JPS6160613B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a frequency component separation device. Traditionally, to separate frequency components, the analog output from a voltage or current transformer is routed through a filter whose passband is selected to correspond to the frequency components to be separated. was. However, according to this method, in order to improve selectivity, it is necessary to increase the sharpness of the filter, but this inevitably slows down the response speed. , some selectivity must be sacrificed. Also, digital transformers have recently been developed,
This outputs voltage and current waveforms as digital codes as they are, making it impossible to separate frequency components using an analog filter. An object of the present invention is to separate arbitrary frequency components from an input waveform by digital filtering processing. This invention obtains a plurality of sampling values by sampling an input waveform at regular intervals, and calculates these values using an adder/subtractor and a multiplier to obtain fundamental wave components and arbitrary harmonic components. It is. Examples of the present invention will be described below. First, to explain its operating principle, the input waveform g(t) shown in Figure 1 is Suppose we give it as However, k is an integer, ω is an angular frequency, and k is a phase. From now on, according to Fourier's theorem, for integers l>0 holds true. Now, one cycle (2π/ωsec) is divided into 2n equal parts, and as shown in Fig. 1, if the sampling value at time t _-i (i = 0 to 2n) is g _-i , then time t _{-(i+1 )} ≦
The time interval obtained by equally dividing g(t) at t≦t _-i is △
If t, then g _−i −g _−(i+1) /△t(t−t _−i )+g _−i (4
), the approximate value of equations (2) and (3) is is obtained. When we perform the integration on the right side of equations (5) and (6), we get get. Here, if t ₀ = 0, t _-2o = -2π/ω, and △t = π/nω・g _-2o = g ₀ , so from these becomes. Also, since t _-(o+i) = t _-i -π/ω, sin lωt _-(o+i) = sin lω(t _-i -π/ω) = (coslπ)×sin lωt _-i cos lωt _-(o+i) = coslω(t _-i -π/ω) = (cos lπ)×cos lωt _-i Using these relationships and the fact that g _-2o = g ₀ , similarly are obtained respectively. As a result of the above, as the approximate expression (C _l ) of equation (2) and the approximate equation (S _l ) of equation (3), is given. however It is. (13), (14) can be used to find C _l and S _l , but depending on whether n is even or odd, when n is even When n is an odd number becomes. Here, f _-i ≡g _-i + (cos lπ)g _-(o+i) (19). That is, if C _l and S _l are determined from equations (15) to (18), an arbitrary frequency component can be determined from these. Specifically, from the relationship C _l = I _l・cos _l S _l = I _l sin _l √ ² _l + ² _l = I _l , _l = tan ^-1 S _l /C _l From the peak value and the peak value of any frequency component The phase angle will be found. Also, if l=1, each value for the fundamental wave component can be found, and if l is chosen to be an arbitrary value, each value for any frequency component can be found. Furthermore, when sampling the input waveform at intervals of 30 degrees, n=6 may be used. Next, a specific configuration example of the present invention will be explained with reference to FIG. The block diagram shown in Figure 2 is (16)
The configuration based on the formula is shown. Also, although this example shows the case where the input waveform is a current waveform, the same can be done for a voltage waveform. A current transformer 2 is installed on the power system line 1, and the output from the current transformer 2 is converted to an appropriate voltage level by an insulated level converter 3, and then passed through a low-pass filter 4.
is input. Here, aliasing errors due to sampling are removed, and then the signal is input to the sample and hold circuit 5. The input of the sample/hold circuit 5 is sampled and held using a sampling signal issued from the control circuit 6 at a period corresponding to the sampling interval. The held value is converted to A/D by the AD conversion command from the control circuit 6.
A D converter 7 converts it into digital data. The future digital value is set up on the input side of register ₈₀ . Further, the contents of the previous stage registers are set up on the input side of the registers ₈₁ to _82o-1 , and the set up contents are transferred to each register in response to a transfer instruction clock signal from the control circuit 6. After the transfer, the control circuit 6 returns the sample.
A sample instruction is given to the hold circuit 5 and it waits until the next hold time. As a result of the above, the 2n sampling data are registered so that the contents of the register ₈₀ are the latest ones, and the contents of the register _82o-1 are the latest ones 2n-1 times. The contents of the registers ₈₀ to 8o _-1 are input to the arithmetic units ₉₀ to 9o _-1 together with the contents of the registers 80 _{to 82o-1} which register the sampling values n times before. Each arithmetic unit corresponds to the value of coslπ, and when it is 1, it is an adder, and when it is -1, it is a register 8 ₀ ~
This is a subtracter that subtracts the contents of registers _8o to _82o-1 from the contents of register 8o- ₁ . The results of this calculation are the values of equation (19), that is, f ₀ to f _-(o-1) . The calculated value of computing unit 9 ₁ to 9〓 _-1 is calculated by computing unit 9 1 to 9〓 _-1 to
It is input to the computing units 10 ₁ to 10〓 _-1 together with the computed value of _o-1 . As before, each of these arithmetic units corresponds to the value of coslπ, and when it is 1, it is an adder, and when it is -1, it is an adder, and when _{it is -1 ,} the arithmetic unit 9 _o-
1 to 9〓 This is a subtracter that subtracts the calculated value at ₊₁ .
The calculated values of each of these arithmetic units 10 ₁ to 10〓 _-1 are input to multipliers 11 ₁ to 11〓 _-1 . Each multiplier is

[Equation] is set, and each calculation value of each calculation unit 10 ₁ to 10〓 _-1 is multiplied.
The multiplied value of this result is the second value in the parentheses of equation (16).
Each value of the term is from i=1 to i=n/2-1. Separately, the calculated value of the arithmetic unit 9 is given to a multiplier 12. This multiplier 12 is set to coslπ/2, and multiplies the calculated value of the calculator 9. The multiplied value of this result becomes the value of the third term in the parentheses of equation (16). Arithmetic unit 9 ₀ , multipliers 11 ₁ to 11〓 _-1 and 12
Each calculated value is given to the calculator 13. Add each calculated value input here (this added value is (16)
The value within the expression parentheses. ), this additional value is preset Multiply by the value. The result of this calculation is S of equation (16)
Nothing but _l . Note that when calculating C _l in equation (15), omit the calculated value of the calculating unit ₉₀ , and set the values to each calculating unit 11 ₁ to 11〓 _-1 and 12.

[Formula] and sin(-lπ/2), and the arithmetic units 10 ₁ to 10〓 _-1 correspond to the value of coslπ, and when it is -1, it is an adder, and when it is 1, it is an adder, and when it is 1, it is an adder, and when it is 1, it is an adder, and when it is ₁ , it is an adder.
The subtracter may be used to subtract the calculated value of the calculating units 9 _o-1 to 9 ₊₁ from the calculated value of _-1 . Also, when calculating C _l in equation (17), the arithmetic unit 9 ₀ and the multiplier 12
, and each multiplier 11 ₁ to 11〓
Set the value to _-1

[Formula] may be used, and the arithmetic units 10 ₁ to 10〓 _-1 may be configured in the same way as in the configuration of equation (15). Furthermore, when determining S _l in equation (18), the calculated value of the multiplier 12 may be omitted. In these cases, if l is an even number, sin (-lπ/2) in equation (15) becomes 0, so multiplier 12 is not used, and the configuration is the same as when calculating equation (17). It becomes like this. Also, when l is an odd number, cos (-lπ/2) in equation (16) is 0, so multiplier 12 is not used, and the configuration is the same as when finding equation (18). . In addition, in the above configuration, a computer storage device can be used in place of each register,
In that case, the calculations performed by each arithmetic unit may be performed by a computer. As detailed above, according to the present invention, by sampling the input waveform at predetermined time intervals and obtaining sampling values, it is possible to separate the fundamental wave and arbitrary frequency components of the input waveform, and in this case, the response There is no reduction in speed or selectivity, and it uses the difference (when l is an odd number) and sum (when l is an even number) of two data with a time difference corresponding to π/ωsec, that is, a half cycle of the fundamental wave. Therefore, it depends on each person.
The effect is that harmonics with even numbers are completely eliminated, while harmonics with odd numbers l are completely eliminated.

[Brief explanation of the drawing]

FIG. 1 is a waveform diagram for explaining the operation, and FIG. 2 is a block diagram showing an embodiment of the present invention. 5...Sample hold circuit, 7...A/D converter, 80 to _{8 (2o-1)} ...Register, _{90 to 9o-
1} ,10 ₁ ~10〓 _-1 ... Arithmetic unit, 11 ₁ ~11
〓 _-1 , 12... Multiplier, 13... Arithmetic unit.

Claims (1)

[Claims] 1 For the input waveform expressed by [Formula] (where k is an integer and ω is the angular frequency), each time t _-i (i a sample hold device that samples and holds each time = 0 to 2n);
an A/D converter that converts the sampling value obtained by the sample hold device into a digital quantity; a sampling value gi sampled i sampling times before a certain time among the sampling values converted to the digital quantity; n+i) an algebraic sum calculation means that adds the sampled value g−(n+i) before the number of sampling times, when the harmonic to be separated is an even number wave, and subtracts it when it is an odd number wave; weight sin for each of the calculation outputs of
(-ilπ/n); a first addition means that calculates the sum of the calculation outputs over half a cycle among the calculation outputs from the first multiplication means; a first calculation means that multiplies the output of the means by a proportionality constant and makes the calculation output an approximate value of a cosine wave component of the lth harmonic separated from the input waveform; and calculation output from the algebraic sum calculation means. a second multiplier that multiplies each of the two by a weight cos(-ilπ/n), and a second adder that calculates the sum of the arithmetic outputs over half a cycle among the arithmetic outputs from the second multiplier; Frequency component separation comprising a second calculation means that multiplies the output of the second addition means by a proportionality constant and uses the calculation output as an approximate value of the sine wave component of the lth harmonic separated from the input waveform. Device. 2 Among the calculation outputs from the algebraic sum calculation means, the calculation outputs with the same absolute value of the weights to be multiplied are subjected to an algebraic sum calculation with the same positive and negative signs as the weights, and the value obtained by multiplying the calculation outputs by the weights is calculated. , first or second
Claim 1 is defined as the calculation output of the adding means.
The frequency component separation device described in .