High and medium voltage distribution network coordination index weight determination method based on AHP-XGBoost model

Abstract

The invention belongs to the technical field of power distribution network line parameter estimation, and particularly discloses a high and medium voltage power distribution network coordination index weight determination method based on an AHP-XGBoost model, and the method comprises the following steps: firstly, building a high and medium voltage power distribution network coordination influence factor evaluation system; secondly, collecting historical data for data preprocessing; then, the subjective weight of each index is calculated based on an AHP analytic hierarchy process; the objective weight of each index is determined based on an XGBoost-SHAP model; a combined empowerment model based on a minimum identification information principle; and finally, determining the index weight of the coordination of the high-and-medium-voltage power distribution network, and optimizing the development decision of the power distribution network. According to the AHP-XGBoost model-based high and medium voltage power distribution network coordination index weight determination method, on the basis of a previous high and medium voltage power distribution network coordination evaluation system, indexes for connecting high and medium voltage power grids are considered; meanwhile, according to historical data training, a scientific and reasonable evaluation result containing historical experience is obtained by applying a combined empowerment mode.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network line parameter estimation, and particularly to a method for determining the weight of coordination indexes of high-voltage and medium-voltage distribution networks based on the AHP-XGBoost model. Background Art

[0002] As the end of the main power transmission network, the high-voltage distribution network undertakes the task of providing high-quality electric energy to the medium-voltage distribution network; the medium-voltage distribution network is a bridge connecting the high-voltage distribution network and electricity customers. The coordination of high-voltage and medium-voltage distribution networks refers to the degree of mutual matching and compatibility between the two voltage levels of high voltage and medium voltage and different devices. When there is a problem of undercoordination in any link of the high-voltage and medium-voltage distribution networks, it will lead to a reduction in the power supply reliability of the distribution network, a decline in the power supply quality, poor power supply economy, and even an inability to meet the needs of electricity customers. Only by achieving better coordination in the high-voltage and medium-voltage distribution networks can the power supply bottleneck within the distribution system be avoided, and the reliability, safety, and economy of the grid operation be maintained, and the efficiency of the distribution network be improved.

[0003] The coordinated development of urban distribution networks includes both the coordination within the high-voltage distribution network and the coordination within the medium-voltage distribution network. At present, the research on grid coordination mainly focuses on the planning, structure, capacity assessment of high-voltage or medium-voltage distribution networks, as well as aspects such as the grid and power sources, the grid and loads, and the grid and social environment, while lacking research on the coordination degree between the two voltage levels of high-voltage and medium-voltage distribution networks.

[0004] At the same time, the methods for determining the weights of coordination indexes of high-voltage and medium-voltage distribution networks include subjective weighting methods and objective weighting methods. The subjective weighting method needs to rely on expert experience to determine the weights, and the process is simple, which is used for the case of fewer indexes; the objective weighting method is based on mathematical theories and uses mathematical models, and the obtained weight results are objectively quantified, eliminating the influence of human factors, and can be used for the determination of weights of multiple indexes.

[0005] In summary, when studying the coordination of high-voltage and medium-voltage distribution networks, while considering the internal coordination of high-voltage and medium-voltage distribution networks, the coordination indexes between high-voltage and medium-voltage distribution networks should also be considered, so as to comprehensively measure the coordination degree of high-voltage and medium-voltage distribution networks. In terms of the index weight determination method, first use the subjective weighting method to determine the subjective weights of the indexes, then obtain the objective weights of the indexes through the interpretability analysis of the neural network model based on historical data, and finally perform combined weighting to combine and analyze the above two weight values. This can not only solve the problem that the subjective weighting method lacks objective consideration of index data and affects the accuracy of the evaluation results, but also avoid the influence that the objective weighting based on historical data cannot reflect the decision-maker's attention to the attribute importance of different indexes at the current stage, resulting in the evaluation results being inaccurate due to the weights deviating from the actual situation.

[0006] Therefore, the research on determining the weights of coordination indicators for high- and medium-voltage distribution networks based on historical data has important practical significance and application value for the coordination evaluation of distribution networks, and is of great significance for promoting scientific resource allocation and green environmental protection development.

[0007] Similar implementation solutions at the current stage:

[0008] When it comes to determining the weights of coordination indicators for high- and medium-voltage distribution networks, there are various methods that can be used. The following is a brief overview of the names and contents of some of these methods:

[0009] 1. Determining indicator weights based on the Analytic Hierarchy Process (AHP)

[0010] The AHP method is applicable to problems involving multi-level indicators, complex dimensions, and many indicators that are difficult to quantify. This method is a decision-making method that constructs a reasonable multi-level analysis model based on a profound analysis of the internal relationships of multi-objective or multi-scheme problems, and uses mathematical formulas to calculate the weight values of all qualitative indicators at each level to solve complex decision-making problems with multiple objectives. However, the weight assignment of each indicator in this method is too subjective, and the association and characteristics between data are not fully considered. For example, the comparison of the relative importance between different indicators. This may lead to the results being affected by subjective viewpoints, and thus there may be certain uncertainties and biases.

[0011] 2. Determining indicator weights based on the CRITIC method

[0012] This method is an objective method for determining indicator weights. By quantitatively analyzing the correlation coefficients and contrast ratios between indicators, it reduces the interference of subjective factors and improves the objectivity of weight assignment. This method effectively considers the mutual relationships between indicators, can avoid the repeated influence caused by redundant similar indicators, and is applicable to dealing with complex multi-level and multi-indicator decision-making situations. However, it depends on the quality and accuracy of the data. If the input data is not reliable enough, it may lead to unreasonable weight assignment. In addition, the CRITIC method assumes that the relationship between indicators is linear, and may not be able to fully capture the non-linear interactions between indicators in a complex system, thus affecting the accuracy of the weights.

[0013] 3. Determining indicator weights based on the Grey Relational Analysis method

[0014] This method has the advantages of processing a small amount of data, strong adaptability, high intuitiveness, etc. It can conduct analysis under the conditions of a small sample size and incomplete data. At the same time, the requirements for data are relatively loose and do not need to be normally distributed. In addition, the grey correlation degree provides relatively intuitive indicators, which are convenient for decision-makers to understand the relationships between different indicators, and emphasizes the relativity between indicators, thus eliminating the influence of absolute values. However, in the calculation process, complex relationships may be overly simplified, ignoring the potential non-linearity and interaction between the coordination indicators of the high-voltage and medium-voltage distribution networks, thus affecting the rationality of the weights. At the same time, the interpretability of the method is weak, and decision-makers may have difficulty fully understanding the sources of the weights of each indicator and their decision-making basis, thus reducing the transparency of decision-making.

[0015] 4. Determining the indicator weights based on the neural network model

[0016] This model can automatically identify and extract complex non-linear relationships by learning a large amount of data, making the weight allocation more accurate. Secondly, the neural network has strong adaptability and can process high-dimensional and multi-type data, thus being applicable to various decision-making scenarios. In addition, the neural network can continuously optimize and adjust the weight allocation through self-learning, making the decision-making process more intelligent and dynamic. However, the construction and training of the neural network model usually require a large amount of data and computing resources, which may make it difficult to be effectively applied in the case of scarce data or limited computing power. Secondly, the "black box" characteristic of the neural network makes the decision-making process of the model less transparent and difficult to explain the specific sources and meanings of the weights, thus reducing the interpretability of the decision-making process. Summary of the invention

[0017] The purpose of the present invention is to provide a method for determining the coordination index weights of high-voltage and medium-voltage distribution networks based on the AHP-XGBoost model, obtain the objective weights of the indicators through the interpretability analysis of the neural network model based on historical data, and combine subjective weighting to reflect the influence of decision-makers' emphasis on different indicator attributes at the current stage. Finally, combined weighting is carried out through the principle of minimum discrimination information, integrating subjective expert opinions and objective data analysis to improve the reliability and scientificity of the evaluation.

[0018] To achieve the above purpose, the present invention provides a method for determining the coordination index weights of high-voltage and medium-voltage distribution networks based on the AHP-XGBoost model, including the following steps:

[0019] S1. Establish an evaluation system for the influencing factors of the coordination of high-voltage and medium-voltage distribution networks;

[0020] S2. Collect historical data and perform data preprocessing;

[0021] S3. Calculate the subjective weights of each indicator based on the AHP (Analytic Hierarchy Process);

[0022] S4. Determine the objective weights of each indicator based on the XGBoost-SHAP model;

[0023] S5. A combined weighting model based on the principle of minimum discrimination information;

[0024] S6. Determine the indicator weights for the coordination of the high-voltage and medium-voltage distribution networks, and optimize the development decision of the distribution network.

[0025] Preferably, in S1, the evaluation system for the influencing factors of the coordination of the high-voltage and medium-voltage distribution networks includes the coordination indicators of the high-voltage distribution network, the coordination indicators of the medium-voltage distribution network, and the coordination indicators of the high-voltage and medium-voltage distribution networks;

[0026] The coordination indicators of the high-voltage distribution network include the transformer capacity utilization ratio, the load balance of main transformers, the load balance of lines, the single-transformer rate of substations, and the single-line rate of substations;

[0027] The coordination indicators of the medium-voltage distribution network include the load balance of distribution transformers and lines, the utilization rate of outgoing line intervals, the non-transferable load rate, and the over-length rate of main lines;

[0028] The coordination indicators of the high-voltage and medium-voltage distribution networks include the substation capacity, the line capacity, and the coordination degree of substation outgoing lines.

[0029] Preferably, S2 specifically includes the following steps:

[0030] S21. Collect various historical data of the high-voltage and medium-voltage distribution networks from users, regulatory agencies, and power supply enterprises, including the capacity and load data of transformers, the electrical parameters of lines, the load characteristics of distribution areas, the utilization of equipment intervals, and the power supply reliability data of the distribution network;

[0031] S22. Preprocess the collected various historical data, including data cleaning, duplicate removal, and normalization processing.

[0032] Preferably, in S3, the subjective weights of each indicator are calculated, specifically including the following steps:

[0033] S31. Construct an analytic hierarchy process model:

[0034] This analytic hierarchy process model includes an objective layer, a criterion layer, and an indicator layer, corresponding to the goal of the decision-making, the intermediate links, and the influencing factors respectively;

[0035] Take the comprehensive evaluation of the coordination of the high-voltage and medium-voltage distribution networks as the work goal and set it as the objective layer;

[0036] Take the coordination of the high-voltage distribution network, the coordination of the medium-voltage distribution network, and the coordination of the high-voltage and medium-voltage distribution networks as the intermediate links and set them as the criterion layer;

[0037] Take the indicators included in the criterion layer as the factors affecting the goal and set them as the indicator layer;

[0038] S32. Construct a judgment matrix:

[0039] Judge the relative importance between two indicators under the same criterion layer according to the analytic hierarchy process model. Suppose there are n indicators in a certain criterion layer, then the judgment matrix constructed is A = (a ij ) n×n . Introduce the 1-9 scale method, and the expression is:

[0040]

[0041] where a ik represents the importance degree of indicator i to indicator k, and it is necessary to satisfy a ik = 1 / a ki , a ii = 1, i, k = 1, 2, 3,..., n;

[0042] S33. Consistency test:

[0043] Conduct a consistency test according to the maximum eigenvalue λ of the judgment matrix. When λ max = n, the judgment matrix satisfies the consistency test; when λ max ≠ n, then further calculate to determine whether the judgment matrix satisfies the consistency test. If it satisfies, enter S34;

[0044] S34. Obtain the index weights:

[0045] Calculate the eigenvector corresponding to the maximum eigenvalue λ max of the judgment matrix, and after normalization, obtain the weight vector of the evaluation index:

[0046] W = [w1, w2,..., w n (2).

[0047] Preferably, in S33, further calculating to determine whether the judgment matrix satisfies the consistency test includes the following steps:

[0048] First, calculate the consistency index CI:

[0049]

[0050] In the formula, λ max > n, and n is the order of the judgment matrix;

[0051] Second, determine the average random consistency index RI;

[0052] Finally, calculate the consistency ratio CR:

[0053]

[0054] If CR < 0.1, it is considered that the judgment matrix meets the consistency test; if CR ≥ 0.1, the judgment matrix needs to be reconstructed until the consistency test is met.

[0055] Preferably, in S4, the objective function of XGBoost consists of a loss function and a regularization term, and the form of the objective function of XGBoost is as follows:

[0056]

[0057] In the formula: L (t) is an expression in the linear space, is the loss function, ∑ k Ω(f k ) is the regularization term, is the predicted value of the i-th sample x i , and the GBDT gradient boosting tree is used to express Then the objective function L (t) is transformed into the following form:

[0058]

[0059] By performing a second-order Taylor expansion on the loss function and removing the constant term, we get:

[0060]

[0061] Then, by expanding the regularization term and removing the constant term, we get:

[0062]

[0063] Finally, redefine the tree and substitute it into the objective function, group the nodes, and combine the first-order term coefficients and second-order term coefficients to obtain the final objective function:

[0064]

[0065] In the formula: G j is the sum of the first-order partial derivatives of the samples contained in leaf node j, and H j is the sum of the first-order partial derivatives of the samples contained in leaf node j; ]>

[0066] After the samples are determined, G and H are determined. When each leaf node reaches the optimum, the entire objective function also reaches the optimum, and the weights of each leaf node are obtained by solving and the optimum objective value Obj is:

[0067]

[0068] The hyperparameters to be set include the depth of the tree, the weight of the model produced at each iteration, the number of sub-models, and the weight of the regularization term.

[0069] Preferably, in S4, the hyperparameters are optimized by the Bayesian method, and the specific process is as follows:

[0070] By constructing the probability model χ→R d Select the next evaluation point and perform iterative loop calculations on the evaluation points until the optimal solution for the hyperparameters is obtained, and then end the loop:

[0071]

[0072] Among them, x * represents the optimal hyperparameter combination, χ represents the decision space, and f(x) represents the given objective function;

[0073] The SHAP value represents the contribution of individual input features to the model prediction value. It is used to explain the threshold and interaction synergy between the variable and the explained variable. The SHAP formula is:

[0074]

[0075] Where f is the prediction function of the model, x is the observed feature vector, S is the set of all features, n is the number of features, and x S / T is the observed value of all features except T;

[0076] For a single feature x i , the calculation formula of SHAP value is as follows:

[0077] SHAP[f,x,S / {i}]=f(x)-SHAP(f,x,S) (14).

[0078] Preferably, in S5, a combined weighting model based on the minimum discriminant information principle is used to integrate the subjective and objective weights above. The specific model solving steps are as follows:

[0079] Set the objective function:

[0080]

[0081] Where, ω zi 、ω ki 、ω i They refer to the subjective, objective and comprehensive weights of the goal respectively;

[0082] Solve the objective function:

[0083] First construct the Lagrangian function L:

[0084]

[0085] Taking its partial derivative gives:

[0086]

[0087] The combined weight is obtained as:

[0088]

[0089] The final comprehensive weight vector is obtained as W = [ω1, ω2…, ω n .

[0090] Therefore, the present invention adopts the above method for determining the weight of the coordination index of the high - and medium - voltage distribution network based on the AHP - XGBoost model, and the beneficial effects are as follows:

[0091] (1) The present invention considers various influencing factors of the coordination of the high - and medium - voltage distribution network in many aspects: in the evaluation index system serving the coordination of the power grid, it includes the matching indexes between high - voltage and medium - voltage, such as the transformer capacity - load ratio, the load transfer rate, the equipment capacity ratio, etc.; it can comprehensively evaluate various factors such as the coordination between distribution networks of different voltage levels; compared with the traditional single - index evaluation method, the method provided by the present invention can better reflect the coordination of the high - and medium - voltage distribution network.

[0092] (2) The present invention obtains the index weight value based on the AHP - XGBoost - SHAP model through the principle of minimum discrimination information: at present, the coordination evaluation methods of high - and medium - voltage distribution networks not only have problems such as large subjectivity and regional limitations, but also do not consider the potential non - linear and interaction effects between indexes. The present invention innovatively uses the interpretability analysis of the neural network model based on historical data to obtain the objective weight of the index, and combines subjective weighting to reflect the influence of decision - makers' emphasis on different index attributes at the present stage. Finally, combined weighting is carried out through the principle of minimum discrimination information, integrating subjective expert opinions and objective data analysis, and improving the reliability and scientificity of the evaluation.

[0093] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0094] Figure 1 is the overall technical solution flow block diagram of the embodiment of the method for determining the weight of the coordination index of the high - and medium - voltage distribution network based on the AHP - XGBoost model of the present invention;

[0095] Figure 2 is the block diagram of the evaluation system for the influencing factors of the coordination of the high - and medium - voltage distribution network in the embodiment of the method for determining the weight of the coordination index of the high - and medium - voltage distribution network based on the AHP - XGBoost model of the present invention;

[0096] Figure 3It is the flowchart of the XGBoost-SHAP model in an embodiment of the method for determining the weight of the coordination index of the high-voltage and medium-voltage distribution network based on the AHP-XGBoost model of the present invention. Detailed implementation manners

[0097] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0098] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0099] As Figure 1 shown, a method for determining the weight of the coordination index of the high-voltage and medium-voltage distribution network based on the AHP-XGBoost model includes the following steps:

[0100] S1. Establish an evaluation system for the influencing factors of the coordination of the high-voltage and medium-voltage distribution network;

[0101] When conducting the coordination evaluation of the high-voltage and medium-voltage distribution network, various types and a large number of choices are faced. Due to the large differences in capital requirements and implementation durations, the decision-making becomes complex, and the evaluation of investment effectiveness is also not comprehensive enough. In the case where the power grid company cannot bear the total amount of all investment projects and the investment capacity is limited, scientifically and efficiently determining the index weight is the key to the construction of the distribution network. Only when the planning of the high-voltage and medium-voltage distribution network achieves full overall coordination can the power supply quality of the distribution system be guaranteed and the maximum economic benefit of the distribution network be realized.

[0102] This embodiment considers from multiple aspects and establishes a set of evaluation systems for the influencing factors of the coordination of the high-voltage and medium-voltage distribution network in combination with various indicators. Specifically, this evaluation system includes the coordination index of the high-voltage distribution network, the coordination index of the medium-voltage distribution network, and the coordination index of the high-voltage and medium-voltage distribution network.

[0103] 1. The coordination index of the high-voltage distribution network is mainly evaluated by assessing five key indicators of the high-voltage distribution network, including the transformer capacity utilization ratio, the load balance of the main transformer, the load balance of the line, the single-transformer rate of the substation, and the single-line rate of the substation.

[0104] The transformer capacity utilization ratio directly reflects the load-carrying capacity of the substation, ensures power supply safety, and avoids equipment failures caused by overload. The load balance of the main transformer and the load balance of the line are closely related to whether the transformer is overloaded and the line is overloaded. Good balance can improve the operation efficiency and stability of the system. Therefore, improving the load balance of the main transformer and the line is an important content for evaluating coordination.

[0105] The single - transformer rate of a substation refers to the degree of dependence on only a single transformer within the substation, and the single - line rate refers to the degree of dependence of the substation on a single transmission line. Excessively high single - transformer and single - line rates will increase the risk of large - scale power outages caused by faults. It is necessary to rationally allocate the number and capacity of transformers, as well as the layout of lines, to ensure the stability and reliability of the power supply during a fault. Therefore, the single - transformer rate and single - line rate of a substation are important reference indicators for evaluating coordination.

[0106] 2. The coordination indicators of the medium - voltage distribution network mainly include the load balance between distribution transformers and lines, the utilization rate of outgoing line intervals, the non - transferable load rate, and the excessive length rate of the main line.

[0107] The load balance between distribution transformers and lines is to evaluate the load distribution of distribution transformers and distribution lines, ensure the reasonable distribution of load among different equipment and lines, avoid overloading of a certain transformer or line, and thus improve the overall efficiency and safety of system operation. The utilization rate of outgoing line intervals refers to the ratio of the actual load of each outgoing line in the distribution network to its rated load, reflecting the utilization efficiency of outgoing line resources. If there is a problem of tight 10kV interval resources, it may lead to some substations being unable to send out lines, so it is necessary to plan the layout of lines well to improve the utilization rate of outgoing line intervals. When one line fails, another line cannot transfer the load, resulting in power outages at multiple substations at the end. Therefore, reducing the non - transferable load rate is one of the important contents in the evaluation of planning.

[0108] 3. The coordination indicators of the high - voltage and medium - voltage distribution network mainly include the substation capacity, line capacity, and coordination indicators of substation outgoing lines.

[0109] This coordination not only involves the matching of transformer capacities between the high - voltage distribution network and the medium - voltage distribution network, but also covers the load distribution and the rationality of line design during the power transmission process between the two. Specifically, the capacity of the transformer must be able to effectively support the load demand of the downstream low - voltage distribution network, avoiding overloading or insufficient capacity. In this process, the selection and layout of lines also play a key role. They need to have sufficient load - bearing capacity to ensure that electric energy can be efficiently and safely transmitted from the high - voltage end to the medium - voltage end. In addition, to prevent some outgoing lines from being overloaded and causing equipment overload and damage, it is also necessary to consider the load distribution of each outgoing line and improve the balance degree of substation outgoing lines. Therefore, the substation capacity, line capacity, and coordination degree of substation outgoing lines are important reference indicators for coordination evaluation.

[0110] S2. Collect historical data from various places, calculate the index parameters of each part of S1, and perform data pre - processing, which specifically includes the following steps:

[0111] S21. Collect various historical data of users, regulatory agencies, and power supply enterprises for the high-voltage and medium-voltage distribution networks, including the capacity and load data of transformers, electrical parameters of lines, load characteristics of distribution areas, utilization of equipment intervals, and power supply reliability data of the distribution network, etc.

[0112] S22. Preprocess the collected various historical data, including data cleaning, deduplication, and normalization processing to ensure the effectiveness and standardization of the data.

[0113] S3. Calculate the subjective weights of each index based on the AHP (Analytic Hierarchy Process);

[0114] The Analytic Hierarchy Process is a multi-scheme decision-making analysis method that combines expert experience judgment and mathematical model calculation. That is, by analyzing the mutual relationships of the internal decision-making factors of multi-objective or multi-scheme problems, constructing a clear and reasonable multi-level analysis model and hierarchically quantifying the weight values of each factor, avoiding the confusion of weight assignment caused by cumbersome index systems, having good integrity and operability, and being widely used in evaluation analysis fields such as the calculation of subjective weights and the ranking of evaluation results.

[0115] The basic principle of the Analytic Hierarchy Process refers to: decomposing complex problems into several levels methodically according to certain criteria, constructing a judgment matrix that meets the consistency test by comparing the importance degrees between two-by-two indexes within the same level, calculating its maximum eigenvalue and the corresponding eigenvector, obtaining the weights of each index after normalization processing, and using the weights to rank the pros and cons of each scheme to be evaluated, so as to guide the decision-making of the best scheme.

[0116] Calculating the subjective weights of each index specifically includes the following steps:

[0117] S31. Construct an analytic hierarchy model:

[0118] This analytic hierarchy model includes an objective layer, a criterion layer, and an index layer, corresponding to the decision-making goal, intermediate links, and influencing factors respectively;

[0119] In this embodiment, according to its layering principle, the comprehensive evaluation of the coordination of the high-voltage and medium-voltage distribution networks is used as the work goal and set as the objective layer;

[0120] The coordination of the high-voltage distribution network, the coordination of the medium-voltage distribution network, and the coordination of the high-voltage and medium-voltage distribution networks in three aspects are used as intermediate links and set as the criterion layer;

[0121] The indexes included in the three criterion layers are used as the factors affecting the goal and set as the index layer.

[0122] S32. Construct a judgment matrix:

[0123] Refer to the relevant literature on the comprehensive evaluation of the distribution network and combine expert opinions. According to the analytic hierarchy process model, judge the relative importance between two indicators under the same criterion layer.

[0124] To specifically quantify the relative importance, the 1-9 scale method is introduced, as shown in Table 1:

[0125] Table 1 1-9 scale method

[0126]

[0127]

[0128] According to the above judgment principle and method, assume there are n indicators in a certain criterion layer, then the judgment matrix is constructed as A=(a ij ) n×n , and the 1-9 scale method is introduced. The expression is:

[0129]

[0130] Among them, a ik represents the importance of indicator i to indicator k, and it needs to satisfy a ik =1 / a ki , a ii =1, i, k = 1, 2, 3,..., n.

[0131] S33. Consistency test:

[0132] To ensure the feasibility of the judgment matrix, the consistency test can be carried out according to the maximum eigenvalue λ of the judgment matrix. When λ max =n, it indicates that the judgment matrix satisfies the consistency test; when λ max ≠n, then it is necessary to further calculate to determine whether the judgment matrix satisfies the consistency test. If it is satisfied, enter S34, including the following steps:

[0133] First, calculate the consistency index CI:

[0134]

[0135] In the formula, λ max >n, n is the order of the judgment matrix;

[0136] Secondly, determine the average random consistency index RI, as shown in Table 2:

[0137] Table 2 Average random consistency index RI

[0138] n 1 2 3 4 5 6 7 8 9 RI 0.00 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45

[0139] Finally, calculate the consistency ratio CR:

[0140]

[0141] If \(CR < 0.1\), it is considered that the judgment matrix meets the consistency test; if \(CR\geq0.1\), the judgment matrix needs to be reconstructed until the consistency test is met.

[0142] S34. Calculate the index weights:

[0143] Calculate the maximum eigenvalue \(\lambda\) of the judgment matrix max of the corresponding eigenvector, and after normalization, obtain the weight vector of the evaluation index:

[0144] \(W = [w_1, w_2, \ldots, w_{ n}] \ (4)\).

[0145] S4. Determine the objective weights of each index based on the XGBoost - SHAP model;

[0146] The objective function of XGBoost is composed of a loss function and a regularization term. By using the regularization term to limit the complexity of the model, the problem of low model generalization ability can be effectively avoided. The form of the objective function of XGBoost is as follows:

[0147]

[0148] In the formula: \(L_{ (t)}\) is the expression in the linear space, \(l\) is the loss function, \(\sum_{ k}\Omega(f_{ k})\) is the regularization term, \(\hat{y}_i\) is the predicted value of the \(i\)-th sample \(x_{ i}\), and the GBDT gradient - boosting tree is used to express Then the objective function \(L_{ (t)}\) is transformed into the following form:

[0149]

[0150] By performing a second - order Taylor expansion on the loss function and removing the constant term, we can obtain:

[0151]

[0152] Then, by expanding the regularization term and removing the constant term, we can obtain:

[0153]

[0154] Finally, re - define the tree and substitute it into the objective function, group the nodes, and combine the first - order term coefficients and second - order term coefficients to obtain the final objective function:

[0155]

[0156] Where: G j is the sum of the first-order partial derivatives of the samples included in leaf node j, and H j is the sum of the first-order partial derivatives of the samples included in leaf node j.

[0157] The expressions of the leaf nodes of the objective function are relatively independent. After the samples are determined, G and H are determined. When each leaf node reaches the optimum, the entire objective function also reaches the optimum. By solving, the weights of each leaf node are obtained and the optimal objective value Obj is:

[0158]

[0159] Hyperparameters are the tuning parameters in the machine learning model and need to be set manually before building the model. Setting the hyperparameters of the XGBoost model includes the depth of the tree, the weights of the models generated in each iteration, the number of sub-models, and the weights of the regularization terms, etc.

[0160] Bayesian is a good solution in hyperparameter optimization and has achieved good results in a series of global optimization problems. The Bayesian optimization algorithm is a global optimization based on probability distribution. Its principle is to continuously input sample points into the given objective function to update the posterior distribution (Gaussian process) of the objective function until the posterior distribution is close to the true distribution, that is, considering the previous parameter information and then adjusting the current parameters. The Bayesian optimization method is a method that uses a probabilistic f model in hyperparameter decision-making. The specific process of optimizing hyperparameters by the Bayesian method is as follows:

[0161] By constructing a probability model χ→R d Select the next evaluation point and perform iterative loop operations on the evaluation point until the optimal solution of the hyperparameters is obtained and the loop ends:

[0162]

[0163] where, x * represents the combination of the optimal hyperparameters, χ represents the decision space, and f(x) represents the given objective function.

[0164] Although the XGBoost model shows excellent prediction ability, due to the complexity of the ensemble learning algorithm, it is usually regarded as a "black box" with limited interpretability. SHAP is based on the Shapley value principle in game theory and effectively explains the prediction process and feature importance of the machine learning model,

[0165] SHAP values represent the contributions of individual input features to the model's predicted values and are used to reveal the thresholds and interactive synergistic effects between explanatory variables and explained variables. The SHAP formula is as follows:

[0166]

[0167] In the formula, f is the prediction function of the model, x is the observed feature vector, S is the set of all features, n is the number of features, and x S / T is the observed value of all features except T.

[0168] SHAP values can be expressed as the difference between the predicted value of the model when all features are set to their average values and the actual predicted value. Therefore, for a single feature x i , the SHAP value represents the contribution of this feature to the model's prediction. The higher the SHAP value, the greater the contribution of the input feature to the prediction result. By calculating the SHAP values of each feature, a contribution matrix regarding the model's prediction can be obtained, thus helping to understand and interpret the model's decision-making process. For a single specific feature x i , the calculation formula of the SHAP value is as follows:

[0169] SHAP[f, x, S / {i}] = f(x) - SHAP(f, x, S) (14).

[0170] Based on the above XGBoost-SHAP model, it is applied to the evaluation of the coordination planning of high-voltage and medium-voltage distribution networks, and an algorithm for determining the weights of the coordination indexes of high-voltage and medium-voltage distribution networks based on historical data is designed. The overall flowchart is as Figure 3 shown.

[0171] The entire model process is mainly divided into two stages. In the first stage, the data of the training set is preprocessed and the XGBoost model is constructed; in the second stage, the interpretability analysis of the predicted model is carried out. By outputting the SHAP values, the contribution degrees of individual input features to the model's predicted values are determined, and then the weight values of each index in the model are obtained.

[0172] S5. The combined weighting model based on the principle of minimum discrimination information;

[0173] Discrimination information is an important concept in entropy theory, which characterizes the difference between two probability distributions. The principle of minimum discrimination information means that when the evaluator only collects partial statistical information, by taking the minimum of the discrimination information between the prior distribution and the target distribution as the objective function, the collected data is processed and analyzed. On this basis, the target distribution can be closest to the probability distribution under various constraint conditions.

[0174] In order to make the combined weight not overweight any subjective weight or objective weight as much as possible, a combined weighting model based on the principle of minimum discrimination information is used to fuse the subjective and objective weights above. The specific model solving steps are as follows:

[0175] Set the objective function:

[0176]

[0177] In the formula, ω zi , ω ki , ω i respectively refer to the subjective, objective and comprehensive weights of the target;

[0178] Solve the objective function:

[0179] First, construct the Lagrangian function L:

[0180]

[0181] Then, obtain its partial derivatives to get:

[0182]

[0183] Finally, the combined weight is obtained as:

[0184]

[0185] The final comprehensive weight vector is obtained as W = [ω1, ω2..., ω n [[ID=4l]]].

[0186] S6. Determine the index weights for the coordination of the high-voltage and medium-voltage distribution networks, and optimize the development decision of the distribution network.

[0187] By calculating the weight values of each index, it provides a basis for the comprehensive evaluation of the coordination of the high-voltage and medium-voltage distribution networks. Using these index weight values and the evaluation system, evaluate each high-voltage and medium-voltage coordination index, find the problems existing in the coordinated development of the high-voltage and medium-voltage distribution networks in the regional distribution network, and guide the development of the regional distribution network. After obtaining the scoring results, conduct practical verification and compare with the current development strategy. According to the practical results, continuously optimize this method to improve its accuracy and reliability.

[0188] In addition, the differences in the weight coefficients of the distribution network coordination models in different regions can be analyzed, and the decision-making parameters and the value ranges of the relevant weight values in different regions can be summarized; according to the scoring results, analyze the coordination level of the power grid, find the key influencing factors for the indicators with lower scores, and put forward improvement suggestions, such as improving the coordination of line capacity or optimizing the load balance; finally, combined with the evaluation results and regional needs, formulate a reasonable direction for the development of the power grid to support the sustainable development of the region.

[0189] Therefore, the present invention adopts the above method for determining the weight of the coordination index of the medium and high voltage distribution network based on the AHP-XGBoost model, comprehensively considers the influencing factors of the coordination of the medium and high voltage distribution network, and serves in the evaluation index system of the grid coordination, and can comprehensively evaluate various factors such as the coordination between distribution networks of different voltage levels.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining the weight of coordination indicators of high-voltage and medium-voltage distribution networks based on the AHP-XGBoost model, characterized in that It includes the following steps: S1. Establish an evaluation system for the influencing factors of the coordination of the high-voltage and medium-voltage distribution networks; S2. Collect historical data and perform data preprocessing; S3. Calculate the subjective weights of various indicators based on the AHP (Analytic Hierarchy Process); S4. Determine the objective weights of various indicators based on the XGBoost-SHAP model; S5. A combined weighting model based on the principle of minimum discrimination information; S6. Determine the index weights of the coordination of the high-voltage and medium-voltage distribution networks and optimize the development decision of the distribution network.

2. The method for determining the weight of the coordination index of the medium and high voltage distribution network based on the AHP-XGBoost model according to claim 1, wherein In S1, the evaluation system for the influencing factors of the coordination of the high-voltage and medium-voltage distribution networks includes the coordination indicators of the high-voltage distribution network, the coordination indicators of the medium-voltage distribution network, and the coordination indicators of the high-voltage and medium-voltage distribution networks; The coordination indicators of the high-voltage distribution network include the transformer capacity-load ratio, the main transformer load balance, the line load balance, the single-transformer rate of the substation, and the single-line rate of the substation; The coordination indicators of the medium-voltage distribution network include the load balance of the distribution transformer and the line, the utilization rate of the outgoing line interval, the non-transferable load rate, and the over-long rate of the main line; The coordination indicators of the high-voltage and medium-voltage distribution networks include the substation capacity, the line capacity, and the coordination degree of the substation outgoing lines.

3. A method for determining the weight of coordination indicators of a high-voltage and medium-voltage distribution network based on the AHP-XGBoost model according to claim 2, characterized in that, S2 specifically includes the following steps: S21. Collect various historical data of the high-voltage and medium-voltage distribution networks from users, regulatory agencies, and power supply enterprises, including the capacity and load data of transformers, the electrical parameters of lines, the load characteristics of the distribution area, the utilization of equipment intervals, and the power supply reliability data of the distribution network; S22. Preprocess the collected various historical data, including data cleaning, duplicate removal, and normalization processing.

4. The method for determining the weight of the coordination index of the high-voltage and medium-voltage distribution network based on the AHP-XGBoost model according to claim 3, wherein In S3, calculating the subjective weights of various indicators specifically includes the following steps: S31. Construct an analytic hierarchy model: This analytic hierarchy model includes an objective layer, a criterion layer, and an index layer, corresponding to the decision-making objective, intermediate links, and influencing factors respectively; Take the comprehensive evaluation of the coordination of the high-voltage and medium-voltage distribution networks as the work objective and set it as the objective layer; Take the coordination of the high-voltage distribution network, the coordination of the medium-voltage distribution network, and the coordination of the high-voltage and medium-voltage distribution networks as the intermediate links and set them as the criterion layer; Take the indicators included in the criterion layer as the factors affecting the objective and set them as the index layer; S32. Construct a judgment matrix: According to the analytic hierarchy process model, the relative importance between two indicators under the same criterion layer is judged. Suppose there are n indicators in a certain criterion layer, then the judgment matrix is constructed as A=(a ij ) n×n . The 1-9 scale method is introduced, and the expression is as follows: Among them, a ik represents the importance degree of index i to index k, and it is necessary to satisfy a ik = 1 / a ki , a ii = 1, i, k = 1, 2, 3, …, n; S33. Consistency check: Perform a consistency test based on the maximum eigenvalue λ of the judgment matrix. When λ max = n, the judgment matrix satisfies the consistency test; when λ max ≠ n, then further calculations are performed to determine whether the judgment matrix satisfies the consistency test. If it is satisfied, proceed to S34; S34. Obtain the index weights: Calculate the maximum eigenvalue λ of the judgment matrix max The corresponding eigenvector, and after normalization, obtain the weight vector of the evaluation index: W = [w1, w2, …, w n (2).

5. A method for determining the weight of coordination indexes of high-voltage and medium-voltage distribution networks based on the AHP-XGBoost model according to claim 4, characterized in that In S33, further calculating to determine whether the judgment matrix meets the consistency check includes the following steps: First, calculate the consistency index CI: where λ max > n, and n is the order of the judgment matrix; Secondly, determine the average random consistency index RI; Finally, calculate the consistency ratio CR: If CR < 0.1, it is considered that the judgment matrix meets the consistency check; if CR ≥ 0.1, it is necessary to reconstruct the judgment matrix until the consistency check is satisfied.

6. The method for determining the weight of the coordination index of the medium and high voltage distribution network based on the AHP-XGBoost model according to claim 5, characterized in that In S4, the objective function of XGBoost consists of a loss function and a regularization term, and the form of the objective function of XGBoost is as follows: Where: L (t) is an expression on a linear space, is the loss function, ∑ k Ω(f k ) is the regularization term, is the predicted value of the i-th sample x i , and is expressed using the GBDT gradient boosting tree Then the objective function L (t) is transformed into the following form: By performing a second-order Taylor expansion on the loss function and removing the constant term, we obtain: Then for the regularization term Expand and remove the constant term to obtain: Finally, redefine the tree and substitute it into the objective function, group the nodes, and combine the first-order term coefficients and the second-order term coefficients to obtain the final objective function: Where: G j is the sum of the first-order partial derivatives of the samples included in leaf node j, and H j is the sum of the first-order partial derivatives of the samples included in leaf node j; After the samples are determined, G and H are determined. When each leaf node reaches the optimal state, the entire objective function also reaches the optimal state, and the weights of each leaf node are obtained by solving and the optimal objective value Obj is: Set hyperparameters including the depth of the tree, the weight of each model generated by each iteration, the number of sub-models, and the weight of the regularization term.

7. A method for determining the weight of the coordination index of the high and medium voltage distribution network based on the AHP-XGBoost model according to claim 6, characterized in that, In S4, optimize the hyperparameters through the Bayesian method, and the specific process is as follows: By constructing a probability model χ→R d Select the next evaluation point and perform iterative loop operations on the evaluation point until the optimal solution of the hyperparameters is obtained, and end the loop: where x * represents the combination of optimal hyperparameters, χ represents the decision space, and f(x) represents the given objective function; The SHAP value represents the contribution of individual input features to the model's predicted value, and is used to explain the threshold and interactive synergy effect between the explanatory variable and the explained variable. The SHAP formula is as follows: where f is the prediction function of the model, x is the observed feature vector, S is the set of all features, n is the number of features, and x S / T is the observed value of all features except T; For a single feature x i , the calculation formula of the SHAP value is as follows: SHAP[f,x,S / {i}] = f(x) - SHAP(f,x,S) (14).

8. A method for determining the weight of the coordination index of the high-voltage and medium-voltage distribution network based on the AHP-XGBoost model according to claim 7, characterized in that, In S5, the combined weighting model based on the principle of minimum discrimination information fuses the subjective and objective weights above. The specific model solution steps are as follows: Set the objective function: where ω zi , ω ki , ω i respectively refer to the subjective, objective and comprehensive weights of the target; Solve the objective function: First, construct the Lagrangian function L: Obtain its partial derivative to get: The combined weight is obtained as: The final comprehensive weight vector obtained is W = [ω1, ω2…, ω n .

Images