Optimized arrangement method, system and electronic device for current transformer leakage magnetic field sensor

Abstract

The application relates to a current transformer leakage magnetic field sensor optimization arrangement method, system and electronic device, which comprises the following steps: setting a layout candidate measuring point position of a sensor for monitoring a current transformer fault in a current transformer external space, and constructing a candidate measuring point set; constructing a fault simulation library comprising leakage magnetic field response data of each candidate measuring point under a current transformer normal state and multiple fault states; initializing a particle swarm, adopting a binary coding mode to code each particle, each particle being a two-dimensional binary vector, representing a sensor layout scheme; calculating the fitness value of each particle based on the candidate measuring point set and the fault simulation library; the fitness value is used for quantitatively evaluating the sensitivity of the particle to the fault; when the iteration number reaches a preset maximum iteration number or the change amount of the global optimal fitness value is less than a convergence judgment threshold value for continuous multiple generations, the improved particle swarm algorithm stops iteration, and the sensor layout scheme corresponding to the global optimal particle is taken as a final scheme.

Description

Technical Field

[0001] This invention relates to the field of online monitoring and fault diagnosis technology for power equipment, and in particular to a method, system and electronic device for optimizing the arrangement of leakage magnetic field sensors for current transformers. Background Technology

[0002] Current transformers (CTs) are crucial transmission, transformation, measurement, and protection devices in power systems. Their primary function is to convert large currents into smaller ones, and their operational reliability directly impacts the safety and stability of the entire power grid. The windings are the core component of a current transformer, enduring various forces such as electrodynamics and thermal stress over extended periods. This makes them susceptible to defects such as inter-turn short circuits and winding deformation (including radial bulging, axial bending, and compression). Failure to detect and address these defects promptly can lead to equipment failures and even serious power grid accidents.

[0003] In recent years, online monitoring technology based on leakage magnetic field detection has shown great potential. The principle behind this technology is that when early faults occur in the windings, their spatial distribution and ampere-turn ratio change, disrupting the original magnetomotive force balance between the core and the windings. This leads to a measurable and characteristic distortion in the leakage magnetic field distribution around the equipment. By analyzing these distortion characteristics of the leakage magnetic field, the winding condition inside the CT (Cyclic Transformer) can be inverted and diagnosed. Existing research has verified through simulation and experiments that there is a clear mapping relationship between defects such as inter-turn short circuits and winding deformation and specific leakage magnetic field distortion patterns (such as amplitude changes, symmetry disruption, and distortion range expansion).

[0004] Although the principle of leakage magnetic field detection is clear and the effect is significant, there is still a problem in moving this technology from theory to large-scale engineering application: how to determine the optimal installation position of the sensor used to monitor the fault of the current transformer so that the data obtained from measuring the leakage magnetic field of the current transformer winding is the most sensitive.

[0005] Current research largely focuses on the qualitative analysis of the leakage flux mapping law of current transformer defects, lacking a systematic solution to the engineering problem of "where to install sensors to most sensitively and reliably capture these distortion features." Existing methods mostly rely on expert experience-based placement methods or finite element simulation-based trial-and-error placement methods, which have inherent drawbacks: they are highly subjective in their reliance on expert experience, deploying a large number of sensors results in high trial-and-error costs and complex processes, and they have poor portability to different types of electromagnetic transformers. Summary of the Invention

[0006] Based on the above analysis, the present invention aims to provide a method for optimizing the arrangement of leakage magnetic field sensors of current transformers based on an improved particle swarm optimization algorithm, in order to solve the technical problems of existing methods that rely on experience-based placement or trial and error, have subjective dependence on expert experience, high cost, complex process, and poor portability on different types of current transformers.

[0007] The objective of this invention is mainly achieved through the following technical solutions: This invention provides a method for optimizing the arrangement of leakage magnetic field sensors in current transformers based on an improved particle swarm optimization algorithm, comprising the following steps: Set in the external space of the current transformer The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. Initialize the particle swarm, encoding each particle using binary encoding, with each particle being... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; When the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value over multiple consecutive generations is less than the convergence threshold, the improved particle swarm optimization algorithm terminates the iteration and uses the sensor layout scheme corresponding to the global optimal particle as the final sensor layout scheme.

[0008] Furthermore, a candidate measurement point set is constructed, including: Establish a three-dimensional rectangular coordinate system with the geometric center of the current transformer as the origin, and the axial direction of the current transformer as the coordinate system. The axis is the horizontal direction. shaft and axis; Along the surface of the current transformer housing and / or the envelope surface at a predetermined distance from the housing surface. The axial direction is divided at equal intervals according to a first preset spacing, forming in the axial direction. layer; Divide the circumferential direction at equal angular intervals with a second preset angular interval, forming a circumferential shape. One circumferential position; In each angular direction of each layer, extending outward from the surface of the current transformer housing, equal intervals are formed at a third preset spacing, creating a radial shape. layer; get The layout of candidate measurement point locations for a sensor used to monitor faults in a current transformer. The three-dimensional spatial coordinates of each candidate measurement point are obtained, and the three-dimensional spatial coordinates of all candidate measurement points constitute the candidate measurement point set.

[0009] Furthermore, a fault simulation library is constructed, including: A three-dimensional electromagnetic model of a current transformer under normal conditions is established. The three-dimensional electromagnetic model includes the iron core, primary conductor and secondary winding components, and the BH magnetization curve and conductivity material properties of each component are set. Based on the three-dimensional electromagnetic model under normal conditions, the model parameters are modified to construct three-dimensional electromagnetic models under various fault conditions; among them, the fault conditions include inter-turn short circuit faults and winding deformation faults. Steady-state magnetic field simulations were performed on the three-dimensional electromagnetic model under normal conditions and the three-dimensional electromagnetic model under various fault conditions to obtain the magnetic induction intensity data at the positions of each candidate measurement point in the candidate measurement point set under normal conditions and various fault conditions. The magnetic induction intensity data at the corresponding candidate measurement points are associated and stored with the normal state and each fault state to obtain a fault simulation library including normal state samples and fault state samples.

[0010] Furthermore, each particle is encoded using a binary encoding method, with each particle being... A 3D binary vector, including: Each particle corresponds to a sensor layout scheme; Each particle is represented as ,in, , For particle swarm scale, This represents the total number of candidate measurement points. For the The first particle Dimensional components ,like Indicates the first Sensors are installed at candidate measurement point locations. Indicates the first No sensors are installed at the candidate measurement point locations; The number of dimensions with a value of 1 in each particle is equal to the number of preset sensors. ,Right now .

[0011] Further, the fitness value of each particle is calculated based on the candidate test point set and the fault simulation library, including: For any sensor layout scheme represented by a particle, extract the leakage magnetic field response data corresponding to the selected measurement point of the sensor layout scheme from the normal state sample and the fault state sample in the fault simulation library. Using the average magnetic flux density of each candidate measurement point in the normal state sample as a benchmark, the leakage magnetic field response data of the corresponding candidate measurement points in each fault state sample are normalized to obtain the feature vector of each fault state sample. Based on the feature vectors of each fault state sample, calculate the class center corresponding to each fault state sample. Based on the average Euclidean distance between the class centers corresponding to each fault state sample, the inter-class separation degree between each fault state is calculated. Based on the degree of dispersion of the relative class center within the same fault state sample, the intra-class compactness of each fault state is calculated; The average separation degree between normal and fault states is calculated based on the Euclidean distance between the normal state and the class centers of each fault state. Based on the spatial distribution of the selected measurement points in the sensor layout scheme, calculate the spatial dispersion. The fitness value is obtained by weighting and combining the inter-class separation, the normal-fault average separation, the ratio of inter-class separation to intra-class compactness, and the spatial dispersion.

[0012] Furthermore, fitness value The calculation is as follows:

[0013] in, Inter-class separation degree; The normal-to-fault average separation ratio; For intra-class compactness; Spatial dispersion; They are respectively , , and The weight coefficient of the item; To prevent division by a constant.

[0014] Furthermore, the inter-class separation degree is calculated as follows:

[0015] in, The total number of states; They represent different fault states and satisfy the following conditions: ; The first species and first Fault states in layout scheme The class center below; This indicates the calculation of Euclidean distance.

[0016] Furthermore, the intra-class compactness is calculated as follows:

[0017] in, For the first The number of samples in each state; For the first In the first state Each fault state sample in the layout scheme The eigenvectors below; For the first In the layout scheme, the state is... The class center below.

[0018] Furthermore, the normal-to-fault average separation ratio is calculated as follows:

[0019] in, The class center is in a normal state.

[0020] Furthermore, the spatial dispersion is calculated as follows:

[0021] in, The preset number of sensors; Layout schemes The spatial three-dimensional coordinates of any two selected measurement points.

[0022] Furthermore, initializing the particle swarm includes: Set population size Maximum number of iterations Maximum value of inertia weight and minimum value Learning factors and cognitive items Learning Factors Social Items Speed ​​limit Stop judging threshold and convergence judgment threshold ; Randomly generated indivual A binary vector is used as the initial particle swarm, and a quantity constraint repair is performed on each initial particle to ensure that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; The quantity constraint repair includes: When the number of dimensions with a value of 1 in the particle is greater than When the current value is 1, based on the quantity constraint repair rule, the extra 1s are successively set to 0 until the quantity constraint is satisfied; When the number of dimensions with a value of 1 in the particle is less than When the current value is 0, the missing 0s are sequentially set to 1 based on the quantity constraint repair rule until the quantity constraint is satisfied.

[0023] Furthermore, in each iteration, the particle swarm is updated in the following order: The first step is to use a linear decreasing inertia weight strategy to update the inertia weight of the current iteration based on the maximum and minimum values ​​of the inertia weight. The second step is to update the velocity of each particle in each dimension based on the inertial weights and limit the velocity values. The third step involves using the S-shaped transform function to map the velocity value to a probability value of 1 for the position, generating a random number and comparing it with the probability value. Based on the comparison result, the binary representation of each dimension is determined to complete the update of the particle position. The fourth step is to perform quantity constraint repair on the updated particles, ensuring that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; Fifth step: After updating the global optimal solution, check whether the global optimal solution is continuous. If the improvement in each iteration is less than or equal to the preset stagnation threshold, then the particle swarm is determined to be trapped in a local optimum, and a random stagnation perturbation is applied to the current global optimum.

[0024] Furthermore, the linearly decreasing inertia weight strategy is as follows:

[0025] in, This refers to the current iteration round; This represents the inertia weight for the current iteration round; This represents the maximum number of iterations. , These are the maximum and minimum inertial weights, respectively.

[0026] Furthermore, the velocity of each particle in each dimension is updated, and the velocity values ​​are capped, including: The particle velocity is updated using the following velocity update formula:

[0027] in, For the first Particles in the next iteration In the Dimensional speed; For the first Particles in the next iteration In the Dimensional speed; For learning factors, cognitive items, For the social component of the learning factor; and Let [the value] be a random perturbation factor in the interval [0,1]. For particles In the The optimal position of an individual in dimension; For the particle swarm in the th The global optimal position of the dimension; For particles In the The position of the dimension; The limiting of the speed value includes: Limit the updated speed value to Within the interval, if Then let equal ;like Then let equal .

[0028] Furthermore, the S-shaped transform function is as follows:

[0029] in, For particles In the The probability value of a position being 1; The determination of the binary values ​​for each dimension based on the comparison results includes: Generate a random number that is uniformly distributed in the interval [0,1]. The binary value is determined according to the following rules:

[0030] in, For particles In the The position value after the dimension update.

[0031] Furthermore, the quantity constraint repair for particles is performed, including: For the initialized particles and the particles after each iteration, count the number of dimensions with a value of 1. If the number of dimensions with a value of 1 is greater than the preset number of sensors Then, starting from the dimensions currently having a value of 1, the probability values ​​output by the S-shaped transformation function are sorted from smallest to largest. Dimensions with smaller probability values ​​are set from 1 to 0, until the number of dimensions with a value of 1 in each particle equals [the number of dimensions with a value of 1]. ; If the number of dimensions with a value of 1 is less than the preset number of sensors Then, starting from the dimensions currently valued at 0, sort them in descending order according to the probability values ​​output by the S-shaped transformation function, setting the dimensions with larger probability values ​​from 0 to 1, until the number of dimensions with a value of 1 in each particle equals [the specified value]. .

[0032] Furthermore, a random stagnation perturbation is applied to the current global optimal solution, including: If continuous If the improvement of the global optimal solution is less than or equal to the preset stagnation threshold, then the global optimal particle is randomly selected. Flip each dimension; among them... The preset number of flips, and ; Perform the quantity constraint repair on the flipped particles, calculate the fitness value of the repaired particles, and if the fitness value is greater than the fitness value of the current global optimum, then the repaired particle is taken as the new global optimum particle; otherwise, keep the current global optimum particle unchanged.

[0033] The present invention also discloses an optimized arrangement system for leakage magnetic field sensors of current transformers, the system comprising a data preparation module M1, an improved particle swarm optimization arrangement module M2, and a sensor placement result output module M3; The data preparation module M1 is used to set up the data preparation module in the external space of the current transformer. The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. The improved particle swarm optimization layout module M2 is used to initialize the particle swarm, encoding each particle using binary encoding. Each particle is... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; The sensor placement result output module M3 is used to terminate the iteration of the improved particle swarm algorithm when the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value is less than the convergence judgment threshold for multiple consecutive generations, and to take the sensor layout scheme corresponding to the global optimal particle as the final sensor layout scheme.

[0034] The present invention also discloses an electronic device for optimizing the arrangement of leakage field sensors of current transformers, including a memory, a processor, and a computer program stored in the memory and running on the processor. The processor is used to execute the computer program to implement the method for optimizing the arrangement of leakage field sensors of current transformers.

[0035] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. This invention achieves automated and objective optimization of sensor layout schemes, eliminating reliance on expert experience. Addressing the technical problem of existing technologies that rely on subjective point placement based on expert experience and struggle to guarantee the highest sensitivity of measurement points to faults, this invention constructs a fitness function with fault sensitivity as the core evaluation index. It transforms sensor layout optimization into a constrained combinatorial optimization problem, automatically searching for the globally optimal combination of measurement points through an improved particle swarm optimization algorithm. This method eliminates the need for manual experience and repeated trial and error. The selected measurement points can distinguish between the normal state of the current transformer and various inter-turn short circuits and winding deformation faults to the greatest extent possible. This provides the sensor layout scheme with an objective, quantifiable theoretical basis and repeatable calculation results, fundamentally overcoming the shortcomings of traditional point placement methods, which are highly subjective and have poor portability. 2. This invention significantly reduces system complexity and computational overhead, improving engineering practicality and optimization efficiency. Addressing the technical problems of existing technologies that rely on SVM classification accuracy as an evaluation criterion, resulting in massive computational loads and excessively long optimization times, this invention constructs a lightweight fitness function based on the physical characteristics of the leakage magnetic field. It directly evaluates layout schemes using statistical measures such as inter-class Euclidean distance, intra-class dispersion, and normal-fault separation, avoiding nested classifier training and cross-validation during iterative optimization, thus significantly reducing the computation time per round of fitness calculation. Simultaneously, this invention can accurately select a few key measurement points from a large number of candidate measurement points, maximizing the fault information acquisition efficiency of a single sensor, effectively simplifying the on-site deployment structure and subsequent signal processing flow, and significantly reducing the number of physical nodes and the scale of data acquisition channels in the monitoring system while ensuring high detection reliability. 3. This invention enhances the global search capability and convergence stability of the algorithm, ensuring the quality of the optimal layout solution. Addressing the technical problems of the standard particle swarm optimization (PSO) algorithm, such as sensitivity to the initial population, susceptibility to local optima, and lack of discrete optimization constraint handling mechanisms, this invention introduces three targeted improvement strategies into the binary PSO algorithm: a linearly decreasing inertia weight strategy maintains strong global exploration capability in the early stages and enhances fine-grained local search in the later stages, balancing the algorithm's exploration and development; a quantity constraint repair function ensures that each particle always satisfies the hard constraint of a constant number of sensors during iteration, avoiding invalid searches; and a stagnation perturbation strategy actively applies random perturbations when the global optimum remains unchanged for multiple generations, effectively escaping local optima. These improvements collectively ensure stable convergence to a high-quality sensor layout scheme under different initial conditions, providing reliable technical support for the practical application of online leakage magnetic field monitoring technology.

[0036] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0037] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0038] Figure 1 This is a flowchart of an optimized arrangement method for leakage magnetic field sensors of a current transformer based on an improved particle swarm optimization algorithm in an embodiment of the present invention. Figure 2 This is a flowchart illustrating the execution of the improved particle swarm optimization algorithm in an embodiment of the present invention. Figure 3 The flowchart for constructing the fitness function in this embodiment of the invention is shown below; Figure 4 This is a schematic diagram of the functional modules of an optimized arrangement system for a current transformer leakage magnetic field sensor in an embodiment of the present invention; Figure 5 This is a schematic diagram of the physical structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0039] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0040] Current transformers (CTs) are typically deployed in power lines at various stages of a power grid system, including generation, substation, transmission, and distribution. Within the power grid, CTs play two core roles: high-current measurement and electrical isolation, forming the foundation for power system measurement, protection, and control.

[0041] The installation location of current transformers depends on the type of equipment and operating conditions. Common locations include: ① Substations / Power Plants: This is the area with the highest concentration of CTs. CTs are installed on the incoming and outgoing sides of key equipment such as busbars, circuit breakers, and transformers to collect current signals for use by protection and metering devices. The specific installation location of the CTs (e.g., on which side of the circuit breaker) directly affects the range and effectiveness of relay protection, therefore, careful design of the placement is required. ② Switch cabinets and metering boxes: In places such as power distribution rooms, CTs are installed in switch cabinets or metering boxes for line measurement and power metering; ③ Cable lines: Near the cable head, the CT is installed in conjunction with the cable grounding wire. The location of the CT will affect the accuracy of the monitored current.

[0042] The core function of a current transformer: ① Current transformation and standardization: The CT can convert the large primary current (from a few A to tens of thousands A) into a uniform secondary current (standard value of 5A or 1A) at a fixed ratio (such as 400:5), which is easier for measuring instruments and protection devices to process. ② Electrical Isolation and Safety Assurance: The CT achieves electrical isolation between the primary high-voltage equipment and the secondary low-voltage measurement / control equipment, connected only by a magnetic circuit, without any electrical connection. This effectively prevents high voltage from entering the secondary circuit, protecting electrical equipment and personnel safety.

[0043] Therefore, CTs reflect the current status of the power grid system in real time and are a key barrier to protect the safety of power equipment and personnel.

[0044] Example 1: This embodiment proposes an objective, automatic, and optimized method for sensor placement and measurement points. It can accurately select a few key measurement points that are most sensitive to current transformer faults and have the most significant changes in leakage magnetic field from a large number of potential installation points around the current transformer. By maximizing the fault information acquisition efficiency of a single sensor, this invention significantly reduces the number of physical installation points and the scale of data acquisition channels in the monitoring system while ensuring high detection reliability and state recognition accuracy. This effectively simplifies the on-site sensor deployment structure and subsequent signal processing flow, and promotes the practical application of online leakage magnetic field monitoring technology.

[0045] Unlike traditional signal processing methods that use current, this invention utilizes the Particle Swarm Optimization (PSO) algorithm to construct a fitness objective function with fault sensitivity, and searches for an optimal combination of sensor measurement point locations at all possible installation positions outside the CT.

[0046] This allows the leakage magnetic field information obtained after installing sensors at the optimal locations to distinguish different states of the CT to the greatest extent, including normal and fault states (such as inter-turn short circuits and winding deformation at different locations).

[0047] Existing technologies employ sensor deployment schemes based on classification accuracy using SVM (Support Vector Machine) as the evaluation criterion. While these schemes achieve some success, their objective function construction relies on kernel function calculation and high-dimensional feature space mapping during supervised training. Although the algorithm is effective, each fitness evaluation requires executing a complete model training and cross-validation process, resulting in high computational complexity and significant time consumption during optimization. This invention defines a lighter and more direct physical indicator, fault sensitivity, as the fitness objective function.

[0048] This invention abandons the indirect evaluation method that relies on classifier training accuracy and constructs a lightweight objective function based on the physical characteristics of leakage magnetic fields. This fitness objective function directly uses magnetic field response data under normal and various fault conditions as input. By calculating physical statistics such as inter-class Euclidean distance, intra-class dispersion, and normal-fault separation, it quantitatively characterizes the sensitivity of the sensor layout scheme to fault features. This design avoids the huge computational overhead caused by nested classifier training during iterative optimization. While ensuring the clear physical meaning of the evaluation indicators, it defines a lighter and more direct physical indicator, fault sensitivity, as the fitness objective function, significantly reducing the fitness calculation time in each iteration and thus improving overall optimization efficiency.

[0049] This invention is based on the particle swarm optimization algorithm, combining the average Euclidean distance between classes with the ratio of between-class divergence to within-class divergence to overcome the algorithm's shortcomings of being highly sensitive to the initial population and easily getting trapped in local optima. Euclidean distance is primarily used to ensure the measurement stability of the same fault.

[0050] A specific embodiment of the present invention discloses a method for optimizing the arrangement of leakage magnetic field sensors in current transformers based on an improved particle swarm optimization algorithm, such as... Figure 1 As shown, it includes the following steps: Step S1, set in the external space of the current transformer The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. Step S2: Initialize the particle swarm, encoding each particle using binary encoding. Each particle is... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; Step S3: When the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value over multiple generations is less than the convergence threshold, the improved particle swarm algorithm terminates the iteration and the sensor layout scheme corresponding to the global optimal particle is taken as the final sensor layout scheme.

[0051] For example, a precise three-dimensional electromagnetic model of the current transformer to be monitored is established using finite element analysis software (simulation software). This model should include key components such as the iron core, primary conductor, and secondary winding, and its BH (magnetic flux density-magnetic field strength, two core material parameters for electromagnetic simulation) magnetization curve, conductivity, and other material properties should be accurately set.

[0052] The aim is to construct a numerical simulation model that can accurately reflect the normal state of the electromagnetic characteristics of the current transformer under test, serving as the basis for subsequent fault simulation and leakage magnetic field calculation.

[0053] (1) Based on the design drawings or actual measured dimensions of the current transformer to be monitored, construct geometric solid models of the core, primary conductor, and secondary winding in the three-dimensional modeling space of the finite element simulation software. The core model is established according to its actual structural form (such as laminated or wound) and size ratio, the primary conductor is established according to its actual laying path and cross-sectional shape, and the secondary winding is established according to its actual number of turns, winding position, and wire diameter.

[0054] For windings with complex structures, an equivalent volume model or a simplified spiral model can be used for characterization, so as to reduce the difficulty of mesh generation and the consumption of computing resources while ensuring computational accuracy. (2) Assign corresponding material electromagnetic property parameters to each geometric entity. For the iron core component, assign its BH magnetization curve and conductivity. The BH magnetization curve reflects the nonlinear characteristics of the magnetic flux density of the iron core material as a function of the magnetic field strength. For silicon steel sheet materials, the typical BH curve exhibits an S-shaped nonlinear characteristic, with an initial relative permeability range of 8000 to 15000 and a maximum relative permeability range of 40000 to 80000. For the primary conductor and secondary winding components, the electrical conductivity and relative permeability are assigned to the corresponding materials (copper or aluminum). All material property parameters can be obtained from material handbooks or through standard specimen testing.

[0055] (3) Mesh the completed geometric model. Discretize the solution domain using tetrahedral or hexahedral elements, and refine the mesh locally in areas where the leakage magnetic field distribution changes drastically, such as the air gap in the core, the end region of the winding, and the conductor bends, to ensure the accuracy of the finite element calculation. The element size of the mesh is determined based on the balance between calculation accuracy and computational resources. Typically, the mesh element size in the core region does not exceed 1 / 10 of the core thickness, and the mesh element size in the winding region does not exceed 1 / 5 of the wire diameter.

[0056] (4) Set the solution domain and boundary conditions for the simulation. The solution domain is set as a finite spatial region that surrounds the entire current transformer model. Typically, the distance from the boundary of the solution domain to the outer surface of the current transformer is not less than twice the maximum external dimension of the current transformer. The boundary conditions are set as magnetic flux parallel boundary conditions, that is, by default, the magnetic field lines at the boundary of the solution domain are parallel to the boundary surface.

[0057] A primary side rated current excitation is applied to the model, and the solution type is set to steady-state magnetic field solution to obtain a three-dimensional electromagnetic model of normal state that can perform leakage magnetic field simulation.

[0058] The finite element analysis software used in the above modeling process is only one tool choice for achieving this step. Those skilled in the art can use any finite element analysis software with three-dimensional electromagnetic field simulation capabilities to achieve the above modeling purpose.

[0059] Step S1 includes steps S11-S12.

[0060] Step S11, set up in the simulated external space of the current transformer The candidate measurement point locations of a sensor for monitoring current transformer faults are determined, and a candidate measurement point set is constructed.

[0061] Constructing a candidate measurement point set includes: Establish a three-dimensional rectangular coordinate system with the geometric center of the current transformer as the origin, and the axial direction of the current transformer as the coordinate system. The axis is the horizontal direction. shaft and axis; Along the surface of the current transformer housing and / or the envelope surface at a predetermined distance from the housing surface. The axial direction is divided into equal intervals according to a first preset spacing, forming in the axial direction. layer; Divide the circumferential direction at equal angular intervals with a second preset angular interval, forming a circumferential shape. One circumferential position; In each angular direction of each layer, extending outward from the surface of the current transformer housing, equal intervals are formed at a third preset spacing, creating a radial shape. layer; get The layout of candidate measurement point locations for a sensor used to monitor faults in a current transformer. The three-dimensional spatial coordinates of each candidate measurement point are obtained, and the three-dimensional spatial coordinates of all candidate measurement points constitute the candidate measurement point set.

[0062] On the surface of the CT housing or the surrounding space, the space around the winding is pre-gridned evenly to form a grid. One possible sensor measurement point installation location. Denoteed as: Formula (1) in, for A set of coordinates for possible installation locations; These are the three-dimensional coordinates of the points to be measured; The three-dimensional coordinates of the possible installation location of the sensor; A three-dimensional rectangular coordinate system is used, with the modeling coordinate system in the finite element analysis software as the reference coordinate system. The axis is horizontal. The axis is horizontal and vertical. The axis is the vertical vector (CT axis).

[0063] The spatial extent of the gridding includes three options, as shown in Table 1.

[0064] Table 1 - Examples of gridded spatial extent division methods:

[0065] The three methods can be used in combination to simultaneously set sensor candidate measurement points on the outer shell surface and in the external space, providing a richer selection space for improving the particle swarm algorithm.

[0066] The space around the winding is pre-griddled evenly, and the grid spacing directly affects the optimization accuracy and computational cost.

[0067] The grid spacing directly affects the optimization accuracy and computational cost. Examples of grid spacing selection are shown in Table 2.

[0068] Table 2 - Example of grid spacing:

[0069] The core technical idea of ​​this invention is to select a few optimal test points from a large number of candidate points. Therefore, the number of candidate points is not a constraint, and the improved PSO algorithm can handle high-dimensional search problems. However, an excessively dense grid can lead to the curse of dimensionality. Too large a value will reduce search efficiency.

[0070] For example, the grid spacing of the present invention is preferably 5-15mm; in practical applications, it can be flexibly adjusted according to specific needs.

[0071] The candidate measurement point set is constructed using a circumferential-axial-radial three-dimensional meshing strategy. The modeling coordinate system in the finite element analysis software is used as the reference coordinate system, and a three-dimensional rectangular coordinate system is established with the geometric center of the current transformer to be monitored as the origin. The axis is horizontal. The axis is horizontal and vertical. The axis is a vertical vector along the CT axis.

[0072] Current transformers are typically axisymmetric (cylindrical) structures, with their axial direction parallel to the axis of rotation. The axes coincide. This choice of coordinate system ensures that: Axial deformation corresponding Dimensional changes in direction; Radial deformation correspondence Radius variation within the plane; The circumferential position of the candidate measuring point is determined by and The coordinates are determined together.

[0073] Uniform meshing, as shown in the example below: ① Along the axial direction ( Division of axes: In the axial direction of the CT scan, the sections are divided at equal intervals from bottom to top, with the intervals being: ,form layer; ② Division along the circumference (angular direction): Each layer is divided at equal angular intervals, with the angular intervals being... Typically, 15°, 30°, or 45° are chosen to form One circumferential position; ③ Radial division: In each angular direction of each layer, extending outward along the outer shell surface, the layers are divided at equal intervals, with the intervals being... ,form layer.

[0074] Final number of candidate points ,in, .

[0075] For example: take , , =12, , (CT shell surface, 10mm from CT shell surface, 20mm from CT shell surface), then The candidate locations of each sensor are measured to obtain a dense set of candidate measurement points covering the space surrounding the CT scan.

[0076] The locations of candidate measurement points include: The location of the CT shell surface, the location of the envelope surface offset outward from the shell surface by 5mm-20mm, and the area passing through... The position on at least one radial section of the shaft.

[0077] Alternatively, if a spatially uniform grid is not used, a workaround using a non-uniform grid is preferred.

[0078] For example, as an alternative to a spatially uniform grid, a non-uniform grid partitioning strategy can be adopted: In areas with significant spatial gradients in the leakage magnetic field, such as the winding ends, core joints, and primary conductor leads, the mesh is refined. In areas with more uniform magnetic field distribution, the mesh spacing is increased. The mesh spacing in the refined areas is 1 / 3 to 1 / 2 of the base spacing.

[0079] By using non-uniform grid partitioning, the total number of candidate measurement points can be increased without significantly increasing the total number of measurement points. Under the premise of increasing the sampling density of the sensitive area of ​​magnetic field distortion of the current transformer.

[0080] Step S12: Construct a fault simulation library that includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer.

[0081] Build a fault simulation library, including: A three-dimensional electromagnetic model of a current transformer under normal conditions is established. The three-dimensional electromagnetic model includes the iron core, primary conductor and secondary winding components, and the BH magnetization curve and conductivity material properties of each component are set. Based on the three-dimensional electromagnetic model under normal conditions, the model parameters are modified to construct three-dimensional electromagnetic models under various fault conditions; among them, the fault conditions include inter-turn short circuit faults and winding deformation faults. Steady-state magnetic field simulations were performed on the three-dimensional electromagnetic model under normal conditions and the three-dimensional electromagnetic model under various fault conditions to obtain the magnetic induction intensity data at the positions of each candidate measurement point in the candidate measurement point set under normal conditions and various fault conditions. The magnetic flux density data at the corresponding candidate measurement points are associated and stored with the normal state and each fault state to obtain a fault simulation library including normal state samples and fault state samples. Based on the three-dimensional electromagnetic model of the current transformer under normal state established above, electromagnetic models for various fault states are constructed by modifying the parameters of the electromagnetic model to simulate typical faults that may occur in the current transformer winding during actual operation. The fault states include two main categories: inter-turn short circuit faults and winding deformation faults.

[0082] Fault conditions include, but are not limited to, inter-turn short circuit faults and winding deformation faults.

[0083] (1) Constructing an inter-turn short-circuit fault: Inter-turn short circuit refers to an abnormal electrical connection that occurs between adjacent turns in a secondary winding due to damage to the insulation layer.

[0084] In the three-dimensional electromagnetic model of a finite element current transformer, a short-circuit path is simulated by connecting a contact resistance element in parallel at both ends of a specific number of turns in the secondary winding. The resistance value reflects the contact quality at the short-circuit point; the smaller the resistance value, the more severe the inter-turn short circuit. For example, the contact resistance ranges from 0.01Ω to 10Ω.

[0085] To comprehensively cover inter-turn short-circuit faults of different locations and severity, multiple fault conditions are set according to the following dimensions: ① Short circuit location dimension: Short circuit points are set in the upper, middle and lower sections along the winding axis; for example, 1-3 turns are short-circuited in the upper section, 1-3 turns in the middle section, and 1-3 turns in the lower section to simulate short circuit faults of different locations and severity. ② Short-circuit turns dimension: Three levels are set: mild short circuit (short-circuit turns account for 1%-3% of the total number of turns), moderate short circuit (3%-6%), and severe short circuit (6%-10%). ③ Short-circuit resistance dimension: Set contact resistance values ​​of 0.01Ω, 0.1Ω, 1Ω, 10Ω and other levels to cover different situations from metallic short circuit to high-resistivity short circuit.

[0086] (2) Constructing winding deformation faults: Winding deformation refers to the irreversible geometric changes that occur in the windings of a current transformer under the action of electrodynamic or thermal stress.

[0087] This invention covers two main types of deformation: radial deformation and axial deformation, which are simulated by changing the winding geometry. ①Radial deformation: At a specific height position of the winding, along a specific circumferential angle, the radius of a local area of ​​the winding is increased outward (simulating a bulge) or decreased inward (simulating a depression).

[0088] In high-risk areas such as the middle or end of the winding, the radius of the winding is locally changed. At the upper, middle, and lower parts of the winding, eight positions are evenly selected at intervals of 45° (0°, 45°, 90°, 135°, 180°...). The radius of the winding is increased or decreased by 2%, 5%, and 10% respectively to simulate asymmetric deformation.

[0089] ②Axial deformation: A compression displacement is applied axially at the top or bottom of the winding to simulate the compression deformation of the winding under axial electrodynamic force. The axial compression amount is set to four levels: 2%, 5%, 10%, and 15% of the original winding height.

[0090] Compression modes include top-only compression, bottom-only compression, and both top and bottom compression.

[0091] By arranging and combining the above multi-dimensional parameters, a variety of fault conditions are constructed. Each condition is saved as an independent fault model file, forming a complete fault simulation model library.

[0092] Simulation type library: includes normal state, various inter-turn short circuit faults, and various winding deformation faults. There are several states; each state includes Individual samples. Leakage magnetic field magnitude data for each sample in each state.

[0093] The states are as follows: Formula (2) Where 1 represents the normal state; The number of inter-turn short-circuit fault conditions; This represents the number of winding deformation fault conditions. Requirements: The value must be greater than or equal to 2, and must include at least one normal state and one fault state.

[0094] The number of samples for each state is , .

[0095] The reasons for setting multiple samples for each state are as follows: ① Simulated parameter disturbance: Under the same fault type, the parameters are slightly different (such as the short-circuit resistance varying in the range of 0.1Ω-1Ω), forming multiple fault samples; ② Simulated measurement noise: Random noise is superimposed on the simulation data to simulate the measurement error of a real sensor; ③ Simulate operating condition fluctuations: slight fluctuations in primary current, changes in material parameters caused by temperature changes, etc.; ④Statistical significance: Multiple samples are required to calculate class center and spatial dispersion.

[0096] For example, The value range is 5-20 samples, preferably. The value is 10, and each sample is generated by fine-tuning the fault parameters and adding noise.

[0097] No. There are a total of under these states For each sample, the corresponding leakage magnetic field strength modulus value for each state is saved. , No. In the first state The leakage magnetic field of each sample at all candidate measurement points is shown below: Formula (3) in, For status numbers, This is the normal state. This is a fault condition; For sample number, Number the candidate measurement points.

[0098] Data dimensions are A three-dimensional data matrix.

[0099] Steady-state magnetic field simulation calculations were performed on the established normal state model and each fault state model to obtain the steady-state leakage magnetic field distribution in the space around the current transformer under each operating state. The magnetic induction intensity data at each candidate measurement point was extracted from the simulation results to construct a leakage magnetic field simulation database.

[0100] Specifically, for each state (including normal state and multiple fault conditions), the following operations are performed: ① Load the corresponding three-dimensional electromagnetic models of normal and fault states into the finite element analysis software; apply the primary side rated current excitation; ②The steady-state leakage magnetic field distribution in the space surrounding the CT is obtained by simulating and solving using finite element analysis software; ③ Perform finite element calculations until convergence; in the post-processing stage, read predefined... The magnetic induction intensity values ​​at each candidate measurement point location.

[0101] For each state, save its value in The magnetic induction intensity data at each candidate measurement point forms a leakage magnetic field response data sample for that state.

[0102] The above process traverses all Under various working conditions The magnetic flux density at each candidate point was obtained. Each sample contains a leakage magnetic field response sample. The magnetic induction intensity data at each candidate measurement point constitute a leakage magnetic field simulation database.

[0103] Step S1 is used to construct a candidate measurement point set and a fault simulation library, providing a data foundation for subsequent iterative optimization of the particle swarm algorithm.

[0104] Step S2 includes steps S21-S23.

[0105] Step S21: Construct the fitness function of the improved particle swarm optimization algorithm. The fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library. The fitness value is used to quantitatively evaluate the sensitivity of the sensor layout scheme represented by the particle to faults.

[0106] There are three fundamental technical challenges in optimizing the sensor layout for monitoring current transformer faults: ① Whether a layout plan is good or bad cannot be judged by intuition; quantitative indicators are required. ② And it is necessary to consider multiple optimization objectives; A good layout should be able to "distinguish different faults" (classification ability), "accurately measure similar faults" (stability), and "distinguish between normal and faulty conditions" (sensitivity). These three aspects may conflict. ③ It is also necessary to ensure computational efficiency; if the fitness function calculation is too complex (such as the SVM scheme), the entire optimization process will not be able to be completed in a reasonable time.

[0107] like Figure 3 As shown, the fitness function The core tool for solving these three technical problems transforms the abstract concept of "layout quality" into a specific fitness value, with a higher value indicating a better layout.

[0108] Layout scheme As a binary vector, representing in Which points were selected from the candidate measurement points to install sensors? In layman's terms, a comprehensive numerical index, namely the fitness value, is used to quantitatively evaluate "whether a certain sensor layout scheme is good or not".

[0109] The fitness value of each particle is calculated based on the candidate test point set and the fault simulation library, including: For any sensor layout scheme represented by a particle, extract the leakage magnetic field response data corresponding to the selected measurement point of the sensor layout scheme from the normal state sample and the fault state sample in the fault simulation library. Using the average magnetic flux density of each candidate measurement point in the normal state sample as a benchmark, the leakage magnetic field response data of the corresponding candidate measurement points in each fault state sample are normalized to obtain the feature vector of each fault state sample. Based on the feature vectors of each fault state sample, calculate the class center corresponding to each fault state sample. Based on the average Euclidean distance between the class centers corresponding to each fault state sample, the inter-class separation degree between each fault state is calculated. Based on the degree of dispersion of the relative class center within the same fault state sample, the intra-class compactness of each fault state is calculated; The average separation degree between normal and fault states is calculated based on the Euclidean distance between the normal state and the class centers of each fault state. Based on the spatial distribution of the selected measurement points in the sensor layout scheme, calculate the spatial dispersion. The fitness value is obtained by weighting and combining the inter-class separation, the normal-fault average separation, the ratio of inter-class separation to intra-class compactness, and the spatial dispersion. The first step is to normalize the magnetic flux density value.

[0110] To mitigate the significant differences in the absolute amplitude of the leakage magnetic field at different test points (e.g., a stronger magnetic field at test points near the core and a weaker magnetic field at test points farther away), if normalization is not performed, it will greatly affect the evaluation results. Test points with large amplitudes will dominate the calculation, masking the contribution of test points with small amplitudes but sensitive to faults.

[0111] Using the average magnetic induction intensity of each candidate measuring point under normal conditions as a reference, the leakage magnetic field response data of each measuring point under fault conditions are normalized.

[0112] Let the normal state be in the th... The magnetic induction intensity at each candidate measuring point is , as a reference standard, then the first In the state of the first The first sample Normalization over candidate test points is shown below: Formula (4) in, for In the first state, the second The sample, the first The magnetic flux density modulus at each measuring point is the simulation output, and the value ranges from approximately 0.001 to 1000 mT. The first under normal conditions The average magnetic flux density at each measuring point is a statistical quantity, and is related to... Same order of magnitude; To prevent extremely small positive numbers with a denominator of zero, and to ensure the stability of numerical calculations, we must avoid having a denominator of zero. For normalized In the first state, the second The sample, the first The magnetic flux density values ​​at each measuring point are dimensionless and approximately 0.1-10. For example, Values In practical applications, changes can be made according to specific needs.

[0113] The reason for taking values Physical basis: The minimum magnetic induction intensity in the external space of a current transformer is approximately The mT level indicates a location far from the current transformer; therefore Being three orders of magnitude smaller than the minimum value will not change the normalization result, but it can avoid the error of dividing by zero in numerical calculations.

[0114] ①If If the value is too large, such as Then the weak magnetic field measuring point The normalized value loses its physical meaning; ②If The value is too small, such as If the value exceeds the effective representation range of a double-precision floating-point number, numerical overflow may occur.

[0115] The second step is to construct the feature vectors of each fault state sample.

[0116] Regarding the layout scheme ( (a binary vector), the set of selected measurement points is shown below: Formula (5) in, Indicate layout scheme The set of measurement points selected for sensor installation. , The preset number of sensors.

[0117] No. Type of state, first Feature vector of each sample As shown below: Formula (6) in, For set Arranged in ascending order by measurement point number A layout of measurement points.

[0118] Feature vector The dimension is equal to the number of sensors. Instead of the total number of candidate measurement points ; Original data, data dimensions are This includes all candidate measurement points, including a large amount of redundant information; After feature extraction, the data dimension is Only keep the selected ones. One measuring point, .

[0119] Only the selected measurement points are included in the calculation; the unselected points are ignored. High dimension Reduce dimensional data to low dimensionality The dimension reflects the optimization effect of the candidate measurement point layout.

[0120] Each element in It indicates that in the first At each measuring point, the magnetic flux density measured under the current condition is a multiple of the magnetic flux density measured at that point under normal conditions. For example: ① This indicates that the measuring point is exactly the same under the fault condition as under the normal condition; ② This indicates that the strength of the measuring point under the fault condition is 50% higher than that under the normal condition; ③ This indicates that the measuring point is 30% weaker under the fault condition than under the normal condition.

[0121] This method of expressing the eigenvector of "relative change" allows measurement points of different magnitudes to be compared on the same scale.

[0122] The third step is to calculate the class center corresponding to each fault state.

[0123] For the In this state, in the layout scheme The average of the feature vectors of all samples is defined as the class center, as shown below: Formula (7) in, For the first The number of samples in each operating state.

[0124] Sample size Selection principles: ① Too small Its advantages are low computational cost, but insufficient statistical representativeness and unstable class centers. ② Too large Its advantage is good statistical representativeness, but the simulation computation is large. ③ The quantity is moderate. Its advantages are that it is statistically reliable and computationally feasible.

[0125] This solution is preferred. That is, 10 simulations are performed under each fault condition to ensure the statistical stability of the class center.

[0126] The class center is the average position of all samples in this state, representing the typical characteristics of this type of fault; the calculation of the class center is the basis for all subsequent distance calculations.

[0127] For any particle, the sensor layout scheme is represented by Leakage magnetic field response data corresponding to the selected measurement points are extracted from the fault simulation database. The average magnetic field response of each measurement point under normal conditions is used as a reference benchmark to normalize the samples of each fault state, thereby obtaining the layout scheme. The feature vectors of each fault state sample are calculated, and the class center corresponding to each fault state is further calculated.

[0128] The fourth step is to construct three core distance indicators: inter-class separation, intra-class compactness, and normal-fault average separation.

[0129] The inter-class separation index is constructed based on the average Euclidean distance between various centers, the intra-class compactness index is constructed based on the dispersion of samples within the same operating state relative to the class center, and the normal-fault separation index is constructed based on the Euclidean distance between the normal state and each fault state.

[0130] The fitness value of the layout scheme is obtained by weighting and combining the inter-class separation, normal-fault separation, and the ratio of inter-class separation to intra-class compactness.

[0131] The higher the fitness value, the more obvious the difference in leakage magnetic field response between different operating states under this layout scheme, and the more stable the leakage magnetic field response under the same operating state. Therefore, the layout scheme is better.

[0132] (1) Inter-class average Euclidean distance, representing the difference between different fault states.

[0133] Calculate the average Euclidean distance between the class centers of different fault states. .

[0134] Inter-class separation degree is calculated as follows: Formula (8) in, The total number of states; They represent different fault states and satisfy the following conditions: ; The first species and first Fault states in layout scheme The class center below; This indicates the calculation of Euclidean distance.

[0135] Assumption There are 10 states: normal, short circuit fault 1, short circuit fault 2, deformed fault 1, and deformed fault 2. The average value is calculated after calculating the distance between the class centers of each pair.

[0136] The larger the value, the greater the difference in characteristics of different fault states on the sensor, and the easier it is for the classifier to distinguish them.

[0137] Inter-class separation is the average distance between the class centers of any two different fault classes. Inter-class separation calculates the average distance between all operating states (including normal states and all fault states), not just between normal and fault states.

[0138] Inter-class separation The larger the value, the more obvious the signal difference on the sensor for different faults, and the easier it is to distinguish them.

[0139] Euclidean distance is used instead of Mahalanobis distance or other distances because Euclidean distance has a clear physical meaning and is computationally lightweight. Inter-class separation. Examples are shown in Table 3.

[0140] Table 3 - Inter-class Separation Example:

[0141] (2) Intraclass compactness, which indicates the stability of the same fault measurement.

[0142] Calculate the average dispersion of samples within the same state relative to the class center, and the intra-class compactness. .

[0143] Intra-class compactness is calculated as follows: Formula (9) in, For the first The number of samples in each state; For the first In the first state Each fault state sample in the layout scheme The eigenvectors below; For the first In the layout scheme, the state is... The class center below.

[0144] The smaller the value, the more stable the measurement results for the same type of fault, and the stronger the disturbance resistance. Lower intra-class compactness is better, while higher inter-class separation is better. Examples of intra-class compactness values ​​are shown in Table 4.

[0145] Table 4 - Intra-class compactness Example of possible values:

[0146] (3) Average separation between normal and fault states, representing the ability to detect anomalies.

[0147] Considering the need to reliably distinguish between "normal" and "abnormal" states, we further define the average Euclidean distance between the normal state and each fault state, and calculate the average separation degree between normal and fault states. .

[0148] The normal-to-fault average separation ratio is calculated as follows: Formula (10) in, The class center is in a normal state.

[0149] This is the normal state. Represents various fault states.

[0150] The average distance between the normal state and all fault states; The larger the value, the easier it is to distinguish between fault conditions and normal conditions under this sensor layout.

[0151] The reason why the normal-fault separation degree is listed separately and not completely covered by the inter-class separation degree is that in actual engineering, "whether it can reliably identify anomalies" is often more important than "whether it can distinguish different fault types". This is a special design based on practicality.

[0152] Fifth step, sensor spatial dispersion.

[0153] Considering the sensor installation situation in actual engineering, to prevent the sensors from being too close together and affecting the installation, a sensor spatial dispersion term function is introduced. .

[0154] The spatial dispersion is calculated as follows: Formula (11) in, The preset number of sensors; Layout schemes The spatial three-dimensional coordinates of any two selected measurement points.

[0155] The physical meaning of formula (11) is the average distance between all selected measurement points. The larger the sensor size, the more dispersed the sensor distribution becomes.

[0156] Sensors are too concentrated: spatial information is redundant, and they may interfere with each other during installation; Sensors are appropriately dispersed: covering a wider spatial range and acquiring more comprehensive magnetic leakage field information; Pure mathematical optimization might place sensors in the same location (high separation between classes), but this is not feasible in engineering.

[0157] Examples of sensor placement are shown in Table 5. A typical CT sensor size (300mm diameter, 500mm height) is used as an example.

[0158] Table 5 - Sensor Placement Examples:

[0159] Step 6: Construct the comprehensive fitness function.

[0160] Based on inter-class separation Intraclass compactness Normal-fault average separation and sensor spatial dispersion Construct the comprehensive fitness function .

[0161] fitness value The calculation is as follows:

[0162] Formula (12) in, Inter-class separation degree; The normal-to-fault average separation ratio; For intra-class compactness; Spatial dispersion; They are respectively , , and The weight coefficient of the item; To prevent division by a constant.

[0163] Constraints Fitness function The larger the value, the better the sensor arrangement corresponding to the layout scheme.

[0164] Weighting coefficient Examples are shown in Table 6.

[0165] Table 6 - Example of Weighting Coefficients:

[0166] The three indicators are combined to form a fitness function, rather than a single indicator: ① If only the inter-class separation degree is used and stability is ignored, the measurement point with high discrimination degree but unstable measurement may be selected; ② If only intra-class compactness is used and discrimination is ignored, measurement points that are very accurate may be selected but whose faults cannot be seen. ③ If only the normal-fault separation degree is used, it can only determine normal / abnormal, but cannot distinguish the fault type.

[0167] Examples of fitness values ​​are shown in Table 7.

[0168] Table 7 - Examples of fitness values:

[0169] The sensor layout optimization problem is transformed from "classification accuracy evaluation based on classifier training" to "statistical distance evaluation based directly on the physical response of leakage magnetic field". This not only ensures the physical rationality of the optimization direction, but also significantly reduces the time cost of fitness calculation.

[0170] Standard PSO is for continuous space optimization (real vectors). This invention adopts the Binary Particle Swarm Optimization (BPSO) algorithm, which is suitable for binary space, and incorporates improved strategies.

[0171] The core reason for choosing BPSO is that particle coding naturally corresponds to the 0 / 1 decision of sensor placement, its swarm intelligence characteristics are suitable for combinatorial optimization problems, and it converges faster than genetic algorithms.

[0172] Three inherent flaws of the standard BPSO: ① Sensitive to the initial population: The initial solutions are randomly distributed. If the initial quality is poor, subsequent searches will be limited; the search results are unstable, and different solutions may be obtained in each run. ② It is easy to get trapped in local optima: In the later stages of iteration, the diversity of the population is lost, and all particles gather near the local optimum; it is impossible to find the true optimal layout, and the engineering effect is reduced. ③ Lack of constraint processing mechanism: Standard BPSO is unconstrained, and the number of "1"s in the generated particles is random; the number of sensors N is a hard constraint, and solutions that violate the constraint are invalid.

[0173] This invention addresses the aforementioned shortcomings by making targeted improvements: For ①+②, the improved strategy is to linearly decrease the inertia weight, with a large inertia weight in the early stage → to conduct a global exploration; and a small inertia weight in the later stage → to conduct a local fine search. For ③, the improved strategy is a quantity constraint repair function to ensure that each particle always meets the sensor quantity requirement. Hard constraints; For ②, the improved strategy is a stagnation perturbation strategy, which monitors the global optimal solution. Applying random perturbations when the system remains continuous can cause it to escape local optima.

[0174] Step S22: Initialize the particle swarm, encoding each particle using binary encoding. Each particle is... A binary vector. For example... Figure 2 As shown.

[0175] (1) Algorithm initialization. Initialize the particle swarm.

[0176] Initializing the particle swarm includes: Set population size Maximum number of iterations Maximum value of inertia weight and minimum value Learning factors and cognitive items Learning Factors Social Items Speed ​​limit Preset stagnation detection threshold and convergence judgment threshold ; Randomly generated indivual A binary vector is used as the initial particle swarm, and a quantity constraint repair is performed on each initial particle to ensure that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; The quantity constraint repair includes: When the number of dimensions with a value of 1 in the particle is greater than When the current value is 1, based on the quantity constraint repair rule, the extra 1s are successively set to 0 until the quantity constraint is satisfied; When the number of dimensions with a value of 1 in the particle is less than When the current value is 0, the missing 0s are sequentially set to 1 based on the quantity constraint repair rule until the quantity constraint is satisfied.

[0177] Examples of initialization parameters are shown in Table 8.

[0178] Table 8 - Examples of parameters requiring initialization:

[0179] In each iteration, the particle swarm is updated in the following order: The first step is to use a linear decreasing inertia weight strategy to update the inertia weight of the current iteration based on the maximum and minimum values ​​of the inertia weight. The second step is to update the velocity of each particle in each dimension based on the inertial weights and limit the velocity values. The third step involves using the S-shaped transform function to map the velocity value to a probability value of 1 for the position, generating a random number and comparing it with the probability value. Based on the comparison result, the binary representation of each dimension is determined to complete the update of the particle position. The fourth step is to perform quantity constraint repair on the updated particles, ensuring that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; Fifth step: After updating the global optimal solution, check whether the global optimal solution is continuous. If the improvement in each iteration is less than or equal to the preset stagnation threshold, then the particle swarm is determined to be trapped in a local optimum, and a random stagnation perturbation is applied to the current global optimum.

[0180] For example, The preset generation is 5; the preset stagnation detection threshold is 5. Preset or The specific value is determined based on the magnitude of the fitness to ensure the objectivity and adaptability of the judgment criteria.

[0181] (2) Inertia weight linearly decreasing strategy.

[0182] The linearly decreasing inertia weight strategy is as follows: Formula (13) in, This refers to the current iteration round; This represents the inertia weight for the current iteration round; This represents the maximum number of iterations. , These are the maximum and minimum inertial weights, respectively.

[0183] Iteration rounds The inertia weight of the current iteration is shown in Table 9.

[0184] Table 9 - Example of inertia weights for the current iteration round:

[0185] (3) The coordination relationship between parameters Population size With maximum number of iterations Balance: like Large → Large computational load per generation → It can be reduced appropriately; like Small → Small computational load per generation → It needs to be enlarged appropriately.

[0186] For example, the value is: , To balance computational accuracy and efficiency.

[0187] Particle encoding and initialization: Each particle represents a sensor layout scheme, encoded in binary. The particle swarm is randomly initialized, with each particle acting as a unique identifier. A binary vector is used, and a quantity constraint repair function is used to ensure that the number of "1"s in each particle is equal to the preset number of sensors. .

[0188] (1) Binary encoding Each particle It is a length of A binary vector.

[0189] Each particle is encoded using a binary encoding method, and each particle is... A 3D binary vector includes: Each particle corresponds to a sensor layout scheme; Each particle is represented as ,in, , For particle swarm scale, This represents the total number of candidate measurement points. For the The first particle Dimensional components ,like Indicates the first Sensors are installed at candidate measurement point locations. Indicates the first No sensors are installed at the candidate measurement point locations; The number of dimensions with a value of 1 in each particle is equal to the number of preset sensors. ,Right now .

[0190] Each particle middle: ①If : in the Sensors are installed at each candidate measurement point; ②If : in the No sensors are installed at the candidate measurement points.

[0191] Hard constraint condition is That is, the number of "1"s in each particle must be exactly equal to the preset total number of sensors. .

[0192] Step S23, particle swarm optimization.

[0193] (1) Fitness evaluation: For each particle According to the layout scheme it represents The selected set of measurement points is Extract from simulation database Calculate the fitness value of this layout scheme based on the magnetic field data at the corresponding measuring points. And store it for later comparison.

[0194] (2) Update individual optimality and global optimality: Compare the current fitness of each particle with its historical individual optimal value. Compare and update the individual optimal value. Find the particle with the highest fitness value in the current population and update the global optimum. .

[0195] Individual optimal updates are as follows: Formula (14) Each particle remembers the "best position it has ever been" (the layout scheme with the highest fitness value) in each iteration.

[0196] The globally optimal update is as follows: Formula (15) From the individual optimal solutions of all particles, select the one with the largest fitness value as the global optimal solution for the entire population.

[0197] (3) Particle velocity and position update: Update the velocity of each particle in each dimension and limit the velocity values, including: The particle velocity is updated using the following velocity update formula:

[0198] Formula (16) in, For the first Particles in the next iteration In the Dimensional speed; For the first Particles in the next iteration In the Dimensional speed; For learning factors, cognitive items, For the social component of the learning factor; and Let [the value] be a random perturbation factor in the interval [0,1]. For particles In the The optimal position of an individual in dimension; For the particle swarm in the th The global optimal position of the dimension; For particles In the The position of the dimension; The limiting of the speed value includes: Limit the updated speed value to Within the interval, if Then let equal ;like Then let equal .

[0199] ① This is an inertial term, which maintains the original motion trend of the particle, preserves the continuity of the search, and prevents sudden changes. ② As a cognitive term, particles tend to move closer to their historical best positions, preserving individual experience and performing fine-grained local searches. ③ As a social term, particles move closer to the global optimal position of the group, transmitting group information and accelerating convergence.

[0200] random disturbance factor , As shown below: Formula (17) in, These are two independent random perturbation factors (random numbers); This indicates that it follows a certain order, and it represents a probability distribution relationship. It is a continuous uniform distribution with an interval of [0,1].

[0201] Maintain population randomness and avoid complete synchronization of all particles; Regenerate in each iteration to ensure the diversity of search paths.

[0202] Speed ​​limiting is as follows: Formula (18) in, In order to be in In the next iteration, the particles In the Velocity value in dimension; For the truncation function, The value is limited to a specified range Inside; This is the lower limit of speed; This represents the maximum speed.

[0203] For example, .

[0204] In the improved particle swarm optimization algorithm, dimension This refers to the component in the particle vector corresponding to a single candidate measurement point.

[0205] Assuming there are 100 candidate measurement points around the CT (M=100), then the particle is a 100-dimensional vector: Dimension This corresponds to the first candidate measurement point, such as the 0° direction at the top of the CT shell; Dimension This corresponds to the second candidate measurement point, such as the top of the CT shell at a 5° angle. And so on, dimension This corresponds to the 100th candidate measurement point.

[0206] By optimizing each dimension The 0 / 1 states are used to filter out the final results. The optimal layout scheme for sensors monitoring current transformer faults is a measurement point with a dimension of 1 (preset number of sensors).

[0207] Position updates employ a sigmoid transform, which maps continuous velocity values ​​to probability values ​​using a sigmoid transform function.

[0208] The S-shaped transform function is as follows: Formula (19) in, For particles In the The probability value of a position being 1; The determination of the binary values ​​for each dimension based on the comparison results includes: Generate a random number that is uniformly distributed in the interval [0,1]. The binary value is determined according to the following rules: Formula (20) in, For particles In the The position value after the dimension update.

[0209] The S-shaped transform function has the following mathematical properties: ①When As it approaches positive infinity, Infinitely close to 1; ②When As it approaches negative infinity, Infinitely close to 0; ③When When equal to 0, It equals 0.5.

[0210] Generate a random number that is uniformly distributed in the interval [0,1]. The purpose of this random number is: ①When When the value is large, this dimension is more likely to become 1; ②When When the size is very small, this dimension is more likely to become 0.

[0211] Will With probability value The comparison is performed, and the binary position value (i.e., whether the sensor should be installed at the selected measurement point) is determined based on the comparison result. ①When hour, ; ②When hour .

[0212] (4) Quantity constraint repair and random stagnation perturbation strategy: Speed-location updates cannot be guaranteed. Therefore, a quantity constraint repair process must be added.

[0213] The initial particles, and the particles updated in each iteration, all need to undergo quantity constraint repair to ensure that the number of sensors is [value missing]. .

[0214] Meanwhile, the population diversity is monitored. If the population gets stuck in a local optimum (such as the global optimum remaining unchanged for 5 consecutive generations), a slight random stagnation perturbation is applied to the global optimum gbest to help it escape the local optimum.

[0215] Repairing the number constraint of particles: Perform quantity constraint repair on particles, including: For the initialized particles and the particles after each iteration, count the number of dimensions with a value of 1. If the number of dimensions with a value of 1 is greater than the preset number of sensors Then, starting from the dimensions currently having a value of 1, the probability values ​​output by the S-shaped transformation function are sorted from smallest to largest. Dimensions with smaller probability values ​​are set from 1 to 0, until the number of dimensions with a value of 1 in each particle equals [the number of dimensions with a value of 1]. ; If the number of dimensions with a value of 1 is less than the preset number of sensors Then, starting from the dimensions currently valued at 0, sort them in descending order according to the probability values ​​output by the S-shaped transformation function, setting the dimensions with larger probability values ​​from 0 to 1, until the number of dimensions with a value of 1 in each particle equals [the specified value]. .

[0216] Scenario 1: When the number of sensors is too large, At that time, among them, It refers to the first During the next iteration: ① Find the set of all dimensions whose current value is 1. ; ② Each dimension in Obtain the probability value of the particle taking the value 1 at each position in each dimension. That is, the probability calculated before the position is updated; ③According to Arranged from smallest to largest, the smaller the probability value, the less likely the algorithm is to select it; ④ Set the extra 1s to 0 one by one, and the loop ends. .

[0217] From the dimension where the current value is 1, the probability value of taking 1 at each position in the dimension. Sort the data from smallest to largest, and set any extra 1s to 0 until the quantity constraint is met.

[0218] Scenario 2: When the number of sensors is insufficient, At that time, from the dimension where the current value is 1, the probability value of taking 1 at each position in the dimension. Sort from largest to smallest, and set the missing "0"s to "1"s in turn until the quantity constraint is met.

[0219] Repair example: Assumption A certain particle There is one extra "1", so we need to remove one "1".

[0220] An example of performing quantity constraint repair is shown in Table 10.

[0221] Table 10 - Example of execution quantity constraint repair:

[0222] Dimension 4 The probability value is the minimum of 0.2, so change it from 1 to 0. (This is the corrected version.) The quantity constraints are satisfied.

[0223] Random stationary perturbation strategy: The triggering conditions for the random stagnation perturbation strategy are as follows: Formula (21) That is, the current global optimal solution is in continuous Are all values ​​less than or equal to the preset stagnation threshold? .

[0224] Apply random stagnation perturbations to the current global optimal solution, including: If continuous If the improvement of the global optimal solution is less than or equal to the preset stagnation threshold, then the global optimal particle is randomly selected. Flip each dimension; among them... The preset number of flips, and ; Perform the quantity constraint repair on the flipped particles, calculate the fitness value of the repaired particles, and if the fitness value is greater than the fitness value of the current global optimum, then the repaired particle is taken as the new global optimum particle; otherwise, keep the current global optimum particle unchanged.

[0225] Step S2 serves to ensure both feasibility and diversity for particles after velocity-position updates, ensuring that the number of candidate measurement points for each particle is strictly equal to the preset number of sensors. Simultaneously, it employs a random stagnation perturbation strategy to ensure the global optimal solution remains unchanged for multiple generations. Applying controlled random stagnation perturbations helps the population escape local optima. This step eliminates the influence of illegal solutions in the discrete encoding space on the optimization process and avoids the rapid loss of population diversity due to quantity constraint repair. It is a key step in ensuring that the final layout scheme satisfies engineering constraints and has good global search performance.

[0226] Step S3, specifically.

[0227] When the number of iterations reaches the preset maximum number of iterations Or the change in the global optimal fitness value over multiple generations is less than the convergence threshold. When the iteration is terminated, the improved particle swarm algorithm is used to obtain the sensor layout scheme corresponding to the globally optimal particles.

[0228] For example, the convergence judgment threshold Values .

[0229] There are two termination conditions; the program stops when either condition is met.

[0230] When the number of iterations reaches its maximum value or the fitness function converges (e.g., the change is less than the threshold for 10 consecutive generations), When the iteration stops and the globally optimal particle is output, the iteration is stopped. The sensor layout scheme represented.

[0231] Stop iteration judgment function As shown below: Formula (22) in, For continuously changing algebra, Representing the The fitness function value of the globally optimal solution is the current optimal value; For the first The globally optimal fitness value of the generation is the historical baseline value; when When, it indicates continuous The relative change in fitness values ​​within generations is less than When the fitness value no longer increases significantly, the algorithm converges.

[0232] The optimal layout scheme obtained is, The three-dimensional coordinates of the optimal sensor placement points.

[0233] In practical engineering, leakage magnetic field sensors (such as Hall sensors) are installed at these designated locations to collect leakage magnetic signals that are most sensitive to fault detection.

[0234] The obtained optimal layout scheme, the globally optimal particle The encoding, i.e., the length is The binary vector is shown below: Formula (23) Mapped to engineering coordinates: based on The spatial location of the measurement point corresponding to the selected dimension is extracted from the established set of candidate measurement point coordinates, as shown below: Formula (24) in, For the first The three-dimensional coordinates of the candidate measurement points.

[0235] Engineering installation: ① Read the output coordinate set, total Three-dimensional spatial coordinates; ② Mark the location in the space around the CT shell, and use laser positioning or template positioning; ③ Install a leakage magnetic field sensor (such as a Hall sensor); ④ Fix the sensor and lead wires, ensuring that the sensor orientation is consistent, such as installing them radially.

[0236] When the power system is running, early, sensitive and reliable diagnosis of inter-turn short circuits and deformation faults in CT windings can be achieved by monitoring the changes in leakage magnetic field collected by sensors relative to the normal baseline value (such as when an inter-turn short circuit occurs, the leakage magnetic field near the short-circuited turn increases significantly with the severity of the short circuit) or by using pattern recognition algorithms.

[0237] Online monitoring: After commissioning, data from each sensor is collected in real time and compared with normal baseline values. An example of the online monitoring results is shown in Table 11.

[0238] Table 11 - Example of monitoring results:

[0239] Step S3, after the algorithm reaches convergence, maps the globally optimal particle obtained from the optimization search from the binary encoding domain to the actual engineering scenario, providing a clear spatial basis for the physical installation of the leakage magnetic field sensor. Through the dual criteria of maximum iteration count and convergence threshold, the algorithm terminates promptly when the fitness no longer significantly improves, avoiding invalid computation, while ensuring that the output meets the constraint of the preset number of sensors. This step connects the optimization algorithm with engineering implementation, enabling the final selected measurement point coordinates to be directly used for sensor positioning, installation, and online monitoring. This ensures that the deployed leakage magnetic field sensors effectively collect leakage magnetic signals reflecting the CT winding state, providing a reliable data foundation for the early diagnosis of inter-turn short circuits and deformation faults. It is a crucial transformation link from algorithm solution to practical application.

[0240] Example 2: A specific embodiment of the present invention discloses an optimized arrangement system for leakage magnetic field sensors of current transformers, thereby realizing the optimized arrangement method for leakage magnetic field sensors of current transformers in Embodiment 1. The specific implementation of each module is described in the corresponding description in Embodiment 1.

[0241] like Figure 4 As shown, the system includes a data preparation module M1, an improved particle swarm optimization layout module M2, and a sensor placement result output module M3; The data preparation module M1 is used to set up the data preparation module in the external space of the current transformer. The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. The improved particle swarm optimization layout module M2 is used to initialize the particle swarm, encoding each particle using binary encoding. Each particle is... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; The sensor placement result output module M3 is used to terminate the iteration of the improved particle swarm algorithm when the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value is less than the convergence judgment threshold for multiple consecutive generations, and to take the sensor layout scheme corresponding to the global optimal particle as the final sensor layout scheme.

[0242] Since the system in this embodiment and the method in Embodiment 1 are related and can be referenced from each other, this description is redundant and will not be repeated here. Because this system embodiment shares the same principle as the above method embodiment, it also possesses the corresponding technical effects of the above method embodiment.

[0243] Example 3: like Figure 5 As shown, an electronic device for wireless meter reading in a substation includes a memory, a processor, and a computer program stored in the memory and running on the processor. The processor is used to execute the computer program to implement the optimized arrangement method of the leakage magnetic field sensor of the current transformer as described in Embodiment 1.

[0244] Figure 5 A schematic diagram of the physical structure of an electronic device is provided. This device includes a processor 301, a communications interface 302, a memory 303, and a communication bus 304. The processor 301, communications interface 302, and memory 303 communicate with each other via the communication bus 304. The processor 301 can call logical instructions stored in the memory 303 to execute the current transformer leakage magnetic field sensor optimization arrangement method provided in Embodiment 1.

[0245] In summary, the optimized arrangement method, system, and electronic device for a current transformer leakage magnetic field sensor according to embodiments of the present invention have the following beneficial effects: 1. This invention achieves automated and objective optimization of sensor layout schemes, eliminating reliance on expert experience. Addressing the technical problem of existing technologies that rely on subjective point placement based on expert experience and struggle to guarantee the highest sensitivity of measurement points to faults, this invention constructs a fitness function with fault sensitivity as the core evaluation index. It transforms sensor layout optimization into a constrained combinatorial optimization problem, automatically searching for the globally optimal combination of measurement points through an improved particle swarm optimization algorithm. This method eliminates the need for manual experience and repeated trial and error. The selected measurement points can distinguish between the normal state of the current transformer and various inter-turn short circuits and winding deformation faults to the greatest extent possible. This provides the sensor layout scheme with an objective, quantifiable theoretical basis and repeatable calculation results, fundamentally overcoming the shortcomings of traditional point placement methods, which are highly subjective and have poor portability. 2. This invention significantly reduces system complexity and computational overhead, improving engineering practicality and optimization efficiency. Addressing the technical problems of existing technologies that rely on SVM classification accuracy as an evaluation criterion, resulting in massive computational loads and excessively long optimization times, this invention constructs a lightweight fitness function based on the physical characteristics of the leakage magnetic field. It directly evaluates layout schemes using statistical measures such as inter-class Euclidean distance, intra-class dispersion, and normal-fault separation, avoiding nested classifier training and cross-validation during iterative optimization, thus significantly reducing the computation time per round of fitness calculation. Simultaneously, this invention can accurately select a few key measurement points from a large number of candidate measurement points, maximizing the fault information acquisition efficiency of a single sensor, effectively simplifying the on-site deployment structure and subsequent signal processing flow, and significantly reducing the number of physical nodes and the scale of data acquisition channels in the monitoring system while ensuring high detection reliability. 3. This invention enhances the global search capability and convergence stability of the algorithm, ensuring the quality of the optimal layout solution. Addressing the technical problems of the standard particle swarm optimization (PSO) algorithm, such as sensitivity to the initial population, susceptibility to local optima, and lack of discrete optimization constraint handling mechanisms, this invention introduces three targeted improvement strategies into the binary PSO algorithm: a linearly decreasing inertia weight strategy maintains strong global exploration capability in the early stages and enhances fine-grained local search in the later stages, balancing the algorithm's exploration and development; a quantity constraint repair function ensures that each particle always satisfies the hard constraint of a constant number of sensors during iteration, avoiding invalid searches; and a stagnation perturbation strategy actively applies random perturbations when the global optimum remains unchanged for multiple generations, effectively escaping local optima. These improvements collectively ensure stable convergence to a high-quality sensor layout scheme under different initial conditions, providing reliable technical support for the practical application of online leakage magnetic field monitoring technology.

[0246] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0247] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the arrangement of leakage magnetic field sensors in a current transformer, characterized in that, include: Set in the external space of the current transformer The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. Initialize the particle swarm, encoding each particle using binary encoding, with each particle being... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; When the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value over multiple consecutive generations is less than the convergence threshold, the improved particle swarm optimization algorithm terminates the iteration and uses the sensor layout scheme corresponding to the global optimal particle as the final sensor layout scheme.

2. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 1, characterized in that, Constructing a candidate measurement point set includes: Establish a three-dimensional rectangular coordinate system with the geometric center of the current transformer as the origin, and the axial direction of the current transformer as the coordinate system. The axis is the horizontal direction. shaft and axis; Along the surface of the current transformer housing and / or the envelope surface at a predetermined distance from the housing surface. The axial direction is divided at equal intervals according to a first preset spacing, forming in the axial direction. layer; Divide the circumferential direction at equal angular intervals with a second preset angular interval, forming a circumferential shape. One circumferential position; In each angular direction of each layer, extending outward from the surface of the current transformer housing, equal intervals are formed at a third preset spacing, creating a radial shape. layer; get The layout of candidate measurement point locations for a sensor used to monitor faults in a current transformer. The three-dimensional spatial coordinates of each candidate measurement point are obtained, and the three-dimensional spatial coordinates of all candidate measurement points constitute the candidate measurement point set.

3. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 2, characterized in that, Build a fault simulation library, including: A three-dimensional electromagnetic model of a current transformer under normal conditions is established. The three-dimensional electromagnetic model includes the iron core, primary conductor and secondary winding components, and the BH magnetization curve and conductivity material properties of each component are set. Based on the three-dimensional electromagnetic model under normal conditions, the model parameters are modified to construct three-dimensional electromagnetic models under various fault conditions; among them, the fault conditions include inter-turn short circuit faults and winding deformation faults. Steady-state magnetic field simulations were performed on the three-dimensional electromagnetic model under normal conditions and the three-dimensional electromagnetic model under various fault conditions to obtain the magnetic induction intensity data at the positions of each candidate measurement point in the candidate measurement point set under normal conditions and various fault conditions. The magnetic induction intensity data at the corresponding candidate measurement points are associated and stored with the normal state and each fault state to obtain a fault simulation library including normal state samples and fault state samples.

4. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 1, characterized in that, Each particle is encoded using a binary encoding method, and each particle is... A 3D binary vector, including: Each particle corresponds to a sensor layout scheme; Each particle is represented as ,in, , For particle swarm scale, This represents the total number of candidate measurement points. For the The first particle Dimensional components ,like Indicates the first Sensors are installed at candidate measurement point locations. Indicates the first No sensors are installed at the candidate measurement point locations; The number of dimensions with a value of 1 in each particle is equal to the number of preset sensors. ,Right now .

5. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 1, characterized in that, The fitness value of each particle is calculated based on the candidate test point set and the fault simulation library, including: For any sensor layout scheme represented by a particle, extract the leakage magnetic field response data corresponding to the selected measurement point of the sensor layout scheme from the normal state sample and the fault state sample in the fault simulation library. Using the average magnetic flux density of each candidate measurement point in the normal state sample as a benchmark, the leakage magnetic field response data of the corresponding candidate measurement points in each fault state sample are normalized to obtain the feature vector of each fault state sample. Based on the feature vectors of each fault state sample, calculate the class center corresponding to each fault state sample. Based on the average Euclidean distance between the class centers corresponding to each fault state sample, the inter-class separation degree between each fault state is calculated. Based on the degree of dispersion of the relative class center within the same fault state sample, the intra-class compactness of each fault state is calculated; The average separation degree between normal and fault states is calculated based on the Euclidean distance between the normal state and the class centers of each fault state. Based on the spatial distribution of the selected measurement points in the sensor layout scheme, calculate the spatial dispersion. The fitness value is obtained by weighting and combining the inter-class separation, the normal-fault average separation, the ratio of inter-class separation to intra-class compactness, and the spatial dispersion.

6. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 5, characterized in that, fitness value The calculation is as follows: in, Inter-class separation degree; The normal-to-fault average separation ratio; For intra-class compactness; Spatial dispersion; They are respectively , , and The weight coefficient of the item; To prevent division by a constant.

7. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 6, characterized in that, Inter-class separation degree is calculated as follows: in, The total number of states; They represent different fault states and satisfy the following conditions: ; The first species and first Various fault states in the layout scheme The class center below; This indicates the calculation of Euclidean distance.

8. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 6, characterized in that, Intra-class compactness is calculated as follows: in, For the first The number of samples in each state; For the first In the first state Each fault state sample in the layout scheme The eigenvectors below; For the first In the layout scheme, the state is... The class center below.

9. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 6, characterized in that, The normal-to-fault average separation ratio is calculated as follows: in, The class center is in a normal state.

10. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 6, characterized in that, Spatial dispersion is calculated as follows: in, The preset number of sensors; Layout schemes The spatial three-dimensional coordinates of any two selected measurement points.

11. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 1, characterized in that, Initializing the particle swarm includes: Set population size Maximum number of iterations Maximum value of inertia weight and minimum value Learning factors and cognitive items Learning Factors Social Items Speed ​​limit Stop judging threshold and convergence judgment threshold ; Randomly generated indivual A binary vector is used as the initial particle swarm, and a quantity constraint repair is performed on each initial particle to ensure that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; The quantity constraint repair includes: When the number of dimensions with a value of 1 in the particle is greater than When the current value is 1, based on the quantity constraint repair rule, the extra 1s are successively set to 0 until the quantity constraint is satisfied; When the number of dimensions with a value of 1 in the particle is less than When the current value is 0, the missing 0s are sequentially set to 1 based on the quantity constraint repair rule until the quantity constraint is satisfied.

12. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 1, characterized in that, In each iteration, the particle swarm is updated in the following order: The first step is to use a linear decreasing inertia weight strategy to update the inertia weight of the current iteration based on the maximum and minimum values ​​of the inertia weight. The second step is to update the velocity of each particle in each dimension based on the inertial weights and limit the velocity values. The third step involves using the S-shaped transform function to map the velocity value to a probability value of 1 for the position, generating a random number and comparing it with the probability value. Based on the comparison result, the binary representation of each dimension is determined to complete the update of the particle position. The fourth step is to perform quantity constraint repair on the updated particles, ensuring that the number of dimensions with a value of 1 in each particle is equal to the preset number of sensors. ; Fifth step: After updating the global optimal solution, check whether the global optimal solution is continuous. If the improvement in each iteration is less than or equal to the preset stagnation threshold, then the particle swarm is determined to be trapped in a local optimum, and a random stagnation perturbation is applied to the current global optimum.

13. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 12, characterized in that, The linearly decreasing inertia weight strategy is as follows: in, This refers to the current iteration round; This represents the inertia weight for the current iteration round; This represents the maximum number of iterations. , These represent the maximum and minimum inertial weights, respectively.

14. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 12, characterized in that, Update the velocity of each particle in each dimension and limit the velocity values, including: The particle velocity is updated using the following velocity update formula: in, For the first In the next iteration, the particle In the Dimensional speed; For the first In the next iteration, the particle In the Dimensional speed; For learning factors, cognitive items, For the social component of the learning factor; and Let [the value] be a random perturbation factor in the interval [0,1]. For particles In the The optimal position of an individual in dimension; For the particle swarm in the th The global optimal position of the dimension; For particles In the The position of the dimension; The limiting of the speed value includes: Limit the updated speed value to Within the interval, if Then let equal ;like Then let equal .

15. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 14, characterized in that, The S-shaped transform function is as follows: in, For particles In the The probability value of a position being 1; The determination of the binary values ​​for each dimension based on the comparison results includes: Generate a random number that is uniformly distributed in the interval [0,1]. The binary value is determined according to the following rules: in, For particles In the The position value after the dimension update.

16. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 12, characterized in that, Perform quantity constraint repair on particles, including: For the initialized particles and the particles after each iteration, count the number of dimensions with a value of 1. If the number of dimensions with a value of 1 is greater than the preset number of sensors Then, starting from the dimensions currently having a value of 1, the probability values ​​output by the S-shaped transformation function are sorted from smallest to largest. Dimensions with smaller probability values ​​are set from 1 to 0, until the number of dimensions with a value of 1 in each particle equals [the number of dimensions with a value of 1]. ; If the number of dimensions with a value of 1 is less than the preset number of sensors Then, starting from the dimensions currently valued at 0, sort them in descending order according to the probability values ​​output by the S-shaped transformation function, setting the dimensions with larger probability values ​​from 0 to 1, until the number of dimensions with a value of 1 in each particle equals [the specified value]. .

17. The optimized arrangement method for leakage magnetic field sensors of current transformers according to claim 12, characterized in that, Apply random stagnation perturbations to the current global optimal solution, including: If continuous If the improvement of the global optimal solution is less than or equal to the preset stagnation threshold, then the global optimal particle is randomly selected. Flip each dimension; among them... The preset number of flips, and ; Perform the quantity constraint repair on the flipped particles, calculate the fitness value of the repaired particles, and if the fitness value is greater than the fitness value of the current global optimum, then the repaired particle is taken as the new global optimum particle; otherwise, keep the current global optimum particle unchanged.

18. An optimized arrangement system for leakage magnetic field sensors of a current transformer, characterized in that, The system includes a data preparation module (M1), an improved particle swarm optimization layout module (M2), and a sensor placement result output module (M3). The data preparation module (M1) is used to set up the data preparation module in the external space of the current transformer. The layout of candidate measurement point locations for sensors used to monitor current transformer faults is determined, and a candidate measurement point set is constructed. A fault simulation library is constructed, which includes leakage magnetic field response data at each candidate measurement point under normal and various fault conditions of the current transformer. The improved particle swarm optimization layout module (M2) is used to initialize the particle swarm, encoding each particle using binary encoding. Each particle is... A binary vector represents a sensor layout scheme; the fitness value of each particle is calculated based on the candidate measurement point set and the fault simulation library; wherein, the fitness value is used to quantitatively evaluate the sensitivity of the particle to faults; The sensor placement result output module (M3) is used to terminate the iteration of the improved particle swarm algorithm when the number of iterations reaches the preset maximum number of iterations or the change in the global optimal fitness value for multiple consecutive generations is less than the convergence judgment threshold, and the sensor layout scheme corresponding to the global optimal particle is taken as the final sensor layout scheme.

19. An electronic device for optimizing the arrangement of leakage magnetic field sensors in a current transformer, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, The processor is configured to execute the computer program to implement the current transformer leakage field sensor optimization arrangement method as described in any one of claims 1 to 17.

Images