CN106405326A - Time-domain fault range finding method for co-tower double-loop DC power transmission line based on single-loop electrical quantity - Google Patents

Abstract

The invention discloses a time-domain fault location method for double-circuit direct current transmission lines on the same tower based on single-circuit electrical quantity, comprising the following steps: 1. Extracting impedance matrix and admittance matrix; 2. Obtaining voltage decoupling matrix and current decoupling 3. According to the obtained voltage decoupling matrix, construct the phase-mode transformation matrix of the single-circuit voltage that eliminates the ground-mode component, and obtain the single-circuit voltage differential-mode component that eliminates the ground-mode component; 4. According to the obtained current decoupling matrix, construct the eliminated ground-mode The single-circuit current phase-mode transformation matrix of the component is obtained to eliminate the single-circuit current differential mode component of the ground mode component; 5. According to the distribution characteristics of each modulus when different polar lines are faulted, select the most prominent component, and select the corresponding modulus Parameters; 6. Calculation of voltage distribution along the line; 7. Construction of fault location criteria based on mixed modulus; 8. Calculation of fault time; 9. Selection of redundant data windows. It has the advantages of high calculation accuracy, strong reliability, short required data time window and easy implementation.

Description

Time-domain fault location method for double-circuit DC transmission lines on the same tower based on single-circuit electrical quantity

technical field

The invention relates to the technical field of power system relay protection, in particular to a time-domain fault location method for double-circuit DC transmission lines on the same tower based on single-circuit electrical quantity. A dual-terminal time-domain ranging algorithm for single-return measurement data of a line.

Background technique

High-voltage direct current transmission has the advantages of large transmission capacity, flexible and rapid control, and no synchronization and stability problems. It has a wide range of applications in the field of long-distance large-capacity power transmission and asynchronous grid interconnection. With the development of society and economy, the cost of power grid construction is gradually increasing due to the increasingly tight land resources. The erection of high-voltage lines on the same pole can effectively utilize the transmission corridor. It is not only widely used in AC power grids, but also has begun to be specifically applied in DC projects in recent years.

The transmission distance of HVDC transmission lines generally exceeds 1000km and is prone to failure. After a fault occurs, fast and accurate fault location can reduce the workload of line inspection and quickly restore power supply to ensure the safe and stable operation of the AC-DC interconnected grid. Among the fault location methods of HVDC lines, the time-domain location method based on distribution parameters has the advantages of not relying on the accurate capture of the initial traveling wave head and the accurate calibration of the arrival time of the traveling wave, and has the advantages of low requirements on the sampling device. There is an effective complement to the traveling wave ranging method.

However, most current DC line fault location methods are limited to single-circuit bipolar DC lines, and only need to consider the influence of electromagnetic coupling between structurally symmetrical bipolar lines in the method. However, for the double-circuit DC transmission line on the same tower, due to the electromagnetic coupling relationship between the four poles of the double-circuit line, and the double-circuit DC line on the same tower does not use transposition measures in actual engineering, its fault coupling characteristics are very complicated . What is more noteworthy is that in practical applications, since the control and protection of each DC system is still based on the electrical quantity information of the current circuit, it is inevitable that the complete decoupling of each coupled electrical quantity cannot be achieved. Fault analysis of DC transmission lines and the difficulty of accurate fault location.

Therefore, the existing phase-mode conversion methods and fault location algorithms for single-circuit DC transmission lines are no longer applicable to double-circuit DC lines on the same tower. It is urgent to study the applicable fault location method according to the characteristics of double-circuit DC transmission lines on the same tower.

Contents of the invention

The purpose of the present invention is to propose a time-domain fault location method for double-circuit DC transmission lines on the same tower based on single-circuit electrical quantities. Position measures, and the control and protection of each return DC system is still based on the electrical quantity information of this return, and the differential mode component that eliminates the ground mode component is constructed. At the same time, according to the feature that the calculated voltage along the two ends of the line at the non-fault point has the largest difference near the fault time, the present invention defines the maximum voltage difference section at the non-fault point. The proposed fault location algorithm requires a short data window, high fault location accuracy, and is not affected by transition resistance and fault location.

The purpose of the present invention is achieved through the following technical solutions: a time-domain fault location method for double-circuit DC transmission lines on the same tower based on single-circuit electrical quantity, comprising the following steps:

(1) Extract the impedance matrix and admittance matrix of the transmission line: the double-circuit transmission line on the same tower cannot be regarded as a symmetrical line, and the phase-to-mode transformation matrix needs to be constructed according to the actual impedance matrix [Z _phase ] and admittance matrix [Y _phase ].

(2) Construct the decoupling matrix of double-circuit DC transmission lines on the same tower: 1P, 1N and 2P, 2N respectively represent the positive and negative poles of the I circuit and the positive and negative poles of the II circuit erected on the same tower. According to the electromagnetic transient theory of the power system, the equation of the uniform transmission line with double circuits on the same tower can be obtained:

In the formula, [U _phase ]=[u _1P u _1N u _2p u _2N ] ^T is the polar line voltage column vector; [I _phase ]=[i _1P i _1N i _2p i _2N ] ^T is the polar line current column vector.

Arrange the above formula to get the second order differential equation:

According to the matrix eigenvalue theory, the two matrices will be diagonalized. It can be seen that the eigenvalue matrix of [Z _phase ][Y _phase ] is [Λ], and the eigenvector matrix [T _v ], so there is the following formula:

[Z _phase ][Y _phase ]=[T _v ][Λ][T _v ] ^-1 ,

Considering [Z _phase ][Y _phase ]=[[Y _phase ][Z _phase ]] ^T , the following relationship exists:

[T _v ] ^-1 = [T _i ] ^T ,

The voltage decoupling matrix [T _v ] and the current decoupling matrix [T _i ] are obtained above. Let [T _v ]=[T _vab ] _4×4 , [T _i ]=[T _iab ] _4×4 , a,b=1,2,3,4, where T _vab and T _iab are the same as A frequency-dependent value that is a fixed constant only when the line uses symmetrical transposition.

(3) Construct a single-circuit voltage phase-mode transformation matrix that eliminates the ground-mode component:

Since the traditional single-circuit phase-mode transformation decoupling matrix cannot eliminate the ground mode component, and because the ground mode component is greatly affected by the conductivity and frequency of the ground, the resulting differential mode component is relatively unstable, which is critical for accurate fault location. Adverse. Therefore, it is necessary to construct a new single-return transformation matrix to eliminate the influence of the ground model component. According to the voltage decoupling matrix [T _v ] obtained above, each modulus is used to linearly represent the voltage of each pole of the line. Find the instantaneous value of each modulus voltage at the measuring end of the double-circuit DC transmission line on the same tower, where 0 represents the ground mode component, 1, 2 and 3 represent the first line mode component, the second line mode component and the third line mode component, then each pole The voltage quantity can be expressed as:

According to the ratio of the ground mode component in [T _v ] to the positive and negative voltages of the single circuit I and the positive and negative voltages of the single circuit II, the single-circuit transformation matrix is constructed. According to the new single-circuit transformation matrix, the voltage component of the single-circuit line voltage after eliminating the ground mode component can be obtained.

For the I-circuit line, the new single-circuit transformation matrix form is:

In the formula: [T _{v_I_eli0} ] is the voltage transformation matrix of the ground mode component of the I circuit; U _{dif_I_eli0} is the voltage differential mode component of the I circuit line after the ground mode is eliminated; T _v11 and T _v21 are the 1P and 1N voltage components in [ T _v ] in the coefficient of the earth mode component.

For circuit II, the form of the new single-circuit transformation matrix is:

In the formula: [T _{v_II_eli0} ] is the voltage transformation matrix of the ground mode component of the II line; U _{dif_II_eli0} is the voltage differential mode component of the II circuit line after the ground mode is eliminated; T _v31 and T _v41 are the 2P and 2N voltage components in [ T _v ] in the coefficient of the earth mode component.

(4) Construct a single-circuit current phase-mode transformation matrix that eliminates the ground-mode component:

According to the current decoupling matrix [T _i ] obtained above, use each modulus to linearly represent the current of each pole of the line. Find the instantaneous value of each modulus current at the measuring end of the double-circuit DC transmission line on the same tower, where 0 represents the ground mode component, 1, 2 and 3 represent the first line mode component, the second line mode component and the third line mode component, then each pole The voltage quantity can be expressed as:

According to the proportion of the ground mode component in [T _i ] in the positive and negative poles of single-circuit I and the positive and negative poles of single-circuit II, the single-circuit transformation matrix is constructed. According to the new single-circuit transformation matrix, the current component of the single-circuit line current after eliminating the ground-mode component can be obtained.

For the I-circuit line, the new single-circuit transformation matrix form is:

In the formula: [T _{i_I_eli0} ] is the current transformation matrix of the ground mode component of the I line; I _{dif_I_eli0} is the current differential mode component obtained after the ground mode is eliminated in the I circuit line; T _i11 and T _i21 are 1P and 1N current components in [ T _i ] in the coefficient of the earth mode component.

For circuit II, the form of the new single-circuit transformation matrix is:

In the formula: [T _{i_II_eli0} ] is the current transformation matrix of the ground mode component of the II line; I _{dif_II_eli0} is the current differential mode component obtained after the ground mode is eliminated in the II circuit; T _i31 and T _i41 are the 2P and 2N current components in [ T _i ] in the coefficient of the earth mode component.

(5) Extraction modulus: In order to eliminate the influence of the ground mode component, the differential mode voltage and current components obtained above to eliminate the ground mode component are used for calculation. At the same time, it is further considered that the distribution of each modulus is different when different polar faults occur. Since the magnitude of the modulus is also one of the important factors affecting the fault characteristics, when selecting the modulus parameters, choose a more prominent component. Here, we may as well Assumed to be m components.

(6) Calculation of voltage distribution along the line: According to the modulus selected above, based on the Berryron parameter model, and according to the voltage and current obtained from both ends, the following formula is used to calculate the distribution of voltage along the line at both ends:

In the formula: J and K represent the J-terminal and K-terminal of the line respectively; u _jn (x, t) represents the j-mode voltage at a distance x calculated by using the electrical quantity of the n-terminal, and n=J and K represent the voltage of the DC line respectively At both ends, j=com is the modulus label, indicating that the differential mode component is used; r _m , v _m , Z _cm are the resistivity, wave velocity and characteristic impedance of the m mode respectively; m is the modulus label, indicating that different polar faults are used When the more prominent linear mode component.

(7) Construct fault location criterion based on single-pass information volume: According to the above-constructed single-pass phase-mode transformation decoupling matrix that eliminates ground-mode components, select differential-mode components for calculation. Then the fault location criterion can be constructed as follows:

In the formula: u _J (x, t) represents the differential mode component voltage at a distance of x from the J terminal calculated by using the electrical quantity at the J terminal, and x is the distance based on the J terminal; u _K (lx, t) indicates that the K Calculated by the terminal electrical quantity, the differential mode voltage at x from terminal K, where x is the distance based on terminal J; t ₂ -t ₁ is the length of the redundant data window, and t ₁ is the start of the redundant data window time.

(8) Calculation of fault time: the arrival time of the fault voltage traveling wave calculated from both ends of the line at non-fault points is different, so there will be an obvious step mutation area near the fault time, that is, in theory has the largest error value. If this section is used for fault location, the voltage difference of non-fault points can be amplified to the greatest extent, which is conducive to improving the positioning accuracy of fault points. For this reason, this section may be called the maximum voltage difference of non-fault points segment.

Assuming that the distance between the actual fault point and the rectifier side is x _f , if the voltage distribution along the line at x is calculated, then the section size ΔT is:

It can be known from the above formula that the size of the maximum difference section of the non-fault point is proportional to the size of the deviation from the fault point. The farther away from the fault point, the larger the area, and the more obvious the difference between the voltage difference of the non-fault point and the fault point , which is obviously very beneficial for improving the ranging reliability.

Therefore, the wavelet transform is used to obtain the arrival time of the traveling wave head at both ends of the line, and then the fault time is obtained, which is used as the trigger time of the redundant data window.

After the phase voltage obtained from the two ends of the line is transformed by phase mode, the differential mode component is used for calculation. According to the wavelet transform, set the du/dt threshold value to calibrate the arrival time of traveling waves at both ends, and set them as t _{R_1} and t _{I_1} respectively. If the wave velocity is v _m , the initial fault time t ₀ can be obtained as:

In the formula: t _{R_arr} is the fault initial time calculated from the rectifier side; t _{I_arr} is the fault initial time calculated from the inverter side.

According to the above analysis, the initial time of the fault can be obtained, set it as t ₀ , and set the starting time of the redundant data window, that is, t ₁ =t ₀ .

(9) Determine the selected redundant data window: further considering that the different propagation speeds of the linear mode components contained in the actual differential mode components will cause differences in the propagation time of the modulus traveling wave, in order to better reflect the maximum voltage difference of the non-fault point Section, you can add a certain margin to the starting time of the redundant data window:

t′ ₁ =t ₀ -Δt _ω ,

In the formula: t' ₁ is the starting time of the modified redundant data window; Δt _ω is the increased margin.

According to the above analysis, the redundant data window can be determined.

Working principle of the present invention: the method for time-domain fault location of double-circuit direct current transmission lines based on single-circuit electrical quantity of the present invention is to use the single-circuit phase-mode transformation matrix constructed to eliminate the ground-mode component to obtain the differential-mode component, and obtain the differential-mode component from the line Calculate the voltage distribution along the line at both ends, and then according to the characteristic that the calculated voltage at both ends of the non-fault point along the line has the largest difference near the fault time, define the maximum voltage difference section of the non-fault point, and use the wavelet transform to obtain the fault initial time, determine the redundant data window to be used for fault location method.

Since the double-circuit DC transmission line on the same tower not only has phase-to-phase mutual inductance in the same circuit, but also has inter-line mutual inductance between different circuits, the electromagnetic coupling mechanism is complex, and the line needs to be decoupled. Because the control and protection of each circuit system of the same-tower double-circuit DC power transmission project in the existing actual project is based on the electrical quantity information of this circuit. However, the direct application of the phase-mode transformation matrix of the traditional single-circuit DC transmission line to the asymmetrically transposed double-circuit DC transmission line on the same tower has certain limitations. And the differential mode component obtained through the phase mode transformation of the traditional single-circuit DC transmission line includes the ground mode component and all the line mode components. Because the ground mode component is greatly affected by the conductivity and frequency of the earth, for the DC line of long-distance power transmission, the ground mode component is unfavorable for realizing accurate fault location. Therefore, the present invention proposes a single-circuit phase-mode transformation matrix that eliminates the ground-mode component based on the electrical quantity of the single-circuit line, and according to the phase-mode transformation matrix of the double-circuit DC transmission line on the same tower, and then obtains the differential mode component containing only the line-mode component. At the same time, the present invention considers that the distribution of each modulus is different when different polar lines are faulted, and selects more prominent line mode component parameters according to the principal component priority principle, and then obtains the voltage distribution along the two ends. Finally, according to the characteristic that the voltage along the line at both ends of the non-fault point has the largest difference near the fault time, the maximum voltage difference section of the non-fault point is defined. If this section is used for fault location, the voltage difference of non-fault points can be amplified to the greatest extent, which is conducive to improving the distance measurement accuracy of fault points. Therefore, the present invention uses wavelet transform to obtain the arrival time of the traveling wave head of the differential-mode component at both ends of the line, and then obtains the fault time, which is used as the trigger time of the redundant data window, thereby obtaining a dual-mode dual-mode component on the same tower based on the amount of single-return information. Fault location method for DC transmission lines.

Compared with the prior art, the present invention has the following beneficial effects:

First, it is suitable for fault location of double-circuit DC transmission lines on the same tower with asymmetric transposition.

Second, based on the electrical quantity information of single-circuit lines, it is consistent with actual engineering and has good engineering application prospects.

Third, the reliability is high, the influence of the ground model component is eliminated, the fault accuracy is basically not affected by the fault pole line, fault location and transition resistance, and the fault location accuracy can still be guaranteed when the high resistance is grounded.

Fourth, the fault location accuracy is high. The invention defines the maximum voltage difference section of the non-fault point, amplifies the voltage difference at the non-fault point to the greatest extent, makes it easier to identify the fault point, and improves the accuracy of fault distance measurement.

Fifth, the required data time window is short, and only the electrical quantities at both ends of the line need to be extracted, which is easy to implement.

Description of drawings

Fig. 1 is a model diagram of the same-tower double-circuit direct current transmission system of the present invention.

Fig. 2 is a structure diagram of the pole tower of the same-tower double-circuit direct current transmission system of the present invention.

Figure 3 is a fault location map.

detailed description

The present invention will be described in further detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

Example

As shown in Figure 1, the PSCAD/EMTDC simulation software is used to construct the ±500kV same-tower double-circuit HVDC transmission system model in Guangdong for Xiluodu power transmission, and its tower structure is shown in Figure 2; The frequency parameter model, the total length of the line is 1254km; set the fault to occur in different positions, the fault transition resistance includes metallic grounding and grounding through a 300Ω transition resistance; the fault types include the upper polar line fault, the lower polar line fault and the simultaneous fault of the upper and lower polar lines . This system utilizes fault location method of the present invention, specifically comprises the following steps:

S1. Extract unit impedance matrix and unit admittance matrix:

According to the tower model, the unit impedance matrix [Z _phase ] and unit admittance matrix [Y _phase ] of the double-circuit DC transmission line on the same tower are obtained:

S2. Find the phase-mode transformation matrix of the double-circuit DC transmission line on the same tower:

According to the obtained unit impedance matrix [Z _phase ] and unit admittance matrix [Y _phase ], the voltage decoupling matrix [T _v ] and the current decoupling matrix [T _i ] are obtained:

According to the above formula can get:

S3. Construct a single-circuit voltage phase-mode transformation matrix that eliminates the ground-mode component:

According to the voltage decoupling matrix [T _v ] obtained above, the instantaneous value of each modulus voltage at the measuring end of the double-circuit DC transmission line on the same tower is obtained, where 0 represents the ground mode component, 1, 2 and 3 represent the first line mode component, The second linear mode component and the third linear mode component, then the voltage of each pole can be expressed as:

For the I-circuit line, the new single-circuit transformation matrix form is:

Then the differential-mode voltage component of the I-circuit line obtained after eliminating the single-circuit transformation matrix of the ground-mode component is:

U _{dif_I_eli0} =-0.1861u ₁ +0.4494u ₂ +0.4830u ₃ ,

For circuit II, the form of the new single-circuit transformation matrix is:

Then the differential-mode voltage component of the II-circuit line obtained after eliminating the single-circuit transformation matrix of the ground-mode component is:

U _{dif_II_eli0} = -0.1861u ₁ +0.4494u ₂ +0.4830u ₃ ,

S4. Construct a single-circuit current phase-mode transformation matrix that eliminates the ground-mode component:

According to the current decoupling matrix [T _i ] obtained above, the instantaneous value of each modulus current at the measurement end of the double-circuit DC transmission line on the same tower is obtained, where 0 represents the ground mode component, 1, 2 and 3 represent the first line mode component, The second linear mode component and the third linear mode component, then the current of each pole can be expressed as:

For the I-circuit line, the new single-circuit transformation matrix form is:

Then the differential-mode current component of the I-circuit line obtained after eliminating the single-circuit transformation matrix of the ground-mode component is:

I _{dif_I_eli0} =-0.0999i ₁ +0.5150i ₂ +0.5178i ₃ ,

For circuit II, the form of the new single-circuit transformation matrix is:

Then the differential-mode current component of the I-circuit line obtained after eliminating the single-circuit transformation matrix of the ground-mode component is:

I _{dif_II_eli0} =-0.0999i ₁ +0.5150i ₂ +0.5178i ₃ ,

S5. According to the distribution characteristics of each line mode component when different polar faults occur, a more prominent component is selected. Since the component of line mode 3 is more prominent, the corresponding parameter of line mode 3 is selected for the modulus parameter.

S6. Calculate the voltage distribution along the line:

Calculate the voltage distribution along the line at both ends. Use the following formula:

Among them, J and K represent the J-terminal and K-terminal of the line respectively; u _jn (x, t) represents the j-mode voltage at a distance x calculated by using the electrical quantity of the n-terminal, and n=J and K represent the two sides of the DC line respectively. At the end, j=com is the modulus label, indicating that the differential mode component is used; r ₃ , v ₃ , and Z _c3 are the resistivity, wave velocity, and characteristic impedance corresponding to the three modes, respectively.

S7. Fault location:

According to the single-phase phase-mode transformation decoupling matrix constructed above to eliminate the ground-mode component, the differential-mode component is selected for calculation. Then the fault location criterion can be constructed as follows:

Among them, u _J (x, t) represents the differential mode component voltage at a distance of x from the J terminal calculated by using the electrical quantity of the J terminal, and x is the distance based on the J terminal; u _K (lx, t) indicates that using the K terminal The differential mode voltage calculated from the electrical quantity at x from terminal K, where x is the distance based on terminal J; t ₂ -t ₁ is the length of the redundant data window.

S8. Calculate the initial moment of failure:

According to the wavelet transform, set the du/dt threshold value to calibrate the time when the traveling waves at both ends reach the rectification side and the inverter side, respectively set t _{R_1} , t _{I_1} , and the wave velocity is v ₃ , the initial time t ₀ of the fault can be obtained as:

In the formula, t _{R_arr} is the fault initial time calculated from the rectifier side; t _{I_arr} is the fault initial time calculated from the inverter side.

According to the above analysis, the initial time of the fault can be obtained, set it as t ₀ , and set the trigger time of the redundant data window, that is, t ₁ =t ₀ .

S9. Selection of redundant data windows:

In order to better identify the point with the largest voltage difference along the line, a certain margin can be added to the triggering time of the redundant data window:

t′ ₁ =t ₀ -Δt _ω ,

In the formula, t' ₁ is the trigger time of the modified redundant data window; Δt _ω is the increased margin, which is 0.2ms.

As shown in Figure 3, it is the location result when a metallic ground fault occurs at the negative pole of the second circuit line at a distance of 100km from the rectifier side.

As shown in Table 1 below, the fault location results of different locations where the fault occurs in the second circuit line and grounded through different transition resistances are listed.

Table 1

From the fault location results in Table 1, it can be seen that the fault location method proposed in the present invention is accurate and effective, and can achieve accurate distance measurement within the entire length of the line, and the distance measurement accuracy is not affected by the fault pole line, fault location and transition resistance. Impact.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the embodiment, and any other changes, modifications, substitutions and combinations made without departing from the spirit and principle of the present invention , simplification, all should be equivalent replacement methods, and are all included in the protection scope of the present invention.

Claims (10)

1. one kind is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method it is characterised in that including Following steps：

Step 1, the impedance matrix extracting common-tower double-return DC power transmission line and admittance matrix；

Step 2, the impedance matrix according to step 1 and admittance matrix obtain the voltage decoupling matrix of common-tower double-return DC power transmission line With Current Decoupling matrix；

Step 3, pressure phase-model transformation matrix of being wired back according to the list that the voltage decoupling matrix construction that step 2 obtains eliminates ground mold component, Obtain eliminating the list telegram in reply pressure reduction mold component of ground mold component；

Step 4, stream phase-model transformation matrix of being wired back according to the list that the Current Decoupling matrix construction that step 2 obtains eliminates ground mold component, Obtain the list telegram in reply stream differential-mode component eliminating ground mold component；

Step 5, the component being projected the most according to the characteristic distributions selection of each modulus during different polar curve fault, select this modulus pair The modulus parameter answered；

Step 6, calculating voltage's distribiuting along the line, the line mould being obtained using differential mode voltage components and differential-mode current component and step 5 Parameter calculates the distribution along line voltage from circuit two ends respectively；

Step 7, the fault localization criterion based on single time quantity of information for the construction, according to the two ends obtaining voltage's distribiuting along the line in trouble point Place has the characteristics that difference minimum carries out fault localization；

Step 8, using wavelet transformation calculate fault moment；

Step 9, selection redundant data window, the fault initial time being obtained according to step 8, increase certain nargin, revised Redundant data window initial time afterwards, and then determine the selection of redundant data window.

2. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 1, the described impedance matrix of transmission line of electricity is [Z_phase], the described admittance matrix of transmission line of electricity is [Y_phase].

3. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 2, the building method of described phase-model transformation matrix comprises the following steps：

Step 21, return positive pole circuit with the I that 1P, 1N, 2P and 2N represent wiring on the same tower respectively respectively, I returns negative pole circuit, II just returns Polar curve road and II return negative pole circuit；

Step 22, theoretical according to electromagnetic transient in power system, obtain the uniform transmission line equation of common-tower double-return：

$\left\{\begin{array}{c}-\frac{d}{dx}\[U_{phase}\]=\[Z_{phase}\]\[I_{phase}\],\\ -\frac{d}{dx}\[I_{phase}\]=\[Y_{phase}\]\[U_{phase}\],\end{array}\right.$

In formula, [U_phase]=[u_1Pu_1Nu_2pu_2N]^T, it is line voltage column vector；[I_phase]=[i_1Pi_1Ni_2pi_2N]^T, it is Polar curve electric current column vector；[Z_phase] for circuit impedance matrix；[Y_phase] for circuit admittance matrix；

Above formula is arranged and obtains second order differential equation：

$\left\{\begin{array}{c}\frac{d^2}{{\mathrm{dx}}^2}\[U_{phase}\]=\[Z_{phase}\]\[Y_{phase}\]\[U_{phase}\],\\ \frac{d^2}{{\mathrm{dx}}^2}\[I_{phase}\]=\[Y_{phase}\]\[Z_{phase}\]\[I_{phase}\],\end{array}\right.$

In formula, [U_phase]=[u_1Pu_1Nu_2pu_2N]^T, it is line voltage column vector；[I_phase]=[i_1Pi_1Ni_2pi_2N]^T, it is Polar curve electric current column vector；

Step 23, theoretical according to matrix exgenvalue, two diagonalization of matrixs, obtain [Z_phase][Y_phase] eigenvalue matrix be [Λ], eigenvectors matrix [T_v], therefore there is following formula：

[Z_phase][Y_phase]=[T_v][Λ][T_v]^-1；

According to [Z_phase][Y_phase]=[[Y_phase][Z_phase]]^T, obtain relationship below：

[T_v]^-1=[T_i]^T,

I.e.：Obtain voltage decoupling matrix [T_v] and Current Decoupling matrix [T_i]；If [T_v]=[T_vab] 4 × 4, if [T_i]=[T_iab] 4 × 4, a, b=1,2,3,4, wherein, T_vabAnd T_iabIt is all the numerical value relevant with frequency.

4. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 3, the list telegram in reply pressure phase-model transformation matrix that construction eliminates ground mold component comprises the following steps：

Step 31, the voltage decoupling matrix [T being obtained according to step 2_v], with each each pole tension amount of modulus linear expression circuit；Ask Go out each modulus instantaneous voltage of common-tower double-return DC power transmission line measurement end, wherein 0 represents ground mold component, 1,2 and 3 represent the One Aerial mode component, the second Aerial mode component and the 3rd Aerial mode component, then the voltage of each pole can be expressed as：

$\left[\begin{array}{c}{u}_{1P}\\ u_{1N}\\ u_{2P}\\ u_{2N}\end{array}\right]={\[T_v\]}_{4\×4}\left[\begin{array}{c}{u}_0\\ u_1\\ u_2\\ u_3\end{array}\right],$

Step 32, according to voltage decoupling matrix [T_v] in ground mold component in single time I positive pole, negative pole and single time II positive pole, cathode voltage Middle proportion constructs single time transformation matrix；Return transformation matrix according to new list to obtain after single back line voltage elimination ground mold component Component of voltage；

Step 33, for I loop line road, new list returns transformation matrix form and is：

$\[U_{dif\_I\_eli0}\]=\[T_{v\_I\_eli0}\]\left[\begin{array}{c}{U}_{1P}\\ U_{1N}\end{array}\right]=\left[\begin{array}{cc}{T}_{v21}& -T_{v11}\end{array}\right]\left[\begin{array}{c}{U}_{1P}\\ U_{1N}\end{array}\right],$

Wherein：[T_{v_I_eli0}] be I circuit voltage transformation matrix；U_{dif_I_eli0}It is the voltage obtaining after I loop line road eliminates topotype Differential-mode component；T_v11、T_v21Represent the modulus component of voltage of 1P, 1N in voltage decoupling matrix [T respectively_v] in ground mold component distribution Coefficient；

Step 34, for II loop line road, new list returns transformation matrix form and is：

$\[U_{dif\_II\_eli0}\]=\[T_{v\_II\_eli0}\]\left[\begin{array}{c}{U}_{2P}\\ U_{2N}\end{array}\right]=\left[\begin{array}{cc}{T}_{v41}& -T_{v31}\end{array}\right]\left[\begin{array}{c}{U}_{2P}\\ U_{2N}\end{array}\right],$

Wherein：[T_{v_II_eli0}] be II circuit voltage transformation matrix；U_{dif_II_eli0}It is the electricity obtaining after II loop line road eliminates topotype Pressure reduction mold component；T_v31、T_v41It is the modulus component of voltage of 2P, 2N respectively in voltage decoupling matrix [T_v] in ground mold component distribution Coefficient.

5. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 4, the method that described construction eliminates the list telegram in reply stream phase-model transformation matrix of ground mold component includes following step Suddenly：

Step 41, the Current Decoupling matrix [T being obtained according to step 2_i], with each each electrode current amount of modulus linear expression circuit；Ask Go out each modulus current instantaneous value of common-tower double-return DC power transmission line measurement end, wherein 0 represents ground mold component, 1,2 and 3 represent the One Aerial mode component, the second Aerial mode component and the 3rd Aerial mode component, then the voltage of each pole be expressed as：

$\left[\begin{array}{c}{i}_{1P}\\ i_{1N}\\ i_{2P}\\ i_{2N}\end{array}\right]={\[T_i\]}_{4\×4}\left[\begin{array}{c}{i}_0\\ i_1\\ i_2\\ i_3\end{array}\right],$

In formula, i_1P、i_1N、i_2pAnd i_2NIt is respectively single time I positive pole, the polar curve electric current of negative pole, single time II positive pole and negative pole；i₀、i₁、i₂ And i₃It is respectively ground mold component, the first Aerial mode component, the second Aerial mode component and the 3rd Aerial mode component of modulus electric current；

Step 42, according to Current Decoupling matrix [T_i] in ground mold component in single time I positive pole, negative pole, single time II positive pole and cathodal current Middle proportion constructs single time transformation matrix；According to new list return transformation matrix can get single back line electric current eliminate topotype divide Current component after amount；

Step 43, for I loop line road, new list returns transformation matrix form and is：

$\[I_{dif\_I\_eli0}\]=\[T_{i\_I\_eli0}\]\left[\begin{array}{c}{I}_{1P}\\ I_{1N}\end{array}\right]=\left[\begin{array}{cc}{T}_{i21}& -T_{i11}\end{array}\right]\left[\begin{array}{c}{I}_{1P}\\ I_{1N}\end{array}\right],$

In formula, [T_{i_I_eli0}] be I circuit current transformation matrix；I_{dif_I_eli0}It is the electric current obtaining after I loop line road eliminates topotype Differential-mode component；T_i11、T_i21It is the modulus current component of 1P, 1N respectively in Current Decoupling matrix [T_i] in ground mold component distribution system Number；

Step 44, for II loop line road, new list returns transformation matrix form and is：

$\[I_{dif\_II\_eli0}\]=\[T_{i\_II\_eli0}\]\left[\begin{array}{c}{I}_{2P}\\ I_{2N}\end{array}\right]=\left[\begin{array}{cc}{T}_{i41}& -T_{i31}\end{array}\right]\left[\begin{array}{c}{I}_{2P}\\ I_{2N}\end{array}\right],$

In formula, [T_{i_II_eli0}] be II circuit current transformation matrix；I_{dif_II_eli0}It is the electricity obtaining after II loop line road eliminates topotype Stream differential-mode component；T_i31、T_i41It is the modulus current component of 2P, 2N respectively in Current Decoupling matrix [T_i] in ground mold component distribution Coefficient.

6. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in steps of 5, the method for described extraction modulus is as follows：

For eliminating the impact of ground mold component, using the differential-mode component eliminating ground mold component obtained above；Consider further simultaneously During to different polar curve fault, the distribution of each modulus has differences, and when selecting modulus parameter, selects more prominent component to make For modulus parameter it is assumed that more prominent Aerial mode component during different polar curve fault is m.

7. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 6, the method for described calculating voltage's distribiuting along the line is as follows：

The modulus chosen according to step 5, based on Bei Ruilong parameter model, according to the voltage obtaining from two ends, the magnitude of current, under adopting Formula calculates two ends respectively along the distribution of line voltage：

$\begin{array}{c}{u}_{jn}(x,t)=\frac{1}{2}{\left(\frac{Z_{ci}+r_{i}x/4}{Z_{ci}}\right)}^2\·\[u_{nj}(t+x/v_i)-i_{nj}(t+x/v_i)\·(Z_{ci}+r_{i}x/4)\]+\\ \frac{1}{2}{\left(\frac{Z_{ci}-r_{i}x/4}{Z_{ci}}\right)}^2\·\[u_{nj}(t-x/v_i)+i_{nj}(t-x/v_i)\·(Z_{ci}-r_{i}x/4)\]-\\ {\left(\frac{r_{i}x/4}{Z_{ci}}\right)}^2\·u_{nj}\left(t\right)-\frac{r_{i}x}{4}\·\left(\frac{Z_{ci}+r_{i}x/4}{Z_{ci}}\right)\·\left(\frac{Z_{ci}-r_{i}x/4}{Z_{ci}}\right)i_{nj}\left(t\right)\end{array},$

In formula, J and K represents circuit J end and K end respectively；u_jn(x, t) represents the calculate, j at x using n end electrical quantity Mode voltage, n=J, K represent the two ends of DC line respectively, and j=com is modulus label, represents and adopts differential-mode component；r_m、v_m、 Z_cmIt is resistivity, velocity of wave and the characteristic impedance of m respectively；M represents more prominent Aerial mode component during different polar curve fault.

8. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 7, the method for the fault location criterion based on single telegram in reply tolerance for the described construction is as follows：

Phase-model transformation decoupling matrices are returned according to the constructed above list eliminating ground mold component, selects differential-mode component to be calculated, then Fault location criterion such as following formula can be constructed：

$\left\{\begin{array}{c}f\left(x_f\right)=\min \{f\left(x\right);x\∈(0,l)\},\\ f\left(x\right)=\underset{t=t_1}{\overset{t_2}{\Σ}}|u_J(x,t)-u_K(l-x,t)|,\\ u_J(x,t)=u_{com\_J}(x,t),\\ u_K(l-x,t)=u_{com\_K}(l-x,t),\end{array}\right.$

In formula, u_J(x, t) represents calculate, the differential-mode component voltage at the x of J end using J end electrical quantity, and x is J end is base Accurate distance；u_K(l-x, t) represent calculated using K end electrical quantity, at the x of J end differential mode voltage, x is on the basis of J end Distance；t₂-t₁By the length of taken redundant data window, t₁It is redundant data window initial time.

9. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 8, described calculating fault moment determines that the method in the triggered time of redundant data window includes following step Suddenly：

Step 81, the phase voltage obtaining from circuit two ends, after phase-model transformation, take differential-mode component to be calculated；Become according to small echo Change, setting du/dt threshold value is to demarcate two ends traveling wave due in；Assume that the time that modulus traveling-waves reach rectification side is t_{R_1}, mould The time that amount traveling wave reaches inverter side is t_{I_1}, velocity of wave is v_m, therefore obtain fault initial time t₀For：

$t_0=\frac{1}{2}(t_{R\_arr}+t_{I\_arr})=\frac{1}{2}(t_{R\_1}+t_{I\_1}-\frac{l}{v_m}),$

In formula, t_{R_arr}It is from rectification side calculated fault initial time；t_{I_arr}It is from the beginning of the calculated fault of inverter side Begin the moment；

Step 82, fault initial time be can get according to above analysis, be set to t₀, during the triggering of the taken redundant data window of setting Carve, i.e. t₁=t₀.

10. it is based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method as claimed in claim 1, its It is characterised by, in step 9, the method for the described redundant data window determining selection is as follows：

Further contemplate contained Aerial mode component in actual differential-mode component spread speed difference will result in modulus traveling-waves propagate when Between have differences, certain nargin is increased to the initial time of redundant data window：

t′₁=t₀-Δt_ω,

In formula, t '₁Triggering moment for revised redundant data window；Δt_ωBy increasedd nargin.