JPH0668516B2 - AC effective value detection method - Google Patents

Description

The present invention relates to a method for detecting an effective value of alternating current, and more specifically, in the case of protecting a generator or the like with a large frequency change in output by a digital protective relay device. In the above, it relates to a method of detecting an AC effective value capable of accurately detecting an effective value of a current-transforming voltage / current of an arbitrary frequency input to a protective relay device.

(Prior Art) When protecting a device that constitutes an AC power system such as a generator, the instantaneous values of the system voltage and current are detected as analog quantities, then converted to digital quantities, and the voltage and current are converted from these digital quantities. A method is adopted in which the crest value and effective value of the current are obtained, and when the crest value or the like exceeds a certain value, the digital protection relay device is operated to protect the device.

In this case, as a method for detecting the peak value of AC input to the digital protective relay device, the following method has been conventionally known.

That is, in the past, sampling was performed at a frequency of, for example, 600 Hz or 720 Hz with respect to an alternating current having a rated frequency (50 Hz or 60 Hz) for which a peak value or the like should be detected, and among the resulting sampling data, an electrical angle of 90 ° Squared the sampling data at arbitrary two points or arbitrary continuous eight points having a considerable phase difference, add these, and calculate the square root of this added value to obtain the peak value of the alternating current, and then the effective value. Are seeking.

For example, the method of obtaining the peak value V _m of the sinusoidal AC voltage is as follows. Let υ ₁ and υ ₂ be sampling data at arbitrary two points having a phase difference corresponding to the electrical angle of 90 °, and let υ ₁ = V _m sin (ωt + φ) (φ is a phase angle of υ ₁ ), υ ₂ Is υ ₂ = _m sin (ωt + φ
+ 90 °). When the square root of the sum of squares of υ ₁ and υ ₂ is calculated, [{V _m sin (ωt + φ)} ² + {V _m sin (ωt + φ + 90 °} ² ] ^1/2 = V _m {sin ² (ωt + φ) + cos ² (ωt + φ)} ^1/2 = V _m ………………………… (1), and the peak value can be detected.

As described above, since the formula (1) is always satisfied at two points having a phase difference corresponding to an electrical angle of 90 °, the peak value V _{m and} thus the effective value can be obtained even if arbitrary sampling data having the above relationship is adopted. V _m / ▲ √ ▼ can be accurately detected, and the device can be appropriately protected by the digital protective relay device.

(Problems to be Solved by the Invention) However, the following inconvenience arises in the protection of a device such as a generator that involves a change in output frequency.

In other words, the frequency of the generator varies over a wide range from startup (about 20 Hz) to load shedding (about 100 Hz).
Even as a digital protective relay device, it is required to detect an effective value with a small error over a wide frequency range of alternating current. However, in the above-mentioned conventional method, since the sampling data for the alternating current of any frequency has an electrical angle of 90 ° at the rated frequency, the sampling data at the electrical angle of 90 ° is used for frequencies other than the rated frequency. This is not adopted, and an error occurs between the peak value or effective value calculated by the above equation (1) and each actual value.

Here, in FIG. 3, error = {(detection value) − (true value)} ×
The frequency characteristic of the error when the sampling data corresponding to the electrical angle 90 ° interval at the rated frequency with the sampling frequency 600 [Hz] as 100 / true value [%] is adopted is the AC frequency.
The horizontal axis represents [Hz] and the vertical axis represents error [%]. The figure (a) shows the case where the sampling data by the continuous two points described above is adopted, and the figure (b) shows the continuous case. The case where sampling data by 8 points is adopted is shown.

In the figure (a), for example, when the frequency of the alternating current is 100 [Hz], the error may occur in the range of about +41.4 [%] to -100 [%] depending on how the sampling data of two points is taken. However, the conventional detection method cannot accurately detect the effective value of AC due to such a large calculation error at frequencies other than the rated frequency, and is not suitable for protection of generators, etc. by the digital protective relay device. It was suitable.

The present invention has been proposed in order to solve such a problem, and an object of the present invention is to detect the effective value of an alternating current that can detect its effective value with high accuracy even if the frequency of the alternating current changes significantly. It is to provide a value detection method.

(Means for Solving Problems) In order to achieve the above object, the present invention uses all sampling data between a plurality of alternating zero-crossing points, the cycle of the alternating current obtained from the time between the zero-crossing points, and the like. This is to detect the effective value, and to detect the effective value with high accuracy by adding the period to the effective value calculation no matter how the AC frequency changes.

That is, according to the present invention, the instantaneous value of the alternating current for which the effective value is to be detected is sampled at a constant frequency, the presence of two zero-crossing points of the alternating current is confirmed from the positive and negative sign changes of the sampling data, and then these zero-crossing points are detected. The sum of squares of a plurality of sampling data between the zero crossing points is calculated, and the time between the zero crossing points is obtained from the sampling frequency between the zero crossing points, the sampling period, and the sampling data immediately before and after the zero crossing point. Then, a square root of a value obtained by dividing the sum of squares of a plurality of sampling data between the zero crossing points by the sampling period is calculated to obtain the effective value of the alternating current. (Operation) According to the present invention For example, from the sign change of the sampling data, the existence of two zero crossing points corresponding to one cycle or half cycle of the alternating current is confirmed. Then, the effective value is calculated based on the definition of the effective value using all the sampling data between these zero crossing points, the alternating current cycle and the sampling cycle.

(Examples) Examples of the present invention will be described below with reference to the drawings. First,
FIG. 1 is for explaining one embodiment of the present invention, _{in which} a waveform of a sinusoidal wave AC having a frequency _in of approximately one cycle and sampling data when this waveform is sampled at a sampling frequency _s are shown as time (t). Is represented by the horizontal axis, and the amplitude X of the AC voltage or current is represented by the vertical axis.

In the figure, A, B, and C represent points (zero crossing points) at which the amplitude of the AC waveform becomes zero, which are detected by the following inversion of the sign of the sampling data, X _a1 , X _a2 , X _b1 , X _b2 , and X.
_c1 and X _c2 are sampling data adjacent to the zero crossing _points A, B and C, respectively, and are represented by t _a1 , t _a2 , t _b1 and t
_b2 , t _c1 , and t _c2 indicate the times from the respective zero-crossing points A, B, C to the sampling points immediately before and after these zero-crossing points, respectively. Further, t _s is a sampling cycle, T ₁ is a time between A and C, which corresponds to one cycle of alternating current, and T ₂ is A.
The time between −B corresponds to 1/2 cycle of alternating current.

Here, the sampling period t _s and the sampling frequency
the relationship between the _s is a _{t s = 1 / s ................................. (} 2). Further, _{T 1} and _{T 2,} the _{T 1 = 1 / in .............................. (} 3) T 2 = T 1/2 ................................. (4) expressed.

Next, the number of samplings in one cycle T ₁ of alternating current is set to N
_1, the 1/2 the number of sampling times in the period _{T 2} and _{N 2,} T 1, _{T 2} are respectively represented as follows.

_{T 1 = (N 1 -1)} × t s + t a1 + t c2 .................. (5) T 2 = (N 2 -1) × t s + t a1 + t b2 .................. (6) Further, when the waveforms near the zero crossing points A, B, and C are linearly approximated, _ta1 , _tb2 , and _tc2 are respectively expressed as follows.

t _a1 = | X _a1 | × t _s / (| X _a1 | + | X _a2 |) ... (7) t _b2 = | X _b2 | × t _s / (| X _b1 | + | X _b2 |) ……… (8) t _c2 = | X _c2 | × t _s / (| X _c1 | + | X _c2 |)… (9) In this case, as _s becomes larger than _in , the degree of linear approximation Becomes stronger.

Here, considering the definition of the effective value of the alternating current, the effective value X _{rms in} the case of FIG. 1 is approximated as follows.

First, regarding one cycle T ₁ of alternating current (hereinafter referred to as “method 1”), Also, for the 1/2 cycle T ₂ of AC (hereinafter referred to as “method 2”), Becomes Note that X _i is the sampling data between the zero crossing points, and indicates the i-th sampling data in the period T ₁ in the case of method 1, or the i-th sampling data in the 1/2 cycle T ₂ in the case of method 2. There is.

_{Here, N s1,} N _s2 is _{N s1 = s / in = T} 1 × s = T 1 / t s ............ (12) N s2 = s / (in × 2) = (T 1/2) X _s = T ₂ x _s = T ₂ / t _s (13) In this approximation, if _s is made sufficiently larger than _in , it can be regarded as the actual effective value of the alternating current.

Next, from equations (5), (7), and (9) From Eqs. (6), (7), and (8) From equations (12) and (14) From equation (13, (15)) Becomes

As a result, the effective value X _{rms of} AC is
From Formulas (10) and (16), Formula 2 can be obtained from Formulas (11) and (17).

FIG. 2 (a) shows the frequency characteristic of the error of the effective value detected by the method 1, and FIG. 2 (b) shows the frequency characteristic of the error by the method 2, respectively. Sampling frequency _s = 600 [Hz] In the case of Method 2, the error is slightly larger than that of Method 1, but the responsiveness is improved because the calculation can be performed every 1/2 cycle. Also, from these characteristics,
It is apparent that the present invention can accurately detect the effective value of AC over a wide frequency range.

Needless to say, the present invention can be applied not only to the AC input of the digital protective relay device as in the above embodiment, but also to the detection of other general AC effective values.

(Effect of the invention) As described above, according to the present invention, the effective value is directly detected based on the definition by using a plurality of sampling data between AC zero-crossing points and the AC cycle. Even in the case of changing over a wide range, the effective value can be detected with high accuracy and with a small error.

Therefore, the present invention is extremely useful when a device such as a generator whose AC frequency fluctuates greatly is protected by a digital protective relay device, and high-precision protection can be expected.

[Brief description of drawings]

1 and 2 show an embodiment of the present invention. FIG. 1 is a diagram showing an AC waveform and sampling data to which the present invention is applied, and FIGS. 2 (A) and 2 (B) respectively. FIGS. 3A and 3B are diagrams showing the frequency characteristic of the effective value error detected by the present invention, and FIGS. 3A and 3B are diagrams showing the frequency characteristic of the effective value error according to the conventional example. A, B, C ... Zero crossing _{points Xa1} , _Xa2 , _Xb1 , _Xb2 , _Xc1 , _Xc2 ...
Time t _s ...... sampling period between time T ₂ ...... zero crossing point A-B between the sampled data T ₁ ...... zero crossing point A-C

Claims (1)

[Claims] 1. An instantaneous value of alternating current is sampled at a constant frequency, the existence of two zero-crossing points of the alternating current is confirmed from positive and negative sign changes of the sampling data, and then a plurality of sampling data between the zero-crossing points are sampled. The sum of squares is calculated, and the time between the zero crossings is calculated from the number of samplings between the zero crossings, the sampling period, and the sampling data immediately before and after each zero crossing. 2 of multiple sampling data
A method of detecting an AC effective value, characterized in that a square root of a value obtained by dividing a sum of powers by the sampling period is calculated to obtain the AC effective value.