Method, device and storage medium for calculating three-phase unbalance degree of complex power transmission network

Abstract

The application discloses a three-phase unbalance degree calculation method and device for a complex power transmission network and a storage medium, and comprises the following steps: acquiring the spatial position of a tower conductor hanging point; adaptively selecting Carson or complex penetration depth formula to calculate the unit length impedance and admittance matrix according to the line length and soil resistivity; establishing a section π model according to the electrical coupling relationship; acquiring the coupling line transmission capacity, voltage and operation mode to calculate the end equivalent load as a boundary condition; establishing a state equation for each section, and solving together with the boundary condition and the inter-section connection equation to obtain the two-end voltage and current of each section; obtaining the positive, negative and zero sequence components through phase sequence transformation; and calculating the corresponding unbalance degree according to the ratio of the negative sequence and the zero sequence to the positive sequence. Through adaptive selection of the impedance calculation formula and introduction of the coupling line operation condition as the boundary condition, the application realizes high-precision steady-state calculation of the three-phase unbalance degree in the same-tower multi-loop mixed-voltage co-tower scene, and improves the calculation precision and engineering applicability.

Description

Technical Field

[0001] This application relates to the field of power system transmission line design and analysis technology, and in particular to a method, equipment and storage medium for calculating the three-phase imbalance of complex transmission networks. Background Technology

[0002] With the increasing scarcity of land resources and the growing congestion of transmission line corridors, the design of multiple circuits mounted on the same tower has become an important trend in the construction of high-voltage transmission lines. However, the installation of multiple circuits / mixed voltages on the same tower can lead to asymmetry in the spatial position and height above ground of each circuit, as well as asymmetry in the electromagnetic induction of conductors of different voltage levels. This results in a significant increase in the asymmetry of the electrical parameters of the transmission line, exacerbating the asymmetrical current / voltage generated in the system and affecting the service life of equipment such as generators and motors.

[0003] In existing technologies, the main methods for calculating three-phase unbalance include the transmission matrix method, the Thevenin equivalent method, and the segmented Π model method. Furthermore, existing methods do not fully consider the impact of operating parameters such as transmission capacity, voltage level, and operating mode of adjacent coupled lines on the unbalance, nor do they provide adaptive selection strategies for impedance calculation formulas (Carson formula and complex penetration depth formula) under different scenarios.

[0004] The above content is only used to help understand the technical solution of this application and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main purpose of this application is to provide a method, device and storage medium for calculating the three-phase imbalance of complex transmission networks. It aims to solve the technical problems that existing three-phase imbalance algorithms do not fully consider the impact of the operating conditions of adjacent coupled lines on the imbalance, and lack an adaptive selection mechanism for impedance calculation formulas, resulting in insufficient calculation accuracy for multi-circuit mixed voltage co-tower scenarios on the same tower.

[0006] To achieve the above objectives, this application proposes a method for calculating the three-phase imbalance of complex transmission networks, the method comprising: Obtain the spatial position parameters of each conductor suspension point on the transmission tower; The Carson formula or the complex penetration depth formula is adaptively selected based on the line length and soil resistivity, and the impedance matrix and admittance matrix per unit length of the line are calculated using the spatial location parameters. The power transmission network is divided into multiple segments based on the electrical coupling relationship between the lines. A π equivalent model is established for each segment to obtain the impedance matrix and admittance matrix of each segment. Obtain the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower section. Calculate the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and voltage level, and use the three-phase symmetrical equivalent load impedance value as a boundary condition. State equations are established for each segment. The impedance matrix and admittance matrix of each segment, as well as the boundary conditions, are substituted into the state equations. The connection equations between segments are combined to form a set of electrical characteristic equations for the entire network and solved to obtain the voltage and current values ​​of the nodes at both ends of each segment. The voltage and current values ​​are converted into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix. The negative-sequence unbalance is calculated based on the ratio of the negative-sequence component to the positive-sequence component, and the zero-sequence unbalance is calculated based on the ratio of the zero-sequence component to the positive-sequence component.

[0007] In one embodiment, the step of adaptively selecting the Carson formula or the multiple penetration depth formula based on the line length and soil resistivity includes: Obtain the total length of the transmission line to be calculated; When the total length is less than or equal to the first preset length, the Carson formula is used to calculate the impedance matrix and the admittance matrix per unit length. When the total length is greater than the first preset length, the complex penetration depth formula is used to calculate the impedance matrix per unit length and the admittance matrix per unit length. When the total length is equal to the first preset length, the average soil resistivity of the entire line is obtained. If the average value is higher than the preset threshold, the Carson formula is selected. If the average value is lower than or equal to the preset threshold, the multiple penetration depth formula is selected.

[0008] In one embodiment, the step of adaptively selecting the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and calculating the impedance matrix and admittance matrix per unit length of the line using the spatial location parameters, includes: Obtain the measured values ​​of soil resistivity at the locations of each base tower along the line; Calculate the arithmetic mean of all measured values ​​along the entire line, which will serve as the representative value of the soil resistivity along the entire line; When the representative value is lower than a preset threshold, the complex penetration depth formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is not lower than the preset threshold, the Carson formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is within a set floating range centered on the preset threshold, a calculation formula is further selected based on the line length. When the line length is less than or equal to fifty kilometers, the Carson formula is selected, and when the line length is greater than fifty kilometers, the multiple penetration depth formula is selected.

[0009] In one embodiment, the step of dividing the transmission network into multiple segments based on the electrical coupling relationships between lines includes: The multi-circuit transmission line section on the same tower in the power transmission network is divided into a basic section, and the single-circuit incoming line section before the starting point of the multi-circuit transmission line section on the same tower is divided into an independent section. When there is a change in the tower structure type within the multi-circuit erection section of the same tower, the foundation section is divided into multiple sub-segments at the location of the tower with the change in structure type. When there is a change in conductor type within the multi-circuit erection section on the same tower, the foundation section is divided into multiple sub-segments at the location of the tension section where the conductor type changes. When the length of any sub-segment exceeds the set maximum segment length threshold after division, the sub-segment is divided into multiple sub-segments with a length not exceeding the threshold along the line direction.

[0010] In one embodiment, the step of obtaining the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower section, and calculating the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and the voltage level, includes: Calculate the three-phase rated load impedance amplitude at the end of each coupled line based on the transmission capacity and voltage level of each coupled line. Based on the operating mode of each coupled line, determine the number of circuits currently in operation for each coupled line. The operating mode includes single-circuit operation mode and double-circuit operation mode. When the operating mode is a single-circuit operating mode, the amplitude of the three-phase rated load impedance is directly used as the three-phase symmetrical equivalent load impedance value at the end of the coupling line. When the operating mode is a dual-circuit operating mode, the three-phase rated load impedance amplitudes of the two circuits are calculated in parallel to obtain the three-phase symmetrical equivalent load impedance value under the dual-circuit operating mode. When there are multiple coupled lines of different voltage levels in the same tower section, calculate the three-phase symmetrical equivalent load impedance value at the end of each coupled line and use it as the boundary condition for each circuit.

[0011] In one embodiment, the step of substituting the impedance matrix and admittance matrix of each segment and the boundary conditions into the state equation, combining the connection equations between segments to form a set of electrical characteristic equations for the entire network, and solving them to obtain the voltage and current values ​​at the two ends of each segment includes: For each segment, the three-phase voltage and three-phase current at the two ends of each segment are used as state variables to establish a state equation that reflects the relationship between the input and output electrical quantities of the segment. Based on the constraint that the voltages of adjacent segments are equal at the common node, the first type of connection equation between segments is established; Based on the constraint that the algebraic sum of the injected currents at the common node of adjacent segments is zero, a second type of connection equation between segments is established. The state equations of all segments, the first and second type connection equations between all segments, and the boundary conditions are combined to form a closed set of electrical characteristic equations for the entire network. The Newton-Raphson method is used to iteratively solve the electrical characteristic equations of the entire network until the maximum voltage correction value between two adjacent iterations is less than the convergence tolerance, at which point the iteration is terminated and the voltage and current values ​​of the nodes at both ends of each segment are output. When the Newton-Raphson method iteration fails to converge, the current solution is used as the initial value, and the damped Newton method is used to iterate again to obtain the voltage and current values ​​at the two ends of each segment.

[0012] In one embodiment, after the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence imbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence imbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes: Using the length of the same tower segment as a variable, parameter scanning is performed within a preset length range with a set step size. Under each value of the same tower segment length, the process of obtaining spatial location parameters is repeated until the unbalance is calculated. The zero-sequence unbalance and negative-sequence unbalance corresponding to each value of the same tower segment length are recorded respectively. The rate of change of zero-sequence unbalance relative to the length of the same tower section is calculated based on the zero-sequence unbalance for each tower section length value, and the rate of change of negative-sequence unbalance relative to the length of the same tower section is calculated based on the negative-sequence unbalance for each tower section length value. Compare the rate of change of the zero-sequence imbalance with the rate of change of the negative-sequence imbalance. When the rate of change of the zero-sequence imbalance is greater than the rate of change of the negative-sequence imbalance, it is determined that the zero-sequence imbalance has a higher sensitivity to the length of the same tower section. When the rate of change of the negative sequence imbalance is greater than the rate of change of the zero sequence imbalance, it is determined that the negative sequence imbalance has a higher sensitivity to the length of the same tower section.

[0013] In one embodiment, after the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence imbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence imbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes: Using the transmission capacity as a variable, parameter scanning is performed within a preset capacity range with a set step size. Under each transmission capacity value, the three-phase symmetrical equivalent load impedance value of the end of other coupled lines in the same tower section is recalculated, and the state equation establishment and solution are repeatedly executed until the unbalance is calculated. The zero-sequence unbalance and negative-sequence unbalance corresponding to each transmission capacity value are recorded respectively. Based on the zero-sequence unbalance for each conveying capacity value, a first curve showing the change of zero-sequence unbalance with the conveying capacity is plotted, and based on the negative-sequence unbalance for each conveying capacity value, a second curve showing the change of negative-sequence unbalance with the conveying capacity is plotted. The first sensitivity of zero-sequence imbalance to conveying capacity is calculated based on the first change curve, and the second sensitivity of negative-sequence imbalance to conveying capacity is calculated based on the second change curve. By comparing the magnitudes of the first sensitivity and the second sensitivity, the differential sensitivity ranking of zero-sequence imbalance and negative-sequence imbalance to the transmission capacity of the coupled line is determined.

[0014] In addition, to achieve the above objectives, this application also proposes a device for calculating the three-phase imbalance of a complex transmission network. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer program is configured to implement the steps of the method for calculating the three-phase imbalance of a complex transmission network as described above.

[0015] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the method for calculating the three-phase imbalance of complex transmission networks as described above.

[0016] One or more technical solutions proposed in this application have at least the following technical effects: The technical solution of this application involves obtaining the spatial location parameters of each conductor suspension point on the transmission tower; adaptively selecting the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and using the spatial location parameters to calculate the impedance matrix and admittance matrix per unit length of the line; dividing the transmission network into multiple segments based on the electrical coupling relationship between lines, establishing a π equivalent model for each segment, and obtaining the impedance matrix and admittance matrix of each segment; obtaining the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower segment, and calculating the three-phase symmetrical equivalent impedance at the end of the line based on the transmission capacity and the voltage level. The load impedance value is used as the boundary condition; a state equation is established for each segment, and the impedance matrix and admittance matrix of each segment, as well as the boundary condition, are substituted into the state equation. The connection equations between segments are combined to form a set of electrical characteristic equations for the entire network and solved to obtain the voltage and current values ​​at the two ends of each segment. The voltage and current values ​​are converted into positive sequence components, negative sequence components, and zero sequence components using the phase sequence transformation matrix. The negative sequence unbalance is calculated based on the ratio of the negative sequence component to the positive sequence component, and the zero sequence unbalance is calculated based on the ratio of the zero sequence component to the positive sequence component.

[0017] The technical solution of this application, while ensuring the accuracy of impedance calculation under different conditions, realizes the active quantitative introduction of the impact of operating conditions on unbalance. It solves the technical problems of the lack of adaptive capability of fixed impedance formula and the inability to quantitatively include the impact of operating conditions of coupled lines. It realizes the technical leap of three-phase unbalance calculation from static open-loop calculation to condition-adaptive closed-loop fusion, and from single empirical formula to condition-driven intelligent selection. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the first embodiment of the method for calculating the three-phase imbalance of complex transmission networks in this application; Figure 2 This is a detailed step diagram of step S50 in one embodiment; Figure 3 This is a flowchart illustrating the second embodiment of the method for calculating the three-phase imbalance of complex power transmission networks according to the present invention. Figure 4This is a flowchart illustrating the third embodiment of the method for calculating the three-phase imbalance of complex power transmission networks according to the present invention. Figure 5 A schematic diagram of the two-dimensional coordinate system modeling for the tower head of a transmission tower; Figure 6 A schematic diagram of the equivalent π model structure for a segmented three-phase line; Figure 7 A schematic diagram of the equivalent load model considering the operating conditions of the coupled line; Figure 8 This is a schematic diagram of the overall process of the method of the present invention; Figure 9 This is a schematic diagram of the equipment structure of the hardware operating environment involved in the calculation method of three-phase imbalance in complex power transmission networks in the embodiments of this application.

[0021] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0022] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0023] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0024] In the field of three-phase unbalance calculation for multi-circuit mixed-voltage co-tower scenarios, existing methods mainly follow the open-loop calculation path based on fixed model parameters. That is, after establishing an electrical model based on the line geometry and a fixed impedance formula, the unbalance is directly solved. In simple scenarios with regular line structures and stable operating conditions, this approach can achieve basic assessment with a relatively simplified process, making it easy for engineers to implement. However, this approach is essentially a static open-loop calculation paradigm, failing to incorporate the dynamic operating conditions of adjacent coupled lines and the differences in the applicability of impedance formulas into the calculation closed loop. The fixed use of a single impedance formula is limited by the formula's own applicable boundaries. When the line length or soil resistivity exceeds the applicable range, the impedance parameters have inherent deviations. At the same time, the system cannot sense changes in real-time parameters such as the transmission capacity and operating mode of coupled lines, and it lacks the ability to adaptively analyze the unbalance response characteristics after changes in operating conditions. When operating conditions fluctuate frequently or soil conditions change along the line, the deviations introduced by the fixed model will continue to be propagated in the order component decomposition, causing the calculation results to deviate from the actual values, introducing errors that are difficult to eliminate for line design and power quality assessment.

[0025] A comprehensive analysis reveals that the core dilemma faced by the aforementioned technical approaches lies in the fact that the open-loop calculation paradigm based on fixed impedance formulas and static parameters lacks an adaptive mechanism for impedance calculation and cannot quantify the impact of operating conditions. This fundamentally contradicts the inherent need for high-precision calculations and quantitative analysis of influencing factors in mixed-pressure, shared-tower scenarios.

[0026] To address the aforementioned shortcomings, this application proposes a method for calculating the three-phase unbalance of complex transmission networks based on the fusion of a segmented equivalent π model and state equations. This method addresses the core pain points of the lack of an adaptive selection mechanism for impedance formulas and the neglect of the influence of coupled line operating conditions. It constructs a fusion calculation system with adaptive operating condition capabilities by using line length and soil resistivity as criteria for formula selection, and by converting the operating parameters of coupled lines into equivalent loads at the ends and incorporating them as boundary conditions into the state equations. Specifically, this method first accurately obtains the spatial location parameters of each conductor attachment point; secondly, it adaptively selects the Carson formula or the complex penetration depth formula based on line length and soil resistivity to calculate the impedance matrix and admittance matrix per unit length; then, it divides the network into multiple segments based on electrical coupling relationships and establishes an equivalent π model for each segment; simultaneously, it obtains the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower segment, converting them into equivalent load impedance values ​​at the ends and incorporating them as boundary conditions into the state equations; finally, it establishes state equations for each segment, solves the voltage and current at each node by solving the entire network equation system, and calculates the negative-sequence and zero-sequence unbalance through phase sequence transformation.

[0027] Through the above-mentioned technical means, this application can ensure the accuracy of impedance calculation under different conditions while actively quantifying the influence of operating conditions on unbalance. It solves the technical problems of the lack of adaptive capability of fixed impedance formula and the inability to quantify the influence of operating conditions of coupled lines. It realizes the technical leap from static open-loop calculation to condition-adaptive closed-loop fusion in three-phase unbalance calculation, and from single empirical formula to condition-driven intelligent selection.

[0028] Based on this, embodiments of this application provide a method for calculating the three-phase imbalance of complex transmission networks, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the method for calculating the three-phase imbalance of complex transmission networks according to this application. In this embodiment, the method for calculating the three-phase imbalance of complex transmission networks includes steps S10 to S60: Step S10: Obtain the spatial position parameters of each conductor suspension point on the transmission tower; In this embodiment, the core function of acquiring the spatial position parameters of each conductor suspension point on the transmission tower is to provide accurate geometric input data for subsequent impedance parameter calculations. The electrical parameters of a transmission line are closely related to the spatial relative positions of the conductors, including the spacing between conductors, the conductor height above the ground, and the relative position between the conductor and the ground wire. These geometric relationships directly affect the calculation results of the line's impedance matrix and admittance matrix. In multi-circuit mixed-voltage co-tower scenarios, conductors of different voltage levels are suspended on different crossarm layers of the same tower, exhibiting an asymmetrical spatial distribution. This asymmetry is one of the important reasons for the increased three-phase imbalance.

[0029] In practical implementation, a fixed reference point on the tower head needs to be selected as the coordinate origin. In actual engineering, the center point of the lower crossarm on the tower head is usually chosen as the origin, located at the intersection of the center line of the tower main column and the center line of the lower crossarm. A two-dimensional coordinate system is established based on this origin, where the horizontal direction represents the transverse arrangement of the line, and the vertical direction represents the height of the tower. Under this coordinate system, the position of each conductor suspension point can be determined by structural parameters such as the crossarm length and the height of the ground wire support. The crossarm length determines the horizontal offset of the conductor, while the height of the crossarm layer where the conductor suspension point is located determines its coordinate value in the vertical direction.

[0030] In practical implementation, the first step is to select a fixed reference point on the tower head as the coordinate origin. In actual engineering, the center point of the lower crossarm of the tower head is usually chosen as the origin, located at the intersection of the center line of the tower main column and the center line of the lower crossarm. A two-dimensional coordinate system is established based on this origin, where the horizontal direction represents the transverse arrangement of the line, and the vertical direction represents the height of the tower. Under this coordinate system, the position of each conductor suspension point can be determined by structural parameters such as the crossarm length and the height of the ground wire support. The crossarm length determines the horizontal offset of the conductor, while the height of the crossarm layer where the conductor suspension point is located determines its coordinate value in the vertical direction. Based on the above method of establishing a two-dimensional coordinate system with the center of the lower crossarm of the tower head as the origin and recording the spatial position parameters of the conductor suspension points, you can refer to... Figure 5 , Figure 5 A schematic diagram of the two-dimensional coordinate system modeling for the tower head of a power transmission tower.

[0031] The precise location of each conductor suspension point in the two-dimensional coordinate system is recorded as a set of coordinate values ​​using the above method. The accuracy of these coordinate values ​​directly affects the accuracy of subsequent impedance parameter calculations. Therefore, the influence of factors such as the tolerance of tower structure dimensions and construction and installation errors should be fully considered during the coordinate acquisition process. After obtaining the spatial coordinates of each conductor suspension point, these data need to be stored in a tower parameter database for unified management. The database structure design should support data retrieval according to different dimensions such as tower model and tower number, so as to quickly retrieve the corresponding suspension point coordinate data in different calculation scenarios. After establishing the tower parameter database, when facing a complex transmission network containing multiple tower models, the conductor suspension point coordinates of all towers along the entire line can be obtained in batches through database queries, thereby providing data support for subsequent segment-by-segment impedance parameter calculations.

[0032] Step S20: Adaptively select the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and calculate the impedance matrix and admittance matrix per unit length of the line using the spatial location parameters. In this embodiment, the core function of adaptively selecting either the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and calculating the unit-length impedance matrix and unit-length admittance matrix of the line using the aforementioned spatial location parameters, is to establish a unit-length electrical parameter matrix that accurately reflects the electromagnetic characteristics of the line, providing fundamental data for the subsequent construction of the piecewise π model. In the field of power system electromagnetic transient calculations, the mainstream methods for calculating overhead line impedance parameters include the Carson formula and the complex penetration depth formula. Each has its advantages in terms of calculation accuracy and efficiency, and their applicability is closely related to the line length and magnetotelluric characteristics. For multi-circuit mixed-voltage co-tower scenarios on the same tower, due to differences in conductor types for lines of different voltage levels, the differential influence of different conductor parameters on matrix elements must also be considered during the calculation process.

[0033] In practical implementation, the total length of the line to be calculated and the soil resistivity measurements at each tower location along the line are first obtained. Line length is a crucial basis for selecting the impedance calculation formula. For short-distance lines, the Carson formula is sufficient to meet engineering accuracy requirements. However, for long-distance lines or scenarios with abnormal soil resistivity, the complex penetration depth formula is required to ensure calculation accuracy. Soil resistivity can be obtained by conducting on-site measurements at each tower location along the line and then taking the arithmetic mean of all measurements as the representative value of the soil resistivity for the entire line. When the line length is no more than 50 kilometers, the Carson formula is preferred for calculating the impedance matrix and admittance matrix per unit length. The Carson formula is based on the assumption that the earth is an ideal conductor, and the calculation process is relatively simple, sufficient to ensure the required calculation accuracy within this length range. When the line length is greater than 50 kilometers, the complex penetration depth formula is preferred. This formula considers the penetration depth effect of electromagnetic waves in the soil when the earth is a lossy medium, and can more accurately reflect the electromagnetic induction characteristics under long-distance conditions. When the representative value of soil resistivity is lower than the preset threshold, it indicates that the earth's electrical conductivity is good. In this case, the complex penetration depth formula can better handle the influence of the earth's skin effect.

[0034] After determining the applicable calculation formula, the spatial coordinates of each conductor's suspension point need to be substituted into the selected formula to calculate the impedance matrix and admittance matrix per unit length. In the impedance matrix, the diagonal elements represent the self-impedance of each conductor, the magnitude of which is related to the conductor's own parameters and its height above ground; the off-diagonal elements represent the mutual impedance between conductors, the magnitude of which is related to the spatial distance between conductors. In the admittance matrix, the diagonal elements represent the capacitance to ground of each conductor, and the off-diagonal elements represent the mutual capacitance between conductors. During the calculation of these matrices, the spatial coordinates of the conductor suspension points directly affect the calculation of the distance between conductors, thus affecting the values ​​of mutual impedance and mutual capacitance.

[0035] The step of adaptively selecting the Carson formula or the multiple penetration depth formula based on the line length and soil resistivity includes: Obtain the total length of the transmission line to be calculated; When the total length is less than or equal to the first preset length, the Carson formula is used to calculate the impedance matrix and the admittance matrix per unit length. When the total length is greater than the first preset length, the complex penetration depth formula is used to calculate the impedance matrix per unit length and the admittance matrix per unit length. When the total length is equal to the first preset length, the average soil resistivity of the entire line is obtained. If the average value is higher than the preset threshold, the Carson formula is selected. If the average value is lower than or equal to the preset threshold, the multiple penetration depth formula is selected.

[0036] This embodiment defines the specific judgment logic for adaptively selecting the Carson formula or the multiple penetration depth formula based on the line length. The core function of this judgment logic is to establish a formula selection mechanism with line length as the primary criterion, and to introduce soil resistivity as an auxiliary criterion at the length critical point, thereby ensuring both calculation accuracy and calculation efficiency.

[0037] In practical implementation, the first step is to obtain the total length of the transmission line to be calculated. This length refers to the total length between the beginning and end of the line, usually expressed in kilometers. It can be obtained directly from the line design documents or by accumulating the spans between each tower. After obtaining the total length, it is compared with a pre-set first length, preferably fifty kilometers. When the total length is less than or equal to the first pre-set length, it indicates that the transmission line is a short-distance line. In this case, the Carson formula is used to calculate the impedance matrix and admittance matrix per unit length. The Carson formula is based on the assumption that the earth is an ideal conductor, and its calculation process is relatively simple. Under short-distance line conditions, it can obtain impedance parameters that meet engineering accuracy requirements with relatively small computational overhead, thus exhibiting a significant efficiency advantage in short-line scenarios.

[0038] When the total line length exceeds the first preset length, it indicates that the transmission line is a long-distance line. In this case, the complex penetration depth formula is used to calculate the impedance matrix and admittance matrix per unit length. The complex penetration depth formula considers the penetration depth effect of electromagnetic waves in the soil when the earth is a lossy medium, and can more accurately reflect the characteristics of electromagnetic induction attenuation with distance under long line conditions. Therefore, it has higher calculation accuracy in scenarios where the line length exceeds fifty kilometers. When the total line length is exactly equal to the first preset length, the length alone cannot uniquely determine the selection of the optimal formula. In this case, it is necessary to further obtain the average value of the soil resistivity along the entire line as an auxiliary criterion. This average value is obtained by collecting soil resistivity measurements at each tower location along the line and taking the arithmetic mean. After obtaining the average value, it is compared with a preset threshold. When the average value is higher than the preset threshold, it indicates that the earth's conductivity is poor. In this case, the Carson formula can meet the accuracy requirements, and there is no need to use the complex penetration depth formula, which has a larger computational load. When the average value is lower than or equal to the preset threshold, it indicates that the earth's conductivity is good and the penetration depth of electromagnetic waves in the soil is small. In this case, the complex penetration depth formula can more accurately handle the influence of the earth's skin effect.

[0039] Based on the above judgment logic, this embodiment establishes a hierarchical formula selection mechanism with length as the first judgment condition and soil resistivity as the second judgment condition. This mechanism enables the selection of impedance calculation formulas to meet the accuracy requirements of different line lengths, and also achieves a smooth transition in formula selection at the length critical point through the auxiliary judgment of soil resistivity.

[0040] The step of adaptively selecting the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and calculating the impedance matrix and admittance matrix per unit length of the line using the spatial location parameters, includes: Obtain the measured values ​​of soil resistivity at the locations of each base tower along the line; Calculate the arithmetic mean of all measured values ​​along the entire line, which will serve as the representative value of the soil resistivity along the entire line; When the representative value is lower than a preset threshold, the complex penetration depth formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is not lower than the preset threshold, the Carson formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is within a set floating range centered on the preset threshold, a calculation formula is further selected based on the line length. When the line length is less than or equal to fifty kilometers, the Carson formula is selected, and when the line length is greater than fifty kilometers, the multiple penetration depth formula is selected.

[0041] This embodiment defines the specific judgment logic for adaptively selecting the Carson formula or the multiple penetration depth formula based on the representative value of soil resistivity across the entire line. Its core function is to establish a formula selection mechanism based on measured soil resistivity data, and to set a floating range near a threshold to avoid calculation instability caused by frequent formula switching.

[0042] In practice, the soil resistivity measurements at each tower location along the transmission line are first obtained. This is achieved through on-site measurements at each tower location using the four-electrode method or the Wenner method, yielding a series of resistivity data representing the earth's conductivity at that location. Since the transmission line may traverse areas with varying geological conditions, the soil resistivity at each measurement point can differ significantly. Therefore, a single point measurement cannot be used as a representative value for the entire line. After obtaining all measurements, the arithmetic mean of all measurements is calculated as the representative value of the soil resistivity for the entire line. This representative value comprehensively reflects the average conductivity of the earth along the entire line.

[0043] After obtaining the representative value, it is compared with a preset threshold. When the representative value is lower than the preset threshold, it indicates that the overall conductivity of the soil along the line is good, and the skin effect is significant. In this case, the complex penetration depth formula is used to calculate the impedance matrix and admittance matrix per unit length, utilizing the formula's accurate modeling capability of the ground's lossy characteristics to ensure the accuracy of the impedance parameter calculation. When the representative value is not lower than the preset threshold, it indicates that the overall conductivity of the soil along the line is poor or at a moderate level. In this case, the Carson formula is used to calculate the impedance matrix and admittance matrix per unit length, reducing the computational complexity while meeting the accuracy requirements.

[0044] When the representative value falls within a set fluctuation range centered on a preset threshold, it indicates that the difference between the representative soil resistivity value and the threshold is small, and the optimal formula cannot be uniquely determined solely based on soil resistivity. In this case, further analysis based on the line length is needed to assist in determining the calculation formula. The line length is compared to 50 kilometers; when the line length is less than or equal to 50 kilometers, the Carson formula is selected; when the line length is greater than 50 kilometers, the multiple penetration depth formula is selected. This fluctuation range setting avoids frequent oscillations in formula selection when the soil resistivity measurement value fluctuates near the threshold, thus improving the stability of the calculation process.

[0045] Step S30: Divide the power transmission network into multiple segments according to the electrical coupling relationship between the lines, establish a π equivalent model for each segment, and obtain the impedance matrix and admittance matrix of each segment. In this embodiment, the transmission network is divided into multiple segments based on the electrical coupling relationships between lines. To obtain the impedance and admittance matrices of each segment using a π-equivalent model, the complex, long-distance, and structurally uneven transmission network needs to be decomposed into several uniform segments. Each segment uses a π-equivalent circuit for parameter lumping, thus transforming the continuous distributed parameter system into a lumped parameter network that facilitates state equation modeling. In scenarios involving multiple circuits sharing a common tower and voltage, various tower structures may alternate along the transmission line. Different tower structures have different conductor attachment point layouts, leading to differences in the electrical parameters of each line segment. Therefore, segmentation is necessary to ensure calculation accuracy. The π-equivalent model uses a lumped parameter network of resistance, inductance, and capacitance to represent the distributed parameter line. Its parameters are obtained by multiplying the calculated unit-length impedance and admittance matrices by the segment length.

[0046] In practical implementation, the basic principle of segmentation is to treat a multi-circuit transmission line section on the same tower as a whole as a basic segment, while dividing the portion before the start and after the end of the section into independent single-circuit incoming and single-circuit outgoing segments, respectively. When the length of the multi-circuit transmission line section is long, it is necessary to further consider whether there are factors within the section that affect the uniformity of electrical parameters. For example, when there are changes in the tower structure type within the multi-circuit transmission line section, the different conductor suspension point layouts of different tower structures lead to changes in the impedance parameters per unit length. In this case, the basic segment should be divided into multiple sub-segments at the tower location where the structure type changes. Similarly, when there are changes in the conductor type within the multi-circuit transmission line section, the resistance and radius parameters of different conductor types are different. The basic segment should also be further divided at the tension section location where the conductor type changes.

[0047] After the above segmentation operation, it is necessary to check whether the length of each segment exceeds the preset maximum segment length threshold. When the length of a segment exceeds this threshold, the segment needs to be divided into multiple sub-segments with lengths not exceeding the threshold along the line direction. This constraint is to ensure that each π equivalent model satisfies the applicability conditions of the lumped parameter assumption within the frequency range. For each segment after division, the calculated unit length impedance matrix and unit length admittance matrix are multiplied by the segment length to obtain the impedance matrix and admittance matrix of that segment. These matrices constitute the coefficient matrix for subsequently establishing the state equations.

[0048] After the above segmentation operation, it is necessary to check whether the length of each segment exceeds the preset maximum segment length threshold. When the length of a segment exceeds this threshold, the segment needs to be divided into multiple sub-segments with lengths not exceeding the threshold along the line direction. This constraint is to ensure that each π equivalent model satisfies the applicability conditions of the lumped parameter assumption within the frequency range. For each segment after division, the calculated unit length impedance matrix and unit length admittance matrix are multiplied by the segment length to obtain the impedance matrix and admittance matrix of that segment. These matrices constitute the coefficient matrix for subsequently establishing the state equations. For the implementation method of establishing the π equivalent model of each segment and obtaining the segment impedance matrix and admittance matrix, please refer to [link to documentation]. Figure 6 , Figure 6 This is a schematic diagram of the equivalent π model structure for a segmented three-phase line.

[0049] The step of dividing the power transmission network into multiple segments based on the electrical coupling relationships between lines includes: The multi-circuit transmission line section on the same tower in the power transmission network is divided into a basic section, and the single-circuit incoming line section before the starting point of the multi-circuit transmission line section on the same tower is divided into an independent section. When there is a change in the tower structure type within the multi-circuit erection section of the same tower, the foundation section is divided into multiple sub-segments at the location of the tower with the change in structure type. When there is a change in conductor type within the multi-circuit erection section on the same tower, the foundation section is divided into multiple sub-segments at the location of the tension section where the conductor type changes. When the length of any sub-segment exceeds the set maximum segment length threshold after division, the sub-segment is divided into multiple sub-segments with a length not exceeding the threshold along the line direction.

[0050] This embodiment defines specific operational rules for dividing a power transmission network into multiple segments based on the electrical coupling relationships between lines. Specifically, the core function of this division rule is to decompose a complex power transmission network with uneven structure into several computationally uniform segments with uniform electrical parameters, providing a basis for independently establishing a π-equivalent model for each segment. When transmission lines cross different geographical regions, the tower structure type and conductor type may change. These changes lead to variations in the electrical parameters per unit length of the line. Therefore, segmenting at the locations of parameter changes ensures that the electrical parameters within each segment remain uniform, thus satisfying the modeling prerequisites for the π-equivalent model.

[0051] In practical implementation, it is necessary to identify whether there are multi-circuit sections on the same tower in the transmission network. A multi-circuit section on the same tower refers to a section where multiple transmission lines share the same tower corridor. The electrical coupling between different circuits within this section is strong; therefore, during segmentation, the entire multi-circuit section on the same tower is divided into a single basic segment. Simultaneously, it is necessary to identify the starting and ending points of the multi-circuit section on the same tower. The single-circuit incoming line segment before the starting point is divided into one independent segment, and the single-circuit outgoing line segment after the ending point is divided into another independent segment. Through these operations, the transmission network is initially divided into three independent segments. These three segments correspond to the inlet segment from the beginning of the line to the entrance segment on the same tower, the core segment of the multi-circuit section on the same tower, and the outlet segment from the outlet of the same tower to the end of the line.

[0052] After initial segmentation, further investigation is needed to determine if factors causing uneven electrical parameters exist within multi-circuit tower sections. One crucial factor is the variation in tower structure type. Within a multi-circuit tower section, various tower types may be used alternately due to different terrain features or to meet varying electrical clearance requirements. The crossarm length, conductor suspension point height, and horizontal conductor spacing differ between these tower types, directly impacting the calculation results of the impedance matrix and admittance matrix per unit length. Therefore, when variations in tower structure type are identified within a multi-circuit tower section, the foundation segment needs to be divided into multiple sub-segments at the locations where the structure type changes, ensuring consistency in tower structure type within each sub-segment.

[0053] Another significant factor contributing to uneven electrical parameters is the variation in conductor type. Within a multi-circuit section on the same tower, different voltage level circuits may use different conductor types, and the same circuit may also use conductors with different cross-sections depending on the transmission capacity requirements between different tension sections. Different conductor types have different resistance per unit length and conductor radii, which directly affect the values ​​of the diagonal elements in the impedance matrix. Therefore, when variations in conductor type are identified within a multi-circuit section on the same tower, the foundation section needs to be further divided into multiple sub-segments at the location of the tension section where the conductor type varies, ensuring that all conductors within each sub-segment maintain consistent conductor type.

[0054] After the above sub-segmentation operation based on changes in tower structure type and conductor type, the length of each sub-segment needs to be checked. The π equivalent model replaces distributed parameters with lumped parameters, and its applicability requires that the segment length cannot exceed a certain upper limit. When the length of any sub-segment exceeds the set maximum segment length threshold after division, the sub-segment needs to be equally divided along the line direction into multiple sub-segments with lengths not exceeding the threshold. The equal division method ensures that the length of each sub-segment is uniform and that all sub-segments meet the applicable conditions of lumped parameters.

[0055] Through the above multi-level partitioning operation, the power transmission network is decomposed into a series of computational segments with uniform internal electrical parameters and lengths that meet the applicable conditions of the π equivalent model, laying a structural foundation for the subsequent independent establishment of the π equivalent model and state equations for each segment.

[0056] Step S40: Obtain the transmission capacity, voltage level and operating mode of other coupled lines in the same tower section; calculate the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and voltage level; and use the three-phase symmetrical equivalent load impedance value as a boundary condition. The core function of this embodiment is to transform the operating parameters of adjacent coupled lines on the same tower into quantifiable electrical network boundary conditions, enabling the unbalance calculation to reflect the impact of the actual operating state of the coupled lines. In a multi-circuit mixed-voltage co-tower scenario, multiple transmission lines of different voltage levels are erected on the same tower, and these lines influence each other through electromagnetic coupling. The actual transmission power and operating mode of adjacent coupled lines will change the value of the equivalent load impedance at the end of the line, thereby affecting the current distribution on the coupled line, and ultimately affecting the unbalance calculation result of the target line through electromagnetic induction.

[0057] In practical implementation, for each coupled line within the same tower section, its current transmission capacity, voltage level, and operating mode are first obtained. Transmission capacity reflects the active power and power factor currently transmitted by the line, typically given in megavolt-amperes (MVA) or megawatts (MW). The voltage level determines the line's rated voltage and is a crucial basis for calculating the load impedance amplitude. Operating modes include single-circuit operation and double-circuit operation, with different numbers of load circuits connected to the line's end under different operating modes. Based on these parameters, the three-phase symmetrical equivalent load impedance value at the end of the coupled line is calculated using the basic formulas of the power system. Specifically, the rated current is first calculated based on the transmission capacity and voltage level, and then the resistive and reactive components of the equivalent load impedance are calculated using the power factor.

[0058] When a coupled line operates in single-circuit mode, a set of three-phase loads is connected to the end of the line. The calculated three-phase rated load impedance is directly used as the three-phase symmetrical equivalent load impedance at the end of the coupled line. When a coupled line operates in double-circuit mode, a set of three-phase loads is connected to the ends of each of the two lines. The three-phase rated load impedances of the two lines are combined in parallel to obtain the equivalent load impedance under double-circuit operation. When there are multiple coupled lines of different voltage levels within the same tower section, the above calculation process is performed on each coupled line to obtain its own three-phase symmetrical equivalent load impedance, which is then used as the boundary condition for each circuit. These boundary conditions are treated as known quantities and substituted into the corresponding nodal equations during the solution of the state equations.

[0059] The step of obtaining the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower section, and calculating the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and voltage level, includes: Calculate the three-phase rated load impedance amplitude at the end of each coupled line based on the transmission capacity and voltage level of each coupled line. Based on the operating mode of each coupled line, determine the number of circuits currently in operation for each coupled line. The operating mode includes single-circuit operation mode and double-circuit operation mode. When the operating mode is a single-circuit operating mode, the amplitude of the three-phase rated load impedance is directly used as the three-phase symmetrical equivalent load impedance value at the end of the coupling line. When the operating mode is a dual-circuit operating mode, the three-phase rated load impedance amplitudes of the two circuits are calculated in parallel to obtain the three-phase symmetrical equivalent load impedance value under the dual-circuit operating mode. When there are multiple coupled lines of different voltage levels in the same tower section, calculate the three-phase symmetrical equivalent load impedance value at the end of each coupled line and use it as the boundary condition for each circuit.

[0060] This embodiment defines specific operational rules for calculating the three-phase symmetrical equivalent load impedance value at the end of a line based on the transmission capacity, voltage level, and operating mode of other coupled lines on the same tower. The core function of this calculation rule is to transform the actual operating conditions of the coupled lines into quantifiable electrical network boundary conditions, enabling the unbalance calculation to accurately reflect the electromagnetic induction effects of adjacent lines under different operating conditions. In multi-circuit lines on the same tower, the circuits are coupled to each other through electromagnetic fields. The size of the load connected to the end of a circuit directly affects the current distribution on that circuit, and changes in the current distribution will change the voltage and current of adjacent lines through mutual inductance. Therefore, when calculating the unbalance of the target line, the operating conditions of the coupled lines must be incorporated into the calculation model in the form of an equivalent load.

[0061] In practical implementation, the transmission capacity, voltage level, and operating mode of each coupled line within the same tower section are obtained. Transmission capacity is typically given in megavolt-amperes (MVA) or megawatts (MW), representing the active power and power factor currently transmitted by the line; voltage level is given in kilovolts (kV), representing the rated operating voltage of the line; and operating mode describes whether the line is currently operating in single-circuit or double-circuit mode. For each coupled line, based on its transmission capacity and voltage level, the three-phase rated load impedance amplitude at the end of the line is calculated using the basic power formula for three-phase AC circuits. This calculation process first divides the transmission capacity by the voltage level to obtain the rated current, then combines the power factor angle (sine and cosine values) with the voltage and current to obtain the resistive and reactive components of the impedance, finally combining them to obtain the complete impedance amplitude.

[0062] After obtaining the three-phase rated load impedance amplitudes at the ends of each coupled line, the final equivalent load impedance value is determined based on the operating mode of each line. When a coupled line operates in single-circuit mode, only one set of three-phase loads is connected at the end of that line. In this case, the three-phase rated load impedance amplitudes calculated in step one are directly used as the three-phase symmetrical equivalent load impedance value at the end of that coupled line, without the need for additional combination calculations. When a coupled line operates in dual-circuit mode, each of the two lines is connected to one set of three-phase loads. In this case, the three-phase rated load impedance amplitudes of the two lines need to be calculated in parallel.

[0063] In parallel calculations, the terminal loads of two circuits are electrically connected in parallel. Therefore, the equivalent impedance value is less than the impedance value of any single circuit. The specific parallel calculation method follows the basic rule of parallel resistance, that is, the reciprocal of the equivalent impedance is equal to the sum of the reciprocals of the impedances of each branch. For cases where multiple coupled circuits of different voltage levels exist within the same tower section, the terminal load impedance values ​​differ significantly due to the different voltage levels of each circuit. Therefore, coupled circuits of different voltage levels cannot be combined to calculate the equivalent load. The correct approach is to perform the above calculation process separately for each coupled circuit, obtaining its own three-phase symmetrical equivalent load impedance value. Then, these impedance values ​​are used as boundary conditions for their respective loops, and the terminal nodes of each loop are substituted into the corresponding boundary conditions during the subsequent solution of the state equations.

[0064] When multiple coupled lines of different voltage levels exist within the same tower section, their terminal load impedance values ​​differ significantly due to the varying voltage levels. Therefore, coupled lines of different voltage levels cannot be combined to calculate the equivalent load. The correct approach is to perform the above calculation process separately for each coupled line, obtaining its own three-phase symmetrical equivalent load impedance value. These impedance values ​​are then used as boundary conditions for their respective loops. In the subsequent solution of the state equations, the terminal nodes of each loop are substituted into the corresponding boundary conditions. For details on how to calculate the equivalent load impedance value at the end of the coupled line based on transmission capacity, voltage level, and operating mode, and use it as a boundary condition, please refer to [link to documentation]. Figure 7 , Figure 7 A schematic diagram of the equivalent load model considering the operating conditions of the coupled line.

[0065] By using the above calculation rules, the operating condition parameters of the three dimensions of the coupled line—transmission capacity, voltage level, and operating mode—are uniformly transformed into network boundary conditions, so that the electromagnetic induction effects of different coupled lines under different operating conditions can be accurately reflected in the subsequent solution of the state equation.

[0066] Step S50: Establish state equations for each segment, substitute the impedance matrix and admittance matrix of each segment and the boundary conditions into the state equations, combine the connection equations between segments to form a set of electrical characteristic equations for the whole network and solve them to obtain the voltage and current values ​​of the nodes at both ends of each segment. In this embodiment, the core function of establishing state equations for each segment, substituting the impedance and admittance matrices of each segment along with the aforementioned boundary conditions into the state equations, and combining them with the connection equations between segments to form a set of electrical characteristic equations for the entire network, and solving them to obtain the voltage and current values ​​at the nodes at both ends of each segment, lies in combining the lumped parameter models and boundary conditions of each segment into a complete set of electrical network equations. Through numerical solution, the voltage and current distribution at each node of the entire network is obtained. The state equations use the three-phase voltage and three-phase current at both ends of each segment as state variables, describing the electrical quantity relationships between the input and output ports of the segment. In the state equations, the segment impedance matrix establishes the relationship between current and voltage drop, and the admittance matrix establishes the relationship between voltage and charging current. The entire network consists of multiple segments connected through common nodes. At the common node, each segment satisfies the constraints of Kirchhoff's laws, i.e., the voltages are equal and the algebraic sum of the injected currents is zero.

[0067] In practical implementation, for each segment, the three-phase voltage and three-phase current at the two endpoints of that segment are used as state variables to establish a state equation reflecting the relationship between the input and output electrical quantities of that segment. The specific form of the state equation uses the impedance matrix, admittance matrix, and segment length of that segment as coefficients to establish a linear relationship between the voltage and current at both ends of the segment. For the entire transmission network, in addition to the state equations within each segment, connection constraints between segments also need to be considered. At the common node of adjacent segments, the voltages of the two segments at that node must be equal; this is a voltage continuity constraint, thus establishing a first-type connection equation. Simultaneously, at the common node, the algebraic sum of the current injected into that node by each segment and the externally injected current must be zero; this is a constraint of Kirchhoff's Current Law, thus establishing a second-type connection equation.

[0068] By combining the state equations of all segments, the first and second type connection equations between all segments, and the obtained boundary conditions, a closed set of electrical characteristic equations for the entire network is formed. This set of equations contains algebraic equations for all unknown node voltages and currents, with the number of equations equal to the number of unknowns, thus possessing a unique mathematical solution. For the solution method, the Newton-Raphson method is used for iterative solving, which effectively handles nonlinear problems in power system network equations. During the iteration process, the voltage correction is calculated in each iteration. When the maximum voltage correction between two adjacent iterations is less than the preset convergence tolerance, the iteration is considered converged and the calculation is terminated, outputting the voltage and current values ​​at the two ends of each segment. If the Newton-Raphson method fails to converge, the current solution is used as the initial value, and the damped Newton method is used to iterate again to ensure stable convergence of the solution process.

[0069] Step S60: The voltage and current values ​​are converted into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix. The negative-sequence unbalance is calculated based on the ratio of the negative-sequence component to the positive-sequence component, and the zero-sequence unbalance is calculated based on the ratio of the zero-sequence component to the positive-sequence component.

[0070] In this embodiment, the voltage and current values ​​are converted into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix. The negative-sequence unbalance is calculated based on the ratio of the negative-sequence to the positive-sequence components, and the zero-sequence unbalance is calculated based on the ratio of the zero-sequence to the positive-sequence components. The core function of this step is to decompose the obtained three-phase voltage and current values ​​using the symmetrical component method to obtain an evaluation index that can quantitatively describe the degree of three-phase asymmetry. In a three-phase power system, any set of asymmetrical three-phase phasors can be decomposed into three sets of symmetrical phasors: positive-sequence, negative-sequence, and zero-sequence components. The positive-sequence component represents the balanced component of the three phases, while the negative-sequence and zero-sequence components represent the unbalanced components. Therefore, the degree of unbalance can be quantitatively characterized by the ratio of the negative-sequence or zero-sequence component to the positive-sequence component.

[0071] In practical implementation, the obtained three-phase voltage and current values ​​at each node need to be decomposed into sequence components using a phase sequence transformation matrix. The phase sequence transformation matrix is ​​constructed based on the fundamental principle of the symmetrical component method, and its elements consist of complex numbers rotated 120 degrees by the operator. By multiplying the three-phase voltage or current phasors as input vectors with the phase sequence transformation matrix, the corresponding positive-sequence, negative-sequence, and zero-sequence components can be obtained. These three sequence components are all in complex form, where the positive-sequence component corresponds to the symmetrical component of the three-phase quantities arranged in positive phase sequence, the negative-sequence component corresponds to the symmetrical component of the three-phase quantities arranged in reverse phase sequence, and the zero-sequence component corresponds to the symmetrical component of the three-phase quantities in phase.

[0072] After obtaining the positive-sequence, negative-sequence, and zero-sequence components of each node, the unbalance is calculated according to the standard definitions in the field of power system power quality. The negative-sequence unbalance is defined as the ratio of the amplitude of the negative-sequence component to the amplitude of the positive-sequence component, reflecting the relative magnitude of the reverse-sequence unbalance component in the three-phase system. The zero-sequence unbalance is defined as the ratio of the amplitude of the zero-sequence component to the amplitude of the positive-sequence component, reflecting the relative magnitude of the zero-sequence unbalance component in the three-phase system. These two unbalance indices are calculated separately for voltage and current, namely, negative-sequence voltage unbalance, zero-sequence voltage unbalance, negative-sequence current unbalance, and zero-sequence current unbalance. These indices can quantitatively assess the degree of three-phase asymmetry in the transmission network from different dimensions, providing quantitative technical references for scheme selection during the line design phase and power quality assessment during the operation phase. These indicators can quantitatively assess the degree of three-phase asymmetry in transmission networks from different dimensions, providing quantitative technical references for scheme comparison during the line design phase and power quality assessment during the operation phase. Based on the above description of the complete process from obtaining spatial location parameters to calculating the imbalance, please refer to... Figure 8 , Figure 8 This is a schematic diagram of the overall process of the method of the present invention.

[0073] Further, see Figure 2 , Figure 2 This is a detailed step diagram of step S50 in one embodiment, based on the shown... Figure 2 The steps of substituting the impedance matrix and admittance matrix of each segment and the boundary conditions into the state equation, combining the connection equations between segments to form a set of electrical characteristic equations for the entire network, and solving them to obtain the voltage and current values ​​at the two ends of each segment include S51~S56: Step S51: For each segment, using the three-phase voltage and three-phase current at the two ends of each segment as state variables, establish a state equation reflecting the relationship between the input and output electrical quantities of the segment. Step S52: Based on the constraint that the voltage of adjacent segments is equal at the common node, establish the first type of connection equation between segments; Step S53: Based on the constraint that the algebraic sum of the injected currents at the common node of adjacent segments is zero, establish the second type of connection equation between segments; Step S54: Combine the state equations of all segments, the first-type connection equations and the second-type connection equations between all segments, and the boundary conditions to form a closed set of electrical characteristic equations for the entire network. Step S55: The Newton-Raphson method is used to iteratively solve the electrical characteristic equations of the entire network until the maximum voltage correction value between two adjacent iterations is less than the convergence tolerance, and the iteration is terminated. The voltage and current values ​​of the nodes at both ends of each segment are output. Step S56: When the Newton-Raphson method iteration fails to converge, the current solution is used as the initial value, and the damped Newton method is used to iterate again to obtain the voltage and current values ​​at the two ends of each segment.

[0074] This embodiment defines the specific operational rules for substituting the segment parameters and boundary conditions into the state equations and solving the entire network's electrical characteristic equations. The core function of this solution rule is to integrate the lumped parameter models of each segment of the transmission network into a complete algebraic equation system, and solve the numerical solutions of the voltage and current at each node through numerical iteration methods, providing accurate electrical quantity inputs for subsequent unbalance calculations.

[0075] In practical implementation, state equations are established for each segment using the three-phase voltages and currents at both ends of the segment as state variables. These state equations are based on known parameters such as the impedance matrix, admittance matrix, and segment length. The equations describe the electrical relationships between the input and output terminals of the segment. Specifically, a linear or nonlinear algebraic relationship is established between the input and output voltages and currents through the impedance and admittance matrices of the segment. For a network containing multiple segments, each segment contributes a set of equations, where the unknowns include the voltages and currents at each node.

[0076] The first type of connection equations between segments are established based on the constraint that adjacent segments have equal voltages at a common node. Since the entire transmission network is composed of multiple segments connected in series or parallel via nodes, at the common connection node of two adjacent segments, the voltage at the end node of the preceding segment must be equal to the voltage at the beginning node of the following segment. This voltage continuity requirement constitutes the content of the first type of connection equations. The second type of connection equations between segments are established based on the constraint that the algebraic sum of the currents injected into adjacent segments at a common node is zero. At the common node, the algebraic sum of the currents flowing into and out of the node is zero; this current balance constraint constitutes the content of the second type of connection equations.

[0077] By combining the state equations of all segments, the first and second type connection equations between all segments, and the obtained boundary conditions, a closed set of electrical characteristic equations for the entire network is formed. The unknowns in this set of equations include the three-phase voltages and three-phase currents at the two endpoints of all segments. The number of equations is kept consistent with the number of unknowns through the summation of the state equations, connection equations, and boundary conditions. This set of equations employs a modeling approach that integrates network topology constraints and component characteristic constraints, accurately reflecting the electrical behavior of the entire transmission network.

[0078] The Newton-Raphson method is used to iteratively solve the above equation system. The Newton-Raphson method transforms the solution of the original equation system into an iterative process of solving a series of linear equations by performing a Taylor expansion of the nonlinear equation system near the initial solution and retaining first-order terms. In each iteration, the voltage correction vector is calculated. When the maximum voltage correction value between two consecutive iterations is less than a preset convergence tolerance, the iteration is considered converged and the calculation terminates, outputting the voltage and current values ​​at the two ends of each segment. A backup solution is provided for cases where the Newton-Raphson method does not converge. In the event of an abnormal situation where the iteration does not converge, the damped Newton method is used as the initial value to iterate again. The damped Newton method introduces a step-size damping factor to limit the change range of each iteration, effectively expanding the convergence domain and improving the solution stability, ultimately outputting the voltage and current values ​​at the two ends of each segment.

[0079] Furthermore, you can also view Figure 3 , Figure 3 This is a flowchart illustrating the second embodiment of the method for calculating the three-phase imbalance of complex transmission networks according to the present invention. Figure 3 After the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence unbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence unbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes steps S70~S100: Step S70: Using the length of the same tower segment as a variable, perform parameter scanning within a preset length range with a set step size. Repeat the process of obtaining spatial position parameters to calculate the imbalance for each value of the same tower segment length, and record the zero-sequence imbalance and negative-sequence imbalance for each value of the same tower segment length. Step S80: Calculate the rate of change of zero-sequence unbalance relative to the length of the same tower section based on the zero-sequence unbalance value for each tower section length, and calculate the rate of change of negative-sequence unbalance relative to the length of the same tower section based on the negative-sequence unbalance value for each tower section length. Step S90: Compare the rate of change of the zero-sequence imbalance with the rate of change of the negative-sequence imbalance. When the rate of change of the zero-sequence imbalance is greater than the rate of change of the negative-sequence imbalance, it is determined that the zero-sequence imbalance has higher sensitivity to the length of the same tower section. Step S100: When the rate of change of the negative sequence imbalance is greater than the rate of change of the zero sequence imbalance, it is determined that the negative sequence imbalance has higher sensitivity to the length of the same tower section.

[0080] This embodiment defines specific operational rules for performing parameter scanning and quantitative analysis of the sensitivity of zero-sequence and negative-sequence unbalance to the difference in the length of the same-tower section after completing the three-phase unbalance calculation. The core function of this analysis rule is to reveal the difference in the response of different sequence component unbalance to the length of the same-tower section through parameter scanning, providing a quantitative technical reference for optimizing the length of the same-tower section in the transmission line design stage. The length of the same-tower section is a key geometric parameter affecting the electromagnetic coupling strength of multi-circuit lines on the same tower. The degree of mutual inductance coupling between circuits in the same-tower section of different lengths is different. This difference in coupling strength will cause the zero-sequence and negative-sequence unbalance to show different trends and rates of change with the length of the same-tower section.

[0081] In practical implementation, the length of the same tower segment is used as a variable, and parameter scanning is performed within a preset length interval with a set step size. The lower and upper limits of the preset length interval are determined based on the typical range of the same tower segment length in actual transmission lines. The set step size determines the precision of the scan; a smaller step size results in more scan points and a smoother curve, but also increases computational overhead. For each same tower segment length, the entire calculation process is repeated, starting from obtaining the spatial location parameters of the conductor suspension point, through adaptive selection of impedance formula, construction of a segmented π model, modeling of coupled line operating conditions, solving state equations, and finally calculating the unbalance. The zero-sequence and negative-sequence unbalance corresponding to that same tower segment length is recorded. Through this scanning process, a set of discrete data points is obtained, each corresponding to a same tower segment length and its corresponding two unbalance calculation results.

[0082] Based on the recorded zero-sequence imbalance for each segment length, the rate of change of the zero-sequence imbalance relative to the segment length is calculated. The rate of change can be calculated using numerical differentiation, i.e., the difference in imbalance between adjacent scan points divided by the difference in segment length, yielding the average rate of change within that interval. To obtain a more stable estimate of the rate of change, curve fitting can be performed on the discrete data points, and the derivative of the fitted curve can be calculated. Similarly, based on the negative-sequence imbalance for each segment length, the rate of change of the negative-sequence imbalance relative to the segment length is calculated. These two rates of change characterize the sensitivity of the zero-sequence imbalance and the negative-sequence imbalance to changes in the segment length, respectively. A larger rate of change indicates that the imbalance of that sequence component is more sensitive to changes in the segment length.

[0083] Compare the rate of change of zero-sequence unbalance with the rate of change of negative-sequence unbalance. When the rate of change of zero-sequence unbalance is greater than that of negative-sequence unbalance, it indicates that the change in the length of the same-tower segment has a greater impact on zero-sequence unbalance than on negative-sequence unbalance. In this case, zero-sequence unbalance is determined to be more sensitive to the length of the same-tower segment. Conversely, when the rate of change of negative-sequence unbalance is greater than that of zero-sequence unbalance, negative-sequence unbalance is determined to be more sensitive to the length of the same-tower segment. These findings provide line designers with a clear direction for optimization. When controlling zero-sequence unbalance, the focus should be on the appropriate selection of the length of the same-tower segment. When controlling negative-sequence unbalance, the impact of the length of the same-tower segment is relatively small, and other influencing factors can be considered first.

[0084] Furthermore, you can also view Figure 4 , Figure 4 This is a flowchart illustrating the third embodiment of the method for calculating the three-phase imbalance of complex transmission networks according to the present invention. Figure 4 After the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence unbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence unbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes steps S110~S140: Step S110: Using the transmission capacity as a variable, perform parameter scanning within a preset capacity range with a set step size. Under each transmission capacity value, recalculate the three-phase symmetrical equivalent load impedance value of the end of other coupled lines in the same tower section, and repeatedly execute the state equation establishment and solution until the unbalance is calculated. Record the zero-sequence unbalance and negative-sequence unbalance corresponding to each transmission capacity value. Step S120: Plot the first curve of zero-sequence unbalance as a function of conveying capacity based on the zero-sequence unbalance for each conveying capacity value, and plot the second curve of negative-sequence unbalance as a function of conveying capacity based on the negative-sequence unbalance for each conveying capacity value. Step S130: Calculate the first sensitivity of zero-sequence imbalance to conveying capacity based on the first change curve, and calculate the second sensitivity of negative-sequence imbalance to conveying capacity based on the second change curve. Step S140: Compare the magnitude relationship between the first sensitivity and the second sensitivity to determine the differential sensitivity ranking of zero-sequence imbalance and negative-sequence imbalance to the transmission capacity of the coupled line.

[0085] This embodiment defines specific operational rules for performing parameter scanning and quantitative analysis of the sensitivity of zero-sequence and negative-sequence unbalance to the differential sensitivity of coupled line transmission capacity after completing the three-phase unbalance calculation, using transmission capacity as a variable. The core function of this analysis rule is to reveal the differences in the response of different sequence unbalance components to changes in coupled line transmission capacity through parameter scanning, providing a quantitative technical reference for transmission capacity scheduling and operation mode optimization during the transmission line operation phase. Transmission capacity directly determines the amplitude of the equivalent load impedance at the end of the coupled line, thus affecting the magnitude and distribution of current on the coupled line. This current change is transmitted to the target line through electromagnetic induction, causing zero-sequence and negative-sequence unbalance to exhibit differentiated response characteristics with changes in transmission capacity.

[0086] In practical implementation, the transmission capacity is used as a variable, and parameter scanning is performed within a preset capacity range with a set step size. The lower and upper limits of the preset capacity range are determined based on the actual transmission capacity adjustment range of the coupled lines on the same tower segment, and the set step size determines the precision of the scan. For each transmission capacity value, the three-phase symmetrical equivalent load impedance value at the end of other coupled lines on the same tower segment is recalculated. In this step, the change in transmission capacity directly changes the input parameters for calculating the equivalent load impedance. After updating the equivalent load impedance value, the process of re-establishing and solving the entire network state equation is repeated to obtain the voltage and current values ​​of each node, and then the corresponding zero-sequence unbalance and negative-sequence unbalance are calculated through phase sequence transformation. Through this scanning process, a set of discrete data points is obtained, each data point corresponding to a transmission capacity value and its corresponding two unbalance calculation results.

[0087] Based on the recorded zero-sequence imbalance for each conveying capacity value, a first curve showing the change in zero-sequence imbalance with conveying capacity is plotted; simultaneously, based on the recorded negative-sequence imbalance for each conveying capacity value, a second curve showing the change in negative-sequence imbalance with conveying capacity is plotted. The horizontal axis of both curves represents the conveying capacity value, and the vertical axes represent the corresponding zero-sequence imbalance value and negative-sequence imbalance value, respectively. The curves can be plotted using conventional data visualization tools, connecting discrete data points as line graphs or spline curves to facilitate observation and comparison of the trends and slopes of the two curves. The first and second curves visually demonstrate the trends of zero-sequence and negative-sequence imbalance with conveying capacity, and the slope of the curves indicates the degree of response of the two imbalances to changes in conveying capacity.

[0088] The first sensitivity of zero-sequence imbalance to conveying capacity is calculated based on the first change curve. Sensitivity is defined as the partial derivative of imbalance with respect to conveying capacity, reflecting the change in imbalance caused by a unit change in conveying capacity. The sensitivity can be calculated by averaging the absolute values ​​of the slopes at each point on the change curve, or by dividing the absolute value of the difference in imbalance between the maximum and minimum conveying capacity by the difference between the maximum and minimum conveying capacity. Similarly, the second sensitivity of negative-sequence imbalance to conveying capacity is calculated based on the second change curve. These two sensitivity values ​​quantitatively characterize the response strength of zero-sequence and negative-sequence imbalance to changes in conveying capacity; a higher sensitivity indicates that the imbalance component is more sensitive to changes in conveying capacity.

[0089] Finally, the relationship between the first and second sensitivities is compared, and the differential sensitivity ranking of zero-sequence imbalance and negative-sequence imbalance to the transmission capacity of coupled lines is determined based on the comparison results. When the first sensitivity is greater than the second sensitivity, the sensitivity of zero-sequence imbalance to transmission capacity is higher than that of negative-sequence imbalance, and the ranking result is zero-sequence priority over negative-sequence; conversely, negative-sequence priority over zero-sequence. The above sensitivity ranking results provide a clear reference for line operation dispatchers. In operation scenarios where zero-sequence imbalance needs to be prioritized, the adjustment strategy of coupled line transmission capacity should be the focus; in operation scenarios where negative-sequence imbalance needs to be prioritized, the impact of transmission capacity is relatively minor, and optimization schemes can be formulated in combination with other influencing factors.

[0090] This application provides a device for calculating the three-phase imbalance of a complex power transmission network. The device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method for calculating the three-phase imbalance of a complex power transmission network as described in Embodiment 1 above.

[0091] The following is for reference. Figure 9 This document illustrates a structural schematic diagram of a complex transmission network three-phase imbalance calculation device suitable for implementing embodiments of this application. The complex transmission network three-phase imbalance calculation device in this application embodiment may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 9 The illustrated device for calculating the three-phase imbalance of complex transmission networks is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0092] like Figure 9 As shown, the complex power transmission network three-phase imbalance calculation device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage device 1003 into a random access memory (RAM) 1004. The RAM 1004 also stores various programs and data required for the operation of the complex power transmission network three-phase imbalance calculation device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the complex power transmission network three-phase unbalance calculation device to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows a complex power transmission network three-phase unbalance calculation device with various systems, it should be understood that it is not required to implement or possess all the systems shown. More or fewer systems can be implemented alternatively.

[0093] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0094] The complex transmission network three-phase unbalance calculation device provided in this application adopts the complex transmission network three-phase unbalance calculation method in the above embodiments. It can solve the technical problems of existing three-phase unbalance algorithms not fully considering the impact of the operating conditions of adjacent coupled lines on the unbalance, and lacking an adaptive selection mechanism for impedance calculation formulas, resulting in insufficient calculation accuracy for multi-circuit mixed voltage shared tower scenarios. Compared with the prior art, the beneficial effects of the complex transmission network three-phase unbalance calculation device provided in this application are the same as those of the complex transmission network three-phase unbalance calculation method provided in the above embodiments, and other technical features in this complex transmission network three-phase unbalance calculation device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0095] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0096] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0097] This application provides a storage medium, which is a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, which are used to execute the method for calculating the three-phase imbalance of complex transmission networks in the above embodiments.

[0098] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0099] The aforementioned computer-readable storage medium may be included in a complex transmission network three-phase imbalance calculation device; or it may exist independently and not be assembled into the complex transmission network three-phase imbalance calculation device.

[0100] The aforementioned computer-readable storage medium carries one or more programs. When the aforementioned one or more programs are executed by the complex transmission network three-phase imbalance calculation device, the complex transmission network three-phase imbalance calculation device implements the technical content of the complex transmission network three-phase imbalance calculation method embodiment shown above.

[0101] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—and conventional procedural programming languages—such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0102] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0103] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0104] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., a computer program) for executing the above-described method for calculating the three-phase imbalance of complex transmission networks. This solves the technical problem that existing three-phase imbalance algorithms do not fully consider the impact of the operating conditions of adjacent coupled lines on the imbalance, and lack an adaptive selection mechanism for impedance calculation formulas, resulting in insufficient calculation accuracy for scenarios involving multiple circuits sharing voltage on the same tower. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the three-phase imbalance calculation method for complex transmission networks provided in the above embodiments, and will not be elaborated upon here.

Claims

1. A method for calculating the three-phase unbalance of complex transmission networks, characterized in that, Includes the following steps: Obtain the spatial position parameters of each conductor suspension point on the transmission tower; The Carson formula or the complex penetration depth formula is adaptively selected based on the line length and soil resistivity, and the impedance matrix and admittance matrix per unit length of the line are calculated using the spatial location parameters. The power transmission network is divided into multiple segments based on the electrical coupling relationship between the lines. A π equivalent model is established for each segment to obtain the impedance matrix and admittance matrix of each segment. Obtain the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower section. Calculate the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and voltage level, and use the three-phase symmetrical equivalent load impedance value as a boundary condition. State equations are established for each segment. The impedance matrix and admittance matrix of each segment, as well as the boundary conditions, are substituted into the state equations. The connection equations between segments are combined to form a set of electrical characteristic equations for the entire network and solved to obtain the voltage and current values ​​of the nodes at both ends of each segment. The voltage and current values ​​are converted into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix. The negative-sequence unbalance is calculated based on the ratio of the negative-sequence component to the positive-sequence component, and the zero-sequence unbalance is calculated based on the ratio of the zero-sequence component to the positive-sequence component.

2. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, The step of adaptively selecting the Carson formula or the multiple penetration depth formula based on the line length and soil resistivity includes: Obtain the total length of the transmission line to be calculated; When the total length is less than or equal to the first preset length, the Carson formula is used to calculate the impedance matrix and the admittance matrix per unit length. When the total length is greater than the first preset length, the complex penetration depth formula is used to calculate the impedance matrix per unit length and the admittance matrix per unit length. When the total length is equal to the first preset length, the average soil resistivity of the entire line is obtained. If the average value is higher than the preset threshold, the Carson formula is selected. If the average value is lower than or equal to the preset threshold, the multiple penetration depth formula is selected.

3. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, The step of adaptively selecting the Carson formula or the complex penetration depth formula based on the line length and soil resistivity, and calculating the impedance matrix and admittance matrix per unit length of the line using the spatial location parameters, includes: Obtain the measured values ​​of soil resistivity at the locations of each base tower along the line; Calculate the arithmetic mean of all measured values ​​along the entire line, which will serve as the representative value of the soil resistivity along the entire line; When the representative value is lower than a preset threshold, the complex penetration depth formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is not lower than the preset threshold, the Carson formula is used to calculate the unit length impedance matrix and the unit length admittance matrix. When the representative value is within a set floating range centered on the preset threshold, a calculation formula is further selected based on the line length. When the line length is less than or equal to fifty kilometers, the Carson formula is selected, and when the line length is greater than fifty kilometers, the multiple penetration depth formula is selected.

4. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, The step of dividing the power transmission network into multiple segments based on the electrical coupling relationship between lines includes: The multi-circuit transmission line section on the same tower in the power transmission network is divided into a basic section, and the single-circuit incoming line section before the starting point of the multi-circuit transmission line section on the same tower is divided into an independent section. When there is a change in the tower structure type within the multi-circuit erection section of the same tower, the foundation section is divided into multiple sub-segments at the location of the tower with the change in structure type. When there is a change in conductor type within the multi-circuit erection section on the same tower, the foundation section is divided into multiple sub-segments at the location of the tension section where the conductor type changes. When the length of any sub-segment exceeds the set maximum segment length threshold after division, the sub-segment is divided into multiple sub-segments with a length not exceeding the threshold along the line direction.

5. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, The step of obtaining the transmission capacity, voltage level, and operating mode of other coupled lines in the same tower section, and calculating the three-phase symmetrical equivalent load impedance value at the end of the line based on the transmission capacity and voltage level, includes: Calculate the three-phase rated load impedance amplitude at the end of each coupled line based on the transmission capacity and voltage level of each coupled line. Based on the operating mode of each coupled line, determine the number of circuits currently in operation for each coupled line. The operating mode includes single-circuit operation mode and double-circuit operation mode. When the operating mode is a single-circuit operating mode, the amplitude of the three-phase rated load impedance is directly used as the three-phase symmetrical equivalent load impedance value at the end of the coupling line. When the operating mode is a dual-circuit operating mode, the three-phase rated load impedance amplitudes of the two circuits are calculated in parallel to obtain the three-phase symmetrical equivalent load impedance value under the dual-circuit operating mode. When there are multiple coupled lines of different voltage levels in the same tower section, calculate the three-phase symmetrical equivalent load impedance value at the end of each coupled line and use it as the boundary condition for each circuit.

6. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, The steps of substituting the impedance and admittance matrices of each segment and the boundary conditions into the state equations, combining the connection equations between segments to form a set of electrical characteristic equations for the entire network, and solving them to obtain the voltage and current values ​​at the two ends of each segment include: For each segment, the three-phase voltage and three-phase current at the two ends of each segment are used as state variables to establish a state equation that reflects the relationship between the input and output electrical quantities of the segment. Based on the constraint that the voltages of adjacent segments are equal at the common node, the first type of connection equation between segments is established; Based on the constraint that the algebraic sum of the injected currents at the common node of adjacent segments is zero, a second type of connection equation between segments is established. The state equations of all segments, the first and second type connection equations between all segments, and the boundary conditions are combined to form a closed set of electrical characteristic equations for the entire network. The Newton-Raphson method is used to iteratively solve the electrical characteristic equations of the entire network until the maximum voltage correction value between two adjacent iterations is less than the convergence tolerance, at which point the iteration is terminated and the voltage and current values ​​of the nodes at both ends of each segment are output. When the Newton-Raphson method iteration fails to converge, the current solution is used as the initial value, and the damped Newton method is used to iterate again to obtain the voltage and current values ​​at the two ends of each segment.

7. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, After the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence imbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence imbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes: Using the length of the same tower segment as a variable, parameter scanning is performed within a preset length range with a set step size. Under each value of the same tower segment length, the process of obtaining spatial location parameters is repeated until the unbalance is calculated. The zero-sequence unbalance and negative-sequence unbalance corresponding to each value of the same tower segment length are recorded respectively. The rate of change of zero-sequence unbalance relative to the length of the same tower section is calculated based on the zero-sequence unbalance for each tower section length value, and the rate of change of negative-sequence unbalance relative to the length of the same tower section is calculated based on the negative-sequence unbalance for each tower section length value. Compare the rate of change of the zero-sequence imbalance with the rate of change of the negative-sequence imbalance. When the rate of change of the zero-sequence imbalance is greater than the rate of change of the negative-sequence imbalance, it is determined that the zero-sequence imbalance has a higher sensitivity to the length of the same tower section. When the rate of change of the negative sequence imbalance is greater than the rate of change of the zero sequence imbalance, it is determined that the negative sequence imbalance has a higher sensitivity to the length of the same tower section.

8. The method for calculating the three-phase imbalance of complex transmission networks as described in claim 1, characterized in that, After the steps of converting the voltage and current values ​​into positive-sequence, negative-sequence, and zero-sequence components using a phase sequence transformation matrix, calculating the negative-sequence imbalance based on the ratio of the negative-sequence component to the positive-sequence component, and calculating the zero-sequence imbalance based on the ratio of the zero-sequence component to the positive-sequence component, the method further includes: Using the transmission capacity as a variable, parameter scanning is performed within a preset capacity range with a set step size. Under each transmission capacity value, the three-phase symmetrical equivalent load impedance value of the end of other coupled lines in the same tower section is recalculated, and the state equation establishment and solution are repeatedly executed until the unbalance is calculated. The zero-sequence unbalance and negative-sequence unbalance corresponding to each transmission capacity value are recorded respectively. Plot the first curve of zero-sequence unbalance as a function of conveying capacity for each conveying capacity value, and plot the second curve of negative-sequence unbalance as a function of conveying capacity for each conveying capacity value. The first sensitivity of zero-sequence imbalance to conveying capacity is calculated based on the first change curve, and the second sensitivity of negative-sequence imbalance to conveying capacity is calculated based on the second change curve. By comparing the magnitudes of the first sensitivity and the second sensitivity, the differential sensitivity ranking of zero-sequence imbalance and negative-sequence imbalance to the transmission capacity of the coupled line is determined.

9. A device for calculating the three-phase imbalance of a complex power transmission network, characterized in that, The complex power transmission network three-phase imbalance calculation device stores a computer program, which, when executed by a processor, implements the complex power transmission network three-phase imbalance calculation method according to any one of claims 1-8.

10. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method for calculating the three-phase imbalance of complex power transmission networks as described in any one of claims 1-8.

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