Power distribution network line loss reasonable interval calculation method considering distributed power supply access

Abstract

The invention discloses a power distribution network line loss reasonable interval calculation method considering distributed power supply access. The method comprises the following steps: a, extracting line loss influence factors of wiring from five dimensions of management, metering, technology, new energy access and environment dimension; b, determining the value of a clustering number k through an elbow method, and dividing the data of the five dimensions into k classes by means of a K-means clustering analysis algorithm; c, performing significance verification on the k types of data; d, respectively constructing multiple linear regression models for the k types of data; and e, based on a line loss rate prediction result, taking a 95% confidence interval as a line loss reasonable interval. According to the method, the influence of five factors of power distribution network management, metering, technology, new energy access and environment on the line loss is comprehensively considered, the multiple linear regression model is constructed through classification, the prediction of the line loss rate and the calculation of the reasonable line loss interval are realized, the economic operation of the power grid is favorably evaluated and optimized, and the calculation of the reasonable line loss interval is facilitated. And an important reference basis is provided for construction, transformation and management of a power grid.

Description

Technical Field

[0001] The present invention belongs to the technical field of power distribution network loss reduction, and relates to a method for calculating a reasonable interval of power distribution network line losses, in particular to a method for calculating a reasonable interval of power distribution network line losses in a power distribution network system taking into account distributed power generation access. Background Art

[0002] Line loss is an important economic indicator for assessing the power grid operation and management level of power supply enterprises. The level of line loss not only objectively reflects the level of power grid operation and management, but also relates to the economic benefits of the enterprise itself. Moreover, under the construction of new power systems, the large-scale development of distributed power sources has brought more uncertainties to the operation of distribution networks, causing a series of problems such as high three-phase imbalance in medium and low voltage distribution networks and rising line loss rates. Therefore, it is urgent to carry out research on reasonable interval calculation methods for distributed power access and scientifically and reasonably judge the reasonable range of line loss.

[0003] In the new power system, the access of a high proportion of distributed power sources has led to changes in the distribution of power flow in the distribution network, and even the situation of power reverse transmission, which has led to an increase in the fluctuation of the line loss rate. The reasonable formulation of the reasonable interval of line loss in the distribution network has become the focus and difficulty of line loss management. Under the increasingly high requirements for lean management of line loss in the distribution network, relying solely on expert experience or simple and crude line loss reasonable interval formulation strategies is obviously unable to meet the management requirements. Therefore, it is necessary to comprehensively consider the factors affecting line loss and propose a more scientific and reliable method for formulating a reasonable interval of line loss. The calculation of the reasonable interval of line loss not only helps to evaluate and optimize the economic operation of the power grid, but also provides an important reference basis for the construction, transformation and management of the power grid, which is of great significance to improving the overall efficiency and economic benefits of the power system. Summary of the invention

[0004] In order to improve the scientificity and accuracy of the reasonable interval of comprehensive line loss under the condition of distributed power supply access, the present invention designs a method for calculating the reasonable interval of distribution network line loss considering the access of distributed power supply, and optimizes the multivariate regression model in turn by using the goodness of fit test, F test and t test to obtain an accurate multivariate regression model, and establishes the corresponding multivariate regression model for different power consumption conditions, which is convenient for subsequent call and can display the line loss rate in real time and automatically.

[0005] The technical solution adopted by the present invention is a method for calculating the reasonable interval of line loss in a distribution network considering the access of distributed power sources. The steps of the calculation method are as follows:

[0006] a. Extract the line loss influencing factors of wiring from five dimensions: management, measurement, technology, new energy access, and environment;

[0007] b. Determine the value of the cluster number k by the elbow method, and divide the data of the above five dimensions into k categories with the help of K-means clustering analysis algorithm;

[0008] c. Perform a significance test on the k-type data, and the F test statistic is:

[0009]

[0010] In Formula 1, n is the number of samples, SSE is the clustering error of all samples, SSR is the regression sum of squares, and F α2 (k,n-1-k) is the critical value, when the test value F<F α When the data is in this category, it is removed;

[0011] d. Construct multiple linear regression models for k types of data respectively to predict the line loss rate;

[0012] e. Based on the line loss rate prediction results, the 95% confidence interval is used as the reasonable line loss interval, and the lower and upper limits of the line loss rate are calculated respectively by using the confidence interval method.

[0013] Lower limit of interval:

[0014] Upper limit of interval:

[0015] In Formula 2 and Formula 3, is the average value of the predicted line loss rate, α is 1-confidence level, α=0.05 for a 95% confidence interval, and σ is the standard deviation of the population. The 95% confidence interval can be obtained by looking up the standard normal distribution table. The value is 1.96.

[0016] Add step d1 after step d to check the goodness of fit of k types of models and define the coefficient of determination R 2 :

[0017]

[0018] In formula 4, SSR is the regression sum of squares, SST is the total deviation sum of squares, and SSE is the residual sum of squares. The calculation formula is:

[0019]

[0020] In formula 5-7, y i is the actual value of the dependent variable, is the fitted value of the dependent variable, is the mean value of the dependent variable,

[0021] Coefficient of determination R 2 The value of R is between 0 and 1.2 The closer it is to 1, the better the regression fitting effect is.

[0022] In the step b, the value of the cluster number k is determined by the elbow method. The core indicator of the elbow method is the SSE error square sum, and the formula is:

[0023]

[0024] In formula 8, C i is the i-th cluster, p is C i The sample points in m i It is C i The center of mass, C i The mean of all samples in , SSE is the clustering error of all samples, which represents the quality of clustering effect. The relationship graph between SSE and k is in the shape of an elbow, and the elbow of this elbow corresponds to the k value.

[0025] The beneficial effect of the present invention is that the present invention comprehensively considers the influence of five factors on line loss, namely, distribution network management, metering, technology, new energy access, and environment, and constructs a multivariate linear regression model through classification to realize the prediction of line loss rate and the calculation of reasonable range of line loss. The calculation of reasonable range of line loss not only helps to evaluate and optimize the economic operation of the power grid, but also provides an important reference for the construction, transformation and management of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a residual PP diagram of a specific embodiment.

[0027] Figure 2 It is the calculation result of the reasonable range of line loss in a specific embodiment. DETAILED DESCRIPTION

[0028] First, the prior art and some related algorithms used in the present invention are introduced.

[0029] K-means clustering algorithm is an iterative clustering analysis algorithm. Its steps are: divide the data into K groups in advance, randomly select K objects as the initial cluster centers, and then calculate the distance between each object and each seed cluster center, and assign each object to the cluster center closest to it. The cluster centers and the objects assigned to them represent a cluster. Every time a sample is assigned, the cluster center of the cluster will be recalculated based on the existing objects in the cluster. This process will be repeated until a certain termination condition is met. The termination condition can be that no (or a minimum number) of objects are reassigned to different clusters, no (or a minimum number) of cluster centers change again, and the sum of squared errors is locally minimized.

[0030] The elbow method is a clustering algorithm used to determine the optimal number of clusters in a data set. It calculates the clustering effects under different numbers of clusters and selects the optimal number of clusters based on the changes in these effects. The elbow method evaluates the effects of different numbers of clusters k based on the sum of squared errors (SSE) of clustering, thereby helping to select the appropriate number of clusters for cluster analysis.

[0031] Multiple linear regression algorithm. A single linear regression is a major influencing factor used as an independent variable to explain the change of the dependent variable. In the study of real problems, the change of the dependent variable is often affected by several important factors. At this time, two or more influencing factors are needed as independent variables to explain the change of the dependent variable. This is multiple regression, also known as multiple regression. When there is a linear relationship between multiple independent variables and the dependent variable, the regression analysis performed is multiple linear regression.

[0032] Let y be the dependent variable, x1,x2,···,x k When is the independent variable and there is a linear relationship between the independent variable and the dependent variable, the multiple linear regression model is:

[0033] y=b0+b1x1+b2x2+.....+b k x k +e

[0034] In the above formula, b0 is a constant term, b1, b2, .... b k is the regression coefficient, b1 is x2, x3, ···, x k When x1 is fixed, the effect of each unit increase in x1 on y is the partial regression coefficient of x1 on y; similarly, b2 is x1, x k When x2 is fixed, the effect of each unit increase in x2 on y is the partial regression coefficient of x2 on y, and so on.

[0035] The technical solution of the present invention is described in detail below.

[0036] 1. Analysis of factors affecting line loss. The size of line loss is mainly affected by technical line loss and management line loss. With the continuous advancement of the construction of new power systems, more and more multi-loads are connected, and the impact on distribution network losses is becoming more and more obvious. Therefore, the factors affecting distribution line loss are extracted from multiple dimensions, including management, measurement, technology, new energy access, and environment.

[0037] 2. Data classification. From the analysis of factors affecting line loss, it can be seen that the line loss rate is affected by five factors: management, measurement, technology, new energy access, and environment. Simply using all data to build a reasonable range calculation model for line loss often leads to problems such as low model accuracy and poor applicability. Therefore, we choose to use management factors to perform K-means cluster analysis on the data, divide the data into K categories, and then build models separately, thereby improving the accuracy and applicability of the model.

[0038] (1) Determine the number of clusters k. K-means cluster analysis belongs to unsupervised learning, and there is no predefined number of clusters. Therefore, the elbow criterion is used to determine the number of clusters k, and the clustering effects under different k values ​​are evaluated to find the appropriate number of clusters and improve the clustering effect.

[0039] The core indicator of the elbow method is SSE, sum of the squared errors, sum of squared errors

[0040]

[0041] In the formula, C i is the i-th cluster, p is C i The sample points in m i It is C i The center of mass, C i SSE is the mean of all samples in the clustering error, which represents the quality of clustering effect.

[0042] As the number of clusters k increases, the sample division will be more refined, and the degree of aggregation of each cluster will gradually increase, so the error square sum SSE will naturally gradually decrease. Moreover, when k is less than the actual number of clusters, since the increase in k will greatly increase the degree of aggregation of each cluster, the decrease in SSE will be large. When k reaches the actual number of clusters, the degree of aggregation obtained by increasing k will rapidly decrease, so the decrease in SSE will decrease sharply, and then tend to be flat as the k value continues to increase. In other words, the relationship between SSE and k is in the shape of an elbow, and the k value corresponding to this elbow is the actual number of clusters of the data.

[0043] (2) Classification using K-means cluster analysis method: Based on the analysis results of line loss influencing factors, several management factors with greater impact on line loss are selected as variables, and K-means cluster analysis is carried out to divide the data into k categories.

[0044] According to the k value determined by the elbow method, k cluster centers are randomly initialized.

[0045] Assign each data point to the nearest cluster center.

[0046] After the data is grouped, there are a total of k sets, and the cluster center of each set is recalculated.

[0047] If the distance between the newly calculated cluster center and the original cluster center is less than a certain set threshold, it is considered that the clustering has achieved the desired result and the algorithm terminates.

[0048] If the distance between the new cluster center and the original cluster center changes greatly, repeat the first three steps.

[0049] 3. Construction of multiple linear regression model.

[0050] (1) Significance test of regression equation - F test

[0051] The main test variables are x1, x2, ···, x k Whether there is a significant linear relationship between the dependent variable and y, that is, the significance test of the equation.

[0052] The F-test statistic is:

[0053]

[0054] Where n is the number of samples. Given a significance level, when the test value F is greater than the critical value F α2 (k,n-1-k), prove that x1,x2,···,x k The linear relationship between y and F is significant. The regression equation is significant, F<F α , then the regression equation has no significant meaning and the regression effect is not significant. Therefore, the significance test is performed on the k types of data respectively.

[0055] (2) Indicator screening: Based on the significance test results, factors that do not meet the significance requirements are eliminated by category, and factors that meet the requirements are retained.

[0056] (3) Constructing a multivariate linear regression model

[0057] Based on the indicator screening results, taking the daily line loss rate as the dependent variable and the indicators screened in each category as the independent variables, multiple linear regression models were constructed to obtain the multiple linear regression equations.

[0058] (4) Goodness of fit test

[0059] Like the univariate linear regression model, the multivariate regression model also requires necessary testing and evaluation after obtaining the least squares estimate of the parameters to determine whether the model can be applied.

[0060] The coefficient of determination can be defined, where R 2 The closer it is to 1, the better the regression fitting effect is. 2 If it is not close to 1 but close to 0, it means that the fitting effect of a certain type of model is not good. At this time, it is necessary to increase the number of samples, eliminate unreasonable data or adjust the regression factor, rebuild the multivariate linear regression model and refit it. The formula is:

[0061]

[0062] SSR is the regression sum of squares, SST is the total deviation sum of squares, and SSE is the residual sum of squares. The calculation formula is:

[0063]

[0064]

[0065] In the formula, y i is the actual value of the dependent variable, is the fitted value of the dependent variable, is the mean value of the dependent variable.

[0066] Coefficient of determination R 2 The value of R is between 0 and 1. 2 The closer it is to 1, the better the regression fitting effect is. The goodness of fit test is performed on each type of model.

[0067] 4. Verification of multiple linear regression model.

[0068] The residual PP diagram is used to verify the multivariate linear regression model and determine the applicability of the model. The PP diagram is a scatter plot drawn based on the cumulative probability of the variable corresponding to the specified theoretical distribution cumulative probability. It is used to visually detect whether the sample data conforms to a certain probability distribution. If the sample data obeys the assumed normal distribution, the scatter points fall preferably near the 45° line starting from the origin.

[0069] 5. Calculate the reasonable range of line loss.

[0070] Based on the line loss rate prediction results, the reasonable line loss interval is calculated using the credible interval of the overall regression plane, also known as the confidence band of the regression line. The confidence interval is a commonly used interval estimation method. The so-called confidence interval is an interval composed of the upper and lower confidence limits of the statistic as the upper and lower limits, and the 95% confidence interval is used as the reasonable line loss interval.

[0071] (1) Lower limit of the interval:

[0072] (2) Upper limit of the interval:

[0073] In the formula, is the average value of the predicted line loss rate; α is "1-confidence level", and the 95% confidence interval is α=0.05; σ is the "standard deviation of the population"; We can check the normal distribution table and find that the 95% confidence interval is 1.96.

[0074] Using the calculated reasonable range of line loss rate, the line loss rate of the distribution network can be evaluated. Data falling outside the reasonable range of line loss rate can be preliminarily diagnosed as abnormal line loss rate, which can provide support for subsequent line loss management work.

[0075] A specific embodiment is given below:

[0076] 1. Analysis of factors affecting line loss

[0077] Collect distribution network data, and based on the causes of distribution network line losses, extract line loss influencing factors from five dimensions, as shown in the following table:

[0078] Table 1 Line loss influence factors

[0079] Serial number manage Measurement technology New Energy environment 1 Power supply radius Area power Average wiring load factor Distributed online active power Date Type 2 Overall length Special transformer power Voltage pass rate Distributed online reactive power month 3 Public variables Collection success rate The proportion of public transformers with low power factor Proportion of distributed online electricity Maximum temperature 4 Special variables Daily load factor fluctuation coefficient Proportion of three-phase unbalanced transformer Number of distributed power sources Minimum temperature 5 Cable rate Ratio of empty and light load distribution transformer Cloud Opacity 6 Energy-saving distribution transformer ratio Proportion of heavily overloaded distribution transformers Weather Type 7 Main line cross-sectional area

[0080] 2. Data Classification

[0081] According to the collected distribution network data, six management factors, including line power supply radius, public transformers, special transformers, cable rate, proportion of energy-saving distribution transformers, and total length, were selected for K-means cluster analysis. The number of data categories was determined to be 3 using the elbow method, and the distance center was obtained.

[0082] Table 2 K-means cluster analysis results

[0083] Serial number Indicator name 1 2 3 1. Feeder power supply radius 3.400 10.8682 15.4593 2. Overall length 6 20 25 3. Public variables 4 29 26 4. Special variables 12 11 7 5. Cable rate 86 36 4 6. Energy-saving distribution transformer ratio 4.2 27.15 57.63

[0084] (1) Characteristics of the first category: The total length of wiring and the power supply radius are short, the cabling rate is high, the number of public transformers is small, and the proportion of energy-saving distribution transformers is low.

[0085] (2) Characteristics of the second category: The total length of wiring and the power supply radius are long, the cabling rate is low, the number of public transformers is large, and the proportion of energy-saving distribution transformers is high.

[0086] (3) Characteristics of the third category: The total length of wiring and the power supply radius are long, the cabling rate is high, the number of public transformers is large, and the proportion of energy-saving distribution transformers is low.

[0087] 3. Multiple Linear Regression Model Construction

[0088] (1) Significance check

[0089] Taking the second type of wiring data as an example, there are a total of 2883 data, 1922 of which are randomly selected for model construction, and the remaining 961 data are used for model verification. The significance test results are as follows:

[0090] Table 3 Significance test results

[0091] Serial number Indicator name The second type of significance Serial number Indicator name The second type of significance 1 Power supply radius 0 15 Voltage pass rate 0 2 Overall length 0 16 The proportion of public transformers with low power factor 0.009 3 Public variables 0 17 Proportion of three-phase unbalanced transformer 0 4 Special variables 0.001 18 Ratio of empty and light load distribution transformer 0.947 5 Cable rate 0 19 Proportion of heavily overloaded distribution transformers 0.103 6 Cross-sectional area 0 20 Average wiring load factor 0 7 Energy-saving distribution transformer ratio 0.732 21 Daily load factor fluctuation coefficient 0 8 Collection success rate 0 22 Date Type 0.775 9 Area power 0 23 month 0 10 Special transformer power 0 24 Maximum temperature 0.004 11 Distributed online active power 0.007 25 Minimum temperature 0.003 12 Distributed online reactive power 0.341 26 Cloud Opacity 0.17 13 Proportion of distributed online electricity 0.608 27 Weather Type 0.145 14 Number of distributed power sources 0.067

[0092] (2) Indicator screening. According to the significance test results, the indicators with significance greater than 0.05 were eliminated, including the proportion of energy-saving distribution transformers, distributed online reactive power, proportion of distributed online power, number of distributed power sources, proportion of light-load distribution transformers, proportion of heavy-overload distribution transformers, date type, cloud opacity, and weather type. The remaining 18 indicators were used to build the model.

[0093] (3) Goodness of fit test. Calculate the goodness of fit of the second type of model, the coefficient of determination R 2 =0.86, indicating that the regression fitting effect is good.

[0094] (4) Classification model construction: Taking the second type of wiring data as an example, the daily line loss rate of wiring is taken as the dependent variable, and the remaining 18 indicators are taken as independent variables to construct a multivariate linear regression model. The results are as follows:

[0095] y=-0.6834x1-0.1009x2+0.0743x3+0.2872x4-0.0331x5+0.0089x6-0.2241x7-0.0001x8

[0096] -0.00004363x9-0.0001x 10 +0.7307x 11 -0.003x 12 -0.0046x 13 +0.059x 14 -3.0185x 15 -0.0196x 16 +0.014x 17 -0.0183x 18 +20.1405

[0097] Table 4 Factor correspondence table

[0098]

[0099] 4. Multiple Linear Regression Model Verification

[0100] The line loss rate is predicted based on the multivariate linear regression model, and the line loss rate residual PP graph is drawn to verify the regression model. Figure 1 .

[0101] Depend on Figure 1 It can be seen that the data scatter points of the line loss rate residuals basically fall near the 45° line starting from the origin and obey the normal distribution, which shows that the constructed multivariate linear regression model is reasonable and applicable.

[0102] 5. Calculation of reasonable line loss range

[0103] Based on the constructed multivariate linear regression model, 961 validation data were used to calculate the reasonable range of line loss. Figure 2 Display. Figure 2The calculation results of the reasonable range of line loss show that among the 961 model verification data, 806 data fell within the reasonable range and were considered to be lines with line loss rates that met the standards. The line loss rates of 155 lines fell outside the reasonable range and were considered to be lines with line loss rates that did not meet the standards. The reasons for the abnormal line loss rates can be further analyzed to provide support for line loss management.

Claims

1. A method for calculating the reasonable interval of line loss in a distribution network considering the access of distributed power sources, characterized in that: The calculation method steps are as follows: a. Extract the line loss influencing factors of wiring from five dimensions: management, measurement, technology, new energy access, and environment; b. Determine the value of the cluster number k by the elbow method, and divide the data of the above five dimensions into k categories with the help of K-means clustering analysis algorithm; c. Perform a significance test on the k-type data, and the F test statistic is: In Formula 1, n is the number of samples, SSE is the clustering error of all samples, SSR is the regression sum of squares, and F α2 (k,n-1-k) is the critical value, when the test value F<F α When the data is in this category, it is removed; d. Construct multiple linear regression models for k types of data respectively to predict the line loss rate; e. Based on the line loss rate prediction results, the 95% confidence interval is used as the reasonable line loss interval, and the lower and upper limits of the line loss rate are calculated respectively by using the confidence interval method. Lower limit of interval: Upper limit of interval: In Formula 2 and Formula 3, is the average value of the predicted line loss rate, α is 1-confidence level, α=0.05 for a 95% confidence interval, and σ is the standard deviation of the population. The 95% confidence interval can be obtained by looking up the standard normal distribution table. The value is 1.

96.

2. According to claim 1, a method for calculating a reasonable range of line loss in a distribution network considering the access of distributed power sources is characterized by: Add step d1 after step d to check the goodness of fit of k types of models and define the coefficient of determination R 2 : In formula 4, SSR is the regression sum of squares, SST is the total deviation sum of squares, and SSE is the residual sum of squares. The calculation formula is: In formula 5-7, y i is the actual value of the dependent variable, is the fitted value of the dependent variable, is the mean value of the dependent variable, Coefficient of determination R 2 The value of R is between 0 and 1. 2 The closer it is to 1, the better the regression fitting effect is.

3. According to claim 1, a method for calculating a reasonable range of line loss in a distribution network considering the access of distributed power sources is characterized in that: In the step b, the value of the cluster number k is determined by the elbow method. The core indicator of the elbow method is the SSE error square sum, and the formula is: In formula 8, C i is the i-th cluster, p is C i The sample points in m i It is C i The center of mass, C i The mean of all samples in , SSE is the clustering error of all samples, which represents the quality of clustering effect. The relationship graph between SSE and k is in the shape of an elbow, and the elbow of this elbow corresponds to the k value.

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