CN116388178B - Flexible direct current power grid fault direction criterion method based on waveform correlation coefficient - Google Patents
Flexible direct current power grid fault direction criterion method based on waveform correlation coefficient Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
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- H—ELECTRICITY
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- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
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Abstract
The invention relates to the technical field of direct current line fault protection, in particular to a flexible direct current power grid fault direction criterion method based on waveform correlation coefficients. On the basis of deriving the fault traveling wave transmission characteristics of the flexible direct current power grid, the invention discovers the variation difference between the line mode fault voltage and the line mode fault current measured on the fault line and the non-fault line on the same direct current bus. When the direct current line breaks down, the change trend between the line mode fault voltage and the line mode fault current measured at the fault line port is irrelevant, and the correlation coefficient of the line mode fault voltage and the line mode fault current is almost zero. The change trend between the line mode fault voltage and the line mode fault current measured on the non-fault line port of the same direct current bus is linearly related, and the related coefficient of the line mode fault voltage and the line mode fault current is close to 1. The direction criterion method is hardly influenced by the state of the fault point, can reliably identify high-resistance faults, has clear setting threshold and excellent protection performance, and is suitable for flexible direct current power grids with different voltage levels and different wiring structures.
Description
Technical Field
The invention relates to the technical field of fault protection after a direct current line of a flexible direct current power grid has faults, in particular to a fault direction criterion method of the flexible direct current power grid based on waveform correlation coefficients.
Background
Future power systems will be new power systems that are subject to new energy sources. How to access high-proportion renewable energy sources (such as wind power, solar energy and the like) with intermittence and randomness into a power grid is a difficult problem to be solved. With the long-term development of high-capacity power semiconductor devices, a high-voltage direct current transmission (Voltage source converter high voltage direct current, VSC-HVDC) technology (called flexible direct current transmission in China) based on a voltage source converter has the advantages of no commutation failure, flexible control, flexible interconnection and the like, and is an important technical means for solving the problem of new energy scale grid connection. After the direct current circuit of the flexible direct current power grid breaks down, on the one hand, the impedance of a fault loop is small, the rising speed of fault current is high, and the overcurrent capacity of a turn-off semiconductor device is weak, so that the speed requirement on fault protection is extremely high (several milliseconds), the direct current fault current does not have zero crossing points, and the high-capacity direct current circuit breaker (DC circuit breaker, DCCB) breaking technology is still immature and high in cost. On the other hand, in the network flexible direct current system, the transient characteristic difference between the fault line and the non-fault line is small, and the single-end transient protection method based on the characteristic of the line protection boundary element of the current limiting reactors (Fault current limiting reactor, FCLR) at the two ends of the line is difficult to identify all complex and changeable line faults, and the protection threshold is complex to set, and particularly when the transition resistance of the direct current line fault is large, the high requirement is put forward on the single-end main protection.
The fault direction criterion can judge the direction information of fault occurrence according to the nature of boundary elements of the flexible direct current power grid and the geometric topology structure of system wiring, and naturally distinguish fault lines and non-fault lines on the same direct current bus. The fault direction criterion not only can improve the performance of main protection and remove the influence of non-fault lines of the same direct current bus, but also can utilize a communication system to set a spare protection scheme of a longitudinal direction by adopting fault direction information of two ends of the lines, and is used as a supplement of main protection to identify high-resistance faults of the lines. The performance of the main protection scheme and the backup protection scheme is determined to a great extent by the performance of the fault direction criterion, and the existing methods of utilizing the voltage polarity, the difference of forward traveling wave and reverse traveling wave on the FCLR are likely to be influenced by the transition resistance of the line (the larger the transition resistance is, the smaller the amplitude of the characteristic quantity is), and are also likely to be influenced by the fault position (the fault traveling wave is subjected to multiple refraction and reflection between the line port and the fault point when the near-end fault occurs), so that the performance of the fault direction criterion is likely to be influenced by the fault condition.
On the basis of deriving the traveling wave transmission characteristics of the fault of the flexible direct current power grid, the invention discovers the variation difference of the line mode fault voltage and the line mode fault current measured on the fault line and the non-fault line on the same direct current bus, provides a flexible direct current power grid fault direction criterion based on the correlation coefficient of the line mode fault voltage and the line mode fault current, can assist single-end-quantity main protection to improve performance, and can also be used as backup protection in the longitudinal direction of the line.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a flexible direct current power grid fault direction criterion method based on waveform correlation coefficients, which is not influenced by fault point states, has clear protective threshold boundaries and has good protective performance.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a flexible direct current power grid fault direction criterion method based on waveform correlation coefficient, the waveform is a line mode fault voltage and a line mode fault current obtained after processing voltage and current measured by a flexible direct current power grid line port;
the processing method of the voltage and the current measured by the line port comprises the following steps: firstly subtracting a fault component from an actual measurement value, and then decoupling by using a pole mode decoupling matrix to obtain a line mode fault voltage and a line mode fault current component; the correlation coefficient of the waveform is a correlation coefficient of line mode fault voltage and line mode fault current obtained by calculating the pearson correlation coefficient;
the provided fault direction information can judge a fault line and a non-fault line which are connected on the direct current bus simultaneously, wherein the number of the fault lines is 1, and the number of the non-fault lines is n, wherein n is more than or equal to 1; on the basis of deriving the fault traveling wave transmission characteristics of the flexible direct current power grid, the invention discovers the variation difference of the line mode fault voltage and the line mode fault current measured on the fault line and the non-fault line on the same direct current bus. When the direct current line breaks down, the change trend between the line mode fault voltage and the line mode fault current measured at the fault line port is irrelevant, and the correlation coefficient of the line mode fault voltage and the line mode fault current is zero; the change trend between the line mode fault voltage and the line mode fault current measured on the non-fault line port of the same direct current bus is linearly related, and the related coefficient of the line mode fault voltage and the line mode fault current is close to 1;
the fault direction criterion of the flexible direct current power grid is as follows: and at any line port in the flexible direct current power grid, the reverse direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is more than or equal to 0.5, and the forward direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is less than 0.5. The fault direction criterion provided herein can assist single-ended magnitude main protection to improve protection performance, and can also be used as backup protection in the longitudinal direction of the circuit.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention utilizes the variation difference between the fault voltage of the line mode and the fault current of the line mode on the fault line and the non-fault line on the flexible direct current power grid and the direct current bus to identify the fault direction, is not influenced by the state of the fault point, can reliably identify the high-resistance fault, and has excellent protection performance.
2. The flexible direct current power grid fault direction criterion has the advantages of clear setting threshold, low sampling rate requirement, simple principle and easy configuration and deployment.
3. The flexible direct current power grid fault direction criterion provided by the invention has strong anti-interference capability, is insensitive to noise, measurement errors and the like, can assist single-end-quantity main protection to improve the protection performance, can also be used as backup protection in the direct current line longitudinal direction, and has good application prospect.
Drawings
Fig. 1 is a schematic diagram of the topology of a four-terminal flexible dc power grid of the present invention;
fig. 2 is a transient equivalent circuit diagram of the four-terminal flexible dc power grid after dc line fault;
FIG. 3 is a flow chart of the present invention;
fig. 4 is a diagram of simulation verification results according to an embodiment of the present invention.
Detailed Description
The following technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, and thus the protection scope of the present invention is more clearly defined. The described embodiments of the present invention are intended to be only a few, but not all embodiments of the present invention, and all other embodiments that may be made by one of ordinary skill in the art without inventive faculty are intended to be within the scope of the present invention.
A typical four-terminal flexible direct current power grid is shown in a structural schematic diagram in fig. 1, the structural schematic diagram is simplified from Zhang Bei-Beijing four-terminal flexible direct current power grid engineering, the whole network is in a shape of a Chinese character 'kou', a true bipolar wiring mode is adopted, two ends of each direct current line are provided with high-performance DCCBs and FCLRs, the DCCBs are used for direct current on-off, and the FCLRs are used for limiting the rising speed of fault currents. Each modularized multi-level converter (Modular Multilevel Converter, MMC) adopts a half-bridge sub-module, neutral points are connected by metal return lines, and the lengths of the lines are shown in the figure. In FIG. 1, two DC lines are connected to either DC bus, if F on line 12 1 The position is in ground fault, in the case of the dc bus 1, the signal measurement point R12 is a fault line, the signal measurement point R14 is a non-fault line on the same dc bus, and the fault direction criterion requires that R12 be able to be determined as a positive fault and R14 be determined as a negative fault.
The invention is particularly implemented as a flexible direct current power grid fault direction criterion method based on waveform correlation coefficients, in fig. 1, the number of fault lines on a direct current bus 1 is 1, and the number of non-fault lines is n=1. The invention is applicable to flexible direct current power grids with different wiring forms, namely n >1, and is applicable to direct current line faults with different voltage levels (such as +/-500 kV, +/-320 kV, +/-160 kV and the like), different line lengths (from tens of km to hundreds of km) and different fault types (positive electrode grounding, negative electrode grounding, bipolar short circuit faults and the like).
Fig. 2 is obtained according to the superposition theorem, pole mode decoupling, fault point boundary conditions and the like, and fig. 2 is a diagram of F of the four-terminal flexible direct current power grid shown in fig. 1 on the direct current line 12 1 And a transient equivalent circuit diagram obtained after the position of the single-pole ground fault occurs, wherein: the transition resistance is R f The fault distance R12 is d, l 12 Is the total length of the fault line, l 14 Is a common DC busUpper total length of non-fault line, U N For the nominal voltage of the line, the converter station 1 is provided with a FCLR of size L 1 FCLR of size L configured for converter station 2 2 ，Z t1 、Z t2 And Z t4 For the equivalent impedance of the respective MMC before the blocking of the sub-modules, it can be expressed for the converter station 1 as:
Z t ＝sL eq +1/sC eq (1)
wherein L is eq Is equivalent reactance of MMC, C eq The equivalent resistance is much smaller than the wave impedance of the line and is therefore ignored for the equivalent capacitance of the MMC. In fig. 2, the dc line with frequency dependent characteristics adopts the davin equivalent model, where the line mode component can be expressed as:
wherein: h 1(d) Transfer function DeltaU after d length is transferred to line mode fault traveling wave f1 And DeltaI f1 1 Initial line mode fault traveling wave, delta U, generated respectively for fault point positions t1 And DeltaI t1 Traveling wave of line mode fault transmitted to port position of fault line respectively, Z c1 Line mode wave impedance of direct current line, B t1 And B f1 The reverse and forward line mode fault voltage traveling waves are respectively. The zero-modulus component can also be equivalent to Thevenin, where H 0(d) Transfer function delta U after d length is transferred to zero-mode fault traveling wave f0 And DeltaI f0 1 Initial zero-mode fault traveling wave, delta U, generated for fault point positions respectively t0 And DeltaI t0 Zero mode fault traveling wave transmitted to fault line port position respectively, Z c1 Is the zero mode wave impedance of the direct current line.
Solving the equivalent circuit of fig. 2 by using laplace transformation can obtain transfer functions of line mode fault voltage and line mode fault current at the position of a fault line R12 on the direct current bus 1 as follows:
wherein: u (U) t1-tf And I t1-tf Transfer functions of line mode fault voltage and line mode fault current of fault line port respectively, delta U t1 And DeltaI t1 Line mode fault voltage and line mode fault current measured by fault line port respectively, U s To take into account the equivalent voltage of the fault point location after multiple refraction and reflection of the traveling wave ρ t1 The magnitude of the reflection coefficient at the line port for the line mode fault voltage can be expressed as:
similarly, according to the laplace transform, in fig. 2, the transfer functions of the line mode fault voltage and the line mode fault current at the position of the non-fault line R14 on the dc bus 1 can be obtained as follows:
wherein: deltaU h1 And DeltaI h1 Line mode fault voltage and line mode fault current obtained by measuring non-fault line R14 position respectively, U h1-tf And I h1-tf Transfer functions of line mode fault voltage and line mode fault current of non-fault line port of same direct current bus are respectively, U b1-tf The transfer function of the fault voltage of the line mode on the direct current bus can be expressed as
By using the transfer functions of the fault line and the line mode fault voltage and the line mode fault current of the same direct current bus non-fault line, namely formulas (3) and (5), the following can be obtained:
from equation (6), it can be found that, for a faulty line (e.g., at signal measurement point R12), the line mode failsVoltage DeltaU t1 And line mode fault current ΔI t1 Ratio of (2) and reflectance ρ t1 Concerning ρ t1 Is a coefficient that varies with the variation of the reflected waveform, thus DeltaU t1 And DeltaI t1 The correlation of (3) is small. For non-faulty wires on the same dc bus (e.g., at signal measurement point R14), the line mode fault voltage Δu h1 And line mode fault current ΔI h1 Is a constant and therefore DeltaU h1 And DeltaI h1 Is a linear correlation. It can be summarized that when the direct current line fails, the trend of change between the line mode fault voltage and the line mode fault current measured on the failed line is uncorrelated, and the correlation coefficient of the line mode fault voltage and the line mode fault current is almost zero. The change trend between the line mode fault voltage and the line mode fault current measured on the non-fault line of the same direct current bus is linearly related, and the related coefficient of the line mode fault voltage and the line mode fault current is close to 1.
The protection flow chart of the fault direction criterion of the flexible direct current power grid is shown in figure 3, and the signal measuring points at the two ends of the direct current line detect the current I of the positive and negative lines in real time P (t)、I N (t) and a polar Voltage U P (t)、U N (t). And judging whether the system has abnormal conditions or not by using the common pole current change rate, pole voltage amplitude, gradient amplitude and the like as starting criteria so as to distinguish steady-state operation states. When the starting criterion identifies that the system is abnormal, the corresponding sampling time k is recorded, and data with the data length of N is continuously recorded for identifying faults, wherein the length of N is preferably 1-2ms, and 100-200 sampling points are corresponding under the sampling rate of 100kHz. The measured pole current I P (t)、I N (t) and a polar Voltage U P (t)、U N (t) subtracting the steady-state operation values respectively, wherein the steady-state operation values can be taken as the Mth sampling point before the sampling time k and respectively recorded as: i P (k-M)、I N (k-M) and U P (k-M)、U N (k-M), wherein M preferably takes 10, resulting in fault components respectively expressed as pole fault currents DeltaI P (t)＝I P (t)-I P (k-M)、ΔI N (t)＝I N (t)-I N (k-M) and pole failure voltage DeltaU P (t)＝U P (t)-U P (k-M)、ΔU N (t)＝U N (t)-U N (k-M). There is a coupling between the bipolar lines of the same rod and rack, and decoupling is needed. The normal practice is adopted, positive and negative fault components are decoupled by utilizing a pole mode decoupling matrix, and a line mode component and a zero mode component are obtained and expressed as follows:
analysis of the magnitude of the correlation between two fault vectors using the common pearson correlation coefficient, pearson correlation coefficient ρ, of line mode fault voltage and line mode fault current UI1 Can be expressed as:
wherein: cov (DeltaU) 1 ,ΔI 1 ) Is the line mode fault voltage vector delta U 1 And line mode fault current vector Δi 1 Covariance, sigma between U Sum sigma I Standard deviations of the line mode fault voltage vector and the line mode fault current vector, respectively.And->The average value of the line mode fault voltage vector and the line mode fault current vector is respectively shown, and N is the data length of the line mode fault voltage or the line mode fault current vector.
According to the conclusion, the fault direction criterion of the flexible direct current power grid is as follows: at any line port signal measuring point, the reverse direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is more than or equal to 0.5, and the forward direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is less than 0.5. The provided direction criterion can assist single-end quantity main protection to improve performance and can also be used as backup protection in the longitudinal direction of the circuit.
In order to verify the performance of the proposed direction criterion, the method is performed electricallyA four-terminal + -500 kV simulation system shown in figure 1 is built in a magnetic transient simulation software PSCAD/EMTDC, a detailed equivalent model with locking capability is adopted by MMC, a phase-domain frequency-dependent model is adopted by overhead lines, and the sampling rate is 100kHz. Simulation of F on line 12 1 The position, at which the positive electrode ground fault occurs at a distance of 60km from R12, is respectively 0.01Ω, 100deg.OMEGA, and 400Ω, and the line mode fault current component ΔI measured at R12 t1 And line mode fault current component DeltaU t1 As shown in fig. 4 (a) and (c), respectively, the simulation value is close to the calculated value, and the correctness of the theoretical derivation is verified. In addition, when the direct current line fault occurs, the conclusion that the change trend between the line mode fault voltage and the line mode fault current measured at the fault line port is uncorrelated and the correlation coefficient of the line mode fault voltage and the line mode fault current is almost zero is also verified from the figure. The measured line mode fault current component ΔI at R14 h1 And line mode fault current component DeltaU h1 As shown in fig. 4 (b) and (d), it was also verified from the graph that when a dc line fault occurred, the trend of change between the line mode fault voltage and the line mode fault current measured on the same dc bus non-faulty line was linearly related, and the correlation coefficient of the two was close to the conclusion of 1. Taking the data length of N=100, namely 1ms, respectively taking 0.01Ω, 100deg.OMEGA and 400Ω at the transition resistance, calculating by using the formula (8) for the R12 measuring point to obtain the association coefficients which are respectively 0.0846, -0.0574, -0.2149 and are far smaller than 0.5, calculating by using the formula (8) for the R14 measuring point to obtain the association coefficients which are respectively 0.9999, 0.9999 and far larger than 0.5, wherein the simulation result shows that the extracted direction criterion is hardly influenced by the size of the transition resistance, the fault direction can be reliably identified, and the fault line and the non-fault line on the same direct current bus can be naturally distinguished.
In summary, the invention provides a flexible direct current power grid fault direction criterion based on the correlation coefficient between the line mode fault voltage and the line mode fault current on the basis of deriving the traveling wave transmission characteristics of the flexible direct current power grid fault, finding the variation difference of the line mode fault voltage and the line mode fault current measured on the fault line and the non-fault line on the same direct current bus. The direction criterion is hardly influenced by the state of the fault point, can reliably identify the high-resistance fault, and has clear setting threshold and excellent protection performance.
The description and practice of the invention disclosed herein will be readily apparent to those skilled in the art, and may be modified and adapted in several ways without departing from the principles of the invention. Accordingly, modifications or improvements may be made without departing from the spirit of the invention and are also to be considered within the scope of the invention.
Claims (1)
1. A flexible direct current power grid fault direction criterion method based on waveform correlation coefficients is characterized in that the waveform is line mode fault voltage and line mode fault current obtained after the voltage and current obtained through measurement of a flexible direct current power grid line port are processed;
the processing method of the voltage and the current measured by the line port comprises the following steps: firstly subtracting a fault component from an actual measurement value, and then decoupling by using a pole mode decoupling matrix to obtain a line mode fault voltage and a line mode fault current component; the correlation coefficient of the waveform is a correlation coefficient of line mode fault voltage and line mode fault current obtained by calculating the pearson correlation coefficient;
the provided fault direction information can judge a fault line and a non-fault line which are connected on the direct current bus simultaneously, wherein the number of the fault lines is 1, and the number of the non-fault lines is n, wherein n is more than or equal to 1; when the direct current line breaks down, the change trend between the line mode fault voltage and the line mode fault current measured at the fault line port is irrelevant, and the correlation coefficient of the line mode fault voltage and the line mode fault current is zero; the change trend between the line mode fault voltage and the line mode fault current measured on the non-fault line port of the same direct current bus is linearly related, and the related coefficient of the line mode fault voltage and the line mode fault current is close to 1;
the fault direction criterion of the flexible direct current power grid is as follows: in any line port in the flexible direct current power grid, the reverse direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is more than or equal to 0.5, and the forward direction fault is generated when the pearson correlation coefficient of the line mode fault voltage and the line mode fault current is less than 0.5;
according to the superposition theorem, the polar mode is decoupled, soF of four-terminal flexible direct current power grid on direct current line 12 is obtained by barrier point boundary conditions 1 And a transient equivalent circuit diagram obtained after the position of the single-pole ground fault occurs, wherein: the transition resistance is R f The fault distance R12 is d, l 12 Is the total length of the fault line, l 14 For the total length of non-fault lines on the same direct current bus, U N For the nominal voltage of the line, the converter station 1 is provided with a FCLR of size L 1 FCLR of size L configured for converter station 2 2 ，Z t1 、Z t2 And Z t4 For the equivalent impedance of the respective MMC before the blocking of the sub-modules, it is expressed for the converter station 1 as:
Z t ＝sL eq +1/sC eq (1)
wherein L is eq Is equivalent reactance of MMC, C eq The equivalent resistance is much smaller than the wave impedance of the line and is therefore ignored for the equivalent capacitance of the MMC; the DC line with frequency dependent characteristics adopts a Thevenin equivalent model, wherein the linear mode component is expressed as follows:
wherein: h 1(d) Transfer function DeltaU after d length is transferred to line mode fault traveling wave f1 And DeltaI f1 1 Initial line mode fault traveling wave, delta U, generated respectively for fault point positions t1 And DeltaI t1 Traveling wave of line mode fault transmitted to port position of fault line respectively, Z c1 Line mode wave impedance of direct current line, B t1 And B f1 The fault voltage traveling waves of the reverse line mode and the forward line mode are respectively; the zero-modulus component can also be equivalent to Thevenin, where H 0(d) Transfer function delta U after d length is transferred to zero-mode fault traveling wave f0 And DeltaI f0 1 Initial zero-mode fault traveling wave, delta U, generated for fault point positions respectively t0 And DeltaI t0 Zero mode fault traveling wave transmitted to fault line port position respectively, Z c1 Zero mode impedance of the direct current line;
solving an equivalent circuit by utilizing Laplace transformation to obtain transfer functions of line mode fault voltage and line mode fault current at the position of a fault line R12 on a direct current bus 1, wherein the transfer functions are respectively as follows:
wherein: u (U) t1-tf And I t1-tf Transfer functions of line mode fault voltage and line mode fault current of fault line port respectively, delta U t1 And DeltaI t1 Line mode fault voltage and line mode fault current, deltaU, respectively measured for a faulty line port s To take into account the equivalent voltage of the fault point location after multiple refraction and reflection of the traveling wave ρ t1 The reflection coefficient of the line mode fault voltage at the line port is expressed as:
similarly, according to the Laplace transformation, the transfer functions of the line mode fault voltage and the line mode fault current at the position of the non-fault line R14 on the direct current bus 1 are respectively obtained as follows:
wherein: deltaU h1 And DeltaI h1 Line mode fault voltage and line mode fault current obtained by measuring non-fault line R14 position respectively, U h1-tf And I h1-tf Transfer functions of line mode fault voltage and line mode fault current of non-fault line port of same direct current bus are respectively, U b1-tf The transfer function of the fault voltage of the line mode on the direct current bus is expressed as
The transfer functions of the fault line and the line mode fault voltage and the line mode fault current of the same direct current bus non-fault line are utilized, namely formulas (3) and (5), so as to obtain:
from equation (6), it is found that for the faulty line, the line mode fault voltage ΔU t1 And line mode fault current ΔI t1 Ratio of (2) and reflectance ρ t1 Concerning ρ t1 Is a coefficient that varies with the variation of the reflected waveform, thus DeltaU t1 And DeltaI t1 Has little correlation; for non-fault lines on the same DC bus, line mode fault voltage DeltaU h1 And line mode fault current ΔI h1 Is a constant and therefore DeltaU h1 And DeltaI h1 Is linearly related; it can be summarized that when the direct current circuit fails, the change trend between the line mode fault voltage and the line mode fault current measured on the failed circuit is irrelevant, and the correlation coefficient of the line mode fault voltage and the line mode fault current is almost zero; the change trend between the line mode fault voltage and the line mode fault current measured on the non-fault line of the same direct current bus is linearly related, and the related coefficient of the line mode fault voltage and the line mode fault current is close to 1.
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