Kernel density estimation-based seasonal rural power distribution network load prediction method and system

Abstract

The invention discloses a seasonal rural power distribution network load prediction method and system based on kernel density estimation. A power distribution network load sample is collected; carrying out stable processing on the load sample sequence by adopting a run test method to obtain a stable load sample sequence; based on a kernel density estimation method, establishing a load random prediction model of the seasonal rural power distribution network by using the stable load sample sequence; establishing a cross validation function to meet the minimum model order of the cross validation function, and taking the minimum model order as the optimal lag order; calculating a confidence interval of the short-term load prediction value; and obtaining a short-term load prediction value based on the load random prediction model under the optimal lag order, and taking the short-term load prediction value in the confidence interval as a seasonal rural power distribution network load prediction result. The problem of load instability is solved, more accurate load prediction is realized, and the reliability of power supply is improved.

Description

Technical Field

[0001] The present invention relates to the field of electric power, and in particular to a method and system for seasonal rural distribution network load forecasting based on kernel density estimation. Background Art

[0002] The nonparametric kernel density estimation method is only based on data-driven, completely avoiding the influence of subjective experience, and does not require prior knowledge of data distribution and any assumptions about the form of probability distribution.

[0003] As the contradiction between power supply and demand becomes increasingly prominent, it is very important to develop a daily operation risk assessment model and related methods for power system research to fully utilize the system's transmission capacity while maintaining an appropriate safety margin. It is also an important safety barrier for the safe and stable operation of the power system. For real-time risk assessment, the role of load forecasting is becoming more and more obvious, and the accuracy of its results has a direct impact on the safe, reliable and economical operation of the power system. Short-term power load forecasting refers to daily load forecasting or hourly load forecasting, that is, estimating the load curve for the next few days or more than one hour in advance for the next few hours. Since load demand is always changing dynamically, it is affected by many factors such as day type, weather conditions, special events, etc. Therefore, it is necessary to explore the correlation between influencing factors and power load changes and seek methods with good adaptability. Summary of the invention

[0004] In order to solve the deficiencies in the prior art, the present invention provides a seasonal rural distribution network load forecasting method and system based on kernel density estimation, which solves the problem of load instability, achieves more accurate load forecasting, and improves the reliability of power supply.

[0005] The present invention adopts the following technical solution.

[0006] The present invention proposes a seasonal rural distribution network load forecasting method based on kernel density estimation, comprising:

[0007] Collect distribution network load samples; use the run test method to process the load sample sequence to obtain a stable load sample sequence;

[0008] Based on the kernel density estimation method and using the stable load sample sequence, a stochastic load forecasting model for seasonal rural distribution network is established.

[0009] Establish a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order; calculate the confidence interval of the short-term load forecast value;

[0010] The short-term load forecast value is obtained based on the load stochastic forecasting model under the optimal lag order, and the short-term load forecast value within the confidence interval is used as the seasonal rural distribution network load forecast result.

[0011] The run test method is used to perform stationary processing on the load sample sequence to obtain a stationary load sample sequence, including:

[0012] For the time series of load samples {x t}, let the sample mean be For the sequence Smaller load samples are marked with a “-” sign. Large load samples are marked with a "+" sign, which is equal to The load samples of are recorded as unsigned to form a symbol sequence, and the number of runs of the symbol sequence is calculated; wherein, before and after a given symbol and connected to the given symbol are symbols different from the given symbol or unsigned, which is defined as a run;

[0013] For the load sample sequence, the expectation and variance of the total number of runs r are:

[0014]

[0015]

[0016]

[0017] Where Z is a statistic and follows a normal distribution; N1 is the total number of occurrences of one symbol; N2 is the total number of occurrences of another symbol; r is the total number of runs; the sequence length N = N1 + N2;

[0018] When the significance level is given, the standard normal distribution table is checked to obtain the critical value of the sampling distribution - Z α , Z α ; If -Z α <Z<Z α , then the series is stationary; otherwise, the series is non-stationary.

[0019] For non-stationary series, the difference method is executed repeatedly until a stationary load sample series is obtained.

[0020] Based on the kernel density estimation method and using the stable load sample sequence, a load stochastic forecasting model for seasonal rural distribution network is established, including:

[0021] The load vector is formed by a stable load sample sequence;

[0022] Based on the kernel density estimation method, a kernel density estimation model of the joint probability density function of the load vector is established;

[0023] Based on the kernel density estimation model, the expected value model of the kth load sample sequence is obtained using the known load vector before the prediction time;

[0024] Based on the expected value model, a load random prediction model is established.

[0025] The load random prediction model satisfies the following relationship:

[0026]

[0027] In the formula, is the short-term load forecast value at time k; E(x k ) is the kth load sample sequence x k The expected value of y i is the i-th sample of the k-load sample sequence; x j is the jth load sample sequence; h j is the jth load sample sequence x j The smoothing coefficient of y ji is the jth load sample sequence x j The i-th sample of .

[0028] A cross validation function is established to satisfy the minimum model order of the cross validation function as the optimal lag order, including:

[0029] A set of sampling samples is drawn from the load vector to form a removal vector;

[0030] After removing the removal vector from the load vector, the short-term load forecast value is obtained by using the load random forecast model; a cross-validation function is established for the short-term load forecast value;

[0031] Set the upper bound of the order of the load random forecasting model to L, minimize the cross validation function cv(k) on {1, 2, …, L}, and satisfy k is the optimal lag order.

[0032] The cross validation function cv(k) satisfies the following relationship:

[0033]

[0034] In the formula, y t is the tth sample in the removal vector, and k+1≤t≤n; W(X t (k)) is the removal vector X t (k) is a non-negative weight function; is to remove the removal vector X t The short-term load forecast value after (k) satisfies the following relationship:

[0035]

[0036] In the formula, y sis to remove the sth sample in the vector, and k+1≤s≤n, s≠1; y t To remove the tth sample in the vector, y s-t is the st-th sample after removing the t-th sample in the removal vector, and 1≤t≤k; h is the standard smoothing coefficient.

[0037] Calculating the confidence interval of the short-term load forecast value includes: constructing an estimation function of the short-term load forecast value, solving the estimation function, and obtaining the confidence interval under a given significance level.

[0038] The estimation function of the short-term load forecast value satisfies the following relationship:

[0039]

[0040]

[0041] In the formula, is the square of the estimated function of the short-term load forecast value x, is the short-term load forecast value, is the kernel density estimation function at time k-1; W(x) is the non-negative weight function of short-term load forecast x; n is the number of sampling samples; y ji is the jth load sample sequence x j The i-th sample of ; K(·) is the kernel function; k is the number of time-series continuous load sample sequences; X k-1 =(x1, x2, ..., x k-1 ) is the load vector of the previous k-1 moments;

[0042] The confidence interval [β, γ] satisfies the following relationship:

[0043]

[0044]

[0045] In the formula, z α is the integral value of the standard normal distribution density function; h is the standard smoothing coefficient.

[0046] The present invention also proposes a seasonal rural distribution network load forecasting system based on kernel density estimation, comprising:

[0047] Input data module, prediction module establishment module, prediction data module;

[0048] The input data module is used to collect the load samples of the distribution network; the run test method is used to perform a stable processing on the load sample sequence to obtain a stable load sample sequence;

[0049] The prediction module establishes a module for establishing a load random prediction model for seasonal rural distribution networks based on the kernel density estimation method and using a stable load sample sequence; establishing a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order; and calculating the confidence interval of the short-term load prediction value;

[0050] The forecast data module is used to obtain short-term load forecast values ​​based on the load random forecast model under the optimal lag order, and use the short-term load forecast values ​​within the confidence interval as the seasonal rural distribution network load forecast results.

[0051] The beneficial effects of the present invention are that, compared with the prior art, at least the seasonal variation of load data is captured by non-parametric statistical methods, thereby more accurately predicting the load pattern in different seasons. Secondly, by considering the randomness and uncertainty of load data, the model can better cope with the instability of load, especially in rural areas affected by weather, season and other factors. In addition, kernel density estimation also allows the establishment of high-resolution load models, providing more refined load forecasting results, which helps to better manage and plan power supply. This method is based on actual load data for modeling, so it can better reflect current and past load conditions and improve the accuracy of the model.

[0052] The present invention constructs a good short-term forecasting model that reflects the load in the region, which can help determine the fuel supply plan, provide an advance notice of the output requirements of the operating power plant, and estimate the output changes of the generator sets in advance. It can economically and reasonably arrange the start and stop of each unit in the network, reduce the rotating reserve capacity, and reasonably arrange the unit maintenance plan while ensuring normal power consumption. It can also be used for preventive control of safe operation or emergency processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The present invention provides a flow chart of a seasonal rural distribution network load forecasting method based on kernel density estimation. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only embodiments of a part of the present invention, rather than all embodiments. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the protection scope of the present invention.

[0055] This paper proposes a seasonal rural distribution network load forecasting method based on kernel density estimation. Figure 1 As shown, including:

[0056] Step 1: Collect distribution network load samples; use the run test method to perform stationary processing on the load sample sequence to obtain a stationary time series.

[0057] A seasonal rural distribution network load stochastic forecasting model based on kernel density estimation method is established for short-term load forecasting. The forecasting process is based on a stationary time series, and the sequence composed of load sample data is stationary. Therefore, the load sample data must be tested for stationarity before forecasting.

[0058] Specifically, it includes:

[0059] The runs test method is used to stabilize the load samples. The specific process is as follows:

[0060] For the time series of load samples {x t}, let the sample mean be For the sequence Smaller load samples are marked with a “-” sign. Large load samples are marked with a "+" sign, which is equal to The load samples are recorded as unsigned, forming a symbol sequence, and the number of runs of the symbol sequence is calculated; where the symbols before and after the given symbol and connected to the given symbol are different from the given symbol or unsigned, which is defined as a run. Set: N1 = the total number of occurrences of a symbol, such as the total number of occurrences of "-"; N2 = the total number of occurrences of another symbol, such as the total number of occurrences of "+"; r = the total number of runs. Where: r is used as the test statistic; the sequence length N = N1 + N2.

[0061] Among them, the null hypothesis judged by the run test is: "The order in which the sample data appears has no obvious trend and is stable." Before and after a given symbol and connected to a given symbol is a symbol different from the given symbol or no symbol, which is defined as a run. For example, the symbol sequence obtained is: "++---+----++-+-" with a total of 8 runs. If the symbol sequence is random, then "+" and "-" will appear randomly, so its number of runs will not be too many or too few; conversely, if the total number of runs of the symbol sequence is too few or too many, it is believed that the time series of the load sample has some trend or periodicity.

[0062] For the load sample sequence, the expectation and variance of the total number of runs r are:

[0063]

[0064]

[0065]

[0066] Where Z is a statistic and follows a normal distribution.

[0067] When the significance level α is given (usually 0.05), check the standard normal distribution table and get the critical value of the sampling distribution - Z α , Z α If -Z α <Z<Z α , then the series is stationary; otherwise, the series is non-stationary.

[0068] For non-stationary series, the trend term is removed by the difference method, and the difference is performed cyclically (once or twice) until the series becomes stationary.

[0069] Step 2: Based on the kernel density estimation method and using the stable load sample sequence, a seasonal rural distribution network load stochastic forecasting model is established.

[0070] Specifically, it includes:

[0071] Step 2.1, construct a load vector with a stable load sample sequence;

[0072] Let X k =(x1, x2, ..., x k ), X k represents the load vector composed of k time-series continuous and stable load sample sequences. If the load vector X is known, k n samples of i=1,2,...,n,y 1i ,y 2i ,……,y ki are load sample sequences x1, x2, ..., x k The i-th sample in .

[0073] Step 2.2, based on the kernel density estimation method, establish a kernel density estimation model of the joint probability density function of the load vector;

[0074] A nonparametric regression model is established to satisfy the following relationship:

[0075] F(X k )=m(X k )+ε t (1)

[0076] In the formula, F(X k ) is a nonparametric regression model, m(·) is an autoregressive function; ε t is the error term.

[0077] For the estimation of the autoregressive function m(·), when the assumed model of the function is correct and the parameters in the model are unknown, parameter estimation is the best estimation method. However, in practice, it is often difficult for us to determine the function model and its parameters that meet the actual problem. The data-driven nonparametric estimation method can estimate m(·) only based on the large amount of observation data we have. The commonly used nonparametric estimation method for the estimation of the autoregressive function m(·) is the kernel density estimation method, also known as the Nadaraya-Watson (NW) kernel estimation. Therefore, through the load vector X k The joint probability density function f(X k ) can be used to calculate the short-term load forecast value at time k.

[0078] Based on the nonparametric kernel density estimation technology and the characteristics of the power load itself, the present invention establishes a seasonal rural distribution network load random model based on the kernel density estimation theory for load forecasting, explores the joint probability density distribution law of load values ​​at different times, and focuses on the model order and prediction confidence interval calculation. This method can avoid the influence of subjective experience. It does not require any prior knowledge of the load data distribution and the assumption of the probability distribution form, but only assumes that the probability density function of the load exists and is continuously differentiable, so it is suitable for analyzing power loads with randomness and correlation.

[0079] Load vector X k The joint probability density function f(X k )’s kernel density estimation model satisfies the following relationship:

[0080]

[0081] In the formula, is the kernel density estimation function; h j is the jth load sample sequence x j The smoothing coefficient is also called bandwidth or window width; ji is the jth load sample sequence x j The i-th sampling sample of ; K(·) is the kernel function, and the standard Gaussian kernel function is adopted in the embodiment; n is the number of sampling samples; k is the number of time-series continuous load sample sequences.

[0082] Step 2.3, based on the kernel density estimation model, using the known load vector before the prediction time, obtain the expected value model of the kth load sample sequence;

[0083] Formula (2) provides the joint probability density distribution of k time-series continuous load sample sequences. In short-term load forecasting, the load vector X at the previous k-1 moments is usually k-1 =(x1, x2, ..., x k-1) is known, and we hope to obtain the load forecast value x at the next moment, i.e., at moment k. k , this is actually a problem of solving the conditional probability density function, which satisfies the following relationship:

[0084]

[0085] In the formula, f(x k |(x1,x2,…,x k-1 )) is the conditional probability density function; f(X k )、f(X k-1 ) are joint probability density functions.

[0086] According to formula (3), we can get x k The expected value model satisfies the following relationship:

[0087]

[0088] In the formula, E(x k ) is the kth load sample sequence x k expected value.

[0089] Step 2.4, based on the expected value model, establish a load random prediction model;

[0090] Substituting formula (2) into formula (4), the NW kernel estimation method is used to obtain the load stochastic forecasting model of seasonal rural distribution network, which satisfies the following relationship:

[0091]

[0092] In the formula, is the short-term load forecast value of the rural distribution network at time k obtained by using the model; i is the i-th sample in the k-load sample sequence.

[0093] Step 3, establish a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order.

[0094] When short-term load forecasting is performed using a seasonal rural distribution network stochastic load model based on kernel density estimation theory, the primary issue is to determine the optimal lag order k.

[0095] Specifically, it includes:

[0096] Step 3.1: Extract a set of samples from the load vector to form the removal vector X t (k);

[0097] For the load vector X k n samples of i = 1, 2, ..., n, where a set of sample y1, y2, ..., y n , let the removal vector X t (k) = (y1, y2, ..., y n ).

[0098] Step 3.2, after removing the removal vector from the load vector, the short-term load forecast value is obtained using the load random forecast model; a cross-validation function cv(k) is established for the short-term load forecast value:

[0099]

[0100] In the formula, y t is the tth sample in the removal vector, and k+1≤t≤n; W(X t (k)) is the removal vector X t (k) is a non-negative weight function; is to remove the removal vector X t The short-term load forecast value after (k) satisfies the following relationship:

[0101]

[0102] In the formula, y s is to remove the sth sample in the vector, and k+1≤s≤n, s≠1; y t To remove the tth sample in the vector, y s-t is the st-th sample after removing the t-th sample in the removal vector, and 1≤t≤k; h is the standard smoothing coefficient.

[0103] Step 3.3, set the upper bound of the order of the load random prediction model to L, and minimize the cross-validation function cv(k) on {1, 2, ..., L} to satisfy k is the optimal lag order.

[0104] Step 4, calculating the confidence interval of the short-term load forecast value;

[0105] According to the above steps, the load forecast value obtained by the seasonal rural distribution network load stochastic model based on kernel density estimation theory can be obtained. The reliability of the forecast value can be enhanced by solving the confidence interval.

[0106] Specifically, it includes:

[0107] Step 4.1, construct an estimation function for the short-term load forecast value, satisfying the following relationship:

[0108]

[0109]

[0110] In the formula, is the estimation function of the short-term load forecast value x, is the short-term load forecast value, is the kernel density estimation function at time k-1; W(x) is the non-negative weight function of short-term load forecast x.

[0111] Step 4.2, solve the estimation function and obtain the confidence interval [β, γ] at a given significance level, which satisfies the following relationship:

[0112]

[0113]

[0114] In the formula, z α is the integral value of the standard normal distribution density function.

[0115] Step 5: Obtain a short-term load forecast value based on the load stochastic forecasting model under the optimal lag order, and use the short-term load forecast value within the confidence interval as the seasonal rural distribution network load forecast result.

[0116] The present invention also proposes a seasonal rural distribution network load forecasting system based on kernel density estimation. It includes:

[0117] Input data module, prediction module establishment module, prediction data module;

[0118] The input data module is used to collect the load samples of the distribution network; the run test method is used to perform a stable processing on the load sample sequence to obtain a stable load sample sequence;

[0119] The prediction module establishes a module for establishing a load random prediction model for seasonal rural distribution networks based on the kernel density estimation method and using a stable load sample sequence; establishing a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order; and calculating the confidence interval of the short-term load prediction value;

[0120] The forecast data module is used to obtain short-term load forecast values ​​based on the load random forecast model under the optimal lag order, and use the short-term load forecast values ​​within the confidence interval as the seasonal rural distribution network load forecast results.

[0121] The input data module uses the run test method to process the load sample sequence smoothly and obtain a stable load sample sequence, including:

[0122] For the time series of load samples {x t}, let the sample mean be For the sequence Smaller load samples are marked with a “-” sign. Large load samples are marked with a "+" sign, which is equal to The load samples of are recorded as unsigned to form a symbol sequence, and the number of runs of the symbol sequence is calculated; wherein, before and after a given symbol and connected to the given symbol are symbols different from the given symbol or unsigned, which is defined as a run;

[0123] For the load sample sequence, the expectation and variance of the total number of runs r are:

[0124]

[0125]

[0126]

[0127] Where Z is a statistic and follows a normal distribution; N1 is the total number of occurrences of one symbol; N2 is the total number of occurrences of another symbol; r is the total number of runs; the sequence length N = N1 + N2;

[0128] When the significance level is given, the standard normal distribution table is checked to obtain the critical value of the sampling distribution - Z α , Z α ; If -Z α <Z<Z α , then the sequence is stationary; otherwise the sequence is non-stationary;

[0129] For non-stationary series, the difference method is executed repeatedly until a stationary load sample series is obtained.

[0130] The prediction module is based on the kernel density estimation method and uses a stable load sample sequence to establish a load random prediction model for seasonal rural distribution networks, including:

[0131] The load vector is formed by a stable load sample sequence;

[0132] Based on the kernel density estimation method, a kernel density estimation model of the joint probability density function of the load vector is established;

[0133] Based on the kernel density estimation model, the expected value model of the kth load sample sequence is obtained using the known load vector before the prediction time;

[0134] Based on the expected value model, a load random prediction model is established.

[0135] The load random prediction model satisfies the following relationship:

[0136]

[0137] In the formula, is the short-term load forecast value at time k; E(x k ) is the kth load sample sequence x k The expected value of y i is the i-th sample of the k-load sample sequence; x j is the jth load sample sequence; h j is the jth load sample sequence x j The smoothing coefficient of y ji is the jth load sample sequence x j The i-th sampling sample; n is the number of sampling samples; k is the number of time-series continuous load sample sequences.

[0138] The prediction module establishes a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order, including:

[0139] A set of sampling samples is drawn from the load vector to form a removal vector;

[0140] After removing the removal vector from the load vector, the short-term load forecast value is obtained by using the load random forecast model; a cross-validation function is established for the short-term load forecast value;

[0141] Set the upper bound of the order of the load random prediction model to L, minimize the cross validation function cv(k) on {1, 2, ..., L}, and satisfy k is the optimal lag order;

[0142] Among them, the cross validation function cv(k) satisfies the following relationship:

[0143]

[0144] In the formula, y t is the tth sample in the removal vector, and k+1≤t≤n; W(X t (k)) is the removal vector X t (k) is a non-negative weight function; is to remove the removal vector X t The short-term load forecast value after (k) satisfies the following relationship:

[0145]

[0146] In the formula, y s is to remove the sth sample in the vector, and k+1≤s≤n, s≠1; y t To remove the tth sample in the vector, y s-t is the st-th sample after removing the t-th sample in the removal vector, and 1≤t≤k; h is the standard smoothing coefficient.

[0147] The prediction module establishes a module to calculate the confidence interval of the short-term load prediction value, including: constructing an estimation function of the short-term load prediction value, solving the estimation function, and obtaining the confidence interval under a given significance level;

[0148] Among them, the estimation function of the short-term load forecast value satisfies the following relationship:

[0149]

[0150]

[0151] In the formula, is the square of the estimated function of the short-term load forecast value x, is the short-term load forecast value, is the kernel density estimation function at time k-1; W(x) is the non-negative weight function of short-term load forecast x; n is the number of sampling samples; y ji is the jth load sample sequence x j The i-th sample of ; K(·) is the kernel function; k is the number of time-series continuous load sample sequences; X k-1 =(x1, x2, ..., x k-1 ) is the load vector of the previous k-1 moments;

[0152] The confidence interval [β, γ] satisfies the following relationship:

[0153]

[0154]

[0155] In the formula, z α is the integral value of the standard normal distribution density function; h is the standard smoothing coefficient.

[0156] The beneficial effects of the present invention are as follows: a random model of seasonal rural distribution network load based on kernel density estimation theory is established, and the seasonal changes of load data are captured by non-parametric statistical methods, so as to more accurately predict the load patterns in different seasons. Secondly, by considering the randomness and uncertainty of load data, the model can better cope with the instability of load, especially in rural areas affected by weather, season and other factors. In addition, kernel density estimation also allows the establishment of high-resolution load models, providing more refined load forecasting results, which helps to better manage and plan power supply. This method is based on actual load data for modeling, so it can better reflect current and past load conditions and improve the accuracy of the model.

[0157] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0158] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0159] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0160] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0161] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A seasonal rural distribution network load forecasting method based on kernel density estimation is characterized by: include: Collect distribution network load samples; The run test method is used to process the load sample sequence to obtain a stable load sample sequence. Based on the kernel density estimation method and using the stable load sample sequence, a stochastic load forecasting model for seasonal rural distribution network is established. A cross validation function is established to satisfy the minimum model order of the cross validation function as the optimal lag order; Calculate confidence intervals for short-term load forecasts; The short-term load forecast value is obtained based on the load stochastic forecasting model under the optimal lag order, and the short-term load forecast value within the confidence interval is used as the seasonal rural distribution network load forecast result.

2. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 1 is characterized in that: The run test method is used to perform stationary processing on the load sample sequence to obtain a stationary load sample sequence, including: For the time series of load samples {x t }, let the sample mean be For the sequence Smaller load samples are marked with a "-" sign. Large load samples are marked with a "+" sign, which is equal to The load samples of are recorded as unsigned to form a symbol sequence, and the number of runs of the symbol sequence is calculated; wherein, before and after a given symbol and connected to the given symbol are symbols different from the given symbol or unsigned, which is defined as a run; For the load sample sequence, the expectation and variance of the total number of runs r are: Where Z is a statistic and follows a normal distribution; N1 is the total number of occurrences of one symbol; N2 is the total number of occurrences of another symbol; r is the total number of runs; the sequence length N = N1 + N2; When the significance level is given, the standard normal distribution table is checked to obtain the critical value of the sampling distribution - Z α , Z α ; If -Z α <Z<Z α , then the series is stationary; otherwise, the series is non-stationary.

3. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 2 is characterized in that: For non-stationary series, the difference method is executed repeatedly until a stationary load sample series is obtained.

4. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 1 is characterized in that: Based on the kernel density estimation method and using the stable load sample sequence, a load stochastic forecasting model for seasonal rural distribution network is established, including: The load vector is formed by a stable load sample sequence; Based on the kernel density estimation method, a kernel density estimation model of the joint probability density function of the load vector is established; Based on the kernel density estimation model, the expected value model of the kth load sample sequence is obtained using the known load vector before the prediction time; Based on the expected value model, a load random prediction model is established.

5. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 4 is characterized in that: The load random prediction model satisfies the following relationship: In the formula, is the short-term load forecast value at time k; E(x k ) is the kth load sample sequence x k The expected value of y i is the i-th sample of the k-load sample sequence; x j is the jth load sample sequence; h j is the jth load sample sequence x j The smoothing coefficient of y ji is the jth load sample sequence x j The i-th sampling sample; n is the number of sampling samples; k is the number of time-series continuous load sample sequences.

6. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 5 is characterized in that: A cross validation function is established to satisfy the minimum model order of the cross validation function as the optimal lag order, including: A set of sampling samples is drawn from the load vector to form a removal vector; After removing the removal vector from the load vector, the short-term load forecast value is obtained by using the load random forecast model; a cross-validation function is established for the short-term load forecast value; Set the upper bound of the order of the load random forecasting model to L, minimize the cross-validation function cv(k) on {1, 2, ..., L}, and satisfy k is the optimal lag order.

7. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 6 is characterized in that: The cross validation function cv(k) satisfies the following relationship: In the formula, y t is the tth sample in the removal vector, and k+1≤t≤n; W(X t (k)) is the removal vector X t (k) is a non-negative weight function; is to remove the removal vector X t The short-term load forecast value after (k) satisfies the following relationship: In the formula, y s is to remove the sth sample in the vector, and k+1≤s≤n, s≠1; y t To remove the tth sample in the vector, y s-t is the st-th sample after removing the t-th sample in the removal vector, and 1≤t≤k; h is the standard smoothing coefficient.

8. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 1 is characterized in that: Calculating the confidence interval of the short-term load forecast value includes: constructing an estimation function of the short-term load forecast value, solving the estimation function, and obtaining the confidence interval under a given significance level.

9. The seasonal rural distribution network load forecasting method based on kernel density estimation according to claim 8 is characterized in that: The estimation function of the short-term load forecast value satisfies the following relationship: In the formula, is the square of the estimated function of the short-term load forecast value x, is the short-term load forecast value, is the kernel density estimation function at time k-1; W(x) is the non-negative weight function of short-term load forecast x; n is the number of sampling samples; y ji is the jth load sample sequence x j The i-th sample of ; K(·) is the kernel function; k is the number of time-series continuous load sample sequences; X k-1 =(x1, x2, ..., x k-1 ) is the load vector of the previous k-1 moments; The confidence interval [β, γ] satisfies the following relationship: In the formula, z α is the integral value of the standard normal distribution density function; h is the standard smoothing coefficient.

10. A seasonal rural distribution network load forecasting system based on kernel density estimation, characterized in that: include: Input data module, prediction module establishment module, prediction data module; Input data module, used to collect distribution network load samples; The run test method is used to process the load sample sequence to obtain a stable load sample sequence. The prediction module establishes a module for establishing a load random prediction model for seasonal rural distribution networks based on the kernel density estimation method and using a stable load sample sequence; establishing a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order; and calculating the confidence interval of the short-term load prediction value; The forecast data module is used to obtain short-term load forecast values ​​based on the load random forecast model under the optimal lag order, and use the short-term load forecast values ​​within the confidence interval as the seasonal rural distribution network load forecast results.

11. The seasonal rural distribution network load forecasting system based on kernel density estimation according to claim 10, characterized in that: The input data module uses the run test method to process the load sample sequence smoothly and obtain a stable load sample sequence, including: For the time series of load samples {x t }, let the sample mean be For the sequence Smaller load samples are marked with a "-" sign. Large load samples are marked with a "+" sign, which is equal to The load samples of are recorded as unsigned to form a symbol sequence, and the number of runs of the symbol sequence is calculated; wherein, before and after a given symbol and connected to the given symbol are symbols different from the given symbol or unsigned, which is defined as a run; For the load sample sequence, the expectation and variance of the total number of runs r are: Where Z is a statistic and follows a normal distribution; N1 is the total number of occurrences of one symbol; N2 is the total number of occurrences of another symbol; r is the total number of runs; the sequence length N = N1 + N2; When the significance level is given, the standard normal distribution table is checked to obtain the critical value of the sampling distribution - Z α , Z α ; If -Z α <Z<Z α , then the sequence is stationary; otherwise the sequence is non-stationary; For non-stationary series, the difference method is executed repeatedly until a stationary load sample series is obtained.

12. The seasonal rural distribution network load forecasting system based on kernel density estimation according to claim 10, characterized in that: The prediction module is based on the kernel density estimation method and uses a stable load sample sequence to establish a load random prediction model for seasonal rural distribution networks, including: The load vector is formed by a stable load sample sequence; Based on the kernel density estimation method, a kernel density estimation model of the joint probability density function of the load vector is established; Based on the kernel density estimation model, the expected value model of the kth load sample sequence is obtained using the known load vector before the prediction time; Based on the expected value model, a load random prediction model is established.

13. The seasonal rural distribution network load forecasting system based on kernel density estimation according to claim 12, characterized in that: The load random prediction model satisfies the following relationship: In the formula, is the short-term load forecast value at time k; E(x k ) is the kth load sample sequence x k The expected value of y i is the i-th sample of the k-load sample sequence; x j is the jth load sample sequence; h j is the jth load sample sequence x j The smoothing coefficient of y ji is the jth load sample sequence x j The i-th sampling sample; n is the number of sampling samples; k is the number of time-series continuous load sample sequences.

14. The seasonal rural distribution network load forecasting system based on kernel density estimation according to claim 12, characterized in that: The prediction module establishes a cross-validation function to satisfy the minimum model order of the cross-validation function as the optimal lag order, including: A set of sampling samples is drawn from the load vector to form a removal vector; After removing the removal vector from the load vector, the short-term load forecast value is obtained by using the load random forecast model; a cross-validation function is established for the short-term load forecast value; Set the upper bound of the order of the load random forecasting model to L, minimize the cross-validation function cv(k) on {1, 2, ..., L}, and satisfy k is the optimal lag order; Among them, the cross validation function cv(k) satisfies the following relationship: In the formula, y t is the tth sample in the removal vector, and k+1≤t≤n; W(X t (k)) is the removal vector X t (k) is a non-negative weight function; is to remove the removal vector X t The short-term load forecast value after (k) satisfies the following relationship: In the formula, y s is to remove the sth sample in the vector, and k+1≤s≤n, s≠1; y t To remove the tth sample in the vector, y s-t is the st-th sample after removing the t-th sample in the removal vector, and 1≤t≤k; h is the standard smoothing coefficient.

15. The seasonal rural distribution network load forecasting system based on kernel density estimation according to claim 14, characterized in that: The prediction module establishes a module to calculate the confidence interval of the short-term load prediction value, including: constructing an estimation function of the short-term load prediction value, solving the estimation function, and obtaining the confidence interval under a given significance level; Among them, the estimation function of the short-term load forecast value satisfies the following relationship: In the formula, is the square of the estimated function of the short-term load forecast value x, is the short-term load forecast value, is the kernel density estimation function at time k-1; W(x) is the non-negative weight function of short-term load forecast x; n is the number of sampling samples; y ji is the jth load sample sequence x j The i-th sample of ; K(·) is the kernel function; k is the number of time-series continuous load sample sequences; X k-1 =(x1, x2, ..., x k-1 ) is the load vector of the previous k-1 moments; The confidence interval [β, γ] satisfies the following relationship: In the formula, z α is the integral value of the standard normal distribution density function; h is the standard smoothing coefficient.

16. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 9.

17. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 9 are implemented.

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