JP2014014208A - Ground directional relay - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform correct system fault determination even if a system frequency varies, in a ground directional relay in which a maximum sensitivity angle is set.SOLUTION: The ground directional relay includes a memory 1 for storing instantaneous values of voltage and current of power system, an extraction unit 2 for extracting instantaneous value data of voltage and the instantaneous value data of current from the memory, an inner product calculation unit 3 for determining an inner product VIcosθ of voltage and current on the basis of the instantaneous value data extracted in the extraction unit, an outer product calculation unit 5 for determining an outer product VIsinθ of voltage and current on the basis of the instantaneous value data extracted in the extraction unit, a phase difference calculation unit 5 for determining a phase difference θ from the inner product and outer product thus determined, and a determination unit 6 for determining a ground fault point by using the phase difference θ determined in the phase difference calculation unit, and a maximum sensitivity angle φ of the ground directional relay given from an input section 7.

Description

  The present invention determines the direction of the ground fault point from the phase relationship between two or more zero-phase electric quantities, such as zero-phase voltage and zero-phase current in the power system, and in the case of an accident within the protection range, This is related to a ground fault direction relay device that outputs a trip signal, and more specifically, an arithmetic technique that performs phase difference calculation on zero-phase electric quantity using instantaneous value data of the power system obtained by sampling at a predetermined cycle Regarding improvements.

  The ground fault direction relay device determines the direction of the ground fault point by comparing the phase relationship of two or more zero phase electric quantities such as zero phase voltage and zero phase current in the power system, and the fault within the protection range. In this case, the circuit breaker trip signal is output. As for this ground fault direction relay device, for example, as disclosed in Patent Document 1 and the like, a ground fault determination is performed using analog input data of voltage and current obtained by sampling at a constant cycle. is there.

In the determination of the direction of the ground fault point, when zero phase voltage and zero phase current are used as two or more zero phase electric quantities, as shown in FIG. 1, zero phase voltage −V ₀ is used as a phase reference, When the zero-phase current I ₀ is delayed with respect to the zero-phase voltage −V ₀ , it is determined that a ground fault has occurred ahead, and the zero-phase current I ₀ has advanced with respect to the zero-phase voltage −V ₀ . In the case, it is determined that there is a ground fault at the rear. Φ shown in the figure is an angle formed by a perpendicular to the boundary with the determination threshold, and is the maximum sensitivity angle of the ground fault direction relay device.

When the maximum sensitivity angle is 0 degree, the ground fault can be investigated by calculating the inner product of the zero phase voltage and the zero phase current (see FIG. 2). Therefore, the direction of the ground fault point is determined by calculating the inner product of the zero-phase voltage V ₀ and the zero-phase current I ₀ and comparing the calculation result with a predetermined value K. The determination formula (1) is


| V ₀ | · | I ₀ | · cos θ ≧ K (1)

And θ is the phase difference between the zero-phase voltage V ₀ and the zero-phase current I ₀ .

The left side of the judgment formula (1) can be obtained by calculating the zero phase voltage V ₀ and the zero phase current I ₀ from the instantaneous voltage value and the instantaneous current value of each phase. The calculation method that uses and calculates is applied.

  However, such a conventional calculation method has the following problems. When the frequency fluctuates in the power system, the relationship of periodicity established between the sampling frequency and the amount of electricity in the power system does not hold, and the left side of the judgment formula (1) shows the calculation error due to the frequency fluctuation. It will be included. In addition, sampling with respect to a periodic waveform is affected by the time of sampling, that is, the waveform position (sampling position) viewed on the time axis, and there is a calculation error due to this. For this reason, there is a problem that the ground fault direction relay device malfunctions due to a calculation error.

The influence on the fluctuation of the frequency is as follows. When the two electric quantities to be captured in the ground fault direction relay device are voltage v and current i, they are sine functions.


vn (t) = Vn · sin (ωt + θ) (2)
in (t) = In · sin (ωt) (3)

And each shows an instantaneous value at time t. Here, Vn is the amplitude value of the voltage, In is the amplitude value of the current, ω is the angular frequency of the voltage and current, and θ is the leading phase of the voltage with respect to the current. The angular frequency ω has a relationship of ω = 2πf with respect to the frequency f of the power system. In each quantity of electricity, the subscript n means a phase, b phase, and c phase.

  The voltage vn (t) and the current in (t) are obtained by sampling at a predetermined cycle in each phase. For this, the instantaneous values of voltage and current are sampled and stored at a sampling frequency 12 times the rated frequency in the power system. To do. When the rated frequency of the power system is 50 Hz, if the sampling frequency is twelve times that is 600 Hz, the sampling period T is 1/600 sec.

The zero phase electric quantity is calculated by synthesizing all phases of the instantaneous voltage value and the instantaneous current value of each phase in the sampling period T, and the zero phase voltage V _0b and the zero phase current I _0b are

V _0b = V ₀ · sin (ωkT + θ) (4)
I _0b = I ₀ · sin (ωkT) (5)

It can be expressed as.

Here, V ₀ is the amplitude value of the zero-phase voltage, I ₀ is the amplitude value of the zero-phase current, θ is the phase difference between the zero-phase voltage and the zero-phase current, and the subscript k is the instantaneous value data in each electric quantity. This means the time point, and the time point k of the instantaneous value data takes values of 1, 2, 3,.
The fluctuation (frequency fluctuation rate α) of the frequency f of the power system is related to the fundamental frequency f _b .


α = (f−f _b ) / f _b (6)

Is defined as, for example, when the fundamental frequency f _b is 50 Hz, if the frequency f of the electric power system fluctuates to 60Hz frequency variation rate α of 0.2.

Therefore, in the ground fault direction relay, when the frequency fluctuation rate α is considered in the zero-phase electric quantity, the above formulas (4) and (5) are


V _0b = V ₀ · sin {ω (1 + α) kT + θ} (7)
I _0b = I ₀ · sin {ω (1 + α) kT} (8)

It becomes.

Sampling can be set at a sampling position m, and a certain time point k can be set as a reference time point (m-0). Zero-phase voltage at the reference time point k = m-0 and k = m−3 90 ° before the reference time point. , Zero-phase current is

V _{0 (m−0)} = V ₀ sin {ω (1 + α) (m−0) T + θ} (9)
I _{0 (m−0)} = I ₀ sin {ω (1 + α) (m−0) T} (10)

V _{0 (m−3)} = V ₀ sin {ω (1 + α) (m−3) T + θ} (11)
I _{0 (m−3)} = I ₀ sin {ω (1 + α) (m−3) T} (12)

It becomes. Since these expressions (9) to (12) are substituted for the left side of the determination expression (1), that is, the phase difference calculation,

| V _0b | · | I _0b | · cos θ =
V _{0 (m-0)} · I _{0 (m-0)} + V _{0 (m-3)} · I _{0 (m-3)}
... (13)

This equation (13) becomes the equation (14) shown in equation (1).

…（１４）

... (14)

  Since the expression (14) includes the term of the frequency variation rate α and the term of the sampling position m, the phase difference can be accurately calculated when there is no frequency variation (α = 0). An error will occur.

  That is, by applying the equation (14), the error rate characteristics shown in FIG. 3 are obtained. In the figure, the horizontal axis represents the frequency variation rate α, the vertical axis represents the error rate in the phase difference calculation, and the calculation condition is assumed to be θ = 0, that is, the phase difference between voltage and current is 0 °. The solid line in the figure is the characteristic when the sampling position m is m-0, and the dotted line is the characteristic when the sampling position m is changed. As is apparent from the figure, an error occurs when there is a frequency variation, and an error also occurs due to a difference in sampling position m on the time axis.

  In order to suppress the influence of this frequency, a certain time point is set as a reference time point, an instantaneous voltage value and an instantaneous current value at the reference time point, and an instantaneous voltage value and an instantaneous current value at an electrical angle 90 ° before the rated frequency of the power system from the reference time point. There has been proposed a technique for obtaining a zero-phase electric quantity for two or more electric quantities from a value and an instantaneous voltage value and an instantaneous current value at a time point 180 degrees before the electrical angle of the rated frequency of the power system from the reference time point. Thereby, even when there is a frequency variation in the power system, the phase relationship between two or more zero-phase electric quantities in the power system can be calculated with sufficient accuracy. This type of technology is disclosed in, for example, Patent Documents 1 and 2.

On the other hand, for the ground fault direction relay device, an optimum maximum sensitivity angle is selected in consideration of the grounding method, the charging current, and the reactor current. For example, the maximum sensitivity angle of the direct grounding system is delayed by 60 ° with respect to −V ₀ , and in the high resistance grounding system, the optimum maximum sensitivity angle is selected in consideration of the charging current and the reactor current. If the charging current is large strains, the characteristics of the advance against -V ₀ is used.

In the case of the ground fault direction relay device in which the maximum sensitivity angle φ is selected in advance, the direction determination of the ground fault point is V _{0 obtained} by shifting the _zero phase voltage V ₀ by the maximum sensitivity angle φ as shown in FIG. Is calculated by calculating the inner product of 'and the zero-phase current I ₀ and comparing the calculation result with a predetermined value K.


| V ₀ '| · | I ₀ | · cos (θ−φ) ≧ K (15)

It becomes. Here, φ is a preselected maximum sensitivity angle and is a fixed value. Similarly, when the maximum sensitivity angle φ is determined by setting, when the frequency variation rate α (for example, 30 °) is taken into consideration, the error rate characteristics shown in FIG. 5 are obtained.

JP 57-106336 A

In the conventional apparatus, it is necessary to obtain the effective value of V ₀ ′ obtained by shifting the zero-phase voltage V ₀ by the maximum sensitivity angle φ. For example, the sampling period can be appropriately set according to the maximum sensitivity angle φ, or | V _{Finding 0} ′ | with high accuracy is complicated, and the maximum sensitivity angle φ corresponds to a fixed value. Therefore, there is a problem that it is desired to accurately determine the ground fault direction with respect to the arbitrarily set maximum sensitivity angle φ.

  Furthermore, although the conventional device disclosed in Patent Document 1 is intended to develop a device that is resistant to frequency fluctuations, the frequency fluctuation index α remains in the arithmetic expression, so that the influence of frequency fluctuations can be completely avoided. There is also a problem that cannot be done.

  The present invention solves the above-described problems, and its object is to calculate the phase relationship between two or more zero-phase electric quantities in the power system with sufficient accuracy even when there are frequency fluctuations in the power system. Another object of the present invention is to provide a ground fault direction relay device that can perform a correct determination regardless of the sampling position on the time axis, and that can perform the determination for a maximum sensitivity angle that is arbitrarily set.

  In order to solve the above-described problems, a ground fault direction relay device of the present invention includes (1) a memory unit that stores instantaneous values of voltage and current of an electric power system, and instantaneous value data and current of voltage from the memory unit. An instantaneous value data extracted by the extraction unit, an inner product value calculation unit for obtaining VI · cos θ which is an inner product value of voltage and current based on the instantaneous value data extracted by the extraction unit, and an instantaneous value extracted by the extraction unit Based on the data, an outer product value calculation unit for obtaining VI · sin θ, which is the outer product value of the voltage and the current, an inner product value obtained by the inner product value calculation unit, and a phase difference from the outer product value obtained by the outer product value calculation unit a phase difference calculation unit for obtaining θ, a determination unit that performs a ground fault point determination using the phase difference θ obtained by the phase difference calculation unit and the maximum sensitivity angle φ of the set ground fault direction relay device, Prepared. The maximum sensitivity angle φ may be 0 degrees.

  In the present invention, since the phase difference θ is directly calculated from the sin component and the cos component, it is not affected by fluctuations in the system frequency, and even if the system frequency fluctuates from the fundamental wave, the level of the two electric quantities is not affected. The phase difference can be calculated correctly. Further, by directly obtaining the phase difference θ, in the ground fault direction relay device in which the maximum sensitivity angle φ is set, correct system fault determination can be performed even if the system frequency varies. Furthermore, the sampling period can be set to an arbitrary predetermined period, and there is no need to change to an arithmetic expression corresponding to the sampling frequency, so that versatility is enhanced.

(2) The inner product value calculation unit calculates the following equation:

The outer product value calculation unit calculates the following equation:

In each of the above formulas,
At the reference time point (m−a), m is a sampling position, a is an integer of 0 or more, and x is a positive integer in the sampling step.

  If a = 0, the reference time point is the current time point, that is, the time point when the determination process is performed. A specific value of m is incremented by sequentially sampling in time series. Since the determination process in the present invention is not limited to the sampling position, it may be determined at any time. When a becomes a positive integer, it is determined whether there has been a ground fault at that time with reference to a certain point in the past. The smaller the value of a, the smaller the number of data stored and held in the memory unit. The larger x is, the more data is stored and held in the memory unit, but there is an advantage of minimizing the influence of calculation errors caused by an instantaneous change in electricity such as noise and surge.

  Also, if x is 1, the data used are (m−a) instantaneous value data at the reference time, the previous (m−1−a) instantaneous value data, and the previous (m−a) instantaneous value data. -A) instantaneous value data and the previous (m-4-a) instantaneous value data, and the past data going back from the reference time is up to four previous. If x is 2, the past data going back from the reference time is required up to 8 data. That is, as x is smaller, the number of data stored in the memory unit can be reduced.

を演算するものとするとよい。 (3) The determination unit

Should be calculated.

  (4) It is good to provide the input means which inputs the maximum sensitivity angle (phi) of the said ground fault direction relay apparatus. By the input means, the user can easily set the maximum sensitivity angle φ and perform ground fault determination based on the maximum sensitivity angle φ.

  In the present invention, since the outer product value calculation unit and the inner product value calculation unit are provided and the phase difference θ is directly obtained based on the calculation results, even when there is a frequency variation in the power system, two or more in the power system The phase relationship of the zero-phase electric quantity can be calculated with sufficient accuracy, correct judgment can be made regardless of the sampling position on the time axis, and such judgment should be made for the maximum sensitivity angle that is arbitrarily set Can do.

It is a graph which shows an example of the phase characteristic which concerns on determination of a ground fault direction. It is a figure explaining the determination algorithm of a ground fault direction in case a maximum sensitivity angle is 0 degree | times. It is a graph which shows the error rate in the conventional phase difference calculating formula (14). It is a figure explaining the determination algorithm of a ground fault direction in case a maximum sensitivity angle is (phi) (other than 0 degree | times). It is a graph which shows the error rate in case the maximum sensitivity angle is 30 degree | times. It is a block diagram which shows suitable one Embodiment of the direction relay apparatus which concerns on this invention. It is a graph which shows the error rate of the phase difference calculation when the frequency fluctuates.

  FIG. 6 shows a preferred embodiment of the present invention. In the present embodiment, the ground fault direction relay device includes a memory unit 1, an extraction unit 2, an inner product value calculation unit 3, an outer product value calculation unit 4, a phase difference calculation unit 5, and a determination unit 6. Furthermore, an input unit 7 for setting the maximum sensitivity angle φ is provided for the determination unit 6. The input unit 7 can use various input man-machine interfaces, for example, and selects one of a plurality of candidates prepared in advance, such as a numeric keypad or the like for directly specifying the value of the maximum sensitivity angle θ. A switch or the like may be used. The maximum sensitivity angle φ is specified by the user in a range of 60 to 90 °, for example, and is recorded as a set value in the determination unit 6. The angle range is not limited to the above, and may be various ranges.

  In the present embodiment, the instantaneous value data of the voltage v and current i of the power system is sampled at a predetermined cycle, fetched into the memory unit 1 for each phase, and the current and predetermined values stored in the memory unit 1 by the extraction unit 2 The past instantaneous value data is extracted, and the arithmetic units 3, 4 and 5 are processed using the extracted instantaneous value data to obtain the phase difference θ between the two electric quantities (for example, voltage and current). Then, the determined phase difference θ is given to the determination unit 6, and the determination unit 6 uses the set value φ to determine the ground fault point. Specifically, it is as follows.

For example, when the rated frequency of the power system is 50 Hz, the 12-fold sampling frequency is 600 Hz and the cycle T = 1/600. The sampling interval is, for example, an electrical angle of 30 ° when the rated frequency is 50 Hz. Here, the sampling is performed at an electrical angle of 30 °, but it is preferable to sample in a shorter cycle. The memory unit 1 samples and stores instantaneous values of the voltage v _nk and the current i _nk in each phase by the sampling period T. This sampling takes the values of 1, 2, 3,... In the instantaneous value data indicated by the subscript k in each of the a phase, b phase, and c phase indicated by the subscript n.

The extraction unit 2 extracts specific data from the instantaneous value data stored in the memory unit 1. The specific data includes a certain time point as a reference time point, an instantaneous voltage value v _m0 and an instantaneous current value i _{m0 at} the reference time point, and an instantaneous voltage value v _m3 at a time point 90 degrees prior to the electrical angle of the rated frequency of the power system from the reference time point. And the instantaneous current value i _m3 , and the instantaneous voltage value v _m6 and the instantaneous current value i _m6 at the time point of the electrical frequency 180 ° before the rated frequency of the power system from the reference time point are extracted. In each quantity of electricity, the subscript n means a phase, b phase, and c phase. The extraction unit 2 gives the extracted instantaneous value data of each phase to the inner product value calculation unit 3 and the outer product value calculation unit 4, respectively.

The inner product value calculation unit 3 calculates the inner product value of voltage and current.
VI ・ cosθ
And the obtained inner product value is passed to the phase difference calculation unit 5 in the next stage. Specifically, the inner product value calculation unit 3 substitutes the acquired six specific data into the following equation (16), and executes the inner product value calculation process.

・・・（１６）

... (16)

The inner product value calculation is obtained by the above equation (16) as follows. First, the arithmetic expression of Expression (16) is expanded. Each term constituting the numerator is as follows.

となる。 So the molecule is

It becomes.

Similarly, the terms constituting the denominator are as follows.

となる。本実施形態では、式（１６）の分母を算出するのに電気量として電圧のサンプリングデータを適用したが、電流を利用してもよい。 So the denominator is

It becomes. In the present embodiment, voltage sampling data is applied as the amount of electricity to calculate the denominator of Expression (16), but a current may be used.

となり、ｃｏｓ成分を算出することができる。
Therefore, from the denominator and numerator obtained above, equation (16) is

Thus, the cos component can be calculated.

The cross product value calculation unit 4 performs cross product value calculation of voltage and current.
VI ・ sinθ
And the obtained outer product value is passed to the phase difference calculation unit 5 in the next stage. Specifically, the outer product value calculation unit 4 assigns each of the acquired six specific data to the following equation (17), and executes the outer product value calculation process.

・・・（１７）

... (17)

The calculation of the outer product value by the above equation (17) is as follows. First, the arithmetic expression of Expression (17) is developed. Each term constituting the numerator is as follows.

となる。 So the molecule is

It becomes.

Similarly, the terms constituting the denominator are as follows.

となり、ｓｉｎ成分を算出することができる。
In the present embodiment, voltage sampling data is applied as an electric quantity to calculate the denominator of Expression (17), but a current may be used. Therefore, from each of the obtained denominator and numerator, equation (17) is

Thus, the sin component can be calculated.

・・・（１８）
The phase difference calculation unit 5 uses the inner product value and the outer product value acquired from the inner product value calculation unit 3 and the outer product value calculation unit 4 and substitutes them into the following equation (18) to obtain the phase difference θ.

... (18)

・・・（１９）
The above equation (18) can be converted from the equations (16) and (17) as shown in the following equation (19).

... (19)

Equation (19) does not include terms of the frequency variation rate α and the sampling position m. Therefore, the phase difference between the voltage and current can be accurately calculated.
The determination unit 5 performs a ground fault direction detection calculation. Specifically, the left side of the following equation (20) is calculated and obtained, and the direction of the ground fault point is determined based on whether or not it is equal to or greater than the set value K.


| V ₀ | · | I ₀ | · cos (θ−φ) ≧ K (20)

In Expression (20), θ obtains and substitutes the value obtained by the phase difference calculation unit 5. The maximum sensitivity angle φ is substituted into equation (20) using the value given from the input unit 7. Further, for each effective value | V ₀ | and | I ₀ |, for example, by adopting the technique disclosed in Japanese Patent Application Laid-Open No. 2008-292227, a correct effective value can be calculated regardless of fluctuations in the system frequency. It becomes possible. That is, for example, the power system condition is that the rated frequency fb is 50 Hz, the sampling frequency fs is 12 times 600 Hz, the sampling interval is 30 ° electrical angle, the reference time point (m-0), the time point before 60 ° electrical angle (m -2), using the time point 120 m before the electrical angle (m−4) and the time point 240 m before the electrical angle (m−8), each instantaneous value data i _m−0 and _{im − 2} , i _m-4 , i _m-8 can be used to obtain the amplitude value and effective value of the electric quantity from the following equation (21).

・・・（２１）

... (21)

  Since each value to be substituted on the left side of Expression (20) is a value that is not affected by the fluctuation of the system frequency, the calculation result is also not affected by the fluctuation of the system frequency. Therefore, accurate determination processing can be performed.

  FIG. 7 shows the error rate characteristics of the phase difference calculation when the frequency fluctuates. In the figure, the horizontal axis represents the frequency variation rate α, and the vertical axis represents the error rate of the ground fault direction determination calculation result. As a calculation condition, the maximum sensitivity angle φ = 30 °. The solid line shown in the figure is the characteristic when the sampling position m-0 is set, and the dotted line is the sampling position m-3. As is clear from the figure, the two coincide with each other, and only a solid line is shown in the figure.

  In the present embodiment, since the voltage and current phase difference θ can be accurately calculated, even when the maximum sensitivity angle φ is arbitrarily given, it is possible to determine the ground fault without being affected by the frequency fluctuation. . In addition, it is possible to correctly determine the direction of the ground fault point regardless of the sampling position m on the time axis. And malfunction due to systematic errors can be avoided.

(Modification)
In the above-described embodiment, the sampling data to be used has a certain arbitrary time point as the reference time point and m-0, and the data (m-3, m-6) three times before and six times before are used. Is not limited to this, and for example, the following general formula (x is a positive integer) is used to perform outer product value calculation or inner product value calculation to calculate the phase difference.

・・・（１６）′

... (16) '

・・・（１７）′

... (17) '

  As shown in the above-described embodiments and modifications, calculation / determination processing can be performed with a certain time point as a reference time point (m-0), and therefore determination processing can be performed at any time in real time. Further, in the present invention, the reference time is not limited to the present time, and determination processing can be performed based on past instantaneous value data sampled and stored. For example, using the sample data a times before the current time as the reference time point (m−a), the outer product value calculation or inner product value calculation is performed based on the following general formulas (16) ″ and (17) ″, and the phase difference is calculated. It is good to calculate. Here, a ≧ 0 and x is an integer other than 0.

・・・（１６）″

... (16) "

・・・（１７）″

... (17) "

DESCRIPTION OF SYMBOLS 1 Memory part 2 Extraction part 3 Inner product value calculation part 4 Outer product value calculation part 5 Phase difference calculation part 6 Determination part 7 Input part

Claims (4)

A memory unit for storing instantaneous values of voltage and current of the power system;
An extraction unit that extracts instantaneous voltage value data and current instantaneous value data from the memory unit;
Based on the instantaneous value data extracted by the extraction unit, an inner product value calculation unit for obtaining VI · cos θ which is an inner product value of voltage and current;
Based on the instantaneous value data extracted by the extraction unit, an outer product value calculation unit for obtaining VI · sin θ, which is an outer product value of the voltage and the current,
A phase difference calculation unit for obtaining a phase difference θ from the inner product value obtained by the inner product value calculation unit and the outer product value obtained by the outer product value calculation unit;
A determination unit that performs a ground fault point determination using the phase difference θ obtained by the phase difference calculation unit and the maximum sensitivity angle φ of the set ground fault direction relay device;
A ground fault direction relay device comprising: The inner product value calculation unit calculates the following equation:

The outer product value calculation unit calculates the following equation:

In each of the above formulas,
2. The ground fault direction relay device according to claim 1, wherein at a reference time (m−a), m is a sampling position m, a is an integer greater than or equal to 0, and an integer x is a positive integer in a sampling step. The ground determination direction relay device according to claim 1, wherein the determination unit calculates the following expression.

  The ground fault direction relay device according to any one of claims 1 to 3, further comprising input means for inputting a maximum sensitivity angle φ of the ground fault direction relay device.

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