JPH07229933A - Digital calculation method for a.c. electricity quantity - Google Patents

Abstract

PURPOSE:To calculate effective electric power and phase difference with high precision even under fluctuation in A.C. circuit's frequency by storing three samplings of voltage/current data in a memory for calculation. CONSTITUTION:Three sampling of voltage/current data are stored in a memory, and the current, previous and the one before previous data for voltage and current, the current data for voltage and the one before previous data for current, and the one before previous data for voltage and the current data for current are multiplied each other, thus the first product calculation 11 - the fifth product calculation 15 are performed. Then, sampling phase angle calculation 24 is performed for its sine value calculation 45 to be done, and after processed with square value calculation 25, it is multiplied by four, so that the sixth product calculation 16 is conducted. Then, from the sum of the first and third products 11 and 13, both the fourth and fifth products 14 and 15 are subtracted so that the first addition calculation 31 is conducted, and the result is divided by the sixth product 16, or the first quotient calculation 41 is conducted. Further, the first quotient 41 and the second product 12 are added together as the second addition calculation 32, and that is taken as the effective electric power of A.C. circuit.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of digitally calculating an AC electric quantity for obtaining active power and phase difference from voltage data, current data and frequency of an AC circuit sampled at a predetermined cycle.

[0002]

2. Description of the Related Art Since an AC circuit is often controlled by a digital controller or protected by a digital protection relay, the active power P of the AC circuit and the phase difference Δθ between the voltage and the current are digitally measured. It has become necessary to detect in. FIG. 4 is a calculation procedure diagram showing a conventional example of a method of calculating active power. Although the illustration in FIG. 4 is omitted in calculating the active power P, the voltage data and the current data are obtained at a sampling frequency 12 times the frequency of the AC circuit, and at least the current voltage is stored in the memory 66. The sample data V _n , the previous voltage sample data V _{n- 1} , the _two- preceding voltage sample data V _{n- 2} , the three previous voltage sample data V _n-3 , the current current sample data I _n , the previous current sample data I _{n- 1} , _two- preceding current sample data I _n-2 , and three-preceding current sample data I
Store _n-3 . The first product operation 11 calculates the product of the current voltage sample data V _n read from the memory 66 and the current current sample data I _n, and the eleventh product operation 21 is three times the previous voltage sample data V _n-3 and three times. The product with the previous current sample data I _n-3 is calculated. The fourth addition operation 34 adds the operation result of the first product operation 11 and the operation result of the eleventh product operation 21, and the addition result is the active power P.

The operation shown in FIG. 4 is represented by a mathematical expression as the following formula 1.

[0004]

[Number 1] _{P = V n · I n +} V n-3 · I n-3 and FIG. 5 is a calculation procedure diagram showing a conventional example of a method of calculating the phase difference. When calculating the phase difference Δθ, the voltage data and the current data are obtained at a sampling frequency that is 12 times the frequency of the AC circuit in the same manner as the above-described calculation of the active power P. The voltage sample data before and 3 times, and the current sample data, the previous time, the previous two times, and the current sample data before 3 times are stored, and these data are read out to perform the calculation.

That is, the first product operation 11 calculates the product of the current voltage sample data V _n and the current current sample data I _n, and the eleventh product operation 21 calculates the voltage sample data V three times before.
calculates the product of the _n-3 and three times before the current sample data I _n-3, the fourth addition operation 34 adds the calculation result of the calculation results and the 11 multiply operation 21 of the first AND operation 11 This is the same as the case of FIG. 4 described above, but the twelfth product operation 22 further includes the current voltage sample data V _n and the current sample data I three times before.
calculates the product of the _n-3, the product of the first 13 AND operation 23 3 times before voltage sample data V _n-3 and the current current sample data I _n is calculated, the second subtract operation 36 12th AND operation An operation of subtracting the operation result of the thirteenth product operation 23 from the operation result of No. 22 is performed. Next, in the third quotient operation 43, the second subtraction operation 36
The operation result is divided by the operation result of the fourth addition operation 34, and the operation result is tan Δθ. In the arctangent value calculation 47, the arctangent of this tan Δθ is calculated to calculate the phase difference Δθ.
Is getting

The operation shown in FIG. 5 is represented by a mathematical expression as the following expression 2.

[0007]

[Equation 2]

[0008]

By the way, in the calculation shown in the conventional example of FIG. 4 (that is, the calculation of Equation 1) and the calculation shown in the conventional example of FIG. 5 (that is, the calculation of Equation 2), the sampling frequency is Since it is assumed that the frequency is 12 times the AC circuit frequency, if the frequency of the AC circuit fluctuates, there is a disadvantage that an error occurs in the calculation result due to this fluctuation. Therefore, there is a problem in that these digital calculation results cannot be used in the case where there is a circuit with frequency fluctuation or when the calculation result is required to be highly accurate even if the frequency fluctuation is slight. .

Therefore, an object of the present invention is to accurately measure the active power P and the phase difference Δ even if the frequency of the AC circuit varies.
It is to be able to calculate θ.

[0010]

In order to achieve the above object, a method for digitally calculating an AC electric quantity according to the present invention is a voltage obtained by separately sampling a voltage and a current of an AC circuit at a predetermined sampling cycle. At least three times of the data and the current data are stored in the memory, the first product is calculated by multiplying the current sampling data of the voltage and the current sampling data of the current, and the previous sampling data of the voltage and the previous sampling of the current are sampled. A second product is calculated by multiplication with the data, and a third product is calculated by multiplication of the voltage before-second batch sampling data and the current before-second batch sampling data, and the current current sampling data and the current before-second batch sampling data are calculated. The fourth product is calculated by multiplying by, and the sampling data of the voltage before the current and the current sampling of the current are sampled. It calculates a fifth product by multiplication with over motor, the frequency of the AC voltage sampling period and 2
The sampling phase angle is calculated by multiplying with π, the sine value of this sampling phase angle is calculated, the square of this sampling phase angle sine value is calculated, and the sixth product that multiplies this square value by 4 is calculated. , A first addition that subtracts the fourth product and the fifth product from the sum of the first product and the third product, and a first quotient that divides the first addition result by the sixth product , The sum of the first quotient and the second product is calculated by the second addition, and the result of the second addition is used as the active power of the AC circuit.

Alternatively, at least three times of the voltage data and the current data obtained by separately sampling the voltage and the current of the AC circuit at a predetermined sampling period are stored in the memory, and the current sampling data of the voltage and the current sampling of the current are stored. The first product is calculated by multiplication with the minute sampling data, and the second product is calculated by multiplying the previous minute sampling data of the voltage and the previous minute sampling data of the current, and the pre-preceding sampling data of the voltage and the pre-preceding sampling of the current are calculated. The third product is calculated by multiplication with the data, and the fourth product is calculated by multiplying the current sampling data of the voltage and the pre-preceding sampling data of the current, and the pre-preceding sampling data of the voltage and the current sampling data of the current are calculated. The fifth product is calculated by multiplying by The seventh product is calculated by multiplication with the sampling data, and the eighth product is calculated by multiplying the previous sampling data of the voltage and the current sampling data of the current, and the eighth product of the frequency of the AC voltage, the sampling period and 2π is calculated. The sine value of the sampling phase angle obtained by the multiplication is calculated, the square of the sine value of the sampling phase angle is calculated, and the first subtraction that subtracts the eighth product from the seventh product is calculated. A ninth product is calculated by multiplying the sampling phase angle sine value by 4, and a tenth product is calculated by multiplying the squared value of the sampling phase angle sine value by the second product by 4. A third addition that subtracts the fourth product and the fifth product from the sum of the product, the third product, and the tenth product is calculated, and a second quotient that divides the ninth product by the third addition result is calculated. , Calculate the arctangent value of this second quotient Then, this arctangent value is used as the phase difference between the voltage and current of the AC circuit.

[0012]

According to the present invention, at least three times of the sampled voltage data and current data (that is, the current sampling data, the previous sampling data, and the pre-previous sampling data) are stored in the memory. Further, from the sampling period T and the frequency f of the AC circuit, θ = 2π ·
Obtain the sampling phase angle θ by the calculation f · T s
In θ is calculated, and the sampling data for 3 times and sin
From θ, the effective power P and the phase difference Δθ that are not affected by the frequency of the AC circuit are calculated.

[0013]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a calculation procedure diagram showing a first embodiment of the present invention, showing a case of calculating active power P.
In the first embodiment shown in FIG. 1, the memory 66 stores the current voltage sample data V _n , the previous voltage sample data V _n-1 , the _{two -} preceding voltage sample data V _n-2 , the current current sample data I _n , and the previous current sample data. I _n-1 , the current sample data I _n-2 before two times, the frequency f and the sampling period T are stored, and the following calculation is performed from these data. That is, the first product calculation 11 calculates the product of the current voltage sample data V _n and the current current sample data I _n, and the second product calculation 12 calculates the previous voltage sample data V _n-1.
And the previous current sample data I _n-1 are calculated, and the third
The product operation 13 calculates the product of the previous-previous-time voltage sample data V _n-2 and the previous _- previous _- time current sample data I _n-2, and the fourth product operation 14 calculates the present-time voltage sample data V _n and the previous-previous-time current sample data I _n-2 . The fifth product operation 15 calculates the product of the voltage sample data V _n−2 before this time and the current current sample data I _n, and further the sampling phase angle operation 24
Calculates the sampling phase angle θ which is the product of the frequency f, the sampling period T and 2π.

The sine value calculation 45 calculates sin θ which is the sine value of the sampling phase angle θ, and the square value calculation 25 calculates this s
In θ is squared to obtain sin ² θ, and the sixth product operation 1
6 calculates the 4 sin ² theta from the sin ² theta. On the other hand, the first addition operation 31 is an operation of subtracting the operation result of the fourth product operation 14 and the operation result of the fifth product operation 15 from the sum of the operation result of the first product operation 11 and the operation result of the third product operation 13. Therefore, the calculation result is the following Expression 3.

[0015]

[Formula 3] V _n · I _n + V _n-2 · I _n-2 −V _n · I _n-2 −
The V _n−2 · I _n first quotient operation 41 divides the operation result of the first addition operation 31, that is, Formula 3, by the operation result of the sixth product operation 16, that is, 4 sin ² θ. The second addition operation 32 is the result of this division and the second product operation 1
The sum of the calculation result and the calculation result of 2 is calculated, and this calculation result is the active power P. That is, the calculation shown in FIG.

[0016]

[Equation 4]

FIG. 2 is a calculation procedure diagram showing the second embodiment of the present invention, and shows the case where the phase difference Δθ is calculated. In the second embodiment shown in FIG. 2, the memory 66 stores the current voltage sample data V as in the first embodiment shown in FIG.
_n , the previous voltage sample data V _n-1 , the voltage sample data V _{n-2 two} times before, and the current sample data I _n ,
The previous current sample data I _n-1 and the _{two -} preceding current sample data I _{n- 2} , the frequency f and the sampling period T are stored, and the following calculation is performed from these data.
That is, the first product calculation 11 calculates the product of the current voltage sample data V _n and the current current sample data I _n, and the second product calculation 12 calculates the previous voltage sample data V _n-1 and the previous current sample data I _{n-. 1} calculates the product of the third aND operation 13 calculates the product of the second last voltage sample data V _n-2 and the second last current sample data I _n-2, the fourth aND operation 14 this voltage sample data V _n And the _two- preceding current sample data I _n-2
And the fifth product calculation 15 calculates the product of the voltage sample data V _n−2 before this time and the current current sample data I _n, and the seventh product calculation 17 calculates the current voltage sample data V _n and the previous current. The product of the sample data I _n-1 is calculated, the eighth product calculation 18 calculates the product of the previous voltage sample data V _n-1 and the current current sample data I _n, and the sampling phase angle calculation 24 calculates the frequency f. And the sampling phase angle θ which is the product of the sampling period T and 2π.

The sine value calculation 45 calculates sin θ which is the sine value of the sampling phase angle θ, and the first subtraction calculation 35
Is a subtraction of the operation result of the eighth product operation 18 from the operation result of the seventh product operation 17, and the ninth product operation 19 is the product of the operation result of these first subtraction operation 35 and the operation result of sine value operation 45. 4 times is calculated. Therefore, the operation result of the ninth product operation 19 is the following Expression 5.

[0019]

Equation 5] _{4 (V n · I n-} 1 -V n-1 · I n) sinθ Meanwhile, squared value calculation 25 2 the calculation result of the sine value calculation 45
And multiply achieved a sin ² theta, since the tenth AND operation 20 square value calculation 25 calculates four times the product of the operation result of sin ² theta and a second AND operation 12 that operation, the operation The result is A
Is the following expression 6.

[0020]

[6] _{A = 4 · V n-1} · I n-1 · sin 2 θ Furthermore, the third addition operation 33 the calculation result of the calculation result and the third AND operation 13 of the first AND operation 11 described above and the A calculation is performed by subtracting the calculation result of the fourth product calculation 14 and the calculation result of the fifth product calculation 15 from the sum of the calculation result of the 10 product calculation 20 and the calculation result is the following Expression 7.

[0021]

[Formula 7] V _n · I _n + V _n-2 · I _n-2 −V _n · I _n-2 −
V _n−2 · I _n + 4 · V _n−1 · I _n−1 · sin ² θ The second quotient operation 42 is the result of the operation of the ninth product operation 19 (see equation 5) described above in the third addition operation 33. An operation that divides by the operation result (see Equation 7) is performed, and the operation result is tan
Δθ. By calculating the arctangent value of this tan Δθ by the arctangent value calculation 47, the phase difference Δθ can be obtained.

The operation of FIG. 2 can be expressed by the following mathematical expression 8. However, A described in the denominator on the right side of Expression 8 is the value described in Expression 6 described above.

[0023]

[Equation 8]

FIG. 3 is a circuit diagram showing an application example of the first embodiment of FIG. 1 and the second embodiment of FIG. In the application example circuit of FIG. 3, an AC voltage detector 7 is provided in the AC circuit 6 to convert an analog voltage signal into an analog filter 51, a sample holder 53, an A /
It is converted into a digital amount by the D conversion 55 and given to the digital arithmetic circuit 60. Similarly, the current signal detected by the AC current detector 8 also includes the analog filter 52, the sample holder 54, and the A / D converter 56 that form the analog input circuit 50.
Is converted into a digital amount by and is given to the digital arithmetic circuit 60.

The digital voltage signal is supplied to the digital filter 61.
The unnecessary harmonic component is removed by and stored in the memory 66 via the gain correction 63. The digital current signal is also stored in the memory 66 via the digital filter 62 and the gain correction 64. On the other hand, the frequency calculator 65 calculates the frequency of the AC circuit 6 from the output of the digital filter 61. If this frequency fluctuates, the gains of the analog filters 51 and 52 and the digital filters 61 and 62 change. Therefore, the gain corrections 63 and 64 correct the change in gain due to this frequency fluctuation. However, when the changes in the gains of the analog filters 51 and 52 and the digital filters 61 and 62 due to the frequency change are so small as to be negligible and the accuracy of the calculation result is not affected, the gain corrections 63 and 64 can be omitted. is there.

If the frequency f calculated by the frequency calculator 65 and the sampling data read from the memory 66 are given to the active power calculation circuit 70, the active power P is output and the phase difference calculation circuit 80 outputs the phase difference Δθ. The arithmetic circuit 70 is configured by the calculation procedure shown in FIG.
The phase difference calculation circuit 80 is configured by the calculation procedure shown in FIG.

[0027]

The conventional calculation method for calculating the active power P by using the equation 1 and the conventional calculation method for calculating the phase difference Δθ by using the equation 2 are based on the calculation principle when the frequency of the AC circuit changes. It causes an error. For example, if the frequency of the AC circuit is 60Hz and the sampling frequency is 720Hz, the AC frequency is ±
A 5% fluctuation (that is, a fluctuation from 57Hz to 63Hz) causes a maximum error of 7.8% in the active power calculation. On the other hand, the calculation of the active power P represented by the equation 4 and the equation 8
In the calculation of the phase difference Δθ represented by, no error occurs in principle even if the frequency changes. The arithmetic circuit is configured according to the calculation procedure of the present invention, the total error of the active power P when the AC frequency fluctuates from 57 Hz to 63 Hz is within 0.13%, and the total error of the phase difference Δθ can be within 0.1 degree. Therefore, it is possible to obtain an effect that an error when performing digital control or when using a digital protection relay can be reduced to a negligible level.

[Brief description of drawings]

FIG. 1 is a calculation procedure diagram showing a first embodiment of the present invention.

FIG. 2 is a calculation procedure diagram showing a second embodiment of the present invention.

FIG. 3 is a circuit diagram showing an application example of the first embodiment of FIG. 1 and the second embodiment of FIG.

FIG. 4 is a calculation procedure diagram showing a conventional example of a method for calculating active power.

FIG. 5 is a calculation procedure diagram showing a conventional example of a phase difference calculation method.

[Explanation of symbols]

6 AC circuit 7 AC voltage detector 8 AC current detector 11-23 First product operation-13th product operation 24 Sampling phase angle operation 25 Square value operation 31-34 First addition operation-4th addition operation 35-36 First subtraction operation to second subtraction operation 41 to 43 First quotient operation to third quotient operation 45 Sine value operation 47 Arctangent value operation 50 Analog input circuit 51,52 Analog filter 53,54 Sample holder 55,56 A / D Conversion 60 Digital calculation circuit 61,62 Digital filter 63,64 Gain correction 65 Frequency calculation 66 Memory 70 Active power calculation circuit 80 Phase difference calculation circuit f AC circuit frequency I _n Current current sample data I _n-1 Previous current sample data I _{n -2} second last current sample data I _n-3 3 times before the current sample data P active power T sampling period V _n now Voltage sample data V _n-1 the previous voltage sample data V _n-2 before last voltage sample data V _n-3 3 times before voltage sample data Δθ phase difference θ sampling phase angle

Claims (2)

[Claims] 1. A memory stores at least three times of voltage data and current data obtained by separately sampling a voltage and a current of an AC circuit at a predetermined sampling period,
The first product is calculated by multiplying the current sampling data of the voltage and the current sampling data of the current, and the second product is calculated by multiplying the previous sampling data of the voltage and the previous sampling data of the current. The third product is calculated by multiplying the previous-second batch sampling data and the current previous-second batch sampling data, and the fourth product is calculated by multiplying the current-time previous sampling data by the current and the current previous-second batch sampling data. A fifth product is calculated by multiplying the sampling data by the current sampling data of the current, the frequency of the AC voltage is multiplied by the sampling period by 2π to obtain a sampling phase angle, and the sine value of this sampling phase angle is calculated. The square product of this sampling phase angle sine value is calculated, and the sixth product that multiplies this square value by 4 is obtained. Calculated and calculates a first adder subtracting said fourth product and the fifth product from the sum of the first product and the third product,
The first quotient of dividing the first addition result by the sixth product is calculated, the sum of the first quotient and the second product is calculated by the second addition, and the second addition result of the AC circuit is calculated. A method of digitally calculating the amount of alternating current electricity, which is characterized by using active power. 2. A memory stores at least three times of voltage data and current data obtained by separately sampling the voltage and current of the AC circuit at a predetermined sampling period,
The first product is calculated by multiplying the current sampling data of the voltage and the current sampling data of the current, and the second product is calculated by multiplying the previous sampling data of the voltage and the previous sampling data of the current. The third product is calculated by multiplying the previous-second batch sampling data and the current previous-second batch sampling data, and the fourth product is calculated by multiplying the current-time previous sampling data by the current and the current previous-second batch sampling data. The fifth product is calculated by multiplying the sampling data by the current sampling data of the current, and the seventh product is calculated by multiplying the current sampling data of the voltage by the previous sampling data of the current, and the previous sampling data of the voltage is calculated. And the current sampling data of the current are multiplied to calculate the eighth product, The wavenumber sampling period and 2
The sine value of the sampling phase angle obtained by multiplication with π is calculated, the square of the sine value of the sampling phase angle is calculated, and the first subtraction that subtracts the eighth product from the seventh product is calculated. A ninth product is calculated by multiplying the subtraction result by the sampling phase angle sine value and 4, and a tenth product is calculated by multiplying the squared value of the sampling phase angle sine value by the second product and 4. A second quotient that calculates a third addition that subtracts the fourth product and the fifth product from the sum of the first product, the third product, and the tenth product, and divides the ninth product by the third addition result. Is calculated, and the arctangent value of the second quotient is calculated, and the arctangent value is used as the phase difference between the voltage and the current of the AC circuit.