage input terminal 111 with an operational amplifier. The A / D converter 113 A / D converts the signal normalized by the voltage input circuit 112 at a predetermined sampling period, and outputs an instantaneous voltage value to the DSP 140. The zero-cross data generation unit 114 binarizes the voltage signal value based on whether the voltage signal value is positive, such as “1” if the voltage signal value is positive and “0” if the voltage signal value is negative. Generated zero-cross data.

  The current input circuit 116 normalizes the current signal input from the current input terminal 115 with an operational amplifier. The A / D converter 117 performs A / D conversion on the signal normalized by the current input circuit 116 at a predetermined sampling period, and outputs an instantaneous current value to the DSP 140. The zero-cross data generation unit 118 binarizes the current signal value based on whether the current signal value is positive, such as “1” if the current signal value is positive and “0” if the current signal value is negative. Generated zero-cross data.

  The external signal zero-cross data generation unit 122 generates zero-cross data obtained by binarizing the external signal value based on the sign of the external signal value (voltage signal value) input from the external signal input terminal 121.

  The selector 130 selects any one of the voltage signal or current signal to be measured or the external signal set by the user as a synchronization signal, and the zero cross data generated by the zero cross data generation unit 114. The zero cross data generated by the zero cross data generation unit 118 or the zero cross data of the external signal generated by the external signal zero cross data generation unit 122 is output to the DSP 140.

  The data update cycle setting unit 170 sets a cycle for updating data based on a user operation instruction.

  The DSP 140 is based on the instantaneous voltage value output from the A / D converter 113, the instantaneous current value output from the A / D converter 117, and the zero cross data of the synchronization signal output from the selector 130, for each data update cycle. Output measurement data (voltage, current, power) to.

FIG. 15 is a functional block diagram of the DSP 140.
As illustrated in FIG. 15, the DSP 140 includes a sampling unit 141, an instantaneous data storage unit 142, an update cycle detection unit 143, a measurement data calculation unit 144, a measurement data storage unit 145, and a transfer unit 146.

The sampling unit 141 acquires the instantaneous voltage value output from the A / D converter 113 and the instantaneous current value output from the A / D converter 117, multiplies the instantaneous voltage value and the instantaneous current value, and multiplies them. The result is the instantaneous power value.
The instantaneous data storage unit 142 stores an instantaneous voltage value, an instantaneous current value, and an instantaneous power value.

  In addition, the sampling unit 141 acquires zero-cross data of the synchronization signal output from the selector 130.

  The update cycle detection unit 143 detects the data update cycle set by the data update cycle setting unit 170. Further, the update cycle detection unit 143 detects n (n is an integer) cycle measurement intervals within the data update cycle based on the rising edge or falling edge of the zero cross data of the synchronization signal acquired by the sampling unit 141. To do.

The measurement data calculation unit 144 calculates measurement data (voltage, current, power) based on the instantaneous voltage value, instantaneous current value, and instantaneous power value in the measurement period for n cycles detected by the update cycle detection unit 143.
The measurement data storage unit 145 stores the measurement data calculated by the measurement data calculation unit 144.

  The transfer unit 146 transfers the measurement data stored in the measurement data storage unit 145 to the CPU 150 at each data update period.

  The CPU 150 acquires the measurement data output from the DSP 140, generates display data, and causes the display 160 to display the data.

  The display device 160 displays measurement data according to instructions from the CPU 150.

Next, with reference to FIG. 16, the operation of the conventional measuring apparatus 100 in the DSP 140 will be described.
First, the sampling unit 141 acquires the instantaneous voltage value output from the A / D converter 113 and the instantaneous current value output from the A / D converter 117 (steps S11 and S12). Next, the instantaneous voltage value and the instantaneous current value are multiplied by the sampling unit 141 to calculate an instantaneous power value (step S13). The acquired instantaneous voltage value, instantaneous current value, and calculated instantaneous power value are stored in the instantaneous data storage unit 142 (step S14).

  Next, the zero cross data of the synchronization signal output from the selector 130 is acquired by the sampling unit 141 (step S15). Then, the update cycle detection unit 143 determines whether or not the data update cycle set by the data update cycle setting unit 170 has ended (step S16). When the data update cycle has not ended (step S16; No), the process returns to step S11, and the processes of steps S11 to S16 are repeated.

  In step S16, when the data update cycle is completed (step S16; Yes), measurement periods for n cycles are detected within the data update cycle based on the rising edge or falling edge of the zero-cross data of the synchronization signal. The measurement data calculation unit 144 calculates measurement data (voltage, current, power) based on the instantaneous voltage value, instantaneous current value, and instantaneous power value for n cycles stored in the instantaneous data storage unit 142. (Step S17). The calculated measurement data for each data update cycle is stored in the measurement data storage unit 145 (step S18).

  Next, the measurement data (voltage, current, power) stored in the measurement data storage unit 145 is transferred to the CPU 150 by the transfer unit 146 for each data update period (step S19).

  A conventional measurement section will be described with reference to FIG. 17A is the synchronization signal, FIG. 17B is the zero cross data of the synchronization signal, FIG. 17C is the data update cycle, FIG. 17D is the measurement period, FIG. 17E is the voltage U, FIG. 17 (f) shows the time change of the current I. Here, the voltage U is used as a synchronization signal.

As shown in FIGS. 17A and 17B, the zero-cross data of the synchronization signal is data obtained by binarizing the synchronization signal based on the sign of the synchronization signal. The data update cycle shown in FIG. 17C is a value set by the data update cycle setting unit 170. As shown in FIG. 17 (d), n measurement periods are detected within a data update period, with one period from the rising edge of the zero-cross data of the synchronization signal to the next rising edge as one period. Specifically, measurement data (voltage U11, current I11) corresponding to the data update period is calculated based on the instantaneous voltage value and instantaneous current value for two periods of the measurement section T11. Similarly, measurement data (voltage U12, current I12) corresponding to the data update period is calculated based on the instantaneous voltage value and instantaneous current value for one period of the measurement section T12.
JP-A-7-922209

  However, in the conventional measuring apparatus, the voltage, current, power, and the like are calculated every data update cycle (currently 50 msec is the fastest), and therefore, analysis cannot be performed for each cycle of the physical quantity to be measured. Further, when displaying voltage, current, power, etc., it is displayed every display update cycle longer than the data update cycle (currently 200 msec is the fastest).

  The present invention has been made in view of the above-described problems in the prior art, and an object of the present invention is to calculate measurement data for each period of a physical quantity to be measured.

In order to solve the above-mentioned problem, the measuring apparatus according to claim 1, based on any one of the acquisition unit that acquires instantaneous values of the plurality of measurement target physical quantities and the plurality of measurement target physical quantities , For each period detected by the period detection means, a synchronization signal source that generates a synchronization signal that is zero-cross data binarized by the value of the physical quantity to be measured, and a period detection means that detects the period of the synchronization signal And calculating means for calculating measurement data, which are representative values of the respective measurement target physical quantities, based on instantaneous values of the plurality of measurement target physical quantities acquired during one cycle by the acquisition means. And

According to a second aspect of the present invention, in the measurement apparatus according to the first aspect, the synchronization signal source generates a common synchronization signal for the plurality of measurement target physical quantities .

  A third aspect of the present invention is the measuring apparatus according to the first or second aspect, further comprising a display unit that displays the measurement data calculated by the calculation unit.

According to the first aspect of the present invention, the measurement data is calculated for each period of the measurement target physical quantity by detecting the period of the synchronization signal generated based on any one of the plurality of measurement target physical quantities. be able to. Further, even if the cycle of the physical quantity to be measured varies, measurement for each cycle can be performed accurately.

According to the second aspect of the present invention, it is possible to maintain the simultaneity of measurement data by generating a common synchronization signal for a plurality of physical quantities to be measured.

  According to invention of Claim 3, the measurement data calculated for every period can be displayed.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 shows a basic configuration of a measuring apparatus 1 according to an embodiment of the present invention.
As shown in FIG. 1, the measuring apparatus 1 includes elements 10a, 10b, 10c, 10d, an external signal input terminal 21, an external signal zero-cross data generation unit 22, selectors 30a, 30b, 30c, 30d, DSPs 40a, 40b, 40c, 40d, CPU 50, and display 60 are provided.

  The element 10a includes a voltage input terminal 11a, a voltage input circuit 12a, an A / D converter 13a, a zero cross data generation unit 14a, a current input terminal 15a, a current input circuit 16a, an A / D converter 17a, and a zero cross data generation unit 18a. Prepare.

  The voltage input circuit 12a normalizes the voltage signal input from the voltage input terminal 11a with an operational amplifier. The A / D converter 13a performs A / D conversion on the signal normalized by the voltage input circuit 12a at a predetermined sampling period, and outputs an instantaneous voltage value to the DSP 40a. The zero-cross data generation unit 14a binarizes the voltage signal value based on whether the voltage signal value is positive, such as “1” if the voltage signal value is positive and “0” if the voltage signal value is negative. Generated zero-cross data.

  The current input circuit 16a normalizes the current signal input from the current input terminal 15a with an operational amplifier. The A / D converter 17a A / D converts the signal normalized by the current input circuit 16a at a predetermined sampling period, and outputs an instantaneous current value to the DSP 40a. The zero-cross data generation unit 18a binarizes the current signal value based on whether the current signal value is positive, such as “1” if the current signal value is positive and “0” if the current signal value is negative. Generated zero-cross data.

  Since the elements 10b, 10c, and 10d have the same configuration as the element 10a, corresponding parts are denoted by the same reference numerals and description thereof is omitted. That is, the measuring apparatus 1 can measure up to four sets of voltages and currents simultaneously. Although FIG. 1 illustrates the case where the measuring apparatus 1 includes four elements, the number of elements is not limited to four and may be any number.

  The external signal zero cross data generation unit 22 generates zero cross data in which the external signal value is binarized based on the sign of the external signal value (voltage signal value) input from the external signal input terminal 21.

The selector 30a selects any one of the voltage signal or current signal to be measured or the external signal set by the user as the synchronization signal, and the zero cross data generated by the zero cross data generation unit 14a. , Zero cross data generated by the zero cross data generator 18a, zero cross data generated by the zero cross data generator 14b, zero cross data generated by the zero cross data generator 18b, zero cross data generated by the zero cross data generator 14c, zero cross Zero cross data generated by the data generator 18c, zero cross data generated by the zero cross data generator 14d, zero cross data generated by the zero cross data generator 18d, or external signal zero cross Of the zero-cross data from the external signal generated by the over data generating unit 22, and outputs one of the DSP40a. That is, the zero cross data generation unit 14a, the zero cross data generation unit 18a, the zero cross data generation unit 14b, the zero cross data generation unit 18b, the zero cross data generation unit 14c, the zero cross data generation unit 18c, the zero cross data generation unit 14d, the zero cross data generation unit 18d, and The selector 30a is a synchronization signal source described in the claims.

  Since the selectors 30b, 30c, and 30d have the same configuration as the selector 30a, description thereof is omitted.

  The DSP 40a determines the period of the synchronization signal based on the instantaneous voltage value output from the A / D converter 13a, the instantaneous current value output from the A / D converter 17a, and the zero cross data of the synchronization signal output from the selector 30a. Measurement data (voltage, current or power) is output every time (so-called cycle-by-cycle measurement).

FIG. 2 is a functional block diagram of the DSP 40a.
As shown in FIG. 2, the DSP 40a includes a sampling unit 41a, an instantaneous data storage unit 42a, a synchronization signal period detection unit 43a, a measurement data calculation unit 44a, a measurement data storage unit 45a, and a transfer unit 46a.

The sampling unit 41a acquires the instantaneous voltage value output from the A / D converter 13a and the instantaneous current value output from the A / D converter 17a. In addition, the sampling unit 41a multiplies the instantaneous voltage value and the instantaneous current value, and acquires the result of the multiplication as an instantaneous power value. That is, the sampling unit 41a is an acquisition unit described in the claims.
The instantaneous data storage unit 42a stores an instantaneous voltage value, an instantaneous current value, and an instantaneous power value.

  In addition, the sampling unit 41a acquires zero-cross data of the synchronization signal output from the selector 30a.

  The synchronization signal cycle detection unit 43a detects a rising edge from the zero cross data of the synchronization signal acquired by the sampling unit 41a, and detects the cycle of the synchronization signal. That is, the synchronization signal cycle detection unit 43a is cycle detection means described in the claims. In the present embodiment, the period is detected based on the rising edge of the zero-cross data of the synchronization signal, but the period may be detected based on the falling edge.

The measurement data calculation unit 44a calculates measurement data based on the instantaneous voltage value, instantaneous current value, and instantaneous power value acquired during one period for each period of the synchronization signal detected by the synchronization signal period detection unit 43a. To do. That is, the measurement data calculation unit 44a is a calculation unit described in the claims. Here, the measurement data is a representative value of the physical quantity to be measured corresponding to one cycle of the synchronization signal. In the case of voltage, RMS (Root Mean Square: true effective value), MEAN (average value rectification effective value calibration) , RMEAN (Rectified MEAN: average value rectification), DC (simple average), etc. For current, RMS, MEAN, RMEAN, DC, etc. For power, active power, apparent power, reactive power, etc. as measurement data Calculated.
The measurement data storage unit 45a stores the measurement data for each period calculated by the measurement data calculation unit 44a.

  When the measurement data for a predetermined cycle is stored in the measurement data storage unit 45a, the transfer unit 46a collectively transfers the measurement data for the specified cycle to the CPU 50.

  Since the DSPs 40b, 40c, and 40d have the same configuration as the DSP 40a, corresponding parts are denoted by the same reference numerals, and illustration and description thereof are omitted.

  The CPU 50 acquires measurement data output from the DSPs 40a, 40b, 40c, and 40d, generates display data, and causes the display 60 to display the measurement data.

  The display device 60 displays measurement data according to instructions from the CPU 50. That is, the display device 60 is a display means described in the claims.

Next, the operation of the measuring apparatus 1 will be described.
FIG. 3 is a flowchart showing the cycle-by-cycle measurement process executed by the DSP 40a of the measurement apparatus 1.

  First, the sampling unit 41a acquires the instantaneous voltage value output from the A / D converter 13a (step S1), and acquires the instantaneous current value output from the A / D converter 17a (step S2). Next, the instantaneous voltage value and the instantaneous current value are multiplied by the sampling unit 41a to calculate an instantaneous power value (step S3). The acquired instantaneous voltage value, instantaneous current value, and calculated instantaneous power value are stored in the instantaneous data storage unit 42a (step S4).

  Next, the zero cross data of the synchronization signal output from the selector 30a is acquired by the sampling unit 41a (step S5). Then, the synchronization signal period detection unit 43a determines whether or not a rising edge is detected from the zero cross data of the synchronization signal, that is, whether or not one period of the synchronization signal has ended (step S6). If one cycle of the synchronization signal has not ended (step S6; No), the process returns to step S1 and the processes of steps S1 to S6 are repeated.

  In step S6, when one cycle of the synchronization signal is completed (step S6; Yes), the measurement data calculation unit 44a causes the instantaneous voltage value and instantaneous current value for one cycle stored in the instantaneous data storage unit 42a. Based on the instantaneous power value, measurement data for each cycle is calculated (step S7). The calculated measurement data for each period is stored in the measurement data storage unit 45a (step S8).

  Next, it is determined whether or not the measurement for the designated period has been completed (step S9). If the measurement for the designated period has not been completed (step S9; No), the process returns to step S1, and steps S1 to S1 are performed. The process of step S9 is repeated.

In step S9, when the measurement for the designated cycle is completed (step S9; Yes), the transfer unit 46a collectively transfers the measurement data for the designated cycle stored in the measurement data storage unit 45a to the CPU 50. (Step S10).
Thus, the period-by-cycle measurement process ends.

  Similar processing is performed in the DSPs 40b, 40c, and 40d. Then, the CPU 50 acquires measurement data output from the DSPs 40 a, 40 b, 40 c, and 40 d, generates display data, and displays it on the display device 60.

  Next, with reference to FIG. 4, the measurement interval of the measurement for each cycle will be described. 4A is the synchronization signal, FIG. 4B is the zero cross data of the synchronization signal, FIG. 4C is the measurement period, FIG. 4D is the voltage U, and FIG. Indicates. Here, the voltage U is used as a synchronization signal.

  As shown in FIGS. 4A and 4B, the zero cross data of the synchronization signal is data obtained by binarizing the synchronization signal based on the sign of the synchronization signal. As shown in FIGS. 4B and 4C, the measurement intervals T1, T2, T3,... For each period are detected based on the rising edge of the zero-cross data of the synchronization signal. Specifically, as shown in FIGS. 4C, 4D, and 4E, the instantaneous voltage value and the instantaneous current value for one cycle stored in the instantaneous data storage unit 42a during the measurement section T1. Measurement data (voltage U1, current I1) for each cycle is calculated based on one cycle, and one cycle based on the instantaneous voltage value and instantaneous current value for one cycle stored in the instantaneous data storage unit 42a during the measurement section T2. Each measurement data (voltage U2, current I2) is calculated.

  As described above, according to the measurement apparatus 1, it is possible to calculate measurement data for each period of the physical quantity to be measured by detecting the period of the synchronization signal. In addition, by generating the synchronization signal based on the physical quantity to be measured, even if the period of the physical quantity to be measured fluctuates, it is possible to accurately measure every period. Therefore, for example, it becomes possible to analyze in more detail transient phenomena, phenomena during the start-up period when power is turned on, and the like.

  The description in the above embodiment is an example of the measurement apparatus according to the present invention, and the present invention is not limited to this. The detailed configuration and detailed operation of each part constituting the measuring apparatus can be changed as appropriate without departing from the spirit of the present invention.

  For example, the selectors 30a, 30b, 30c, and 30d may select different synchronization signals, but by selecting a common synchronization signal, the simultaneity of the measurement data of the elements 10a, 10b, 10c, and 10d is selected. Can keep.

<Measurement results>
Measurement was performed for each cycle of the inverter drive motor (three-phase three-wire system) using the measuring device 2 shown in FIG. Since the measuring device 2 has the same configuration as the measuring device 1 described in the above embodiment, the same components are denoted by the same reference numerals, and illustration and description thereof are omitted. The measuring device 2 is further provided with a torque input terminal and a rotational speed input terminal, and the torque, rotational speed, and mechanical power can be measured for each period.

  As shown in FIG. 5, the motor 4 is driven by the inverter 3, and the load 5 is rotated by the motor 4. Torque and rotational speed are output from the torque meter 7 via a torque / rotational speed sensor 6 provided on the rotational shaft of the load 5.

  The input voltage (U phase) of the motor 4 is input to the voltage input terminal 11a as the voltage Ua, the input current (U phase) of the motor 4 is input to the current input terminal 15a as the current Ia, and the voltage Ub is input to the voltage input terminal 11b. The input voltage (V phase) of the motor 4 is inputted, the input current (V phase) of the motor 4 is inputted as the current Ib to the current input terminal 15b, and the input voltage (W phase) of the motor 4 is inputted as the voltage Uc to the voltage input terminal 11c. ) And the input current (W phase) of the motor 4 was input as the current Ic to the current input terminal 15c. Further, the torque and the rotational speed were inputted to the torque input terminal and the rotational speed input terminal of the measuring device 2.

  Data measurement was performed for 100 periods when the output frequency of the inverter 3 was increased using the synchronization signal as the current Ia (input current (U phase) of the motor 4).

  In FIG. 6, the frequency [Hz], current [A], power [W], rotation speed [rpm], and torque [N · m] of the synchronization signal measured for each period of the synchronization signal displayed on the display device 60. ] Is displayed.

  7 to 13 are graphs of measurement data obtained by the cycle-by-cycle measurement process. 7 shows the frequency [Hz] of the synchronization signal with respect to the cycle count, FIG. 8 shows the voltage [V] with respect to the cycle count, FIG. 9 shows the current [A] with respect to the cycle count, FIG. Is the rotational speed [rpm] with respect to the cycle count, FIG. 12 is the torque [N · m] with respect to the cycle count, and FIG. 13 is the mechanical power [W] with respect to the cycle count.

  As described above, in the evaluation of the inverter drive motor, the transient phenomenon from the start of the motor 4 to the steady operation in which the frequency of the physical quantity to be measured is increased or decreased is expressed as the inverter output current (the input current (U phase of the motor 4)). )).

It is a basic lineblock diagram of measuring device 1 in an embodiment of the invention. It is a functional block diagram of DSP40a. It is a flowchart which shows the measurement process for every period performed by DSP40a of the measuring apparatus 1. It is a figure for demonstrating the measurement area of a measurement for every period. It is a block diagram at the time of measuring every period of an inverter drive motor using the measuring apparatus. It is a display example of measurement data displayed on the display device 60. It is a graph which shows the frequency [Hz] of the synchronizing signal with respect to cycle count. It is a graph which shows voltage [V] with respect to cycle count. It is a graph which shows electric current [A] with respect to cycle count. It is a graph which shows active power [W] with respect to cycle count. It is a graph which shows the rotational speed [rpm] with respect to cycle count. It is a graph which shows torque [N * m] with respect to cycle count. It is a graph which shows mechanical power [W] with respect to cycle count. It is a basic block diagram of the conventional measuring apparatus 100. FIG. It is a functional block diagram of the conventional DSP140. It is a flowchart for demonstrating the operation | movement in the conventional DSP140. It is a figure for demonstrating the conventional measurement area.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Measuring apparatus 2 Measuring apparatus 3 Inverter 4 Motor 5 Load 6 Torque / rotation speed sensor 7 Torque meter 10a, 10b, 10c, 10d Element 11a, 11b, 11c, 11d Voltage input terminal 12a, 12b, 12c, 12d Voltage input circuit 13a , 13b, 13c, 13d A / D converters 14a, 14b, 14c, 14d Zero cross data generators 15a, 15b, 15c, 15d Current input terminals 16a, 16b, 16c, 16d Current input circuits 17a, 17b, 17c, 17d A / D converters 18a, 18b, 18c, 18d Zero cross data generator 21 External signal input terminal 22 External signal zero cross data generators 30a, 30b, 30c, 30d Selectors 40a, 40b, 40c, 40d DSP
41a Sampling unit 42a Instantaneous data storage unit 43a Synchronization signal period detection unit 44a Measurement data calculation unit 45a Measurement data storage unit 46a Transfer unit 50 CPU
60 Display 100 Measuring Device 111 Voltage Input Terminal 112 Voltage Input Circuit 113 A / D Converter 114 Zero Cross Data Generation Unit 115 Current Input Terminal 116 Current Input Circuit 117 A / D Converter 118 Zero Cross Data Generation Unit 121 External Signal Input Terminal 122 External signal zero-cross data generator 130 selector 140 DSP
141 Sampling unit 142 Instantaneous data storage unit 143 Update cycle detection unit 144 Measurement data calculation unit 145 Measurement data storage unit 146 Transfer unit 150 CPU
160 Display 170 Data update cycle setting section

Claims (3)

Acquisition means for acquiring instantaneous values of a plurality of measurement target physical quantities;
A synchronization signal source that generates a synchronization signal that is zero-cross data binarized based on the value of the measurement target physical quantity based on any one of the plurality of measurement target physical quantities;
Period detection means for detecting the period of the synchronization signal;
For each period detected by the period detection unit, measurement data that is a representative value of each measurement target physical quantity is calculated based on instantaneous values of a plurality of measurement target physical quantities acquired during one cycle by the acquisition unit. Calculating means for
A measuring apparatus comprising:   The measurement apparatus according to claim 1, wherein the synchronization signal source generates a common synchronization signal for the plurality of measurement target physical quantities.   The measuring apparatus according to claim 1, further comprising display means for displaying the measurement data calculated by the calculating means.

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