JP2013092391A - Frequency measurement device and frequency measurement method of electric power system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To measure a fundamental frequency with high precision even when a frequency component close to a commercial frequency is included.SOLUTION: A frequency measurement method of an electric power system that introduces and converts a voltage of a three-phase AC power system into digital data, and introduces a system voltage of the digital data to perform frequency operation includes: generating first time-series data x(t) from the system voltage of the digital data; generating second time-series data g(t) by integrating the first time-series data on a numeral basis; determining an effective value (X) of the first time-series data and an effective value (G) of the second time-series data; and deriving a frequency (f) by multiplying the ratio of the effective value (X) to effective value (G) by a predetermined constant.

Description

  Embodiments described herein relate generally to a power system frequency measurement device and a frequency measurement method.

  The frequency of the power system is maintained with high precision by the power company, but the frequency fluctuates when the balance of power supply and demand is lost. Frequency measurement is necessary to stably operate the power system while maintaining the frequency, and various methods have been devised and applied so far.

  The frequency is the wave number of a sine wave for 1 second, but it is too long for 1 second to use the measured value of the frequency without delay for maintaining the frequency. Therefore, the period of the sine wave corresponding to the reciprocal of the frequency (50 Hz system) In this case, the frequency is measured from the voltage waveform data for a short time.

  The voltage waveform of the power system is obtained by superimposing a fractional harmonic or a harmonic on a sine wave component of a commercial frequency (≈50 Hz or 60 Hz) called a fundamental wave. In general, the frequency of the power system refers to the frequency of this fundamental wave. In the measurement of the frequency of the power system, the frequency is measured on the assumption that the voltage waveform of the power system is a periodic wave.

  In power systems, various disturbances occur due to sudden changes in loads and accidents. Such a disturbance is an event independent of the period or frequency, but disturbs the periodicity of the voltage waveform, and therefore cannot be ignored as a factor that interferes with the frequency measurement and affects the measurement result.

Hereinafter, an example will be described.
When an accident occurs in the power system, the voltage phase may change suddenly. Since a sudden change in voltage phase results in an increase or decrease in the time of one cycle, the measurement result may show a decrease or increase in frequency. Since such a transient disturbance does not continue for a long time, the frequency relay has an operation time of about 100 ms or more and measures are taken so as not to be affected by the disturbance included in the frequency measurement result. However, a large error is included in the frequency measurement value during this period, which is not preferable. Voltage waveform distortion due to non-transient noise sources also affects frequency measurement.

  In other words, the frequency is measured at the observation point due to transient disturbances and non-transient waveform distortions at the point where the voltage is observed, even though the power system is operating stably. Expect different values. This phenomenon is not preferable because protection and control by frequency are performed in cooperation for the entire power system.

JP-A-57-95136

Protected relay system engineering supervised by Yoshifumi Oura, The Institute of Electrical Engineers of Japan, March 2002, P.102, P.150-151, IEEJ Technical Report No. 1127, “Accident Ripple Prevention Technology by Frequency Relay System”, IEEJ, September 2008, P.72-75, Yoshihide Hase, “Practical Theory of Power System Technology Handbook”, Maruzen Co., Ltd., published in March 2004, pages 123-134,

  Although the frequency component far from the commercial frequency is reduced by using an analog filter or a digital filter in the prior art, it is difficult to remove the frequency component close to the commercial frequency by the filter.

  Therefore, the present invention makes it possible to measure the fundamental frequency with high accuracy even when frequency components close to the commercial frequency are included, and to measure the frequency of the power system that is not easily affected by disturbances caused by a power system accident. An apparatus and a frequency measurement method are provided.

  In order to achieve the above object, the power system frequency measurement device according to Embodiment 1 introduces a voltage of a three-phase AC power system, converts the voltage into digital data, and outputs the digital data, and is output from the input unit. And a frequency calculation unit that performs frequency calculation by introducing a system voltage of the digital data, and the frequency calculation unit generates a first time-series data x (t) from the system voltage of the introduced digital data. And second means for numerically integrating the first time series data x (t) generated by the first means to generate second time series data g (t), and the first The third means for deriving the effective value (X) of the first time series data x (t) obtained by the means of the above, and the effective of the second time series data g (t) obtained by the second means A fourth means for deriving a value (G), an effective value (X) obtained by the third means, and the fourth hand Fifth means for deriving obtained rms frequency multiplied by a constant appointment to the ratio of (G) (f), characterized by comprising a.

The lineblock diagram of the frequency measuring device and frequency measuring method of an electric power system concerning Embodiment 1 of the present invention. The figure which shows the calculation flow of the software which performs the frequency calculation in the frequency calculating part of FIG. The lineblock diagram of the frequency measuring device and frequency measuring method of an electric power system concerning Embodiment 2 of the present invention. The figure which shows the calculation flow of the software which performs the frequency calculation in the frequency calculating part of FIG.

  DESCRIPTION OF EMBODIMENTS Embodiments of a power system frequency measuring device and a frequency measuring method according to the present invention will be described below with reference to the drawings. In addition, the overlapping description shall be abbreviate | omitted suitably by attaching | subjecting the same code | symbol to the element which is common throughout each figure.

[Embodiment 1]
First, a power system frequency measurement device and a frequency measurement method according to Embodiment 1 will be described with reference to FIG.

(Constitution)
FIG. 1 is a diagram illustrating a frequency measurement device and a frequency measurement method for a power system according to an embodiment of the present invention.

  The power system frequency measuring device and frequency measuring method according to the first embodiment can be realized by a digital arithmetic device composed of, for example, a peripheral circuit including a microprocessor and a memory. An instrument transformer installed in the power system An input unit 1 for introducing a system voltage amount Va, Vb, Vc derived from (not shown) and outputting a “digitally converted quantity of electricity” [V]; The frequency calculation unit 2 performs frequency calculation using the “amount of electricity” [V].

  The input unit 1 performs level conversion by insulating the input voltage and performs analog-digital conversion. The input unit 1 corresponds to the input converter and analog / digital conversion unit of the digital relay unit described in Non-Patent Document 1. Here, the “digitally converted quantity of electricity” is expressed in brackets [] such as [V].

  The frequency calculation unit 2 corresponds to the calculation processing unit of the digital relay unit described in Non-Patent Document 1. Here, the frequency calculation unit 2 performs a predetermined frequency calculation according to software built in the digital calculation device, and the power system. Frequency [f] is measured. The measured frequency [f] can be used for various purposes such as maintaining the frequency of the power system, protecting or controlling the power system.

FIG. 2 is a diagram illustrating a calculation flow of software for the frequency calculation unit 2 to perform frequency calculation.
The frequency calculation unit 2 of the first embodiment mainly executes the following four calculation processes.

First, in the first processing step S11, the electric quantity [V] input by the input unit 1 is calculated to generate time series data [x (t)].
Next, in the second processing step S12, the time series data [g (t)] generated in step S11 is numerically integrated to generate time series data [g (t)].

Further, in the first processing step S13, the effective values X and G are calculated from these two time series data [x (t)] and [g (t)] that have already been obtained.
In the final fourth processing step S14, the ratio of the two effective values X and G described above is calculated to obtain the frequency [f].

(Function)
The operation of the first embodiment will be described. First, frequency calculation will be described.
For the electric quantity x (t), when the effective values of x (t) and g (t) are X and G, respectively, the frequency of the power system is calculated by the equation (1).

As is well known, the effective values X and G are calculated by the following equations (2) and (3).

First, it will be described that the frequency is calculated by the equation (1).
As is well known, the time function of the period T is expressed as the following equation (4) using a Fourier series, and the constants in the equation (4) are the equations (5), (6 ) Expression.

であるとき、

と表される。 Hereinafter, the effective values of these functions are obtained.

When

It is expressed.

The ratio between these equations (7) and (8) is expressed by the following equation (9).

In Expression (9), when only the fundamental wave component is present, c _n = 0 (where n ≠ 1), and therefore Expression (9) is ω (= 2πf). This represents the angular frequency of the fundamental wave.
Therefore, it can be understood from this that the frequency can be calculated by the equation (1).

とすると、

となり、（１）式が

となって“周波数”と一致することから、容易に理解できる。 This is, for example,

Then,

And the formula (1) becomes

This is easy to understand because it matches the “frequency”.

  In the diagram showing the calculation flow of the software for performing the frequency calculation shown in FIG. 2, first, the time series data [x (t)] is calculated from [V] in the processing step S11, and then the series data is processed in the subsequent processing step S12. [X (t)] is numerically integrated to calculate time-series data [g (t)], and in subsequent processing step S13, the effective values X and G of these two time-series data are calculated, and the final processing is performed. In step S14, the ratio (X / G) of these two effective values X and G is calculated to calculate the frequency [f].

  Since the difference between the continuous quantity and the discrete quantity and the difference between the integral and the numerical integration are not essential differences, it can be said that the calculation flow in FIG. 2 calculates the frequency according to the equation (1).

  An object of the present invention is to provide an apparatus or method for measuring a fundamental frequency with high accuracy even when a frequency component close to a commercial frequency is included.

ここで、ωは基本波の角周波数、右辺第二項は重畳した基本波に近接した成分（大きさ；α、角周波数の差分；ωn）を示す。 A voltage including a frequency component close to the commercial frequency is normalized by the amplitude of the fundamental wave voltage and expressed as the following equation (10).

Here, ω represents the angular frequency of the fundamental wave, and the second term on the right side represents a component (size; α, difference between angular frequencies; ωn) close to the superimposed fundamental wave.

である。 At this time,

It is.

Next, in order to calculate the frequency with high accuracy, the effective value X is obtained by equation (12) and the effective value G is obtained by equation (13).

これら（１２）式および（１３）式より、周波数は次の（１４）式で計算される。

Also,

From these equations (12) and (13), the frequency is calculated by the following equation (14).

  By this equation (14), it is evaluated how much error occurs when the frequency calculation of the first embodiment includes a “frequency component close to the commercial frequency”.

  For example, in a power system with a fundamental frequency f = 50 Hz, when the frequency component separated by fn = 10 Hz from the fundamental frequency is superimposed by 2% (α = 0.02), the calculated value is 500.003 Hz and the difference between the fundamental frequency is Small enough.

  For comparison with the first embodiment, the same calculation is performed by a known method in which the period is measured and the frequency is obtained from the reciprocal thereof.

と表記する。 Similarly, a voltage including “a frequency component close to a commercial frequency” is expressed as follows (normalized by the amplitude of the fundamental voltage).

Is written.

の解であるので、同様に、例えば、ｆ＝５０Ｈｚ、ｆｎ＝１０Ｈｚ、α＝０．０２とすると、
ｔ＝１９．９４ｍｓとなり、周期の逆数を周波数とするとｆ≒５０．１５Ｈｚとなって、基本波の周波数５０Ｈｚに対して、ｆ≒０．１５Ｈｚだけ外れた値となり、「商用周波数に近接した周波数成分」を含む場合に、大きな影響を受けることが分かる。 The period of this equation is

Similarly, for example, when f = 50 Hz, fn = 10 Hz, and α = 0.02,
When t = 19.94 ms and the frequency of the reciprocal of the cycle, f≈50.15 Hz, which is a value deviated by f≈0.15 Hz from the fundamental frequency 50 Hz. It can be seen that when the component is included, it is greatly affected.

  Therefore, according to the frequency measurement device and the frequency measurement method of the first embodiment, the basics of the power system can be obtained even when “frequency components close to the commercial frequency” that are difficult to remove by a filter are included compared to the known method. The frequency can be measured more accurately.

  In the above description, the phase to be used in the calculation is not specified as [V], but it is clear that the result obtained is the same regardless of which of the three phases is selected. In addition to selecting only one of the three phases as described above to obtain one frequency calculation result, two or more of three phases can be used to obtain two or more frequency calculation results. May be obtained.

(effect)
As described above, according to the first embodiment, it is possible to measure the fundamental frequency with high accuracy even when the frequency component close to the commercial frequency is included.

[Embodiment 2]
Next, the frequency measurement apparatus and frequency measurement method for the power system according to the second embodiment will be described with reference to FIG.

(Constitution)
The main difference between the second embodiment and the first embodiment is that the amount of electricity introduced into the frequency calculation unit 2 is the system voltage amount in the first embodiment, whereas the second embodiment is different from the first embodiment. The amount of positive phase voltage. There is no particular change in the others.

  Similarly to the first embodiment, the frequency measurement device and frequency measurement method for the power system according to the second embodiment shown in FIG. 3 can be realized by a digital arithmetic unit composed of a peripheral circuit including a microprocessor and a memory, and is installed in the power system. An input unit 1 for introducing a voltage derived from an instrument transformer (not shown), and a positive phase synthesis unit 3 for introducing an output of the input unit 1 to synthesize a positive phase voltage amount [V1]; The frequency calculation unit 2 performs frequency calculation using the positive phase voltage amount [V1] synthesized by the positive phase synthesis unit 3.

The positive phase synthesizing unit 3 synthesizes the positive phase voltage amount [V1] using the electric quantities [Va], [Vb], and [Vc] digitally converted for each phase. The positive phase voltage amount is [V1] = [Va] + a × [Vb] + a ² × [Vc] (in the case of a phase reference, where a is exp (j120), where + is a vector sum Is the quantity of electricity known as).

  Several methods are known for synthesizing the positive phase electric quantity, but the description is omitted here because it is not related to the description of the second embodiment. Of course, it goes without saying that the composition operation may be performed faithfully to the definition formula.

  FIG. 4 is a diagram showing a calculation flow of software for performing frequency calculation. Time series data [x (t)] is calculated from the positive phase voltage amount [V1], and the time series data [x (t)] is calculated. Calculate time series data [g (t)] by numerical integration, calculate the effective values X and G of these two time series data, and calculate the ratio (X / G) of these two effective values. The frequency [f] is calculated.

(Function)
Here, the effect by using the positive phase voltage amount [V1] will be described.
A sudden phase change with a large voltage is due to an accident in the power system. For example, Non-Patent Document 2 and Non-Patent Document 3 disclose whether a sudden phase change occurs. Non-Patent Document 3 explains in detail in Chapter 9 Schematic Solution of Transmission Line Voltage / Current and Trends. A large sudden phase change is a phenomenon that cannot be avoided when frequency is measured using line voltages or phase voltages as they are. However, if an amount of electricity that does not cause a large phase sudden change (even during a power system accident) is used, the frequency measurement result does not include a large error.

Patent Document 1 describes the effects of a positive phase voltage, which is an electric quantity with a small voltage phase sudden change even when a power system failure occurs, and frequency measurement using the positive phase voltage.
Although detailed description is omitted in Patent Document 1, repeated description is omitted, but by using the positive phase voltage, a large error is not included in the frequency measurement result even in the case of a power system failure.

(effect)
As described above, according to the second embodiment, by using the positive phase electric quantity [V1], it is possible to measure the fundamental frequency with higher accuracy even in the case of a power system failure, and the power system failure. It is possible to provide a frequency measurement device and a frequency measurement method for an electric power system that are not easily affected by the disturbance caused by the.

  The first and second embodiments described above are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various modifications can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

  DESCRIPTION OF SYMBOLS 1 ... Input part, 2 ... Frequency calculating part, 3 ... Positive phase synthetic | combination part, Va, Vb, Vc ... Each phase voltage of a power system, [Va], [Vb], [Vc] ... Digitally converted power system Voltage amount of each phase, [V1] ... synthesized positive phase voltage amount, [f] ... measured frequency, [x (t)] ... time series data obtained from [V1], [g (t)] ... time-series data obtained by numerical integration of [x (t)], X ... effective value of [x (t)], G ... effective value of [g (t)].

Claims (4)

An input unit that introduces a voltage of a three-phase AC power system, converts it into digital data and outputs it, and a frequency calculation unit that introduces a system voltage of digital data output from the input unit and performs a frequency calculation,
The frequency calculation unit includes first means for generating first time series data x (t) from the system voltage of the introduced digital data, and first time series data x ( a second means for numerically integrating t) to generate second time series data g (t), and an effective value (X) of the first time series data x (t) obtained by the first means. Obtained by the third means, fourth means for deriving the effective value (G) of the second time series data g (t) obtained by the second means, and obtained by the third means A fifth means for deriving a frequency (f) by multiplying a ratio between the effective value (X) and the effective value (G) obtained by the fourth means by a predetermined constant; Frequency measuring device. In the method of measuring the frequency of the power system that introduces the voltage of the power system of the three-phase AC and converts it into digital data, and introduces the system voltage of this digital data to perform the frequency calculation,
First time-series data x (t) is generated from the system voltage of the digital data, and second time-series data g (t) is generated by numerical integration of the first time-series data. The effective value (X) of the time-series data and the effective value (G) of the second time-series data are obtained, and the ratio of the effective value (X) and the effective value (G) is multiplied by a predetermined constant to obtain the frequency. (f) is derived, The frequency measurement method of the electric power system characterized by the above-mentioned. An input unit that introduces a voltage of each phase of a three-phase AC power system, converts it into digital data and outputs it, and introduces a system voltage of the digital data of each phase output from the input unit to calculate the positive phase electric quantity A positive phase synthesis unit to synthesize, and a frequency calculation unit that performs frequency calculation using the positive phase electrical quantity synthesized by the positive phase synthesis unit,
The frequency calculation unit includes sixth means for generating third time series data x (t) related to the positive phase amount of the introduced system voltage, and third time series data generated by the sixth means. A seventh means for numerically integrating x (t) to generate fourth time series data g (t) and an effective value of the third time series data x (t) obtained by the sixth means ( An eighth means for deriving X), a ninth means for deriving the effective value (G) of the fourth time series data g (t) obtained by the seventh means, and an eighth means A tenth means for deriving a frequency (f) by multiplying a ratio of the obtained effective value (X) and the effective value (G) obtained by the ninth means by a predetermined constant; System frequency measuring device. The voltage of each phase of the three-phase AC power system is introduced and converted to digital data of each phase, the system voltage of this digital data of each phase is introduced to synthesize positive phase electricity, and this positive phase electricity is In the frequency measurement method of the power system that is used to perform the frequency calculation,
The third time series data x (t) related to the introduced positive phase amount of the system voltage is generated, and the fourth time series data g (t) is generated by numerical integration of the third time series data. The effective value (X) of the third time series data and the effective value (G) of the fourth time series data are obtained, and a predetermined constant is set as the ratio of the effective value (X) and the effective value (G). A frequency measurement method for an electric power system, wherein the frequency (f) is derived by multiplying.

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