JP2003344463A - Method for detecting frequency fluctuation occurring in electric power system, method for measuring frequency deviation in electric power system, and method for measuring electric power system frequency - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for measuring frequency fluctuation and its deviation in an electric power system with high accuracy in an earlier stage than before. <P>SOLUTION: Instantaneous voltage values of an electric power system are measured at sampling time points for a predetermined sampling time length Ts. Then, recursive discrete Fouriertransformation is performed based on the instantaneous voltage values to find recursive voltage phasors. Frequency components about twice as high as the fundamental frequency are removed from the voltage phasors by using a filter. Phase deviation of phase components (ϕl, r) at a certain sampling time point from phase components (ϕl, r-l or ϕl, r+l) at a sampling time point immediately before or after the sampling time point is calculated from the voltage phasors from which the frequency components about twice as high as the fundamental frequency are removed. A time point when the phase deviation is produced is detected as the occurrence of frequency fluctuation. A frequency deviation Δf at a certain sampling time point is measured based on the phase deviation. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for detecting the occurrence of frequency fluctuations in a power system, a method for measuring frequency deviation, and a method for measuring frequency.

[0002]

2. Description of the Related Art Conventionally, a method for detecting the time between zero crossings of a waveform has been used for the frequency detection of a power system, and a method of obtaining the reciprocal of the time is used. Examination "Proceedings of the Institute of Electrical Engineers of Japan B,
113, No. 5, pp 553/561 (1993)]. However, in this method, the frequency is detected every one cycle or half cycle. In recent years, in power electronics devices and the like, control systems having high-speed response are being introduced into the field of power systems. Therefore, it has been known that the improvement of the detection accuracy of continuous frequency fluctuations (frequency fluctuation occurrence, frequency deviation, fluctuated frequency) synchronized with the response speed further improves the control performance of the device.

As one of the conventional techniques, a positive phase detection type P
A method of obtaining a phase and a frequency by using LL (Phase Locked Loop) has been proposed ["PLL and frequency detection method for coping with abnormal voltage at power system accident", IEEJ Transactions B, Vol. 118, No. 9, pp955. / 961 (199
8)]. Although this method has excellent resistance to abnormal voltage,
There are dead time due to calculation, delay of feedback control system, and the like. On the other hand, in recent years, the application of digital signal processing technology has been actively tried in this field, and DFT (Discrete Four
Phase detection method using (ier Transform) has been proposed
[Error evaluation and correction method of DFT real-time phase detection] IEEJ Transactions B, Volume 120, No. 12, pp1682 / 1690
(2000)]. In this paper, the evaluation of the phase detection error caused by the deviation of the system frequency from the design frequency of the DFT and its correction method are examined. However, there is no discussion about the method of detecting the frequency itself.

[0004]

However, any of the conventional techniques has a problem that the occurrence of frequency fluctuation cannot be detected early and with high accuracy. Further, the conventional technique has a problem that the detection accuracy of the frequency deviation cannot be easily improved. Further, the conventional technique has a problem that the processing by software is not always easy because the calculation becomes complicated.

An object of the present invention is to provide a power system frequency fluctuation occurrence detection method capable of detecting the occurrence of frequency fluctuation at an early stage.

Another object of the present invention is to provide a method capable of measuring the frequency deviation of a power system at an early stage and with high accuracy.

Still another object of the present invention is to provide a method capable of measuring the frequency of a power system early and with high accuracy.

[0008]

According to the present invention, a normal DF is used.
A phasor measurement method using a recursive DFT that can significantly reduce the amount of calculation compared to T (Discrete Fourier Transform) is used to detect the occurrence of frequency fluctuation, measure the frequency deviation, and further measure the frequency. For phasor measurement, see "Improved Control and Protection of Power Sy".
Stems ThroughSynchronized Phasor Measurement ", Control and Dynamic Systems, Vol.43, pp.335 / 37
6 (1991), and entitled "High-performance Simultaneous Measurement System for State of Power System Using DSP and GPS", Journal of High Speed Signal Processing Applied Technology (Electronic Technology September issue), Vol. 3, No. 3. , Pp 20/25 (2000).

From the point of view of frequency measurement, the feature of the present invention is that the phase fluctuation caused by the deviation of the system frequency from the design frequency of the DFT is calculated by the recursive DFT and is inversely calculated to obtain the frequency. In the case of a single-phase power system, the frequency component can be continuously detected by removing the fluctuation component having a frequency about twice that of the contained fundamental wave by a digital filter such as a moving average filter.

Specifically, in the power system frequency fluctuation occurrence detection method, first, when the frequency (f) in the single-phase power system fluctuates by a certain deviation from the fundamental frequency (f ₀ ) is detected as the frequency fluctuation occurrence time, Take the following steps: The basic frequency is 50Hz or 60Hz in Japan.
Is.

First, a predetermined sampling time (T
In s), the voltage instantaneous value νr of the single-phase power system at each sampling time [r × Ts (r is a positive integer of 1 or more)] is measured. Assuming that one cycle of the fundamental frequency is sampled N times, the sampling time T
s becomes Ts = 1 / (f ₀ N). If N is 100 and the fundamental frequency is 60 Hz, Ts is about 0.00017 seconds.

Next, the recursive discrete Fourier transform is performed on the basis of the instantaneous voltage value ν measured sequentially to obtain the recursive voltage phasor. As is well known, in order to perform an accurate calculation by the recursive discrete Fourier transform, it is necessary to accumulate data for a predetermined number of sampling times, and conceptually, it is accumulated when one sampling is performed. The first sampling data of the data for the predetermined number of samplings is discarded, and the operation of adding new sampling data is executed.

The recursive voltage phasor includes a component that does not include the fundamental frequency but includes the deviation Δf, and a fluctuation component that includes the frequency component that is approximately twice the fundamental frequency (f ₀ ) and the deviation Δf. Be done. Therefore, from the recursive voltage phasor, a fluctuation component including a frequency component about twice the fundamental frequency (f ₀ ) is removed by using a filter such as a moving average filter, and noise caused by a quantization error is also generated by this filtering process. Remove.

Next, from the recursive voltage phasor from which the frequency component of about twice the fundamental frequency (f ₀ ) is removed, the phase component (φ1, r) at a certain sampling time and the sampling time immediately before or after the sampling time are obtained. And the phase component (φ1, r-1 or φ1, r + 1) in each of them are calculated, and the difference between them, that is, the phase deviation is calculated. Then, when the phase deviation occurs, it is detected as the frequency variation. As described above, in order to accurately measure the deviation at a certain ampling time based on the recursive voltage phasor, sampling values for a predetermined number of samplings (preferably half cycle or one cycle of the fundamental frequency) are collected. is necessary. However, when the frequency fluctuation occurs, the fluctuation immediately appears in the calculation result of the phase deviation. Therefore, by observing the presence / absence of the occurrence of this phase deviation as a comparison between the phase deviation and a predetermined threshold value, it is possible to detect the occurrence of frequency fluctuation (specifically, the time) earlier, and the electric power system It is possible to speed up the response speed in the control system.

In order to measure the deviation Δf from the fundamental frequency (f ₀ ), the above-mentioned phase deviation may be used. Specifically, [(φ1, r) − (φ1, r-1 or φ1, r + 1)] / 2π
The deviation can be obtained by executing the calculation of Ts. As described above, in order to perform an accurate calculation by the recursive discrete Fourier transform, it is necessary to store the data for the predetermined number of samplings, so in reality, the data for the predetermined number of samplings is stored. The calculation result after accumulation is used.

Further, when obtaining the frequency of the power system,
The deviation Δf obtained as described above may be added to the fundamental frequency f ₀ .

Occurrence of frequency fluctuations in the three-phase power system,
When measuring the phase deviation and the frequency, at each sampling time [r ×
Ts (r is a positive integer of 1 or more)], the voltage instantaneous value of each phase of the three-phase power system is measured, and the recursive discrete Fourier transform is performed based on the voltage instantaneous value of each phase. The phase recursive voltage phasor is obtained, and the positive phase voltage phasor is obtained by the symmetric coordinate method using the recursive voltage phasor of each phase. And from this positive phase voltage phasor,
The phase deviation between the phase component at a certain sampling time and the phase component at the sampling time immediately before or after the sampling time is calculated. In the calculation process of the positive phase voltage phasor, the fluctuation components including the deviation Δf cancel each other out. Therefore, when the frequency fluctuation is generated in the three-phase power system and the phase deviation and the frequency are measured, it is theoretically necessary. Does not require a filtering process such as a moving average filter.

[0018]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the method of the present invention will be described below with reference to the drawings. FIG. 1 shows a case in which the power system frequency fluctuation occurrence detection method of the present invention is performed, in which the frequency fluctuation occurrence detection method of the present invention detects when the frequency (f) in the single-phase power system fluctuates from the basic frequency (f ₀ ) by a certain deviation. 7 illustrates steps of the embodiment.

In this embodiment, the recursive discrete Fourier transform is performed on the basis of the voltage instantaneous value ν to obtain the recursive voltage phasor (Xr represented as a vector). First, it will be explained that when the recursive voltage phasor is obtained, the number of calculations is small. First, when the voltage instantaneous value ν for one cycle is subjected to the discrete Fourier transform, the voltage phasor at the sampling time [r × Ts (r is a positive integer greater than or equal to 1 indicating the sampling position)] is expressed by the following equation (1). Can be asked according to.

[0020]

[Equation 1] In the above formula (1), f ₀ is a design frequency or a fundamental frequency, which is 50 Hz or 60 Hz in Japan. Further, Ts is a sampling time, and N (= 1/1 /
(F ₀ Ts) is the number of samplings for one cycle of the fundamental frequency. A recursive voltage phasor (X represented as a vector) obtained by recursively discrete Fourier transforming an instantaneous voltage value ν represented using this voltage phasor.
r) is as in the following expression (2).

[0021]

[Equation 2] Substituting the equation (1) into the equation (2), the time (r +
1) When the recursive voltage phasor at Ts is obtained, it can be expressed by the following equation (3).

[0022]

[Equation 3] As can be seen by comparing the above equations (1) and (3),
When the voltage phasor is obtained by using the discrete Fourier transform according to the above equation (1), the number of product-sum operations of the real part and the imaginary part needs to be (4N + 1) times, while the above equation (3) is used. When the recursive discrete phasor transform is used to obtain the recursive voltage phasor, the number of product-sum operations for the real part and the imaginary part is 6, which is a significant reduction in the number of operations. Therefore, when the recursive discrete Fourier transform is used, the arithmetic processing in the case of using software is greatly simplified, and the processing can be performed in one arithmetic process. As is well known, in order to perform an accurate calculation by the recursive discrete Fourier transform, it is necessary to accumulate data for a predetermined number of sampling times (half cycle, one cycle, etc.), and conceptually When sampling is performed once, the first sampling data of the accumulated number of sampling times of data is discarded, and an operation of adding new sampling data is executed. This is seen from equation (3), where ν _{r + 1} in the imaginary part is
It is the voltage instantaneous value (latest sampling value) at time (r + 1) Ts, and ν _{r−N + 1} is the voltage instantaneous value acquired in the sampling N + 1 times before, and in the recursive discrete Fourier transform, the voltage instantaneous value (ν _{r + 1} and ν
_This can be understood from the fact that _{r-N + 1} ) is added and subtracted.

Therefore, in this embodiment, each sampling time [r × Ts] is set at a predetermined sampling time (Ts).
(R is a positive integer greater than or equal to 1)], the voltage instantaneous value νr of the single-phase power system is measured, and the recursive discrete Fourier transform is performed based on the sequentially measured voltage instantaneous value νr to calculate the recursive voltage phasor (vector). Xr) represented by

The instantaneous voltage value νr is expressed by the following equation (4).

[0025]

[Equation 4] In the equation (4), V is the amplitude, φ ₀ is the initial phase, and f is the frequency of the input voltage waveform. When the frequency f of the input voltage waveform fluctuates from the fundamental frequency f ₀ by the deviation Δf, the recursive voltage phasor (Xr represented as a vector) is obtained by the Taylor expansion using the above equations (1) and (2). When it is performed, it is converted as shown in the following equation (5), and finally, it includes a component that does not include the fundamental frequency but includes the deviation Δf, a frequency component that is approximately twice the fundamental frequency (f ₀ ), and the deviation Δf. It is expressed as the sum of two vectors consisting of a fluctuation component that fluctuates in. The expression (4) is substituted for ν _{k + r−N} in the first expression of the expression (5). However (5)
The amplitude components B1 and B2 and the phase components φ _{1, r} and φ _{2, r in the} equation are as shown in (6) below.

[0026]

[Equation 5]

[Equation 6] Further, in order to express the above equation (5) as the final sum of two vectors, the geometric progression of the following equation (7) is used.

[0027]

[Equation 7] Next, consider the amplitude components B1 and B2 and the phase components φ _{1, r} and φ _{2, r} . Frequency deviation Δf is ± 5 Hz
The results of calculating B1 and B2 by the equation (6) are shown in FIG. As can be seen from FIG. 2, B1≈1.0, B2≈0.
It is 0, which means that the effective value of the recursive voltage phasor is V / √2. Furthermore, the phase component φ _{1, r}
As shown in the equation (6) _, φ _{2 and r} have a proportional coefficient of 2πΔf and a proportional coefficient of 2π (2f ₀ + Δf) with respect to time rTs. In particular, 2π (2f ₀ +
Δf) is a fluctuation component that fluctuates together with the fundamental frequency. Even if B2 is almost 0, this fluctuation component has a great influence. Therefore, in order to remove such a fluctuation component, in this embodiment, a moving average filter having a cutoff frequency of 2f ₀ (or having a width of N / 2) is used to obtain about 2 of the fundamental frequency (f ₀ ). Double frequency component, ie (2f
₀ + Δf) frequency components are removed. Then, the noise associated with the quantization error is removed by this filtering process.

As a result, the recursive voltage phasor can be expressed by the following equation (8).

[0029]

[Equation 8] By substituting the recursive voltage phasor value obtained by performing the filtering process into the above equation (8), the phase component (φ1, r)
Can be asked. Thus, from the recursive voltage phasor, the phase component (φ1,
r) and the phase component (φ1, r-1 or φ1, r + 1) at the sampling time immediately before or after the sampling time, respectively, and the difference between them, that is, the phase deviation is calculated, and the expression (9) By executing the calculation, the frequency deviation Δf can be obtained.

[0030]

[Equation 9] FIG. 3 shows the relationship between the time and the frequency deviation Δf when the frequency fluctuates from 60 Hz by 0.1 Hz at the time of 0.033 seconds. A data curve A in FIG. 3 shows the frequency deviation Δf when the filter processing is not performed [when the calculation is performed by the equation (5)], and includes a vibration error. Further, the data curve B shows the frequency deviation Δf when the filter processing is performed as in the present embodiment.
As can be seen from this figure, when frequency fluctuations occur, 1
The frequency deviation occurs before the period of about 0.017 seconds elapses. In the steady state after the fluctuation, the maximum error rate is reduced from about 100% to 0.2% or less by the filter. As described above, in order to accurately measure the deviation at a certain sampling time based on the recursive voltage phasor (in this example, to measure the frequency deviation of 0.1 Hz), a predetermined number of sampling times ( In this example, it is necessary to collect sampling values for 1.5 cycles, that is, 150 samplings. However at time 0.0
When the frequency fluctuation of 33 seconds occurs, the fluctuation immediately appears in the calculation result of the phase deviation. Therefore, if the occurrence of this phase deviation or frequency deviation is observed by comparing the phase deviation or frequency deviation with a predetermined threshold value, the occurrence of frequency fluctuation (specifically time) can be detected early. can do. Therefore, by using the measuring method of the present embodiment, the response speed in the control system of the power system can be increased. When obtaining the frequency of the electric power system, the deviation Δf obtained as described above may be added to the fundamental frequency f ₀ .

FIG. 4 is a diagram showing a flow in the case of generating a frequency fluctuation, measuring a phase deviation and a frequency in a three-phase power system. In this case, each sampling time [r × Ts (r is 1
The above positive integers]] are used to measure the voltage instantaneous value of each phase of the three-phase power system, and the recursive discrete Fourier transform is performed based on the voltage instantaneous value of each phase to calculate the recursive voltage phasor of each phase. Then, the positive phase voltage phasor is obtained by the symmetrical coordinate method using the recursive voltage phasor of each phase. At the time of three-phase equilibrium, the phase of the recursive voltage phasor (Xa, r, Xb, r, Xc, r represented by a vector) of each phase is (2 /
3) Positive phase component due to three-phase symmetric coordinate transformation, that is, positive phase voltage phasor (Xp displayed as a vector with a difference of π
r) is expressed by the following equation (10).

[0032]

[Equation 10] As can be seen from the above formula (10), in the calculation process of the positive phase voltage phasor, the fluctuation components that fluctuate including the deviation Δf cancel each other out, so that the occurrence of frequency fluctuations, the phase deviation and the phase deviation in the three-phase power system When measuring the frequency, in principle, filter processing such as a moving average filter is unnecessary. The processing after the equation (10) may use the above equation (9).

In FIG. 3, the frequency deviation when the positive phase voltage phasor is used is shown as a data curve C. Here, 60.0 Hz to 60.1 Hz at time 0.033 seconds
A three-phase equilibrium voltage that fluctuates stepwise was used. N = 1
00. When the positive phase component voltage of the equation (10) is used, the frequency deviation changes like a ramp, and the accurate frequency deviation Δf can be detected in one cycle.

In detecting frequency fluctuations, detection of fluctuation time, settling time until steady state, and detection accuracy are important. In order to accurately detect the steady value of the frequency deviation, it is necessary to wait at least one cycle after the start of fluctuation. In this embodiment,
Since the instantaneous value for one cycle is continuously integrated and averaged by the discrete Fourier transform, the data curve C in FIG.
As in the case of (normal phase), it has ideal characteristics regarding the detection of the fluctuation time and the settling time. However, in the single-phase analysis, as described above, a filter for eliminating vibration is required, and a half cycle delay is required. Regarding accuracy, the high frequency cutoff characteristic originally possessed by the discrete Fourier transform [[D
High-performance power system state quantity simultaneous measurement system using SP and GPS ", High-speed Signal Processing Applied Technology Journal (September of Electronic Technology, Vol. 3, No. 3, pp 20/25 (2000)] Has a high S / N ratio against waves and measurement noise.

[0035]

According to the present invention, the occurrence of frequency fluctuations in the power system can be detected earlier (eg, in an extremely short time of 100 microseconds), and the frequency deviation and frequency of the power system can be detected. It is possible to measure with high accuracy. The method of the present invention also has the advantage that the measurement can be performed by a complete software process using one digital processor.

[Brief description of drawings]

FIG. 1 shows steps of an embodiment for carrying out a power system frequency fluctuation occurrence detection method of the present invention, which detects when a frequency in a single-phase power system fluctuates by a certain deviation as a frequency fluctuation occurrence time. FIG.

[FIG. 2] The frequency deviation Δf is set within ± 5 Hz, and (6)
It is a figure which shows the result of having calculated | required B1 and B2 by a formula.

FIG. 3 shows a relationship between time and frequency deviation Δf when the frequency fluctuates from 60 Hz by 0.1 Hz at a time of 0.033 seconds.

FIG. 4 is a diagram showing a flow in the case of generating a frequency fluctuation and measuring a phase deviation in a three-phase power system.

Claims (6)

[Claims] 1. A power system frequency fluctuation occurrence detection method for detecting when the frequency (f) in a single-phase power system fluctuates by a certain deviation from the fundamental frequency (f ₀ ) as the frequency fluctuation occurrence time, which is predetermined. The instantaneous voltage value νr of the single-phase power system at each sampling time [r × Ts (r is a positive integer greater than or equal to 1)] at each sampling time (Ts) is measured, and the recursive discrete value is calculated based on the instantaneous voltage value νr.・
Calculated recursively voltage phasor performing a Fourier transform, the recursive from the voltage phasor using a digital filter to remove the approximately 2 times the frequency component of the fundamental frequency (f _0), about the fundamental frequency (f ₀₎ From the recursive voltage phasor from which the double frequency component is removed, the phase component (φ1, r) at a certain sampling time and the phase component (φ1, r-1 at the sampling time immediately before or after the sampling time.
Or φ1, r + 1) and a phase deviation is calculated, and when the phase deviation occurs, it is detected as the frequency fluctuation occurrence. 2. A power system frequency deviation measuring method for measuring that a frequency (f) in a single-phase power system fluctuates by a certain deviation Δf from a fundamental frequency (f ₀ ), and a predetermined sampling time (Ts) Then, the instantaneous voltage value νr of the single-phase power system at each sampling time [r × Ts (r is a positive integer greater than or equal to 1)] is measured, and the recursive discrete value is calculated based on the instantaneous voltage value νr.
Calculated recursively voltage phasor performing a Fourier transform, using a filter from the recursive voltage phasor removing the twice frequency component of the fundamental frequency (f _0), about 2 of the fundamental frequency (f ₀₎ From the recursive voltage phasor with doubled frequency component removed, the phase component (φ1, r) at a certain sampling time and the phase component (φ1, r-1 at the sampling time immediately before or after the sampling time
Or φ1, r + 1), and a deviation Δf of the frequency at the certain sampling time is measured based on the phase deviation. 3. The deviation Δ obtained by the method of claim 2.
A power system frequency measuring method comprising measuring the frequency of the power system based on f. 4. A power system frequency fluctuation occurrence detection method for detecting when a frequency (f) in a three-phase power system fluctuates by a certain deviation from a fundamental frequency (f ₀ ) as a frequency fluctuation occurrence, which is predetermined. At each sampling time [r × Ts (r is a positive integer of 1 or more)] at each sampling time (Ts), the voltage instantaneous value of each phase of the three-phase power system is measured, and the voltage instantaneous value of each phase is obtained. Based on the recursive discrete Fourier transform to obtain the recursive voltage phasor of each phase, the recursive voltage phasor of each phase is used to obtain the positive phase phasor by the symmetrical coordinate method. The phase deviation between the phase component at the sampling time and the phase component at the sampling time immediately before or after the sampling time is calculated to generate the phase deviation. Power system frequency change occurrence detection method characterized by detecting, as the frequency variation occurs when the. 5. A power system frequency deviation measuring method for measuring that a frequency (f) in a three-phase power system has fluctuated by a certain deviation Δf from a fundamental frequency (f ₀ ), and a predetermined sampling time (Ts) At each sampling time [r × Ts (r is a positive integer of 1 or more)], the instantaneous voltage value of each phase of the three-phase power system is measured, and the recursive discrete value is calculated based on the instantaneous voltage value of each phase. Obtaining the recursive voltage phasor of each phase by performing Fourier transform, obtaining the positive phase voltage phasor by the symmetrical coordinate method using the recursive voltage phasor of each phase, the phase component at a certain sampling time from the positive phase phasor And a phase deviation between the phase component at the sampling time immediately before or after the sampling time, and based on the phase deviation, the deviation of the frequency. Power system frequency deviation measuring method characterized by measuring the Delta] f. 6. The deviation Δ obtained by the method according to claim 5.
A power system frequency measuring method comprising measuring the frequency of the power system based on f.