CN-121681979-B - Load curve decomposition method and system based on curvature average rational B-spline basis function

CN121681979BCN 121681979 BCN121681979 BCN 121681979BCN-121681979-B

Abstract

Calculating the curvature of a historical load sequence, generating a continuous curvature function, and determining a group of B spline node sequences meeting the accumulated absolute curvature sharing condition according to the continuous curvature function, so that node distribution is self-adaptive to load fluctuation intensity; and establishing a fitting model by combining a time period virtual variable, and decomposing a load curve into two parts of a time period characteristic load level representing the reference power consumption intensity of different time periods and a time characteristic load curve representing the continuous variation fluctuation form. The method overcomes the defect of poor adaptability of the traditional uniform spline to the non-uniform load form, realizes self-adaptive and definite-physical-meaning decomposition, and provides a better data base for load analysis and prediction.

Inventors

YE JING
XIONG HUIMIN
DAI QIQI
ZHANG XUETING
LI YINGXUE
CHEN JUNZHI
CHEN RIHUAN
ZHANG YUHUA
WANG CUI
ZHANG JINDUO

Assignees

国网江西省电力有限公司经济技术研究院
江西水利电力大学

Dates

Publication Date: 20260512
Application Date: 20260210

Claims (9)

1. The load curve decomposition method based on the curvature average rational B-spline basis function is characterized by comprising the following steps of: for a given T point historical load sequence, calculating the curvature of each load point in the T point historical load sequence, and obtaining a continuous curvature function corresponding to the T point historical load sequence through local linear interpolation; Determining a group of B spline node sequences meeting curvature equipartition conditions according to the continuous curvature function, wherein the B spline node sequences comprise at least one curvature equipartition spline node; calculating a p-order B-spline basis function by using a B-spline recurrence formula based on the at least one curvature equipartition spline node and the selected spline order p; Taking the fitting error of the minimized historical load curve as an objective function, and solving the objective function based on a particle swarm algorithm to obtain optimal weight; constructing a curvature average rational B spline basis function based on the optimal weight and the p-order B spline basis function; Dividing the history period into m periods, and constructing a virtual variable for each period i Wherein when time t belongs to period i =1, Otherwise =0; Averaging the rational B-spline basis function and the virtual variables using the curvature Establishing a fitting model, and solving the fitting model by adopting a least square method to obtain a control vertex estimated value and a load level estimated value of each period; And decomposing the T point historical load sequence into a time period characteristic load level part and a time characteristic load curve part according to the control vertex estimated value and the time period load level estimated values.
2. The method for decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 1, wherein said continuous curvature function is calculated The expression of (2) is: , , In the formula, And Respectively is Is used to determine the first and second derivatives of (a), For the moment t of time t of loading, For the number of points of the historical load curve, As a function of the parameters, Is the curvature at the moment of t-1, The curvature is time t.
3. The method for decomposing the load curve based on the curvature-sharing rational B-spline basis function according to claim 1, wherein the constraint condition of the curvature-sharing spline nodes is as follows: , In the formula, For the i+1th B spline node, For the ith B-spline node, For the initial B-spline node, For the 1 st B-spline node, Is the first The nodes of the B-spline, Is the number of the B-spline basis functions, Is the first The nodes of the B-spline, Is the first The nodes of the B-spline, Is the first The nodes of the B-spline, For the number of B-spline steps, Is the curvature of the interpolated time point u.
4. The method for decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 1, wherein the expression for calculating the p-order B-spline basis function is: , In the formula, For the i+j-1B spline node, For the ith B-spline node, Is the ith j-1 order B spline basis function, For the i + j B spline node, Is the i+1th order B-spline basis function.
5. The method for decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 1, wherein the expression of the objective function is: , In the formula, Weights for the ith B-spline basis function, The vertex is controlled for the ith B-spline curve, For the number of points of the historical load curve, Is the number of the B-spline basis functions, Is the j-th p-order B-spline basis function, The j-th B-spline basis function weight, Is time t load.
6. The method for decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 1, wherein the curvature-averaged rational B-spline basis function The expression of (2) is: , In the formula, The optimal weight for the ith rational B-spline basis function, Is the ith p-th order B-spline basis function, The optimal weight for the jth rational B-spline basis function, Is the j-th p-order B-spline basis function, The number of B spline basis functions.
7. The method for decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 5, wherein the expression of the fitting model is: , In the formula, For a period of time The level of the load is set, For the number of time periods, Is that Period virtual variable load.
8. The method of decomposing a load curve based on a curvature-averaged rational B-spline basis function according to claim 7, wherein the expression of the period-characteristic load level section is: , In the formula, The load level of the period characteristic is represented for the time t, For the period i load level estimation, Counting historical load curves; the expression of the time characteristic load curve part is as follows: , In the formula, The time t represents the load of the time characteristic.
9. A load curve decomposition system based on curvature equipartition rational B-spline basis function, comprising: The interpolation module is configured to calculate the curvature of each load point in the T point historical load sequence for a given T point historical load sequence, and obtain a continuous curvature function corresponding to the T point historical load sequence through local linear interpolation; the determining module is configured to determine a group of B spline node sequences meeting curvature average condition according to the continuous curvature function, wherein the B spline node sequences comprise at least one curvature average spline node; A computation module configured to compute a p-order B-spline basis function using a B-spline recurrence formula based on the at least one curvature-averaged spline node and the selected spline order p; the solving module is configured to take the fitting error of the minimized historical load curve as an objective function, and solve the objective function based on a particle swarm algorithm to obtain optimal weight; The first construction module is configured to construct a curvature average rational B-spline basis function based on the optimal weight and the p-order B-spline basis function; A second construction module configured to divide the history period into m periods, construct a virtual variable for each period i Wherein when time t belongs to period i =1, Otherwise =0; A fitting module configured to average the rational B-spline basis function and the virtual variables using the curvature Establishing a fitting model, and solving the fitting model by adopting a least square method to obtain a control vertex estimated value and a load level estimated value of each period; and a decomposition module configured to decompose the T point historical load sequence into a period characteristic load level part and a time characteristic load curve part according to the control vertex estimated value and the each period load level estimated value.

Description

Load curve decomposition method and system based on curvature average rational B-spline basis function Technical Field The invention belongs to the technical field of load curve division, and particularly relates to a load curve decomposition method and system based on a curvature average rational B-spline basis function. Background Load curve decomposition is commonly used in the fields of power system load prediction, energy scheduling optimization, power market analysis and the like. The currently prevailing load curve decomposition techniques include fourier transforms, wavelet transforms, empirical mode decomposition (EMPIRICAL MODE DECOMPOSITION, EMD), variational mode decomposition (Variational Mode Decomposition, VMD), singular spectrum analysis (Singular Spectrum Analysis, SSA), etc. The key decomposition technology is characterized in that complex load sequences are disassembled into components with definite physical significance such as trend items, period items, random items (or fluctuation items and noise items) and the like, and support is provided for subsequent data analysis. Although the above technology has played an important role in the field of power systems, the influence of the variation of the power time period characteristics is not fully considered, and it is difficult to accurately describe the actual power consumption behavior of the power consumer. Therefore, a method for decomposing a load curve of a response time-sharing electricity price is needed to extract a load level component representing a time period characteristic and a load curve component representing a time evolution characteristic. Under the background of energy structure transformation deepening and smart grid construction acceleration, the decomposition method provides key technical support for fine operation management (such as scientific time division, customized retail electricity price package design and the like) of the power system. Disclosure of Invention The invention provides a load curve decomposition method and a system based on a curvature average rational B-spline basis function, which are used for solving the technical problem that the electricity utilization behavior rule of a power user is difficult to accurately describe. In a first aspect, the present invention provides a load curve decomposition method based on a curvature average rational B-spline basis function, including: for a given T point historical load sequence, calculating the curvature of each load point in the T point historical load sequence, and obtaining a continuous curvature function corresponding to the T point historical load sequence through local linear interpolation; Determining a group of B spline node sequences meeting curvature equipartition conditions according to the continuous curvature function, wherein the B spline node sequences comprise at least one curvature equipartition spline node; calculating a p-order B-spline basis function by using a B-spline recurrence formula based on the at least one curvature equipartition spline node and the selected spline order p; Taking the fitting error of the minimized historical load curve as an objective function, and solving the objective function based on a particle swarm algorithm to obtain optimal weight; constructing a curvature average rational B spline basis function based on the optimal weight and the p-order B spline basis function; Dividing the history period into m periods, and constructing a virtual variable for each period i Wherein when time t belongs to period i=1, Otherwise=0; Averaging the rational B-spline basis function and the virtual variables using the curvatureEstablishing a fitting model, and solving the fitting model by adopting a least square method to obtain a control vertex estimated value and a load level estimated value of each period; And decomposing the T point historical load sequence into a time period characteristic load level part and a time characteristic load curve part according to the control vertex estimated value and the time period load level estimated values. In a second aspect, the present invention provides a load curve decomposition system based on a curvature-averaged rational B-spline basis function, comprising: The interpolation module is configured to calculate the curvature of each load point in the T point historical load sequence for a given T point historical load sequence, and obtain a continuous curvature function corresponding to the T point historical load sequence through local linear interpolation; the determining module is configured to determine a group of B spline node sequences meeting curvature average condition according to the continuous curvature function, wherein the B spline node sequences comprise at least one curvature average spline node; A computation module configured to compute a p-order B-spline basis function using a B-spline recurrence formula based on the at least one curvature-averaged spline nod