Distribution line thermal sensor position optimization method

Abstract

The invention provides a distribution line thermal sensor position optimization method, which comprises the following steps of: randomly generating a plurality of individuals according to initial conditions by setting the probability of generating a certain value by elements of the individuals, and calculating the probability of individual selection according to the fitness of the individuals; the fitness is related to the difference degree between individual temperature distribution and theoretical temperature distribution and the number of sensors. Two individuals are selected according to the calculated probability, whether the two individuals meet constraint conditions or not is judged firstly, if yes, the optimal individual is reserved, and the global optimal individual and population are updated; if not, the two individuals are subjected to crossover and mutation operation, the probability of crossover and individual mutation between the two individuals is related to the difference degree between the two individuals and the diversity of the population, and after crossover and mutation operation is carried out, the global optimal individual and population are updated; the number of execution times of the method is controlled through the number of iterations in the initial conditions; according to the method, the accuracy of temperature distribution measurement is ensured, and meanwhile, the number of the sensors is small.

Description

Technical Field

[0001] The technical field of this invention is the optimization of the arrangement of thermal sensors in power distribution lines, and in particular, it relates to a method for optimizing the location of thermal sensors in power distribution lines. Background Technology

[0002] With the continuous improvement of people's living standards, the demand for electricity is also constantly increasing, especially during peak hours when the load growth is particularly significant. This phenomenon has spurred the continuous advancement of the construction of new power systems based on new energy sources, and the large-scale integration of distributed power sources has become an important trend in the development of distribution networks. However, the overall utilization rate of current distribution networks remains low, especially during peak hours, where the problem of insufficient power transmission capacity is becoming increasingly prominent. Therefore, how to safely, economically, and efficiently improve the transmission capacity of distribution networks has become an important issue that urgently needs to be addressed.

[0003] Among numerous possible solutions, dynamic capacity expansion technology has garnered widespread attention due to its ability to monitor line status and operating environment information in real time and calculate the line's transmission capacity accordingly. The core of this technology lies in dynamically adjusting the load capacity of power distribution lines through real-time data acquisition and analysis, thereby achieving more efficient power transmission. To achieve this goal, optimizing the number of sensors and ensuring accurate monitoring of overhead power line temperature have become key factors for the successful implementation of dynamic capacity expansion technology.

[0004] Specifically, the proper configuration of sensors can not only improve monitoring accuracy but also effectively reduce equipment investment and maintenance costs. Real-time monitoring of line temperature allows for the timely detection of potential overload risks, enabling appropriate measures to be taken to ensure the safe and stable operation of the distribution network. Furthermore, optimizing sensor placement can reduce redundant monitoring, improve overall system efficiency, and thus provide strong support for the efficient utilization of the distribution network.

[0005] Currently, the method for configuring thermal sensors on overhead power distribution lines is uniform placement. First, basic data about the overhead power distribution line needs to be collected, including the line length, geographical direction, commissioning time, and tower type. Next, appropriate thermal sensors are selected based on this basic data and monitoring requirements. Finally, according to the length of the overhead power distribution line, as well as the coverage area and measurement accuracy requirements of the selected sensors, the thermal sensors are evenly placed along the line.

[0006] A method for optimizing the placement of temperature sensors in chicken coops based on genetic algorithms has been disclosed on the Chinese patent website. Its application number is 202110163035.7. In this patent, the deployment positions of temperature sensors are solved by genetic algorithms, and the temperature of the position where no temperature sensor is deployed is calculated based on the temperature value of the solved position. However, this method does not set the probability of initial individuals and crossover, and it also eliminates individuals with low fitness. Therefore, it is relatively slow to converge to the optimal solution. Summary of the Invention

[0007] The purpose of this invention is to optimize the deployment of thermal sensors in power distribution lines of different spans, so that fewer thermal sensors can be used to construct a temperature distribution that closely resembles the actual situation based on the temperature values ​​they measure.

[0008] Another objective of this invention is to set the probability of individual element values ​​in the initial population by the degree of drastic temperature change and connectivity of the distribution wire corresponding to individual elements, so that there are some individuals in the initial population that are close to the optimal individuals. Furthermore, based on this, the probability of crossover is set according to the degree of difference between individuals, so that the method involved in this invention can converge to the optimal solution more quickly.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows.

[0010] The thermal sensor location optimization steps are as follows: S1: Obtain relevant information for different time periods of each span of power distribution line and set initial and iteration conditions. Calculate the probability of deploying a thermal sensor on each span of power distribution line based on the relevant information. Randomly generate several different individuals based on the calculated probability. Different elements in each individual correspond to different spans of power distribution line, and the value of the element represents whether a sensor is deployed on that span of power distribution line. S2: Calculate the fitness of the individuals and calculate the probability. Select individuals based on the calculated probability, perform crossover among the selected individuals, and then perform mutation. The crossover probability between individuals is related to the degree of difference between individuals. S3: Retain several individuals with high fitness, eliminate several individuals with low fitness, and update the optimal individual. If the iteration conditions are met, the entire step ends; if the iteration conditions are not met, continue with step S2.

[0011] Preferably, in step S1, the relevant information includes: the ambient temperature, wind speed, and solar radiation intensity of each span of power distribution line at different time periods, as well as the number of power distribution lines connected to that span of power distribution line. The theoretical temperature and connectivity of each span of power distribution line at different time periods are calculated based on the relevant information in the heat balance equation, and the value of the connectivity is equal to the number of power distribution lines connected to that span of power distribution line.

[0012] Preferably, in step S1, the value of each element in an individual ranges from two values, which indicate whether a thermal sensor has been deployed on the span of the power distribution line corresponding to that element. One value indicates yes, and the other indicates no. The probability distribution of the individual is obtained as follows: if the temperature change rate and connectivity value corresponding to the element of the individual are higher, the probability that the element value indicates yes is greater; conversely, the probability that the element value indicates no is greater. By obtaining the probability of each element value in the individual in the above manner, the probability distribution of the element values ​​of the individual is obtained.

[0013] Preferably, the probability of crossover between individuals is related to the degree of difference between individuals. The greater the degree of difference between individuals, the higher the probability of crossover between individuals; the smaller the degree of difference between individuals, the lower the probability of crossover between individuals.

[0014] Preferably, the probability of an element mutating in an individual is related to the diversity of the population to which the individual belongs. The higher the diversity of the population, the lower the probability of an element mutating in the individual; the lower the diversity of the population, the higher the probability of an element mutating in the individual.

[0015] Preferably, in step S2, the fitness value is: the difference between the global temperature and the theoretical temperature distribution fitted based on the temperature values ​​of the thermal sensors measured according to the element-corresponding span distribution wires of the individual, plus the reciprocal of the number of thermal sensors.

[0016] Preferably, the iteration condition includes: in step S2, if the crossover between the selected individuals fails, then individuals are randomly selected again and crossover is performed.

[0017] Preferably, the constraints include a threshold for the degree of difference between the individual temperature distribution and the theoretical temperature distribution; the initial conditions include the population size, the number of elements in each individual, and the iteration conditions.

[0018] Preferably, in step S3, if the optimal individual is the global optimal solution, the global optimal individual is updated, and the probability is calculated based on the individual fitness to reselect individuals to form the population; if it is not the global optimal solution, the global optimal individual remains unchanged, and the probability is calculated directly based on the individual fitness to reselect individuals to form the population.

[0019] Preferably, in step S1, if the population formed by randomly generated individuals does not reach the population size value, then individuals continue to be randomly generated; if the number of randomly generated individuals reaches the population size value, then the fitness of the individuals is calculated and the probability of selection is calculated based on the fitness of the individuals.

[0020] The beneficial effects of this invention are that, while ensuring the detection of temperature distribution throughout the entire line, it significantly reduces the number of thermal sensors required on the power distribution lines, thereby lowering the deployment cost of thermal sensors.

[0021] Furthermore, this invention fully considers the impact of microclimate on overhead power distribution lines, calculates the theoretical temperature of the lines, and calculates the approximation between the theoretical temperature and the measured temperature of the lines at different installation points, thereby improving the accuracy of temperature monitoring at the thermal sensor monitoring points.

[0022] Furthermore, this invention sets the probability of generating individual element values ​​based on temperature changes and connectivity, and also sets the probability of crossover between individuals based on the degree of difference between them. In its initial population, there is a high probability of individuals close to the optimal solution, accelerating the speed of optimal convergence. Setting the crossover probability based on the degree of difference between individuals allows the method to search a larger space and reduces the probability of getting trapped in local optima. Through these two designs, the method involved in this invention can achieve a faster convergence speed in finding the optimal solution while minimizing the probability of getting trapped in local optima. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method involved in the present invention.

[0024] Figure 2 The flowchart for generating an individual in this invention.

[0025] Figure 3 This describes the distribution of power distribution lines across each span of a given line.

[0026] Figure 4 This is a topology diagram of the power distribution lines for a specific line. Detailed Implementation

[0027] In some embodiments, this embodiment discloses the overall process by which the present invention optimizes the sensor location and number, such as Figure 1 The flowchart shown in the figure illustrates the optimization of the thermal sensor position according to the present invention. The steps in the flowchart are as follows.

[0028] S1: Collect historical data on wind speed, solar radiation intensity, ambient temperature, connectivity, and temperature of power distribution lines for each span at different time periods. Based on this historical data, calculate the theoretical temperature of each span's power distribution line at different time periods using the heat balance equation. Calculate the probability of deploying sensors in each span based on the temperature variance and connectivity, obtain the element value probability distribution of an individual, and generate an individual based on this probability distribution. Obtain the temperature of the corresponding span's power distribution line based on the element values ​​in the individual, fit the temperature distribution of the entire line, calculate the fitness based on the difference between the theoretical temperature and the temperature distribution, and the number of sensors in that individual. Calculate the selection probability of that individual based on the fitness.

[0029] Individuals are randomly generated. The value of the i-th element of each individual is 0 or 1. This means that if the value of the i-th element of an individual is 1, then a thermal sensor is deployed on the i-th span of the power distribution line; if the value is 0, then no sensor is deployed on the i-th span of the power distribution line. The higher the value of the temperature change rate and the connectivity of a power distribution line, the higher the probability that the value of the corresponding element is 1, and vice versa.

[0030] The initial conditions set determine the number of individuals generated. If the number of individuals generated does not reach the set population size, individuals will continue to be generated randomly until the required number of individuals is reached.

[0031] The theoretical temperature of each span of power distribution line at different times is calculated as follows.

[0032] For the i-th span power distribution line and the wind speed, solar radiation intensity, and ambient temperature corresponding to the j-th time period, respectively v ij S ij and t ij .

[0033] The actual measured temperature for the i-th span distribution line and the j-th time period is denoted as r. ij .

[0034] According to the heat balance equation Solve for the theoretical temperature of the conductor. Where P r P is the heat dissipation power radiated by the conductor. c For convective heat dissipation power; P s This refers to the solar heat absorption power. For the wire at temperature r ij When the alternating current in the conductor is at a certain value, the resistance of the conductor is considered.

[0035] And P r P c and P sThe expressions are as follows: P r =π(ε1+ε2)SD(g) ij 4 -t ij 4 ), where ε1 and ε2 are the radiation coefficients of the aluminum conductor and insulation layer, respectively; S is the Stephen-Boltzmann constant; D is the outer radius of the conductor; g ij P is the theoretical temperature of the i-th span distribution line; c =0.57π(λ1+λ2)θR e 0.485 Where λ1 and λ2 are the heat transfer coefficients of the aluminum conductor and the insulation layer, respectively; R e R is the Reynolds number. e =v ij D / v f v f air viscosity; P s =γDS ij , where γ is the heat absorption coefficient of the surface of the insulated conductor layer.

[0036] Based on the above formula, the theoretical temperature variance for the i-th span distribution line and the j-th time is obtained, and its theoretical temperature equation is: Solving this equation will yield the theoretical temperature.

[0037] Therefore, the theoretical temperature of each span of power distribution line at different time periods can be calculated based on the above formula and data.

[0038] In the generated individuals, not all elements have a value of 1. This means that there are some spans of power distribution lines without deployed sensors. Therefore, it is necessary to infer the temperature values ​​of the spans of power distribution lines without deployed thermal sensors based on the temperature values ​​of the spans of power distribution lines with deployed thermal sensors.

[0039] Here's an example to illustrate: If an individual has a length of 5 and its characteristics are [1,0,1,0,1], this means that thermal sensors are deployed on the power distribution lines in the 1st, 3rd, and 5th spans, while no thermal sensors are deployed on the 2nd and 4th spans. Therefore, it is necessary to infer the temperature values ​​of the power distribution lines in the 2nd and 4th spans based on the temperature sensor values ​​on the power distribution lines in the 1st, 3rd, and 5th spans. This process is called temperature fitting.

[0040] After performing temperature fitting on a specific individual, the temperature values ​​of all span distribution lines over a certain time period are calculated. The differences between the temperature values ​​of all span distribution lines and the calculated theoretical temperatures are then summed to obtain the sum of the squares of the differences between the temperature values ​​of all span distribution lines and the theoretical temperatures over a certain time period. The square root of this value is then taken to obtain the degree of difference between the temperature distribution of all span distribution lines and the theoretical temperature distribution over a certain time period. The differences between the temperature distribution of all span distribution lines and the theoretical temperature distribution over all time periods are then summed to obtain the total degree of difference between the temperature distribution of distribution lines and the theoretical temperature distribution. This value is then added to the number of thermal sensors deployed in that individual to obtain the target value.

[0041] This target value comprehensively considers the difference between the distribution line temperature and the theoretical temperature distribution, as well as the number of sensors. In the actual deployment of thermal sensors on distribution lines, fewer sensors mean lower deployment costs; and the smaller the difference between the fitted distribution line temperature and the theoretical temperature distribution, the higher the accuracy. Finding the minimum target value through the optimization method of this invention means that while deploying a smaller number of thermal sensors, the accuracy of measuring the distribution line temperature distribution can still be guaranteed.

[0042] The smaller the target value of an individual, the higher its fitness level in the population. Therefore, the fitness value of an individual is the reciprocal of the target value, i.e., fitness = 1 / target value. The larger the target value, the smaller the fitness; the smaller the target value, the larger the fitness.

[0043] For a given individual, the probability of being selected for crossover is: the individual's fitness / the sum of the fitness of all individuals in the population.

[0044] S2: Randomly select two individuals and determine whether they meet the constraints. If they do, proceed to step S3. If not, randomly select two more individuals and cross them. If the crossover is successful, perform a mutation operation on the resulting individuals. If the crossover fails, select two more individuals and cross them again until the selected individuals successfully cross over.

[0045] The probability of crossover between individuals is related to the degree of difference between them. Specifically, the greater the difference between individuals, the higher the probability of crossover, and the smaller the difference between individuals, the lower the probability of crossover.

[0046] If the degree of difference between individuals is relatively high, it means that the individual generated after the intersection of these two individuals is likely to be relatively different from the original individual. It also means that the generation of new individuals greatly expands the search space of this method, making the probability of the individual obtained by this method getting trapped in a local optimum relatively low.

[0047] After the crossover, the elements within each individual need to be mutated. Here, the probability of mutation is independent for different elements within the same individual. The setting of the mutation probability is also a crucial issue. If the mutation rate is too high, the differences between individuals will be too large, significantly reducing the convergence speed of the method; conversely, if the mutation probability is too low, it will increase the probability of the method getting trapped in a local optimum.

[0048] Therefore, the mutation rate of elements within an individual is typically set between 0.01 and 0.05, as the problem addressed in this invention is actually a combinatorial optimization problem. Furthermore, existing methods dynamically adjust the mutation rate based on the diversity of the population. If the population diversity is low, the mutation rate of elements within an individual needs to be adjusted to a higher value to promote the expansion of the solution space and prevent getting trapped in local optima; if the population diversity is high, the mutation rate is lowered to avoid excessive perturbation.

[0049] S3: Keep the individual with the highest fitness among the two individuals, and determine whether this optimal individual is the best in the current population. If it is the best in the current population, update the globally optimal individual; if this optimal individual is not the best in the current population, update the globally optimal individual to be the same as the original globally optimal individual.

[0050] Based on the fitness of individuals in the existing population, the probability of an individual being selected is calculated using the formula: individual fitness / sum of the fitness of all individuals in the population. Based on the set initial conditions, i.e., the population size, a number of individuals equal to the population size are randomly selected to form a new population.

[0051] After performing the above operations, whether to continue solving for the optimal individual depends on the number of times step S2 has been executed, i.e., whether the number of iterations has met the requirement. If the requirement has not been met, step S2 needs to be executed again in the new population; if the number of iterations has met the requirement, step S2 does not need to be executed in the new population, the entire optimization solution process ends, the globally optimal individual is obtained, and thermal sensors are deployed on the corresponding span of the power distribution line based on the values ​​of the elements on the optimal individual.

[0052] The criteria for determining whether the two selected individuals meet the constraints are: whether the difference between the temperature distribution of the two individuals and the theoretical temperature distribution is less than a set threshold.

[0053] This threshold is set manually according to actual needs, which is a common technical method and will not be elaborated on here.

[0054] The process of randomly generating individuals is described in detail below through another embodiment.

[0055] In some embodiments, this embodiment discloses a specific process for randomly generating individuals, such as... Figure 2 Please refer to the flowchart of the present invention for generating individuals. Figure 2 The process is as follows: Based on the rate of temperature change and connectivity of different time periods in each span, the probability distribution of element values ​​in an individual corresponding to each span is calculated. Several individuals are then generated based on the calculated element probability distribution. An example is given below to illustrate this.

[0056] For example, if there are 5 distribution lines in the entire line, the probabilities of each span of the distribution line having an element value of 1 are 70%, 65%, 49%, 81%, and 91%, respectively. (1 indicates that a thermal sensor has been deployed on the corresponding span of the distribution line, and 0 indicates that no thermal sensor has been deployed on the corresponding span of the distribution line.)

[0057] The probabilities that the first, second, third, fourth, and fifth elements of an individual are all 1 are 70%, 65%, 49%, 81%, and 91%, respectively. For example, in the process of generating an individual, if the characteristic value of the generated individual is [1,1,0,1,1], then in the process of generating an individual, it is necessary to randomly generate the values ​​of all elements in that individual before proceeding to the generation of the next individual.

[0058] The number of individual features corresponds to the number of spans in the entire route. Please refer to [reference needed]. Figure 3 ,exist Figure 3 The entire line has N spans, meaning there are N spans of distribution wires. Therefore, in this application scenario, the number of individual features is N.

[0059] How to calculate the probability of the element value at the corresponding position based on the rate of temperature change and the degree of connectivity of a certain span power distribution line at different times is also a very important technical feature of this invention.

[0060] In this invention, the probability of calculating the temperature change rate and connectivity of a certain span power distribution line at different time periods is as follows.

[0061] In a power distribution line of a certain span, the temperatures of the line at different time periods constitute a power distribution line temperature dataset. The variance of this dataset is calculated to obtain the variance of the temperature across different time periods for that span of the power distribution line. The squared value of the connectivity of the power distribution line is then calculated. The variance of the temperature across different time periods is added to the squared value of the connectivity. The reciprocal of the sum is then taken as the square root, and this squared value is negative. Using the natural logarithm as the base, and raising the resulting value to the power of the power of the sum, the probability of generating the corresponding element value for that span of the power distribution line can be obtained; the probability of a value of 1 is calculated by subtracting this probability from the value of 1.

[0062] It is important to note that 1 indicates that a thermal sensor has been deployed on the corresponding span of the power distribution line, while 0 indicates that no thermal sensor has been deployed on the corresponding span of the power distribution line. In practice, other symbols or values ​​can be used to replace 1 and 0, which will not be elaborated upon here.

[0063] Therefore, based on the above calculation method, the expression for the element generation probability is: Where σ 2 d represents the variance of the temperature of the power distribution line across different time periods. 2 is the squared value of the connectivity of that span; e is the natural logarithm.

[0064] Temperature variance can reflect, to some extent, the degree of drastic change in the temperature range of the power distribution line, while connectivity indicates the number of power distribution lines connected to the power distribution line of that span. The higher the connectivity, the more likely the temperature change of the power distribution line of that span is to be unstable.

[0065] The purpose of considering the temperature change rate over this span together with the connectivity is that, in the process of training the optimal sensor location and number in the method of this invention, the training data used is historical data. In the historical data, there may be power distribution lines with higher connectivity that have a lower temperature change rate during that period. If only the temperature change rate is considered, it is very likely that as the power consumption of a certain user increases, the temperature change of the power distribution line with higher connectivity will differ significantly from the historical data in subsequent monitoring. Therefore, it is also necessary to consider the drastic degree of future temperature change of the power distribution line based on the connectivity.

[0066] For certain span distribution lines with high temperature change rate and high connectivity, these span distribution lines have a significant impact on the temperature distribution of the entire line. Therefore, when generating individuals, the probability of generating 1 (where 1 indicates that the element corresponds to the span distribution line where the thermal sensor is deployed, and other values ​​have no effect) is high for elements in these span distribution lines. The generated individuals are closer to the optimal solution than randomly generated individuals, which makes the method of this invention less likely to get stuck in a local optimum and converges faster.

[0067] If the number of individuals generated is less than the population size, then continue generating individuals; if the number of individuals generated is greater than or equal to the population size, then end the entire process of generating individuals.

[0068] It should be noted that if an individual has a large number of characteristics, the population size will increase accordingly; if an individual has a small number of characteristics, the population size will decrease accordingly. That is, the population size is positively correlated with the number of characteristics of an individual.

[0069] For a population, if the number of features of individuals in the population is large, it means that the solution space is relatively large, and more individuals need to be generated to expand its search range and reduce the probability of the method involved in this invention getting trapped in a local optimum. If the number of features of individuals in the population is small, it means that the solution space is relatively small, so the population size can be appropriately reduced to save the running time of the method.

[0070] How to perform cross-fertilization based on the differences between individuals is also an important technical feature of this invention, which will be explained in detail below through an embodiment.

[0071] In some embodiments, the differences between individuals are measured by the absolute value of the weighted sinusoidal distance. That is, the smaller the differences between individuals, the smaller the sinusoidal distance between individuals; the larger the differences between individuals, the larger the weighted sinusoidal distance between individuals. The weighted sinusoidal distance takes the value from 0 to 1, so it can be mapped to a probability value.

[0072] In the process of calculating the sinusoidal distance, the contribution of each element's data to the differences between individuals will vary. Therefore, it is necessary to assign corresponding weights to each element. These weights are related to the temperature change rate and connectivity of the power distribution line corresponding to that element's span. If the temperature change rate and connectivity are higher, the weight of that element will be higher; if the temperature change rate and connectivity are lower, the weight of that element will be lower.

[0073] The weight is calculated as follows: the standard deviation of the temperature of the span of the distribution line corresponding to the element is multiplied by the connectivity of the span of the distribution line corresponding to the element, divided by the sum of the standard deviation of the temperature of the span of the distribution lines corresponding to all elements multiplied by the connectivity of the span of the distribution line corresponding to the element.

[0074] Its expression is: Where σ i Let d be the standard deviation of the temperature of the i-th span distribution line. i Let represent the connectivity of the i-th span distribution wire.

[0075] The weighted sinusoidal distance between individuals is calculated as follows: In two individuals, multiply the values ​​of all elements corresponding to the span distribution lines by the weight of the corresponding span distribution line and add them together. Divide the sum by the product of the weight moduli of the two individuals. Divide this value by the product of the weight moduli of the two individuals to obtain the weighted cosine distance between the two individuals. The sinusoidal distance is then calculated based on the weighted cosine distance.

[0076] The following example illustrates this point. Figure 4 As shown, Figure 4The diagram shows the topology of a certain power line. There are seven spans of distribution wires along this line, which, for ease of description, are named distribution wire 1, distribution wire 2, distribution wire 3, distribution wire 4, distribution wire 5, distribution wire 6, and distribution wire 7. The connectivity degrees of distribution wires 1 to 7 are 1, 1, 4, 1, 2, 2, and 1, respectively; and the temperature standard deviations of distribution wires 1 to 7 are 2.16, 1.97, 13.28, 1.76, 3.12, 2.91, and 2.14, respectively.

[0077] The process of generating individuals involves generating two individuals: A = [0,0,1,1,0,1,0] and B = [1,0,1,0,1,0,0].

[0078] Among these elements, the first element corresponds to the first span of the power distribution line, and its value represents whether a thermal sensor is deployed on the first span of the power distribution line; the second element corresponds to the second span of the power distribution line, and its value represents whether a thermal sensor is deployed on the first span of the power distribution line; and so on, which will not be elaborated here.

[0079] It should also be noted that 1 represents the deployment of a thermal sensor on the power distribution line of that span, while 0 represents the absence of a thermal sensor on the power distribution line of that span.

[0080] Based on the connectivity and the standard deviation of temperature change, the weights corresponding to the first span of the power distribution line to the seventh span are calculated as follows: 0.02950417, 0.02690889, 0.72558394, 0.02404043, 0.08523426, 0.07949734, 0.02923098, denoted as β1, β2, β3, β4, β5, β6, β7.

[0081] Therefore, the sinusoidal distance between A and B is calculated as follows.

[0082] First, calculate the weighted product between A and B, using the following formula: ∑ i A i *B i *β i A i B i Let β be the element value in individuals A and B. i Let be the weight corresponding to the i-th span of the power distribution line.

[0083] The calculated weighted product between A and B is 0.7255839366206802.

[0084] The individual weight modulus can be represented as: Where X i For each individual element value.

[0085] That is, the weighted cosine distance between A and B is: the weighted product of A and B divided by the product of the magnitudes of the weights of A and B.

[0086] That is, the weighted cosine distance between A and B is 0.8692717329393591.

[0087] Based on the weighted cosine distance between A and B, and according to the property of trigonometric functions: the square of the cosine plus the square of the sine equals one, we can deduce that the sine distance between A and B is 0.4943345570689991.

[0088] Therefore, the probability of crossover between individuals A and B is 49.43% (rounded to two decimal places).

[0089] As can be seen from the above examples, the smaller the difference between A and B, the larger the cosine distance between A and B, and the smaller the corresponding sine distance between A and B, which means that the probability of A and B intersecting is small. Conversely, if the difference between A and B is large, the smaller the cosine distance between A and B, and the larger the corresponding sine distance between A and B, which means that the probability of A and B intersecting is large.

[0090] Therefore, by calculating the sinusoidal distance between two individuals, the crossover probability between individuals can be inferred, making the probability of crossover between two individuals with large differences higher, and the probability of crossover between two individuals with small differences lower. This design makes the search space of the population larger after crossover, and the probability of getting trapped in a local optimum is lower.

[0091] How population diversity arises from adaptive adjustment of the mutation rate is also a significant technical feature of this invention. Since the number of characteristics of an individual in a population is at least greater than 1, variance cannot be used to measure population diversity; therefore, a suitable method is needed to reflect population diversity.

[0092] The following examples illustrate this.

[0093] In some embodiments, this embodiment discloses a method for solving the mutation rate of individual elements in a population by solving for the largest eigenvalue of the covariance matrix corresponding to the individual datasets in the population.

[0094] Given a population with a number of individuals, perform principal component analysis on the data of these individuals. Calculate the maximum principal component (MPC) of this data and use the MPC values ​​to determine the probability of element mutation within each individual.

[0095] Here, we need to explain Principal Component Analysis (PCA). If the feature space of individuals in a population has several dimensions, PCA aims to find a vector of several dimensions such that the variance of the values ​​projected onto this vector by these individuals is maximized. The variance of the values ​​projected onto this vector by the individuals corresponds precisely to the eigenvalues ​​of the covariance matrix of the individual dataset. Therefore, the eigenvector corresponding to the eigenvalue of the largest eigenvector of this covariance matrix is ​​the optimal projection vector. Similarly, the eigenvector corresponding to the eigenvalue of the second largest eigenvector of this covariance matrix is ​​the second most suitable projection vector.

[0096] The covariance matrix is ​​a conventional technical concept and will not be elaborated upon here.

[0097] After finding the largest eigenvalue of the covariance matrix of the individuals in the population, it should be noted that if the largest eigenvalue of the covariance matrix of a population is higher, the diversity of the population is higher; if the largest eigenvalue of the covariance matrix of a population is smaller, the diversity of the population is lower.

[0098] For populations with low diversity, a higher mutation rate needs to be set to increase population diversity, thereby increasing the population's search space and preventing it from getting trapped in local optima. For populations with high diversity, a lower mutation rate needs to be set to reduce population perturbation, thereby increasing the probability of avoiding a situation where convergence to the optimal individual is slow.

[0099] The individual element variation rate is usually set between 0.01 and 0.05. Therefore, a function needs to be set so that the value of the function is mapped to the feature value between 0.01 and 0.05.

[0100] In this embodiment, the variation rate calculation function used is: the first correction parameter plus the power of the eigenvalue of the negative covariance matrix of the natural logarithm multiplied by the second correction parameter.

[0101] The first correction parameter C1 ranges from 0.030 to 0.033, and the second parameter C2 ranges from 0.017 to 0.02. Their expressions are as follows: λ is the largest eigenvalue of the covariance matrix.

[0102] In this embodiment, the first correction parameter is 0.31 and the second correction parameter is 0.18.

[0103] As can be seen from the expression of this function, the larger the eigenvalue λ is, the smaller the function value becomes, and the closer it is to 0.031; the smaller the eigenvalue λ is, the larger the function value becomes, and the closer it is to 0.049.

[0104] The following example illustrates this point. If the largest eigenvalue of the covariance matrix of an individual dataset in a population is 2.72, then the probability of mutation of an individual element in that population is: Substituting into the above expression, we obtain a value of 0.034459518811747906, which means the probability of mutation of an individual element in the population is 3.446% (rounded to three decimal places).

[0105] If the largest eigenvalue of the covariance matrix of an individual dataset in a population is 13.13, then the probability of mutation of an individual element in that population is 0.031480387394600906, which is 3.148% (rounded to three decimal places).

[0106] By setting the first and second correction parameters, adjustments can be made dynamically according to actual production needs to adapt to more line environment conditions.

[0107] How to infer the temperature value of a span of power distribution line without a thermal sensor based on the measurement value of the thermal sensor of the span power distribution line with a thermal sensor is also an important technical feature of this invention.

[0108] The following examples provide a detailed explanation.

[0109] In some embodiments, this embodiment discloses how to infer the temperature value of a span of power distribution line without a thermal sensor based on the measurements of the thermal sensor on the span of the power distribution line with the thermal sensor deployed, i.e., a temperature fitting process. Let's continue with... Figure 4 For example, if in Figure 4 The optimal individual's characteristics are found to be [1,1,1,0,0,1,0]. Thermal sensors are then deployed on the first span power distribution line, the second span power distribution line, the third span power distribution line, and the sixth span power distribution line.

[0110] At this point, it is necessary to infer the values ​​of the thermal sensors on the fourth span, fifth span, and seventh span of the power distribution line based on the values ​​of the aforementioned thermal sensors, so as to fit the temperature distribution of the entire line and obtain the temperature distribution of the entire line.

[0111] Based on the values ​​of thermal sensors at a certain moment for some span distribution lines with deployed thermal sensors, the temperature value at the corresponding moment for span distribution lines without deployed thermal sensors can be inferred. Here, the RBF interpolation method is used to predict the temperature value of span distribution lines without deployed thermal sensors.

[0112] Here, RBF stands for Gaussian kernel function. The RBF interpolation method involves first defining x, where x represents the corresponding span and time feature, obtaining the temperature of the power distribution line at different times for each span as training data, and then setting the interpolation temperature function. in Let T be a Gaussian kernel function, and for the k-th span distribution line at time q, the temperature T... k，q ,get The equations are used to construct n*p equations (where n is the number of spans and p is the number of time periods) based on the temperature of each span of the power distribution line in each time period. These equations form a system of equations, and λ is obtained by solving this system of equations. i，j The trained RBF interpolation model is obtained. Thus, for any span and any time, as long as the span and time characteristics are input, the corresponding temperature value can be obtained. The temperature of the span distribution line without thermal sensors can be fitted in this way.

[0113] Using the above method, the temperature distribution of the entire line can be fitted, that is, the temperature of each span at different time periods. Based on this method, the degree of difference between the temperature distribution fitted by the location of a specific thermal sensor and the theoretical temperature distribution can be measured.

[0114] The technical solution of the present invention will be fully described below in conjunction with the above content.

[0115] In some embodiments, this embodiment discloses a complete set of steps for optimizing the location and number of thermal sensors, as follows.

[0116] S1: Collect historical data on wind speed, solar radiation intensity, ambient temperature, connection degree of distribution lines and temperature of distribution lines at different time periods for each span and set initial conditions. Based on the temperature of each span of distribution lines at different time periods, construct a temperature dataset for each span of distribution lines and calculate the variance of the temperature dataset for that span of distribution lines.

[0117] Calculate the temperature variance of the span distribution line and the square of the connectivity, and calculate the probability of generating 1 and 0 for the corresponding element of the span (1 indicates that a thermal sensor is deployed on the distribution line of the span, and 0 indicates the opposite).

[0118] The calculation method is as follows: add the variance of the temperature of each span of the power distribution line over different time periods to the square of the connectivity. Take the reciprocal of the sum and then take the square root, with the value being negative. Raise the result to the power of the natural logarithm to obtain the probability.

[0119] The initial conditions include the population size, the number of features (elements) of each individual, and the number of iterations.

[0120] The constraints set include a threshold for the degree of difference between the individual's temperature distribution and the theoretical temperature distribution.

[0121] After the process is completed, individuals with values ​​corresponding to the population size are generated. The number of elements in an individual must be the same as the number of features set for that individual.

[0122] For all generated individuals, based on the values ​​of the elements in the individual, the combination of locations of the distribution wires across the span of the thermal sensor and the number of thermal sensors deployed in each individual are obtained. Based on the temperature values ​​of the distribution wires across different spans at different times for each individual, RBF interpolation is used to fit the temperature values ​​of each span and each time period.

[0123] After obtaining the temperature distribution of an individual, it is necessary to calculate the theoretical temperature for different time periods across each span.

[0124] Based on the temperature, solar radiation intensity, wind speed, and ambient temperature at different times for each span, the theoretical temperature of the power distribution line at different times for each span is calculated through thermal balance.

[0125] The theoretical temperature distribution of the entire line can be obtained through the above calculation method.

[0126] Calculate the difference between the temperature distribution of each individual and the theoretical temperature distribution, and the total number of thermal sensors. Sum these two values ​​to obtain the target value.

[0127] After obtaining the target value, the fitness of each individual is calculated. The fitness value of each individual is the reciprocal of the target value for that individual. Based on the fitness of each individual, the probability of selection for that individual is calculated as: the fitness value of that individual / the sum of the fitness values ​​of all individuals in the population.

[0128] S2: Based on the calculated probability of selecting each individual, randomly select two individuals. Determine whether the two selected individuals meet the constraint condition, i.e., whether the difference between the temperature distribution of the two individuals and the theoretical temperature distribution is less than a threshold. If it is less, proceed to step S3. If it is not less, two individuals need to be randomly selected again, and the two selected individuals are crossed. Before crossing the two selected individuals, calculate the weighted sinusoidal distance between the two individuals, and calculate the probability of crossing between the two individuals based on the calculated weighted sinusoidal distance.

[0129] If crossover between two individuals is successful, a mutation operation is performed on the two resulting individuals. Before the mutation operation, an individual dataset needs to be constructed based on the individuals in the population. A covariance matrix is ​​then constructed based on this dataset, and the largest eigenvalue of the covariance matrix is ​​obtained. After this operation is completed, the first correction parameter and the second correction parameter are set, and the mutation probability of the individual elements is calculated. That is, the first correction parameter plus the power of the largest eigenvalue of the negative covariance matrix of the natural logarithm multiplied by the value of the second correction parameter.

[0130] If the crossover between two individuals fails, two individuals are randomly selected again for crossover.

[0131] S3: Retain the individual with the highest fitness among the two individuals, and determine whether this optimal individual is the best in the current population (i.e., the individual with the highest fitness in the current population). If it is the best in the current population, update the globally optimal individual; if this optimal individual is not the best in the current population, update the globally optimal individual to be the same as the original globally optimal individual.

[0132] Update the fitness of the current population. Calculate the probability of each individual being selected based on the fitness of the current population. In this population, the probability of an individual being selected is: the fitness value of that individual / the sum of the fitness values ​​of all individuals in the population.

[0133] Based on the population size value set in step S1, select the same number of individuals as that value to form a new population. Let M be the population size value set in the initial settings.

[0134] Then, based on the calculated probability of each individual being selected, M selections are performed to select M individuals to form a new population.

[0135] After the operation of generating a new population is completed, it is determined whether the number of iterations is satisfied, that is, whether the number of times the S2 step is executed is greater than or equal to the number of iterations.

[0136] If the number of times step S2 is executed is less than the number of iterations, then step S2 is executed again. That is, in the new population, two individuals are selected for judgment or crossover and mutation based on the probability of each individual being selected in the population.

[0137] If the number of times step S2 is executed is greater than or equal to the number of iterations, the entire solution process ends, the globally optimal individual is obtained, and thus the optimal thermal sensor deployment scheme for the entire line is obtained.

[0138] By analyzing the element values ​​of the optimal individual data, it is possible to effectively identify which spans of power distribution lines require the deployment of thermal sensors and which do not. This process involves not only meticulous observation and data analysis of the power distribution lines but also a comprehensive evaluation combining actual operating conditions and theoretical models. In this way, the number of thermal sensors can be rationally configured while ensuring the safety and stable operation of the lines, thereby achieving the optimal balance between economy and measurement accuracy.

[0139] Specifically, the first step is to conduct comprehensive temperature monitoring and data collection across all spans of the power distribution line. This data will serve as the basis for analysis to understand the temperature variations across different spans under varying conditions.

[0140] In-depth statistical analysis of this data can identify significant temperature fluctuations, which are typically caused by overload, environmental factors, or equipment aging. Therefore, deploying thermal sensors for these specific fluctuations is necessary to monitor temperature changes in real time and prevent equipment malfunctions or safety hazards caused by overheating.

[0141] Meanwhile, for span distribution lines without deployed heat transfer sensors, the temperature of that span can be estimated using RBF interpolation, thus obtaining the temperature distribution of the entire line. This process involves fitting the temperature distribution of the entire line to ensure that the difference between the fitted result and the theoretical temperature distribution is as small as possible. The method described in this invention not only reduces the number of heat sensors required but also ensures the effectiveness and reliability of the overall monitoring system.

[0142] In practical applications, the advantages of this method are particularly evident. Firstly, it significantly reduces equipment investment and maintenance costs. Reducing the number of thermal sensors means lower initial investment, while also reducing subsequent maintenance and management workload.

[0143] Secondly, a well-planned deployment scheme enables comprehensive monitoring of power distribution lines, timely detection of potential safety hazards, and ensures the stable operation of the power system. Furthermore, this method improves data acquisition efficiency, allowing the monitoring system to respond more quickly to various emergencies and ensuring the continuity and reliability of power supply.

[0144] In summary, by analyzing the element values ​​in the optimal individual, the method of this invention can not only identify which spans require the deployment of thermal sensors, but also accurately predict the temperature distribution of the entire line through data fitting techniques.

[0145] The core of this process lies in combining economic efficiency with measurement accuracy to ultimately develop a reasonable deployment scheme for power distribution line thermal sensors. This scheme can improve the safety and stability of the power distribution system.

[0146] This invention has illustrated its purpose, technical solutions, and beneficial effects through specific embodiments. However, these embodiments are merely examples to demonstrate the application of the invention and do not constitute a limitation on the scope of protection of this invention. We explicitly state that any reasonable modifications, equivalent substitutions, or technical improvements guided by the spirit and principles of this invention should be included within the scope of protection of this invention. This means that as long as these changes do not deviate from the core idea and basic function of the invention, they should be protected by patent rights. The scope of protection of this invention should be broad, including all directly obvious variations as well as non-obvious innovations that a technical expert can reasonably deduce from the disclosure of this invention. This broad protection aims to promote further research and development based on this invention, while ensuring that its innovativeness and practicality are fully protected by law.

Claims

1. A method for optimizing the location of thermal sensors in power distribution lines, characterized in that, The thermal sensor position optimization steps are as follows: S1: Obtain relevant information for each span of power distribution line, set initial conditions and constraints, obtain the probability distribution of individual element values ​​based on relevant information and randomly generate several different individuals, and calculate the individual selection probability based on the individual's fitness. S2: Randomly select individuals. If the selected individuals meet the constraints, proceed to step S3; otherwise, reselect individuals and perform crossover and mutation. S3: Update the optimal global individual, reselect individuals to form the population. If the iteration condition is met, end the entire step; otherwise, continue with step S2.

2. The method for optimizing the location of thermal sensors in power distribution lines according to claim 1, characterized in that, In step S1, the relevant information includes: the temperature of each span of power distribution line at different time periods, ambient temperature, wind speed, solar radiation intensity, and the number of power distribution lines connected to the span of power distribution line. Based on the relevant information, the theoretical temperature and connectivity of each span of power distribution line at different time periods are calculated, and the connectivity value is equal to the number of power distribution lines connected to the span of power distribution line.

3. The method for optimizing the location of a thermal sensor in a power distribution line according to claim 2, characterized in that, In step S1, the value of each element in an individual ranges from two values, and the value of the element indicates whether a thermal sensor is deployed on the power distribution line corresponding to that element. The method for obtaining the probability distribution of an individual is as follows: calculate the probability based on the temperature change rate and connectivity of the power distribution line corresponding to the element of the individual, and obtain the probability of each element value in the individual, thereby obtaining the probability distribution of the element values ​​of the individual.

4. The method for optimizing the location of thermal sensors in power distribution lines according to claim 1, characterized in that, The probability of overlap between individuals is related to the degree of difference between them; the greater the difference between individuals, the higher the probability of overlap.

5. The method for optimizing the location of a thermal sensor in a power distribution line according to claim 1, characterized in that, The probability of an element mutating within an individual is related to the diversity of the population to which that individual belongs. The higher the diversity of the population, the lower the probability of an element mutating within that individual; conversely, the lower the diversity of the population, the higher the probability of an element mutating within that individual.

6. A method for optimizing the location of a thermal sensor in a power distribution line according to any one of claims 1 to 5, characterized in that, The fitness value is: the difference between the global temperature and the theoretical temperature distribution fitted based on the temperature values ​​of the thermal sensors measured by the thermal sensors corresponding to the element span of the individual, plus the reciprocal of the number of thermal sensors.

7. A method for optimizing the location of a thermal sensor in a power distribution line according to any one of claims 1 to 5, characterized in that, In step S2, if the crossover between the selected individuals fails, individuals are randomly selected again and crossover is performed.

8. A method for optimizing the location of a thermal sensor in a power distribution line according to any one of claims 1 to 5, characterized in that, The constraints include a threshold for the degree of difference between the individual temperature distribution and the theoretical temperature distribution; the initial conditions include the population size, the number of elements in each individual, and the iteration conditions.

9. A method for optimizing the location of a thermal sensor in a power distribution line according to any one of claims 1 to 5, characterized in that, In step S3, if the optimal individual is the global optimal solution, the global optimal individual is updated, and the probability is calculated based on the individual fitness to reselect individuals to form the population; if it is not the global optimal solution, the global optimal individual remains unchanged, and the probability is directly calculated based on the individual fitness to reselect individuals to form the population.

10. The method for optimizing the location of a thermal sensor in a power distribution line according to claim 9, characterized in that, In step S1, if the population formed by randomly generated individuals does not reach the population size value, then individuals continue to be randomly generated; if the number of randomly generated individuals reaches the population size value, then the fitness of the individuals is calculated, and the probability of the individual being selected is calculated based on the fitness of the individuals.

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