CN114565259A

CN114565259A - Power distribution network line loss calculation method for optimizing BP neural network by improving sparrow search

Info

Publication number: CN114565259A
Application number: CN202210171261.4A
Authority: CN
Inventors: 丁李; 谢沅霏; 孔政敏; 刘智伟; 陈超洋
Original assignee: Wuhan University WHU
Current assignee: Wuhan University WHU
Priority date: 2022-02-24
Filing date: 2022-02-24
Publication date: 2022-05-31

Abstract

The invention discloses a power distribution network line loss calculation method for improving sparrow search and optimizing a BP (back propagation) neural network, which comprises the steps of continuously collecting data of a plurality of required historical moments through a power grid advanced measurement system, and preprocessing the data; secondly, inputting the preprocessed data of each historical moment into a BP (back propagation) neural network for prediction to obtain the predicted line loss rate of each historical moment, constructing a BP neural network loss function model by combining the predicted line loss rate with the data, and further performing optimization solution by a sparrow search algorithm which is improved by chaotic initialization and t-distribution variation fusion to obtain an optimized BP neural network; finally, the data collected in real time are input into the optimized BP neural network for prediction to obtain the real-time predicted line loss rate.

Description

Power distribution network line loss calculation method for optimizing BP neural network by improving sparrow search

Technical Field

The invention belongs to the technical field of power distribution network optimization, and particularly relates to a power distribution network line loss calculation method for improving a sparrow search optimization BP neural network.

Background

In the transmission process of a power grid, electric energy passes through each power element and generates a part of active loss due to factors such as impedance, the part of active loss is line loss, the ratio of the line loss to the power supply amount is line loss rate, the line loss is one of important indexes of the power grid, accurate calculation of theoretical line loss can provide data support for fine management and formulation of energy-saving and loss-reducing measures of power grid enterprises, the aim of double carbon is achieved by assistance, and the call for green development of energy conservation and emission reduction in China is responded. With the development of power systems, the structure of a power distribution network is gradually complicated, the data volume of the power grid is larger and larger, and the method for calculating the line loss more accurately has important significance.

The research on the line loss calculation of the power grid can be traced back to the thirties of the twentieth century, researchers in various countries put forward various methods for calculating the line loss of the power distribution network, the line loss calculation methods for the power distribution network can be divided into two major categories till now, one is that the traditional theoretical calculation methods and related improved algorithms which are widely applied are put forward according to physical models, the traditional theoretical calculation methods comprise a root-mean-square current method, an equivalent resistance method, an average current method, a power flow method and the like, the methods are based on the physical model of the power grid, and required data comprise current, voltage, line resistance, distribution network topology and the like; and a calculation method provided by using the learning capability of machine learning on large-scale data, such as a calculation method based on a support vector machine, a neural network, a heuristic algorithm and the like, and a line loss calculation model is trained by learning a large amount of data.

The line loss calculation result is that the power grid is firstly seen from a traditional line loss calculation method based on a physical model, the formula of a loss formula calculation method such as an equivalent resistance method is simple, and the method is a line loss calculation method which is used by a power supply enterprise for many years, but a plurality of simplification and estimation parts exist, so that the problem that the line loss calculation precision is not high and a certain gap exists between the line loss calculation precision and the actual line loss calculation precision is caused, and the management level and the loss reduction efficiency of the power supply enterprise are influenced; in the traditional algorithm, the load flow calculation method is relatively high in accuracy, but has the problem of high requirements on the quality of original data, besides load electric quantity, the load flow calculation also needs to know the topological structure of a network and the resistance of a line, but the low-voltage distribution network is often difficult to acquire the information due to the complex structure, so that the method is limited in applicable voltage level. In the existing machine learning method for calculating the line loss of the power distribution network, a standard BP neural network model is a relatively mature main calculation method, but the problem that hidden layer weights and thresholds lack effective adjustment exists, so that the calculation accuracy of the line loss of the power distribution network has a further improved space.

The line loss of the power distribution network is used as an important economic and technical index of the power grid, and the theoretical calculation precision of the power distribution network has great influence on the planning rationality, the operation economy, the management level and the establishment of loss reduction measures of the power grid. The calculation method based on the machine learning algorithm is a popular method for the current power grid line loss calculation research, wherein a neural network is used as a model of the machine learning algorithm, can carry out sufficient adaptive learning on related information and store knowledge, has strong fault tolerance performance, has the capability of carrying out very complex logic operation and fitting nonlinear relation, is the most main calculation method in the current line loss research, but has some defects. The invention aims to solve the problem that a standard BP neural network calculation method is easy to fall into local optimization and further improve the calculation precision of the line loss of a power distribution network, and selects a Sparrow Search Algorithm to optimize the Algorithm of the BP neural network to establish a power distribution network line loss calculation model according to the excellent group optimization effect of a Sparrow Search Algorithm (SSA), but the Sparrow Search Algorithm still has the problems of possible falling into local optimization and weak global Search capability.

Disclosure of Invention

In order to solve the problem that a standard BP neural network calculation method is easy to fall into local optimum and further improve the accuracy of power distribution network line loss calculation, the invention provides a power distribution network line loss calculation method based on improved sparrow search optimization BP neural network.

The technical scheme of the invention is a power distribution network line loss calculation method for optimizing a BP neural network by improving sparrow search, which is characterized by comprising the following steps of:

step 1: continuously acquiring the summary active reactive electric quantity at a plurality of historical moments, the load point active reactive electric quantity at a plurality of historical moments and the line loss rate at a plurality of historical moments through a power grid advanced measurement system;

step 2: respectively and sequentially carrying out abnormal data removing processing, missing data filling processing, repeated data filtering processing and data standardization processing on the summary table active reactive electric quantities at a plurality of historical moments, the load point active reactive electric quantities at a plurality of historical moments and the line loss rates at a plurality of historical moments to obtain the preprocessed summary table active reactive electric quantities at a plurality of historical moments, the preprocessed load point active reactive electric quantities at a plurality of historical moments and the preprocessed line loss rates at a plurality of historical moments;

and step 3: introducing a BP (back propagation) neural network, inputting the total table active reactive electric quantity of each preprocessed historical moment and the load point active reactive electric quantity of each preprocessed historical moment into the BP neural network for prediction to obtain the predicted line loss rate of each historical moment, constructing a BP neural network loss function model by combining the line loss rate of each preprocessed historical moment, and further performing optimization solution by a modified sparrow search algorithm through chaotic initialization and t-distribution variation fusion to obtain the optimized BP neural network;

and 4, step 4: inputting the real-time collected summary table active reactive electric quantity and the real-time collected load point active reactive electric quantity into the optimized BP neural network for prediction to obtain a real-time predicted line loss rate;

preferably, the loss function model in step 3 is specifically defined as:

in the formula, Y_iIs the sample line loss rate of the i-th sample, y_iThe line loss rate is calculated for the ith sample, n is the total number of samples, and the loss function is the calculated mean square error.

And 3, further performing optimization solution through a sparrow search algorithm improved by chaotic initialization and t distribution variation fusion to obtain an optimized BP neural network, wherein the optimized object of the improved sparrow optimization algorithm is the weight and the threshold of the BP neural network, and the specific steps are as follows:

and 3.1, setting the size of the sparrow population, the maximum iteration times, the upper weight boundary, the lower weight boundary, the upper threshold boundary, the lower threshold boundary, the safety value, the proportion of discoverers and the proportion of cautionary users.

The dimension D of the improved sparrow optimization algorithm is as follows:

D＝m×n+n×l+n+l

in the formula, m is the number of neurons in an input layer of the BP neural network, n is the number of neurons in an implicit layer of the BP neural network, and l is the number of neurons in an output layer of the BP neural network.

The sparrow population may be represented as:

wherein X_iFor sparrow population at the ith iteration，x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold, and when D belongs to [1, mxn ∈]When x is_i,p,dIs the connection weight between the input layer and the hidden layer in the neural network, when d belongs to [ m x n +1, m x n + n]When x_i,p,dFor the hidden layer threshold in the neural network, when d is in the range of [ m × n + n +1, m × n + n + n × l]When x_i,p,dIs the connection weight between the hidden layer and the output layer in the neural network, when d belongs to [ m × n + n + n × l +1, m × n + n + n × l + l]When x_i,p,dThe method comprises the following steps of (1) setting an output layer threshold value in a neural network, wherein m is the number of neurons in an input layer of a BP neural network, n is the number of neurons in a hidden layer of the BP neural network, and l is the number of neurons in an output layer of the BP neural network;

initializing the sparrow population by adopting Bernoulli chaotic mapping, wherein the formula is as follows:

wherein x is_i,p,dPosition, x, of dimension d of the p-th sparrow position at the i-th iteration_i+1,p,dThe position of the d-th dimension of the position of the p-th sparrow in the (i + 1) -th iteration is defined as lambda epsilon (0,1) as a segmentation parameter. The dimension of the chaotic matrix is the same as that of a sparrow population matrix, and the chaotic matrix is generated and then is carried to the upper and lower boundaries of a weight threshold value, so that the chaotic initialized sparrow population is obtained.

And 3.2, defining a fitness function and calculating an initial individual fitness value. The fitness function is used for explaining the calculation accuracy of the model, the individual fitness value is obtained by taking the position corresponding to the individual as a weight and a threshold value and then carrying the weight and the threshold value into the neural network for calculation, and the specific fitness function is as follows:

in the formula, Y_iThe sample line loss rate of the ith sample,y_ithe line loss rate is calculated for the ith sample, n is the total number of samples, and the loss function is the calculated mean square error.

F_iThe fitness values of all sparrow populations at the ith iteration and the optimal fitness value f of the sparrow individual_bThe corresponding sparrow positions are optimization targets, namely weights and thresholds of the neural network, and then the individual fitness values of all sparrows can be expressed as:

in the formula (f)_i,p([x_i,p,1,...,x_i,p,d,...,x_i,p,d]) Representing the individual fitness value, x, of the p-th sparrow at the ith iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]And D is the dimension to be optimized, namely the total number of the network weight and the threshold.

And 3.3, dividing the sparrows in the sparrow searching algorithm into a finder, a jointer and an alerter, wherein the finder and the jointer dynamically change but have constant proportion, and different types of sparrows have different updated position rules.

The sparrows are rich in resources in the population, namely the fitness value is high, and the sparrows are responsible for searching food and leading the participants, when danger occurs, the alarm of the sparrows is higher than the early warning value, and the discoverer leads the participants to turn to a safe area. The position is updated as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimizedThat is, the total number of network weights and thresholds, c is a random constant, and c belongs to (0,1)]，t_mFor maximum number of iterations, r is a random number obeying a normal distribution, I_1×dAll 1 matrices of 1xd, ST being the security value, R₂For a warning value, R₂∈[0,1]；

Changing an exponential decrement factor into a normally distributed random number, introducing a global optimal fitness value of the last iteration into an updating formula of a finder, simultaneously having better global search capability in the early stage of the iteration and better local search capability in the later stage according to the characteristic that a nonlinear decrement inertia weight is better, and adopting the following weight omega according to an algorithm:

where i is the current iteration number, t_mIs the maximum number of iterations.

The improved discoverer location update formula is as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, i.e. the total number of the network weight and the threshold, omega is the inertia weight,

for global optimal fitness of the last iteration, rand (0,1) is normally distributed randomly, r is a random number obeying normally distribution, and I_1×dAll 1 matrices of 1xd, ST being the security value, R₂For a warning value, R₂∈[0,1]。

The participants will compete for food following the discoverer with the best resources, the less well suited sparrow location will be, and the less energy participants may go to other areas looking for food. The position is updated as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P belongs to [1, P ]]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold,

the d-th dimension global worst position of the p-th sparrow position at the ith iteration,

is the global optimum position of the d-th dimension of the p-th sparrow position in the (i + 1) th iteration, c is a random constant, and c belongs to (0,1)]，A⁺1xd matrix of elements 1 and-1, A⁺＝A^T(A A^T)^-1，I_1×dIs a full 1 matrix of 1 xds.

Individuals on the position comparison edge in the alarm can be transferred to a safety zone, and individuals in the safety zone randomly change positions in the safety zone. The position is updated as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold,

for the global optimal position of the d-th dimension of the p-th sparrow position at the ith iteration,

is the d-dimensional global worst position of the p-th sparrow position at the ith iteration, s is a random number obeying (0,1) normal distribution and used for controlling the step length, h is a constant between-1 and represents the individual moving direction, f_iIs the current individual fitness value, f_i ^bCurrent global optimum fitness value, f_i ^wIs the current global worst fitness value. ε prevents the denominator from being 0.

Step 3.4, generating a random number, and judging whether t-distribution sparrow population variation is carried out or not;

the t distribution is an intermediate transition form of Gaussian distribution and Cauchy distribution, and can be converted into other distribution matrixes by adjusting the degree of freedom n. The mutation process is as follows:

in the formula (I), the compound is shown in the specification,

the position of the d-dimension of the p-th sparrow position after the variation of the t distribution at the ith iteration, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, i.e. the total number of network weights and thresholds, t (i) is the t distribution with the degree of freedom i, rand is the random number generated by the iteration, pr is the dynamic selection probability, omega₁For dynamic selection of the probability upper bound, ω₂Selecting probability changes for dynamicsAmplitude.

When the sparrow search algorithm starts iteration, the iteration times are small, the t distribution is close to Cauchy distribution, and the algorithm has strong global search capability; when the iteration times are continuously increased, the t distribution is close to Gaussian distribution, and the algorithm has strong local search capability. Therefore, the sparrow search algorithm carries out population variation by using t distribution, the global search capability is enhanced at the initial stage, the local search capability is enhanced at the later stage, and the convergence accuracy of the algorithm is improved.

And 3.5, calculating individual fitness values of the two populations before and after the variation, acquiring the current optimal value of the two populations, comparing the current optimal value with the last time, and updating the global optimal value if the global optimal value is better.

Step 3.6, repeating the steps 3.3-3.5 until the maximum iteration number is reached, and stopping; the final global optimal position, i.e. the optimal individual fitness value f_b([x_i,p,1,...,x_i,p,d,...,x_i,p,D]Corresponding position [ x ]_i,p,1,x_i,_p,2,...,x_i,p,D]Building a complete network model as weight and threshold inputs to a neural network, x_i,p,dThe position of the d-dimension of the position of the p-th sparrow in the ith iteration is shown, and p is the sparrow corresponding to the optimal fitness.

The method effectively solves the problem of BP neural network adjustment, improves the network convergence speed, further improves the calculation precision of the line loss of the power distribution network, and provides data support for realizing fine management of the power grid and promoting energy-saving and loss-reducing work.

Drawings

FIG. 1: is a flow chart of the method of the present invention;

FIG. 2: improving a BP neural network training flow chart of sparrow search optimization;

FIG. 3: cross validation results of ten folds;

FIG. 4: comparing the SSA-BP neural network line loss calculation result with the sample value;

FIG. 5: comparing the BtSSA-BP line loss calculation result with the sample value;

FIG. 6: calculating an error curve of the SSA-BP neural network line loss;

FIG. 7 is a schematic view of: calculating an error curve of line loss of the BtSSA-BP neural network;

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In order to test the effect of the line loss calculation method designed by the invention, the original data collected by the example is the electricity consumption data of 396 days from 9 months in 2019 to 9 months in 2020 in a certain platform area of the Zhuhai city, the line loss calculation model designed by the invention is trained by the platform area data, and the calculation result is compared with the sample result to evaluate the effect. The total table and the sub-table of the transformer area have 5 metering points, the input characteristic variables are active and reactive electric quantities of the metering points, and the output characteristic variables are daily line loss rate, wherein the input characteristic variables are active and reactive electric quantities of the metering points, and the output characteristic variables are 1.

The data collected are shown in table 1.

Table 1 electric network acquisition of partial raw data

A power distribution network line loss calculation method based on an improved sparrow search optimization BP neural network is characterized by comprising the following steps:

step 2: respectively and sequentially carrying out abnormal data removing processing, missing data filling processing, repeated data filtering processing and data standardization processing on the total table active and reactive electric quantity at a plurality of historical moments, the load point active and reactive electric quantity at a plurality of historical moments and the line loss rate at a plurality of historical moments to obtain the total table active and reactive electric quantity at a plurality of preprocessed historical moments, the load point active and reactive electric quantity at a plurality of preprocessed historical moments and the line loss rate at a plurality of preprocessed historical moments to obtain a sample data set of 10 multiplied by 396;

the loss function model in step 3 is specifically defined as:

step 3.1, according to the sample data, the number m of the neurons in the input layer is 10, the number l of the neurons in the output layer is 1, and the hidden layer firstly calculates n is log according to an empirical formula ₂10 is approximately equal to 3, then a ten-fold cross-validation method is adopted to determine the number of hidden layer nodes with the best effect near the value, namely, the sample data set is averagely divided into 10 parts, training and testing are carried out for 10 times, 9 parts of samples in the sample data set are used as a training set and 1 part of samples are used as a testing set each time, and the sample data set must be guaranteed to be the training set and the testing setThe training set and the testing set of each time are different from each other, the whole sample data set participates in training and testing, and the hidden layer number with the minimum corresponding calculation error is taken. The ten-fold cross-validation result for the sample set is shown in fig. 3, and the number of hidden layer nodes can be determined to be 3. The structure of the BP neural network is 10-3-1, the learning rate α of the BP neural network is set to be 0.01, the calculation precision e is 0.01, the maximum iteration number is 10000, the hidden layer activation function is a Sigmoid function, the output layer activation function is a purelin function, and the back propagation training function is a thingdx function.

The sparrow population scale is set to be 20, the maximum iteration number is 30, the upper weight boundary is 5, the lower weight boundary is-5, the upper threshold boundary is 5, the lower threshold boundary is-5, the safety value is 0.6, the ratio of discoverers to surrmers is 0.7, and the ratio of surrmers to surrmers is 0.2.

The dimension D of the improved sparrow optimization algorithm is as follows:

D＝m×n+n×l+n+l

in the formula, m ═ 10 is the number of input layer neurons of the BP neural network, n ═ 3 is the number of hidden layer neurons of the BP neural network, and l ═ 1 is the number of output layer neurons of the BP neural network.

Sparrow populations may be represented as:

wherein, X_iFor sparrow population at the ith iteration, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈ [ ]]P20 is the number of sparrows in the population, D is equal to [1, D ]]D is 37, namely the dimension to be optimized, namely the total number of the network weight values and the threshold values, and when D belongs to [1, m is multiplied by n]When x_i,p,dIs the connection weight between the input layer and the hidden layer in the neural network, when d belongs to [ m x n +1, m x n + n]When x_i,p,dFor the hidden layer threshold in the neural network, when d is in the range of [ m × n + n +1, m × n + n + n × l]When x_i,p,dIs the connection weight between the hidden layer and the output layer in the neural network, when d belongs to [ m × n + n + n × l +1, m × n + n + n × l + l]When x_i,p,dThe method is characterized in that the threshold value of an output layer in a neural network is defined, m is 10 and n is 3, and l is 1, wherein the number of neurons of the input layer of the BP neural network is defined as the number of neurons of an implicit layer of the BP neural network;

wherein x is_i,p,dPosition, x, of dimension d of the p-th sparrow position at the i-th iteration_i+1,p,dThe position of the d-th dimension of the p-th sparrow position in the (i + 1) -th iteration is represented by λ e (0,1) which is a segmentation parameter, and λ is 0.4. The dimension of the chaotic matrix is the same as that of a sparrow population matrix, and the chaotic matrix is generated and then is carried to the upper and lower boundaries of a weight threshold value, so that the chaotically initialized sparrow population is obtained.

in the formula, Y_iIs the sample line loss rate of the i-th sample, y_iFor the calculated line loss rate of the ith sample, n-396 is the total number of samples, and the loss function is the calculated mean square error.

F_iThe fitness values of all sparrow populations at the ith iteration and the optimal fitness value f of the sparrow individual_bThe corresponding sparrow positions are the optimization targets, namely the weights and the threshold values of the neural network, and the individual fitness values of all sparrows can be expressed as follows:

in the formula (f)_i,p([x_i,p,1,...,x_i,p,d,...,x_i,p,d]) Representing the individual fitness value, x, of the p-th sparrow at the ith iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈ [ ]]P20 is the number of sparrows in the population, D is the E [1, D ∈]And D is 37, namely the dimension to be optimized, namely the total number of the network weight and the threshold.

And 3.3, dividing the sparrows in the sparrow searching algorithm into a finder, a jointer and an alerter, wherein the finder and the jointer dynamically change but do not change the proportion, and different types of sparrows have different updating position rules.

The sparrow is rich in resources in the population, namely the fitness value is high, and the sparrow is responsible for searching food and leading the participators, when danger occurs, the alarm of the sparrow individual is higher than the early warning value, and the discoverer leads the participators to go to a safe area. The position is updated as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈]P20 is the number of sparrows in the population, D is the E [1, D ∈]D is 37, namely the dimension to be optimized, namely the total number of the network weight values and the threshold values, c is a random constant, and c belongs to (0,1)]R is a random number following a normal distribution, I_1×D1 matrix of 1x37, ST ═ 0.6 is the guard value, R₂Is a random constant, R, for the early warning value₂∈[0,1]；

where i is the current iteration number, t_m30 is the maximum number of iterations.

The improved discoverer location update formula is as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈]P20 is the number of sparrows in the population, D is the E [1, D ∈]D-37 is the dimension to be optimized, i.e. the total number of network weights and thresholds, ω is the inertial weight,

for the global optimal fitness of the last iteration, rand (0,1) is normally distributed randomly, r is a random number obeying the normally distribution, I_1×D1 matrix of 1x37, ST ═ 0.6 is the guard value, R₂As a precaution value, is a random constant, R₂∈[0,1]。。

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dFor the position of the d-th dimension of the position of the p-th sparrow at the ith iteration, i belongs to [1, t ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈]P20 is the number of sparrows in the population, D is the E [1, D ∈]D is 37, which is the dimension to be optimized, i.e. the total number of network weights and thresholds,

is the global optimum position of the d-th dimension of the p-th sparrow position in the (i + 1) th iteration, c is a random constant, and c belongs to (0,1)]，A⁺1x37 matrix of elements 1 and-1, A⁺＝A^T(A A^T)^-1，I_1×DAn all 1 matrix of 1x 37.

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈]P20 is the number of sparrows in the population, D is the E [1, D ∈]D is 37, which is the dimension to be optimized, i.e. the total number of network weights and thresholds,

the global optimal position of the d-th dimension of the p-th sparrow position at the ith iteration,

is the d-dimensional global worst position of the p-th sparrow position at the ith iteration, s is a random number obeying (0,1) normal distribution and used for controlling the step length, and h is a constant between-1 and 1Denotes the direction of movement of the individual, f_iIs the current individual fitness value, f_i ^bCurrent global optimum fitness value, f_i ^wIs the current global worst fitness value. 10 ∈ ═ 10^-8The prevented denominator is 0.

in the formula (I), the compound is shown in the specification,

the position of the d-dimension of the p-th sparrow position after the variation of the t distribution at the ith iteration, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_m30 is the maximum number of iterations of the population, P ∈ [1, P ∈]P20 is the number of sparrows in the population, D is the E [1, D ∈]D37 is the dimension to be optimized, i.e. the total number of network weights and thresholds, t (i) is the t distribution with degree of freedom i, rand is the random number generated by the iteration, pr is the dynamic selection probability, ω is₁0.5 is the upper limit of the dynamic selection probability, ω₂The dynamic selection probability variation amplitude is 0.1.

Step 3.6, repeating the steps 3.3-3.5 until the maximum iteration number is reached, and stopping; the final global optimal position, i.e. the optimal individual fitness value f_b([x_i,p,1,...,x_i,p,d,...,x_i,p,D]Corresponding position [ x ]_i,p,1,x_i,p,2,...,x_i,p,D]Building a complete network model as weight and threshold inputs for neural networks, x_i,p,dThe position of the d-dimension of the position of the p-th sparrow in the ith iteration is shown, and p is the sparrow corresponding to the optimal fitness.

in order to illustrate the effect of the line loss calculation method designed by the invention, the calculation result of the BtSSA-BP method is compared with the calculation result of the SSA-BP method, the comparison of the line loss rate of the test sample and the theoretical line loss rate calculated by the two methods is respectively shown in fig. 4 and 5, and the calculation error curves of the two methods are respectively shown in fig. 6 and 7. As can be seen from the figure, the calculation result of the line loss calculation method based on BtSSA-BP provided by the invention is superior to the results of a standard BP neural network and SSA-BP, and the MSE and R of the SSA-BP calculation method²0.15576 and 0.80484, respectively, and the MSE and R of the BtSSA-BP line loss calculation method of the invention²0.12067 and 0.84881 respectively, the two indexes show that the error is reduced, the fitting degree is increased, and the method can effectively improve the calculation accuracy of the line loss of the power distribution network.

The method for calculating the line loss of the power distribution network based on the improved sparrow search optimization BP neural network is described in detail above. The principles and embodiments of the present invention have been described herein using several examples, which are presented only to assist in understanding the method and its core concepts of the present invention; meanwhile, for those skilled in the art, based on the idea of the present invention, there may be variations in the specific embodiments and applications, and in summary, the present disclosure should not be construed as a limitation of the present invention, and those skilled in the art should include modifications, equivalent substitutions, improvements and the like without inventive labor.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, but not to limit it: while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A power distribution network line loss calculation method for optimizing a BP neural network by improving sparrow search is characterized by comprising the following steps:

step 1: continuously acquiring the summary table active and reactive electric quantity at a plurality of historical moments, the load point active and reactive electric quantity at a plurality of historical moments and the line loss rate at a plurality of historical moments through a power grid advanced measurement system;

and 4, step 4: and inputting the real-time collected summary table active reactive electric quantity and the real-time collected load point active reactive electric quantity into the optimized BP neural network for prediction to obtain a real-time predicted line loss rate.

2. The method for calculating the line loss of the power distribution network of the improved sparrow search optimized BP neural network according to claim 1, wherein the loss function model in the step 3 is specifically defined as:

in the formula, Y_iSample line loss rate, y, for the ith sample_iCalculating the line loss rate of the ith sample, wherein n is the total number of samples, and the loss function is the calculated mean square error;

step 3.1, setting the size of the sparrow population, the maximum iteration times, the upper weight boundary, the lower weight boundary, the upper threshold boundary, the lower threshold boundary, the safety value, the proportion of discoverers and the proportion of cautionary users;

the dimension D of the improved sparrow optimization algorithm is as follows:

D＝m×n+n×l+n+l

in the formula, m is the number of neurons in an input layer of the BP neural network, n is the number of neurons in an implicit layer of the BP neural network, and l is the number of neurons in an output layer of the BP neural network;

sparrow populations may be represented as:

wherein, X_iIs sparrow population at the ith iteration, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold, and when D belongs to [1, mxn ∈]When x_i,p,dIs the connection weight between the input layer and the hidden layer in the neural network, when d belongs to [ m x n +1, m x n + n]When x_i,p,dFor the hidden layer threshold in the neural network, when d is in the range of [ m × n + n +1, m × n + n + n × l]When x_i,p,dIs the connection weight between the hidden layer and the output layer in the neural network, when d belongs to [ m × n + n + n × l +1, m × n + n + n × l + l]When x_i,p,dThe method comprises the following steps of (1) setting an output layer threshold value in a neural network, wherein m is the number of input layer neurons of a BP neural network, n is the number of hidden layer neurons of the BP neural network, and l is the number of output layer neurons of the BP neural network;

wherein x is_i,p,dPosition, x, of dimension d of the p-th sparrow position at the i-th iteration_i+1,p,dThe position of the d dimension of the position of the p sparrow in the (i + 1) th iteration is shown, and the lambda epsilon (0,1) is a segmentation parameter; the dimension of the chaotic matrix is the same as that of a sparrow population matrix, and the chaotic matrix is generated and then is carried to the upper and lower boundaries of a weight threshold value, so that a chaotically initialized sparrow population is obtained;

step 3.2, defining a fitness function and calculating an initial individual fitness value; the fitness function is used for explaining the calculation accuracy of the model, the individual fitness value is obtained by taking the position corresponding to the individual as a weight and a threshold value and then carrying the weight and the threshold value into the neural network for calculation, and the specific fitness function is as follows:

in the formula, Y_iIs the sample line loss rate of the i-th sample, y_iCalculating the line loss rate of the ith sample, wherein n is the total number of samples, and the loss function is the calculated mean square error;

in the formula (f)_i,p([x_i,p,1,...,x_i,p,d,...,x_i,p,d]) Representing the individual fitness value, x, of the p-th sparrow at the ith iteration_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the network weight and the total number of the threshold values;

3.3, dividing the sparrows in the sparrow search algorithm into discoverers, joiners and cautionars, wherein the discoverers and the joiners change dynamically but do not change in proportion, and different types of sparrows have different updated position rules;

the sparrow is rich in resources in the population, namely the fitness value is high, and the sparrow is responsible for searching food and leading the participators, when danger occurs, the alarm of the sparrow individual is higher than the early warning value, and the discoverer leads the participators to go to a safe area; the position is updated as follows:

in the formula, x_i+1,p,dThe p-th sparrow position in the (i + 1) th iterationPosition of d-th dimension, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold, c is a random constant, and c belongs to (0,1)]，t_mFor maximum number of iterations, r is a random number obeying a normal distribution, I_1×dAll 1 matrices of 1xd, ST being the security value, R₂As a warning value, R₂∈[0,1]；

where i is the current iteration number, t_mIs the maximum number of iterations;

the improved discoverer location update formula is as follows:

for the global optimal fitness of the last iteration, rand (0,1) is normally randomly distributed, rTo obey a normally distributed random number, I_1×dAll 1 matrices of 1xd, ST being the security value, R₂For a warning value, R₂∈[0,1]；

The participants compete for food along with the discoverer with the best resources, the lower the fitness of the sparrows, the lower the energy of the participants possibly go to other areas to search for food; the position is updated as follows:

in the formula, x_i+1,p,dThe position of the d-th dimension, x, of the p-th sparrow position at the i +1 th iteration_i,p,dFor the position of the d-th dimension of the position of the p-th sparrow at the ith iteration, i belongs to [1, t ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold,

is the global optimum position of the d-th dimension of the p-th sparrow position in the (i + 1) th iteration, c is a random constant, and c belongs to (0,1)]，A⁺1xd matrix of elements 1 and-1, A⁺＝A^T(A A^T)^-1，I_1×dAn all 1 matrix of 1 xd;

individuals on the position comparison edge in the alarm can be transferred to a safety zone, and the individuals in the safety zone randomly change positions in the safety zone; the position is updated as follows:

in the formula, x_i+1,p,dIs the (i + 1) th iterationPosition of dimension d, x, at the position of the p-th sparrow_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P is an element [1, P ∈]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, namely the total number of the network weight and the threshold,

is the d-dimensional global worst position of the p-th sparrow position at the ith iteration, s is a random number obeying (0,1) normal distribution and used for controlling the step length, h is a constant between-1 and represents the individual moving direction, f_iFor the current value of the individual fitness value,

the current global optimal fitness value is then used,

is the current global worst fitness value; ε prevents the denominator from being 0;

the t distribution is an intermediate transition form of Gaussian distribution and Cauchy distribution, and can be converted into other distribution matrixes by adjusting the degree of freedom n; the mutation process is as follows:

in the formula (I), the compound is shown in the specification,

the position of the d-dimension of the p-th sparrow position after the variation of the t distribution at the ith iteration, x_i,p,dThe position of the d-th dimension of the p-th sparrow position at the ith iteration, i ∈ [1, t [ ]_m]，t_mFor the maximum number of iterations of the population, P belongs to [1, P ]]P is the number of sparrows in the population, D is equal to [1, D ]]D is the dimension to be optimized, i.e. the total number of network weights and thresholds, t (i) is the t distribution with the degree of freedom i, rand is the random number generated by the iteration, pr is the dynamic selection probability, omega₁For dynamic selection of the probability upper bound, ω₂Selecting a probability variation amplitude for the dynamics;

when the sparrow search algorithm starts iteration, the iteration times are small, the t distribution is close to Cauchy distribution, and the algorithm has strong global search capability; when the iteration times are continuously increased, the t distribution is close to Gaussian distribution, and the algorithm has strong local searching capacity; therefore, the sparrow search algorithm carries out population variation by using t distribution, the global search capability is enhanced at the initial stage, the local search capability is enhanced at the later stage, and the convergence accuracy of the algorithm is improved;

step 3.5, calculating individual fitness values of the two populations before and after mutation, acquiring the current optimal value of the two populations, comparing the current optimal value with the last time, and updating the global optimal value if the global optimal value is better;

step 3.6, repeating the steps 3.3-3.5 until the maximum iteration number is reached, and stopping; the final global optimal position, i.e. the optimal individual fitness value f_b([x_i,p,1,...,x_i,p,d,...,x_i,p,D]) Corresponding position [ x ]_i,p,1,x_i,p,2,...,x_i,p,D]Building a complete network model as weight and threshold inputs to a neural network, x_i,p,dThe position of the d dimension of the position of the p sparrow in the ith iteration is shown, and p is the sparrow corresponding to the optimal fitness.