Same-tower double-circuit transmission line zero-sequence parameter estimation method considering distributed parameter characteristics

Abstract

The invention relates to a same-tower double-circuit alternating-current transmission line zero-sequence parameter estimation method based on internal faults. The method comprises the following steps: establishing different mathematical models according to line length differences, adopting a single-section pi lumped parameter model for medium-short distance transmission lines to approximate a distributed parameter model, and adopting a distributed parameter model for medium-long distance transmission lines, therefore, the electromagnetic characteristics during the single-phase earth fault can be accurately represented. Based on voltage and current measurement data at two ends of the line, establishing a parameter equation set in a fault state by combining a Kirchhoff's law, and performing linear approximate processing on a nonlinear equation by using Taylor series expansion; through algebraic operation and matrix solution, an explicit analytical expression of a zero-sequence parameter is deduced, and precise calculation without iteration is realized. According to the method, zero-sequence parameters such as zero-sequence self-impedance and mutual impedance are estimated based on the single-phase earth fault of the same-tower double-circuit line, and the method is suitable for online identification of the zero-sequence parameters of transmission lines with different lengths and has the characteristics of high calculation efficiency, clear physical significance and high engineering applicability.

Description

Technical Field

[0001] This invention relates to a method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower in a high-voltage power transmission system. The method is based on the measurement of the voltage and current at both ends of the double-circuit line during a fault in the line area to achieve zero-sequence parameter estimation. Background Technology

[0002] In power systems, the zero-sequence parameters of transmission lines have a significant impact on the setting and operation performance of relay protection. Accurate zero-sequence parameters ensure the sensitivity and reliability of transmission line relay protection, thereby improving the safe and stable operation of the power system. However, traditional zero-sequence parameter measurement methods have many limitations and are difficult to meet the requirements of efficient and safe operation of modern power systems.

[0003] Currently, the acquisition of zero-sequence parameters mainly relies on manual measurement methods, such as conducting single-phase grounding tests when the line is out of service. This method not only requires the line to be taken out of service, affecting the power flow distribution and power supply reliability of the grid, but also carries high safety risks due to manual operation, especially in high-voltage or ultra-high-voltage environments. In recent years, with the widespread application of digital relays and fault recorders, parameter estimation methods based on fault data have gradually become a research hotspot. Compared with traditional methods, zero-sequence parameter estimation technology based on intra-regional faults can directly calculate zero-sequence parameters using voltage and current measurements recorded by fault recorders during faults at both ends of the line, without requiring line shutdown, thus meeting the requirements for continuous operation of the power system. At the same time, this method avoids manual on-site measurement, significantly improving safety and reducing economic losses caused by line shutdowns. Therefore, developing a zero-sequence parameter estimation method for double-circuit transmission lines on the same tower based on intra-regional faults is of great significance for improving relay protection accuracy, ensuring stable operation of the power system, and protecting personnel safety. Summary of the Invention

[0004] The purpose of this invention is to provide a method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower, which can make full use of existing fault data to achieve online estimation of zero-sequence parameters and provide strong support for the development of smart grids.

[0005] To achieve the above objectives, the technical solution of the present invention provides a method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower, considering the characteristics of distributed parameters, characterized by comprising the following steps:

[0006] Step 1: Establish corresponding mathematical models based on the different lengths of transmission lines, where:

[0007] For medium- and short-distance lines, a single-segment π-type lumped parameter model is established;

[0008] For medium- and long-distance transmission lines, the accurate model used is the distributed parameter model;

[0009] Step 2: For a single-segment π-type lumped parameter model, use the electrical quantity data obtained by the measuring devices at both ends of the line, combined with the known positive sequence parameters and fault location information, to establish a set of parametric equations under the fault state using Kirchhoff's circuit laws.

[0010] For the distributed parameter model, the Taylor series expansion method is used for linearization approximation to obtain a solvable closed equation.

[0011] Step 3: Perform algebraic transformations and matrix operations on the system of equations established in Step 2 to derive the explicit analytical solution with zero-order parameters that can be directly calculated.

[0012] Preferably, in step 2, for a single-segment π-type lumped parameter model, the positive sequence parameters can be obtained by measuring the line during normal operation, and the fault location information is determined using a fault location method that does not depend on parameters.

[0013] Preferably, in step 2, for a single-segment π-type lumped parameter model, the established set of parametric equations is as follows:

[0014]

[0015] In the formula: L represents the per-unit fault distance from the fault location to the line input terminal; it is a real, known quantity. f-l L represents the distance from the fault location to the line input terminal. total R represents the total length of the transmission line; f Indicates the fault resistor; This represents the phasor domain voltage value at the fault location of a line with a positive sequence fault. This represents the phasor domain voltage value at the fault location of a line with a negative sequence fault. This represents the zero-sequence self-impedance of the entire line. This represents the zero-sequence mutual impedance across the entire line; This indicates zero-sequence self-admittance across the entire line. Indicates the zero-sequence mutual admittance across the entire line; This represents the phasor domain voltage value at the fault location of a zero-sequence fault line. This represents the phasor domain voltage value at the output terminal of the zero-sequence circuit. This represents the phasor domain voltage value at the zero-sequence line input terminal; This represents the phasor domain current value flowing through the impedance closest to the input terminal of the zero-sequence fault line. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the phasor domain current value flowing through the impedance closest to the output terminal of the zero-sequence fault line. This represents the phasor domain current value flowing through the impedance closest to the output terminal of a zero-sequence healthy circuit. This represents the phasor domain voltage value at the location of a zero-sequence healthy circuit fault. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit.

[0016] Preferably, in step 3, for a single-segment π-type lumped parameter model, the relevant analytical form is as follows:

[0017]

[0018] The correlation coefficient is expressed as follows:

[0019]

[0020] Where, Σ Y Σ represents the sum of the zero-sequence self-admittance and mutual admittance across the entire line. Z This represents the sum of the zero-sequence self-impedance and mutual impedance of the entire line. This represents the phasor domain voltage value at the zero-sequence line input terminal. This represents the phasor domain voltage value at the output terminal of the zero-sequence circuit. This represents the zero-sequence self-impedance of the entire line. This represents the zero-sequence mutual impedance across the entire line. This represents the phasor domain current value flowing through the impedance closest to the input terminal of the line with a zero-sequence fault. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit. This represents the sum of the zero-sequence phasor domain currents of the two input circuits. This represents the sum of the zero-sequence phasor domain currents of the two output circuits. This represents the zero-sequence voltage value in the input phasor domain. This represents the zero-sequence voltage value in the phasor domain of the output terminal.

[0021] Preferably, step 2, for the distributed parameter model, specifically includes the following steps:

[0022] Step 201: For the zero-sequence network of a double-circuit line on the same tower, based on the distributed parameter model, its equivalent hyperbolic function form is further derived to accurately describe the transmission characteristics of long-distance transmission lines. Kirchhoff's current law and voltage law are applied to construct a complete set of fault equations:

[0023]

[0024] In the formula, This represents the phasor domain voltage value at the fault location of a line with a positive sequence fault. This represents the phasor domain voltage value at the fault location of a line with a negative sequence fault. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence faulty circuit and the healthy circuit. This represents the phasor domain current value at the input terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the input terminal of the zero-sequence healthy circuit. This represents the phasor domain current value at the output terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the output terminal of the zero-sequence healthy circuit. This represents the equivalent hyperbolic function form of the impedance to ground near the input under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the line impedance near the input under conditions of summation and decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output under both take-off and decoupling conditions. This represents the line impedance in the form of an equivalent hyperbolic function near the output under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the impedance to ground near the input end under differential decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output end under differential decoupling. This represents the equivalent hyperbolic function form of the line impedance near the input under differential decoupling. This represents the line impedance in the form of an equivalent hyperbolic function near the output end under differential decoupling.

[0025] Step 202: Perform Taylor series expansion on the nonlinear terms at a reasonable operating point, retain the first-order linear terms, and achieve a linearized approximation of the system of equations.

[0026] Preferably, in step 2, for the distributed parameter model, an explicit analytical expression for the zero-order parameter is derived through matrix operations and algebraic transformations:

[0027]

[0028] In the formula, the relevant physical quantities are expressed as follows:

[0029]

[0030] k L k represents the distance from the fault location to the line input terminal. R Indicates the distance from the fault location to the line output terminal, A i The functional expression representing the coefficients of the equation, p - p represents the square root of the product of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance. + This represents the square root of the product of the sum of zero-sequence self-impedance and mutual impedance per unit length and the sum of zero-sequence self-admittance and mutual admittance for a double-circuit line on the same tower. This represents the root of the quotient of the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower, and the sum of zero-sequence self-admittance and mutual admittance. The square root of the quotient of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance.

[0031] Based on the analysis, p + , p - , Further solving yields the analytical form of the zero-sequence parameters for a double-circuit AC transmission line on the same tower:

[0032]

[0033] In the formula, This represents the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower. This represents the difference between the zero-sequence self-impedance and the mutual impedance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-capacitance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual capacitance per unit length of a double-circuit line on the same tower.

[0034] This invention can accurately estimate the zero-sequence parameters of a double-circuit AC transmission line on the same tower, specifically including the imaginary parts of the zero-sequence self-impedance and mutual impedance of the double-circuit AC transmission line on the same tower, the sum of the zero-sequence self-impedance and mutual impedance, and the sum of the zero-sequence self-admittance and mutual admittance. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 A schematic diagram of a single-segment π-lumped parameter transmission line model;

[0037] Figure 3 This is a schematic diagram of a transmission line model in the equivalent hyperbolic function form based on a distributed parameter model. Detailed Implementation

[0038] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0039] Example 1

[0040] Combination Figure 1 This invention discloses a method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower based on an intra-regional fault, comprising the following steps:

[0041] Step 1: For short-to-medium distance transmission lines, a single-segment π-lumped parameter mathematical model of a double-circuit AC transmission line on the same tower is constructed to approximate the distributed parameters. This model can accurately characterize the electromagnetic characteristics of a double-circuit AC transmission line on the same tower during a single-phase ground fault. Through double-ended voltage and current measurement data, combined with the physical laws of the line, analytical calculation of the zero-sequence parameters of the line can be further achieved.

[0042] like Figure 2 As shown: Let the phasor domain voltage measurement value at the input terminal of the double-circuit AC transmission line on the same tower and the current measurement value of each of the two circuits be V respectively. l and I lr1 ,I lr2 The phasor domain voltage measurement value at the output terminal of the double-circuit AC transmission line on the same tower and the current measurement value of each of the two circuits are respectively V r and I rl1 ,I rl2 The phasor domain voltage values ​​of the faulted line and the healthy line at the fault location in a double-circuit AC transmission line on the same tower are V, respectively. f and V nor The phasor domain fault current value of a single-phase grounding fault on a double-circuit AC transmission line on the same tower is I. f The internal impedance of the generator at the input and output ends of the double-circuit AC transmission line on the same tower is Z. sl and Z sr The positive sequence voltage of the generator phasor domain at the input and output ends of the double-circuit AC transmission line on the same tower is V. sl and V sr The measured values ​​and parameters of the positive, negative, and zero sequences are represented by the superscripts +, -, and 0, respectively.

[0043] Step 2: Based on the known electrical quantities obtained by the measuring devices at both ends of the line, the positive sequence parameters of the line, and the fault location information, apply KCL and KVL to establish a set of parametric equations under the fault state.

[0044] In a preferred embodiment of the present invention, the following system of equations is derived by applying the KCL and KVL theorems to zero-order networks and faulty networks:

[0045]

[0046] In the formula, L represents the per-unit fault distance from the fault location to the line input terminal; it is a real, known quantity. f-l L represents the distance from the fault location to the line input terminal. total R represents the total length of the transmission line; f The fault resistance is a real unknown quantity, which can be considered as 0 under metallic or low-resistance fault conditions. The phasor domain voltage value at the fault location of the positive sequence fault line can be obtained by applying the KVL theorem to the positive sequence network. The phasor domain voltage value at the fault location of the negative-sequence faulted line can be obtained by applying the KVL theorem to the negative-sequence network. This represents the zero-sequence self-impedance of the entire line. This represents the zero-sequence mutual impedance across the entire line; This indicates zero-sequence self-admittance across the entire line. This indicates the zero-sequence mutual admittance across the entire line. This represents the phasor domain voltage value at the fault location of a zero-sequence fault line. This represents the phasor domain voltage value at the output terminal of the zero-sequence circuit. This represents the phasor domain voltage value at the zero-sequence line input terminal. This represents the phasor domain current value flowing through the impedance closest to the input terminal of the line with a zero-sequence fault. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the phasor domain current value flowing through the impedance closest to the output terminal of the zero-sequence fault line. This represents the phasor domain current value flowing through the impedance closest to the output terminal in a zero-sequence healthy circuit. This represents the phasor domain voltage value at the location of a zero-sequence healthy line fault. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit; the relevant physical quantities are represented as follows:

[0047]

[0048] Step 3: Based on the (simplified) set of equations obtained in Step 2, derive the explicit analytical expression of the zero-sequence parameters of the double-circuit AC transmission line on the same tower through algebraic operations and matrix solving, while ensuring that the calculation process does not require iteration and has a clear physical meaning.

[0049] In this embodiment, by solving the system of equations in step 2, a closed-form expression for the sum of zero-sequence self-admittance and mutual admittance can be obtained:

[0050]

[0051] In the formula, The zero-sequence self-admittance and cross-admittance are represented as follows: The correlation coefficient is expressed as follows:

[0052]

[0053] In the formula, This represents the sum of the zero-sequence phasor domain currents of the two input circuits; This represents the sum of the zero-sequence phasor currents of the two output circuits. This represents the zero-sequence voltage value in the phasor domain of the input terminal; This represents the zero-sequence voltage value in the phasor domain of the output terminal; Σ Y Σ represents the sum of the zero-sequence self-admittance and mutual admittance across the entire line. Z This represents the sum of the zero-sequence self-impedance and mutual impedance of the entire line. This represents the phasor domain voltage value at the zero-sequence line input terminal. This represents the phasor domain voltage value at the output terminal of the zero-sequence circuit. This represents the zero-sequence self-impedance of the entire line. This represents the zero-sequence mutual impedance across the entire line. This represents the phasor domain current value flowing through the impedance closest to the input terminal of the line with a zero-sequence fault. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit.

[0054] By solving the system of equations in step 2, we can obtain the equation relating the sum of zero-sequence self-impedance and mutual impedance to the sum of zero-sequence self-admittance and mutual admittance:

[0055]

[0056] In the formula, This represents the sum of zero-sequence self-impedance and mutual impedance; Σ... Y Substituting the closed-form solution into the equation yields Σ Z The closed-form solution.

[0057] Through Σ Z The electrical physics law that both the real and imaginary parts are positive numbers allows us to filter out one solution and retain the other analytical solution as the parameter estimation result.

[0058] By solving the system of equations in step 2 and combining the above conclusions, we can obtain the closed-form solutions for the zero-sequence self-impedance and mutual impedance respectively:

[0059]

[0060] in, Therefore, it can be considered a real number; due to the fault location m and the fault resistance R f Since all terms are real numbers, the second term of the equation can be considered a real number.

[0061] Therefore, for a double-circuit AC transmission line on the same tower modeled based on a single-segment π lumped parameter model, this invention proves that, theoretically, the imaginary parts of the zero-sequence self-impedance and mutual impedance, the sum of the zero-sequence self-impedance and mutual impedance, and the sum of the zero-sequence self-admittance and mutual admittance can be accurately estimated based on a single-phase ground fault within the area, and provides the corresponding analytical method.

[0062] Table 1 below is a specific example. This example uses a single-segment π lumped parameter model to model and estimate the parameters of a double-circuit AC transmission line on the same tower. The transmission line is 200km long and a single-phase ground fault occurs 100km from the input end of the line. The fault occurs at 0.25 seconds.

[0063]

[0064] Table 1

[0065] Example 2

[0066] Combination Figure 1 This invention discloses a method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower based on an intra-regional fault, comprising the following steps:

[0067] Step 1: For medium-to-long-distance transmission lines, construct a distributed parameter mathematical model for a double-circuit AC transmission line on the same tower. This model can accurately characterize the electromagnetic characteristics of a double-circuit AC transmission line on the same tower during a single-phase ground fault. Using voltage and current measurement data at both ends, combined with the physical laws of the line, analytical calculations of the zero-sequence parameters of the line can be further achieved.

[0068] Step 2, as follows Figure 3 As shown, in the zero-sequence network, based on the distributed parameter model of a double-circuit transmission line on the same tower, an equivalent hyperbolic function model is further constructed. The KCL and KVL theorems are applied to the equivalent hyperbolic function model of the zero-sequence network and the fault network to compose a system of equations:

[0069]

[0070]

[0071] In the formula, The phasor domain voltage value at the fault location of the positive sequence fault line can be obtained by applying the KVL theorem to the equivalent hyperbolic function model of the positive sequence network. The phasor domain voltage value at the fault location of the negative-sequence fault line can be obtained by applying the KVL theorem to the equivalent hyperbolic function model of the negative-sequence network. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence faulty circuit and the healthy circuit. This represents the phasor domain current value at the input terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the input terminal of the zero-sequence healthy circuit. This represents the phasor domain current value at the output terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the output terminal of the zero-sequence healthy circuit. This represents the equivalent hyperbolic function form of the impedance to ground near the input under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the line impedance near the input under conditions of summation and decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output under both take-off and decoupling conditions. This represents the line impedance in the form of an equivalent hyperbolic function near the output under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the impedance to ground near the input end under differential decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output end under differential decoupling. This represents the equivalent hyperbolic function form of the line impedance near the input under differential decoupling. This represents the equivalent hyperbolic function form of the line impedance near the output end under differential decoupling.

[0072] Using Taylor's expansion theorem, the above system of equations can be simplified and approximated:

[0073]

[0074] Step 3: By solving the simplified approximation system of equations, the closed-form solution with zero-sequence parameters can be obtained:

[0075]

[0076] The above equation presents a quartic equation in x, which can be solved analytically using the quadratic formula. Given p... + Based on:

[0077]

[0078] l L Indicates the distance from the fault location to the line input terminal, l R Indicates the distance from the fault location to the line output terminal, A i The functional expression representing the coefficients of the equation, p +p represents the square root of the product of the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the sum of zero-sequence self-admittance and mutual admittance. - This represents the square root of the product of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance. This represents the root of the quotient of the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower, and the sum of zero-sequence self-admittance and mutual admittance. The square root of the quotient of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance.

[0079] Based on the analysis, p + , p - , The zero-sequence parameters of a double-circuit AC transmission line on the same tower can be obtained by analysis:

[0080]

[0081] In the formula, the subscript pu in the lower right corner represents the per-unit parameter of the length. This represents the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower. This represents the difference between the zero-sequence self-impedance and the mutual impedance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-capacitance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual capacitance per unit length of a double-circuit line on the same tower.

[0082] Table 2 provides a specific example where zero-sequence parameters are estimated for a 200km-long transmission line. A single-phase ground fault occurs 100km from the line input end, and the fault occurs at 0.25 seconds.

[0083]

[0084] Table 2

Claims

1. A method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower, considering the characteristics of distributed parameters, characterized in that, Includes the following steps: Step 1: Establish corresponding mathematical models based on the different lengths of transmission lines, where: For medium- and short-distance lines, a single-segment π-type lumped parameter model is established; For medium- and long-distance transmission lines, the accurate model used is the distributed parameter model; Step 2: For a single-segment π-type lumped parameter model, use the electrical quantity data obtained by the measuring devices at both ends of the line, combined with the known positive sequence parameters and fault location information, to establish a set of parametric equations under the fault state using Kirchhoff's circuit laws. For the distributed parameter model, the Taylor series expansion method is used for linearization approximation to obtain a solvable closed equation. Step 3: Perform algebraic transformations and matrix operations on the system of equations established in Step 2 to derive the explicit analytical solution with zero-order parameters that can be directly calculated.

2. The method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower considering distributed parameter characteristics as described in claim 1, characterized in that, In step 2, for a single-segment π-type lumped parameter model, the positive sequence parameters can be obtained through measurements of the normally operating line, and the fault location information is determined using a parameter-independent fault location method.

3. The method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower considering distributed parameter characteristics as described in claim 1, characterized in that, In step 2, for a single-segment π-type lumped parameter model, the established set of parametric equations is as follows: In the formula: L represents the per-unit fault distance from the fault location to the line input terminal; it is a real, known quantity. f-l L represents the distance from the fault location to the line input terminal. total R represents the total length of the transmission line; f Indicates the fault resistor; This represents the phasor domain voltage value at the fault location of a line with a positive sequence fault. This represents the phasor domain voltage value at the fault location of a line with a negative sequence fault. This represents the zero-sequence self-impedance of the entire line. Indicates the zero-sequence mutual impedance of the entire line; Y l 0 This indicates zero-sequence self-admittance across the entire line. Indicates the zero-sequence mutual admittance across the entire line; This represents the phasor domain voltage value at the fault location of a zero-sequence fault line. V represents the phasor domain voltage value at the output terminal of the zero-sequence circuit; l 0 This represents the phasor domain voltage value at the zero-sequence line input terminal; This represents the phasor domain current value flowing through the impedance closest to the input terminal of the zero-sequence fault line. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the phasor domain current value flowing through the impedance closest to the output terminal of the zero-sequence fault line. This represents the phasor domain current value flowing through the impedance closest to the output terminal of a zero-sequence healthy circuit. This represents the phasor domain voltage value at the location of a zero-sequence healthy circuit fault. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit.

4. The method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower considering distributed parameter characteristics as described in claim 1, characterized in that, In step 3, for a single-segment π-type lumped parameter model, the relevant analytical form is as follows: The correlation coefficient is expressed as follows: Where, Σ Y Σ represents the sum of the zero-sequence self-admittance and mutual admittance across the entire line. Z This represents the sum of the zero-sequence self-impedance and mutual impedance of the entire line. This represents the phasor domain voltage value at the zero-sequence line input terminal. This represents the phasor domain voltage value at the output terminal of the zero-sequence circuit. This represents the zero-sequence self-impedance of the entire line. This represents the zero-sequence mutual impedance across the entire line. This represents the phasor domain current value flowing through the impedance closest to the input terminal of the line with a zero-sequence fault. This represents the phasor domain current value flowing through the impedance closest to the input terminal of a zero-sequence healthy circuit. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence healthy circuit and the faulty circuit. This represents the sum of the zero-sequence phasor domain currents of the two input circuits. V represents the sum of the zero-sequence phasor currents of the two output circuits. l =V l 0 This represents the zero-sequence voltage value in the phasor domain of the input terminal. This represents the zero-sequence voltage value in the phasor domain of the output terminal.

5. The method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower considering distributed parameter characteristics as described in claim 1, characterized in that, Step 2, specifically for the distributed parameter model, includes the following steps: Step 201: For the zero-sequence network of a double-circuit transmission line on the same tower, based on the distributed parameter model, its equivalent hyperbolic function form is further derived to accurately describe the transmission characteristics of long-distance transmission lines. Kirchhoff's current law and voltage law are applied to construct a complete set of fault equations: In the formula, This represents the phasor domain voltage value at the fault location of a line with a positive sequence fault. This represents the phasor domain voltage value at the fault location of a line with a negative sequence fault. This represents the sum of the phasor domain current values ​​at the input and output terminals of the negative-sequence faulty circuit and the healthy circuit. This represents the phasor domain current value at the input terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the input terminal of the zero-sequence healthy circuit. This represents the phasor domain current value at the output terminal of a line with a zero-sequence fault. This represents the phasor domain current value at the output terminal of the zero-sequence healthy circuit. This represents the equivalent hyperbolic function form of the impedance to ground near the input under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the line impedance near the input under conditions of summation and decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output under both take-off and decoupling conditions. This represents the line impedance in the form of an equivalent hyperbolic function near the output under both take-off and decoupling conditions. This represents the equivalent hyperbolic function form of the impedance to ground near the input end under differential decoupling. This represents the equivalent hyperbolic function form of the impedance to ground near the output end under differential decoupling. This represents the equivalent hyperbolic function form of the line impedance near the input under differential decoupling. This represents the line impedance in the form of an equivalent hyperbolic function near the output end under differential decoupling. Step 202: Perform Taylor series expansion on the nonlinear terms at a reasonable operating point, retain the first-order linear terms, and achieve a linearized approximation of the system of equations.

6. The method for estimating zero-sequence parameters of a double-circuit transmission line on the same tower considering distributed parameter characteristics as described in claim 1, characterized in that, In step 2, for the distributed parameter model, through matrix operations and algebraic transformations, the explicit analytical expression for the zero-order parameter is derived: In the formula, the relevant physical quantities are expressed as follows: k L k represents the distance from the fault location to the line input terminal. R Indicates the distance from the fault location to the line output terminal, A i The functional expression representing the coefficients of the equation, p - p represents the square root of the product of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance. + This represents the square root of the product of the sum of zero-sequence self-impedance and mutual impedance per unit length and the sum of zero-sequence self-admittance and mutual admittance for a double-circuit line on the same tower. This represents the root of the quotient of the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower, and the sum of zero-sequence self-admittance and mutual admittance. The square root of the quotient of the difference between zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower and the difference between zero-sequence self-acceptance and mutual admittance. Based on the analysis, p + , - p, Further solving yields the analytical form of the zero-sequence parameters for a double-circuit AC transmission line on the same tower: In the formula, This represents the sum of zero-sequence self-impedance and mutual impedance per unit length of a double-circuit line on the same tower. This represents the difference between the zero-sequence self-impedance and the mutual impedance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the sum of zero-sequence self-admittance and mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual impedance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual resistance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual inductance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual admittance per unit length of a double-circuit line on the same tower. This represents the zero-sequence self-capacitance per unit length of a double-circuit line on the same tower. This represents the zero-sequence mutual capacitance per unit length of a double-circuit line on the same tower.

Images