Direct current line fault location method and system based on port complex impedance frequency domain characteristics

Abstract

The application discloses a DC line fault distance measurement method and system based on port complex impedance frequency domain characteristics, relates to the technical field of DC power system fault diagnosis, and comprises the following steps: an equivalent representation of a port complex impedance under a fault state is constructed by using a frequency domain distribution parameter model, and a fault channel is equivalent to a complex impedance to uniformly represent multiple fault types such as transition resistance, electric arc and insulation degradation; secondly, based on the sensitivity characteristics of the port complex impedance to fault parameters and the frequency combination condition number, an optimal multi-feature diagnosis frequency set is quantitatively screened; subsequently, a measured port complex impedance under the multi-feature frequency is used to construct a weighted residual error objective function; finally, a fault distance and a fault equivalent complex impedance are obtained by joint inversion through initial value screening, damping iteration and physical boundary projection. The application can realize distance measurement by using only single-port electrical quantities, does not need remote synchronous measurement and communication, and can effectively improve the precision and numerical stability of DC line fault distance measurement under a complex fault scene.

Description

Technical Field

[0001] This invention relates to the field of DC power system fault diagnosis technology, and in particular to a DC line fault location method and system based on the frequency domain characteristics of port complex impedance. Background Technology

[0002] In DC power systems, line fault location is a core technology for ensuring safe and stable system operation and shortening fault diagnosis and repair cycles. In practical engineering scenarios, fault location is generally limited by the number of measurement points, site communication conditions, protection action sequence, and changes in system operation modes. In some scenarios, fault analysis can only rely on single-ended voltage and current information from the power supply side, bus side, or the location of the protection and control device. The line length between the fault point and the measurement end, the transition impedance of the fault path, line distributed parameters, system-side equivalent impedance, and the interface characteristics of the power conversion device all affect the electrical response at the measurement end, resulting in a strongly nonlinear relationship between the electrical quantity at the measurement end and the fault distance. Especially in high-resistance faults, insulation degradation faults, arc faults, or line faults with strong capacitive coupling, relying solely on steady-state voltage, current amplitude, or a single impedance quantity for distance measurement easily leads to increased location errors and decreased result stability.

[0003] Currently, DC line fault location technologies mainly fall into four categories: traveling wave and transient quantity methods, steady-state electrical quantity and traditional impedance methods, signal injection methods, and data-driven methods. While these methods have certain application value under specific line structures and measurement conditions, they still have significant shortcomings in DC power systems where measurement points are limited, fault impedance changes are significant, line frequency domain characteristics are complex, and equipment interface coupling is strong. Traveling wave and transient measurement methods require high accuracy in wavefront identification and high synchronization in measurement. The transient process of DC line faults is significantly affected by line parameters, filter branches, power conversion device operation, and protection timing. Fault transient waveforms are prone to attenuation, distortion, and multiple reflections. For branch lines, high-resistance faults, or lines with power electronic interfaces, fault wavefronts and reflection characteristics are difficult to extract accurately, and ranging results are easily affected by transient feature identification errors, limiting their engineering applicability.

[0004] Steady-state electrical quantity methods and traditional impedance methods are highly sensitive to changes in fault transition impedance and the equivalent operating state of the system. After a fault, the voltage and current at the measurement end are jointly determined by the line impedance, the fault branch, the load branch, the bus capacitance, and the converter interface. If only simplified line resistance or a single equivalent impedance relationship is used, it is difficult to accurately characterize the effect of the fault channel on the response at the measurement end. When the fault transition impedance is large or the equivalent impedance on the system side changes, the accuracy of the fault distance calculation will decrease significantly.

[0005] Existing signal injection methods fail to adequately utilize frequency domain response differences, and the selection of diagnostic frequencies lacks quantitative basis. DC lines and related electrical units exhibit differentiated impedance characteristics at different frequencies. Line inductance, capacitance, filter branches, stray capacitance, and power conversion device interfaces all affect the response characteristics of diagnostic signals. Some methods use fixed or empirical frequencies for injection, lacking a comprehensive consideration of fault distance sensitivity, the degree of influence of fault impedance, and measurement stability. This results in a lack of stable correlation between frequency selection and ranging performance, making it difficult to balance ranging sensitivity and anti-interference capability.

[0006] Data-driven methods are highly dependent on the consistency between the coverage of training samples and operating conditions. The operating modes, line parameters, load levels, control states, and fault impedance combinations of DC power systems are complex, making it difficult for training samples to cover all fault states. When the system topology, equipment parameters, or operating modes change, the model's generalization ability and engineering interpretability are insufficient, making it difficult to directly adapt to DC power systems with variable structures.

[0007] In summary, existing DC line fault location technologies cannot simultaneously meet the requirements of high location accuracy, strong resistance to fault impedance interference, scientific frequency selection criteria, and stable nonlinear solution performance under single-end measurement conditions. There is an urgent need to propose a DC line fault location method that is suitable for scenarios with limited measurement points and can effectively cope with the characteristics of complex fault channels. Summary of the Invention

[0008] To address the aforementioned issues, this application proposes a DC line fault location method and system based on the frequency domain characteristics of port complex impedance. This method solves the problems of insufficient accuracy in DC line fault location under limited measurement point conditions, large errors in high-impedance faults, lack of quantitative basis for diagnostic frequency selection, and poor stability of nonlinear solutions. The specific details are as follows: On the one hand, this application proposes a DC line fault location method based on the frequency domain characteristics of port complex impedance, which realizes DC line fault location through the voltage and current signals of measurable ports, including the following steps: S1. Constructing the port complex impedance equivalent model under fault conditions: Using impedance propagation characteristics, define the fault distance, fault equivalent complex impedance, and equivalent impedance of the network behind the fault point. Through the transmission line impedance conversion relationship, establish a port theoretical input complex impedance model that simultaneously relates diagnostic frequency, fault distance, and fault complex impedance. The impedance propagation characteristics are characterized by frequency domain distributed parameters of the DC line. S2. Quantitative screening of multi-feature diagnostic frequency set: Define candidate frequency ranges, calculate the distance sensitivity and fault impedance sensitivity of each candidate frequency based on the sensitivity characteristics of port complex impedance to fault parameters, and screen out a feature diagnostic frequency set containing at least two frequency points by combining the numerical stability evaluation index of frequency combination. S3. Construct a multi-frequency weighted residual objective function: Apply multi-frequency low-amplitude diagnostic signals to the measurable port, simultaneously acquire the time-domain voltage and current signals of the port, extract the complex amplitude values ​​of voltage and current corresponding to each characteristic frequency, and calculate the complex impedance of the measured port. Based on the real and imaginary deviations between the theoretical and measured complex impedances at each characteristic frequency, a residual vector is constructed, and a frequency-divided weighting matrix is ​​introduced to establish a weighted least squares objective function. S4. Joint inversion solution of fault distance and fault complex impedance: Set the physical feasible region of fault parameters, select multiple sets of initial parameters within the feasible region and screen high-quality initial values ​​for iteration, use the damped iteration method to solve the minimum value of the objective function, impose physical boundary constraints on the parameters during the iteration process, and output the target fault distance and fault complex impedance after the convergence condition is met, thus completing the fault distance measurement of DC line.

[0009] Furthermore, the specific process of constructing the port theoretical input complex impedance model in S1 is as follows: Based on the resistance, inductance, capacitance, and conductance per unit length of the line as basic parameters, the series impedance per unit length and the parallel admittance per unit length are calculated, and the propagation constant and characteristic impedance of the line are further derived. The equivalent impedance of the back-end network at the fault point is connected in parallel with the equivalent complex impedance of the fault to obtain the parallel equivalent impedance of the fault point. By using the hyperbolic tangent form of the transmission line impedance conversion relationship, the parallel equivalent impedance of the fault point is converted to the measurable port, thus obtaining the theoretical input complex impedance of the port.

[0010] Understandably, if we define the resistance per unit length of the circuit as r, the inductance per unit length as l, the capacitance per unit length as c, and the conductance per unit length as g, then the diagnostic angular frequency is... If the imaginary unit is j, then the series impedance per unit length of the line is... Parallel admittance per unit length satisfy: ; In the formula, Indicates the angular frequency per unit length of the line. The series impedance below, Indicates the angular frequency per unit length of the line. Parallel admittance below.

[0011] The propagation constant of the line can be obtained from the above formula. and line characteristic impedance : ; In the formula, This represents the line propagation constant, used to characterize the amplitude attenuation and phase change of electrical disturbances propagating along the line at the ranging frequency; This represents the characteristic impedance of the line, used to characterize the inherent impedance characteristics of the line at that frequency.

[0012] Let the fault distance be The equivalent impedance of the network behind the fault point is The fault equivalent complex impedance is The parallel equivalent impedance at the fault point for: ; By using the hyperbolic tangent form of the transmission line impedance conversion relationship, the parallel equivalent impedance at the fault point is converted to the measurable port, thus obtaining the theoretical input complex impedance of the port. ; The expression for the theoretical input complex impedance of the port is: ; in, To diagnose angular frequency, The distance to the fault. The fault equivalent complex impedance, Let be the line propagation constant. The characteristic impedance of the line. The equivalent impedance in parallel to the fault point.

[0013] Furthermore, in S2, the process of quantifying and filtering the multi-feature diagnostic frequency set specifically involves: Define a fault parameter vector containing fault distance, fault impedance resistance component, and fault impedance reactance component, and construct a sensitivity matrix of port complex impedance to fault parameters for each candidate angular frequency; The average L2 norm of the partial derivative of the port complex impedance with respect to the fault distance is used as the distance sensitivity to characterize the degree of discernibility of the fault distance change at this frequency. The average L2 norm of the partial derivative of the port complex impedance with respect to the fault impedance is used as the fault impedance sensitivity to characterize the degree of interference of fault impedance fluctuation on ranging. The sensitivity matrices of multiple candidate frequencies are stacked to form a combined sensitivity matrix. The condition number of the combined matrix is ​​used as the numerical stability evaluation index of the frequency combination. The smaller the condition number, the stronger the solution stability. By considering factors such as distance sensitivity threshold, fault impedance interference level, measurement signal-to-noise ratio requirements, and numerical stability indicators, a set of characteristic diagnostic frequencies is obtained.

[0014] It is understandable that a fault parameter vector is defined. ; in, Represents the fault parameter vector. This represents the transpose of a vector. Indicates the distance to the fault. The resistive component representing the fault impedance. The reactive component representing the fault impedance; Regarding the first q candidate angular frequencies Construct the sensitivity matrix of port complex impedance to fault parameters. : ; in, Indicates at angular frequency and fault parameters The complex impedance sensitivity matrix under the following conditions Re[.] represents taking the partial derivative with respect to the fault parameter vector, where Re[.] represents taking the real part of the complex number and Im[.] represents taking the imaginary part of the complex number. The average L2 norm of the partial derivative of the port complex impedance with respect to the fault distance is used as the distance sensitivity. The degree of identifiability of changes in fault distance: ; in, Represents candidate angular frequency Fault impedance sensitivity under the following conditions This represents taking the partial derivative with respect to the fault impedance, where N is the total number of fault parameter samples. , For the fault distance and fault impedance of the nth sample group, It is a norm 2; The average L2 norm of the partial derivatives of the port complex impedance with respect to the fault impedance is used as the fault impedance sensitivity. This characterizes the degree of interference of fault impedance fluctuations on ranging. ; Where, in the formula, Represents candidate angular frequency Fault impedance sensitivity under the following conditions This represents taking the partial derivative with respect to the fault impedance; Combine the frequencies to be evaluated By stacking the sensitivity matrices of all frequencies within the range, a combined sensitivity matrix is ​​obtained. The average condition number of the matrix As a numerical stability evaluation index; Furthermore, the condition number of the combination matrix is ​​expressed as follows: ; in, This represents the average conditional evaluation value of frequency combinations. Indicates the first One fault parameter sample, Represents the matrix condition number. Represents frequency combination The corresponding combined sensitivity matrix, where N is the number of calculation samples selected within the allowable range of fault parameters.

[0015] Furthermore, the residual vector described in S3 is formed by sequentially concatenating the real and imaginary deviations corresponding to all characteristic frequencies; The weighting matrix is ​​a diagonal matrix, and the diagonal elements are the weighting coefficients corresponding to the real part deviation and the imaginary part deviation at each characteristic frequency. The weighting coefficients are dynamically determined based on the measurement signal-to-noise ratio, distance sensitivity and fault impedance sensitivity at the corresponding frequency points. The weighted least squares objective function is the weighted sum of squares of the residual vector, used to quantify the degree of matching between candidate fault parameters and measured port responses.

[0016] Furthermore, the damping iteration method in S4 employs damped Gauss-Newton iteration, the specific process of which is as follows: Calculate the Jacobian matrix of the residual vector of the current iteration step with respect to the fault parameters; Introducing a damping factor to construct an iterative correction equation, and adjusting the iteration step size by the damping factor: When the objective function decreases significantly, the damping factor is reduced to improve the convergence speed; when the objective function increases or oscillates, the damping factor is increased to enhance the iteration stability. Calculate the parameter correction amount and update the parameter vector. After each parameter update, constrain the parameters to the physical feasible region using the projection operator.

[0017] Let the first k The measured port complex impedance at each characteristic frequency is: Define the real part deviation between the theoretical complex impedance and the measured complex impedance at this frequency. Deviation from the imaginary part : ; In the formula, This indicates taking the real part of a complex number. This indicates taking the imaginary part of a complex number.

[0018] Concatenate the real and imaginary biases corresponding to all characteristic frequencies in sequence to construct the residual vector. : ; Construct a weighted matrix W in diagonal form: ; In the formula, Represents the residual weighting matrix. This represents a diagonal matrix consisting of the elements within the parentheses. Indicates the first The weighting coefficients for the real part deviation at the angular frequency of each feature diagnosis. Indicates the first The weighting coefficients for the imaginary part deviation at the angular frequency of the feature diagnosis.

[0019] Establish a weighted least squares objective function This is used to quantify the degree of matching between candidate fault parameters and measured port responses. ; In the formula, This represents the objective function for multi-frequency complex impedance residuals. This function simultaneously incorporates resistive and reactive biases at multiple characteristic diagnostic angular frequencies, used to evaluate the degree of matching between candidate fault parameters and the measured complex impedance.

[0020] It is understandable that the damping iteration method uses damped Gauss-Newton iteration, and the specific process is as follows: In the In this iteration, let the current parameter vector be... The residual vector is Define the Jacobian matrix. for: ; Furthermore, by introducing the damping factor and the identity matrix, an iterative correction equation is constructed. The expression for the correction equation is: ; in, Indicates the first The parameter adjustment amount for the next iteration. Represents the identity matrix. Indicates the first The Jacobian matrix of the residual vector to the fault parameter vector at the next iteration. Represents the residual weighting matrix. This represents the residual vector composed of the real and imaginary deviations of the complex impedance at all characteristic diagnostic angular frequencies. This represents the damping factor.

[0021] Adjusting the iteration step size by damping factor: When the objective function decreases significantly, reduce the damping factor to improve the convergence speed; when the objective function increases or oscillates, increase the damping factor to enhance the iteration stability. Parameter updates and boundary constraints are achieved using projection operators: ; in, Indicates the first The parameter vector after the nth iteration. Represents the parametric physical feasible region The projection operator is used to constrain parameters to a reasonable engineering range and avoid non-physical solutions.

[0022] Furthermore, the physical feasible domain mentioned in S4 includes the line length constraint of the fault distance and the reasonable range of engineering values ​​for the fault impedance resistance component and reactance component. The method for selecting the initial values ​​for iteration is as follows: generate multiple sets of initial parameters uniformly within the physical feasible region, calculate the objective function value corresponding to each set, and select the sets with the smallest objective function value as the initial values ​​for iteration. The convergence criteria include the objective function threshold, the parameter correction threshold, and the maximum number of iterations. The iteration terminates when any one of these conditions is met. If multiple sets of initial values ​​yield multiple feasible solutions, the solution with the smallest objective function value is selected as the final output.

[0023] The physical feasible region Represented as: ; In the formula, and These represent the lower and upper limits of the fault impedance resistive component, respectively. and These represent the lower and upper limits of the reactive component of the fault impedance, respectively. If the fault impedance is in purely resistive form, then the reactive component can be removed. The range of values ​​is constrained.

[0024] The method for selecting the initial values ​​for iteration is as follows: generate multiple sets of initial parameters uniformly within the physical feasible region, calculate the objective function value corresponding to each set, and select the sets with the smallest objective function value as the initial values ​​for iteration. The convergence criterion terminates the iteration if any of the following conditions are met: ; in, This represents the convergence threshold of the objective function. This represents the convergence threshold for the parameter correction. Indicates the maximum number of iterations. Represents the L2 norm; If multiple sets of initial values ​​yield multiple feasible solutions, the solution with the smallest objective function value is selected as the final output.

[0025] Furthermore, the fault equivalent complex impedance includes a resistive component and a reactive component, which are used to uniformly characterize transition resistance faults, arc faults, insulation degradation faults, and faults with stray capacitance coupling. When the fault path exhibits pure resistive characteristics, the reactance component is set to zero, and the fault equivalent complex impedance degenerates into a pure fault resistance form.

[0026] On the other hand, this application proposes a DC line fault location system based on port complex impedance frequency domain characteristics, including a signal injection module, a signal acquisition module, a parameter storage module, a frequency optimization module, a modeling and calculation module, a joint inversion module, and a result output module; The signal injection module is used to output multi-frequency low-amplitude diagnostic signals to the measurable port of the DC line; The signal acquisition module is used to synchronously acquire the time-domain voltage and current signals of the measurable port; The parameter storage module is used to store DC line distributed parameters, fault parameter physical boundaries, convergence thresholds, and maximum number of iterations; The frequency optimization module is used to execute the feature diagnosis frequency set screening process described in S2; The modeling and calculation module is used to execute the port complex impedance modeling, measured complex impedance calculation and multi-frequency weighted objective function construction process described in S1 and S3; The joint inversion module is used to execute the joint damping iterative solution process of fault distance and fault complex impedance described in S4; The result output module is used to output the final fault distance and fault equivalent complex impedance results.

[0027] In summary, the DC line fault location method and system based on port complex impedance frequency domain characteristics of the present invention have the following advantages compared with traditional technologies: 1. This invention utilizes the frequency domain characteristics of measurable port complex impedance for fault location, which can adapt to application conditions where measurement points are limited in some DC power systems. This method converts the voltage and current responses of measurable ports into port complex impedance information and establishes the electrical relationship between port complex impedance and fault distance, reducing reliance on multi-point synchronous measurement and remote communication information, and improving the applicability of fault location under limited measurement conditions. 2. This invention incorporates fault impedance into the fault location model, enabling a more comprehensive characterization of the impact of the fault channel on the measurement end response. For fault scenarios involving factors such as transition resistance, arcing, insulation degradation, stray capacitance, and branch coupling, the fault channel may exhibit complex impedance characteristics at the location frequency. This invention uses a port complex impedance equation to simultaneously describe the effects of fault distance and fault impedance on the measurement response, helping to reduce the impact of fault impedance variations on the location results. 3. This invention determines the characteristic frequency based on the frequency domain response characteristics of the port complex impedance, which can improve the matching between the ranging frequency and the fault ranging task. Compared with signal diagnostic methods that use fixed or empirical frequencies, this invention comprehensively considers fault distance sensitivity, fault impedance influence, and measurement stability, and selects a more suitable ranging frequency for fault ranging, thereby improving the solvability and solution stability of the ranging equation; 4. This invention employs a joint inversion method of fault distance and fault impedance, which can improve the solution stability of the nonlinear fault location equation. Through residual vector construction, weighted objective function, initial value selection, damping iteration, and physical boundary projection, the solution results meet the requirements of the line length range and the physical range of the fault channel, which helps to avoid non-physical solutions and locally unstable solutions, and improves the engineering applicability of DC line fault location.

[0028] The technical method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0029] Figure 1 This is the equivalent model of port impedance for DC line fault conditions in this invention. Figure 2 This is a schematic diagram illustrating the selection of characteristic frequencies in this invention; Figure 3 This is a complete flowchart of the fault location method of the present invention; Figure 4 This is the simulation model for the present invention. Detailed Implementation

[0030] The technical method of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application.

[0031] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the scope of this application and its application or use.

[0032] Techniques, systems, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the instruction manual.

[0033] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0034] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0035] This invention addresses the fault location requirements of DC power system lines, focusing on changes in the line's electrical structure, port complex impedance response characteristics, and the relationship for fault distance calculation under fault conditions. After a fault occurs, line parameters, system-side equivalent impedance, and the faulted branch collectively influence the frequency domain response at the measurable port. Fault distance and fault transition impedance can be characterized by changes in port complex impedance. Based on this, this invention establishes an equivalent characterization of port impedance under fault conditions, constructs a fault location model under multi-frequency complex impedance constraints, determines characteristic frequencies suitable for fault location calculation, and obtains the line fault location through joint inversion of fault distance and transition impedance.

[0036] Example 1 This embodiment provides the construction process of a DC line fault location method based on the frequency domain characteristics of port complex impedance.

[0037] 1. Equivalent characterization of port impedance under DC line fault conditions.

[0038] When a line fault occurs in a DC power system, an additional fault branch forms at the fault point, changing the original impedance distribution of the line and the equivalent electrical characteristics at the measurable ports. This change is related to the line length from the measurable port to the fault point, the equivalent impedance of the fault branch, and the equivalent impedance of the line and related electrical units on the other side of the fault point at the ranging frequency. To characterize these electrical relationships, the DC line under fault conditions can be represented as follows: Figure 1 The port impedance equivalent model is shown.

[0039] Figure 1 middle, This represents the time-domain voltage signal acquired at the measurable port. This represents the time-domain current signal acquired at the measurable port. This represents the complex input impedance as seen from the measurable port into the faulty line. The total length of the line is denoted as... ,in This represents the physical length of the DC line under test. Distance coordinates are established along the line direction. ,in This represents the distance from any point on the line to the measurable port. The fault occurred at a distance from the measurable port. place, Indicates the distance to the fault and satisfies The branch extending outward from the fault point is called the faulty branch, and its equivalent impedance is denoted as... . The equivalent impedance of the fault path at the ranging frequency represents the combined effect of factors such as fault transition resistance, arc impedance, grounding dielectric impedance, inter-electrode short-circuit impedance, or insulation degradation path. The equivalent impedance of the lines, load branches, busbar-side equipment, power conversion devices, and related electrical units on the other side of the fault point, referred to the fault point, is denoted as... ,in Indicates the diagnostic angular frequency. It reflects the impact of the network on the other side of the fault point on the electrical state of the fault point at the ranging frequency.

[0040] At ranging frequency Below, the angular frequency satisfies DC lines can be described using frequency-dependent line parameters. Let... , , , These represent the resistance per unit length, inductance per unit length, capacitance per unit length, and conductance per unit length of the circuit, respectively. If the imaginary unit is used, then the series impedance per unit length of the line is... and unit length parallel admittance They are represented as follows: .

[0041] In the formula, Indicates the angular frequency per unit length of the line. The series impedance below, Indicates the angular frequency per unit length of the line. The parallel admittance is given by equation (1). The line propagation constant can be obtained from equation (1). and line characteristic impedance : .

[0042] In the formula, This represents the line propagation constant, used to characterize the amplitude attenuation and phase change of electrical disturbances propagating along the line at the ranging frequency; This represents the characteristic impedance of the line, used to characterize the inherent impedance characteristics of the line at that frequency. For short- to medium-distance DC lines, several methods can be used depending on the engineering accuracy requirements. Equivalent unit cascade description; for long-distance lines or lines with significant frequency response changes, the frequency domain propagation characteristics can be described using the distributed parameter form shown in equations (1) and (2).

[0043] according to Figure 1 The equivalent relationship shown indicates that the fault point is caused by... impedance of the faulty branch Forming a parallel equivalent impedance, denoted as Its expression is: .

[0044] In the formula, This represents the parallel equivalent impedance formed at the fault point by the faulty branch and the equivalent network on the other side of the fault point. This equivalent impedance is equal to the length between the measurable port and the fault point. The line segments together determine the input impedance of the measurable port.

[0045] The fault input impedance at the port can be measured using the line impedance conversion relationship. Represented as: .

[0046] In the formula, Let represent the hyperbolic tangent function. Equation (4) shows that the input impedance of the measurable port is determined by the diagnostic angular frequency. Fault distance and fault impedance Jointly decided. Fault distance Change the line impedance conversion relationship between the measurable port and the fault point, fault impedance By altering the strength of the faulty branch's participation in current distribution, the angular frequency can be diagnosed. The combined effect of line resistance, inductance, capacitance, and conductance in the frequency domain is determined. Therefore, It can simultaneously characterize the fault location and the fault channel status.

[0047] For DC power systems with multiple DC lines or branch structures, the impedance of each line segment can be calculated segment by segment according to the line connection relationship, and the equivalent network on the other side of the fault point can be uniformly represented as follows: For systems containing power conversion devices, filter capacitors, load branches, or protection branches, they can be expressed as the corresponding equivalent impedance at the ranging frequency and incorporated into the system. Under this characterization, the input impedance of the measurable port under fault conditions remains a complex function of the diagnostic angular frequency, fault distance, and fault impedance.

[0048] 2. Complex impedance frequency domain response and fault location equation.

[0049] Under fault conditions, the input impedance of the measurable port can be measured. The diagnostic angular frequency has been represented by equation (4). Fault distance and fault impedance The complex-valued function of the fault location equation reflects the port frequency domain response after considering the impedance reduction of the line upstream of the fault point, the electrical state of the fault branch, and the equivalent network on the other side of the fault point. The goal of constructing the fault location equation is to establish the correspondence between the theoretical port complex impedance and the actual port complex impedance, so that the fault distance and fault impedance can be characterized by the port frequency domain response.

[0050] Let at any diagnostic angular frequency Below, the actual measurable port complex input impedance is: ,in Indicates diagnostic angular frequency The corresponding measured complex impedance. Based on the equivalent port impedance under fault conditions, the theoretical complex impedance... With measurement of complex impedance The following fault location equation applies between them: .

[0051] In the formula, This represents the theoretical port complex impedance calculated from line parameters, fault distance, and fault impedance. This represents the complex impedance of the measured port obtained at the same diagnostic angular frequency. Equation (5) indicates the fault distance. and fault impedance A correspondence is established between the port complex impedance and the measurement results. The port complex impedance at the ranging frequency contains both resistive and reactive components, reflecting the combined effects of line resistance, inductance, capacitance, conductance, and faulty branches in the frequency domain.

[0052] In DC line faults, the fault path is typically described by transition resistance in steady-state DC analysis; however, under the influence of the ranging frequency, the fault path may exhibit more general frequency-domain equivalent characteristics. If factors such as arcing, stray capacitance to ground, insulation polarization, converter filter branch coupling, and line capacitor discharge paths exist in the fault path, then the fault point may present as a complex impedance at the ranging frequency. To maintain the model's adaptability to different fault path states, the fault impedance... It can be represented as: .

[0053] In the formula, The resistive component representing the fault impedance is used to characterize the energy dissipation characteristics of the fault path. The reactance component, representing the fault impedance, characterizes the equivalent reactance of the fault path at the ranging frequency caused by arc dynamics, dielectric polarization, stray capacitance, filter branch coupling, or line capacitance discharge. When the fault path primarily exhibits resistive characteristics within the ranging frequency range... It can be taken as zero, at this time It degenerates into a fault resistor.

[0054] Since equation (5) is a complex equation, it can be decomposed into a real part equation and an imaginary part equation. Let... This represents the real part deviation between the theoretical port complex impedance and the measured port complex impedance. To represent the imaginary part of the deviation between the two, we have: .

[0055] In the formula, This indicates taking the real part of a complex number. This indicates taking the imaginary part of a complex number. Real part deviation. It mainly reflects the influence of line resistance components, fault path energy consumption characteristics, and the system's equivalent active power path on the port complex impedance; imaginary part deviation It mainly reflects the influence of line inductance, capacitance, fault path reactance characteristics, and energy storage characteristics of related electrical units on the port complex impedance. The real and imaginary equations together characterize the positional shift of the port complex impedance in the complex plane under fault conditions.

[0056] Under ideal model and no measurement error conditions, fault distance With fault impedance Both the real and imaginary deviations should be zero, that is: .

[0057] Equation (8) is the diagnostic angular frequency. The following complex impedance fault location equation relates fault distance, fault path state, and port complex impedance response. Wherein, fault distance... The effect is caused by changing the line impedance conversion relationship between the measurable port and the fault point. Fault impedance By altering the current distribution of the faulty branch and the equivalent electrical state at the fault point, the influence is... .

[0058] Considering the voltage and current sampling errors, amplitude and phase extraction errors, line parameter deviations, and system equivalent parameter disturbances in actual engineering, equation (8) is usually difficult to strictly satisfy. To quantify the degree of deviation between the theoretical complex impedance and the measured complex impedance, a diagnostic angular frequency can be defined. Complex impedance residual function : .

[0059] In the formula, Indicates diagnostic angular frequency Complex impedance residual function under the given conditions; Weighting coefficients representing the deviation of the real part; This represents the weighting factor for the imaginary part bias. The weighting factor is used to balance the differences between the real and imaginary parts in terms of numerical scale, measurement reliability, and fault distance sensitivity. When the measurement accuracy and magnitude of the real and imaginary parts are similar, and The same value can be taken; when a certain component has a higher ability to identify changes in fault distance, the weight of that component can be increased accordingly.

[0060] By repeatedly establishing the relationships shown in equations (5) to (9) at different diagnostic angular frequencies, multiple sets of complex impedance ranging equations can be obtained. Due to the fault distance... For the same fault state, the fault remains unique, while the port complex impedance exhibits different real and imaginary responses as the diagnostic angular frequency changes. Multiple sets of frequency domain equations can characterize the same fault location from different electrical perspectives. Therefore, the frequency domain response of the complex impedance provides a mathematical basis for the joint solution of fault distance and fault impedance.

[0061] 3. Selection of characteristic frequencies for ranging sensitivity and solution stability.

[0062] The determination of the characteristic frequency directly affects the solvability, sensitivity, and noise immunity of the complex impedance fault location equation. DC lines exhibit different port impedance response characteristics at different location frequencies. In the lower frequency range, the port complex impedance is easily affected by DC bus capacitance, load branch changes, power conversion device control loops, and system operating point variations; in the higher frequency range, line parasitic parameters, measurement noise, signal attenuation, and high-frequency characteristics of equipment interfaces are enhanced. The characteristic frequency used for fault location should ensure that the port complex impedance has sufficient sensitivity to fault distance, while guaranteeing stable amplitude and phase characteristics in the voltage and current responses.

[0063] To limit the frequency search range, let the candidate range for ranging frequencies be denoted as . ,in Indicates the lower limit of candidate ranging frequencies. This represents the upper limit of candidate ranging frequencies. Based on the relationship between angular frequency and frequency, the set of candidate angular frequencies is... It can be represented as: .

[0064] In the formula, Represents the set of candidate angular frequencies. Indicates the first One candidate angular frequency, Indicates the first Candidate frequencies, Indicates the candidate frequency point number. This indicates the total number of candidate frequency points. The candidate frequency range can be determined based on the output capability of the diagnostic device, the voltage and current sampling bandwidth, the line frequency domain response range, and the permissible disturbance level of the equipment.

[0065] To characterize the degree of change in port complex impedance with respect to fault parameters, a fault parameter vector is defined. for: .

[0066] In the formula, Represents the fault parameter vector. This represents the transpose of a vector. Indicates the distance to the fault. The resistive component representing the fault impedance. This represents the reactive component of the fault impedance. If the fault path primarily exhibits resistive characteristics within the ranging frequency range, then it can be set as follows: At this point, the fault parameter vector can be simplified to... and The two-dimensional vector formed.

[0067] In candidate angular frequency Below, the local response of the port complex impedance to fault parameters can be derived from the sensitivity matrix. express: .

[0068] In the formula, Indicates at angular frequency and fault parameters The complex impedance sensitivity matrix under the following conditions This represents the partial derivative with respect to the fault parameter vector. Each column of this matrix describes the response of the real and imaginary parts of the port complex impedance to changes in fault distance, fault resistance component, and fault reactance component, respectively. The value of the sensitivity matrix can be obtained by analytical differentiation or calculated using the finite difference method according to equation (4).

[0069] To highlight the impact of fault distance on the ranging equation, distance sensitivity is defined. for: .

[0070] In the formula, Represents candidate angular frequency Distance sensitivity at the following levels This indicates the number of calculation samples selected within the allowable range of fault parameters. Indicates the first The fault distance corresponding to each sample Indicates the first The fault impedance corresponding to each sample This represents the L2 norm. The larger the value, the more pronounced the response of the port complex impedance to changes in fault distance at that frequency.

[0071] The effect of fault impedance on the port complex impedance also affects the stability of the ranging equation. To characterize the role of fault impedance variation in the complex impedance response, a fault impedance sensitivity is defined. for: .

[0072] In the formula, Represents candidate angular frequency Fault impedance sensitivity under the following conditions This represents taking the partial derivative with respect to the fault impedance. When use When expressed, equation (14) can be used for respectively and The partial derivatives are calculated, and the corresponding sensitivities are synthesized for evaluation. This parameter is used to determine whether changes in fault impedance at the candidate frequency will significantly affect the fault distance solution.

[0073] Characteristic frequencies should also avoid providing highly similar equation information. If the directions of complex impedance changes are similar across multiple candidate frequencies, the resulting ranging equations may form similar error distributions in the parameter space, reducing the joint distinguishing ability of fault distance and fault impedance. To evaluate the equation independence of candidate frequency combinations, let a frequency combination consisting of several candidate angular frequencies be... ,in This represents the combination of diagnostic angular frequencies to be evaluated. Indicates the first in the combination angular frequency, Indicates the frequency index within the combination. This indicates the number of frequency points within the combination. The combined sensitivity matrix is ​​obtained by superimposing the sensitivity matrices at each frequency row by row. : .

[0074] In the formula, Represents frequency combination The corresponding combined sensitivity matrix. This matrix simultaneously contains the real and imaginary parts of the complex impedance at multiple ranging frequencies in response to changes in fault parameters. The lower the column correlation of the combined sensitivity matrix, the stronger the ability of the ranging equation to distinguish different fault parameters.

[0075] To characterize the solution stability of frequency combinations, a conditional evaluation quantity can be defined. for: .

[0076] In the formula, Represents frequency combination The average conditional evaluation quantity, Indicates the first One fault parameter sample, Represents the matrix condition number. Smaller... This indicates that the ranging equation corresponding to this frequency combination has better numerical stability and can reduce the impact of parameter coupling and measurement disturbance on the fault distance solution.

[0077] In the candidate frequency selection process, distance sensitivity, fault impedance sensitivity, measurement stability, and combined condition evaluation quantities are comprehensively considered. Specifically, candidate frequencies or frequency combinations that meet the following conditions are retained: the port complex impedance has sufficient sensitivity to fault distance; both the real and imaginary parts of the response have identifiable changes at the selected frequency; the amplitudes of the port voltage and current responses meet the measurement requirements; and the condition evaluation quantities corresponding to the frequency combinations are within the allowable range. The characteristic frequency set determined in this way is denoted as […]. : .

[0078] In the formula, This represents the set of characteristic diagnostic angular frequencies ultimately used for fault location. Indicates the first One characteristic for diagnosing angular frequency, , This represents the number of characteristic diagnostic angular frequencies. To ensure sufficient equation information for fault distance and fault impedance, it is typically taken as... When the fault impedance is expressed in complex form and solved simultaneously and When solving for stability, the number of characteristic frequencies can be increased.

[0079] Figure 2 A schematic diagram of the characteristic frequency selection process is provided. Figure 2 In the middle, the horizontal axis represents the ranging frequency. The low-frequency region is mainly affected by changes in the operating point, control circuit, and load branch, while the high-frequency region is mainly affected by parasitic parameters, measurement noise, and signal attenuation. The intermediate region corresponds to the frequency range where the port complex impedance has a significant response to fault distance and exhibits good measurement stability. Distance sensitivity can also be plotted in the figure. Fault impedance sensitivity The distribution of candidate frequency points is also shown, and the final selected set of feature frequencies is represented by solid markers. .

[0080] 4. Joint inversion method of fault distance and fault impedance.

[0081] Determining the set of characteristic diagnostic angular frequencies Then, the voltage and current frequency domain responses at the corresponding frequencies can be obtained at the measurable ports, and the fault distance and fault impedance can be jointly inverted based on the complex impedance ranging equation. Let... ,in Represents the set of characteristic diagnostic angular frequencies. Indicates the first One characteristic for diagnosing angular frequency, Indicates the index of the characteristic frequency point. This indicates the number of characteristic frequencies participating in the joint inversion. After the system enters the fault diagnosis state, a low-amplitude diagnostic signal is applied to the measurable port, and the port voltage signal is acquired simultaneously. and port current signal .right and After extracting the same-frequency components, the characteristic diagnostic angular frequency can be obtained. voltage complex amplitude under and current complex amplitude .

[0082] exist At this location, the complex impedance can be measured at the port. Represented as: .

[0083] In the formula, Indicates the measurable port voltage at The following complex amplitude value, Indicates the measurable port current at The following complex amplitude value, This represents the measured complex impedance calculated from the port voltage and current response. The diagnostic signal can be a frequency-sequential sinusoidal signal, a swept-frequency signal, or a multi-frequency combination signal, and its amplitude must meet the requirements of the diagnostic device's output capability, system insulation safety margin, and measurement signal-to-noise ratio.

[0084] The fault parameter vector defined by equation (11) is used. and will Substituting into the port input impedance expression shown in equation (4), a complex impedance residual vector can be constructed at all characteristic frequencies. Based on the real and imaginary deviations defined in equation (7), the residual vector is constructed at all characteristic frequencies. : .

[0085] In the formula, This represents the residual vector composed of the real and imaginary deviations of the complex impedance at all characteristic diagnostic angular frequencies. Each term in the residual vector is derived from the theoretical port complex impedance. With measurement port complex impedance The difference is determined. This residual vector unifies the resistive and reactive deviations at different frequencies into the same parameter space, and is used to characterize the degree of consistency between the candidate fault distance and candidate fault impedance and the measured port frequency domain response.

[0086] To balance the numerical scale, measurement reliability, and fault distance sensitivity at different frequency points and with different impedance components, a weighting matrix is ​​introduced. The weighted matrix can be represented as: .

[0087] In the formula, Represents the residual weighting matrix. This represents a diagonal matrix consisting of the elements within the parentheses. Indicates the first The weighting coefficients for the real part deviation at the angular frequency of each feature diagnosis. Indicates the first The weighting coefficients for the imaginary part deviation at the characteristic diagnostic angular frequency are determined based on the measurement signal-to-noise ratio, complex impedance amplitude scale, distance sensitivity, and fault impedance sensitivity. When the real or imaginary part at a certain frequency point exhibits a strong response to changes in fault distance and good measurement stability, the corresponding weight can be increased; conversely, when a certain frequency point is significantly affected by noise, attenuation, or parameter uncertainty, the corresponding weight can be decreased.

[0088] Joint inversion objective function of fault distance and fault impedance Defined as: .

[0089] In the formula, This represents the objective function for multi-frequency complex impedance residuals. This function simultaneously incorporates resistive and reactive biases at multiple characteristic diagnostic angular frequencies, used to evaluate the matching degree between candidate fault parameters and the measured complex impedance. The solution for the fault parameters can be expressed as: .

[0090] In the formula, This represents the fault parameter solution vector. Represents the physical feasible region of the parameters. This represents the parameter values ​​that minimize the objective function. The physical feasible region of the parameters. It can be represented as: ).

[0091] In the formula, and These represent the lower and upper limits of the fault impedance resistance component, respectively. and These represent the lower and upper limits of the reactive component of the fault impedance, respectively. If the fault impedance is in purely resistive form, then the reactive component can be removed. The range of values ​​is constrained. The physical feasible region of the parameters is used to ensure that the solution results meet the requirements of the DC line length range and the electrical characteristics of the fault path.

[0092] To improve the solution stability of the nonlinear ranging equation, a joint solution method of "initial value screening—damped iteration—physical boundary projection" can be adopted. First, in the parametric physical feasible region... Several initial candidate points are set, and the objective function corresponding to each candidate point is calculated. Several parameters with smaller residuals are selected as initial values ​​for iteration. This approach reduces the impact of local extrema and parameter coupling of the complex impedance equation on the inversion process, resulting in better initial stability for the joint solution of fault distance and fault impedance.

[0093] In the In this iteration, let the current parameter vector be... The residual vector is Define the Jacobian matrix. for: .

[0094] In the formula, Indicates the first The Jacobian matrix of the residual vector with respect to the fault parameter vector at the next iteration can be calculated analytically or using finite difference methods. To improve the numerical stability of the nonlinear iterative process, a damping factor is introduced. ,in Indicates the first Damping adjustment coefficient in the next iteration. Parameter correction amount. It can be obtained from the following formula: .

[0095] In the formula, Indicates the first The parameter adjustment amount for the next iteration. Represents the identity matrix. Damping factor. Used to adjust the iteration step size. When the objective function decreases significantly, it can be reduced. To improve the convergence speed; when the objective function does not decrease sufficiently or increases, it can be increased. To enhance iterative stability.

[0096] The parameter iteration process is represented as: .

[0097] In the formula, Indicates the first The parameter vector after the nth iteration. Represents the parametric physical feasible region The projection operator ensures that the fault distance does not exceed the line length range and that the fault impedance is within a preset physical range. By projecting onto the physical boundary, negative distances, distances exceeding the line length, or impedance values ​​that do not conform to the physical characteristics of the fault path can be avoided during the iteration process.

[0098] The convergence criterion for the iterative process can be determined jointly by the changes in residuals and parameters. The joint inversion process can be considered convergent when one of the following conditions is met: .

[0099] In the formula, This represents the convergence threshold of the objective function. This represents the convergence threshold for the parameter correction. Indicates the maximum number of iterations. This represents the L2 norm. In practical applications, it can be set in conjunction with the measured noise level, line parameter errors, and the accuracy of complex impedance calculations. and .

[0100] If multiple initial points yield multiple candidate solutions, then the selection is based on the objective function value, the physical range of the parameters, and the multi-frequency residual distribution. For candidate solutions... and If both satisfy the physical range requirements, the solution with the smaller objective function is preferred as the result of the fault parameter solution. The final output fault distance and fault impedance can be expressed as: .

[0101] In the formula, This represents the fault parameter solution vector. This indicates the result of the fault distance calculation. This represents the result of solving for the resistance component of the fault impedance. This represents the result of solving the fault impedance reactance component. This represents the result of the fault impedance solution.

[0102] The joint inversion process of fault distance and fault impedance in this invention can be used Figure 3 express. Figure 3 In the process, the diagnostic process begins with the switching between fault detection and diagnostic states, and includes, in sequence, reading line parameters and characteristic frequencies, applying diagnostic signals to measurable ports, acquiring voltage and current responses, calculating complex impedances, constructing residual vectors, generating initial candidate points, solving damping iteratively, projecting parameters into the physical domain, determining convergence, and outputting fault parameters. Figure 3 In Represents the set of characteristic diagnostic angular frequencies. Indicates the first Measurement of complex impedance at characteristic frequencies This represents the objective function for multi-frequency complex impedance residuals. and These represent the output results for fault distance and fault impedance, respectively.

[0103] Example 2 To verify the DC line fault location method based on the frequency domain characteristics of port complex impedance proposed in this invention, a method as follows is constructed: Figure 4The DC line verification model shown is composed of a power supply measurement terminal, three series-connected DC lines, three grounded load nodes, and measurement points. The measurement points are located at the power supply measurement terminal outlet and are used to obtain the port voltage and current response under distance measurement conditions and to calculate the port input impedance. Figure 4 middle, Indicates the total length of the DC line. , , These represent the line lengths between adjacent nodes. The three load nodes are grounded through load branches to form a DC line structure with multi-load distribution characteristics.

[0104] The total length of the verification line is The lengths of each line segment are as follows: , , ,satisfy The line is described using a distributed parameter transmission line model. Let... , , , These represent the resistance, inductance, capacitance, and conductance per unit length of the line, respectively, and their values ​​are shown in Table 1. These parameters are used to calculate the line propagation constant and characteristic impedance at different ranging frequencies, thereby obtaining the port complex impedance response.

[0105] Table 1 System Parameters

[0106] The three load nodes are located at , and To illustrate the impact of load distribution on port impedance in a DC line, all three loads are represented as grounded equivalent impedances. The impedance of the first load is... The second load impedance is The third load impedance is .in, , , These represent the equivalent load resistances of the first, second, and third load nodes, respectively. In this verification, the load is presented in resistive form to highlight the impact of line distributed parameters and fault impedance on the ranging results.

[0107] Fault Distance This represents the line distance from the fault location to the power supply measurement terminal outlet measurement point, and its value range satisfies... The fault path uses the equivalent fault impedance. It means that among them , Represents the fault impedance resistance component. This represents the reactance component of the fault impedance. To verify the applicability of the method under different fault locations and fault impedance conditions, [the following parameters are selected]. , , and Four fault distances, and settings for each fault distance. , and Three fault impedances were used to form 12 verification conditions. This condition setting can simultaneously reflect the impact of changes in fault distance and fault channel impedance on the port complex impedance ranging results.

[0108] The ranging frequency is determined by calculating the frequency domain response of the complex impedance at the line port. In the simulation, first... The input impedance of the scanning port within the range was analyzed, and the sensitivity of the port complex impedance to fault distance and fault impedance at different frequencies was calculated. The calculation results show that at lower frequencies, the port complex impedance's ability to distinguish changes in fault distance is relatively limited; at higher frequencies, the response changes caused by line distributed parameters are enhanced, but at excessively high frequencies, the port response becomes more sensitive to measurement errors and parameter disturbances. Considering the combined evaluation of distance sensitivity, fault impedance sensitivity, and frequency combination conditions, the suitable frequency range for fault location in this verification model is determined to be [frequency range to be filled in]. .

[0109] Within the aforementioned ranging frequency range, further selection , , These frequencies serve as characteristic ranging frequencies for the joint inversion of fault distance and fault impedance. They cover the low-frequency, mid-frequency, and higher-frequency portions of the effective ranging range, providing information on the real and imaginary parts of the port complex impedance from different frequency domain response perspectives, thereby improving the stability of the fault distance solution. In the simulation, the port complex impedance at the measurement point is calculated from the voltage and current responses at the aforementioned three characteristic ranging frequencies.

[0110] When calculating the complex impedance at the port, each segment of the DC line is modeled using a distributed parameter transmission line. For a length of... The Section of the line, among which Its input impedance is determined by the line propagation constant, characteristic impedance, and the equivalent impedance of the load branch or subsequent line connected to the end of the segment. The port input impedance of the line before the fault can be obtained by segment-by-segment calculation from the end load node to the power measurement terminal; when the fault is located within any line segment, the fault branch... The corresponding fault location is incorporated, and the port input impedance under fault conditions is obtained according to the same transmission line conversion relationship. Thus, the model is verified to reflect the combined effects of distributed parameters, load distribution, and fault impedance on the port complex impedance of long-distance DC lines.

[0111] Table 2 Fault location results under different fault conditions

[0112] As shown in Table 2, in the 100km DC line verification model, the proposed method can obtain effective distance measurement results under different fault distances and different fault impedances, and the relative error of the fault distance is within the acceptable range. Within the range. The maximum error occurs when... , The high-impedance condition at the far end conforms to the electrical principle that the response attenuation of a far-end fault is more significant, and the impact of a high-impedance fault on the port complex impedance is weaker. Results at the same fault distance show that the overall ranging error increases with increasing fault impedance; similarly, the ranging error also increases as the fault location moves from the near end to the far end. These results indicate that both fault distance and fault impedance affect the port complex impedance ranging results, and incorporating both into the joint inversion process helps reduce the ranging deviation caused by changes in a single parameter.

[0113] Example 3 To further verify the numerical stability of the joint inversion process, the damping iteration process of 12 operating conditions was statistically analyzed. All operating conditions met the convergence criterion, with the number of iterations ranging from 5 to 13, and an average of 8.6 iterations. The near-end low-resistance operating condition converged faster, while the far-end high-resistance operating condition, due to the weaker response of the port complex impedance to changes in fault parameters, had a relatively higher number of iterations, but still managed to converge stably within the maximum number of iterations. The objective function showed an overall decreasing trend during the iteration process, without exhibiting long-term oscillations or divergence.

[0114] Example 4 This embodiment proposes a DC line fault location system based on the frequency domain characteristics of port complex impedance, including a signal injection module, a signal acquisition module, a parameter storage module, a frequency optimization module, a modeling and calculation module, a joint inversion module, and a result output module; The signal injection module is used to output multi-frequency low-amplitude diagnostic signals to the measurable port of the DC line; The signal acquisition module is used to synchronously acquire the time-domain voltage and current signals of the measurable port; The parameter storage module is used to store DC line distributed parameters, fault parameter physical boundaries, convergence thresholds, and maximum number of iterations; The frequency optimization module is used to execute the feature diagnosis frequency set screening process described in S2; The modeling and calculation module is used to execute the port complex impedance modeling, measured complex impedance calculation and multi-frequency weighted objective function construction process described in S1 and S3; The joint inversion module is used to execute the joint damping iterative solution process of fault distance and fault complex impedance described in S4; The result output module is used to output the final fault distance and fault equivalent complex impedance results.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical methods of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical methods of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical methods to deviate from the spirit and scope of the technical methods of the present invention.

Claims

1. A DC line fault location method based on port complex impedance frequency domain characteristics, characterized in that, Includes the following steps: S1. Constructing the port complex impedance equivalent model under fault conditions: Using impedance propagation characteristics, define the fault distance, fault equivalent complex impedance, and equivalent impedance of the network behind the fault point. Through the transmission line impedance conversion relationship, establish a port theoretical input complex impedance model that simultaneously relates diagnostic frequency, fault distance, and fault complex impedance. The impedance propagation characteristics are characterized by frequency domain distributed parameters of the DC line. S2. Quantitative screening of multi-feature diagnostic frequency set: Define candidate frequency ranges, calculate the distance sensitivity and fault impedance sensitivity of each candidate frequency based on the sensitivity characteristics of port complex impedance to fault parameters, and screen out a feature diagnostic frequency set containing at least two frequency points by combining the numerical stability evaluation index of frequency combination. S3. Construct a multi-frequency weighted residual objective function: Apply multi-frequency low-amplitude diagnostic signals to the measurable port, simultaneously acquire the time-domain voltage and current signals of the port, extract the complex amplitude values ​​of voltage and current corresponding to each characteristic frequency, and calculate the complex impedance of the measured port. Based on the real and imaginary deviations between the theoretical and measured complex impedances at each characteristic frequency, a residual vector is constructed, and a frequency-divided weighting matrix is ​​introduced to establish a weighted least squares objective function. S4. Joint inversion solution of fault distance and fault complex impedance: Set the physical feasible region of fault parameters, select multiple sets of initial parameters within the feasible region and screen high-quality initial values ​​for iteration, use the damped iteration method to solve the minimum value of the objective function, impose physical boundary constraints on the parameters during the iteration process, and output the target fault distance and fault complex impedance after the convergence condition is met, thus completing the fault distance measurement of DC line.

2. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The specific process of constructing the port theory input complex impedance model in S1 is as follows: Based on the resistance, inductance, capacitance, and conductance per unit length of the line as basic parameters, the series impedance per unit length and the parallel admittance per unit length are calculated, and the propagation constant and characteristic impedance of the line are further derived. The equivalent impedance of the back-end network at the fault point is connected in parallel with the equivalent complex impedance of the fault to obtain the parallel equivalent impedance of the fault point. By using the hyperbolic tangent form of the transmission line impedance conversion relationship, the parallel equivalent impedance at the fault point is converted to the measurable port, yielding the theoretical input complex impedance of the port. The expression for the theoretical input complex impedance of the port is: ； in, To diagnose angular frequency, The distance to the fault. The fault equivalent complex impedance, Let be the line propagation constant. The characteristic impedance of the line. The equivalent impedance in parallel to the fault point.

3. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The specific process of quantitatively screening the multi-feature diagnostic frequency set in S2 is as follows: Define a fault parameter vector containing fault distance, fault impedance resistance component, and fault impedance reactance component, and construct a sensitivity matrix of port complex impedance to fault parameters for each candidate angular frequency; The average L2 norm of the partial derivative of the port complex impedance with respect to the fault distance is used as the distance sensitivity to characterize the degree of discernibility of the fault distance change at this frequency. The average L2 norm of the partial derivative of the port complex impedance with respect to the fault impedance is used as the fault impedance sensitivity to characterize the degree of interference of fault impedance fluctuation on ranging. The sensitivity matrices of multiple candidate frequencies are stacked to form a combined sensitivity matrix, and the condition number of the combined matrix is ​​used as the numerical stability evaluation index of the frequency combination. By considering factors such as distance sensitivity threshold, fault impedance interference level, measurement signal-to-noise ratio requirements, and numerical stability indicators, a set of characteristic diagnostic frequencies is obtained.

4. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The condition number of a combination matrix is ​​expressed as: ； in, This represents the average conditional evaluation value of frequency combinations. Indicates the first One fault parameter sample, Represents the matrix condition number. Represents frequency combination The corresponding combined sensitivity matrix, where N is the number of calculation samples selected within the allowable range of fault parameters.

5. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The residual vector described in S3 is formed by sequentially concatenating the real and imaginary deviations corresponding to all characteristic frequencies. The weighting matrix is ​​a diagonal matrix, and the diagonal elements are the weighting coefficients corresponding to the real part deviation and the imaginary part deviation at each characteristic frequency. The weighting coefficients are dynamically determined based on the measurement signal-to-noise ratio, distance sensitivity and fault impedance sensitivity at the corresponding frequency points. The weighted least squares objective function is the weighted sum of squares of the residual vector, used to quantify the degree of matching between candidate fault parameters and measured port responses.

6. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The damping iteration method in S4 uses damped Gauss-Newton iteration, and the specific process is as follows: Calculate the Jacobian matrix of the residual vector of the current iteration step with respect to the fault parameters; Introducing a damping factor to construct an iterative correction equation, and adjusting the iteration step size by the damping factor: When the objective function decreases significantly, the damping factor is reduced to improve the convergence speed; when the objective function increases or oscillates, the damping factor is increased to enhance the iteration stability. Calculate the parameter correction amount and update the parameter vector. After each parameter update, constrain the parameters to the physical feasible region using the projection operator.

7. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The corrected equation is expressed as follows: ； in, Indicates the first The parameter adjustment amount for the next iteration. Represents the identity matrix. Indicates the first The Jacobian matrix of the residual vector to the fault parameter vector at the next iteration. Represents the residual weighting matrix. This represents the residual vector composed of the real and imaginary deviations of the complex impedance at all characteristic diagnostic angular frequencies. This represents the damping factor.

8. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The physical feasible region in S4 includes the line length constraint of fault distance and the reasonable range of engineering values ​​for the fault impedance resistive and reactive components. The method for selecting the initial values ​​for iteration is as follows: generate multiple sets of initial parameters uniformly within the physical feasible region, calculate the objective function value corresponding to each set, and select the sets with the smallest objective function value as the initial values ​​for iteration. The convergence criteria include the objective function threshold, the parameter correction threshold, and the maximum number of iterations. The iteration terminates when any one of these conditions is met. If multiple sets of initial values ​​yield multiple feasible solutions, the solution with the smallest objective function value is selected as the final output.

9. The DC line fault location method based on port complex impedance frequency domain characteristics according to claim 1, characterized in that, The fault equivalent complex impedance includes resistive and reactive components, and is used to uniformly characterize transition resistance faults, arc faults, insulation degradation faults, and faults with stray capacitance coupling. When the fault path exhibits pure resistive characteristics, the reactance component is set to zero, and the fault equivalent complex impedance degenerates into a pure fault resistance form.

10. A DC line fault location system based on the frequency domain characteristics of port complex impedance, characterized in that, It includes a signal injection module, a signal acquisition module, a parameter storage module, a frequency optimization module, a modeling and calculation module, a joint inversion module, and a result output module; The signal injection module is used to output multi-frequency low-amplitude diagnostic signals to the measurable port of the DC line; The signal acquisition module is used to synchronously acquire the time-domain voltage and current signals of the measurable port; The parameter storage module is used to store DC line distributed parameters, fault parameter physical boundaries, convergence thresholds, and maximum number of iterations; The frequency optimization module is used to execute the feature diagnosis frequency set screening process described in S2; The modeling and calculation module is used to execute the port complex impedance modeling, measured complex impedance calculation and multi-frequency weighted objective function construction process described in S1 and S3; The joint inversion module is used to execute the joint damping iterative solution process of fault distance and fault complex impedance described in S4; The result output module is used to output the final fault distance and fault equivalent complex impedance results.

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