CN114935682A - Algorithm for rapidly calculating effective value through alternating current sampling - Google Patents
Algorithm for rapidly calculating effective value through alternating current sampling Download PDFInfo
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- CN114935682A CN114935682A CN202210624504.5A CN202210624504A CN114935682A CN 114935682 A CN114935682 A CN 114935682A CN 202210624504 A CN202210624504 A CN 202210624504A CN 114935682 A CN114935682 A CN 114935682A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/02—Measuring effective values, i.e. root-mean-square values
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R21/00—Arrangements for measuring electric power or power factor
- G01R21/006—Measuring power factor
Abstract
The invention discloses an algorithm for fast calculating an effective value by AC sampling, which relates to the field of effective value algorithms and comprises the steps of sampling sinusoidal AC signals at 2 points continuously to obtain data values of 2 points, obtaining an expression of a signal peak value through the data values of two points, the invention only needs 2 points of data to obtain the effective value of the AC signal, the time for actually obtaining the effective value is only related to the sampling frequency, has no relation with the period of the actual tested alternating current signal, the method can be widely applied to the occasions with strict real-time requirements, for various protection systems, the algorithm can obtain the effective value of the sample in a very short time (the time is irrelevant to the measured signal), and effective data support is provided for realizing various protection strategies by the protection system.
Description
Technical Field
The invention relates to the field of effective value algorithms, in particular to an algorithm for rapidly calculating an effective value by alternating current sampling.
Background
The AC sampling technique is a measuring method which samples the instantaneous value of a measured signal according to a certain rule and then processes the value according to a certain algorithm so as to obtain the measured value. Ac sampling techniques are required in many instances in data acquisition and automation systems. In a typical situation, such as an electric power system, a high voltage and high current strong electric signal is converted into an electric signal which can be accepted by an a/D converter through a voltage sensor or a current sensor, the electric signal which is input to the a/D converter and has the same frequency and the same size as the primary current and the primary voltage of the electric power system is input, and parameters such as voltage, current, power and the like of an actual power grid are obtained through various algorithms.
Nowadays, the capacity of a power grid is continuously increased, the structural form is also complicated, and the monitoring and control of a power system are necessary means for ensuring the safe operation of the power grid and realizing the power automation. The real-time performance and the accuracy of alternating current sampling are the key points of monitoring and control, and are particularly more important for protection systems, such as a residual current protection system, a short circuit and an instantaneous protection system;
the prior art has the following defects: the theoretical basis of the ac sampling technique is the sampling theorem, that is, the sampling frequency is required to be more than 2 times of the highest frequency in the frequency spectrum of the signal to be measured. The measured instantaneous value is sampled according to a certain rule, and then the measured value can be solved according to a certain algorithm, and the current commonly used alternating current sampling algorithm comprises the following steps: maximum value method, integral method, fourier transform method, and the like. The maximum method is to sample the voltage signal for many times in a period, take the maximum value Um of all sampling values, and then use a formula
And obtaining an effective value U. The integration method comprises the steps of continuously sampling n point data U (1.) U (n) in one period and then passing through a formula
The Fourier transform method is to sample n point data in a period by a certain frequency, and to obtain the contents of direct current components, fundamental waves and each harmonic wave by Fourier transform of the data, thereby obtaining the required fundamental wave data.
The above calculation methods all require at least one continuous sampling period of data to calculate the actual effective value of the signal, for example, if the grid frequency of our country is 50Hz, the time of one period is 20ms, that is, the effective value calculated by the above methods is actually data before 20 ms. Because the standard alternating current signal is completely symmetrical, the negative half-axis signal can be inverted through a hardware rectification method, two same signals can be obtained in one period, and therefore the actual effective value can be obtained through the algorithm only by sampling time of 10 ms.
The time of 10ms is used for obtaining an actual effective value, and the actual effective value can well meet the requirement of real-time performance in a measuring system. However, for the protection system, the faster the protection time, the safer the system is, so that the quick obtaining of the effective value of the alternating current sampling is crucial to the protection system.
Disclosure of Invention
The invention aims to provide an algorithm for quickly calculating an effective value by alternating current sampling, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: an algorithm for fast calculating effective value by AC sampling comprises the following steps:
the method comprises the following steps: sampling sine alternating current signals at 2 continuous points;
step two: obtaining data values of 2 points in the first step;
step three: obtaining an expression of the signal peak value through the data values of the two points in the second step;
step four: and limiting the period of the sinusoidal alternating current signal in the first step, and obtaining the effective value of the signal peak value.
Preferably, the sinusoidal ac signal in step one is expressed as y ═ a × sin (t), and the signal is sampled at a rate of frequency f for 2 consecutive points.
Preferably, in the second step, the data values are y1 ═ a × sin (Φ), y2 ═ a × sin (Φ + w), respectively;
where in these two equations y1, y2 are known actual measurements and w is a known fixed sample time.
Preferably, the expression in step three is specifically defined as follows:
the specific expression of phi is obtained from y1 ═ a × sin (phi):
φ＝arcsin(y1/a)
substituting the expression phi of phi into arcsin (y1/a) according to y2, to obtain y2, arcsin (y1/a) + w);
thus, the relationships a with y1, y2, and w are obtained:
preferably, the period of the sinusoidal ac signal in the fourth step is T, and a specific expression of w is given as w ═ 2 pi/T (1/f).
Preferably, the value of a, i.e., the effective value of a/√ 2, can be found by substituting the expression of w into the expression of a.
In conclusion, the beneficial effects of the invention are as follows:
1. the invention only needs to sample 2 point data to obtain the effective value of the alternating current signal, the time for actually obtaining the effective value is only related to the sampling frequency and has no relation with the period of the actually measured alternating current signal, and the method can be widely applied to occasions with harsh requirements on real-time performance, such as various protection systems.
2. The algorithm of the invention can obtain the effective value of the sampling in a very short time (the time is irrelevant to the measured signal), and provides effective data support for realizing various protection strategies for the protection system.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
FIG. 1 is a schematic view of the overall flow of an algorithm for rapidly calculating an effective value by AC sampling according to the present invention;
fig. 2 is a diagram of an algorithm sinusoidal ac signal for ac sampling fast calculation of effective value according to the present invention.
Detailed Description
All of the features disclosed in this specification, or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
The invention will now be described in detail with reference to fig. 1-2, wherein for ease of description the orientations described hereinafter are now defined as follows: the up, down, left, right, front and rear directions described below correspond to the front, back, left, right, top and bottom directions of the view direction of fig. 1, fig. 1 is a front view of the apparatus of the present invention, and the directions shown in fig. 1 correspond to the front, back, left, right, top and bottom directions of the apparatus of the present invention.
Referring to fig. 1-2, an embodiment of the present invention is shown: an algorithm for fast computing effective value by AC sampling comprises the following steps:
the method comprises the following steps: sampling sine alternating current signals at 2 continuous points;
step two: obtaining data values of 2 points in the first step;
step three: obtaining an expression of the signal peak value through the data values of the two points in the second step;
step four: and limiting the period of the sinusoidal alternating current signal in the first step, and obtaining the effective value of the signal peak value.
In addition, in one embodiment, the sinusoidal ac signal in the first step is expressed as y ═ a × sin (t), and the signal is sampled at 2 consecutive points at a frequency f.
In addition, in one embodiment, the data values in the second step are y1 ═ a × sin (Φ), y2 ═ a × sin (Φ + w), respectively;
where in these two equations y1, y2 are known actual measurements and w is a known fixed sample time.
In addition, in one embodiment, the specific method of the expression in step three is as follows:
the specific expression of phi is obtained from y1 ═ a × sin (phi):
φ＝arcsin(y1/a)
substituting the expression phi of phi into arcsin (y1/a) according to y2, to obtain y2, arcsin (y1/a) + w);
thus, the relationships a with y1, y2, and w are obtained:
in addition, in one embodiment, the period of the sinusoidal ac signal in the fourth step is T, and a specific expression of w is given as w ═ 2 pi/T (1/f).
In one embodiment, the value of a, i.e., the effective value of a/v 2, can be found by substituting the expression of w into the expression of a.
In embodiment 1, it is assumed that a 50Hz ac voltage signal is sampled at a 2kHz rate, and the time of actually sampling 2 points is (1/2000) × 2 ═ 0.001s, that is, 1ms, by the above calculation method, the sampling rate of 2kHz can obtain an effective value of the signal within 1ms, the time of actually obtaining the effective value is only related to the sampling frequency, and is not related to the period of the actually measured ac signal.
The above description is only an embodiment of the invention, but the scope of the invention is not limited thereto, and any changes or substitutions that are not thought of through the inventive work should be included in the scope of the invention. Therefore, the protection scope of the invention should be subject to the protection scope defined by the claims.
Claims (6)
1. An algorithm for fast computing effective value by AC sampling is characterized in that: the method comprises the following steps:
the method comprises the following steps: sampling sine alternating current signals at 2 continuous points;
step two: obtaining data values of 2 points in the first step;
step three: obtaining an expression of the signal peak value through the data values of the two points in the second step;
step four: and limiting the period of the sinusoidal alternating current signal in the first step, and obtaining the effective value of the signal peak value.
2. An algorithm for fast computing an effective value of an alternating current sample according to claim 1, characterized in that: in the first step, the sinusoidal ac signal is expressed as y ═ a × sin (t), and the signal is sampled at 2 consecutive points at a frequency f.
3. The algorithm for fast computing effective values of alternating current sampling according to claim 1, wherein: the data values in the second step are y1 ═ a × sin (Φ) and y2 ═ a × sin (Φ + w), respectively;
where in these two equations y1, y2 are known actual measurements and w is a known fixed sample time.
4. The algorithm for fast computing effective values of alternating current sampling according to claim 1, wherein: the expression in the third step is specifically as follows:
the specific expression of phi is obtained from y1 ═ a × sin (phi):
φ＝arcsin(y1/a)
substituting the expression phi of phi into arcsin (y1/a) according to y2, to obtain y2, arcsin (y1/a) + w);
thus, the relationships a with y1, y2, and w are obtained:
5. the algorithm for fast computing effective values of alternating current sampling according to claim 1, wherein: the limited period of the sinusoidal alternating current signal in the fourth step is T, and a specific expression of w is given as w ═ 2 pi/T (1/f).
6. The algorithm for fast computing effective values of alternating current sampling according to claim 1, wherein: the value of a, i.e., the effective value of a/v 2, can be obtained by substituting the expression of w into the expression of a.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116840544A (en) * | 2023-06-12 | 2023-10-03 | 北京科荣达航空科技股份有限公司 | Method and device for acquiring effective value of alternating current signal |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116840544A (en) * | 2023-06-12 | 2023-10-03 | 北京科荣达航空科技股份有限公司 | Method and device for acquiring effective value of alternating current signal |
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