JP2011080986A - Phaser measuring device - Google Patents

Abstract

A phasor measurement device capable of calculating a phasor calculation in a short time, estimating a current / voltage waveform including a damped DC component in a short time, and performing a calculation in a short time with little vibration error. The purpose is to provide.
A phasor measuring device according to the present embodiment includes an analog / digital conversion means for sampling an alternating current waveform at a constant period and converting it into a digital signal, and sampling converted into a digital signal by the analog / digital conversion means. The apparatus includes a means for generating a virtual vector using data, and a phasor calculating means for performing a Fourier calculation using actual sampling data and virtual vector data to measure an effective value of current.
[Selection] Figure 1

Description

  Embodiments of the present invention relate to an apparatus for measuring a phasor with respect to a current or voltage of a power system.

  A discrete Fourier transform (DFT) may be used when performing a phasor operation from measured voltage and current waveforms. In particular, a recursive discrete Fourier transform (RDFT) calculation as described in Non-Patent Document 1 is known as a calculation method with a low calculation load.

Nakano, Ota, Ukai, Nakamura, Fujita: “Real-time power system frequency detection based on synchronous phasor measurement”, Electrical Engineering C, Vol.122, No.12

  The conventional DFT calculation method is effective for a steady waveform because the power system is normally operated, but may not be applied to a fault current waveform. A major factor is the attenuated DC component included in the fault current. When a DFT operation is performed on a fault current containing a damped DC component, there is a problem that a vibrational error is superimposed on the operation result of the fundamental phasor. In order to correct this error, the attenuation time constant for the attenuated DC component must be known, but the attenuation time constant may change when the configuration of the power system changes. For this reason, in order to suppress the vibration error in a state where the attenuation time constant is unknown, a complicated calculation is required.

  In addition, even in a steady state, it is also required to analyze a voltage / current waveform at the time of power system failure in as short a time as possible according to the purpose of use. However, the conventional DFT calculation method has a problem that it takes time for one cycle or half cycle of the waveform when performing the phasor calculation.

  As described above, the conventional phasor measuring device requires a long time for the phasor calculation. Further, when a damped DC component is included, more calculation time is required to suppress the vibrational error that occurs during analysis.

  Therefore, the embodiment of the present invention is proposed in order to solve the above-described problems of the prior art, and the current required for the phasor calculation is shortened and further includes a damped DC component. An object of the present invention is to provide a phasor measuring device that can estimate a voltage waveform in a short time and can calculate in a short time with little vibration error.

  In order to achieve the above object, the phasor measuring device according to the present embodiment includes an analog / digital conversion means that samples an alternating current waveform at a constant period and converts it into a digital signal, and the analog / digital conversion means performs a digital signal. Characterized in that it comprises means for generating a virtual vector using the sampling data converted into a phasor, and phasor calculation means for performing a Fourier calculation using the actual sampling data and virtual vector data to measure the effective value of the current. To do.

The block diagram which shows the structure of the current phasor measuring device in Example 1 of this invention. The figure which shows the flowchart of operation | movement of the current phasor measuring device in Example 1 of this invention. The figure which shows the calculation flowchart in Example 1 of this invention. FIG. 3 is a diagram illustrating a generation principle of a virtual vector in Embodiment 1 of the present invention Vector diagram of sampled signal in Embodiment 1 of the present invention The figure which shows the flowchart of the fundamental wave phasor calculation in Example 2 of this invention. The figure which shows the flowchart of the fundamental wave phasor calculation in Example 3 of this invention. The figure which shows the phasor calculation result (execution value) comparison in Example 3 of this invention The figure which shows the enlarged view of FIG. 5 in Example 3 of this invention. The figure which shows the phasor calculation result (phase angle) comparison in Example 3 of this invention

  Hereinafter, each Example of the electric power system current phasor measuring device will be described with reference to FIGS.

[1-1. Constitution]
Example 1 will be described with reference to FIG. FIG. 1 is a configuration diagram of a current phasor measuring device according to a first embodiment of the present invention. Reference numeral 1 in FIG. 1 is a current transformer (CT) that measures an alternating current of a power system and converts it into an analog current signal. The output side of the current transformer 1 is connected to a calculator 2 that takes in the measured current signal and performs a calculation.

  Inside the arithmetic unit 2, an analog / digital converter 3 for sampling the acquired analog current waveform at a constant period and converting it into a digital signal is disposed. On the output side of the analog / digital converter 3, a temporary storage device (RAM) 4 for storing sampling data converted into a sampled digital signal is arranged. The temporary storage device 4 is connected to a CPU 6 connected to a ROM 5 that stores a program necessary for calculation. The CPU 6 reads the sampling data stored in the temporary storage device 4 and executes a calculation to calculate a current phasor. The calculated current phasor is stored in the temporary storage device 4 again. A communication port 7 is connected to the output side of the temporary storage device 4. The communication port 7 is an output means of the computing unit 2 and outputs the current phasor data calculated by the computing unit 2 to a display device 8 such as a personal computer arranged on the output side of the computing unit 2.

[1-2. Operation of current phasor measurement device]
Next, the operation of the current phasor measuring apparatus having the above configuration will be described. FIG. 2 shows a flowchart of the operation of the current phasor measuring device of this embodiment.

  In STEP 1, an AC current signal of the power system is taken into the current transformer 1. In STEP 2, the alternating current signal taken into the current transformer 1 is measured and converted into an analog current signal. In STEP 3, an analog current signal is sampled at a constant period and converted into a digital signal. The sampling data converted into the digital signal in STEP 4 is stored in the temporary storage device 4 for saving.

  Next, in STEP 5, the sampling data is read from the temporary storage device 4 by the CPU 6. In STEP 6, the CPU 6 performs a phasor calculation from the read sampling data. For the calculation in STEP6, it is necessary to read a program for the phasor calculation from the ROM 5 before STEP6. However, if this timing is before STEP6, even before STEP1 is started. Is possible. In STEP 7, the calculation result calculated by the CPU 6 is stored in the temporary storage device 4. In STEP 8, the result of the phasor calculation is transmitted to the display device 8 via the communication port 7.

[1-3. Phaser calculation method]
In the phasor calculation in this embodiment, a virtual vector is generated using sampled data, and a phasor is calculated by performing a Fourier calculation using the actual sampling data and virtual vector data.

  The phasor calculation method in this embodiment will be described with reference to the flowchart of FIG. FIG. 4 is a vector diagram of the sampled signal, and FIG. 5 is a diagram illustrating the principle of creating a virtual vector.

As STEP 1 in FIG. 3, data sampling is performed. When a current or voltage signal that does not include an attenuated DC component is input from the power system as data, the waveform is a sine wave, and one cycle is analog / When converted into digital data by the digital conversion means, it is expressed by the following formula (1).

  However, N is the number of samplings in one waveform period.

  When N = 12, this signal can be displayed as a vector as shown in FIG. 4, and Equation (1) can be expressed as its imaginary part. x (n) represents the nth sampling data.

  Next, in STEP2, based on the sampling data obtained in STEP1, a virtual vector X '(n-5) is generated from X (n + 2) and X (n) as shown in FIG. In the actual calculation, the latest sampling data x (n + 2) and the data x (n) two samples before are used to obtain the following equation (2).

  However, K is a constant and is uniquely determined by the difference between each phase of x (n + 2) and x (n). In FIG. 4, when the phase angle between −X (n + 2) and X ′ (n−5) is γ, K is expressed by the following formula (3).

  In STEP 3, phasor calculation is performed. Since x ′ (n−5) generated in STEP 2 is data before a half cycle of x (n + 1), the following formula is used by using two values of x (n + 1) and x ′ (n−5). By using (4), phasor calculation is performed.

[1-4. effect]
As an effect of such an embodiment, the phasor operation can be performed by Expression (4). That is, the phasor operation can be performed with sampling data of three points x (n + 2), x (n + 1), and x (n), so that the voltage and the voltage can be reduced with a smaller calculation amount and a short time window width. The effective value of the current can be calculated.

[2-1. Constitution]
The present embodiment has the same configuration as that of the first embodiment, but the phasor calculation method in the calculator 2 is changed. That is, the sampling data of the first embodiment does not include the attenuated DC component, but in this embodiment, the sampling data including the attenuated DC component is used.

  In the present embodiment, in the phasor calculation in the CPU 6 of the computing unit 2, an AC current waveform including the attenuated DC component is sampled, and the phasor operation is performed by Fourier calculation of the sampling data, and the attenuated DC component is estimated from the phasor value. The phasor value of the fundamental wave is obtained using the estimated attenuation component and the phasor value obtained by the phasor calculation. This attenuated DC component is seen in the current waveform when a failure occurs in the power system as described above.

[2-2. Phaser calculation method]
The phasor calculation method for the fault current of the power system including the attenuated DC component in this embodiment will be described with reference to the flowchart of FIG.

ただし、f：周波数、φ１：初期位相、であり、
B0：直流成分の大きさ、τ：直流成分の減衰時定数である。 In STEP 1 of FIG. 6, data sampling is performed. The data to be sampled includes a DC attenuation component. When one cycle is converted into digital data by the analog / digital conversion means at N points, it is expressed by the following formula (5).

Where f: frequency, φ1: initial phase,
B0: DC component magnitude, τ: DC component decay time constant.

ただし、Ｘ1：基本波フェーザ、Ψ：減衰直流成分要素、n：サンプル番号である。 In STEP2, a phasor operation is performed. When a DFT operation (discrete Fourier transform) is performed on the signal represented by Expression (5), a phasor represented by the following Expression (6) is obtained.

However, X1: Fundamental phase phasor, Ψ: Attenuating DC component, n: Sample number.

ただし、Ｔsはサンプリング間隔である。 Since X (n) can be obtained by Equation (6), the fundamental phasor X1 can be obtained if the damped DC component element Ψ can be obtained. This damped DC component element Ψ can be expressed by the following formula (7).

However, Ts is a sampling interval.

The attenuation DC component element ψ expressed by the above formulas (7) and (8) can be correctly estimated if the attenuation time constant τ is known. Take. Here, in Equation (7), if the sampling interval is sufficiently smaller than τ, Γ approximates to 1. When Γ is close to 1, τ has a value of about several tens of milliseconds to several hundreds of milliseconds, so that the sampling interval is several thousand Hz to several tens of thousands Hz. That is, for example, in the case of 5760 Hz sampling, it is 0.17 ms, so it can be said that the attenuation time constant is sufficiently small. The attenuation direct current component in the case of such approximation is expressed by the following formula (9).

The fundamental phasor X ₁₀ (n) approximated using the estimated damped DC component is represented by the following formula (10).

When the fundamental wave phasor is obtained from the approximated fundamental wave phasor, it is expressed by the following formula (11).

De ^jδ / (De ^jδ +1) in the equation (11) is the error, and De ^jδ can be expressed by the following equation (12).

  Therefore, the phasor can be obtained by using the calculation result of the previous sample.

[2-3. effect]
As an effect of the second embodiment, the phasor can be obtained by using the calculation result of one sample before. That is, even when the attenuation time constant of the damped DC component is unknown, the effective value of the voltage or current including the DC damped component can be calculated with a small amount of calculation and a short time window width.

[3-1. Constitution]
The present embodiment has the same configuration as that of the first embodiment, but the phasor calculation method in the calculator 2 is changed. In the present embodiment, the means for performing the phasor operation in the second embodiment is the means of the first embodiment, and as shown in FIG. 7, the flowcharts of FIGS. 3 and 6 are combined. That is, STEPs 1-3 in FIG. 7 are the same as STEPs 1-3 in FIG. 3, and STEPs 4-7 in FIG. 7 are the same as STEPs 3-6 in FIG.

[3-2. Concrete example]
Next, the operation of the current phasor measuring apparatus having the above configuration will be described. As an example of calculation by such a current phasor measuring device, a current waveform simulating a power system failure is considered.

  As the waveform parameters, the amplitude of the current waveform before failure at a frequency of 50 Hz is 30 × √2 [A] and the phase angle is 26 [deg], the amplitude of the current waveform after failure is 5000 × √2 [A], and the phase angle is −45. [deg], DC component amplitude 5000 [A], and decay time constant 0.063 [s]. FIG. 6 shows the results when the number of samples is 2048, the failure occurrence time is 0.04 [s], and the window width is 1/16 cycle for this current waveform. FIG. 8 is an enlarged view of the vicinity of 0.04 seconds in FIG. 7, and FIG. 9 is obtained for the phase angle.

  8 to 10, it can be seen that transient vibration occurs in the time within the window width, but in the subsequent time, both the effective value and the phase angle are stable in a short time.

[3-3. effect]
As an effect of the third embodiment as described above, it is possible to calculate the effective value of the voltage and current including the direct-current attenuation component after high-speed and short-time vibration as compared with the first and second embodiments.

[4. Other embodiments]
In the analog / digital converter 3 of each embodiment, the current transformer 1 measures the alternating current of the power system, and measures the phasor based on the alternating current. The current transformer 1 is converted into a voltage converter (VT). It can also be replaced. By using a voltage converter (VT), it can be set as the voltage phasor measuring device which measures a phasor based on the voltage of an electric power grid | system.

  Further, the arithmetic unit 2 may include a plurality of analog / digital converters 3. Thus, by connecting the analog / digital converter 3 to the current transformer 1 and the voltage converter (VT), it is possible to configure a phasor measuring device that measures the phasor based on the voltage and current of the power system. .

1 ... Current transformer (CT)
2 ... arithmetic unit 3 ... analog / digital converter 4 ... temporary storage (RAM)
5 ... ROM
6 ... CPU
7 ... Communication port 8 ... Display device

Claims (5)

An analog / digital conversion means for sampling an alternating current waveform or voltage waveform at a constant period and converting it into a digital signal;
Of the sampling data converted into a digital signal by the analog / digital conversion means, the phasor performs the Fourier calculation using the sampling data having less than one cycle of the alternating current waveform or the voltage waveform and measures the effective value of the current or voltage. Computing means;
A phasor measuring device comprising: The phasor computing means, means for generating a virtual vector using the sampling data converted into the digital signal;
Means for performing a Fourier calculation using actual sampling data and virtual vector data, and measuring an effective value of current or voltage;
The phasor measuring device according to claim 1, comprising: An analog / digital conversion means for sampling an alternating current waveform or a voltage waveform including a damped direct current component at a constant period and converting it into a digital signal;
Among the sampling data converted into a digital signal by this analog / digital conversion means, Fourier calculation is performed using sampling data that is less than one cycle of the AC current waveform, and the error of the effective value due to the attenuated DC component is suppressed, A computing means for measuring the effective value of the current in a short time;
A phasor measuring device comprising: The phasor calculating means calculates phasor values by Fourier calculation using the sampling data converted into the digital signal;
Means for estimating the attenuated DC component from this phasor value;
Means for obtaining a phasor value of a fundamental wave using a phasor value calculated from an estimated attenuated DC component and sampling data;
The phasor measuring device according to claim 3, comprising: In the phasor measuring device according to claim 1 or 2,
Means for estimating the attenuated DC component from the phasor value;
An arithmetic means for obtaining a phasor value of a fundamental wave using a phasor value calculated from an estimated attenuated DC component and sampling data;
A phasor measuring device comprising:

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