A sensor position optimal arrangement method for real-time monitoring of dynamic ampacity of overhead transmission line

Abstract

An optimal sensor deployment method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines includes: initializing key parameters of the MBPSO algorithm; loading preprocessed historical meteorological and current data, using the heat balance equation as the input to the fitness function; generating a particle swarm representing different sensor deployment schemes; introducing a comprehensive fitness function composed of a cost function, a weight function, and a coverage function; calculating and comparing the fitness value of each particle; dynamically adjusting particle position updates by calculating the Hamming distance ratio between the particle and its individual optimal solution and the global optimal solution; and randomly flipping several bits in the particle encoding by introducing a mutation function; outputting the global optimal solution as the final optimal sensor deployment scheme when the maximum number of iterations is reached or the solution has converged. This method overcomes the problems of high sensor deployment cost, insufficient monitoring accuracy, and susceptibility to local optima in existing technologies.

Description

Technical Field

[0001] This invention relates to the field of dynamic current carrying capacity monitoring technology for overhead transmission lines, and specifically to an optimal sensor placement method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines. Background Technology

[0002] With the rapid development of my country's economy and the rapid growth of social electricity demand, increasing the transmission capacity of overhead transmission lines has become an urgent task. Therefore, it is of great significance to accurately assess and monitor the dynamic current carrying capacity (maximum allowable current) of the lines in real time. To this end, it is necessary to install micro-meteorological (ambient temperature, wind direction, wind speed, solar radiation intensity) sensors at each span of the line, as the dynamic current carrying capacity is closely related to these factors. However, installing sensors at every span of the line would inevitably lead to extremely high economic costs. Therefore, it is crucial to achieve optimal sensor placement while ensuring accurate real-time monitoring of the dynamic current carrying capacity, thereby minimizing the number of sensors required. However, existing sensor deployment methods all have different limitations. For example:

[0003] Reference [1]: Zhang Yi, Yuan Jiawei, Tang Bo, et al. Configuration method of dynamic capacity expansion thermal sensor for overhead distribution lines based on GPCA-GA [J]. Automation of Electric Power Systems, 2025, 49(6): 187-197. This paper is based on principal component analysis of missing data and genetic algorithm. Although it can reconstruct the line temperature distribution through the heat balance equation, it has a heavy computational burden in long-distance and multi-span lines and is prone to getting trapped in local optima. It fails to fully take into account the priority of key spans, resulting in insufficient monitoring coverage of the current carrying capacity bottleneck area.

[0004] Reference [2]: Xu Yixuan, Wu Yiqun, Wang Xuefeng, et al. Optimization of dynamic capacity expansion system for overhead distribution lines based on improved genetic algorithm [J]. Journal of Shanghai University of Electric Power, 2025, 41(5): 482-488. This paper optimizes the number and location of acquisition terminals in the dynamic capacity expansion system based on an improved genetic algorithm. However, this method relies on complex parameter tuning and covariance matrix eigenvalues, has poor adaptability to different line structures and voltage levels, weak generalization ability, and lacks an efficient local optimum avoidance mechanism in the convergence process, making it difficult to control costs while ensuring accuracy.

[0005] In summary, there is currently no optimal sensor placement method that can both ensure real-time and accurate monitoring of the dynamic current carrying capacity of transmission lines and effectively reduce sensor installation costs. Therefore, it is urgent to research an optimal sensor placement model and method for real-time assessment of the dynamic current carrying capacity of overhead transmission lines, laying a solid theoretical and technical foundation for the realization of dynamic capacity expansion technology for overhead transmission lines, real-time and accurate monitoring of line current carrying capacity, and optimal sensor deployment methods. Summary of the Invention

[0006] The problem this invention aims to solve is to address the shortcomings of existing models and methods by providing an optimal sensor deployment method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines. By introducing an improved binary particle swarm optimization (MBPSO) algorithm, the multi-target sensor deployment problem is addressed. This method reduces the number of sensors required while collecting complete and accurate micro-meteorological information and transmission line data, thus laying the foundation for the realization of dynamic capacity expansion technology for overhead transmission lines. This method overcomes the problems of high sensor deployment cost, insufficient monitoring accuracy, and susceptibility to local optima in existing technologies.

[0007] The technical solution adopted in this invention is as follows: An optimal sensor placement method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines includes the following steps: S1: Initialize the key parameters of the MBPSO algorithm by loading preprocessed externally collected historical meteorological data and current data, with the heat balance equation as the input to the fitness function; S2: Generate a swarm of particles representing different sensor deployment schemes, and encode each particle as a binary array; S3: Introducing the cost function f cost Weighting function f weight Covering functions f coverage The comprehensive fitness function is constructed to calculate and compare the fitness value of each particle. During the iteration process, the individual historical best solution of each particle and the global best solution of the entire population are updated. S4: By calculating the Hamming distance ratio between the particle and the individual optimal solution and the global optimal solution, logical judgment is made to dynamically adjust the update of the particle position. By introducing a mutation function to randomly flip several bits in the particle code, the position of the particle in the binary space is updated to increase the population diversity and avoid the algorithm from getting stuck in local optima. S5: When the number of iterations reaches the maximum number of iterations or the solution has converged, the algorithm terminates and outputs the global optimal solution as the final optimal sensor placement scheme.

[0008] In S1, the key parameters for initializing the MBPSO algorithm include: number of particles. N Maximum number of iterations k max Total number of transmission line segments P and ideal sensor placement ratio ispr .

[0009] The historical meteorological data includes ambient temperature, wind speed, wind direction, and solar radiation intensity; the current data is the operating current of the transmission lines.

[0010] In S1, the expression for the heat balance equation is: ; In the formula: For solar thermal gain; Line current; Resistance of a conductor; , These are convective and radiative heat losses, respectively.

[0011] In S2, the particle position is represented as follows:

[0012] In the formula: Indicates the first k In the nth iteration n The position of each particle; Indicates the first p The layout status of the first span; if the value is 1, it indicates the first span. p Sensors are installed at intervals; 0 indicates no sensors are installed. This represents the total number of spans in the transmission line.

[0013] In S3, the expressions for each function in the comprehensive fitness function are as follows: ; In the formula: For cost function, Indicates the first k In the nth iteration n The position of each particle; Indicates in k In the nth iteration, the 1st n The position string of the i-th particle p Bit.

[0014] ; In the formula: The weighting function evaluates whether the solution prioritizes coverage of the most critical spans, i.e., the spans most frequently becoming bottlenecks in load capacity; the exponential function... The numerical value indicates the criticality of the selected range set; the larger the inner product of the function, the higher the bottleneck range coverage. f weight The smaller; This represents the frequency at which the historical lowest current carrying capacity occurred. ; In the formula, This is a coverage function used to verify whether the arrangement scheme can effectively monitor high-temperature events in the conductors during actual operation; For the total time point, For a point in time, The value is 1 when a high-temperature event is detected, and 0 otherwise.

[0015] In S3, the overall fitness function is derived from the cost function. Weighting function and covering functions constitute; By using a reverse mapping method on the original partial fitness function, specifically: a: Cost function The original value is taken directly without any additional mapping. Since smaller values ​​are better, it can be directly used in weighted summation.

[0016] b: Weighting function Through exponential function Will The transformation makes the function value fall between 0 and 1, and the larger the inner product, the closer the function value is to 0, which means the smaller the penalty and the better the solution; c: Overriding function functions in The value ranges from [0,1]. A larger value indicates a better solution. This is achieved by taking the complement of the set (1- The goal is to unify the approach by making the smaller the better.

[0017] All sub-objectives are unified into a minimization objective, which can be directly weighted and summed. The overall fitness value is the sum of the three, i.e.: ; In the formula, The overall fitness value is the sum of the three fitness values. The smaller the output of the fitness function, the better the solution.

[0018] f cost This represents the total number of sensors; For key gear distance coverage; This represents the percentage of high-temperature events that were successfully monitored.

[0019] During the iteration process, the overall fitness value of each particle is compared. The smaller the overall fitness function, the better the solution. This updates the individual historical best solution of each particle and the global best solution of the entire population.

[0020] In S4, the Hamming distance is defined as: ; In the formula, X and Y represent two binary arrays. This is an operation that compares each corresponding position of two vectors (or strings) X and Y bit by bit. When two corresponding positions are different, the result is 1; when they are the same, the result is 0.

[0021] The Hamming distance reflects the distance between the current particle and the optimal solution; Hamming distance ratio is: ; .

[0022] In the formula, dp represents and individual optimal The distance ratio; dp represents and the global optimal solution The distance ratio; P represents the total number of spans of the transmission line; The larger the Hamming distance ratio, the greater the distance, and the more the particle needs to move to approach the optimal solution.

[0023] In S4, the particle position updates are dynamically adjusted as follows: A random function was introduced. ,in, The random function is a random number between 0 and 1.

[0024] By introducing a random function, the algorithm is endowed with necessary randomness and exploratory capabilities, balancing the ability to utilize known optimal solutions while exploring unknown regions. rand > dg The particle learns from gbest, that is, it changes its current position to be the same as gbest, and then uses subsequent ISPR to determine whether it has mutated; if rand <dg The particle learns from pbest and combines this with subsequent ispr to determine whether it has mutated.

[0025] This effectively avoids the algorithm getting stuck in local optima and increases the probability of finding the global optimum.

[0026] In S4, the specific expression for the introduced mutation function is: ; In the formula, The introduced mutation function, For the ideal sensor placement ratio, This refers to the desired proportion of a span over which sensors are installed.

[0027] The introduced mutation function also adds a Variables, where, This refers to the ideal sensor placement ratio, which introduces... This parameter control makes the mutation operation somewhat directional, tending to generate solutions that meet the expected sensor deployment density, thereby increasing diversity while improving search efficiency and accelerating convergence to a high-quality solution.

[0028] In S4, a mutation function is introduced to randomly flip several bits in the particle's code to update the particle's position in the binary space, specifically: The mutation function generates another random number. If the random number is less than ispr, then... x np k+1 Setting it to 1 determines that a sensor will be placed in the p-th segment; otherwise, setting it to 0 means that no sensor will be placed in the p-th segment.

[0029] In S5, when the number of iterations reaches the maximum number of iterations, i.e., the maximum number of iterations... k Equal to the maximum number of iterations k max If the solution does not change in multiple iterations, the iteration stops.

[0030] Furthermore, the historical best individual fitness of all particles is compared with the global best fitness. If any historical best individual fitness is better than the global best fitness, then the historical best individual fitness is updated to the global best fitness, and the global optimal solution is output as the final optimal sensor placement scheme. For example: With a transmission line span number P=10, the output result is: [0,1,0,0,1,0,0,0,1,0] The plan indicates that sensors will be deployed in segments 2, 5, and 9, for a total of 3.

[0031] The global optimal solution is a binary array, which directly guides the installation location and number of physical sensors on the corresponding span of the transmission line.

[0032] This invention provides an optimal sensor deployment method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines. It overcomes the problems of high sensor deployment costs, insufficient monitoring accuracy, and slow convergence speed or susceptibility to local optima in existing technologies, significantly improving the reliability and capacity utilization of the power system. Compared to existing technologies, the beneficial effects of this invention include: 1) An MBPSO algorithm based on Hamming distance ratio and mutation function is proposed. By dynamically calculating the difference ratio between particles and the optimal solution, the position update strategy is intelligently adjusted. Combined with random mutation operation, it effectively avoids the defects of traditional genetic algorithm or standard particle swarm optimization that are prone to getting trapped in local optima. At the same time, compared with traditional genetic algorithm, MBPSO algorithm only needs 10-15 iterations to converge to the optimal solution, which significantly improves global search capability and convergence speed.

[0033] 2) An innovative multi-objective integrated fitness function was constructed, unifying cost, weight, and coverage function into a minimization objective, and simplifying the optimization process through weighted summation. The weight function prioritizes coverage of key spans based on historical current carrying capacity frequency, and the coverage function verifies the effectiveness of the scheme through high-temperature event monitoring, achieving a balance between economy and monitoring accuracy. Compared with traditional full-span deployment, this invention requires only 1-2 sensors, reducing deployment costs by more than 50%.

[0034] 3) A guided mutation mechanism is introduced, which controls the mutation operation by using the ideal sensor placement ratio parameter to make the generated solution more consistent with the expected deployment density. This increases population diversity and accelerates convergence to a high-quality solution, adapting to different voltage levels and line structures, and improving the versatility of the method. The deployment scheme generated by the MBPSO algorithm maintains high accuracy in complex terrain, and the root mean square error of reconstructing the conductor temperature distribution is less than 0.8°C. Attached Figure Description

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Figure 1 A flowchart of the overall sensor deployment scheme.

[0036] Figure 2 This is a flowchart of the covered function.

[0037] Figure 3 A schematic diagram illustrating the optimal sensor placement method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines. Detailed Implementation

[0038] like Figure 1 As shown, an optimal sensor placement method for real-time monitoring of dynamic current carrying capacity of overhead transmission lines includes the following steps: Step 1: Initialize the key parameters of the MBPSO algorithm by loading preprocessed historical meteorological and current data collected externally, and provide input to the fitness function through the heat balance equation.

[0039] First, initialize the number of particles. N Maximum number of iterations k max Total number of transmission line segments P The ideal sensor placement ratio (ISPR) is used to prepare for subsequent iterative operations. Historical meteorological and current data of the target transmission line are loaded from an external data source. Based on this data, following the IEEE Std. 738 standard, the dynamic heat rating of the conductor and the minimum current carrying capacity of each span of the line are calculated using the heat balance equation, generating a weighted reference vector. The heat balance equation is as follows: ; Step 2: Generate a particle swarm representing different sensor deployment schemes, and encode each particle as a binary array.

[0040] First, a set of candidate solutions is randomly generated, and each solution is called a particle. Each particle N in the... K Position at the next iteration x n k It is a binary array. x n k Each bit in the array represents a specific span of the power transmission line; a bit value of 1 indicates that a sensor is deployed on that span, while a bit value of 0 indicates that no sensor is deployed on that span. The length of this array is equal to the total number of spans of the power transmission line. P .

[0041] Step 3: Introduce the cost function f cost Weighting function f weight Covering functions f coverage The constructed comprehensive fitness function calculates and compares the fitness of each particle, initially determines and updates the historical best solution of the particle and the global best solution of the entire population in subsequent iterations.

[0042] First, such as Figure 2 The flowchart shown obtains the fitness function to compare the merits of different solutions. Fitness is determined by the cost function. f cost Weighting function f weight Covering functions f coverage The three sub-functions are calculated together, including the cost function. f cost The expression is: ; In the formula: x np k Indicates in k In the nth iteration, the 1st n The position string of the i-th particle p Bit.

[0043] Among them, the cost function evaluates the economics of the scheme, that is, the fewer the number of sensors, the better.

[0044] Weighting function f weight The expression is: ; In the formulaR This represents the frequency at which the historical lowest current carrying capacity occurred.

[0045] The weighting function evaluates whether the solution prioritizes coverage of the most critical spans, i.e., the spans most frequently becoming bottlenecks in load capacity. First, a weighting reference vector is obtained based on historical data. R Each element R p Indicates the first p The frequency of the lowest current carrying capacity occurring in each span during the statistical period is used to further calculate the layout scheme. x n k With weight vector R inner product x n k. R The larger this inner product value, the more critical the selected range set is. Finally, the exponential function e is used. -(xnk.R) The transformation is performed so that the function value falls between 0 and 1. The larger the inner product, the closer the function value is to 0, which means the smaller the penalty and the better the solution.

[0046] Overriding function f coverage The expression is: ; The coverage function verifies whether this arrangement can effectively monitor high-temperature events in the conductors during actual operation.

[0047] like Figure 2 The flowchart of the coverage function is shown below. Set a variable c m Used at each time point m Record whether any sensors are deployed across the span where the temperature reaches the warning threshold. c m Initialize to 0 and then perform a loop operation to determine the current deployment scheme. x np k In the middle, in the p Whether sensors have been deployed across the segment; if so, then at this time... x p =1 At the same time, determine the current time point. m , No. p Does the estimated conductor temperature across the segment exceed the preset warning temperature threshold T? max If both conditions are met, c m Set to 1 and immediately skip to the cross-segment pThe internal loop is used because as long as one deployed sensor detects a high-temperature event, that point in time is considered valid coverage. If neither condition is met, then... p=p+1 The loop operation continues according to the above conditions until the specified time point. m Equal to the total time point M The time loop ends, and the input result represents the percentage of all high-temperature event time points that were successfully monitored by the deployed sensors. Combined with the coverage function's expression, the sensor deployment scheme's ability to monitor key high-temperature events in actual operation is determined.

[0048] By using reverse mapping or complement operations on the three functions to make their outputs as small as possible, all sub-objectives are unified into a minimization objective, allowing for direct weighted summation and simplifying the design and implementation of the multi-objective optimizer. Furthermore, based on weighted summation, the computational results of the three sub-functions are combined into a single fitness value. Each particle's individual position is initialized to its optimal position, and the position with the highest fitness among all particles is set as the global optimal position for subsequent iterative calculations.

[0049] Step 4: The Hamming distance ratio between the particle and the individual best solution and the global best solution is calculated to make subsequent logical judgments and dynamically adjust the particle position update. The particle position in the binary space is updated by randomly flipping some bits of the particle code through the introduction of a mutation function, which increases the population diversity and avoids the algorithm from getting stuck in local optima.

[0050] First, such as Figure 1 The process shown by the dashed line involves iterative optimization, specifically calculating the current particle's... x n k pbest individual solution n Hamming distance ratio between d p ,particle x n k Hamming distance ratio between the global best solution gbest and the global best solution gbest d g : ; ; The expression for Hamming distance is: ; Generate a random number between 0 and 1, rand(0,1).

[0051] 1) If the random number is greater than the Hamming distance ratio between the particle and the global optimum, it means the difference between the current particle and the global optimum is relatively small, i.e., the current particle tends to move closer to the global optimum. In this case, to increase the algorithm's exploration capability and avoid getting trapped in local optima before proceeding to the next step, a new random number is generated. If this new random number is greater than the ipsilateral distance ratio (ispr), no mutation occurs. The algorithm then determines that the current particle should be more inclined to learn from the global best historical performance, and the particle is guided to directly adopt the global optimum at the ipsilateral distance ratio. p For decisions at each position, if the new random number is greater than ispr, then a mutation operation is performed using a mutation function. That is, the mutation function generates another random number; if this random number is less than ispr, then... x np k+1 Setting it to 1 determines the number of... p The sensor is placed across the first segment; otherwise, the value is 0. p No sensors are placed in each span.

[0052] 2) If the random number is less than or equal to the Hamming distance ratio between the particle and the global optimal solution, it means that the difference between the current particle and the global optimal solution is relatively large, and the current particle tends to move closer to the individual optimal solution. In this case, a new random number is generated for subsequent logical judgment. If this new random number is greater than the Hamming distance ratio between the particle and the individual optimal solution, it means that the difference between the current particle and the individual optimal solution is relatively small, i.e., the current particle tends to move closer to the individual optimal solution. Therefore, in this iteration, the particle believes that its best historical decision is worth using, and so it adopts the decision of the individual optimal solution. Otherwise, the same mutation operation as above is performed.

[0053] 3) Repeat the above operations until all p Once the deployment status of each segment has been updated, the new particle position is obtained. x n k+1 and for all updated particles x n k+1 Step two is performed to calculate the new fitness of each particle. After evaluating the new positions of all particles, the current fitness of each particle is compared with its historical best fitness. If the fitness of the current position is better than the historical best individual fitness, then the position is updated to the historical best individual fitness. Furthermore, the historical best individual fitness of all particles is compared with the global best fitness. If any historical best individual fitness is better than the global best fitness, then the historical best individual fitness is updated to the global best fitness.

[0054] The expression for the variogram is: ; Step 5: When the maximum number of iterations is reached or the solution has converged, the algorithm terminates and outputs the global optimal solution as the final optimal sensor placement scheme.

[0055] First, the iteration terminates when the system reaches the maximum number of iterations, or when the global optimal solution has not significantly improved over multiple iterations. At this point, the final global optimal solution is output as the optimal sensor deployment scheme, which includes the optimal number of sensors and their specific deployment locations across each span of the transmission line. For example: With a transmission line span number P=10, the output result is: [0,1,0,0,1,0,0,0,1,0] The proposed solution involves deploying three sensors in segments 2, 5, and 9, which reduces costs by approximately 70% compared to a full coverage solution (10 sensors).

[0056] The MBPSO algorithm proposed in this invention has a concise analytical expression and a simple parameter identification process, requiring only a small amount of historical current carrying capacity data to complete the deployment scheme optimization. Furthermore, the algorithm employs dynamic Hamming distance adjustment and a directional mutation mechanism, enabling monitoring errors to be controlled within 0.8°C. It can adapt to the rapid deployment needs of different voltage levels and line structures without repeated modeling, significantly improving computational efficiency and providing an efficient and economical solution for dynamic capacity expansion technology.

Claims

1. A method for optimal sensor placement for real-time monitoring of dynamic ampacity of overhead power transmission lines, characterized in that Includes the following steps: S1: Initialize the key parameters of the MBPSO algorithm by loading preprocessed historical meteorological data and current data, with the heat balance equation as the input to the fitness function; S2: Generate a swarm of particles representing different sensor deployment schemes, and encode each particle as a binary array; S3: Introducing the cost function f cost Weighting function f weight Covering functions f coverage The comprehensive fitness function is constructed to calculate and compare the fitness value of each particle. During the iteration process, the individual historical best solution of each particle and the global best solution of the entire population are updated. S4: By calculating the Hamming distance ratio between the particle and the individual optimal solution and the global optimal solution, logical judgment is made to dynamically adjust the update of the particle position, and by introducing a mutation function to randomly flip several bits in the particle code to update the particle's position in the binary space. S5: When the number of iterations reaches the maximum number of iterations or the solution has converged, the algorithm terminates and outputs the global optimal solution as the final optimal sensor placement scheme.

2. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 1 wherein: In S1, the key parameters for initializing the MBPSO algorithm include: number of particles. N Maximum number of iterations k max Total number of transmission line segments P and ideal sensor placement ratio ispr The historical meteorological data includes ambient temperature, wind speed, wind direction, and solar radiation intensity; the current data is the operating current of the transmission lines.

3. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 2 wherein: In S1, the expression for the heat balance equation is: ； In the formula: For solar thermal gain; Line current; Resistance of a conductor; , These are convective and radiative heat losses, respectively.

4. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 3 wherein: In S2, the particle position is represented as follows: In the formula: Indicates the first k In the nth iteration n The position of each particle; Indicates the first p The layout status of the first span; if the value is 1, it indicates the first span. p Sensors are installed at intervals; 0 indicates no sensors are installed. This represents the total number of spans in the transmission line.

5. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 4 wherein: In S3, the expressions for each function in the comprehensive fitness function are as follows: ； In the formula: For cost function, Indicates the first k In the nth iteration n The position of each particle; Indicates in k In the nth iteration, the 1st n The position string of the i-th particle p Bit; ； In the formula: The weighting function evaluates whether the solution prioritizes coverage of the most critical spans, i.e., the spans most frequently becoming bottlenecks in load capacity; the exponential function... The numerical value indicates the criticality of the selected range set; the larger the inner product of the function, the higher the bottleneck range coverage. f weight The smaller; This represents the frequency at which the historical lowest current carrying capacity occurred. ； wherein is a coverage function, verifying that the arrangement is able to effectively monitor the high temperature event of the conductor in actual operation; is the total time point, is the time point, is 1 when a high temperature event is detected, otherwise 0.

6. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 5 wherein: The overall fitness function is derived from the cost function. Weighting function and covering functions The structure involves using a reverse mapping method to transform the original partial fitness function, specifically: a: cost function Directly take the original value, no need for additional mapping, directly participate in weighted sum; b: Weighting function Through exponential function Will The transformation makes the function value fall between 0 and 1, and the larger the inner product, the closer the function value is to 0, which means the smaller the penalty and the better the solution; c: coverage function in the function The value range is [0, 1], the larger the value represents the better the scheme, and by taking the complement transformation (1- ) way, the target is unified as the smaller the better; All sub-objectives are unified into a minimization objective, and a weighted sum is directly performed. The overall fitness value is the sum of the three sub-objectives, i.e.: ； In the formula, is a comprehensive fitness value, is the sum of three fitnesses, and the smaller the fitness function output is, the better the scheme is. f cost This represents the total number of sensors; For key gear distance coverage; The percentage of high-temperature events that were successfully monitored; During the iteration process, the overall fitness value of each particle is compared. The smaller the overall fitness function, the better the solution. This updates the individual historical best solution of each particle and the global best solution of the entire population.

7. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 6 wherein: In S4, the Hamming distance is defined as: ； In the formula, X and Y represent two binary arrays. This is a calculation method that compares each corresponding position of two vectors X and Y bit by bit. When two corresponding positions are different, the result is 1; when they are the same, the result is 0. Hamming distance reflects the distance between the current particle and the optimal solution. The Hamming distance ratio is: ； ； In the formula, dp represents and individual optimal The distance ratio; dp represents and the global optimal solution The distance ratio; P represents the total number of spans of the transmission line; The larger the Hamming distance ratio, the greater the distance, and the more the particle needs to move to approach the optimal solution.

8. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 7 wherein: In S4, the particle position updates are dynamically adjusted as follows: A random function is introduced wherein, is a random function is a random number between 0 and 1 ; By introducing a random function, the algorithm is endowed with necessary randomness and exploratory capabilities, balancing the ability to utilize known optimal solutions while exploring unknown regions. rand > dg The particle learns from gbest, that is, it changes its current position to be the same as gbest, and then uses subsequent ISPR to determine whether it has mutated; if rand <dg The particle learns from pbest and combines this with subsequent ispr to determine whether it has mutated.

9. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 8 wherein: In S4, the specific expression for the introduced mutation function is: ； In the formula, The introduced mutation function, For the ideal sensor placement ratio, That is, what proportion of a span the sensors are expected to be installed over; A mutation function is introduced to randomly flip several bits in the particle's code to update the particle's position in the binary space, specifically as follows: The mutation function generates another random number. If the random number is less than ispr, then... x np k+1 Setting it to 1 determines that a sensor will be placed in the p-th segment; otherwise, setting it to 0 means that no sensor will be placed in the p-th segment.

10. The method for optimal placement of sensor locations for real-time monitoring of dynamic ampacity of overhead power transmission lines as claimed in claim 9 wherein: In S5, when the number of iterations reaches the maximum number of iterations, i.e., the maximum number of iterations... k Equal to the maximum number of iterations k max If the solution does not change in multiple iterations, the iteration stops. The historical best individual fitness of all particles is compared with the global best fitness. If there is a historical best individual fitness that is better than the global best fitness, the historical best individual fitness is updated to the global best fitness, and the global optimal solution is output as the final optimal sensor layout scheme. The global optimal solution is a binary array, which is used to directly guide the installation position and number of physical sensors on the corresponding span of the transmission line.

Images