CA2929382A1 - Method of removing decaying dc component from power system fault signal - Google Patents
Method of removing decaying dc component from power system fault signal Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
- G01R19/2513—Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/12—Arrangements for reducing harmonics from ac input or output
- H02M1/123—Suppression of common mode voltage or current
Abstract
A method for removing the attenuating DC component from a power system fault signal, comprising the following steps: 1) acquiring a normal signal I0 and a fault signal I1 in a power system; 2) sampling the acquired fault signal I1 to obtain an amplitude of the fault signal I1 at each sampling point; 3) calculating the amplitude of the fault signal I1 at each sampling point obtained in step 2) according to the following formula: I2 (N) = K[2 I1 (N) - I1 (N-1) - I1 (N+1)]; 4) obtaining from step 3) the signal amplitude of the fault signal I1 at each sampling point after the attenuating DC component is removed from the fault signal I1, and finally obtaining a signal I2 having the attenuating DC component removed. The method provides simple steps, involves fewer calculations, and has low delay.
Description
Method of Removing Decaying DC Component from Power System Fault Signal Field of the Invention The present invention relates to technical fields of power system protective relaying, fault recording and synchronized phasor measurement technologies, and particularly, to a method of removing a decaying DC component from a power system fault signal.
Description of the Related Art With continuous development of computer technologies and computer algorithms, many practicable devices based on microcomputer AC sampling technologies (e.g., a protective relaying device, a fault recorder, a synchronized phasor measurement unit, and the like) have been widely applied in power systems. With the microcomputer AC sampling, filtering functions achieved by some of the computer algorithms themselves can be sufficiently utilized, thereby omitting practical filtering circuits. For example, a full-wave Fourier algorithm, which is widely used currently, has a function of filtering DC components and harmonic components being integral multiples of the fundamental frequency. When the power system is faulted, however, a transient signal comprises not only a fundamental component, but also harmonic components and decaying DC components with uncertain amplitudes and decaying time constant. Since the decaying DC component is not a periodic signal and has a wide frequency band, and thus cannot be completely filtered by a common full-wave Fourier algorithm. Thus, when the transient signal is directly processed by the full-wave Fourier algorithm, there are larger errors in computed amplitudes and phase angles of the fundamental component and harmonics.
In currently published patents, there are substantially described methods and circuits for removing constant DC components. These methods and circuits have a better filtering effect to constant DC components, but have a poorer filtering effect to decaying DC
components.
Nevertheless, filtering methods and circuits which are developed specially for the decaying DC
components have not been published. In journals and conference papers, many researchers have widely studied on how to eliminate adverse effects caused by the decaying DC
component, and proposed quite a number of methods with certain effective effects. However, there are still defects, such as long data window, low precision, heavy calculation load, in these methods.
A paper "An Innovative Decaying DC Component Estimation Algorithm for Digital Relaying" (IEEE Transactions on Power Delivery, VOL.24, NO.1, 2009) presented by Yoon-Sung Cho, etc. from the LSIS Co., Ltd of Korea provides a method of computing parameters of the decaying DC components by utilizing the facts that, within one cycle, an integral of sinusoidal AC signals is zero while the integral of a decaying DC
component is not zero. This method is high in precision, but needs a time window of one fundamental frequency cycle, resulting in a large delay. When a high resistance grounded short circuit occurs in power system transmission lines, a time constant of the decaying DC component in the faulted power system may be less than a half of one cycle; under such a case, the method has a poor applicability.
A paper "Decaying DC Offset Removal Operator Using Mathematical Morphology for Phasor Measurement" (Innovative Smart Grid Technologies Conference Europe, 2010) presented by J. Buse, D. Y. Shi, T. Y. Ji and Q. H. Wu from the University of Liverpool of the United Kingdom provides a method of extracting decaying DC component using Mathematical Morphology. This method has a better real-time performance, because the symmetry of the sine wave is sufficiently utilized so that the time delay is shortened to be a quarter of one cycle. The Mathematical Morphology performs addition and subtraction operations, which will not result in any large computational load. This method, however, shall be conducted under three situations related to different fault initial angles and phase shift conditions, which is relatively fussy in processing.
A paper "A New DC Offset Removal Algorithm Using an Iterative Method for Real-Time Simulation" (IEEE Transactions on Power Delivery, VOL.26, NO.4, 2011) presented by GilsungByeon from the Korea University, Seaseung Oh etc. from the Yongji University of Korea provides a method of computing decaying DC components by using iterative approximation and solutions of equations, with which the time window is shortened to be four sampling intervals. This method, however, is complicated in calculation, and will perform operations including selection of initial values, iterative approximation, solving a transcendental equation, time compensation and the like. Even in the optimal case, in order to remove the decaying DC components of each sampling point, it is required to perform three comparison operations, three inverse trigonometric function operations, three trigonometric function operations, nine addition and subtraction operations, and thirteen multiplication and division operations. In some cases, the number of iterations is more than 20, resulting in multiplied increase in calculation load.
SUMMARY OF THE INVENTION
An object of the present invention is aimed to overcome detects and disadvantages in prior arts, and to provide a method of removing decaying DC components from a power system fault signal, which is simple in calculation steps, of low computational load and with a short time delay.
Description of the Related Art With continuous development of computer technologies and computer algorithms, many practicable devices based on microcomputer AC sampling technologies (e.g., a protective relaying device, a fault recorder, a synchronized phasor measurement unit, and the like) have been widely applied in power systems. With the microcomputer AC sampling, filtering functions achieved by some of the computer algorithms themselves can be sufficiently utilized, thereby omitting practical filtering circuits. For example, a full-wave Fourier algorithm, which is widely used currently, has a function of filtering DC components and harmonic components being integral multiples of the fundamental frequency. When the power system is faulted, however, a transient signal comprises not only a fundamental component, but also harmonic components and decaying DC components with uncertain amplitudes and decaying time constant. Since the decaying DC component is not a periodic signal and has a wide frequency band, and thus cannot be completely filtered by a common full-wave Fourier algorithm. Thus, when the transient signal is directly processed by the full-wave Fourier algorithm, there are larger errors in computed amplitudes and phase angles of the fundamental component and harmonics.
In currently published patents, there are substantially described methods and circuits for removing constant DC components. These methods and circuits have a better filtering effect to constant DC components, but have a poorer filtering effect to decaying DC
components.
Nevertheless, filtering methods and circuits which are developed specially for the decaying DC
components have not been published. In journals and conference papers, many researchers have widely studied on how to eliminate adverse effects caused by the decaying DC
component, and proposed quite a number of methods with certain effective effects. However, there are still defects, such as long data window, low precision, heavy calculation load, in these methods.
A paper "An Innovative Decaying DC Component Estimation Algorithm for Digital Relaying" (IEEE Transactions on Power Delivery, VOL.24, NO.1, 2009) presented by Yoon-Sung Cho, etc. from the LSIS Co., Ltd of Korea provides a method of computing parameters of the decaying DC components by utilizing the facts that, within one cycle, an integral of sinusoidal AC signals is zero while the integral of a decaying DC
component is not zero. This method is high in precision, but needs a time window of one fundamental frequency cycle, resulting in a large delay. When a high resistance grounded short circuit occurs in power system transmission lines, a time constant of the decaying DC component in the faulted power system may be less than a half of one cycle; under such a case, the method has a poor applicability.
A paper "Decaying DC Offset Removal Operator Using Mathematical Morphology for Phasor Measurement" (Innovative Smart Grid Technologies Conference Europe, 2010) presented by J. Buse, D. Y. Shi, T. Y. Ji and Q. H. Wu from the University of Liverpool of the United Kingdom provides a method of extracting decaying DC component using Mathematical Morphology. This method has a better real-time performance, because the symmetry of the sine wave is sufficiently utilized so that the time delay is shortened to be a quarter of one cycle. The Mathematical Morphology performs addition and subtraction operations, which will not result in any large computational load. This method, however, shall be conducted under three situations related to different fault initial angles and phase shift conditions, which is relatively fussy in processing.
A paper "A New DC Offset Removal Algorithm Using an Iterative Method for Real-Time Simulation" (IEEE Transactions on Power Delivery, VOL.26, NO.4, 2011) presented by GilsungByeon from the Korea University, Seaseung Oh etc. from the Yongji University of Korea provides a method of computing decaying DC components by using iterative approximation and solutions of equations, with which the time window is shortened to be four sampling intervals. This method, however, is complicated in calculation, and will perform operations including selection of initial values, iterative approximation, solving a transcendental equation, time compensation and the like. Even in the optimal case, in order to remove the decaying DC components of each sampling point, it is required to perform three comparison operations, three inverse trigonometric function operations, three trigonometric function operations, nine addition and subtraction operations, and thirteen multiplication and division operations. In some cases, the number of iterations is more than 20, resulting in multiplied increase in calculation load.
SUMMARY OF THE INVENTION
An object of the present invention is aimed to overcome detects and disadvantages in prior arts, and to provide a method of removing decaying DC components from a power system fault signal, which is simple in calculation steps, of low computational load and with a short time delay.
2 The object of the present invention can be achieved through the following technical solutions:
A method of removing a decaying DC component from a power system fault signal, which comprises the following steps:
(1) acquiring a fault signal I in a power system;
(2) performing ADC (analog-to-digital conversion) sampling on the acquired fault signal Ii to obtain the amplitude of the fault signal I at each sampling point;
A method of removing a decaying DC component from a power system fault signal, which comprises the following steps:
(1) acquiring a fault signal I in a power system;
(2) performing ADC (analog-to-digital conversion) sampling on the acquired fault signal Ii to obtain the amplitude of the fault signal I at each sampling point;
(3) processing the amplitude of the fault signal I at each sampling point obtained in step (2) by the following formula:
1 12 (N)= K[2I1(N)¨ il(N ¨1)¨ Ii(N +1)1,N = 2,3,...,-1At 1 ,J /2 (1) = /2 (2) 12(N)= 12(N-1),N =¨+
At where K=1/(2-2cos(ca610), co is a system angular frequency, ti is the duration of the fault signal, and At is a sampling time interval; 11(N-1), /1(N) and /1 (N+ 1) are respectively amplitudes of the fault signal I at the N-lst, Nth and N+lst sampling points, and form a data window for three successive sampling points with its center located at the Nth sampling point; 12(N) is an amplitude of a signal obtained after removing the decaying DC component from the fault signal Ii at the Nth sampling point;
1 12 (N)= K[2I1(N)¨ il(N ¨1)¨ Ii(N +1)1,N = 2,3,...,-1At 1 ,J /2 (1) = /2 (2) 12(N)= 12(N-1),N =¨+
At where K=1/(2-2cos(ca610), co is a system angular frequency, ti is the duration of the fault signal, and At is a sampling time interval; 11(N-1), /1(N) and /1 (N+ 1) are respectively amplitudes of the fault signal I at the N-lst, Nth and N+lst sampling points, and form a data window for three successive sampling points with its center located at the Nth sampling point; 12(N) is an amplitude of a signal obtained after removing the decaying DC component from the fault signal Ii at the Nth sampling point;
(4) obtaining from step (3) the signal amplitude of the fault signal /1 at each sampling point after the decaying DC component is removed, and finally obtaining a signal 12 which has the decaying DC component removed.
Preferably, the three successive samples I1(N-1), 11(IV) and 11(N+1) in step(3) and I2(N) are linearly dependent.
Preferably, the power system in step( I) includes a normal signal /0 and the fault signal /1;
the normal signal /0 is expressed as:
= cos(ot +
the fault signal I is expressed as:
= Ai cos(cot + + fl) +Be r ;
where Ao and A I are amplitudes of the normal signal and the fault signal, respectively; co is the system angular frequency, (0 is an initial phase angle, /3 is phase shift generated when the fault signal occurs; in the formula, /Dr (N)= Be is the decaying DC component, B and r are initial amplitude and time constant of the decaying DC component, respectively.
A main principle for the method of the present invention is described as follows:
(1) assuming that a current signal /0 under normal operation state of a power system is expressed as:
= 4 cos(cot + 0;
When the power system is faulted, network parameters of the system are suddenly changed, which results in changes in the amplitude and phase of fundamental frequency component. As the inductive component in the system has a characteristic of suppressing the current from being suddenly changed, the fault current normally consists of a decaying DC
component; therefore, the detected fault current signal I can be expressed as:
cos(cot + + fl) +Be T ;
where Ao and A1 are amplitudes of the pre-fault current and the post-fault current, respectively; co is a system angular frequency, is an initial phase angle, /1 is phase shift generated when the fault occurs; B and r are respectively the initial amplitude and time constant of the decaying DC component.
(2) performing ADC sampling on the fault signal I, the amplitude I1(N) of the fault signal It at the Nth sampling point is expressed as:
I i(N) = Alcos(coN At + ç + P)+ Be'';
where At is a sampling time interval, /1,---1/r is the negative reciprocal of the time constant r;
(3) the decaying DC component is in a form of exponential function, and may be approximated by using a Taylor series:
/DcM =BerAmf B+.1At;
Thus, the amplitude I1(N) of I at the Nth sampling point is expressed as:
11(N) = A1 cos(coNAt + q,+)(3)+ B + AN At;
According the above equation for /1(N), expressions for the amplitudes 11(N-l), and /1(N+1) at the N-lst and the N+lst sampling points are obtained as follows:
I i(N ¨1), A1 cos(co(N ¨1)At + çz + ,8) + B+ 2(1\T ¨1)At;
11(N +1)= Aicos(o(N +1)At + co+ 13)+ B + +1)At;
It can be calculated and obtained from the equations for /1(N-1), (N) and /1(N+1) that I (N ¨1)+ +1)-21.1(N)cos(coAt) Dc (N)= B + =
2 (1 ¨ cos(coAt)) (4) a subtraction operation is made between /1(N) and /Dc(N) to obtain an amplitude I2(N) of a signal obtained after removing the decaying DC component /Dc(N) of the fault signal I at the Nth sampling point, /2(1\) is specifically expressed as follows:
I2(N)= K[2I,(N)¨Ii(N ¨1)¨ I,(N +1)1,N = 2,3,.., At /2 (1) = 12(2) 12(N) where K=1/(2-2cos(wAt)).
Based on the above principle, relationships between the signal /2 after removing the decaying DC component and the fault signal Ii at respective sampling points can be obtained, thereby achieving the object of removing the decaying DC component from the fault signal.
Compared with the prior arts, the present invention provides the following advantages and effects:
(1) In the method of the present invention, the decaying DC component is removed from the fault signal by using a linear combination of the three successive samples within the data window. The calculation requires only include three addition and subtraction operations and one multiplication operation, thereby the computational load is very small and can be performed in few steps.
(2) In the method of the present invention, the decaying DC component at one sampling point can be removed from the fault signal in a data window of the three successive sampling points, thereby the method has a lower time delay, which is only one sampling interval.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a schematic diagram showing a fault occurring in single phase line of a power system.
Fig. 2 is a schematic diagram showing a fault signal, a decaying DC component, and signal after removing a decaying DC component in a method of the present invention.
Preferably, the three successive samples I1(N-1), 11(IV) and 11(N+1) in step(3) and I2(N) are linearly dependent.
Preferably, the power system in step( I) includes a normal signal /0 and the fault signal /1;
the normal signal /0 is expressed as:
= cos(ot +
the fault signal I is expressed as:
= Ai cos(cot + + fl) +Be r ;
where Ao and A I are amplitudes of the normal signal and the fault signal, respectively; co is the system angular frequency, (0 is an initial phase angle, /3 is phase shift generated when the fault signal occurs; in the formula, /Dr (N)= Be is the decaying DC component, B and r are initial amplitude and time constant of the decaying DC component, respectively.
A main principle for the method of the present invention is described as follows:
(1) assuming that a current signal /0 under normal operation state of a power system is expressed as:
= 4 cos(cot + 0;
When the power system is faulted, network parameters of the system are suddenly changed, which results in changes in the amplitude and phase of fundamental frequency component. As the inductive component in the system has a characteristic of suppressing the current from being suddenly changed, the fault current normally consists of a decaying DC
component; therefore, the detected fault current signal I can be expressed as:
cos(cot + + fl) +Be T ;
where Ao and A1 are amplitudes of the pre-fault current and the post-fault current, respectively; co is a system angular frequency, is an initial phase angle, /1 is phase shift generated when the fault occurs; B and r are respectively the initial amplitude and time constant of the decaying DC component.
(2) performing ADC sampling on the fault signal I, the amplitude I1(N) of the fault signal It at the Nth sampling point is expressed as:
I i(N) = Alcos(coN At + ç + P)+ Be'';
where At is a sampling time interval, /1,---1/r is the negative reciprocal of the time constant r;
(3) the decaying DC component is in a form of exponential function, and may be approximated by using a Taylor series:
/DcM =BerAmf B+.1At;
Thus, the amplitude I1(N) of I at the Nth sampling point is expressed as:
11(N) = A1 cos(coNAt + q,+)(3)+ B + AN At;
According the above equation for /1(N), expressions for the amplitudes 11(N-l), and /1(N+1) at the N-lst and the N+lst sampling points are obtained as follows:
I i(N ¨1), A1 cos(co(N ¨1)At + çz + ,8) + B+ 2(1\T ¨1)At;
11(N +1)= Aicos(o(N +1)At + co+ 13)+ B + +1)At;
It can be calculated and obtained from the equations for /1(N-1), (N) and /1(N+1) that I (N ¨1)+ +1)-21.1(N)cos(coAt) Dc (N)= B + =
2 (1 ¨ cos(coAt)) (4) a subtraction operation is made between /1(N) and /Dc(N) to obtain an amplitude I2(N) of a signal obtained after removing the decaying DC component /Dc(N) of the fault signal I at the Nth sampling point, /2(1\) is specifically expressed as follows:
I2(N)= K[2I,(N)¨Ii(N ¨1)¨ I,(N +1)1,N = 2,3,.., At /2 (1) = 12(2) 12(N) where K=1/(2-2cos(wAt)).
Based on the above principle, relationships between the signal /2 after removing the decaying DC component and the fault signal Ii at respective sampling points can be obtained, thereby achieving the object of removing the decaying DC component from the fault signal.
Compared with the prior arts, the present invention provides the following advantages and effects:
(1) In the method of the present invention, the decaying DC component is removed from the fault signal by using a linear combination of the three successive samples within the data window. The calculation requires only include three addition and subtraction operations and one multiplication operation, thereby the computational load is very small and can be performed in few steps.
(2) In the method of the present invention, the decaying DC component at one sampling point can be removed from the fault signal in a data window of the three successive sampling points, thereby the method has a lower time delay, which is only one sampling interval.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a schematic diagram showing a fault occurring in single phase line of a power system.
Fig. 2 is a schematic diagram showing a fault signal, a decaying DC component, and signal after removing a decaying DC component in a method of the present invention.
5 Fig. 3 is schematic diagram showing a comparison of calculated results for amplitudes of the fault signal before and after applying the method of the present invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE
INVENTION
The present disclosure will be described hereinafter in detail with reference to the embodiments and drawings, however the embodiments of the present invention are not limited to those.
Embodiment Fig. 1 is a schematic diagram of the power system model, in a single phase view, used in this embodiment, where in the equivalent resistance R=3.15,Q, the inductance L=0.0637H, the voltage VI = 230L0 , the voltage V2 = 228L50', and the system frequency f=501-1z. A
grounded short circuit fault occurs at time t=0.04s at a middle point (point F) on the transmission line of the power system, and an ADC sampling is performed on a fault current signal at an end A of the transmission line. In this embodiment, the method of removing a decaying DC component from a fault signal sampled at the end. A of the transmission line comprises steps of:
(1) acquiring a fault signal /1 generated when the fault occurs at the point F
on the transmission line of the power system; where the acquired fault signal /I is expressed as:
11 = cos(cot + co+ fl)+Be r where A1 is the amplitude of the fault signal, the system angular frequency co=27rf; rig is an initial phase angle, /3 is phase shift when the fault signal occurs, B and r are the amplitude and time constant of the decaying DC component, respectively.
(2) performing ADC sampling on the fault signal Li acquired in step(1) to obtain an amplitude of the fault signal Ii at each sampling point; where the sampling time interval At is 200 us, the signal amplitude of the acquired fault signal at the Nth sampling point is /1(N).
(3) calculating the amplitudes of the fault signal I sampled and obtained in step (2) at each sampling point according to the following formula:
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE
INVENTION
The present disclosure will be described hereinafter in detail with reference to the embodiments and drawings, however the embodiments of the present invention are not limited to those.
Embodiment Fig. 1 is a schematic diagram of the power system model, in a single phase view, used in this embodiment, where in the equivalent resistance R=3.15,Q, the inductance L=0.0637H, the voltage VI = 230L0 , the voltage V2 = 228L50', and the system frequency f=501-1z. A
grounded short circuit fault occurs at time t=0.04s at a middle point (point F) on the transmission line of the power system, and an ADC sampling is performed on a fault current signal at an end A of the transmission line. In this embodiment, the method of removing a decaying DC component from a fault signal sampled at the end. A of the transmission line comprises steps of:
(1) acquiring a fault signal /1 generated when the fault occurs at the point F
on the transmission line of the power system; where the acquired fault signal /I is expressed as:
11 = cos(cot + co+ fl)+Be r where A1 is the amplitude of the fault signal, the system angular frequency co=27rf; rig is an initial phase angle, /3 is phase shift when the fault signal occurs, B and r are the amplitude and time constant of the decaying DC component, respectively.
(2) performing ADC sampling on the fault signal Li acquired in step(1) to obtain an amplitude of the fault signal Ii at each sampling point; where the sampling time interval At is 200 us, the signal amplitude of the acquired fault signal at the Nth sampling point is /1(N).
(3) calculating the amplitudes of the fault signal I sampled and obtained in step (2) at each sampling point according to the following formula:
6 I,(N)= K[2I,(N)¨ I,(N ¨1)¨ I,(N +1)],N = 2,3,... ¨t,-1 At 12(1) = 12(2) 112(N) At where t1 is the duration of the fault signal, /1(N-1), 1i(N) and Ii(N+1) are respectively amplitudes of the fault signal /1 at the N-Is!, Nth and N+lst sampling points, which form a data window of three successive sampling points centering on the Nth sampling point; 12(N) is an amplitude of a signal obtained after removing the decaying DC component of the fault signal Ii at the Nth sampling point(except the first and the last sampling points); the sampling time interval zit is 2001.ts, and thus K=1/(2-2cos(co4 0)=253.38. The three successive samples 11(N-1), 1i(N) and 11(N +1) are linearly related to I 2(N) =
The fault signal /1 of this embodiment is shown by in the dotted dash line in Fig. 2, the duration t1 of the fault signal /1 is 0.1s in the power system of the present embodiment, and the fault signal of this embodiment has 500 sampling points.
(4) through step (3), the signal amplitudes of the fault signal hat each sampling point after the decaying DC component is removed, and finally obtaining a signal 12 having the decaying DC component removed, as shown in the solid line in Fig. 2.
In Fig. 2, the decaying DC component signal removed by the above method is indicated in the dashed line.
In Fig. 3, the amplitude of the fundamental component of the fault signal calculated directly by using the fall-wave Fourier algorithm is shown in the dashed line.
There is an oscillation error with larger margin within the fault period, and it needs several cycles to converge to the steady state value. Wherein, the solid line shows a result where a signal /2, which has the decaying DC component removed firstly by using the method of the present invention, is calculated by using the full-wave Fourier algorithm. There is almost no oscillation within the fault period, and the convergence to steady state value can be quickly achieved.
In the method of the present invention, the decaying DC component can be removed at each sampling point through the data window of the three successive samples, thereby the method has a lower time delay, which is only one sampling interval. Further, in the method of the present invention, the amplitude of the decaying DC component removed by the method of the present invention is obtained through a linear combination of the three successive sampling values within the data window, only three addition and subtraction operations and one multiplication operation are required to perform the calculation, thereby computational load is very small.
The fault signal /1 of this embodiment is shown by in the dotted dash line in Fig. 2, the duration t1 of the fault signal /1 is 0.1s in the power system of the present embodiment, and the fault signal of this embodiment has 500 sampling points.
(4) through step (3), the signal amplitudes of the fault signal hat each sampling point after the decaying DC component is removed, and finally obtaining a signal 12 having the decaying DC component removed, as shown in the solid line in Fig. 2.
In Fig. 2, the decaying DC component signal removed by the above method is indicated in the dashed line.
In Fig. 3, the amplitude of the fundamental component of the fault signal calculated directly by using the fall-wave Fourier algorithm is shown in the dashed line.
There is an oscillation error with larger margin within the fault period, and it needs several cycles to converge to the steady state value. Wherein, the solid line shows a result where a signal /2, which has the decaying DC component removed firstly by using the method of the present invention, is calculated by using the full-wave Fourier algorithm. There is almost no oscillation within the fault period, and the convergence to steady state value can be quickly achieved.
In the method of the present invention, the decaying DC component can be removed at each sampling point through the data window of the three successive samples, thereby the method has a lower time delay, which is only one sampling interval. Further, in the method of the present invention, the amplitude of the decaying DC component removed by the method of the present invention is obtained through a linear combination of the three successive sampling values within the data window, only three addition and subtraction operations and one multiplication operation are required to perform the calculation, thereby computational load is very small.
7 The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above described embodiment, and any change, modification, alternation, combination and simplification made without departing from essential spirits and principles of the present invention should be regarded as equivalent substitutions, and are included within the scope of the present invention.
8
Claims (3)
1. A method for removing a decaying DC component from a power system fault signal, comprising steps of:
(1) acquiring a fault signal I1 in a power system;
(2) performing ADC sampling on the acquired fault signal I1 to obtain the amplitude of the fault signal I1 at each sampling point;
(3) processing the amplitude of the fault signal I1 at each sampling point obtained in step (2) according to the following formula:
where K=1 /(2-2cos(.omega..DELTA.t)), .omega. is a system angular frequency, t1 is the duration of the fault signal, and .DELTA.t is a sampling time interval;
I1(N),I1(N) and I1(N+1) are respectively amplitudes of the fault signal I1 at the N-1st, Nth and N+1st sampling points, and form a data window for three successive sampling points centering on the Nth sampling point; I2(N) is an amplitude of a signal obtained after removing the decaying DC component of the fault signal I1 at the Nth sampling point;
(4) obtaining from step (3) the signal amplitude of the fault signal I1 at each sampling point after the decaying DC component is removed, and finally obtaining a signal I2 having the decaying DC component removed.
(1) acquiring a fault signal I1 in a power system;
(2) performing ADC sampling on the acquired fault signal I1 to obtain the amplitude of the fault signal I1 at each sampling point;
(3) processing the amplitude of the fault signal I1 at each sampling point obtained in step (2) according to the following formula:
where K=1 /(2-2cos(.omega..DELTA.t)), .omega. is a system angular frequency, t1 is the duration of the fault signal, and .DELTA.t is a sampling time interval;
I1(N),I1(N) and I1(N+1) are respectively amplitudes of the fault signal I1 at the N-1st, Nth and N+1st sampling points, and form a data window for three successive sampling points centering on the Nth sampling point; I2(N) is an amplitude of a signal obtained after removing the decaying DC component of the fault signal I1 at the Nth sampling point;
(4) obtaining from step (3) the signal amplitude of the fault signal I1 at each sampling point after the decaying DC component is removed, and finally obtaining a signal I2 having the decaying DC component removed.
2. The method for removing a decaying DC component from a power system fault signal according to claim 1, wherein the three successive samples I1(N-1), I1(N) and I1(N+1) in step(3) are related linearly to the I2(N).
3. The method for removing a decaying DC component from a power system fault signal according to claim 1, where in the power system in step(1) includes a normal signal I0 and the fault signal I1;
the normal signal I0 is expressed as:
I0 = A0 cos(.omega.t + .phi.);
the fault signal I1 is expressed as:
I1 =A1 cos(.omega.t + .phi. + .beta.) +Be ~;
where A0 and A1 are respectively amplitudes of the normal signal and the fault signal; .omega.
is the system angular frequency; .phi. is an initial phase angle; .beta. is the phase shift generated in the fault signal; B and .tau. are respectively the amplitude and time constant of the decaying DC component.
the normal signal I0 is expressed as:
I0 = A0 cos(.omega.t + .phi.);
the fault signal I1 is expressed as:
I1 =A1 cos(.omega.t + .phi. + .beta.) +Be ~;
where A0 and A1 are respectively amplitudes of the normal signal and the fault signal; .omega.
is the system angular frequency; .phi. is an initial phase angle; .beta. is the phase shift generated in the fault signal; B and .tau. are respectively the amplitude and time constant of the decaying DC component.
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| US20190386485A1 (en) * | 2018-06-15 | 2019-12-19 | Schweitzer Engineering Laboratories, Inc. | Fault magnitude calculation during current transformer saturation |
| US11162994B2 (en) | 2020-01-23 | 2021-11-02 | Schweitzer Engineering Laboratories, Inc. | Fault current calculation during transformer saturation using the waveform unsaturated region |
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| JP2002233045A (en) * | 2001-02-02 | 2002-08-16 | Canon Inc | Ground detecting device for photovoltaic power generation system and method |
| CN100476443C (en) * | 2006-10-10 | 2009-04-08 | 浙江大学 | Wide-zone electric-net phasor synchronous measuring device with freely-set synchronous time scale |
| CN100485734C (en) * | 2007-07-17 | 2009-05-06 | 东北大学 | Electric energy quality and electrical power system malfunction detection wave recording device and method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20190386485A1 (en) * | 2018-06-15 | 2019-12-19 | Schweitzer Engineering Laboratories, Inc. | Fault magnitude calculation during current transformer saturation |
| US10637233B2 (en) * | 2018-06-15 | 2020-04-28 | Schweitzer Engineering Laboratories, Inc. | Fault magnitude calculation during current transformer saturation |
| US11474139B2 (en) | 2019-04-05 | 2022-10-18 | Schweitzer Engineering Laboratories, Inc. | Fault direction calculation during current transformer saturation |
| US11480601B2 (en) | 2019-09-26 | 2022-10-25 | General Electric Technology Gmbh | Systems and methods to improve distance protection in transmission lines |
| US11162994B2 (en) | 2020-01-23 | 2021-11-02 | Schweitzer Engineering Laboratories, Inc. | Fault current calculation during transformer saturation using the waveform unsaturated region |
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