JP2012154764A - Measurement device and measurement method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To shorten processing time for specifying Lagrangian interpolation formula.SOLUTION: The measurement device includes a processing unit 15 that specifies instantaneous values at Q divided time points from Lagrangian interpolation formula (formula (1) below) specified based on n+1 instantaneous values in the measuring target of AC signals (S1 to S3). The processing unit 15 substitutes, when specifying the formula (1) of Q corresponding to each divided time point of one AC signal, x,xwith values of subscripts in x,xof the L(x) formula of each term, stores a value calculated by substituting x of the L(x) formula with a division value obtained by dividing a multiplication value of an order value K counting the order of Q divided time points from 0 and the total number m of sampling frequencies in the measuring target by Q as a coefficient in a storage unit 14, and specifies formulas (1) of other AC signals by using the coefficient: p(x)=Σ[j=0,n]L(x)y(L(x)=Π[i=0(i≠j),n](x-x)/(x-x)).

Description

  The present invention relates to a measuring apparatus and a measuring method for acquiring an instantaneous value of an input AC signal and measuring the AC signal.

  As this type of measuring apparatus, an AC signal measuring apparatus disclosed by the applicant in Japanese Patent Laid-Open No. 2005-337980 is known. This AC signal measurement device includes a filter unit, a detection signal generation unit, a frequency measurement unit, a frequency calculation unit, a clock generation unit, an A / D conversion unit, a signal processing unit, and the like, and measures a physical quantity of an input AC signal. To do. In this case, the filter unit removes a noise component included in the input AC signal, and the detection signal generation unit detects a zero cross of the AC signal and outputs a detection signal. The frequency measurement unit measures the time from the detection signal indicating the beginning (start time) of each cycle of the AC signal to the detection signal indicating the end (end time), and measures the frequency of the AC signal based on the time. Output frequency data. The frequency calculation unit calculates a sampling frequency based on the frequency data and outputs setting data indicating the sampling frequency. The clock generation unit generates a sampling clock having a frequency indicated by the setting data. The A / D conversion unit samples the AC signal in synchronization with the sampling clock and outputs digital data indicating the instantaneous value of the AC signal, and the signal processing unit measures the physical quantity of the AC signal based on the digital data. Execute the process. In this case, for example, when a physical quantity for one period in an AC signal is measured by FFT calculation, the number of instantaneous values (digital data) in one period is the effective power of 2 for efficient FFT calculation. (This number is assumed to be L). For this reason, the applicant has developed an interpolation processing function that specifies an interpolation expression representing the waveform (time change) of an AC signal and obtains L instantaneous values from the interpolation expression. In this case, in this interpolation processing function, an interpolation formula is specified based on the output digital data, and the time at the tip of each divided section obtained by equally dividing one cycle into L pieces is substituted into the interpolation formula. Find the instantaneous value of.

  On the other hand, a Lagrangian interpolation formula is known as an interpolation formula used (specified) in this type of interpolation processing. This Lagrangian interpolation formula is given by a summation formula (polynomial) of a plurality of terms defined by the sum of a plurality of columns, and is specified by using a plurality of instantaneous values of AC signals indicated by digital data. Since this Lagrangian interpolation formula is relatively complicated, it may take a relatively long time to specify it. As means for solving this problem, an interpolation method disclosed in Japanese Patent Laid-Open No. 6-204798 is known. In this interpolation method, the value of the denominator part that does not include the variable x in each term constituting the Lagrangian interpolation formula is calculated in advance and stored in the memory, and when the digital data is output, By calculating the value of the portion including the variable x by substituting the indicated instantaneous value into the variable x, the Lagrange interpolation formula is specified using the value and the value of the denominator portion read from the memory, thereby requiring processing. Time is being shortened.

Japanese Patent Laying-Open No. 2005-337980 (page 4-6, FIG. 1-2) JP-A-6-204798 (page 3-4)

  However, the above-described interpolation method has the following problems to be solved. That is, in the above interpolation method, the value of the denominator part in the Lagrangian interpolation equation that does not include the variable x is calculated in advance and stored in the memory, thereby reducing the time required for the process of specifying the Lagrangian interpolation equation. . However, in a multi-channel measuring apparatus that inputs a plurality of AC signals and measures each AC signal, it is necessary to perform a process for specifying a Lagrangian interpolation formula for each AC signal. Even if it is adopted, much time is still required for the process of specifying the Lagrangian interpolation formula, and further reduction of the processing time is desired.

  The present invention has been made in view of the problems to be improved, and it is a main object of the present invention to provide a measuring apparatus and a measuring method capable of shortening the processing time of processing for specifying a Lagrangian interpolation formula for an AC signal. .

In order to achieve the above object, the measuring apparatus according to claim 1 includes a sampling unit that performs a sampling process for inputting a plurality of AC signals and acquiring an instantaneous value of each AC signal at a predetermined sampling period; An interpolation formula representing a waveform of a part of the AC signal defined as a target, and a Lagrange interpolation formula given by the following formula (1), is obtained by calculating the instantaneous value obtained by the sampling process in the measurement target. The time length of the measurement object is specified by Q (Q is an integer greater than or equal to 2 in advance), while being specified based on n + 1 (n is an integer greater than or equal to a predetermined integer) instantaneous values continuous in time. A processing unit for performing an interpolation process for obtaining the instantaneous values from the Lagrangian interpolation formulas at a total of Q division points corresponding to the tips of the respective divided sections; A measuring unit that measures the AC signal using the instantaneous value calculated by the interpolation process, and the processing unit corresponds to each of the Q divisional points on a one-to-one basis. When identifying the Q Lagrangian interpolation equations and identifying each Lagrangian interpolation equation for any one of the AC signals, the Lagrange interpolation equations are summed by the summation symbol in each Lagrange interpolation equation. And subscript values of x _j and x _i in the L _j (x) expression of each term are substituted as the values of x _j and x _i , respectively, and Multiplying the rank value k (k is an integer greater than or equal to 0) counting the temporal rank in the Q points at the time of division from 0 and the total number m of the sampling periods in the measurement target (m is a value greater than or equal to 0) The value is Q Calculated by the division value (k × m / Q) wherein L _{j (x)} is stored in the storage unit the value of the expression of the L _j which is calculated by substituting the x _(x) equation as coefficient, each AC signal The Lagrangian interpolation formulas for other AC signals other than the one AC signal are specified using the coefficients stored in the storage unit.
p (x) = Σ [j = 0, n] L _j (x) y _j (where L _j (x) = Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i )) ... (1)

Further, in the measurement apparatus according to claim 2, in the measurement apparatus according to claim 1, the processing unit calculates a value of a denominator part in the L _j (x) equation prior to specifying the total number m. After storing the total number m, the value of the expression L _j (x) is calculated using the value of the denominator part stored in the storage unit.

  The measuring device according to claim 3 is the measuring device according to claim 1 or 2, wherein the processing unit calculates a zero cross based on the instantaneous values before and after the zero cross of the AC signal acquired by the sampling process. And an interval for one or a plurality of periods of the AC signal divided by the time of the zero cross is calculated as the measurement object. It prescribes as

According to a fourth aspect of the present invention, there is provided the measurement method according to the present invention, wherein a plurality of alternating current signals are input, a sampling process for acquiring an instantaneous value of each alternating current signal at a predetermined sampling period is executed, and the alternating current signal defined as a measurement target The Lagrangian interpolation equation representing the waveform of a part of the interval and given by the following equation (1) is temporally continuous among the instantaneous values acquired by the sampling process in the measurement object. Each division is specified based on n + 1 (n is a predetermined integer of 1 or more) instantaneous values and the time length of the measurement target is divided into Q (Q is a predetermined integer of 2 or more). Interpolation processing for obtaining the instantaneous values at a total of Q division time points corresponding to the tip of the section from the Lagrange interpolation formula is performed, and the instantaneous values calculated by the interpolation processing are calculated. And measuring the AC signal, specifying Q Lagrangian interpolation formulas corresponding one-to-one to the Q division points, and selecting any one of the AC signals. When specifying each Lagrangian interpolation formula for an AC signal, each subscript in x _j and x _i in the L _j (x) formula of each term summed by the summation symbol in each Lagrangian interpolation formula Is substituted as the value of x _j and x _i , and the rank value k (k Is an integer greater than or equal to 0) and the total value m (m is a value greater than or equal to 0) of the sampling period in the measurement object, a division value (k × m / Q) obtained by dividing the product by Q is L _j (x L _j calculated by substituting x in the formula The value of the formula (x) is stored as a coefficient in the storage unit, and the Lagrangian interpolation formulas for other AC signals other than the one AC signal among the AC signals are stored in the storage unit. Specify using a coefficient.
p (x) = Σ [j = 0, n] L _j (x) y _j (where L _j (x) = Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i )) ... (1)

In the measurement apparatus according to claim 1 and the measurement method according to claim 4, the Lagrange interpolation formula P (x) is specified when Q Lagrangian interpolation formulas P (x) for one of the plurality of AC signals are specified. The value of the expression L _j (x) in each term summed by the summation symbol (Σ) is calculated, and the value is stored as a coefficient in the storage unit. Therefore, in this measurement apparatus and measurement method, when specifying the Lagrangian interpolation formula P (x) for other AC signals excluding the AC signal that has been subjected to the above-described processing among the plurality of AC signals, The Lagrange interpolation formula P (x) is specified by a simple operation that reads the value of each L _j (x) stored as, calculates the terms by multiplying the coefficient by the instantaneous value, and sums them up can do. Therefore, according to this measurement apparatus and measurement method, unlike the conventional configuration and method in which only the value of the denominator part that is a part of the L _j (x) equation in the Lagrange interpolation equation is calculated and stored in advance, the Lagrange When specifying the interpolation formula P (x), it is not necessary to calculate the entire L _j (x) formula in the Lagrangian interpolation formula, so the processing time for specifying the Lagrange interpolation formula P (x) is sufficiently reduced. Can be made.

In the measuring apparatus according to claim 2, the value of the denominator part in the L _j (x) equation is calculated and stored in the storage unit prior to the specification of the total number m of the sampling periods in the measurement target, and the total number m is stored after the specification. The value of L _j (x) is calculated using the value of the denominator part stored in the part. Therefore, according to this measuring apparatus, for example, the value of the denominator part is calculated and stored in the storage unit until the total number m is specified from the time of starting the measuring apparatus, and the total number m is specified. Thus, the time until the Lagrange interpolation formula P (x) is specified using the total number m can be further shortened.

  In the measuring apparatus according to claim 3, the processing unit specifies an interpolation formula for calculating the zero crossing based on instantaneous values before and after the zero crossing of the AC signal acquired by the sampling process, and determines the time point of the zero crossing for the zero crossing calculation. A section corresponding to one or a plurality of periods of the AC signal divided by the time of zero crossing is calculated as an object to be measured. For this reason, the measuring apparatus can calculate the zero cross accurately, and thereby can accurately calculate the period of the AC signal. Therefore, according to this measuring apparatus, for example, the instantaneous value at each division time point corresponding to the tip of each divided section obtained by equally dividing one or a plurality of sections of the AC signal period into Q pieces is obtained as a Lagrange interpolation formula P ( In the case of trying to obtain from x), since the divided section becomes an accurate value, the instantaneous value can be obtained accurately.

1 is a configuration diagram showing a configuration of a measuring device 1. FIG. It is a signal waveform diagram which shows an example of AC signal S1-S3 which the measuring apparatus 1 inputs. FIG. 3 is a first explanatory view explaining the operation of the measuring apparatus 1. FIG. 6 is a second explanatory diagram for explaining the operation of the measuring apparatus 1. FIG. 6 is a third explanatory diagram for explaining the operation of the measuring apparatus 1.

  Hereinafter, embodiments of a measurement apparatus and a measurement method will be described with reference to the accompanying drawings.

  Initially, the structure of the measuring apparatus 1 as an example of a measuring apparatus is demonstrated. A measuring apparatus 1 shown in FIG. 1 includes a signal processing unit 11, a sampling unit 12, a storage control unit 13, a storage unit 14, a processing unit 15, and a measurement unit 16. A plurality of input AC signals S1 to S3 (as an example, As shown in FIG. 2, physical quantities (for example, AC signals S) when the waveforms are sine waves, the frequencies (periods Ta) are the same and the phases are different from each other: , Voltage and power), and the harmonic order and amplitude included in the AC signal S can be measured. The measuring device 1 is configured to be able to determine whether the input AC signal S is good or bad.

  The signal processing unit 11 executes an anti-aliasing filter process that removes noise components included in the input AC signal S. Further, as shown in FIG. 1, the signal processing unit 11 receives a plurality of AC signals S (in this example, three AC signals S1 to S3) and can execute the above-described anti-aliasing filter processing. It has a configuration of channels (in this example, three channels from Ch1 to Ch3).

  The sampling unit 12 has a plurality of channels (three channels from Ch1 to Ch3 in this example) including one sampling clock generation circuit and a plurality (three in this example) of sampling circuits (all not shown). It has a configuration. The sampling clock generation circuit generates a sampling clock having a predetermined sampling period Ts (see FIG. 3). Each sampling circuit samples each AC signal S in synchronization with the sampling clock to obtain an instantaneous value Af of each AC signal S1 to S3, and digital data (sampling data) Df1, Df2, D2 indicating the instantaneous value Af. Sampling processing for outputting Df3 (hereinafter also referred to as “digital data Df” when not distinguished) is executed. In this case, the digital data Df is used for measuring an effective value of a physical quantity (for example, voltage or power) of the AC signal S in an effective value calculation process, which will be described later, executed by the effective value calculation processing circuit 31 of the measurement unit 16. At the same time, it is used to specify a Lagrangian interpolation formula P (x) described later, which is performed by the interpolation processing circuit 22 of the processing unit 15.

  The storage control unit 13 stores the digital data Df output from each sampling circuit of the sampling unit 12 in the storage unit 14. The storage unit 14 stores the digital data Df according to the control of the storage control unit 13. In this case, the storage unit 14 can specify the sampling time Tz (for example, the sampling time Tz0 to Tz32 shown in FIG. 3) at which the instantaneous value Af is acquired (sampled) (corresponding to each sampling time Tz). Remember.

  The processing unit 15 includes a zero cross detection circuit 21 and an interpolation processing circuit 22. The zero cross detection circuit 21 reads one of the digital data Df1, Df2, and Df3 (for example, digital data Df1) stored in the storage unit 14, and determines in advance the instantaneous value Af indicated by the digital data Df1. It is detected whether or not the AC signal S (AC signal S1 in this example) crosses the reference value (zero crossing) by comparing the obtained reference value (for example, a value of 0V). In this case, for example, when the rising zero cross is detected, the zero cross detection circuit 21 specifies the digital data Df indicating the instantaneous value Af immediately before and after the zero cross and outputs the digital data Df to the interpolation processing circuit 22. Further, the zero-cross detection circuit 21 starts from the sampling time Tz (in the example of FIG. 3, the sampling time Tz0) from which the instantaneous value Af (in the example of FIG. 3, the instantaneous value Af0) immediately after detecting the rising zero-cross is acquired. Each sampling time Tz up to the sampling time Tz (sampling time Tz32 in the example in the figure) at which the instantaneous value Af (instantaneous value Af32 in the example in the figure) immediately before the rising zero cross is detected is started time And the total number m of each sampling period Ts whose end time is the sampling time Tz next to each start time (m is an integer greater than or equal to 1 (an example of a value greater than or equal to 0). In the example of FIG. ), In other words, the number of instantaneous values Af from the sampling time point Tz0 to the sampling time point Tz32 (33 in the example in the figure) Counting and outputs the interpolation circuit 22. Note that from the beginning of the sampling period Tz starting at the sampling time Tz0 (sampling time Tz0 in the example in the figure) to the end of the sampling period Ts starting from the sampling time Tz32 (in the example shown in the figure, the sampling time Tz32). Until the next sampling time Tz33) is a measurement object Uj to be described later.

  As shown in FIG. 3, the interpolation processing circuit 22 defines a part of the AC signal S as the measurement target Uj. Specifically, the interpolation processing circuit 22 is divided by sampling time points Tz0 and Tz33 respectively corresponding to the instantaneous values Af0 and Af33 indicated by the digital data Df output from the zero cross detection circuit 21, as shown in FIG. A section corresponding to approximately one period Ta of the AC signal S is defined as the measurement target Uj.

  Further, the interpolation processing circuit 22 reads out the digital data Df stored in the storage unit 14, and based on the instantaneous value Af (instantaneous value acquired by the sampling processing) indicated by each digital data Df, the AC signal S. A Lagrange interpolation formula P (x) representing the waveform of (measurement object Uj) is specified. 4 and 5, the interpolation processing circuit 22 sets the time length Tc of the measurement object Uj to Q (Q is a predetermined integer equal to or larger than 2, for example, a power of 2 ( For example, a total of Q (16) divided time points Td0 to Td15 (hereinafter referred to as “divided time point Td” when not distinguished) corresponding to the leading end (starting end) of each divided section Ud equally divided into 16)). ) Q instantaneous values At0 to At15 (hereinafter also referred to as “instantaneous value At” when not distinguished) are interpolated from the Lagrange interpolation formula P (x) and digital data indicating the calculated instantaneous value At Dt is output. In this case, the digital data Dt is used in an FFT process and a determination process, which will be described later, executed by the measurement unit 16.

  In the measuring apparatus 1, as an example, the zero cross detection circuit 21 of the processing unit 15 is configured by an FPGA (Field Programmable Gate Array), and the interpolation processing circuit 22 of the processing unit 15 is configured by a CPU. The circuit 21 and the interpolation processing circuit 22 can be configured by one CPU.

  The measurement unit 16 includes an effective value calculation processing circuit 31, an FFT processing circuit 32, and a determination processing circuit 33. The effective value calculation processing circuit 31 performs an effective value calculation process for measuring an effective value of a physical quantity (for example, voltage or power) of the AC signal S using the digital data Df (instantaneous value Af) output from the sampling unit 12. Execute. The FFT processing circuit 32 performs FFT processing using the digital data Dt output from the processing unit 15 (instantaneous value At calculated by interpolation processing), and the order and amplitude of harmonics included in the AC signal S. Measure. In this case, the FFT processing circuit 32 executes the FFT processing for each measurement target Uj (in this example, for each cycle Ta).

  The determination processing circuit 33 executes determination processing for determining the quality of the measurement target Uj in the AC signal S using the digital data Dt output from the processing unit 15 (instantaneous value At calculated by the interpolation processing). In this determination process, the determination processing circuit 33 has the same number of periods (in this example, one period Ta) as the measurement object Uj, which is input earlier (as an example, immediately before) the measurement object Uj. An AC signal S is defined as a comparison target, an upper limit value obtained by adding a predetermined addition value to each instantaneous value At indicated by each digital data Dt in the comparison target, and a subtraction value determined in advance from each instantaneous value At Is compared with each instantaneous value At in the measurement target Uj, and pass / fail is determined based on the comparison result.

  The measurement unit 16 also measures the effective value of the physical quantity measured by the effective value calculation process, the order and amplitude of the harmonics included in the AC signal S measured by the FFT process, and the AC signal S determined by the determination process. The result of pass / fail judgment for the measurement target Uj is displayed on a display unit (not shown).

  Next, a measuring method using the measuring apparatus 1 and an operation of the measuring apparatus 1 at that time will be described with reference to the drawings. Note that “n”, which will be described later, used in the Lagrange interpolation formula P (x) is defined as “3” as an example.

  In this measuring apparatus 1, when an operation for instructing the measurement unit to start measurement is performed, the filter circuit of the signal processing unit 11 receives the AC signal S (AC signal S1) input via the signal cable. To S3), the anti-aliasing filter process for removing the noise components is started, and the processed AC signal S is output to the sampling unit 12. Further, the sampling clock generation circuit of the sampling unit 12 generates a sampling clock having a predetermined sampling period Ts (see FIG. 3). In addition, each sampling circuit of the sampling unit 12 performs sampling processing, samples the AC signal S in synchronization with the sampling clock, acquires the instantaneous value Af of the AC signal S, and indicates the instantaneous value Af. Digital data Df is output.

  Next, the storage control unit 13 provides the digital data Df1, Df2, Df3 output from each sampling circuit of the sampling unit 12 in association with each digital data Df1, Df2, Df3 in the storage unit 14, respectively. Store in each storage area.

  In the processing unit 15, the zero cross detection circuit 21 reads out one of the digital data Df1, Df2, and Df3 (for example, digital data Df1) stored in the storage unit 14, and indicates the digital data Df1. The instantaneous value Af of the AC signal S1 is compared with a reference value (0V value), and it is detected whether or not the AC signal S1 crosses the reference value (zero cross). At this time, when detecting the rising zero cross, the zero cross detection circuit 21 specifies the digital data Df indicating the instantaneous value Af immediately before and after the zero cross and outputs the digital data Df to the interpolation processing circuit 22. Further, the zero-cross detection circuit 21 starts from the sampling time Tz (in the example of FIG. 3, the sampling time Tz0) from which the instantaneous value Af (in the example of FIG. 3, the instantaneous value Af0) immediately after detecting the rising zero-cross is acquired. Each sampling time Tz up to the sampling time Tz (sampling time Tz32 in the example in the figure) at which the instantaneous value Af (instantaneous value Af32 in the example in the figure) immediately before the rising zero cross is detected is started time Then, the total number m of each sampling period Ts whose end time is the sampling time Tz next to each start time is counted and output to the interpolation processing circuit 22.

  Further, as shown in FIG. 3, the interpolating circuit 22 has an AC signal S divided by sampling times Tz0 and Tz33 respectively corresponding to the instantaneous values Af0 and Af33 indicated by the digital data Df output from the zero cross detecting circuit 21. Is defined as a measurement target Uj. Further, the interpolation processing circuit 22 sets the time length Tc (in this example, the time length of one of the periods Ta) of the measurement target Uj in each AC signal S1 to S3 to Q (Q is a power of 2). As an example, a total of Q (16 in this example) division time points Td (divided in the figure) corresponding to the leading end (starting end) of each divided section Ud (see FIG. 4) equally divided into 16). Interpolation processing for obtaining Q instantaneous values At (instantaneous values At0 to At15 in the figure) at the time points Td0 to Td15) from the Lagrange interpolation formula P (x) is performed.

  In this interpolation processing, the interpolation processing circuit 22 performs Q (one Q signals for one AC signal S: one for each AC signal S1 to S3) in a one-to-one correspondence with the Q division times Td. 16 × 3) Lagrange interpolation formulas P (x) are specified, and an instantaneous value At at one division time Td is obtained from one Lagrange interpolation formula P (x).

Here, the Lagrangian interpolation equation P (x) is a high-order interpolation equation in which the time is x, the instantaneous value Af is y, and the relationship between x and y is expressed by a high-order polynomial of x. It is given by equation (1).
p (x) = Σ [j = 0, n] L _j (x) y _j
However, L _j (x) = Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i ) (1)
Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i ) is the sum of the columns of (xx _i ) and each column of (x _j -x _i ) Divided by the power of, that is,
(xx ₀ ) ... (xx _i-1 ) (xx _{i + 1} ) ... (xx _n ) / (x _j -x ₀ ) ... (x _j -x _i-1 ) (x _j -x _{i + 1} ) ... (x _{j- xn} )
The value given by.

In this case, since n is defined as “3” in this example, the Lagrange interpolation formula P (x) is given by the following formula (2).
p (x) = Σ [j = 0,3] L _j (x) y _j
= ((xx ₁ ) (xx ₂ ) (xx ₃ ) / (x ₀ -x ₁ ) (x ₀ -x ₂ ) (x ₀ -x ₃ )) y ₀
+ ((xx ₀ ) (xx ₂ ) (xx ₃ ) / (x ₁ -x ₀ ) (x ₁ -x ₂ ) (x ₁ -x ₃ )) y ₁
+ ((xx ₀ ) (xx ₁ ) (xx ₃ ) / (x ₂ -x ₀ ) (x ₂ -x ₁ ) (x ₂ -x ₃ )) y ₂
+ ((xx ₀ ) (xx ₁ ) (xx ₂ ) / (x ₃ -x ₀ ) (x ₃ -x ₁ ) (x ₃ -x ₂ )) y ₃ (2)

  Specifically, the interpolation processing circuit 22 specifies each Lagrangian interpolation formula P (x) as follows. First, each Lagrangian interpolation formula P (x) for any one of the AC signals S1 to S3 (for example, the AC signal S1) is specified. Further, in each Lagrangian interpolation formula P (x) for the AC signal S1, first, the first division time point Td0 that is earliest in time among the above-mentioned Q (16) division time points Td (FIG. 4). , 5)), the Lagrange interpolation formula P (x) is specified. At this time, as shown in FIG. 5, the interpolation processing circuit 22 has n + 1 pieces close to the division time point Td0 among the sampling time points Tz in the measurement target Uj (in this example, n is defined as “3”). Therefore, four sampling times Tz0 to Tz3 are specified based on the digital data Df stored in the storage unit 14.

Then, the interpolation processing circuit 22, L in terms (L _{j (x)} y _j) which is the sum by the total symbol (sigma) of the Lagrange interpolation formula in P (x) given by equation (1) described above _j ( x) is substituted for sampling instant Tz0~Tz3 within an expression of x _j and x _i. More specifically, if the values are the sampling time Tz0~Tz3 to _x 0 ~x ₃ in equation (2) described above. Here, since the time length between adjacent sampling points Tz is constant corresponding to the sampling period Ts, assuming that the sampling period Ts is “1” with the sampling point Tz0 as the origin, the sampling points Tz0 to Tz3 are These correspond to 0, 1, 2, 3 respectively. Based on this assumption, ₀ , 1, 2, and 3 are assigned to x ₀ to x ₃ in the above equation (2), that is, x _j and x _i in the above L _j (x) equation. Substituting the values of the subscripts ( _j and _i ) in x as the values of x _j and x _i , the Lagrange interpolation formula P (x) is given by the following formula (3).
p (x) = Σ [j = 0,3] L _j (x) y _j
= ((x-1) (x-2) (x-3) / (0-1) (0-2) (0-3)) y ₀
+ ((x-0) (x-2) (x-3) / (1-0) (1-2) (1-3)) y ₁
+ ((x-0) (x-1) (x-3) / (2-0) (2-1) (2-3)) y ₂
+ ((x-0) (x-1) (x-2) / (3-0) (3-1) (3-2)) y ₃
= ((x-1) (x-2) (x-3) /-6) y ₀
+ ((x-0) (x-2) (x-3) / 2) y ₁
+ ((x-0) (x-1) (x-3) /-2) y ₂
+ ((x-0) (x-1) (x-2) / 6) y ₃ ... Formula (3)

On the other hand, the division time point Td0 corresponding to the Lagrangian interpolation formula P (x) is substituted for x in the above formulas (2) and (3). In this example, since the total number m of the sampling periods Ts in the measurement target Uj is 33, assuming that the sampling period Ts is “1” as described above, the time length Tc of the measurement target Uj is m = 33. Become. In addition, since Q = 16 division time points Td exist in the measurement target Uj, the time length of the adjacent division time points Td (that is, the division interval Ud) is m / Q = 33/16 = 2.0625. Further, a ranking value obtained by counting the temporal ranking (order) of Q division times Td corresponding to the Lagrangian interpolation formula P (x) from 0 as k (k is an integer of 0 or more), and the division time Td0. Is the same origin as the sampling time Tz0, the first division time Td0 is k × m / Q = 0. Assuming this, 0 is substituted for each x in the above equation (3), that is, the division time point corresponding to the Lagrange interpolation equation P (x) is substituted for x in the above-mentioned L _j (x). When a division value (k × m / Q) obtained by dividing the product of the rank value k indicating the temporal rank in Q of Td and the total number m of the sampling periods Ts in the measurement target Uj by Q is substituted, Lagrange interpolation The expression P (x) is given by the following expression (4).
p (x) = Σ [j = 0,3] L _j (x) y _j
= ((0-1) (0-2) (0-3) /-6) y ₀
+ ((0-0) (0-2) (0-3) / 2) y ₁
+ ((0-0) (0-1) (0-3) /-2) y ₂
+ ((0-0) (0-1) (0-2) / 6) y ₃
= (-6 / -6) y ₀ + (0/2) y ₁ + (0 / -2) y ₂ + (0/6) y ₃
= y ₀ ... Formula (4)
Y ₀ is an instantaneous value Af ₀ at the sampling time Tz ₀ .

Thus, the interpolation processing circuit 22 specifies the above-described equation (4) as the Lagrange interpolation equation P (x) corresponding to the first division time Td0 for the AC signal S1. Further, the interpolation processing circuit 22 determines the value of L _j (x) calculated in the process of specifying the Lagrange interpolation formula P (x), specifically, x _j in the L _j (x) formula as described above. and the value of each subscript in x _i is substituted as a value of x _j and x _i, and the total number of the sampling period Ts in a rank value k indicating the temporal order in the Q of the divided time Td0 measured Uj m A value obtained by substituting the value obtained by dividing the multiplication value by Q with x in the expression L _j (x) (L ₀ (x) = (-6 / -6), L ₁ (x) = ( 0/2), L ₂ (x) = (0 / −2), L ₃ (x) = (0/6): refer to the above equation (4)), and the coefficient e is stored in the storage unit 14.

Next, the interpolation processing circuit 22 specifies a Lagrange interpolation formula P (x) corresponding to the second division time Td1 (see FIGS. 4 and 5) for the AC signal S1. At this time, as shown in FIG. 5, the interpolation processing circuit 22 has n + 1 pieces close to the division time point Td0 among the sampling time points Tz in the measurement target Uj (in this example, n is defined as “3”). Therefore, four sampling times Tz1 to Tz4 are specified based on the digital data Df stored in the storage unit 14. Subsequently, the interpolation processing circuit 22 performs sampling to x _j and x _i in the L _j (x) equation in the same manner as the processing for specifying the Lagrange interpolation equation P (x) corresponding to the division time Td0 described above. The time points Tz1 to Tz4 are substituted.

In this case, as described above, assuming that the sampling time Tz0 is the origin and the sampling period Ts is “1”, the sampling time points Tz1 to Tz4 correspond to 1, 2, 3, and 4, respectively. Substituting 1, 2, _3, and 4 for x ₀ to x ₃ in (2), that is, subscripts ( _j and _i ) of x _j and x _i in the above expression L _j (x) When the values are substituted as the values of x _j and x _i , the Lagrange interpolation formula P (x) is given by the following formula (5).
p (x) = Σ [j = 0,3] L _j (x) y _j
= ((x-2) (x-3) (x-4) / (1-2) (1-3) (1-4)) y ₀
+ ((x-1) (x-3) (x-4) / (2-1) (2-3) (2-4)) y ₁
+ ((x-1) (x-2) (x-4) / (3-1) (3-2) (3-4)) y ₂
+ ((x-1) (x-2) (x-3) / (4-1) (4-2) (4-3)) y ₃
= ((x-2) (x-3) (x-4) /-6) y ₀
+ ((x-1) (x-3) (x-4) / 2) y ₁
+ ((x-1) (x-2) (x-4) /-2) y ₂
+ ((x-1) (x-2) (x-3) / 6) y ₃ ... Formula (5)

In this case, as is clear from the above equations (2) and (5), the value of the denominator portion in L _j (x) in both equations (hereinafter, the value of the denominator portion is also referred to as “value g”) is It becomes the same value. That is, even select the m which n sampling time Tz of, when substituting the value of each subscript in x _j and x _i as the values of x _j and x _i are, n sampling time Tz As long as is a continuous sampling time Tz, the value g of the denominator portion in L _j (x) is the same value.

Further, as described above, assuming that the sampling period Ts is “1” and the division time point Td0 is the same origin as the sampling time point Tz0, the second division time point Td1 is k × m / Q = 1 × 33/16. = 2.0625, therefore, if 2 is substituted for each x in the above equation (5), the Lagrange interpolation equation P (x) is given by the following equation (6).
p (x) = Σ [j = 0,3] L _j (x) y _j
= ((2.0625-2) (2.0625-3) (2.0625-4) /-6) y ₀
+ ((2.0625-1) (2.0625-3) (2.0625-4) / 2) y ₁
+ ((2.0625-1) (2.0625-2) (2.0625-4) /-2) y ₂
+ ((2.0625-1) (2.0625-2) (2.0625-3) / 6) y ₃ ... Formula (6)
Incidentally, y ₁ is the instantaneous value Af2 at the sampling time Tz2.

Thus, the interpolation processing circuit 22 specifies the above-described equation (6) as the Lagrange interpolation equation P (x) corresponding to the second division time Td1 for the AC signal S1. Further, the interpolation processing circuit 22 calculates the value of L _j (x) (L ₀ (x) = (0 / -6), L ₁ (x) = () calculated in the process of specifying the Lagrangian interpolation formula P (x). 2/2), L ₂ (x) = (0 / −2), L ₃ (x) = (0/6): refer to the above equation (6)) is stored in the processing unit 15 as the coefficient e.

Hereinafter, the interpolation processing circuit 22 specifies Lagrange interpolation formulas P (x) respectively corresponding to the third division time Td1 to the 16th division time Td16 for the AC signal S1 in the same procedure as described above. The value of L _j (x) calculated in the process of specifying the Lagrangian interpolation formula P (x) is stored in the processing unit 15 as the coefficient e.

Thus, the identification of the Lagrangian interpolation formula P (x) corresponding to each division time Td for the AC signal S1 is completed. Next, the interpolation processing circuit 22 specifies a Lagrangian interpolation formula P (x) corresponding to each division time Td for the AC signals S2 and S3. At this time, the interpolation processing circuit 22 reads and uses the coefficient e stored in the storage unit 14. By performing such processing, it is not necessary to calculate the L _j (x) equation when specifying the Lagrange interpolation equation P (x) for the AC signals S2 and S3. The processing time for specifying x) is sufficiently shortened.

On the other hand, as described above, the values of the subscripts ( _j and _i ) in x _j and x _i in the expression L _j (x) are determined by a predetermined n regardless of the instantaneous value Af or the total number m. . For this reason, the interpolation processing circuit 22 calculates the value g of the denominator part in the L _j (x) expression calculated only by x _j and x _i until the total number m is specified from when the measuring apparatus 1 is started. And stored in the storage unit 14. By performing such processing, the time required for specifying the total number m and specifying the Lagrange interpolation formula P (x) using the total number m is further shortened.

Subsequently, the interpolation processing circuit 22 obtains the instantaneous value At at each division time Td by substituting the instantaneous value At into y _j in each Lagrange interpolation formula P (x) specified as described above, and the instantaneous value At is calculated. The digital data Dt shown is output.

  On the other hand, in the measurement unit 16, the effective value calculation processing circuit 31 executes the effective value calculation processing. In this effective value calculation processing, the effective value calculation processing circuit 31 uses the digital data Df (instantaneous value Af) output from the sampling unit 12 to calculate the effective value of a physical quantity (for example, voltage or power) for the AC signal S. taking measurement.

  Further, the FFT processing circuit 32 performs FFT processing for each measurement target Uj using the digital data Dt (instantaneous value At) output from the processing unit 15 to measure the order and amplitude of the harmonics included in the AC signal S. To do. In this measuring apparatus 1, since the instantaneous value At of the power of 2 is calculated in the measurement target Uj, it is possible to efficiently perform the FFT processing. Further, in the measuring apparatus 1, since each instantaneous value At is accurately calculated as described above, the order and amplitude of the harmonics included in the AC signal S are accurately measured by FFT processing.

  Further, the determination processing circuit 33 executes determination processing. In this determination process, the determination processing circuit 33 determines the quality of the measurement target Uj in the AC signal S using the digital data Dt output from the processing unit 15 (instantaneous value At calculated by the interpolation process). Specifically, the determination processing circuit 33 defines the AC signal S that is input immediately before the measurement target Uj and has the same number of periods Ta as the measurement target Uj (in this example, one period Ta) as a comparison target. The upper limit value and lower limit value set for each digital data Dt in the comparison target are compared with each instantaneous value At in the measurement target Uj, and pass / fail is determined based on the comparison result. In this case, when all of the instantaneous values At in the measurement target Uj are included between the lower limit value and the upper limit value, the determination processing circuit 33 determines that the measurement target Uj is good and determines the lower limit value in the measurement target Uj. If there is even one instantaneous value At that is not included in the range from to the upper limit value, the measurement object Uj is determined to be defective.

  In this measuring apparatus 1, by performing an interpolation process, the number of instantaneous values At calculated in the AC signal S for one cycle Ta specified as the measurement target Uj and the AC for one cycle Ta specified as the comparison target. The number of instantaneous values At calculated in the signal S is the same. For this reason, in this measuring apparatus 1, even if the frequency of the AC signal S is fluctuating, all the instantaneous values At in the measurement target Uj and the instantaneous values in the comparison target corresponding to each instantaneous value At, respectively. The upper limit value and the lower limit value set for At can be compared. As a result, in the measurement apparatus 1, it is possible to sufficiently increase the determination accuracy when determining the quality of the measurement target Uj based on the comparison result between the instantaneous value At and the upper limit value and the lower limit value.

  Thereafter, the processing unit 15 repeatedly executes the above-described interpolation processing to output digital data Dt indicating the instantaneous value At, and the measurement unit 16 repeats the above-described effective value calculation processing, FFT processing, and determination processing. Execute. In addition, the measurement unit 16 displays the measured effective value of the physical quantity, the order and amplitude of the harmonics included in the AC signal S, and the result of the quality determination for the measurement target Uj on a display unit outside the drawing.

As described above, in the measurement apparatus 1 and the measurement method, when specifying the Q Lagrangian interpolation formulas P (x) for one of the AC signals S, the summation symbol (Lagrange interpolation formula P (x)) The value of the expression L _j (x) in each term summed by Σ) is calculated, and the value is stored as a coefficient e in the storage unit. Therefore, in the measurement apparatus 1 and the measurement method, when the Lagrange interpolation formula P (x) is specified for the other AC signals S of the plurality of AC signals S other than the AC signal S that has been subjected to the above-described processing. The Lagrange interpolation formula P is a simple operation that simply reads out the value of each L _j (x) expression stored as a coefficient, multiplies the coefficient by the instantaneous value Af, calculates each term, and sums them up. (X) can be specified. Therefore, according to the measurement apparatus 1 and the measurement method, unlike the conventional configuration and method in which only the value g of the denominator part that is a part of the L _j (x) equation in the Lagrange interpolation equation is calculated and stored in advance. When specifying the Lagrange interpolation equation P (x), it is not necessary to calculate the entire L _j (x) equation in the Lagrange interpolation equation, so that the processing time for specifying the Lagrange interpolation equation P (x) is sufficient. Can be shortened.

Further, in the measuring apparatus 1 and the measuring method, the value g of the denominator part in the L _j (x) equation is calculated and stored in the storage unit 14 prior to specifying the total number m, and the storage unit 14 is specified after the total number m is specified. Is used to calculate the value of the expression L _j (x). Therefore, according to the measurement device 1 and the measurement method, for example, the value g of the denominator portion is calculated and stored in the storage unit 14 from when the measurement device 1 is activated until the total number m is specified. Thus, it is possible to further reduce the time until the Lagrange interpolation formula P (x) is specified by specifying the total number m and using the total number m.

  In addition, the measuring apparatus and measuring method which concern on this invention are not limited to said structure and method. For example, from the sampling time Tz immediately after the rising zero cross (in the above example, the sampling time Tz0 shown in FIG. 3), the sampling time Tz immediately after detecting the next rising zero cross (in the above example, shown in FIG. Although the example in which the section up to the sampling time Tz33) is defined as the measurement target Uj (hereinafter, this section is also referred to as “first section”) has been described above, the configuration and method for defining the measurement target Uj as follows. It can also be adopted.

  In this configuration and method, the processing unit 15 has an instantaneous value Af (for example, shown in FIG. 3) before and after the rising zero cross (hereinafter also referred to as “first zero cross”) of the AC signal S acquired by the sampling process. Based on the instantaneous value Af0 and the instantaneous value Af acquired immediately before the instantaneous value Af0), an interpolation formula for zero cross calculation (for example, a linear interpolation formula) is specified, and one interpolation formula for zero cross calculation is used. Calculate the time of the zero crossing of the eye. Further, the processing unit 15 calculates zero crossing based on instantaneous values Af (for example, instantaneous values Af32 and 33 shown in FIG. 5) before and after the next rising zero cross (hereinafter also referred to as “second zero cross”). The interpolation formula (for example, linear interpolation formula) is specified, and the second zero-cross point is calculated from the zero-cross calculation formula. Further, the processing unit 15 defines, as the measurement target Uj, a section corresponding to one or a plurality of periods Ta of the AC signal S divided by the calculated two zero cross points (first and second zero crosses).

  Further, in this configuration and method, when the one cycle Ta of the AC signal S calculated as described above is different from the length of the first section described above, the processing unit 15 performs Lagrange based on both values. The value of m described above in the interpolation formula P (x) is specified. Specifically, the processing unit 15, for example, in the case where one cycle Ta of the AC signal S calculated as described above is 1% longer than the length of the first section (that is, when it is 1.01 times). ) When 33 sampling periods Ts are counted in the first interval, in the above-described interpolation processing, 33.33 obtained by multiplying the counted 33 by 1.01 is set to m as described above, and the Lagrange interpolation formula P (x ).

  Here, in the above-described configuration and method in which the interval between the sampling points Tz immediately after the two zero crosses is defined as the measurement target Uj, the time from the zero crossing point to the immediately subsequent sampling point Tz may vary. Thereby, the length of the measuring object Uj may be longer or shorter than one cycle Ta of the AC signal S. As a result, in this configuration and method, for example, the instantaneous value At at each division time Td corresponding to the tip of each division section Ud obtained by equally dividing the section corresponding to one period Ta of the AC signal S into Q pieces is represented by a Lagrange interpolation formula. When trying to obtain from P (x), each of the obtained instantaneous values At is an inaccurate value because the length of the measurement object Uj is different from the length of one cycle Ta of the AC signal S. There is a risk of becoming. On the other hand, according to this configuration and method, since one cycle Ta of the AC signal S can be accurately calculated, the one cycle Ta can be defined as the measurement target Uj. The instantaneous value At can be obtained accurately.

  The configuration and method in which “n” is defined as 3 and the number of instantaneous values Af used in the Lagrange interpolation formula P (x) is defined as (n + 1) (that is, 4) has been described above. Can be defined as any integer greater than or equal to one.

  Further, the configuration and the method for defining the section corresponding to approximately one period Ta from the sampling time Tz immediately after detecting the rising zero cross to the next sampling time Tz immediately before detecting the zero cross as the measurement target Uj are described above. However, the measurement object Uj can be defined to have an arbitrary length divided by any two sampling time points Tz.

The configuration and method of calculating and storing the value g of the denominator part in the expression L _j (x) from when the measuring apparatus 1 is started until the total number m is specified in the storage unit 14 are described above. It is also possible to adopt a configuration and method in which the value of the entire L _j (x) expression including the value g of the denominator part is calculated and stored in the storage unit 14 when the total number m is specified.

DESCRIPTION OF SYMBOLS 1 Measuring apparatus 12 Sampling part 15 Processing part 16 Measuring part Af Instantaneous value At Instantaneous value e Coefficient g Value k Rank value m Total number S1-S3 AC signal Ud Division | segmentation area Uj Measurement object Td0-Td15 Division | segmentation time Ts Sampling period

Claims (4)

A sampling unit that performs a sampling process for inputting a plurality of AC signals and acquiring instantaneous values of the AC signals at a predetermined sampling period;
An interpolation formula representing a waveform of a part of the AC signal defined as a measurement target, and a Lagrangian interpolation formula given by the following formula (1), the instantaneous value acquired by the sampling processing in the measurement target: Are specified based on n + 1 (n is a predetermined integer equal to or greater than 1) instantaneous values, and the time length of the measurement target is determined by Q (Q is equal to or greater than 2 determined in advance) A processing unit for performing an interpolation process for obtaining the instantaneous values from the Lagrangian interpolation formula at a total of Q division points corresponding to the tip of each division section divided into (integer) pieces;
A measurement device including a measurement unit that performs measurement on the AC signal using the instantaneous value calculated by the interpolation process,
The processing unit specifies Q Lagrangian interpolation formulas corresponding one-to-one to the Q division time points, and determines the Lagrangian interpolation formulas for any one of the AC signals. When specifying, the subscript values of x _j and x _i in the L _j (x) expression of each term summed up by the summation symbol in each Lagrangian interpolation formula are the x _j and x _i And a measurement value to which the temporal ranking in the Q points at each of the divided points corresponding to each Lagrangian interpolation formula is counted from 0 (k is an integer of 0 or more) and the measurement object The value obtained by dividing the product of the total number of sampling periods m (where m is a value greater than or equal to 0) by Q and divided by Q (k × m / Q) is substituted for x in the expression L _j (x). the said L _{j (x)} equation values stored in the storage unit as a coefficient of the previous The measuring device identified using the coefficients a stored each Lagrange interpolation equation in the storage unit of the other AC signals except for one of the AC signal out of the AC signal.
p (x) = Σ [j = 0, n] L _j (x) y _j (where L _j (x) = Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i )) ... (1) Prior to specifying the total number m, the processing unit calculates a value of a denominator part in the L _j (x) equation and stores it in the storage unit. After specifying the total number m, the processing unit stores the value in the storage unit. The measuring apparatus according to claim 1, wherein the value of the L _j (x) equation is calculated using a value of the denominator portion.   The processing unit specifies an interpolation formula for zero cross calculation based on the instantaneous value before and after the zero cross of the AC signal acquired by the sampling process, and determines the time of the zero cross from the interpolation formula for zero cross calculation. The measuring apparatus according to claim 1, wherein the measurement object defines a section corresponding to one or a plurality of periods of the AC signal calculated and divided according to the time of the zero crossing. A sampling process for inputting a plurality of AC signals and acquiring instantaneous values of the AC signals at a predetermined sampling period is performed.
An interpolation formula representing a waveform of a part of the AC signal defined as a measurement target, and a Lagrangian interpolation formula given by the following formula (1), the instantaneous value acquired by the sampling processing in the measurement target: Are specified based on n + 1 (n is a predetermined integer equal to or greater than 1) instantaneous values, and the time length of the measurement target is determined by Q (Q is equal to or greater than 2 determined in advance) (Integer) performing an interpolation process to obtain the instantaneous values from the Lagrange interpolation formula at the time of Q divisions corresponding to the leading ends of each divided section,
A measurement method for measuring the AC signal using the instantaneous value calculated by the interpolation process,
When identifying the Q Lagrangian interpolation formulas that correspond one-to-one to the Q division time points, and identifying the Lagrangian interpolation formulas for any one of the AC signals, Substituting the subscript values of x _j and x _i in the L _j (x) expression of each term summed by the summation symbol in each Lagrangian interpolation formula as the values of x _j and x _i , And a ranking value k (k is an integer of 0 or more) counting from 0 the temporal ranking among the Q points at each division time point corresponding to each Lagrangian interpolation formula, and the sampling period of the measurement object. total m (m is 0 or a value) quotient multiplied value divided by the Q of the (k × m / Q) said L _{j (x)} the L _j which is calculated by substituting the expressions of x ( x) is stored in the storage unit as a coefficient, and the AC signal Measurement method identified using the coefficients a stored each Lagrange interpolation equation in the storage unit of the other AC signals except the Chino said one ac signal.
p (x) = Σ [j = 0, n] L _j (x) y _j (where L _j (x) = Π [i = 0 (i ≠ j), n] (xx _i ) / (x _j -x _i )) ... (1)

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