A single-end fault location method for transmission lines based on multivariate model fusion analysis

Abstract

The present invention discloses a single-end fault distance measurement method for a transmission line based on multivariate model fusion analysis. A time domain equation group is constructed according to a concentrated parameter line model to preliminarily fit and calculate the fault distance. After determining that the calculation result reaches a steady state, a new calculation starting point x is determined based on theoretical error analysis and considering a certain margin. q(1) , use the Berelon model to calculate the voltage and current to the new starting point x q(1) Based on the voltage and current at the new calculation starting point, the fault distance x is calculated again using the lumped parameter model fitting. q(2) , and the final fault distance is x q =x q(1) +x q(2) Compared with the prior art, the present invention can reduce the ranging error caused by ignoring the distributed capacitance of the line in the concentrated parameter line model.

Description

Technical Field

[0001] The present invention relates to the field of power system relay protection, and in particular to a single-end fault location algorithm for a transmission line based on multivariate model fusion and maximum error estimation. Background Art

[0002] With the development of the national economy, the demand for long-distance and large-scale power transmission has increased. At the same time, high-voltage transmission lines are widely distributed, and the terrain of the areas they cross is complex and changeable. Rapid and accurate fault location after a transmission line failure is not only conducive to the rapid repair of the fault and the improvement of the stability of the power system, but is also crucial to the normal operation of the national economy.

[0003] The single-ended impedance fault distance measurement only needs to measure the information at one end of the transmission line. It has the advantages of low hardware requirements, easy implementation and stable algorithm, so it has been widely used. The traditional fault distance measurement uses a line model based on concentrated parameters. When applied to longer transmission lines, the influence of the line distributed capacitance will become non-negligible, causing large errors in the accuracy of the remote fault distance measurement. Therefore, it is particularly important to study a fault distance measurement model and algorithm suitable for long lines to improve the accuracy of fault distance measurement. Summary of the invention

[0004] Based on the above-mentioned prior art, the present invention proposes a single-end fault distance measurement method for transmission lines based on multivariate model fusion analysis, and constructs a time domain equation group based on this concentrated parameter line model to fit and calculate the fault distance and obtain the final fault distance.

[0005] The present invention is achieved through the following technologies:

[0006] A single-end fault location method for a transmission line based on multivariate model fusion analysis specifically comprises the following steps:

[0007] Step 1: Estimate the fault distance using a lumped parameter line model, where:

[0008] Based on the concentrated parameter line model, the differential equations of the fault phase voltage and fault phase current continuously collected by the protection device within the unit data window length are organized into a matrix form:

[0009] U=Iβ

[0010] The solution is to obtain the fault distance x calculated by unit data window fitting. The solution expression of the fault distance is as follows:

[0011] β=(I T I) -1 I T U,β=[x R' F ] T

[0012] Where x is the fault distance, U is the fault phase voltage matrix, I is the fault phase current matrix, β is the coefficient matrix to be determined, and R′ F is the equivalent transition resistance;

[0013] Step 2: Determine whether the fitting calculation has reached a steady state;

[0014] Step 3: After reaching steady state, calculate the current fault distance x n The corresponding maximum model error, considering the margin to determine the new calculation starting point x q(1) , the expression is as follows:

[0015]

[0016] Among them, k x is the margin coefficient, x n is the steady-state calculation result of fault location based on the lumped parameter line model, E cmax (ω,x,R F ) is the error calculation formula caused by ignoring distributed capacitance, where Y = r1 + jωl1, W = jωc1, R F It represents the transition resistance value and takes the maximum value according to the actual system conditions, and ω is the frequency;

[0017] Step 4: Use the Berelon model to calculate the voltage and current from the protection installation to the above starting point x q(1) ;

[0018] Step 5: Based on the new calculation starting point x q(1) , fault distance calculation using lumped parameter line model;

[0019] Step 6: Determine again whether the fitting calculation has entered a steady state;

[0020] Step 7: After determining that the fitting calculation has reached a steady state, the fault distance calculation result x is obtained based on the new calculation starting point q(2) ;

[0021] Step 8: The final fault distance calculation result is x q =x q(1) +x q(2) .

[0022] Compared with the prior art, the single-end fault location method for power transmission lines based on multivariate model and maximum error of the present invention has the following beneficial effects:

[0023] 1) It can reduce the ranging error caused by ignoring the distributed capacitance of the line in the concentrated parameter line model;

[0024] 2) The influence of distributed capacitance of the line can be almost ignored, which greatly improves the accuracy of fault location measurement of long-distance transmission lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a flow chart of a single-end fault location method for a transmission line based on multivariate model fusion analysis.

[0026] Figure 2 Schematic diagram of single-end fault of transmission line. DETAILED DESCRIPTION

[0027] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0028] The present invention proposes a single-end fault distance measurement algorithm for transmission lines based on multivariate model fusion analysis. Firstly, based on a lumped parameter line model, the fault distance is estimated and solved by a time domain equation. After determining that the fitting calculation enters a steady state, a new calculation starting point is determined by taking into account a certain margin while accurately estimating the maximum distance measurement error range caused by ignoring the distributed capacitance of the lumped model. The voltage and current at the protection installation are calculated to the new starting point through the distributed parameter line model. Based on the new starting point, the fault distance of the transmission line is solved based on the lumped parameter line model to obtain the final fault distance.

[0029] like Figure 1 As shown in the figure, it is a flow chart of the single-end fault distance measurement method of the transmission line based on multivariate model fusion analysis of the present invention. First, based on the concentrated parameter line model, the parameter identification calculation is performed on the sampled data; after determining that the fitting calculation enters the steady state, the fault distance is estimated and solved by the time domain equation, and the fault distance value x corresponding to the current sampling sequence n is calculated. n The maximum model error is determined by accurately estimating the maximum ranging error range caused by ignoring the distributed capacitance of the centralized model, taking into account a certain margin, and determining the new calculation starting point x q(1) ; Use the Berelon model to calculate the voltage and current from the fault protection point to the above starting point x q(1) ; Based on the new calculation starting point x q(1) , use the concentrated parameter line model to calculate the fault distance; after determining that the fitting calculation enters the steady state again, the new calculation starting point x is obtained. q(2) , and the fault distance is x q =x q(1) +x q(2) .

[0030] like Figure 2As shown in the figure, it is a schematic diagram of a single-end fault of a transmission line. A single-phase grounding fault occurs at line F, r0 and l0 are the zero-sequence resistance and inductance of the line per unit length, r1 and l1 are the resistance and inductance of the line per unit length, R F is the transition resistance, i F is the current flowing through the transition resistor, and x is the fault distance.

[0031] Step 1: Estimate the fault distance using a lumped parameter line model; where:

[0032] Taking a single-phase grounding fault as an example, the fault phase (phase A) voltage u of the discrete sampling data at the protection installation is mA (n)) is shown in the following formula:

[0033] u mA (n)=[(i mA (n)+3k r i m0 (n))r1+(i mA (n+1)+3k r i m0 (n+1)

[0034] -i mA (n-1)-3k r i m0 (n-1))l1 / (2Δt)]x+i m0 (n)R' F (1)

[0035] Where n is the sampling sequence, Δt is the sampling interval, R′ F =C F R F , C F is the zero-sequence shunt coefficient at the protection installation, u mA (n) is the fault phase voltage of sampling sequence n, i mA (n), i mA (n+1) are the fault phase currents of sampling sequence n and sampling sequence n+1, respectively. m0 (n), i m0 (n+1) are the fault phase zero-sequence current of sampling sequence n and the fault phase zero-sequence current of sampling sequence n+1, K r =(r o -r1) / 3r1, K l =(l o -l1) / 3l1 are the resistance zero-sequence compensation coefficient and the inductance zero-sequence compensation coefficient, R′ F is the equivalent transition resistance;

[0036] Select a certain data window length, and organize the differential equations of the fault phase voltage and fault phase current within the unit data window length continuously collected by the protection device into a matrix form. The expression is as follows:

[0037] U=Iβ (2)

[0038] in:

[0039] U=[u mA (n-k+1),u mA (n-k+2),...u mA (n)] T

[0040]

[0041] β=[x R' F ] T

[0042] p(n)=i mA (n)+3k r i0(n)

[0043] p d (n)=[i mA (n+1)+3k l i0(n+1)-i mA (n-1)-3k l i0(n-1)] / (2Δt)

[0044] Among them, U is the fault phase voltage matrix, I is the fault phase current matrix, p(n) is the current sampling sequence, p d (n) is the differential derivative sequence of the current sampling points; T represents the matrix transpose; k is the number of sampling points used for fitting calculation in the unit data window, and β is the coefficient matrix; the coefficient matrix β is expressed as follows:

[0045] β=(I T I) -1 I T U(3)

[0046] Among them, I T is the fault phase current transposed matrix;

[0047] Combined with the following formula:

[0048] β=(I T I) -1 I T U,β=[x R' F ] T (4)(5)

[0049] Solving the calculation, we can get the fault distance x and equivalent transition resistance R′ calculated by fitting the unit data window. F ;

[0050] Step 2, determine whether the fitting calculation reaches a steady state;

[0051] Whether the fitting calculation has entered a steady state is determined based on the stability of the calculation results. The specific determination method is as follows:

[0052] The fitting error in the unit data window is defined as:

[0053]

[0054] By continuously fitting the protection sampling data using a sliding data window, the fitting error sequence E is obtained. r =[E r(1) ,E r(2) ,…,E r(Cn) ], C n Solve the fault distance for the current time domain differential equation n Second fitting calculation results;

[0055] The value of the fitting error reflects the stability of the differential equation in the unit data window of the fitting calculation. When the transient process is severe, the differential equation cannot obtain a stable solution, and the fitting error is large. When the calculation begins to enter a steady state, the fitting error approaches zero. The present invention uses whether the value of the fitting error is continuously less than the threshold value in the set data window as a judgment on whether the fitting calculation enters a steady state:

[0056] E r(i) <E r(set) ,i=C n ,C n -1,…,C n -n w (7)

[0057] Among them, n w The number of fits to account for continuity in the calculation;

[0058] Step 3: After reaching steady state, calculate the fault distance value x corresponding to the current sampling sequence n n The maximum model error is taken into account, and a certain margin is considered to determine the new calculation starting point x q(1) , the expression is as follows:

[0059]

[0060] Among them, k x is the margin coefficient, x n is the steady-state calculation result of fault location based on the lumped parameter line model, E cmax (ω,x,RF ) is the error calculation formula caused by ignoring distributed capacitance, where Y = r1 + jωl1, W = jωc1, R F represents the transition resistance value, ω is the frequency;

[0061] According to the line parameters and theoretical derivation, the range of ranging error caused by ignoring distributed capacitance based on concentrated parameter single-ended ranging is determined; the voltage at any point x on the line calculated by the long-line equation can be obtained by the voltage at the protection installation point Current The calculation results are:

[0062]

[0063] Among them, γ is the propagation coefficient, Z c is the line wave impedance;

[0064] Performing Taylor first-order expansion on the above equation at x=0 yields:

[0065]

[0066] Among them, R2(x) is the Lagrangian remainder of Taylor's first-order expansion, as shown in the following formula:

[0067]

[0068] When equation (7) ignores the Lagrangian remainder and is transformed into the time domain, it becomes the time domain lumped parameter line equation, that is, only the resistance and inductance of the transmission line are taken into account, and the distributed capacitance of the line is ignored. It can be seen that R2(x) is the error source of the lumped parameter line model;

[0069] The accurate fault distance is calculated as shown in the following formula:

[0070]

[0071] in:

[0072]

[0073] So we have:

[0074] x CALC -x CALC_1 ≤x CALC_2

[0075] Therefore, the maximum calculation error of the fault distance of the concentrated parameter line model is x CALC_2 ; Since R2(x) Unable to determine the exact value, resulting in x CALC_2 It is impossible to obtain an accurate calculated value, but from the derivation process of the Lagrange remainder, it can be known that it is the voltage at a point between the line head end and the fault point, satisfying So we can get x CALC_2 The value range of is as shown below:

[0076]

[0077] Among them, Z m is the apparent impedance at the head end of the line, and the transmission line is equivalent to the Γ model, then Z m It is expressed as:

[0078]

[0079] Substituting the above formula into formula (8) and rearranging it, we get the expression of the maximum error:

[0080]

[0081] Among them, Y=r1+jωl1, W=jωc1;

[0082] So far, the ranging error expression caused by ignoring distributed capacitance in single-ended ranging based on concentrated parameters is obtained. According to the actual line parameters and actual engineering conditions, the maximum range of distributed capacitance error can be calculated in real time.

[0083] Step 4: Use the Berelon model to calculate the voltage and current from the fault protection point to the above starting point x q(1)， And finally get the fault distance measurement result;

[0084] Taking a single-phase system as an example, u m 、i m is the voltage and current at the protection installation location, x is the distance from a point on the line to the line protection installation location, then the voltage and current at this point can be calculated from the voltage and current at the protection installation location:

[0085]

[0086] In the above formula:

[0087]

[0088] Among them, D e (τ) is the delay factor, that is, f(t+τ)=D e (τ)f(τ), τ=x / v, v is the wave speed, is the wave impedance of the lossless line; x can be calculated by combining the phase mode transformation q The voltage and current at

[0089] Step 5: Based on the new calculation starting point x q(1) , fault distance calculation using lumped parameter line model;

[0090] Step 6: Determine again whether the fitting calculation has entered a steady state;

[0091] Step 7: After the calculation reaches a steady state, based on x q The voltage and current at the point are calculated by solving the line fault distance at this time through the time domain differential equation. When the calculation result reaches the steady-state judgment of formula (2), the fault distance calculation result x at this time based on the new calculation starting point is obtained. q(2) ;

[0092] Step 8: Get the fault distance result as x q =x q(1) +x q(2) .

[0093] It should be noted that the present invention is not limited to the above-mentioned method steps and calculation processes, and the above-mentioned specific implementation methods are merely illustrative and not restrictive. Researchers in this field can, inspired by the present invention, make formal changes and modifications to the present invention without departing from the purpose of the present invention and the scope of protection of the claims, and all of these are within the protection of the present invention.

Claims

1. A single-end fault location method for transmission lines based on multivariate model fusion analysis, characterized in that: The method specifically comprises the following steps: Step 1: Estimate the fault distance using a lumped parameter line model, where: Based on the concentrated parameter line model, the differential equations of the fault phase voltage and fault phase current continuously collected by the protection device within the unit data window length are organized into a matrix form: U=Iβ The solution is to obtain the fault distance x calculated by unit data window fitting. The solution expression of the fault distance is as follows: β=(I T I) -1 I T U,β=[x R' F ] T Where x is the fault distance, U is the fault phase voltage matrix, I is the fault phase current matrix, β is the coefficient matrix to be determined, and R′ F is the equivalent transition resistance; Step 2: Determine whether the fitting calculation has reached a steady state; Step 3: After reaching steady state, calculate the current fault distance x n The corresponding maximum model error, considering the margin to determine the new calculation starting point x q(1) , the expression is as follows: Among them, k x is the margin coefficient, x n is the steady-state calculation result of fault location based on the lumped parameter line model, E cmax (ω,x,R F ) is the error calculation formula caused by ignoring distributed capacitance, where Y = r1 + jωl1, W = jωc1, R F It represents the transition resistance value and takes the maximum value according to the actual system situation, ω is the frequency, r1 and l1 are the resistance and inductance per unit length of the line respectively; Step 4: Use the Berelon model to calculate the voltage and current from the protection installation to the above starting point x q(1) ; Step 5: Based on the new calculation starting point x q(1) , fault distance calculation using lumped parameter line model; Step 6: Determine again whether the fitting calculation has entered a steady state; Step 7: After determining that the fitting calculation has reached a steady state, the fault distance calculation result x is obtained based on the new calculation starting point q(2) ; Step 8: The final fault distance calculation result is x q =x q(1) +x q(2) .

2. A method for single-ended fault location of a transmission line based on a multivariate model and maximum error as claimed in claim 1, characterized in that According to the real-time fitting calculation result of the fault distance, it is determined whether the calculation result reaches a steady state. The specific steps are as follows: The fitting error within the unit data window is defined as: By continuously fitting the protection sampling data using a sliding data window, the fitting error sequence E is obtained. r =[E r(1) ,E r(2) ,…,E r(Cn) ], C n Solve the fault distance for the current time domain differential equation n The fitting calculation result is k, where k is the number of sampling points used for fitting calculation in the unit data window; When the transient process is severe, the differential equation cannot obtain a stable solution and the fitting error is large. When the calculation begins to enter a steady state, the fitting error approaches zero. Whether the value of the fitting error is continuously less than the threshold value within the set data window is used as a judgment on whether the fitting calculation enters a steady state: E r(i) <E r(set) ,i=C n ,C n -1,…,C n -n w Among them, C n Solve the fault distance for the current time domain differential equation n The results of the fitting calculations, n w The number of fits to account for continuity in the calculation.

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