JP3269514B2 - Frequency detection method of sine wave AC signal - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention uses a plurality of digital data obtained by sampling and A / D converting an AC electric quantity such as voltage and current of a power system, and applying a sine wave to the arithmetic processing of a microcomputer. The present invention relates to a method for detecting a frequency of an AC signal.

[0002]

2. Description of the Related Art Japanese Patent Application Nos. 6-32771 and 6-52394 filed by the present applicant are examples of this type of prior art. According to these inventions, for example, the sine wave AC signal is sampled at a constant period, and sampling data at a time earlier by π / 2 in electrical angle from a specific sampling time obtained by A / D conversion is used as a denominator. The sum of the sampling data at and the sampling data at a time earlier by π in electrical angle from the specific sampling time is taken as the numerator, and the calculated value of these denominator and numerator is a value proportional to the known reference frequency of the AC signal. Multiplied by the shift frequency Δf between the reference frequency f ₀ of the sine wave AC signal and the actual frequency f (= f−f ₀ or f ₀ −f)
Is calculated, and the actual frequency f is obtained by adding and subtracting the shift frequency Δf from the reference frequency f ₀ . For convenience, these methods are referred to as a first prior art.

Further, Japanese Patent Application Laid-Open No.
The method described in Japanese Patent No. 42469 and the technique described in the related art check two times when the instantaneous value of the sine wave AC signal becomes zero, and the time difference between these two points is n / 2 of the AC cycle.
This is based on the fact that the time becomes twice as long (n = 1, 2, 3,...). These methods are referred to as a second conventional technique.

[0004]

The first prior art includes:
There are the following problems. First, this prior art, it is possible to detect the actual frequency with high accuracy with respect to the reference frequency f ₀ near the frequency, including direct current, for large off-frequency range than f ₀ In principle, there is a problem that the error increases remarkably. Next, Japanese Patent Application No. 6-327
As shown in Equation 1 of No. 71, the data used for the calculation needs to have a time window corresponding to at least 180 ° electrical angle of f ₀ . Since the width of the data time window is directly related to the detection time, when applied to an apparatus that requires high-speed detection, there is a great restriction, and it has been difficult to perform high-speed detection.

A second prior art is a method of directly calculating a frequency from a cycle of a detected sine wave AC signal.
There is no problem such as an increase in an error in a frequency range deviating from the reference frequency f ₀ as seen in the first related art. However, since the zero value of the AC signal is detected, the size of the time window of the sampling data required for frequency detection is
It will be proportional to the reciprocal of the frequency value f. In other words, there is a problem in that the required data time window increases as the frequency approaches zero, and the detection speed decreases accordingly. Further, in the second conventional technique, a direct current cannot be detected in principle.

The present invention has been made to solve the above-mentioned various problems, and an object of the present invention is to include a practical frequency (= f _s) including the direct current, which is determined by the sampling theorem. For a wide frequency range up to (sampling frequency) / 2), the frequency is detected with a fundamental error of zero, and the required data time window is a sine wave that does not depend on the reference frequency f ₀ or the actual frequency. It is an object of the present invention to provide a method for detecting a frequency of a wave AC signal.

[0007]

In order to achieve the above object, a first aspect of the present invention is directed to a first aspect of the present invention, wherein a plurality of samplings obtained by sampling a sine wave AC signal at a constant cycle and performing A / D conversion are provided. In the method of detecting the frequency of the AC signal from the data, the sum of the sampling data at two sampling times before and after an equal time from an arbitrary sampling time is added to the sum at the arbitrary sampling time.
Add the value multiplied by the sampling data over a certain period
The obtained value is used as the dividend, and the square of the sampling data at the arbitrary sampling time is calculated over the predetermined period.
The frequency of the AC signal is detected by dividing a triangular inverse function of a division value obtained by dividing the function of the added value by a function of a sampling period.

According to a second aspect of the present invention, a sinusoidal wave
The flow signal is sampled at regular intervals, and A / D converted
From the obtained plurality of sampling data, the frequency of the AC signal
In the method of detecting the number, if the sampling time is
Two sampling times before and after the same time
The arbitrary sampling time is added to the sum of the sampling data.
Function of multiplying the sign of sampling data at
The value added over a certain period is taken as the dividend, and
Of sampling data at any sampling time
The function of the value obtained by adding the absolute value over the predetermined period is divided.
The inverse trigonometric function of the division value as a number
The frequency of the AC signal is detected by dividing by a number .

[0009]

[0010]

[0011]

The basic principle of the present invention is as follows:
As shown in 1, it is equal time from any sampling time
Sampling at two sampling times before and after
The function of the sum of the log data is the dividend, and the arbitrary
Excludes the sampling data function at the sampling time.
The inverse trigonometric function of the division value as a number
The frequency f of the sine wave AC signal is calculated by dividing by a number .

[0012]

(Equation 1)

In the equation 1, V _n : a sine wave AC signal at an arbitrary sampling time t m: a positive integer of 1 or more Δt: sampling period V _{n + m} : data at time (t + m · Δt) V _nm : time (t −m · Δt). As is clear from the above, Vn _{+ m} and _Vnm are:
Two sampling times (t + m · Δt), (t
−m · Δt).

The denominator term V _n in the cos ⁻¹ term in Equation 1
Is a zero value depending on the time t. In this case,
Becomes indefinite. To avoid this, in the present invention,
The frequency f is calculated by such a method.

That is, in the cos- ¹ term in the equation 1,
For each of the numerator and denominator terms, it is shifted for a certain time (time).
The frequency f is detected by using Expression 2 that performs dynamic addition.

[0016]

(Equation 2)

In Expression 2, x is a positive integer of 1 or more. According to Equation 2, co which is a problem in Equation 1
The problem that the denominator term in the s ^-1 term becomes zero is caused by adding a total (x + 1) times of data from nx to _n to the denominator term 2V _n in the cos ^-1 term in Expression 1. Even if the sampling data V _na (0 ≦ a ≦ x) at a certain time is zero, if the data sampling frequency f _s is higher than twice the detection frequency f, the data (V _na−1 and V _{n) at the} adjacent time _{Since -a + 1} ) is not zero, it is unlikely that the denominator term in the cos ^-1 term in Equation 2 will be zero.

As described above, Equation 2 has an effect of reducing the chance that the denominator term in the cos ^-1 term becomes zero for the reason described above. However, the denominator term is not completely free of chance, and may be zero if the following relationship holds between the data in the cos ^-1 term in Equation 2.

[0019]

Equation 3] _{V n = -V nx V n-} 1 = -V nx-1:: V nx / 2 = 0 (x is the time of an even number _{only) V n- (x + 1)} / 2 = -V n _{-(x-1) / 2} (only when x is odd)

[0020] That _is, the intermediate time _{t 3} between the sampling time _{t 2} corresponding to the sampling time _{t 1} and _{V n} corresponding to _{V n-x} is a case where exactly zero data.
FIG. 1 shows an example in which Equation 3 is satisfied, in which x = 8. Then, the specific time window (t ₁ to
As a method in which the denominator term in the cos ^-1 term does not become zero at t ₂ ), Equation 4 is adopted instead of Equation 2.
This method corresponds to the first invention.

[0021]

(Equation 4)

[0022] Equation 4 is obtained by multiplying the V _nk in Equation 2 molecules in cos ^-1 Section denominator respectively. In this case, the principle accuracy of the detected frequency, the applicable frequency range,
The required data time window is the same as in the case of Equation 2. However, since the denominator in the cos ^-1 term includes square of V _nk, becomes a positive value by the square when V _nk takes a negative value, the denominator as a result, the all conditions (A saying in also the condition that f <f _s / 2 remains), not give zero value, equation 4 would not include the problems inherent in equation 2.

Further, as a method of solving the problem that the denominator term in the cos ⁻¹ term inherent in Equation 2 becomes zero, there is a method using Equation 5 instead of Equation 4. This method is
This corresponds to the second invention.

[0024]

(Equation 5)

In equation (5), | a | indicates the absolute value of a, and sign (a) is a function represented by equation (6). That is, sign (a) indicates that the sign of a is positive or negative.

[0026]

When a ≧ 0, sign (a) = + 1 When a <0, sign (a) = − 1

According to Formula 5, as for the denominator term of the cos ^-1 term, all the instantaneous data to be added are all positive numbers, so that the denominator term does not become zero under all conditions.
However, since the sign information (positive or negative) of the data is lost by taking the absolute value in the denominator term, the sign information is represented by s
It was decided to multiply the molecular term as ign (V _nk ). According to Expression 5, the same effect as Expression 4 can be obtained.

[0028]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing the embodiments of the present invention, the principle of the above-mentioned formula 1 will be confirmed. Input data V _n in Equation 1, where indicated by Equation 7, the amplitude value at a frequency f | assumed to be composed of sinusoidal AC signal of an arbitrary sampling time t | V.

[0029]

V _n = | V | sin (2πft)

From equation (7), an equal time (m · Δ) from time t
t) two sampling times (t + m · Δ)
t), sampling data V at (tm-Δt)
_{n + m} and V _nm can be expressed by Equation 8, respectively.

[0031]

V _{n + m} = | V | sin {2πf (t + m · Δt)}, V _nm = | V | sin {2πf (tm−Δt)}

Using Equations 7 and 8, Equation 9 is obtained.

[0033]

(Equation 9)

When Equation 9 is solved for the frequency f, the above Equation 1 is obtained. As described above, from Expressions 1 and 9, m may be arbitrarily determined in the detection of the frequency f. By setting m = 1, a time window of 2Δt time determined by the sampling frequency f _s (= 1 / Δt) is obtained. Using only three consecutive sampling data (V _n−1 , V _n , V _{n + 1} )
Can be calculated.

That is, if the sampling frequency f _{s is set} to a sufficiently large value, f _{s is} reduced from DC regardless of the magnitude of the frequency.
A wide range of frequencies f up to / 2 can be detected.
As for the time window, it dealt with in a 2 times the length of the reciprocal of the sampling frequency f _s, which enables high-speed detection.

[0036] However, the denominator _{V n} in ^{cos -1} term in Equation 1 as described above is to avoid becoming zero, and calculates the frequency f according to Equation 4 or Equation 5.
As a result, the frequency f can be detected over a wide range.
Can be. It should be noted that in Equations 4 and 5,
The time window of the log data is (2 + x) △ t when m = 1.
Become.

[0037]

[0038]

[0039] In an embodiment of the present invention, in formula 4
Other than the c os ^-1 function, only the product-sum operation is performed. On the other hand, the mathematical expression 5 includes processing such as an absolute value operation and a sign () function. In a digital signal processor that can perform the above operation at high speed, equation (4) may be selected.

[0040] In the above you施例, Equation 1, Equation 2,
The numerators on the right side of Equations 4 and 5 are both cos ^-1 functions, but these can be easily transformed into s in ^-1 functions. As described above, according to the present invention, the calculation becomes indefinite.
It is possible to always detect the frequency of the sine wave AC signal without the need .

As described above, according to the first or second invention, there is an effect that the frequency of a sine wave AC signal can be detected with high accuracy in a wider frequency range than that of the conventional technology. Also, in principle, the required data time window is determined according to the sampling frequency of the device, so that the faster the sampling is performed, the narrower the time window becomes. As a result, the detection time is shortened, and high-speed detection becomes possible. .

[Brief description of the drawings]

FIG. 1 is an explanatory diagram showing an example of the establishment of Expression 3 in an embodiment .

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G01R 23/02

Claims (2)

(57) [Claims] 1. A method for sampling a sine wave AC signal at a constant period and detecting the frequency of the AC signal from a plurality of sampling data obtained by A / D conversion, comprising: Before the sum of the sampling data at the two sampling times
Sampling data at any sampling time
The value obtained by adding the value obtained by multiplying by a certain period is a dividend, and the value obtained by adding the square of the sampling data at the arbitrary sampling time over the certain period
A frequency detection method for a sine wave AC signal, wherein the frequency of the AC signal is detected by dividing a trigonometric inverse function of a division value obtained by dividing the function by a function of a sampling period. 2. A sine wave AC signal is sampled at a constant period.
Multiple sampling data obtained by A / D conversion
In the method for detecting the frequency of the AC signal from the
Before the sum of the sampling data at the sampling time
Sampling data at any sampling time
Added over a period of time
Value as the dividend, and at the arbitrary sampling time
The absolute value of the sampling data
Triangular inverse function of the division value with the function of the value added by the divisor
Is divided by the function of the sampling period to
Frequency detection method of the sine wave AC signal and detecting the frequency of the issue.