A method and system for optimal design of double circuit transmission lines considering system zero sequence current constraint

Abstract

The application provides a kind of same-tower double-circuit line optimization design method and system considering system zero sequence current constraint: generating full coupling impedance matrix and admittance matrix representing the coupling relationship of six-phase conductor, and integrating the line model with the system model containing the neutral point grounding branch of main transformer, to build a system-line coupling simulation model;With phase sequence arrangement and transposition strategy as design variables, the phase sequence arrangement and transposition strategy are screened and selected to generate a set of candidate design schemes;Batch simulation is carried out on the candidate design scheme set, the three-phase current data of the high-voltage side of the main transformer is extracted, and the neutral point zero sequence current evaluation value of the main transformer corresponding to each scheme is calculated by using the symmetrical component method;With the minimum zero sequence current evaluation value and construction cost as double objectives, and the zero sequence current safety limit and voltage unbalance limit as constraints, a multi-objective optimization algorithm is used to solve the Pareto optimal solution set, and a recommended design scheme is output.

Description

Technical Field

[0001] This invention relates to the field of power system design technology, and in particular to an optimization design method and system for double-circuit lines on the same tower that considers the system's zero-sequence current constraint. Background Technology

[0002] Against the backdrop of the power system's transformation towards clean and low-carbon development, the large-scale development and construction of new energy bases in desert areas and other remote regions has become a core direction, and the demand for efficient transmission of centralized photovoltaic and wind power is increasingly urgent. Double-circuit transmission lines on the same tower have become the mainstream channel for transmitting new energy power due to their advantages such as intensive land use, controllable construction costs, and large transmission capacity. To further reduce construction costs, the length of these new energy transmission lines is mostly controlled within the range of 40-80km. According to the existing "Electrical Design Code for Overhead Transmission Lines" (DL / T 5582-2020), which stipulates that "transmission lines exceeding 100km in length should be transposed," lines within this length range usually do not require transposition measures.

[0003] However, traditional design codes are primarily based on transmission scenarios for conventional power sources such as thermal and hydropower. At that time, the system structure was relatively stable, and the factors influencing line imbalance were relatively simple, focusing only on the electrical characteristics of the line itself. Therefore, using length as the core basis for transposition decisions had some applicability. However, renewable energy transmission scenarios differ significantly from traditional scenarios: renewable energy power plants (such as photovoltaic and wind power) mostly use inverters for grid connection, resulting in strong output fluctuations and a wide adjustable power factor range, which differs significantly from the electrical characteristics of traditional synchronous generators. Furthermore, large renewable energy bases are mostly located at the edge of the grid, where the system short-circuit capacity at the connection point is relatively weak, and the electromagnetic coupling interaction between the line and the grid system is more prominent. These characteristics mean that the electrical imbalance problem of short-distance double-circuit lines on the same tower is no longer determined solely by line length, but is deeply related to multiple factors such as the neutral grounding method of the connected system, the system short-circuit capacity, the expected maximum transmission power of the renewable energy power plant, and the phase sequence arrangement.

[0004] In existing design processes, there are often professional barriers between line design and system design. Line design often focuses on its own insulation coordination and current carrying capacity, failing to fully consider compatibility with the connected system. This results in a lack of system-level constraints supporting key design decisions such as phase sequence arrangement and transposition strategies. As demonstrated by the Kubuqi New Energy Project, its 37.3km double-circuit line on the same tower, using a BCA-BAC phase sequence arrangement, experienced a zero-sequence current at the neutral point of the main transformer at Yunheng Station reaching 137.5A under 800MW full-power transmission conditions. This not only caused abnormal operation of the main transformer but also led to a series of chain reactions, including frequent tripping of the SVG device and power quality exceeding standards, severely impacting the stable absorption of new energy power. Simulation verification showed that simply adjusting the phase sequence to BCA-ACB reduced the zero-sequence current to 41.4A, meeting safe operation requirements. Such cases clearly illustrate that if the phase sequence arrangement and transposition decisions for short-distance double-circuit new energy transmission lines on the same tower continue to use a "one-size-fits-all" length standard, it is highly likely to create operational hazards. Moreover, these problems often only become apparent after the lines are put into operation. At this point, remedial measures such as relocation and phase sequence adjustment not only incur high construction costs but also cause prolonged power outages, resulting in huge economic losses and losses in renewable energy consumption. Existing technologies are no longer sufficient to meet the actual needs of safe and efficient transmission from large renewable energy bases. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides an optimization design method and system for double-circuit transmission lines on the same tower, considering system zero-sequence current constraints. The method first inputs line geometric and electrical parameters, system-side parameters, and zero-sequence current safety limits. Based on precise electromagnetic field theory, it calculates the fully coupled impedance and admittance matrices characterizing the coupling relationship of the six-phase conductors and integrates them with a system model including the neutral-point grounded branch of the main transformer to construct a high-precision system-line coupling simulation model. Subsequently, using phase sequence arrangement and transposition strategies as design variables, it innovatively introduces the inverse sequence index between the phase sequences of the double-circuit lines and combines it with line length for intelligent screening, generating a set of candidate design schemes. The coupling model is used to perform batch simulations of the candidate schemes, extracting the high-voltage side current of the main transformer and calculating its neutral-point zero-sequence current evaluation value. Finally, with minimizing zero-sequence current and construction cost as dual objectives, and with safety limits and voltage imbalance limits as constraints, a multi-objective optimization algorithm is used to automatically solve for the Pareto optimal solution set and output the recommended design scheme. This invention realizes a design paradigm shift from "length-based empirical judgment" to "quantitative optimization oriented towards system interaction," which can effectively avoid the risk of excessive zero-sequence current after commissioning during the design phase, while also taking into account engineering economy.

[0006] The present invention specifically adopts the following technical solution:

[0007] An optimization design method for a double-circuit line on the same tower considering system zero-sequence current constraints includes:

[0008] Input the geometric and electrical parameters of the double-circuit line to be designed on the same tower, the system-side parameters to be connected to the power grid, as well as the safety limit of the zero-sequence current of the neutral point of the main transformer, the voltage imbalance limit, and the economic constraints.

[0009] Based on the geometric parameters, the fully coupled impedance matrix and admittance matrix characterizing the coupling relationship of the six-phase conductors are calculated using classical electromagnetic theory. The line model is then integrated with the system model including the neutral grounding branch of the main transformer to construct a system-line coupling simulation model.

[0010] Using phase sequence arrangement and transposition strategy as design variables, and based on engineering safety specifications, reverse sequence index between phase sequences of double-circuit lines and line length, phase sequence arrangement and transposition strategy are screened and selected to generate a set of candidate design schemes.

[0011] The coupled simulation model is used to perform batch simulations on the candidate design scheme set, extract the three-phase current data of the high-voltage side of the main transformer, and use the symmetrical component method to calculate the evaluation value of the neutral point zero-sequence current of the main transformer corresponding to each scheme.

[0012] With minimizing the zero-sequence current assessment value and construction cost as dual objectives, and with the zero-sequence current safety limit and voltage imbalance limit as constraints, a multi-objective optimization algorithm is used to solve for the Pareto optimal solution set and output a recommended design scheme.

[0013] Furthermore, the geometric parameters include the tower structure diagram, the hanging point height of each phase conductor, the phase-to-phase distance, the spacing between split conductors, the span, and the sag data; the electrical parameters include the conductor type, AC resistance, outer diameter, and equivalent radius; the system-side parameters include the main transformer parameters, the neutral point grounding method, the system short-circuit capacity, and the parameters of the planned operation scenario; and the construction cost includes the additional cost of the transposition tower and the additional cost of non-standard phase sequence construction.

[0014] Furthermore, when calculating and generating the fully coupled impedance matrix and admittance matrix, the Carson-Clem formula or the complex image method is used to calculate the ground return current effect, generating a 6×6 matrix, and the average value or approximation is not used; the system model integration is achieved by writing the matrix into a custom model file that can be called by the simulation software, or by dynamically constructing the equivalent circuit chain using the script interface of the simulation software.

[0015] Furthermore, the selection is based on the reverse sequence index, specifically: the matching degree of the reversed phase sequence string of the double-circuit line is calculated as the reverse sequence index, and only phase sequence combinations with an index greater than a preset threshold are retained; the candidate combinations of the phase sequence arrangement are selected from {ABC, ACB, BAC, BCA, CAB, CBA}; the selection is based on the line length, specifically the following rules: if the line length is less than the first length threshold, a no-transposition strategy is selected; if the line length is between the first length threshold and the second length threshold, a no-transposition or single-transposition strategy is selected; if the line length is greater than or equal to the second length threshold, a full-transposition strategy is added.

[0016] Furthermore, the transposition point for a single transposition or a full transposition is selected within the first 1 / 3 to the last 1 / 3 of the line length.

[0017] Furthermore, the batch simulation includes at least a full-load scenario with the maximum planned transmission power; the multi-objective optimization algorithm is the NSGA-II algorithm, and the successful candidate design schemes in the simulation and their corresponding zero-sequence current evaluation values ​​and construction cost evaluation values ​​are directly used as the initial population of the algorithm.

[0018] Furthermore, after outputting the recommended design scheme, a robustness verification step is also included: finely adjust the position of the switching point or change the system operating power factor within a preset range, re-simulate and calculate the rate of change of the zero-sequence current evaluation value. If the rate of change is less than the preset threshold, the robustness of the scheme is determined to be up to standard.

[0019] Furthermore, the voltage imbalance limit is no more than 2%.

[0020] Furthermore, the construction of the system-line coupling simulation model includes: establishing a unified three-dimensional coordinate system, analyzing the spatial coordinates of the suspension points of each phase conductor at each tower, calculating the spatial coordinates of discrete points along the conductor line by combining the span and sag, and generating a topology connection table containing electrical node numbers and conductor segment connection relationships.

[0021] And, an optimized design system for a double-circuit line on the same tower considering zero-sequence current constraints, comprising:

[0022] The parameter and constraint input module is used to input the geometric parameters and electrical parameters of the double-circuit line on the same tower to be designed, the system-side parameters to be connected to the power grid, as well as the safety limit of the neutral point zero-sequence current of the main transformer, the voltage imbalance limit, and the economic constraints.

[0023] The coupled simulation model construction module is used to calculate and generate the fully coupled impedance matrix and admittance matrix representing the coupling relationship of the six-phase conductors based on the geometric parameters and using classical electromagnetic theory. It also integrates the line model with the system model containing the neutral point grounding branch of the main transformer to construct a system-line coupled simulation model.

[0024] The candidate scheme generation module is used to filter and select phase sequence arrangement and transposition strategy as design variables, based on engineering safety specifications, reverse sequence index between phase sequences of double-circuit lines and line length, and generate a set of candidate design schemes.

[0025] The batch simulation evaluation module is used to perform batch simulations of the candidate design scheme set using the coupled simulation model, extract the three-phase current data of the high-voltage side of the main transformer, and calculate the evaluation value of the neutral point zero-sequence current of the main transformer corresponding to each scheme using the symmetrical component method.

[0026] The multi-objective optimization decision module is used to solve the Pareto optimal solution set by employing a multi-objective optimization algorithm, with the dual objectives of minimizing the zero-sequence current assessment value and construction cost, and the constraints of the zero-sequence current safety limit and voltage imbalance limit, and outputs a recommended design scheme.

[0027] Compared to existing technologies, this invention and its preferred solution effectively break down the professional barriers between line design and system design in traditional double-circuit line designs on the same tower. By constructing a coupled simulation model integrating the line and the power grid system, it achieves precise consideration of the interaction between the line and the access system, avoiding operational hazards such as excessive zero-sequence current caused by neglecting system-level constraints from the design source. Relying on the collaborative screening and selection logic of engineering safety specifications, reverse sequence index, and line length, it replaces the traditional "one-size-fits-all" length determination standard, making the design of phase sequence arrangement and transposition strategies more targeted and adaptable, significantly improving the technical rationality of short-distance double-circuit line design schemes on the same tower. By directly using the effective schemes verified by batch simulations as the initial population of the optimization algorithm, the efficiency and accuracy of multi-objective optimization are greatly improved, ensuring that the output design scheme can achieve a balance between technical safety and engineering economy while meeting constraints such as zero-sequence current safety limits and voltage imbalance limits. Meanwhile, the added robustness verification steps further ensure the stability and reliability of the recommended scheme under actual operating condition fluctuations, effectively reducing the risk of modification and economic losses caused by design defects after the line is put into operation, and are generally adapted to the actual needs of safe and efficient transmission of dual-circuit lines on the same tower in large-scale new energy bases. Attached Figure Description

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0029] Figure 1 This is a flowchart illustrating the implementation of the method in an embodiment of the present invention. Detailed Implementation

[0030] In the following, specific embodiments of this application will be described in detail with reference to the accompanying drawings. Based on these detailed descriptions, those skilled in the art will be able to clearly understand and implement this application. Without departing from the principles of this application, features from various embodiments can be combined to obtain new implementations, or certain features from some embodiments can be substituted to obtain other preferred implementations.

[0031] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0032] The core problem this invention aims to solve is: how to accurately predict, in advance during the planning and design phase of transmission lines, the potential system-level zero-sequence current problem that may arise after the commissioning of double-circuit non-transfer lines on the same tower, and accordingly optimize the line design (such as transposition strategies and phase sequence arrangements) to avoid operational problems such as excessive neutral point current of the main transformer and SVG tripping after commissioning. Specifically, this includes:

[0033] (1) Design standard lag problem: make up for the lack of consideration of the system problems that may be caused by "short circuits" in the existing design specifications.

[0034] (2) Design island problem: break down the barriers between circuit design and system design to achieve cross-disciplinary collaboration.

[0035] (3) Post-event management issues: Advance the decision-making of management measures (such as relocation) to the design stage to avoid high renovation costs and power outage losses after commissioning.

[0036] To address the above issues, this invention introduces a "system-line coupling simulation analysis" step during the design phase. A digital twin is constructed, and various design schemes are simulated and iterated. The zero-sequence current constraint is taken as one of the core constraints, guiding the line's design decisions in reverse. The provided systematic implementation is essentially a digital and intelligent decision support platform integrated into the power engineering planning and design phase. It is not a physical device after commissioning, but a software method and system embedded in the design process, aiming to transform the "system zero-sequence current constraint" from a traditional post-conversion verification item to a pre-conversion driving item. The entire system architecture revolves around a core objective: before the design drawings are finalized, to pre-simulate the electrical performance under the most stringent operating conditions after the line is commissioned, and to automatically optimize and recommend the most economical and reliable line design scheme with zero-sequence current as one of the core safety constraints. Its detailed workflow and module interactions are detailed below. Figure 1 Specifically, it can be broken down into five key steps:

[0037] Step 1: Input of Multidimensional Parameters and Constraints

[0038] This step is the cornerstone of the solution analysis (corresponding to...) Figure 1The submodule of step 1 requires input of three types of information: first, line geometry and material parameters; second, system electrical and operating parameters; and third, safety and economic constraints, covering multi-dimensional basic data of conventional line design and system level.

[0039] Step 2: Construct a "system-circuit" coupled digital twin

[0040] This step is the core module of the solution (corresponding to...) Figure 1 Step 2, “Coupled Model Engine”: Based on the kernel of professional power simulation software such as PSCAD / EMTDC, ATP-EMTP, or electromechanical transient programs that support custom models, a refined asymmetric coupled model is constructed: Based on the input precise geometric parameters, the 6×6 order impedance and admittance matrix of the double-circuit line on the same tower is dynamically calculated and generated (fully considering the mutual coupling between the double-circuit lines, without using average or approximate values). Then, the line model is seamlessly connected with the system model containing the main transformer (including the neutral grounding branch), power source, and load to form a complete digital twin power grid that can perform power flow and transient calculations.

[0041] Step 3: Automatically generate candidate design schemes

[0042] pass Figure 1 Step 3, the "Solution Generator," uses rule logic and permutation and combination methods to exhaustively or intelligently search for design variables such as phase sequence and transposition strategy, and outputs a set of feasible candidate design schemes.

[0043] Step 4: Batch Simulation and Core Security Assessment

[0044] This step is the "virtual testing ground" (corresponding to...). Figure 1 (Sub-module of step 4): First, the simulation computing cluster performs automated batch simulations of each candidate scheme; then, the "evaluator" extracts the core indicators: zero-sequence current and negative-sequence voltage imbalance, to complete the quantitative evaluation of each scheme and provide data support for subsequent decision-making.

[0045] Step 5: Intelligent Optimization and Comprehensive Decision-Making

[0046] This step involves making trade-offs in the solutions (corresponding to...) Figure 1 (Module interaction in step 5): First, determine whether the current candidate solution satisfies all constraints and is the optimal solution; if "yes", output the final recommended solution; if "no", start the optimization algorithm engine to adjust the design variables, return to step 3 to generate new candidate solutions, until the optimal solution that meets the requirements is obtained.

[0047] As a preferred implementation of this embodiment, step 1 specifically includes the following steps:

[0048] S1.1 Data Collection and Input: Define the range of basic parameters to be collected, and enter the data into the system after data collection and organization. This includes two types of core parameters:

[0049] (1) Line body parameters:

[0050] 1. Geometric parameters: Accurate tower structure diagram, suspension point height of each phase conductor, phase distance, and spacing of split conductors provide a direct basis for calculating asymmetrical mutual impedance and mutual capacitance.

[0051] 2. Electrical parameters: wire type, resistance, outer diameter.

[0052] (2) System-side parameters:

[0053] 1. Topology and equipment parameters: short-circuit impedance, rated capacity, and planned neutral grounding method of the main transformer connected to the substation (e.g., how many are directly grounded and how many are gap grounded).

[0054] 2. Operating parameters: the planned maximum power output of the new energy power station, the power factor range, and the minimum and maximum short-circuit capacity of the upstream power grid (used to assess the strength of the system).

[0055] S1.2. Reviewing and inputting constraints: By clarifying the safety and economic boundaries of the implementation plan, relevant constraint indicators are compiled and entered.

[0056] 1. Safety constraints: alarm value and trip value of zero-sequence current at the neutral point of the main transformer, national standard for negative-sequence voltage imbalance at the grid connection point (e.g., 2%), and circuit breaker breaking current.

[0057] 2. Economic constraints: the cost difference between transposed towers and ordinary towers, and the weight of construction complexity for different phase sequence arrangements.

[0058] As a preferred implementation of this embodiment, based on the standardized data and constraints output in step 1, refined modeling is performed. Step 2 specifically includes the following steps:

[0059] S2.1: Data Standardization and Conductor Network Topology Generation. To transform the line geometric parameters into structured data usable for electromagnetic coupling calculations, a unified three-dimensional coordinate system must first be established to clarify the quantification standards for conductor spatial positions, laying the foundation for subsequent conductor coordinate analysis and impedance / admittance matrix calculations. Input the original design parameters from step 1. Transform the chaotic design information into structured coordinate data with clearly defined electrical connections. Specific execution includes:

[0060] 1. Establish a unified coordinate system:

[0061] (1) The origin of the coordinate system is the projection of the center of the starting tower of the line onto the ground (0,0,0).

[0062] (2) The X-axis direction is the route of the line (horizontal); the Y-axis direction is the horizontal direction perpendicular to the route of the line (used to distinguish the two circuits of the same tower); the Z-axis direction is the direction perpendicular to the ground and upward (height above the ground).

[0063] 2. Analysis of spatial coordinates of the traverse:

[0064] (1) Based on the tower type (e.g., 2H3-SZ2-33) and phase sequence arrangement, the spatial coordinates (x, y, z) of the suspension point of each phase (6 phases in total) at each tower are analyzed. For example: For a certain tower, the coordinates of the suspension point of phase B of the upper line (e.g., Yunggu Line) can be analyzed as (0, 6.0, 43.2), indicating that it is located at the center of the line (X=0), on the middle line (Y=6.0m), and 43.2 meters above the ground. The coordinates of the suspension point of phase C of the lower line (e.g., Gujie Line) can be analyzed as (0, -6.0, 36.4).

[0065] (2) Along the route, based on the span and sag, calculate the spatial coordinates of the conductor at multiple discrete points to form a three-dimensional spatial path description of the conductor.

[0066] 3. Generate electrical node and topology connection table:

[0067] (1) Define each phase conductor at each important location (such as tower point, switching point, first and last point) as an electrical node and assign it a unique number.

[0068] (2) Generate a “conductor segment connection table” to clearly record which two electrical nodes are connected by which phase conductor and associate the geometric coordinate sequence of the conductor segment. Example: [segment ID:001, start node: N1_Yungu_A, end node: N2_Yungu_A, phase: A, coordinate set: [(x1,y1,z1),(x2,y2,z2),...].

[0069] S2.2: Calculation of the fully coupled parameter matrix based on classical electromagnetic theory: Input the conductor coordinates and topology generated in sub-step S2.1. Calculate the 6×6 impedance matrix [Z] and admittance matrix [Y] that accurately describe the electromagnetic and electrostatic coupling relationship between all 6 conductors.

[0070] 1. Core algorithm logic (for calculating arbitrary elements of the [Z] matrix) (For example)

[0071] (1) Using standard engineering calculation methods: The “Carson-Clem formula” or its equivalent “complex mirror method” is used as the basis for calculating the geodetic backflow effect. This method itself is a well-known technology in this field.

[0072] 2. Detailed calculation process:

[0073] a. Calculate the self-impedance of the conductor :

[0074] ,

[0075] In the formula Let be the AC resistance (Ω / km) of conductor i. Angular frequency, ; Let be the average height (in meters) of conductor i above the ground. For the depth of penetration into the earth, , The value is the soil resistivity (Ω·m). : Equivalent radius of conductor i (meters). j is the imaginary unit.

[0076] b. Calculate the mutual impedance between conductors :

[0077] ,

[0078] ,

[0079]

[0080] In the formula Let be the distance (in meters) between the mirror images of conductor i and conductor j. The actual spatial distance (in meters) between conductor i and conductor j. Let i be the coordinates of conductor i in the defined spatial rectangular coordinate system.

[0081] 3. Matrix assembly and segmentation:

[0082] (1) Traverse all i,j(1-6) to complete the above calculation and fill the 6×6 impedance matrix [Z].

[0083] (2) For long lines, if the tower types or arrangements in different sections are different, multiple different [Z]_{segment} matrices need to be calculated segment by segment.

[0084] (3) Calculate the potential coefficient matrix [P] using the same principle (mirror method), and then inverse it to obtain the admittance matrix. .

[0085] Among them, the potential coefficient , The calculation is as follows:

[0086]

[0087]

[0088] In the formula is the vacuum permittivity.

[0089] S2.3: System Model Integration and Digital Twin Instantiation: Input the line parameter matrix calculated in sub-step S2.2 and the system-side parameters from step 1. Connect the line model to the virtual power grid to form a complete, simulable system digital twin, specifically including:

[0090] 1. Construct a system-side baseline model: In a simulation environment (such as PSCAD, EMTP-RV, or a custom solver), establish grid-side component models, including an ideal voltage source (representing the system equivalent), the main transformer (including YNd winding connections and neutral point grounding branches; the grounding branch can be directly grounded, grounded through resistor R_n, or grounded through reactance X_n), and substation loads / power sources (PV inverter aggregation model), etc. All component parameters are derived from the input in step 1.

[0091] 2. Embedding a custom line model: This embodiment provides the following two specific implementation schemes. The external model injection method is suitable for scenarios where line parameters are fixed and do not require real-time adjustment, and has the advantages of high modeling efficiency and strong simulation stability. The internal script construction method is suitable for scenarios where line geometric parameters need to be dynamically optimized (such as adjusting the position of the switching point), and can realize real-time linkage updates between parameters and the model.

[0092] (1) Method A (External Model Injection): Compile the calculated [Z] and [Y] matrices into a custom line model file according to the format required by the simulation software (e.g., EMTP's DATA card format or PSCAD's Line Constants program output format). In the simulation project, use this file to replace the standard, symmetrical line model.

[0093] (2) Method B (internal script construction): Using the script interface of the simulation software (such as Python API), write a script program to dynamically calculate [Z] and [Y] in real time according to the input geometric parameters during the simulation initialization stage, and construct the corresponding frequency domain correlation equivalent model or π-type equivalent circuit chain inside the software.

[0094] 3. Complete electrical connection and verification: Connect the electrical ports (6 or 3 phase ports) of the custom line model to the corresponding bus nodes in the system-side reference model according to the design topology. Perform a simple no-load charging test or symmetrical power flow calculation to verify that the model has no hardware errors and that the voltage and current are within a reasonable range. This marks the completion of the construction of the "system-line" coupled digital twin, which can be used for batch simulation in step 4.

[0095] As a preferred implementation of this embodiment, step 3 specifically includes the following steps:

[0096] S3.1: Define design variables and coding rules: Input the basic line parameters (such as voltage level and number of circuits) and system constraints from step 1.

[0097] 1. Design variable identification: Identify key, changeable design decision points that affect zero-sequence current.

[0098] (1) Variable A: Phase Sequence. This refers to the spatial arrangement of the three-phase conductors (A, B, C) in each circuit of a double-circuit line on the same tower, either horizontally or vertically. This is the most important variable affecting the asymmetry of electromagnetic coupling.

[0099] (2) Variable B: Transposition Scheme. This refers to whether and how the spatial positions of the three-phase conductors are exchanged at multiple points along the line to average the asymmetric parameters. This is a structural measure to fundamentally eliminate imbalance. 2. Variable Coding Design: Establish a concise and unambiguous digital coding system for each variable to facilitate computer processing and subsequent optimization algorithms. Specifically, this includes:

[0100] ① Phase sequence encoding: A 3-bit string is used to directly represent the phase sequence. For example, "ABC" represents phases A, B, and C from left to right (or from top to bottom); "BCA" represents phases B, C, and A. All possible permutations for a single-circuit line are: S={ABC,ACB,BAC,BCA,CAB,CBA}, a total of 6.

[0101] ② Transposition Strategy Encoding: A "position-operation" sequence encoding is used. For example: "0-NONE-1": indicates "no transposition". (0 and 1 represent the start and end points of the line, NONE represents no operation). "0-ACB-0.5-ABC-1": indicates setting a transposition point at the midpoint of the line (position 0.5), performing an "ACB" transposition at that point (i.e., the positions of the conductors before and after this point are swapped according to the rule A->C, C->B, B->A). "0-ACB-0.33-BCA-0.67-ABC-1": indicates two transposition points, achieving a complete "full transposition" cycle. This is the most effective but also the most costly strategy.

[0102] S3.2: Generation of Feasible Solution Space Based on Engineering Rules: Input the variables and coding rules defined in sub-step 3.1. By fully utilizing professional knowledge in the field of power engineering through expert evaluation and other methods, a more reasonable set of solutions is defined and generated, eliminating obviously invalid or harmful combinations, which helps to significantly improve search efficiency.

[0103] 1. Definition and generation of the rationality rules for phase sequence arrangement:

[0104] (1) Rule 1 (Electrical Coupling Optimization Rule): Prioritize generating phase sequences that can partially cancel the magnetic coupling between double circuits. Define the "Reverse Sequence Index" R. The calculation method is as follows: Compare the phase sequence strings of the double circuits. For example, for the upper line "ABC" and the lower line "CBA", after reversing the lower line string to get "ABC", which is exactly the same as the upper line, then R = 1 (fully reverse sequence, optimal). If only some consecutive characters match after reversal, then 0 < R < 1. The system sets a threshold (such as R > 0.5), and only generates phase sequence pairs that meet the conditions. This rule directly targets the goal of suppressing zero-sequence current.

[0105] (2) Rule 2 (Engineering Safety and Specification Rule): Exclude phase sequence arrangements that will result in insufficient air gaps between conductors with the same potential or conductor crossings on specific tower types. This requires pre-storing or real-time calculating the conductor spatial distances under different arrangements and comparing them with safety regulations.

[0106] (3) Generation Algorithm: Instead of simply performing the Cartesian product on the set S (generating 36 combinations). First, according to Rule 2, screen out the single-circuit phase sequence set S_feasible that is feasible for this tower type from S. Then, for each phase sequence in S_feasible, according to Rule 1, find another phase sequence with the highest R value to pair with it, forming a list of preferred phase sequence pairs. At the same time, a small number of combinations with lower R values but specific ones can also be retained for comparison.

[0107] 2. Definition and Generation of Adaptability Rules for Transposition Strategies:

[0108] (1) Rule 3 (Strategy Classification Rule Based on Line Length): This is a quantitative extension of traditional regulations. According to the total line length L (km) and simulation experience, dynamically generate a strategy set: If L < L_min (for example, 20 km): Strategy set = {"0-NONE-1"} / / Too short, the transposition benefit does not offset the cost; If L_min ≤ L < L_th (for example, L_th = 100 km, which is the regulation threshold): Strategy set = {"0-NONE-1", "0-{Single Transposition Scheme}-1"} / / Consider "no transposition" and "single transposition"; If L ≥ L_th: Strategy set = {"0-NONE-1", "0-{Single Transposition Scheme}-1", "0-{Full Transposition Scheme}-1"} / / Include full transposition.

[0109] (2) Optimization of Transposition Point Positions: For strategies that require transposition, the transposition point position is not simply taken as the midpoint. The system can generate 2 - 3 alternative positions (such as 0.33, 0.5, 0.67) within the interval [0.2, 0.8] based on the line impedance non-uniformity, forming different position sub-variants under the same transposition operation.

[0110] S3.3: Scheme Combination and Output: Input the preferred phase sequence pair list and adaptive transposition strategy set generated in sub-step S3.2. Combine the design variables of the two dimensions into complete candidate design schemes and output them in a formatted manner for the next simulation evaluation, specifically including:

[0111] 1. Combinatorial Logic: For each phase sequence pair (Seq_up, Seq_down) in the preferred phase sequence pair list, it is combined with each transposition strategy TransScheme in the adaptive transposition strategy set to form a complete candidate scheme (Cartesian Product). For example, the phase sequence pair ("BCA", "ACB") is combined with the strategy "0-NONE-1" to obtain the scheme {phase_seq:("BCA", "ACB"), trans_scheme: "0-NONE-1"}.

[0112] 2. Scheme Description and Unique Identifier: Generate a structured description and a unique ID for each generated scheme.

[0113] Structured description: Includes all design decisions and parameters used for simulation.

[0114] For example:

[0115] {

[0116] "scheme_id":"PSQ_BCA-ACB_TRANS_NONE_001",

[0117] "line_a_sequence":"BCA",

[0118] "line_b_sequence":"ACB",

[0119] "transposition_scheme":"0-NONE-1",

[0120] "description": "Upstream phase sequence BCA, downstream phase sequence ACB, no transposition."

[0121] }

[0122] 3. Output: Output all generated candidate solutions in list or database format as the direct input list for step 4 (batch simulation). The system can also output a generation report, indicating the total number of solutions generated and the rules used for selection.

[0123] The generated candidate scheme set contains all feasible phase sequence-transposition combinations and structured parameters, which can be directly used as the input list for batch simulations. Subsequent simulations will evaluate the zero-sequence current and economic performance of each scheme.

[0124] As a preferred implementation of this embodiment, step 4 specifically includes the following steps:

[0125] S4.1: Candidate Solution Import and Simulation Task Initialization: Input the structured candidate solution list output in step 3 to prepare the task queue and parameterized simulation model template for batch simulation.

[0126] 1. Scheme List Parsing: The system reads the candidate scheme list file (such as JSON or CSV format). Each scheme entry contains key fields such as scheme_id, phase_sequence, and transposition_scheme.

[0127] 2. Simulation Template Cloning: Based on the baseline digital twin constructed in step 2 (i.e., a blank line model already connected to the system) that does not contain specific phase sequence and transposition operations, an independent simulation project instance is cloned for each candidate scheme. This ensures that all schemes are evaluated in the exact same system context.

[0128] 3. Dynamic injection of model parameters:

[0129] (1) Phase sequence application: Based on the phase_sequence in the scheme, modify the phase connection relationship of the lines in the clone. For example, if the scheme specifies the upper line as "BCA", then in the simulation model, the electrical nodes connected to the physical locations 1, 2, and 3 of the upper line need to be reassigned as the voltage and current output points of phase B, phase C, and phase A, respectively.

[0130] (2) Implementation of transposition strategy: Parse transposition_scheme encoding. For example, if “0-ACB-0.5-...” is encountered, a “transposition element” is inserted at the position of 50% of the line length in the simulation model. The element internally realizes the cross connection of the three-phase conductors according to the mapping relationship of A->C, C->B, B->A.

[0131] 4. Generate simulation task queue: Each configured simulation instance is bound to a unique task ID and added to the parallel simulation task queue, waiting for computing resource scheduling.

[0132] S4.2: Simulation Scenario Configuration and Calculation Parameter Setting: Input the system operation mode defined in step 1 (e.g., maximum output, minimum output, N-1 fault mode). Define the grid operating conditions under which the design scheme will be "stress-tested," specifically including:

[0133] 1. Determine the assessment scenario:

[0134] At least two decisive scenarios are included: (1) Scenario A (full load stress test): The power output is set to the planned maximum value (e.g., 1600MW in the Kubuqi project), and the load is a typical value. This scenario is used to evaluate the zero-sequence current peak under the worst operating conditions and is a decisive safety verification scenario. (2) Scenario B (light load / special mode): The power output is set to a lower value (e.g., 30% of the rated capacity). This scenario is used to check for resonance risks or light load overvoltage problems.

[0135] 2. Configure the simulation solver:

[0136] (1) Simulation type: Three-phase power flow calculation is selected as the core solver. Because zero-sequence current can be generated under normal unbalanced operation, there is no need to perform transient fault simulation.

[0137] (2) Solution accuracy and convergence: Set the convergence tolerance of the Newton-Raphson method (e.g., 1e-6 pu) and configure a reasonable upper limit for the number of iterations.

[0138] (3) Output request: Explicitly require the simulator to output the three-phase current phasors (amplitude and phase) of all main transformer high-voltage side windings.

[0139] S4.3: Batch Simulation Execution and Monitoring: Input the simulation task queue generated in sub-step S4.1; the simulation scenario configuration defined in sub-step S4.2. Execute large-scale simulation calculations efficiently and reliably, and manage the calculation process.

[0140] 1. Task Scheduling and Parallel Computing: Utilizing high-performance computing clusters or local multi-core resources, tasks in the simulation task queue are dynamically allocated to multiple computing cores for parallel execution. Each core independently runs a simulation software process (such as PSCAD, DigSILENT PowerFactory), loads the corresponding simulation instance file, and performs the computation.

[0141] 2. Operation monitoring and fault tolerance:

[0142] (1) Progress monitoring: Real-time monitoring of the running status of each task (waiting, running, completed, failed).

[0143] (2) Convergence check: Automatically identify tasks that fail to converge in the simulation. For convergence failures caused by difficulties in the grid operating point, automatically adjust the initial values ​​of the power flow calculation (e.g., set the initial value of the node voltage to 1.05 times the rated voltage) or relax the convergence tolerance (e.g., adjust from 1e-6p.u. to 1e-5p.u.) and retry. If convergence still fails after 3 retries, it is marked as an invalid scheme. For failures caused by incorrect model configuration, log the information and mark the scheme as "invalid"; for convergence failures caused by difficulties in the grid operating point, the initial conditions can be automatically adjusted and retryed.

[0144] (3) Resource management: Avoid excessive resource consumption by a single task and ensure that batch tasks are completed efficiently as a whole.

[0145] S4.4: Core Result Extraction and Zero-Sequence Current Calculation: Input the result files from all successfully completed simulation tasks. Automatically and accurately extract and calculate the core evaluation metric: zero-sequence current from massive amounts of raw simulation data. Specifically, this includes:

[0146] 1. Raw Data Analysis: Write a result analysis script to locate and read the three-phase current data of the specified observation points (i.e., the high-voltage side of each main transformer) from the specific output files (such as .out, .csv, .pl4) of each simulation software. The typical data format read is: I_a=Mag_a∠Ang_a,I_b=Mag_b∠Ang_b,I_c=Mag_c∠Ang_c (polar coordinate form).

[0147] 2. Accurate calculation of zero-sequence current:

[0148] (1) First step: Phasor transformation and synthesis. Convert the three-phase currents from polar coordinates to rectangular coordinates: , ; ;

[0149] (2) Second step: Calculation of zero-sequence components. According to the symmetrical component method, the zero-sequence current phasor One-third of the sum of the three-phase current phasors: ,in The three-phase current phasors on the high-voltage side of the transformer, read from the simulation results;

[0150] (3) Third step: Calculate the effective value (amplitude). Calculate the effective value of the zero-sequence current, i.e., its magnitude, as the final quantification index: Example: Suppose that after simulation of a certain scheme, the three-phase current on the high-voltage side of a main transformer is read as (unit: kA): =1.2∠0°, =1.25∠-121°, =1.18∠115°, and the calculated result may be... =0.12∠45°kA, that is, the zero-sequence current amplitude is 120 amperes.

[0151] 3. Structured storage of results:

[0152] (1) Organize the core evaluation results of each candidate scheme into a record and store it in the database or result file.

[0153] For example:{

[0154] "scheme_id":"PSQ_BCA-ACB_TRANS_NONE_001",

[0155] "scenario":"800MW_Max_Output",

[0156] "transformer_bus_1":{

[0157] "I0_mag_A":120.5,

[0158] "I0_angle_deg":45.2

[0159] },

[0160] "transformer_bus_2":{

[0161] "I0_mag_A":41.4,

[0162] "I0_angle_deg":-30.1

[0163] },

[0164] "max_I0_across_transformers":120.5,

[0165] "simulation_status":"Converged",

[0166] "voltage_unbalance_%":1.2

[0167] }

[0168] (2) The key output field max_I0_across_transformers serves as the core security score of this solution in this scenario.

[0169] As a preferred implementation of this embodiment, step 5 specifically includes the following steps:

[0170] S5.1: Mathematical Modeling and Chromosome Encoding of the Optimization Problem: Input the structured evaluation result set output from step 4, the cost parameters and security constraints defined in step 1. Formalize the engineering decision problem as a constrained multi-objective optimization problem and prepare gene representations for the genetic algorithm:

[0171] 1. Define the decision variable vector (X): Map each candidate solution to a decision vector:

[0172] X=[P_up,P_down,T_type,T_pos1,T_pos2]

[0173] Where P_up and P_down are the phase sequence codes for the up and down lines, respectively, represented by integers 1-6 (corresponding to 6 permutations); T_type is the transposition type code, such as 0 = no transposition, 1 = single ACB transposition, 2 = full transposition cycle. T_pos1 and T_pos2: transposition positions (normalized length, between 0 and 1), 0 if no transposition.

[0174] 2. Establish a multi-objective function (MinimizeF(X)):

[0175] (1) Objective 1: Optimal technical performance (minimize maximum zero-sequence current) That is, the maximum value among all relevant zero-sequence currents of the main transformer calculated in step 4.

[0176] (2) Objective 2: Optimal economic cost (minimize estimated construction cost) ,

[0177] in, It represents a design scheme (including variables such as phase sequence and transposition strategy); To achieve the technical performance target, the maximum value among all relevant main transformer zero-sequence currents is selected; Let be the zero-sequence current of the k-th main transformer. The economic cost objective is... Infrastructure construction costs. The number of transposition towers added due to the transposition strategy (determined by T_type, such as N_tower=2 for full transposition). This is an estimate of the additional cost of a single-base transposition tower. Additional costs are incurred for the construction complexity caused by non-standard phase sequences (if P_up or P_down is an uncommon arrangement).

[0178] (3) Define constraints (Subject to):

[0179] a. Hard constraints (must be met, handled using penalty function method): G1(X): F1(X)≤I_0_max (safe upper limit of zero-sequence current); G2(X): VUF(X)≤2% (national standard for voltage unbalance).

[0180] b. Soft constraints (desirable to be met, can be included in the target): such as the relocation site should avoid rivers, highways, etc.

[0181] 4. Chromosome coding scheme: A hybrid coding method is adopted.

[0182] Phase sequence and transposition type are encoded using integers.

[0183] The position of the transposition point is encoded with a real number.

[0184] Example: A scheme is encoded as chromosome [3,5,1,0.33,0.0], representing upper phase sequence 3 (BCA), lower phase sequence 5 (CAB), using a single transposition (T_type=1), the transposition point is at 33%, and the second position is unused (T_pos2=0).

[0185] S5.2: Multi-objective optimization solution based on improved NSGA-II: Input the optimization model defined in sub-step S5.1 and all solutions and their performance data from step 4 (as the initial population). Use an improved genetic algorithm to find the Pareto optimal solution set that is balanced and optimal in the objective space (F1, F2). Specifically, this includes:

[0186] 1. Initialization and Population Loading: Compared with the standard NSGA-II algorithm, the core improvement of this embodiment lies in the following: The standard algorithm usually uses random initialization of the population, which results in slow convergence and a tendency to get trapped in local optima; while this scheme directly uses the successfully simulated candidate solutions and their evaluation values ​​as the initial population, making full use of existing simulation results and significantly improving the algorithm's convergence speed and the quality of the optimal solution.

[0187] (1) All successful simulation schemes in step 4 are directly used as the initial population. This utilizes the previously completed calculation results, which can significantly improve the convergence speed and is a key engineering optimization of this invention.

[0188] (2) Set the population size N to be fixed (e.g., 100).

[0189] 2. Fitness assessment and rapid non-dominated ranking:

[0190] (1) Constraint handling (penalty function method): For individuals that violate hard constraints G1 or G2, a very large penalty term Penalty (such as F1'=F1+1e6) is added to their objective function value, so that they are naturally eliminated in subsequent sorting.

[0191] (2) Quick Non-Dominated Sort:

[0192] a. Traverse the population and compare every pair of individuals p and q.

[0193] b. If all objective values ​​of p are no worse than q, and at least one objective is strictly better than q, then p is said to dominate q.

[0194] c. Calculate how many other individuals dominate each individual (dominance count n_p), and which individuals it dominates (dominance set S_p).

[0195] d. Place all individuals with n_p=0 into the first frontier (Rank 1, i.e., Pareto optimal frontier).

[0196] e. For each individual in Rank 1, visit each member in its dominance set S_p and decrement its dominance count by 1. Individuals whose dominance count reaches 0 are placed in the second frontier (Rank 2).

[0197] f. Repeat this process until all individuals have been stratified.

[0198] 3. Crowding degree calculation: Within the same non-dominated frontier (Rank), calculate the crowding degree of each individual to maintain the diversity of solutions.

[0199] (1) For each objective function Fm, sort the individuals on the frontier by the objective value.

[0200] (2) The crowding degree of the boundary individuals (maximum and minimum values) is set to infinity.

[0201] (3) The crowding degree of the intermediate individual i is the sum of the absolute values ​​of the differences between the adjacent individuals (i+1) and (i-1) on the target Fm, and is accumulated on all targets.

[0202] 4. Elite selection, crossover, and mutation:

[0203] (1) Selection: A binary tournament selection method is used. Two individuals are randomly selected, with priority given to the one with a smaller number of non-dominated layers (smaller Rank value); if the Rank values ​​are the same, the one with a larger crowding degree is selected (to promote diversity).

[0204] (2) Crossover: For the integer encoding part (phase order, transposition type), single-point crossover is used. For the real number encoding part (transposition point), analog binary crossover (SBX) is used, which can better explore the continuous space.

[0205] (3) Mutation: The integer encoding part uses uniform mutation, randomly transforming it into other valid integers. The real number encoding part uses polynomial mutation. A progeny population Q is generated, with a size of N.

[0206] 5. Iteration and Convergence: Merge parent generation P and offspring generation Q (size 2N) and perform a new round of non-dominated ranking and crowding calculation. Based on the ranking and crowding, select the top N individuals as the new parent population. Repeat this process until the preset maximum number of iterations is reached (e.g., 100 generations), or the change in the Pareto front is less than a threshold.

[0207] S5.3: Decision Support and Final Solution Recommendation: Input the final Pareto optimal solution set output from sub-step S5.2. Transform the mathematically optimal solution set into clear recommendations that engineers can directly use for decision-making. Specifically, this includes:

[0208] 1. Pareto Front Visualization: Generates a two-dimensional scatter plot of F1 (maximum zero-sequence current) and F2 (construction cost), intuitively showing the trade-off between "safety" and "economy" for different schemes.

[0209] 2. Automatic recommendation strategy: The system has several built-in recommendation logics and can automatically screen according to user preferences:

[0210] (1) Cost control priority type: Among the solutions that satisfy F1 < I_0_max, select the solution with the smallest F2.

[0211] (2) Maximum safety margin type: Directly select the solution with the smallest F1.

[0212] (3) Compromise recommendation type (default): Calculate the distance to the ideal point for each solution in the solution set. That is, define the ideal point as (min(F1), min(F2)), and recommend the solution closest to this ideal point to achieve relative balance.

[0213] 3. Generate the final recommendation report:

[0214] (1) Core recommendation: Clearly give the recommended phase sequence arrangement, transposition strategy, and transposition point location.

[0215] (2) Expected performance: List the predicted zero-sequence current values, voltage unbalance degrees, and estimated total costs of each main transformer under this solution.

[0216] (3) Comparative analysis: Mark the position of the recommended solution in the Pareto front diagram and briefly explain the reasons for not selecting other extreme solutions (such as the cheapest or the safest).

[0217] (4) System-side suggestions: According to the optimization results, it may output, for example: "To achieve the best effect of this solution, it is recommended to keep at least 2 main transformer neutral points directly grounded."

[0218] S5.4: Scheme verification and sensitivity analysis (an optional recommendation step in this embodiment): Input the final solution recommended in sub-step S5.3. Conduct a final robustness check on the recommended solution to increase the credibility of the decision-making.

[0219] 1. Sensitivity analysis of key parameters: Fine-tune the transposition point position of the recommended solution (±5%), re-run the simulation in step 4, and observe the change rate of the zero-sequence current F1. If the change is gentle, it indicates that the solution has strong robustness. Change the system operation mode (such as the power factor of the power supply varies between capacitive 0.95 and inductive 0.95), and verify whether F1 always satisfies the constraints.

[0220] 2. Generate the final design package: Package all input data, intermediate models, simulation results, optimization process logs, and the final recommendation report to form a complete digital design file that is traceable and auditable.

[0221] To verify the effectiveness and engineering applicability of the present invention, the Kubuqi 2 million kW photovoltaic desertification control project in the Mengxi Base was used as a practical application case. This project has a problem with excessive zero-sequence current in short-distance double-circuit lines on the same tower. Specific parameters and application procedures are as follows: The Kubuqi 2 million kW photovoltaic desertification control project in the Mengxi Base constructed three 220kV step-up substations. The Clean Energy Photovoltaic-Storage Power Station has a photovoltaic capacity of 800MW and a main transformer capacity of 3*320MVA, connected to the 500kV Gushanliang Substation via a single 220kV line, with a line length of approximately 49 kilometers. The Yunheng Photovoltaic-Storage Power Station also has a photovoltaic capacity of 800MW and a main transformer capacity of 3*320MVA, connected to the 500kV Gushanliang Substation via a single 220kV line, with a line length of approximately 39 kilometers. The Clean Energy Station and Yunheng Station have a 37.363-kilometer double-circuit line on the same tower. After the project was put into operation and generated electricity, the 251 outgoing line of the Jie Neng and Yunheng photovoltaic and energy storage power stations had a three-phase voltage and current imbalance. The neutral point of the No. 3 main transformer of the Kubuqi Yunheng photovoltaic and energy storage power station was directly grounded. Under high load (800MW), the zero-sequence current of the neutral point of the No. 3 main transformer of Yunheng station reached 137.5A, which caused problems such as three-phase voltage and current imbalance and SVG tripping.

[0222] The specific governance process after applying the solution in this embodiment includes:

[0223] Step 1: Input of Multidimensional Parameters and Constraints

[0224] S1.1 Input Data

[0225] (1) Line body parameters (derived from actual survey parameters):

[0226] Geometric parameters: Tower type 2H3-SZ2-33, hanging height A phase 30m, B phase 43.2m, C phase 36.4m, phase spacing 6.4m, split spacing 450mm, conductor JL / G1A-400 / 35, diameter 26.8mm.

[0227] Electrical parameters: DC resistance 0.0739Ω / km.

[0228] Grounding parameters: OPGW-120, radius 0.76cm, resistance 0.425Ω / km.

[0229] (2) System-side parameters:

[0230] Main transformer parameters: Yunheng and Clean Energy Station each have 3 320MVA main transformers. The No. 3 main transformer is directly grounded, and the rest are grounded with gaps.

[0231] Operating parameters: Maximum power output 1600MW (800MW each for Yunheng and Clean Energy), power factor approximately 0.99.

[0232] Short-circuit capacity: The short-circuit current at the 500kV Gushanliang substation is approximately 42.5kA (three-phase).

[0233] S1.2 Input Constraints

[0234] Safety constraints: The alarm value for the zero-sequence current at the neutral point of the main transformer is set to 80A, and the trip value is set to 150A;

[0235] Voltage imbalance ≤2%.

[0236] Economic constraints: The cost of a transposition tower is about 1.5 times that of a regular tower; the weighted coefficient for the construction complexity of uncommon phase sequence is 1.2.

[0237] Step 2: Construct a system-line coupled digital twin

[0238] S2.1 Generation of Wire Network Topology

[0239] (1) Establish a three-dimensional coordinate system with the starting point of the double-circuit section on the same tower as the origin (X: line direction, Y: horizontal direction to distinguish the two lines, Z: height above the ground).

[0240] (2) Analyze the tower diagram and generate the spatial coordinate sequence of the 6-phase conductors (Yungu Line A / B / C, Gujie Line A / B / C).

[0241] (3) Generate an electrical node table and a conductor segment connection table to clarify the electrical connection relationship of each phase.

[0242] S2.2 Calculation of Fully Coupled Parameter Matrix

[0243] (1) Calculate the 6×6 impedance matrix using the Carson-Clem formula;

[0244] (2) Key calculation example (wire self-impedance):

[0245]

[0246] In the formula Taken from hanging height data, The equivalent radius is calculated. The parameters of the double-circuit section (37.363km) and the single-circuit section are calculated in segments and combined into a parameter matrix for the entire line.

[0247] S2.3 System Model Integration

[0248] A system-side model was created in PSCAD, including the 500kV Gushanliang equivalent power source, the main transformer (YNd11 connection, neutral grounding branch), and the photovoltaic inverter aggregate model. A custom line model (including an asymmetric coupling matrix) was then integrated into the system to form a complete digital twin.

[0249] Step 3: Automatically generate candidate design schemes

[0250] S3.1 Define design variables

[0251] Variable A (phase sequence arrangement): The phase sequence of each circuit can be {ABC, ACB, BAC, BCA, CAB, CBA}.

[0252] Variable B (transposition strategy): includes "no transposition", "single transposition", and "full transposition".

[0253] S3.2 Scheme Generation Based on Engineering Rules

[0254] Rule 1 (Reverse Sequence Preferred): Calculate the reverse sequence index R of the double-circuit phase sequence. For example, BCA and ACB are partially reverse sequences (R≈0.67).

[0255] Rule 2 (Safety Spacing Verification): Exclude combinations that result in insufficient spacing between conductors at the same potential.

[0256] Rule 3 (Length Adaptation Strategy): The total length of the route in this case is approximately 37.363km (<100km), and the strategy set includes {no transposition, single transposition}.

[0257] The following is an example of a generated solution:

[0258] Option 1: Yunggu Line BCA, Gujie Line BAC (original plan);

[0259] Option 2: Yunggu Line BCA, Gujie Line ACB (preferred in reverse order);

[0260] Option 3: Yunggu Line BCA, Gujie Line BAC + single transposition (transposition point 50%);

[0261] Option 4: Yunggu Line ABC, Gujie Line CBA (completely reversed sequence).

[0262] S3.3 Scheme Combination Output

[0263] A total of 12 candidate solutions are generated, and a structured list is output, for example: {

[0264] "scheme_id":"PSQ_BCA-ACB_TRANS_NONE_001",

[0265] "phase_seq":["BCA","ACB"],

[0266] "trans_scheme":"0-NONE-1",

[0267] "description": "Upload BCA, decommission ACB, no swapping."

[0268] }

[0269] Step 4: Batch Simulation and Core Security Assessment

[0270] S4.1 Simulation Task Initialization

[0271] For each candidate scheme, a baseline simulation model is cloned, and phase sequence and transposition parameters are dynamically injected.

[0272] S4.2 Simulation Scenario Configuration

[0273] Scenario A: Dual stations at full load, 1600MW (800MW each), power factor 0.99.

[0274] Scenario B: Dual stations lightly loaded 300MW (150MW each), power factor 0.95.

[0275] S4.3 Batch Simulation Execution

[0276] Twelve simulation tasks were executed in parallel using a multi-core computing cluster, and convergence was monitored.

[0277] S4.4 Zero-sequence current extraction and calculation

[0278] The three-phase current phasors of each main transformer's high-voltage side are read from the simulation results, and the zero-sequence current is calculated: ;

[0279] The results are stored in a structured format, with key fields including max_I0_across_transformers.

[0280] Simulation results comparison:

[0281]

[0282] Step 5: Intelligent Optimization and Comprehensive Decision-Making

[0283] S5.1 Optimization Problem Modeling

[0284] Objective function: ;

[0285] Constraints: I0≤80A, voltage imbalance≤2%.

[0286] S5.2 Multi-objective optimization solution (improved NSGA-II)

[0287] Using the simulation results as the initial population, non-dominated sorting and crowding calculations were performed.

[0288] After 100 iterations, the Pareto optimal frontier (safety-economy trade-off curve) was obtained.

[0289] S5.3 Decision Support and Solution Recommendation

[0290] Pareto frontier analysis shows:

[0291] The safest option is the full reverse sequence (ABC-CBA), with I0≈38.2A, but it requires phase sequence adjustment and has high construction complexity.

[0292] The most economical solution is BCA-ACB without transposition, with I0≈41.4A, which has the lowest cost and meets safety constraints.

[0293] The system recommends choosing the BCA-ACB non-transposition scheme for the following reasons:

[0294] (1) The zero-sequence current is reduced by 70% compared with the original scheme, which meets the safety constraints.

[0295] (2) No need to add a transposition tower, making it the most economical option.

[0296] (3) Phase sequence adjustment is only implemented at the first and last towers, and the project is highly feasible.

[0297] S5.4 Sensitivity Analysis and Validation

[0298] The recommended scheme was simulated with ±10% power fluctuation, and the I0 change rate was <5%, indicating that the scheme is robust.

[0299] Compared with the measured data: the simulation predicted I0 = 41.4A. If this phase sequence is actually adopted, it is expected to avoid the problem of exceeding the standard of 137.5A, which verifies the accuracy of the prediction of the present invention.

[0300] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0301] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive various other forms of optimization design methods and systems for double-circuit lines on the same tower that consider the zero-sequence current constraint of the system. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. An optimization design method for a double-circuit line on the same tower considering the zero-sequence current constraint of the system, characterized in that, include: Input the geometric and electrical parameters of the double-circuit line to be designed on the same tower, the system-side parameters to be connected to the power grid, as well as the safety limit of the zero-sequence current of the neutral point of the main transformer, the voltage imbalance limit, and the economic constraints. Based on the geometric parameters, the fully coupled impedance matrix and admittance matrix characterizing the coupling relationship of the six-phase conductors are calculated using classical electromagnetic theory. The line model is then integrated with the system model including the neutral grounding branch of the main transformer to construct a system-line coupling simulation model. Using phase sequence arrangement and transposition strategy as design variables, and based on engineering safety specifications, reverse sequence index between phase sequences of double-circuit lines and line length, phase sequence arrangement and transposition strategy are screened and selected to generate a set of candidate design schemes. The coupled simulation model is used to perform batch simulations on the candidate design scheme set, extract the three-phase current data of the high-voltage side of the main transformer, and use the symmetrical component method to calculate the evaluation value of the neutral point zero-sequence current of the main transformer corresponding to each scheme. With minimizing the zero-sequence current assessment value and construction cost as dual objectives, and with the zero-sequence current safety limit and voltage imbalance limit as constraints, a multi-objective optimization algorithm is used to solve for the Pareto optimal solution set and output a recommended design scheme.

2. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: The geometric parameters include the tower structure diagram, the hanging point height of each phase conductor, the phase-to-phase distance, the spacing between split conductors, the span, and the sag data; the electrical parameters include the conductor type, AC resistance, outer diameter, and equivalent radius; the system-side parameters include the main transformer parameters, the neutral point grounding method, the system short-circuit capacity, and the parameters of the planned operation scenario; the construction cost includes the additional cost of the transposition tower and the additional cost of non-standard phase sequence construction.

3. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: When calculating and generating the fully coupled impedance matrix and admittance matrix, the Carson-Clem formula or the complex image method is used to calculate the ground return current effect, generating a 6×6 matrix, and the average value or approximation is not used; the system model integration is achieved by writing the matrix into a custom model file that can be called by the simulation software, or by dynamically constructing the equivalent circuit chain using the script interface of the simulation software.

4. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: The selection is based on the reverse sequence index, specifically: the matching degree of the reversed phase sequence string of the double-circuit line is calculated as the reverse sequence index, and only phase sequence combinations with an index greater than a preset threshold are retained; the candidate combinations of the phase sequence arrangement are selected from {ABC, ACB, BAC, BCA, CAB, CBA}; the selection is based on the line length, specifically: if the line length is less than the first length threshold, a no-transposition strategy is selected; if the line length is between the first length threshold and the second length threshold, a no-transposition or single-transposition strategy is selected; if the line length is greater than or equal to the second length threshold, a full-transposition strategy is added.

5. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 4, characterized in that: The transposition point for a single transposition or a full transposition is selected within the first 1 / 3 to the last 1 / 3 of the line length.

6. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: The batch simulation includes at least a full-load scenario with the maximum planned transmission power; the multi-objective optimization algorithm is the NSGA-II algorithm, and the successful candidate design schemes in the simulation and their corresponding zero-sequence current evaluation values ​​and construction cost evaluation values ​​are directly used as the initial population of the algorithm.

7. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: After outputting the recommended design scheme, a robustness verification step is also included: fine-tuning the position of the switching point or changing the system operating power factor within a preset range, resimulating and calculating the rate of change of the zero-sequence current evaluation value. If the rate of change is less than the preset threshold, the robustness of the scheme is determined to be up to standard.

8. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: The voltage imbalance limit is no more than 2%.

9. The optimization design method for double-circuit lines on the same tower considering system zero-sequence current constraints according to claim 1, characterized in that: The process of constructing the system-line coupling simulation model includes: establishing a unified three-dimensional coordinate system, analyzing the spatial coordinates of the suspension points of each phase conductor at each tower, calculating the spatial coordinates of discrete points along the conductor line by combining the span and sag, and generating a topology connection table containing electrical node numbers and conductor segment connection relationships.

10. An optimization design system for a double-circuit line on the same tower considering zero-sequence current constraints, characterized in that, include: The parameter and constraint input module is used to input the geometric parameters and electrical parameters of the double-circuit line on the same tower to be designed, the system-side parameters to be connected to the power grid, as well as the safety limit of the neutral point zero-sequence current of the main transformer, the voltage imbalance limit, and the economic constraints. The coupled simulation model construction module is used to calculate and generate the fully coupled impedance matrix and admittance matrix representing the coupling relationship of the six-phase conductors based on the geometric parameters and using classical electromagnetic theory. It also integrates the line model with the system model containing the neutral point grounding branch of the main transformer to construct a system-line coupled simulation model. The candidate scheme generation module is used to filter and select phase sequence arrangement and transposition strategy as design variables, based on engineering safety specifications, reverse sequence index between phase sequences of double-circuit lines and line length, and generate a set of candidate design schemes. The batch simulation evaluation module is used to perform batch simulations of the candidate design scheme set using the coupled simulation model, extract the three-phase current data of the high-voltage side of the main transformer, and calculate the evaluation value of the neutral point zero-sequence current of the main transformer corresponding to each scheme using the symmetrical component method. The multi-objective optimization decision module is used to solve the Pareto optimal solution set by employing a multi-objective optimization algorithm, with the dual objectives of minimizing the zero-sequence current assessment value and construction cost, and the constraints of the zero-sequence current safety limit and voltage imbalance limit, and outputs a recommended design scheme.

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