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 range finding method for a co-tower double-loop DC power transmission line based on the single-loop electrical quantity. The method comprises the following steps that an impedance matrix and an admittance matrix are extracted; 2) a voltage decoupling matrix and a current decoupling matrix are obtained; 3) a single-loop voltage phase-mode transformation matrix from which a ground mode component is eliminated is constructed according to the obtained voltage decoupling matrix, and a single-loop voltage differential-mode component from which the ground mode component is eliminated is obtained; 4) a single-loop current phase-mode transformation matrix from which the ground mode component is eliminated is constructed according to the obtained current decoupling matrix, and a single-loop current differential-mode component from which the ground mode component is eliminated is obtained; 5) a most prominent component is selected according to distribution characteristics of different modulus in different pole wire faults, and modulus parameters corresponding to the modulus are selected; 6) voltage distribution along the line is calculated; 7) a fault positioning criterion based on mixed modulus is calculated; 8) fault time is calculated; and 9) a redundant data window is selected. The time-domain fault range finding method has advantages including that the calculating precision and the reliability are high, the needed data time window is short and realization is easy.

Description

Based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method

Technical field

The present invention relates to Relay Protection Technology in Power System field, specifically related to one kind are based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault distance-finding method, this time domain Fault Location Algorithm is a kind of list based on common-tower double-return DC line Return the both-end time domain location algorithm of measurement data.

Background technology

D.C. high voltage transmission has transmission capacity greatly, controls flexibly rapid, there is not the advantages such as synchronism stability problem, remote Apart from the transmission of Large Copacity electric energy, asynchronous Power System Interconnection field has a wide range of applications.With the development of social economy, power grid construction Cost is gradually increased because of land resource growing tension.High-tension line joint uses energy effectively utilizes transmission of electricity corridor, not only exists It is widely used in AC network, also begin in recent years obtain concrete application in DC engineering.

HVDC transmission line power transmission distance generally more than 1000km, is subject to fault.After fault occurs, realize Fast and accurately fault location can reduce line walking workload, and fast recovery of power supply, to ensure the steady safely of AC-DC interconnecting power network Fixed operation.In hvdc transmission line fault distance-finding method, it is independent of due to having based on the time domain distance-finding method of distributed constant Reach the accurate calibration in moment in the accurate seizure of initial wavefront and traveling wave, low advantage, energy are required to sampling apparatuses Enough effective supplements as existing travelling wave ranging method.

However, current DC line fault distance-finding method is confined to single time bipolar DC link mostly, only need in method Consider the electromagnetic coupled impact between the bipolar line of symmetrical configuration.But for common-tower double-return DC power transmission line, due to double back All there is the electromagnetic coupled relation of interaction between four polar curves of circuit, and in Practical Project, common-tower double-return DC line does not adopt Transposition measure, causes its faults coupling characteristic extremely complex.More it is worthy of attention that, in actual applications due to each Hui Zhi The control protection of streaming system is still based on this loop line road electric quantity information, necessarily cannot realize the solution completely of each coupled electric amount Coupling, these factors all considerably increase the analysis of common-tower double-return direct current transmission line fault and its difficulty of exact failure positioning.

Therefore, existing list returns the phase-model transformation method of DC power transmission line and fault location algorithm is no longer suitable for same tower Double back DC line, needs the feature for common-tower double-return DC power transmission line badly, studies its applicable fault distance-finding method.

Content of the invention

It is an object of the invention to propose a kind of list telegram in reply tolerance common-tower double-return DC power transmission line time domain fault that is based on surveying Away from method, this time domain fault distance-finding method considers that in Practical Project, common-tower double-return DC power transmission line is not arranged using symmetrical transposition Apply, and the control protection of each time straight-flow system still is based on this time electric quantity information, the differential mode constructing cancellation ground mold component divides Amount.Circuit two ends according to non-faulting point have the characteristics that maximum difference along line computation voltage near fault moment simultaneously, this Invention defines non-faulting point maximum voltage difference section.Carried Fault Location Algorithm desired data window is short, fault localization precision Height, is not affected by transition resistance and abort situation.

The purpose of the present invention is achieved through the following technical solutions：One kind is based on single telegram in reply tolerance common-tower double-return DC transmission line Road time domain fault distance-finding method, comprises the following steps：

(1) impedance matrix and the admittance matrix of transmission line of electricity are extracted：Same tower double back transmission line is not to be regarded as symmetric line, Need according to actual impedance matrix [Z_phase] and admittance matrix [Y_phase] construction phase-model transformation matrix.

(2) common-tower double-return DC power transmission line decoupling matrices are constructed：Represent same pylon with 1P, 1N and 2P, 2N respectively respectively If I return positive pole, negative pole and II and return positive pole, negative pole circuit.Common-tower double-return can be obtained according to electromagnetic transient in power system theory Uniform transmission line equation：

In formula, [U_phase]=[u_1Pu_1Nu_2pu_2N]^TFor line voltage column vector；[I_phase]=[i_1Pi_1Ni_2pi_2N]^T For polar curve electric current column vector.

Above formula is arranged and can obtain second order differential equation：

Theoretical according to matrix exgenvalue, will be two diagonalization of matrixs it is known that [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,

Consider [Z_phase][Y_phase]=[[Y_phase][Z_phase]]^T, then there is relationship below：

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

Below just obtained voltage decoupling matrix [T_v], Current Decoupling matrix [T_i].Here sets [T_v]=[T_vab]_4×4、[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, only when circuit is replaced using symmetrical When be fixed constant.

(3) construction eliminates the list telegram in reply pressure phase-model transformation matrix of ground mold component：

Ground mold component can not be eliminated due to phase-model transformation decoupling matrices are returned using traditional list, because ground mold component is subject to the earth The impact of electrical conductivity and frequency is larger, thus making the differential-mode component obtaining more unstable, this for realizing exact failure positioning is Unfavorable.Therefore, it is necessary to one new list of construction returns transformation matrix to eliminate the impact of ground mold component.According to derived above Voltage decoupling matrix [T_v], with each each pole tension amount of modulus linear expression circuit.Obtain common-tower double-return DC transmission line drive test Each modulus instantaneous voltage at amount end, wherein 0 represents ground mold component, and 1,2 and 3 represent the first Aerial mode component, the second Aerial mode component With the 3rd Aerial mode component, then the voltage of each pole can be expressed as：

According to [T_v] in ground mold component proportion construction in single time I positive pole, negative pole and single time II positive pole, cathode voltage Single time transformation matrix.According to new list return transformation matrix can get single back line voltage eliminate ground mold component after voltage divide Amount.

For I loop line road, new list returns transformation matrix form and is：

In formula：[T_{v_I_eli0}] be I circuit eliminate ground mold component voltage transformation matrix；U_{dif_I_eli0}It is that I loop line road disappears The voltage differential-mode component obtaining after removing topotype；T_v11、T_v21It is 1P, 1N component of voltage in [T_v] in ground mold component coefficient.

For II loop line road, new list returns transformation matrix form and is：

In formula：[T_{v_II_eli0}] be II circuit eliminate ground mold component voltage transformation matrix；U_{dif_II_eli0}It is II loop line road The voltage differential-mode component obtaining after eliminating topotype；T_v31、T_v41It is 2P, 2N component of voltage in [T_v] in ground mold component coefficient.

(4) construction eliminates the list telegram in reply stream phase-model transformation matrix of ground mold component：

According to Current Decoupling matrix [T derived above_i], with each each electrode current amount of modulus linear expression circuit.Obtain Each modulus current instantaneous value of common-tower double-return DC power transmission line measurement end, wherein 0 represents ground mold component, and 1,2 and 3 represent first Aerial mode component, the second Aerial mode component and the 3rd Aerial mode component, then the voltage of each pole can be expressed as：

According to [T_i] in ground mold component proportion construction in single time I positive pole, negative pole and single time II positive pole, cathodal current Single time transformation matrix.According to new list return transformation matrix can get single back line electric current eliminate ground mold component after electric current divide Amount.

For I loop line road, new list returns transformation matrix form and is：

In formula：[T_{i_I_eli0}] be I circuit eliminate ground mold component current transformation matrix；I_{dif_I_eli0}It is that I loop line road disappears The electric current differential-mode component obtaining after removing topotype；T_i11、T_i21It is 1P, 1N current component in [T_i] in ground mold component coefficient.

For II loop line road, new list returns transformation matrix form and is：

In formula：[T_{i_II_eli0}] be II circuit eliminate ground mold component current transformation matrix；I_{dif_II_eli0}It is II loop line road The electric current differential-mode component obtaining after eliminating topotype；T_i31、T_i41It is 2P, 2N current component in [T_i] in ground mold component coefficient.

(5) extract modulus：For eliminating the impact of ground mold component, using the differential mode electricity eliminating ground mold component obtained above Pressure, current component are calculated.When further contemplating different polar curve fault, the distribution of each modulus has differences simultaneously, by It is also one of important factor in order of fault signature in the size of modulus, therefore when selecting modulus parameter, select more prominent Component, here might as well be assumed to be m component.

(6) calculate voltage's distribiuting along the line：According to the above modulus chosen, based on Bei Ruilong parameter model, according to from two ends The voltage that obtains, the magnitude of current, calculate two ends along the distribution of line voltage respectively using following formula：

In formula：J and K represents circuit J end and K end respectively；u_jn(x, t) represents calculating using n end electrical quantity, apart from x The j mode voltage at place, 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 mould respectively；M is modulus label, and expression adopts during different polar curve fault relatively For prominent Aerial mode component.

(7) the fault location criterion based on single time quantity of information for the construction：Returned according to the constructed above list eliminating ground mold component Phase-model transformation decoupling matrices, select differential-mode component to be calculated.Fault location criterion such as following formula then can be constructed：

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 On the basis of distance；u_K(l-x, t) represent calculated using K end electrical quantity, at the x of K end differential mode voltage, x is to be with J end The distance of benchmark；t₂-t₁By the length of taken redundant data window, t₁For redundant data window initial time.

(8) calculate fault moment：From circuit two ends calculated false voltage traveling wave in non-faulting point at reach when Between be different, so near fault moment, there will be an obvious step Sudden change region, there is maximum in theory Error amount.The voltage difference of non-faulting point if carrying out fault location using this section, can be amplified to greatest extent, thus Be conducive to improving the positioning precision of trouble point, this section might as well be referred to as non-faulting point maximum voltage difference section for this.

Assume that actual fault point is x apart from the distance of rectification side_fIf calculating the voltage's distribiuting along the line at x, this section is big Little Δ T is：

From above formula, the size of non-faulting point maximum difference section is directly proportional to the size deviateing trouble point, deviates event Barrier point is more remote, and this region is bigger, then non-faulting point voltage difference is also more obvious with the difference of trouble point, and this can for raising range finding It is clearly very favorable by property.

Therefore adopt wavelet transformation to obtain circuit two ends wavefront due in, and then ask for obtaining fault moment, will It is as the triggered time of redundant data window.

The phase voltage obtaining from circuit two ends, after phase-model transformation, takes differential-mode component to be calculated.According to wavelet transformation, Setting du/dt threshold value, to demarcate two ends traveling wave due in, is set to t_{R_1}、t_{I_1}If velocity of wave is v_m, can get at the beginning of fault Begin moment t₀For：

In formula：t_{R_arr}It is from rectification side calculated fault initial time；t_{I_arr}It is event calculated from inverter side Barrier initial time.

Fault initial time be can get according to above analysis, be set to t₀, set the initial time of taken redundant data window, I.e. t₁=t₀.

(9) determine the redundant data window chosen：Further contemplate the propagation of contained Aerial mode component in actual differential-mode component Speed difference will result in the modulus traveling-waves propagation time and has differences, and embodies non-faulting point maximum voltage difference section for more preferable, can Certain nargin is increased with the initial time to redundant data window：

t′₁=t₀-Δt_ω,

In formula：t’₁Initial time for revised redundant data window；Δt_ωBy increasedd nargin.

Redundant data window be can determine that according to above analysis.

The operation principle of the present invention：The present invention is surveyed based on single telegram in reply tolerance common-tower double-return DC power transmission line time domain fault It is to return phase-model transformation matrix to obtain differential-mode component using the list eliminating ground mold component of construction away from method, and divide from circuit two ends Do not calculate voltage's distribiuting along the line, then had near fault moment along line computation voltage according to the circuit two ends of non-faulting point The feature of big difference, defines non-faulting point maximum voltage difference section, and obtains fault initial time using wavelet transformation, really The fixed redundant data window adopting is thus the method that carries out fault localization.

Due to common-tower double-return DC power transmission line, not only there is alternate mutual inductance in same loop line, and there is also between different loop line Mutual inductance between line, electromagnetic coupled complicated mechanism, need circuit is decoupled.Due to the common-tower double-return direct current in existing Practical Project The protection that controls of each time system of power transmission engineering is based on this time electric quantity information.But the phase mould of traditional single time DC power transmission line The common-tower double-return DC power transmission line that transformation matrix directly applies to asymmetric transposition has certain limitation.And through passing Ground mold component and all of Aerial mode component is contained in the differential-mode component that single time DC power transmission line phase-model transformation of system obtains.Due to Ground mold component is affected very big by earth conductivity and frequency, and for the DC line of long distance powedr transmission, ground mold component is for reality Now accurately fault localization is unfavorable.Therefore the present invention is based on single back line electric parameters, according to common-tower double-return DC transmission line The phase-model transformation matrix on road, proposes a kind of list eliminating ground mold component and returns phase-model transformation matrix, and then obtain only containing Aerial mode component Differential-mode component.When the present invention considers different polar curve fault simultaneously, the distribution of each modulus has the characteristics that diversity, according to Main constituent priority principle selects more prominent Aerial mode component parameter, and then obtains two ends voltage's distribiuting along the line.Finally in basis The circuit two ends of non-faulting point have the characteristics that maximum difference along line voltage near fault moment, define non-faulting point maximum Voltage difference section.The voltage difference of non-faulting point if carrying out fault location using this section, can be amplified to greatest extent, Thus being conducive to improving the range accuracy of trouble point.Therefore the present invention utilizes wavelet transformation to obtain circuit two ends differential-mode component traveling wave Wave head due in, and then ask for obtaining fault moment, as the triggered time of redundant data window, thus having obtained one kind The fault distance-finding method of the common-tower double-return DC power transmission line based on single time quantity of information.

Compared with prior art, the invention has the advantages that：

Firstth, it is applied to the common-tower double-return direct current transmission line fault range finding of asymmetric transposition.

Secondth, it is based on single back line electric quantity information, consistent with Practical Project, there is good future in engineering applications.

3rd, reliability is high, has eliminated the impact of ground mold component, fault precision is not subject to fault polar curve, abort situation substantially With the impact of transition resistance, during high resistance ground, still ensure that fault localization precision.

4th, fault localization high precision.Invention defines non-faulting point maximum voltage difference section, put to greatest extent Voltage difference at big non-faulting point, trouble point more easy to identify, improve fault localization precision.

5th, during desired data window short it is only necessary to extract circuit two ends electric parameters, it is easy to accomplish.

Brief description

Fig. 1 is the one-tower double-circuit DC transmission system illustraton of model of the present invention.

Fig. 2 is the one-tower double-circuit DC transmission system tower structure figure of the present invention.

Fig. 3 is fault location figure.

Specific embodiment

With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not It is limited to this.

Embodiment

As shown in figure 1, adopting PSCAD/EMTDC simulation software, it is straight that power transmission Guangdong ± 500kV common-tower double-return is crossed in structure small stream Lip river Stream transmission system model, its tower structure is as shown in Figure 2；Common-tower double-return bipolar direct current transmission line model is using according to frequency parameter mould Type, total track length 1254km；Setting fault betides diverse location, and fault resistance includes metallic earthing and through 300 Ω Transition resistance is grounded；Fault type includes upper strata polar curve fault, lower floor's polar curve fault and levels polar curve simultaneous faults respectively. This system utilizes the fault distance-finding method of the present invention, specifically includes following steps：

S1, extraction unit impedance matrix and unit admittance matrix：

Obtain the unit impedance matrix [Z of common-tower double-return DC power transmission line according to the model of shaft tower_phase] and unit admittance Matrix [Y_phase]：

S2, ask for common-tower double-return DC power transmission line phase-model transformation matrix：

According to the unit impedance matrix [Z obtaining_phase] and unit admittance matrix [Y_phase], ask for voltage decoupling matrix [T_v], Current Decoupling matrix [T_i]：

Can be obtained according to above-mentioned formula：

S3, construction eliminate the list telegram in reply pressure phase-model transformation matrix of ground mold component：

According to voltage decoupling matrix [T derived above_v], obtain each modulus of common-tower double-return DC power transmission line measurement end Instantaneous voltage, wherein 0 represents ground mold component, and 1,2 and 3 expression the first Aerial mode components, the second Aerial mode component and the 3rd line mould divide Amount, then the voltage of each pole can be expressed as：

For I loop line road, new list returns transformation matrix form and is：

Then through eliminating the differential mode voltage components on the I loop line road that the list of mold component obtains after returning transformation matrix are：

U_{dif_I_eli0}=-0.1861u₁+0.4494u₂+0.4830u₃,

For II loop line road, new list returns transformation matrix form and is：

Then through eliminating the differential mode voltage components on the II loop line road that the list of mold component obtains after returning transformation matrix are：

U_{dif_II_eli0}=-0.1861u₁+0.4494u₂+0.4830u₃,

S4, construction eliminate the list telegram in reply stream phase-model transformation matrix of ground mold component：

According to Current Decoupling matrix [T derived above_i], obtain each modulus of common-tower double-return DC power transmission line measurement end Current instantaneous value, wherein 0 represents ground mold component, and 1,2 and 3 expression the first Aerial mode components, the second Aerial mode component and the 3rd line mould divide Amount, then the magnitude of current of each pole can be expressed as：

For I loop line road, new list returns transformation matrix form and is：

Then through eliminating the differential-mode current component on the I loop line road that the list of mold component obtains after returning transformation matrix is：

I_{dif_I_eli0}=-0.0999i₁+0.5150i₂+0.5178i₃,

For II loop line road, new list returns transformation matrix form and is：

Then through eliminating the differential-mode current component on the I loop line road that the list of mold component obtains after returning transformation matrix is：

I_{dif_II_eli0}=-0.0999i₁+0.5150i₂+0.5178i₃,

S5, the characteristic distributions for each Aerial mode component during different polar curve fault, choose more prominent component.Due to line Mould 3 component is more prominent, and therefore modulus parameter selection line mould 3 corresponds to parameter.

S6, calculating voltage's distribiuting along the line：

Calculate two ends voltage's distribiuting along the line.Using following formula：

Wherein, J and K represents circuit J end and K end respectively；u_jn(x, t) represents calculating using n end electrical quantity, apart from x The j mode voltage at place, n=J, K represent the two ends of DC line respectively, and j=com is modulus label, represents and adopts differential-mode component； r₃、v₃、Z_c3It is the corresponding resistivity of 3 moulds, velocity of wave and characteristic impedance respectively.

S7, fault location：

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

Wherein, 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 On the basis of distance；u_K(l-x, t) represent calculated using K end electrical quantity, at the x of K end differential mode voltage, x is to be with J end The distance of benchmark；t₂-t₁Length by taken redundant data window.

S8, calculating fault initial time：

According to wavelet transformation, du/dt threshold value is set to demarcate the moment that two ends traveling wave reaches rectification side and inverter side, point It is not set to t_{R_1}、t_{I_1}, velocity of wave is v₃, can get fault initial time t₀For：

In formula, t_{R_arr}It is from rectification side calculated fault initial time；t_{I_arr}It is event calculated from inverter side Barrier initial time.

Fault initial time be can get according to above analysis, be set to t₀, set the triggering moment of taken redundant data window, I.e. t₁=t₀.

S9, the selection of redundant data window：

In order to ensure more preferably to identify voltage differences maximum point along the line, the triggering moment of redundant data window can be increased certain Nargin：

t′₁=t₀-Δt_ω,

In formula, t '₁Triggering moment for revised redundant data window；Δt_ωBy increasedd nargin, take 0.2ms.

As shown in figure 3, being that II loop line road negative pole occurs positioning knot during metallic earthing fault at rectification side 100km Really.

As shown in table 1 below, list and diverse location occurs, passes through different transition resistances ground connection in II time line fault Fault location result.

Table 1

From the fault location result of table 1, the fault distance-finding method that the present invention is carried is accurately and effectively, is capable of Accurate range finding in the range of total track length, and range accuracy is not subject to the impact of fault polar curve, abort situation and transition resistance.

Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not subject to described embodiment Limit, other any spirit without departing from the present invention and the change made under principle, modification, replacement, combine, simplify, All should be equivalent substitute mode, be included within 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.