CN114047406B - Half-wavelength line double-end fault distance measurement method based on park transformation - Google Patents
Half-wavelength line double-end fault distance measurement method based on park transformation Download PDFInfo
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Abstract
The invention relates to a half-wavelength line double-end fault location method based on park transformation, and belongs to the technical field of relay protection of power systems. According to the method, the half-wavelength line increment is calculated according to the relation between the length of the wire and the temperature; calculating a line error based on errors such as survey and sag, and correcting the half-wavelength line length; performing park transformation on three-phase current signals at the first and the tail end protection installation positions of the half-wavelength transmission line to obtain direct-axis components i at two ends of M, N d The method comprises the steps of carrying out a first treatment on the surface of the Introduction of i d Increment c of (2) dif And its energy xi dif Calibrating a wave head at the fault moment; the time when the initial traveling wave reaches both ends of the line M, N is marked as t M1 And t N1 And (3) fault location is carried out according to a double-end ranging formula, so that double-end traveling wave ranging of the half-wavelength transmission line with higher precision is realized. Compared with the traditional algorithm for obtaining the mode maximum value by wavelet transformation, the method is not influenced by wavelet basis functions and decomposition scales, and has strong universality. The problem of line length correction is considered, and fault positioning accuracy is improved.
Description
Technical Field
The invention relates to a half-wavelength line double-end fault location method based on park transformation, and belongs to the technical field of relay protection of power systems.
Background
Half-wavelength ac transmission (Half Wavelength AC Transmission/HWACT) refers to an ultra-long three-phase ac transmission mode in which the transmission line is approximately one half-wave at power frequency, i.e., 3000 km (50 Hz) or 2500 km (60 Hz). The extra-high voltage half-wavelength alternating current transmission technology is used as a long-distance and large-capacity alternating current transmission mode, and has the advantages that reactive power self-balancing can be realized on the whole line, and reactive power compensation equipment is not required to be installed. From the power transmission point of view, the equivalent electrical distance is 0, and the theoretical power transmission capacity is infinity.
The main distance measurement methods at present include a fault analysis method (impedance method) and a traveling wave method, and traveling wave positioning based on fault transient quantity is little influenced by CT saturation, fault resistance and a system operation mode, and has high positioning precision and is always a research hot spot. The transmission line traveling wave distance measurement mainly comprises a double-end method and a single-end method, wherein the double-end method only needs to detect the arrival time of the head waves at two ends of the transmission line, and the accurate judgment of the arrival time of the initial traveling wave is one of key factors for determining the positioning accuracy. The traveling wave continuously attenuates along with the increase of the transmission distance when traveling wave propagates on the half-wavelength transmission line, and the root cause of the traveling wave is the frequency dependent characteristic of the traveling wave on the transmission line and the attenuation of energy when traveling wave propagates. Compared with a common line, the traveling wave propagates on the ultra-long distance transmission line with half wavelength, so that the attenuation and distortion on the waveform are more serious, and the initial wave head of the traveling wave becomes more and more gentle along with the increase of the propagation distance. In many traveling wave positioning schemes, wavelet mode maxima are often adopted to realize wave head calibration, the time calibrated by the method is the time when signal mutation is most obvious, but not the initial traveling wave arrival time, the fault point head cannot be accurately represented, larger errors are brought to fault positioning, and the precision of fault distance measurement by the method is not ideal. The Park's Transformation can process real-time sampling data, and can be used for initial surge detection and arrival time calibration of high-resistance faults. The invention successfully applies the characteristic of park transformation to the accurate calibration of the arrival time of the fault traveling wave head, and the simulation data verification shows the correctness and feasibility of the method on the half-wavelength transmission line.
The existing fault distance measurement method is a fault analysis method or a traveling wave method, and the length of the power transmission line is assumed to be a fixed value, but in practice, the length true value of the power transmission line is influenced by actual running conditions such as sag, ambient temperature, wind speed, icing, current-carrying capacity of a wire and the like. The fault distance measurement has a certain precision requirement, and for a long-distance transmission line such as half wavelength, each span has a slight length change, and the length is expanded to thousands of spans of the whole line, so that line length errors of thousands of meters can be caused, the precision of fault positioning can be greatly reduced, and therefore, the fault distance measurement method has important practical significance in correcting the line length.
Many factors affect the length of the line, including generally: survey, sag, ambient temperature error, load current effects, etc. The length value of each power transmission line is not the true value of the length of the line, but the design length. When the fault location is performed by the conventional method, errors exist. The main factor causing the error of the line length is sag, and the variation range of sag is large according to the tension of the tower and the difference of the topography. The wire has the characteristics of thermal expansion and cold contraction, and the length of the wire can be changed along with the change of seasons. In addition, in the operation of the power system, the load and the temperature of the power transmission line change at any time, the temperature of the wire is low in light load and the temperature of the wire is high in heavy load. The rise in temperature of the wire causes the wire length to become large. The molar root formula can more fully describe the relationship between the current-carrying capacity I and other relevant factors when the lead works normally. The fixed line length generally increases with the temperature, and a certain relation exists between the length and the temperature, so that the increase of the wire caused by the temperature change can be calculated through the relation. Meanwhile, the metal slowly generates irrecoverable permanent deformation with the lapse of time under the actions of temperature, external force and self weight, and the phenomenon is called creep. Creep will increase the length of the line, taking into account the amount of creep to facilitate the correction of the line length.
Disclosure of Invention
The invention aims to provide a half-wavelength line double-end fault distance measurement method based on park transformation, so as to solve the problem that fault traveling wave heads are difficult to calibrate due to unique electrical characteristics of an extra-high voltage half-wavelength alternating current transmission line.
As shown by comparison, for a weak fault mode, such as that the transition resistance is larger than the line wave impedance or the far-end fault of the ultra-long line, the initial traveling wave change of the fault at the observation point is gentle, and for the arrival time of the gentle fault traveling wave head, the accuracy of calibrating the wave head by using the wavelet mode maximum value is not ideal, and the calibration time is delayed. However, after the line fails, the amplitude and the phase of the three-phase voltage and the current can be changed due to the superposition of the additional fault source, and the initial fault wave head is amplified without delay after park transformation, so that the park transformation still has higher precision in a weak fault mode. The half-wavelength transmission line makes the fault traveling wave change smooth due to the ultra-long transmission distance, and the park transformation is utilized to calibrate the wave head when the smooth fault traveling wave head arrives.
The technical scheme of the invention is as follows: a half-wavelength line double-end fault distance measurement method based on park transformation comprises the following specific steps:
step1: and calculating the half-wavelength line increment according to the relation between the length of the wire and the temperature through the line current-carrying capacity.
Step2: and calculating to obtain a half-wavelength line error through the line creep quantity. The lead can generate permanent deformation with time under the influence of temperature, external force and gravity, which is called creep, and the creep amount is 0.3 per mill-0.5 per mill of the length of the lead, so as to obtain the creep amount of the half-wavelength power transmission line.
Step3: and correcting the length of the half-wavelength transmission line according to the half-wavelength line increment and the half-wavelength line error.
Step4: performing park transformation on three-phase current signals at the first and the tail end protection installation positions of the half-wavelength transmission line to obtain direct-axis components i at two ends of M, N d 。
Step5: introducing a direct axis component i d Increment c of (2) dif And its energy xi dif And calibrating the wave head at the fault moment.
Step6: the time when the initial traveling wave reaches both ends of the line M, N is marked as t M1 And t N1 And (3) performing fault location according to a double-end ranging formula to realize double-end traveling wave ranging.
The calculated half-wavelength line increment is specifically:
and calculating the current-carrying capacity I of the wire in normal operation according to a molar root formula.
Obtaining annual average temperature t of region a And (5) calculating the temperature rise of the line under different overload conditions by combining the type of the ultra-high voltage half-wavelength transmission line.
And calculating the half-wavelength line increment according to the relation between the length of the wire and the temperature.
The calculating of the half wavelength line error is specifically:
and obtaining the creep quantity of the half-wavelength power transmission line according to the ratio relation of the creep quantity of the line to the total length of the line.
And equally dividing the error of the power transmission line in actual operation on the whole half-wavelength line to obtain the half-wavelength line length error.
The Step4 specifically comprises the following steps:
step4.1: and constructing a half-wavelength alternating current transmission system model.
Step4.2: when the line runs, three-phase current signals at the M-terminal protection installation position are collected as data samples S 1 Collecting three-phase current signals at the installation position of N-terminal protection as data samples S 2 。
Step4.3: respectively to S 1 、S 2 A clark transformation is performed to transform the three-phase currents into a stationary alpha and beta coordinate system.
Step4.4: the current in the alpha and beta coordinate systems is subjected to park transformation to obtain M, N end direct axis component i d 。
The Step5 specifically comprises the following steps: using two adjacent straight-axis components i d The difference constitutes an increment c dif Defining c in observation time window dif The degree of discontinuity is measured as the mutation energy xi dif And calibrating the fault traveling wave head by using the method.
The beneficial effects of the invention are as follows:
1. the problem that fault traveling wave heads are difficult to calibrate due to unique electrical characteristics of the ultra-high voltage half-wavelength alternating current transmission line is solved.
2. The park transformation is used for representing the fault initial traveling wave head without delay, so that the accuracy of double-end ranging is greatly improved.
3. If directly utilize i d The calibration of the fault moment can be caused by i d The smaller mutation amplitude leads to calibration failure, and i is introduced d Increment c of (2) dif And its energy xi dif Has strong noise resistance and transition resistance.
4. And the factors influencing the length of the line, such as survey, sag, environmental temperature error, load current, line creep and the like, are considered, the length of the half-wavelength transmission line is corrected, and the fault positioning accuracy is improved.
Drawings
FIG. 1 is a diagram of a half-wavelength AC transmission topology of the present invention;
FIG. 2 is a diagram of a simulated hardware system of the present invention;
FIG. 3 is a diagram showing simulation results of example 1 of the present invention;
FIG. 4 is a diagram showing simulation results of example 2 of the present invention;
FIG. 5 is a diagram showing the simulation results of example 3 of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and detailed description.
A half-wavelength line double-end fault distance measurement method based on park transformation is characterized by comprising the following steps of:
step1: the relation among the current-carrying capacity of the line, the length of the wire and the temperature is considered, and the current-carrying capacity I of the wire in normal operation is calculated by a molar root formula.
Wherein:
A＝πεSD[(δ+t a +273) 4 -(t a +273) 4 ]
wherein alpha is s The heat absorption coefficient of the wire is epsilon and the radiation coefficient of the surface of the wire.
Step2: obtaining annual average temperature t of region a The temperature rise of the line under different overload conditions is calculated by combining the type of the ultra-high voltage half-wavelength transmission line conductor, and the temperature rise is calculated according to the length and the length of the conductorAnd calculating the increment of the wire according to the relation between the temperatures:
Δl＝lλΔt
where λ is the coefficient of linear expansion.
Step3: under the influence of temperature, external force and dead weight, the lead can generate permanent deformation with time, which is called creep, and the creep amount is 0.3 per mill-0.5 per mill of the length of the lead, so as to obtain the creep amount of the half-wavelength power transmission line.
Step4: and assuming that errors (such as survey, sag, ambient temperature and the like) of the power transmission line in actual operation are equally divided on the whole half-wavelength line, obtaining a half-wavelength line length error, and carrying out length correction of the half-wavelength line.
Step5: and constructing a half-wavelength alternating current transmission system model. The voltage class of the half-wavelength alternating current transmission system is 1000kV, the whole line length is 3029km, and the frequency is 50Hz.
Step6: when the line runs, three-phase current signals at the M-terminal protection installation position are collected as data samples S 1 Collecting three-phase current signals at the installation position of N-terminal protection as data samples S 2 。
Step7: respectively to S 1 、S 2 The clark transformation is performed to transform three-phase currents into a stationary alpha and beta coordinate system, specifically:
step8: the current in the alpha and beta coordinate systems is subjected to park transformation to obtain M, N end direct axis component i d ：
Step9: introduction of i d Increment c of (2) dif And its energy xi dif Calibrating the fault traveling wave head to avoid the fault traveling wave head caused by i d The smaller the abrupt amplitude of (c) results in calibration failure, which is expressed as:
c dif (k)＝i d (k)-i d (k-1)
step10: by using xi dif Marking the time t when the initial fault traveling wave reaches the two ends of the line M, N M1 And t N1 And (3) carrying out fault location by combining a double-end ranging formula, wherein the double-end ranging formula is as follows:
wherein x is f For fault position, l is total length of line, v is wave speed of electromagnetic wave, 2.98X10 is taken 8 m/s。
The principle of the invention is as follows:
1. the fault traveling wave is a broadband step signal, contains fault information such as time, frequency, polarity, amplitude and the like, and has obvious advantages when used for fault distance measurement. The transmission line traveling wave distance measurement mainly comprises a double-end method and a single-end method, wherein the double-end method only needs to detect the arrival time of the head waves at two ends of the transmission line, and the accurate judgment of the arrival time of the initial traveling wave is one of key factors for determining the positioning accuracy. The extra-high voltage half-wavelength line needs to consider the frequency-dependent characteristic of line parameters when designing a relay protection scheme due to the extra-long transmission distance, the traveling wave can generate certain distortion and attenuation in the process of propagating along the line, the initial wave head of the traveling wave can become more and more gentle along with the increase of the distance, and compared with a common line, the traveling wave propagates on the half-wavelength transmission line to cause more serious waveform attenuation and distortion. Attenuation of the traveling wave can be calculated by the following equation:
wherein A is a propagation constant, the value of which is constantly less than 1 and greater than 0; gamma is a propagation constant, and is composed of an attenuation constant alpha and a phase constant beta, and the relation between the three is determined by the following formula:
for any frequency component, whether it is a forward traveling wave component or a backward traveling wave component, the attenuation of the traveling wave becomes more serious along with the increase of the fault distance, and because the traveling wave head becomes gentle, the arrival time of the traveling wave head becomes difficult to calibrate, and the accuracy of the traveling wave ranging is not ideal by calibrating the arrival time of the fault traveling wave head by using the maximum value of the wavelet transformation mode, so that a surge detection and wave head calibration method for weak faults is needed.
2. The park transformation can process real-time sampling data and can be used for initial surge detection and arrival time calibration of high-resistance faults. The Clark transform converts the time domain components of a three-phase system (in the abc coordinate system) into two components in the orthogonal stationary coordinate system (αβ). The park transform converts two components in the αβ coordinate system into an orthogonal rotational coordinate system (dq). Implementing these two transforms in succession may convert alternating current and voltage waveforms into direct current signals, simplifying the calculation.
In the physical sense, the park transformation is to transform alternating three-phase voltage or current to d, q and 0 coordinate axes, and the symmetrical three-phase voltage or current is changed into direct current after park transformation. After the line fails, as the additional fault source is superimposed, the amplitude and phase of the three-phase voltage and current of the fault can be changed, and the direct current is not generated after park transformation, so that the park transformation can be used as a method for calibrating the double-end traveling wave ranging wave head of the half-wavelength transmission system.
3. In the common fault distance measurement method, the impedance method and the traveling wave method are affected by the length of the line to different degrees, the fault distance measurement has certain precision requirements, and the factors affecting the length of the line are considered, so that the method has practical significance in realizing the correction of the length of the line. Factors that affect the length of the line are typically: survey, sag, ambient temperature error, load current effects, line creep, etc. In the operation of the power system, the load and the temperature of the power transmission line change at any time, the temperature of the wire is low in light load and the temperature of the wire is high in heavy load. The rise in temperature of the wire will cause the wire length to become greater. The molar root formula can more fully describe the relationship between the current-carrying capacity I and other relevant factors when the lead works normally, namely:
in the method, in the process of the invention,
A＝πεSD[(δ+t a +273) 4 -(t a +273) 4 ]
α s the heat absorption coefficient of the wire is epsilon and the radiation coefficient of the surface of the wire.
4. The fixed length generally increases with increasing temperature, and the following relationship exists between the length and the temperature:
Δl＝lλΔt
where λ is the expansion coefficient.
5. Under the action of temperature, external force and self weight, the metal slowly generates irrecoverable permanent deformation along with the time, and the phenomenon is called creep. Creep increases the length of the wire, and theoretically the final creep amount of the wire is 0.3-5 per mill of the wire length.
According to the simulation system, an RTDS is adopted to build a half-wavelength power transmission simulation model, simulation signals of simulation data are output from a GTAO port, signals are collected by a wave recording device, a logic closed loop of the simulation system is formed, and real working conditions are restored to the maximum extent. The simulation model system is shown in figure 1, the simulation hardware system is shown in figure 2, the whole line length of the line is 3029km, the voltage level is 1000kV, and the simulation sampling rate is set to be 1MHz. Three fault conditions are assumed, simulated, and the reliability of the method is verified.
Example 1: a half-wavelength alternating current transmission system shown in fig. 1 is established as a simulation model. The fault is set to occur at 0.1km (simulated half-wavelength transmission line transmitting end outlet) of the M-side bus outlet, the fault type is set to be an A-phase metallic grounding permanent fault, and the fault angle is 70 degrees. The implementation method comprises the following specific steps:
step1: considering the load current influence, the relation between temperature rise and the fixed length of the line, the creep quantity of the line, the survey and sag errors and the like, and calculating the current-carrying capacity I of the lead in normal operation according to a molar root formula:
wherein,
A＝πεSD[(δ+t a +273) 4 -(t a +273) 4 ]
wherein alpha is s The heat absorption coefficient of the wire, epsilon is the radiation coefficient of the surface of the wire, and each symbol unit and meaning are shown in table 1. The relationship between wire length and temperature:
Δl＝lλΔt
where λ is the expansion coefficient.
TABLE 1 Mole root formula symbol Unit and meaning
The length error of the half-wavelength line is calculated to be about 29km, the length correction of the half-wavelength line is carried out, the full length of the half-wavelength line is 3029km, and a simulation model system shown in the figure 1 is built.
Step2: three-phase current signals at two ends of a line M, N are respectively collected as data samples S 1 And S is 2 Data sample S is as follows 1 、S 2 Performing a Clark transformation to transform the three-phase currents into a stationary α and β coordinate system;
step3: performing park transformation according to the following method to obtain M, N end direct axis component i d 。
Step4: introduction of i as follows d Increment c of (2) dif And its energy xi dif And calibrating the fault traveling wave head.
c dif (k)＝i d (k)-i d (k-1)
Step5: the calibration results of wave heads at two sides of M, N are shown in figure 3, and t is obtained M1 ＝536.159ms，t N1 = 546.326ms, the fault was calculated to be located at 0.383km at the M-side exit using the double-ended ranging equation, the ranging error was only 0.00934%, and the accuracy was high.
Wherein x is f For fault position, l is total length of line, v is wave speed of electromagnetic wave, 2.98X10 is taken 8 m/s。
Example 2: in this example, the half-wavelength ac transmission system shown in fig. 1 is also taken as a simulation model, and a fault is set to occur at 1514.5km (midpoint of the simulated half-wavelength transmission line) of the line, the fault type is an AB interphase short circuit, and the fault angle is 80 °. Specific steps of implementation example 1 was repeated to obtain M, N two-sided wavefront calibration results as shown in FIG. 4, where t M1 ＝538.599ms，t N1 The fault was located at 1515.99km on line using the double-ended ranging equation for 538.589ms with a ranging error of 0.04919 ms, indicating that the positioning method also has higher accuracy at the mid-point of the half-wavelength line.
Example 3: the half-wavelength alternating current transmission system shown in the attached figure 1 is used as a simulation model, faults are set to occur at 2423.2km (2400 km which is the most serious fault point of the simulation half-wavelength transmission line), the fault type is A-phase grounding short circuit, the transition resistance is 300 omega, and the fault angle is 90 degrees. Specific steps of implementation example 1 was repeated to obtain M, N two-sided wavefront calibration results as shown in FIG. 5, where t M1 ＝544.963ms,t N1 The fault is located at 2421.612km of the line by using the double-end ranging formula for 538.875s, the ranging error is 0.05242%, and the accuracy is high.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (5)
1. A half-wavelength line double-end fault distance measurement method based on park transformation is characterized by comprising the following steps of:
step1: calculating the half-wavelength line increment according to the relation between the length of the wire and the temperature through the line current-carrying capacity;
step2: calculating to obtain a half-wavelength line length error through the line creep quantity;
step3: performing half-wavelength line length correction through the half-wavelength line increment and the half-wavelength line length error;
step4: performing park transformation on three-phase current signals at the first and the tail end protection installation positions of the half-wavelength line to obtain direct-axis components at two ends of M, N；
Step5: introducing a direct axis componentIncrement of->And energy of +.>Calibrating a fault traveling wave head;
step6: the time when the initial traveling wave reaches the two ends of the line M, N is marked asAnd->And (3) performing fault location according to a double-end ranging formula to realize double-end traveling wave ranging.
2. The park-transformation-based half-wavelength line double-end fault location method of claim 1, wherein the calculating the half-wavelength line increase is specifically:
calculating the current-carrying capacity I of the wire in normal operation according to a molar root formula;
obtaining annual average temperature of regionCalculating the temperature rise of the circuit under different overload conditions by combining the half-wavelength circuit wire types;
and calculating the half-wavelength line increment according to a relation between the length of the lead and the temperature rise.
3. The park-transformation-based half-wavelength line double-end fault location method of claim 1, wherein the calculating half-wavelength line length error is specifically:
obtaining the creep quantity of the half-wavelength line according to the ratio relation of the creep quantity of the line to the total length of the line;
and equally dividing the increment of the power transmission line in actual operation on the whole half-wavelength line to obtain the half-wavelength line length error.
4. The park-transformation-based half-wavelength line double-end fault location method according to claim 1, wherein Step4 is specifically:
step4.1: building a half-wavelength alternating current transmission system model;
step4.2: when the line runs, three-phase current signals at the M-terminal protection installation position are collected as data samplesCollecting N-terminal protection installationThree-phase current signal as data sample +.>；
Step4.3: respectively to、/>Performing Clark conversion to convert three-phase current to rest +.>And->In a coordinate system;
step4.4: will beAnd->Performing park transformation on the current in the coordinate system to obtain M, N end straight axis component +.>。
5. The park-transformation-based half-wavelength line double-end fault location method according to claim 1, wherein Step5 is specifically: using two adjacent straight-axis componentsThe difference constitutes an increment->Define the observation time window +.>The measure of the degree of discontinuity is the mutation energy +.>And calibrating the fault traveling wave head by using the method.
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| CN110618354A (en) * | 2019-10-23 | 2019-12-27 | 国网江苏省电力有限公司检修分公司 | Overhead line fault positioning method, system and storage medium considering electrical distance compensation |
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| CN103926484A (en) * | 2014-03-14 | 2014-07-16 | 广东电网公司电力科学研究院 | Electric transmission line dynamic capacity increasing method based on circuit sag real-time measurement |
| CN110618354A (en) * | 2019-10-23 | 2019-12-27 | 国网江苏省电力有限公司检修分公司 | Overhead line fault positioning method, system and storage medium considering electrical distance compensation |
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