JPH09171038A - Frequency detecting system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately detect the frequency of a power system even when the frequency is largely deviated from a fundamental frequency. SOLUTION: In a system for calculating the frequency of the quantity of AC electricity of a power system, a means 1 calculates the quantity Wm proportional to the integrated value of the quantity (v) of AC electricity of the power system with time from time (m-n) to time (m) based on sampling values vm , vm-1 , vm-2 ,..., vm-n at sampling time m, m-1, m-2,..., m-n and a second means 2 calculates the difference value um =vm -vm-n between the quantity (v) at the time (m-n) and that (V) at time (m). Then a third means 3 calculates the quantity proportional to the effective value or the square of the effective value of the calculated value Wm of the means 1 and a fourth means 4 calculates the quantity proportional to the effective value or the square of the effective value of the calculated value Um of the means 2. A fifth means 5 divides the calculated value of the means 4 by the calculated value of the means 3.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a frequency detecting method for calculating a frequency of an alternating current electricity quantity of a power system with high accuracy.

[0002]

2. Description of the Related Art If the power supply of the power system is insufficient due to a power failure of the power system, the system slows down and the frequency drops. Conversely, when the load drops, the system accelerates and the frequency increases. Therefore, in order to operate the power system stably, it is necessary to detect the frequency with high accuracy. Further, it is necessary to detect the frequency with high accuracy and over a wide range with high accuracy for excitation control of the generator.

[0003]

Conventionally, there has been proposed a method for detecting a deviation from a fundamental frequency by applying the following algorithm.

[Equation 1] The sampling frequency is 12 times the basic frequency of the alternating current electricity quantity.

FIG. 13 shows the frequency characteristic of the calculation by the above equation (1).
Shown in As is clear from the figure, the error increases as the absolute value of ε increases. This is because the true value on the right side of Eq. (1) is sin (2πε) / {cos (πε / 2) × 2π}
It results from being. Therefore, this error has been input in a known table in advance, and the calculation result of the equation (1) has been corrected with the value in this table.

The present invention has been made to solve the above problems, and provides a frequency detection method capable of accurately detecting a frequency even if the frequency of the power system is largely deviated from the fundamental frequency. Is intended.

[0006]

A frequency detecting method according to claim 1 of the present invention is a method for calculating a frequency of an alternating-current electric quantity of a power system, and is a sampling time m, m-1, of the electric quantity v of the system. Sampling value v of m−2, ..., M−n
_{Based on m} , v _m-1 , v _m-2 , ..., V _mn , time _mn
Quantity w proportional to the time integral value of the electric quantity v from m to m
second calculating a first means for calculating the _m, a difference value u _m = v _m -v _mn of the same electric quantity v in the time mn and m
Means and third means for calculating an amount proportional to the effective value or the square of the effective value of the value w _m calculated by the first means,
Fourth means for calculating an effective value of the value u _m calculated by the second means or an amount proportional to the square of the effective value; and a value calculated by the fourth means by a value calculated by the third means. It is provided with a fifth means for removing.

In the present invention, the electric quantity of the electric power system V · sin (ω
In t), the time quantity of electricity from time t-t ₀ to t the integral value _{2V · sin (ωt 0/2} ) · sin (ωt-ωt 0
/ 2) / ω and the difference 2 between the amounts of electricity at times t-t ₀ and t
Since the _{V · sin (ωt 0/2} ) · cos (ωt-ωt 0/2), by paying attention to the point where the amplitude ratio of the latter alternating quantity with respect to the amplitude of the former alternating amount is omega, detects the frequency It is a thing.

[0008] Here, v = a sin (ωt _m), calculates the amount w _m and u _m = v _m -v _mn proportional to the time integral value of v from sampling time mn to m. And the w _m
And an effective value of u _m or an amount proportional to the square of the effective value is calculated,
A value F (ω) obtained by dividing the effective value of u _m or the amount proportional to the square of the effective value by the effective value of w _m or the amount proportional to the square of the effective value.
Was found to be proportional to the angular frequency ω or ω ² . Other claims are also the same.

A frequency detecting method according to a second aspect of the present invention is the frequency detecting method according to the first aspect, wherein the first means is integration by a trapezoidal formula, that is, w _m is calculated by the following equation.

(Equation 2)

A frequency detecting method according to a third aspect of the present invention is the frequency detecting method according to the first aspect, wherein the first means is rectangle integration, that is, w _m is calculated by the following equation.

(Equation 3)

A frequency detecting method according to a fourth aspect of the present invention is the frequency detecting method according to the first aspect, wherein the first means is integration by the Simpson formula, that is, w _m is calculated by the following equation.

(Equation 4)

According to a fifth aspect of the present invention, in the first aspect, the third and fourth means in the first aspect calculate the following electric quantities.

In the third means, w _mk · w _mp −w _m · w _{mkp In} the fourth means, u _mk · u _mp −u _m · u _mkp

According to a sixth aspect of the present invention, in the first aspect, the third and fourth means in the first aspect calculate the following electric quantities.

(Equation 6)

According to a seventh aspect of the present invention, in the first aspect, the third and fourth means in the first aspect calculate the following electric quantities.

(Equation 7)

According to an eighth aspect of the present invention, in the first aspect, the third and fourth means in the first aspect calculate the following electric quantities.

(Equation 8)

According to a ninth aspect of the present invention, in the frequency detecting method according to the first aspect, the value obtained by the fifth means is compared with a predetermined constant, and the operation is performed when the former is larger than the predetermined constant. A sixth means of overfrequency detection for determination is added.

According to a tenth aspect of the present invention, in the frequency detecting method according to the first aspect, the value obtained by the fifth means is compared with a predetermined constant, and the operation is performed when the former is smaller than the predetermined constant. The sixth means for detecting an insufficient frequency is added.

The frequency detection method according to claim 11 of the present invention is the method according to claim 1, wherein the effective value obtained by the fourth means or an amount proportional to the square of the effective value and the effective value obtained by the third means. Alternatively, a sixth means for overfrequency detection is added, which compares an amount proportional to the square of the effective value with a value obtained by multiplying a predetermined constant, and determines the operation when the former is larger than the latter.

According to a twelfth aspect of the present invention, in the frequency detection method according to the first aspect, the effective value obtained by the fourth means or an amount proportional to the square of the effective value and the effective value obtained by the third means are used. Alternatively, a sixth means for detecting an under-frequency is added to compare an amount proportional to the square of the effective value with a value obtained by multiplying a predetermined constant, and determine the operation when the former is smaller than the latter.

[0020]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 2 is a schematic configuration diagram of a digital relay to which the system according to the present invention is applied. In the figure, the input voltage v is first sampled by the sample hold circuit S / H, sequentially switched by the multiplexer MPX and input to the analog / digital converter A / D, and the converted digital value is applied to the arithmetic unit CPU. It

The CPU has a configuration for performing a predetermined operation determination calculation based on the present invention and outputting the result.
In the figure, the output of the S / H circuit of the voltage v is described as v _m , but it is also described in the same manner without distinction in the digital processing in the digital operation unit CPU.

Next, FIG. 1 is a diagram showing an embodiment of a frequency detection system according to the present invention. In FIG. 1, reference numeral 1 is a first means for calculating the following equation using the alternating-current electric quantities v _m , v _m-1 , v _m-2 , ..., V _mn .

(Equation 9)

Reference numeral 2 is a second means for calculating u _m = v _m -v _mn using the same amount of electricity as above. 3 is a third means, and w _mk is obtained by using w _m obtained by the first means described above.
· W by calculating the _{mp -w m · w mkp, w} m
Calculate an amount proportional to the square of the effective value of.

[0024] 4 in the fourth means, by calculating the _{u mk · u mp -u m ·} u mkp using u _m obtained in the second means, to the square of the effective value of u _m Calculate the proportional amount. 5 is a fifth means, the value obtained by the fourth means,
Divide by the value obtained by the third means to calculate an amount proportional to the square of the frequency.

The calculation result of FIG. 1 will be verified. The sampling value v _m of the AC electric quantity at the sampling time t _m, when the _{v m = V · sin (ωt} m), w m, u
_m is obtained as Eqs. (2) and (3).

[0026]

[Equation 10]

When tan (ωT / 2) in the equation (2) is approximated to ωTK / 2, the equation (2) becomes the equation (4).

[Mathematical formula-see original document] w _m = 2Vsin (ωt _m −nωT / 2) ・ sin (nωT / 2) / (ωTK) (4) where K is the approximation error _{0 at} ω = ω ₀ Therefore, K = tan (ω ₀ T / 2) / (ω ₀ T / 2).

Further, the calculation amount of the amount proportional to the square of the effective value of w and u is expressed by the equations (5) and (6).

[ _Formula 12] w _mk · w _mp −w _m · w _mkp = {2V · sin (nωT / 2) / (ωTK)} ² · sin (kωT) · sin (pωT) ………… (5) u _{mk · u mp -u m · u mkp} = {2V · sin (nωT / 2)} 2 · sin (kωT) · sin (pωT) ............ (6)

Here, the value F (ω) obtained by dividing equation (6) by equation (5)
Is a quantity proportional to the square of the angular frequency ω, as in Eq. (7). Also, equation (8) is obtained from equation (7).

[Number 13] _{F (ω) = (u mk} · u mp -u m · u mkp) / (w mk · w mp -w m · w mkp) = (ωTK) 2 .................. (7) (1 + ε) ² = F (ω) / (πf ₀ TK) ² (8) where ε = (f−f ₀ ) / f ₀

FIG. 3 shows the frequency characteristic of ε obtained from the equation (8).
Shown in As can be seen from the figure, it is possible to calculate the frequency of the system with high accuracy over a wide band, as compared with the conventional calculation method shown in equation (1). Note that the error is the error that occurs from the approximation from Eq. (2) to Eq. (4) and can be expressed by Eq. (9).

Equation 14 Error = tan {(1 + ε) ω ₀ T / 2} / tan (ω ₀ T / 2) − (1 + ε) (9)

FIG. 4 shows an embodiment of rectangular integration, that is, a calculation method using the following equation, as a method for calculating the integral value of the first means shown in FIG.

[Equation 15]

Also in this case, as in the verification of the calculation result of FIG. 1, the expression (10) is obtained. Also, sin (ωT /
Equation (11) can be obtained by approximating 2) to ωTK / 2.

W _m = V · sin {ωt _m − (n−1) ωT / 2} · sin (nωT / 2) / sin (ωT / 2) ……… (10) w _m = 2V · sin { ωt _m − (n−1) ωT / 2} · sin (nωT / 2) / (ωTK) (11) where K = sin (ω ₀ T / 2) / (ω ₀ T / 2) And Hereinafter, the same result as in FIG. 1 is obtained.

FIG. 5 is a diagram showing another embodiment of the first means shown in FIG. The figure shows an embodiment of the following calculation method by integration using the Simpson formula.

[Equation 17]

The same verification as the calculation result of FIG. 1 will be made below. First, when v _m = V · sin (ωt _m ), (12)
The equation is obtained, and sin (ωT) / {cos (ω
(13) is obtained by approximating T) +2} to ωTK / 3. However, K = sin (ω ₀ T) / [{cos (ω
₀ T) +2} · (ω ₀ T / 3)]. Hereinafter, the same result as in FIG. 1 is obtained.

[0035]

[Formula 18] w _m = 2V · sin (ωt _m −nωT / 2) · sin (nωT / 2) · {cos (ωT) +2} / sin (ωT) ……… (12) w _m = 6V · sin (Ωt _m −nωT / 2) ・ sin (nωT / 2) / (ωTK) ………… (13)

FIG. 6 shows a known method for calculating the amounts of the alternating-current electricity quantities w _m and u _m proportional to the effective values of the third and fourth means shown in FIG. 1 (Denki Shoin: Electric Calculation, November 1983 issue). VO
L. An embodiment of a calculation method by the following area method, which is P49 (3) of 51) will be described.

[0037]

[Formula 19] By dividing equation (15) by equation (14), it is possible to obtain a quantity proportional to ω.

FIG. 7 is known as a method for calculating the quantities proportional to the effective values of the alternating-current electric quantities w _m and u _m of the third and fourth means, as in FIG. 6 (Denki Shoin: Electric Calculation, 1983 November. An embodiment of a calculation method by the binary addition method which is P49 (4) expression of the monthly issue VOL.51) is shown.

[0039]

[Equation 20]

FIG. 8 shows a method of calculating the amount proportional to the square of the effective value of the AC electric quantities w _m and u _m of the third and fourth means of FIG. An embodiment is shown.

[Equation 21] In any of the above cases, an amount proportional to ω can be obtained.

FIG. 9 shows another embodiment, and in this example, the magnitude of the output F (ω) of the fifth means of FIG. 1 is determined. In the figure, 6 is a sixth means which functions as an overfrequency detecting means. That is, as shown in the following formula, it is judged whether or not it is larger than a preset (ωk) ^2, and if the formula (20) is satisfied, it is determined that the frequency is overfrequency.

[Equation 22] F (ω)> (ωk) ² ………… (20)

FIG. 10 shows still another embodiment. In this example, whether the value of the output F (ω) of the fifth means is smaller than a preset value (ωk) ² by the sixth means 6 or not. To judge.
That is, if it is small, the frequency is insufficient. In short, the sixth means 6 is an underfrequency detection means.

FIG. 11 shows still another embodiment. In this example, the sixth means 6 is an overfrequency detecting means. Then, from the output of the third means and the output of the fourth means, (output of the fourth means)> (ωk) ² · (output of the third means)
Thus, it is determined whether the output of the fourth means is larger than the value obtained by multiplying the output of the third means by (ωk) ² set in advance.

FIG. 12 shows still another embodiment. In this example, the sixth means 6 of FIG. 11 is used as an underfrequency detecting means. Then, the magnitude judgment is (output of the fourth means) <(ω
h) ² · (output of the third means).

[0045]

As described above, according to the present invention, at the electricity amount V · sin (ωt) of the power system, the time t−t
Time integration value of electric quantity from ₀ to t 2V · sin (ωt ₀
/ 2) · sin (ωt- ωt 0/2) / ω and, time t-t
Difference in the quantity of electricity at ₀ and _{t 2V · sin (ωt 0/} 2) ·
by using the _{cos (ωt-ωt 0/2} ), the amplitude ratio of the latter alternating quantity with respect to the amplitude of the former alternating quantity is focused on a point to be omega, intended to detect the frequency of the system with high precision Thus, it becomes possible to detect the frequency with desired accuracy over a wide frequency band.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment for explaining a frequency detection method according to the present invention.

FIG. 2 is a schematic configuration diagram of a digital relay to which the present invention is applied.

FIG. 3 is a diagram for explaining the effect of the present invention.

FIG. 4 is a diagram for explaining another embodiment of the first means of FIG.

FIG. 5 is a view for explaining still another embodiment of the first means shown in FIG.

FIG. 6 is a diagram for explaining another embodiment of the third means and the fourth means of FIG.

FIG. 7 is a diagram for explaining still another embodiment of the third means and the fourth means of FIG.

FIG. 8 is a view for explaining still another embodiment of the third means and the fourth means of FIG.

FIG. 9 is a diagram illustrating an application example of the present invention.

FIG. 10 is a diagram illustrating another application example of the present invention.

FIG. 11 is a diagram illustrating still another application example of the present invention.

FIG. 12 is a diagram illustrating still another application example of the present invention.

FIG. 13 is a diagram illustrating conventional characteristics.

[Explanation of symbols]

 1 1st means 2 2nd means 3 3rd means 4 4th means 5 5th means 6 6th means S / H Sampling hold circuit MPX multiplexer A / D analog-digital conversion circuit CPU arithmetic unit

 ─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Takashi Sekiguchi 1-24-2, Harumi-cho, Fuchu-shi, Tokyo Inside Toshiba System Technology Co., Ltd.

Claims (12)

[Claims] 1. A method for calculating a frequency of an alternating current electricity quantity of a power system, wherein sampling values v _m , v _m of sampling times m, m-1, m-2, ..., Mn of the electricity quantity v of the system. _-1 , v _m-2 , ..., v _mn based on time m-
first means for calculating an amount w _m which is proportional to the time integral value of the electrical quantity v from n to m, the difference value of the same quantity of electricity v at time mn and _m u m = v m -v _mn And a third means for calculating an effective value of the value w _m calculated by the first means or an amount proportional to the square of the effective value, and a calculated value u by the second means. _Comprised of fourth means for calculating an effective value of _m or an amount proportional to the square of the effective value, and fifth means for dividing the calculated value by the fourth means by the calculated value by the third means. A frequency detection method characterized in that 2. The frequency detecting method according to claim 1, wherein the first means calculates w _m by integration by a trapezoidal formula, that is, the following equation. [Equation 1] 3. The frequency detection method according to claim 1, wherein the first means calculates w _m by rectangle integration, that is, the following equation. (Equation 2) 4. The frequency detecting method according to claim 1, wherein the first means calculates w _m by integration by a Simpson formula, that is, the following equation. (Equation 3) 5. The frequency detecting method according to claim 1, wherein the third and fourth means calculate the following electric quantities. In the third means, w _mk · w _mp −w _m · w _{mkp In} the fourth means, u _mk · u _mp −u _m · u _mkp 6. The frequency detecting method according to claim 1, wherein the third and fourth means calculate the following electric quantities. (Equation 5) 7. The frequency detecting method according to claim 1, wherein each of the third and fourth means calculates the following amount of electricity. (Equation 6) 8. The frequency detecting method according to claim 1, wherein each of the third and fourth means calculates the following amount of electricity. (Equation 7) 9. A sixth means of overfrequency detection is added, which compares the value obtained by the fifth means with a predetermined constant and judges that the former is an operation when the former is larger than the predetermined constant. The frequency detection method according to claim 1. 10. A sixth means for detecting an under-frequency, which compares the value obtained by the fifth means with a predetermined constant and determines that the operation is performed when the former is smaller than the predetermined constant, is added. The frequency detection method according to claim 1. 11. An effective value or an amount proportional to the square of the effective value obtained by the fourth means and an effective value or an amount proportional to the square of the effective value obtained by the third means are multiplied by a predetermined constant. 6. The frequency detecting method according to claim 1, further comprising a sixth means for detecting an overfrequency, which is compared with the above value and determines that the operation is performed when the former is larger than the latter. 12. An effective value or an amount proportional to the square of the effective value obtained by the fourth means and an effective value or an amount proportional to the square of the effective value obtained by the third means are multiplied by a predetermined constant. 6. The frequency detecting method according to claim 1, further comprising a sixth means for detecting an underfrequency, which is compared with a value obtained by the above and determines that the former is an operation when the former is smaller than the latter.