CN112531683A - Distribution network line load prediction method based on solution of Ornstein-Urnbek process - Google Patents

Distribution network line load prediction method based on solution of Ornstein-Urnbek process Download PDF

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CN112531683A
CN112531683A CN202011296727.0A CN202011296727A CN112531683A CN 112531683 A CN112531683 A CN 112531683A CN 202011296727 A CN202011296727 A CN 202011296727A CN 112531683 A CN112531683 A CN 112531683A
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line load
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ornstein
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汪司珂
郭雨
明东岳
俞德华
郭玥
蔡文嘉
王尚鹏
庞博
夏天
郑欣
雷鸣
王信
王琪
李君�
李玲华
鄢烈奇
姚红
邓桂平
项勇
潘志
邓琼
浦小玲
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
Huangshi Power Supply Co of State Grid Hubei Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
Huangshi Power Supply Co of State Grid Hubei Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention provides a load prediction method of a distribution line based on an Ornstein-Uhlenbeck (Ornstein-Uhlenbeck) process solution, which models and predicts a line load value by considering the influence of implicit factors of weather conditions on the line load. Belongs to the technical field of electric power system combined with deep learning. The method comprises the following steps: data acquisition and data preprocessing; determining parameter expression of an Ornstein-Urnbek process by using meteorological data, wind speed and temperature; performing grouping training on data samples under different climatic conditions; updating the hidden factor strength according to the training result; and (4) performing line load prediction by solving the process of the Ornstein-Ulunebeck process by using an ITO differential equation.

Description

Distribution network line load prediction method based on solution of Ornstein-Urnbek process
Technical Field
The invention relates to the field of distribution network line load prediction, in particular to a distribution network line load prediction method based on solution of an Ornstein-Ulnbeck process.
Background
At present, the application of renewable energy sources such as wind energy in power systems is rapidly increasing. However, in the power line extension project, the power generation amount for transmitting such power supply has little progress. In addition, due to the intermittence of the renewable energy sources, the power transmission line cannot operate all day after capacity expansion. Thus, adding renewable energy does not promote utilities to use investment costs for transmission extension projects. The concept of dynamic capacity increase (line load) was introduced to cope with this problem. For safe and reliable operation, the line transmission current is usually limited by the quiescent line rating. And estimating the SLR value according to the thermal model of the overhead conductor by using the worst weather condition counted by historical data. Recently, researchers have examined the impact of on-line weather measurements on determining line load.
By introducing the concept of time series, some researchers have been able to demonstrate that future values of line load can be predicted with high accuracy. However, all studies reviewed so far have the fact that: both line load prediction models ignore some information. Historical meteorological data is generally used to predict values of weather conditions such as future wind speed and temperature. Then, in a line load forecasting model based on thermal balance, a line load value is calculated using the forecasted meteorological data. Therefore, the line load forecasting model based on the thermal balance misses information about the deviation of the past value of the line load, and thus, the error of the weather forecast may reduce the accuracy of the line load forecast. Furthermore, in the time series prediction method, the influence of wind speed and solar radiation is ignored. Therefore, these models cannot detect fluctuations in line load.
Disclosure of Invention
The invention aims to provide a distribution network line load prediction method based on solution of an Ornstein-Urnbek process, and the accuracy of a prediction result is improved. Fluctuations in line load can be detected with high accuracy.
The technical scheme of the invention is as follows:
a distribution network line load prediction method based on solution of an Ornstein-Ulnbeck process comprises the following specific steps:
1) after data are collected and preprocessed, applying an Ornstein-Ulnbek equation of a mixed factor to the solution of weather and time series information;
2) substituting the weather data into an oenstein-ulench equation of the mixed factor, determining hidden factors through the oenstein-ulench equation of the mixed factor, and describing the influence of parameters of the hidden factors on the estimation of the line load curve;
3) training parameters under different conditions, and finding out the hidden factor strength of each cluster by training and updating the selection range of hidden factors, the certainty of the parameters and the sampling selection of the hidden factors so as to minimize the line load prediction error;
4) testing the proposed model by using a data set, and evaluating a Brown prediction method for predicting wind speed and air temperature hidden factors;
5) and (4) introducing the parameters obtained in the step into an Ornstein-Ulnbek equation of the mixed factor to be solved, and obtaining a predicted value of the line load.
Based on an ITO random differential equation, a mathematical model of an oenstein-Ulnebeck equation of mixed factors is established by considering a line load time sequence, and the mathematical model is shown in a formula 1.
Figure BDA0002785601300000021
k is the number of hidden factors, and is determined as 2 in the equation definition, and the parameters mainly take into account the influence of temperature and wind speed
Figure BDA0002785601300000022
Is the k-ththIntensity of hidden factor, line load time series XtMean vector μ, vector Ψt∈R1×d，μ∈Rd×1And the parameter d represents the observation time span value.
According to equation (1), let ITO solve equation eΨt(xtμ), equation (1) can be restated as:
d(eΨt(xt-μ))＝eΨtΨ(Xt-μ)dt+eΨtdxt (2)
then, taking the interval [ s; t ], integrating the ITO on both sides of equation (2) to obtain equation (3), as shown in equation (4) by simplification:
Figure BDA0002785601300000031
Figure BDA0002785601300000032
load prediction value x is obtained based on observation time span value d and statistical characteristic line of line history and weather datat；
Dynamic transfer vector ΨtAnd the mean vector mu, by observation
Figure BDA0002785601300000033
Calculation and update are performed taking into account (4), xn-dX ofnThe predicted value is equal to:
xn＝e-ψδxn-1+(I-e-ψδ)μ+εn (5)
in the formula, the parameter epsilonnThe calculation is as follows:
Figure BDA0002785601300000034
the first term of equation (6) is used to determine the psi, mu vector,
the mathematical model of the hidden factor strength is shown in equation (7):
Figure BDA0002785601300000035
Figure BDA0002785601300000036
Figure BDA0002785601300000037
wherein N istIs the Poisson process, explains the fluctuation of the hidden factor,
Figure BDA0002785601300000041
and
Figure BDA0002785601300000042
the expected value of the concealment factor, the standard deviation of the concealment factor value and the upper bound, dw, of the fluctuation are determined separatelytIs the value of Wiener usage.
Compared with the prior art, the invention has the beneficial effects that: the method is beneficial to guiding the noise prediction calculation of the transformer substation boundary and the standard-reaching treatment work of the transformer substation boundary, and provides algorithmic support for the formulation of a noise technical improvement scheme.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
A distribution network line load prediction method based on solution of an Ornstein-Ulnbeck process comprises the following specific steps:
firstly, expanding an Onstein-Ulnbeck equation (OU equation) to simulate the influence of weather on line load forecast by using time series analysis and weather data, and considering the fluctuation detection of line load time series data, so that the OU equation is expanded to the Onstein-Ulnbeck equation with mixed factors, and the Onstein-Ulnbeck equation can determine hidden factors and describe the influence of the hidden factors on line load curve estimation;
and secondly, preprocessing data, substituting weather data into an equation after determining an Ornstein-Ulnbeck equation of the mixed factor, determining hidden factors through the Ornstein-Ulnbeck equation of the mixed factor and describing the influence of the hidden factors on the estimation of the line load curve.
The hybrid factor oenstein-ulench equation considers the fluctuation detection of the line load time sequence data, and when a plurality of unknown parameters exist in the line load prediction, the prediction content can be corrected within a certain time; secondly, performing grouping training on parameters of different conditions, on the basis of preprocessing data, training the parameters of different conditions for optimizing a line load prediction model, and finding out the hidden factor strength of each cluster by training and updating the selection range of hidden factors, the certainty of the parameters and the sampling selection of the hidden factors so as to minimize a line load prediction error;
and finally, optimizing the line load prediction model, and testing the proposed model by using the data set. Then, the brownian prediction method for predicting the hidden factors (wind speed and air temperature) was evaluated and compared with the conventional prediction model. However, in line load prediction, the error of the predicted hidden factor value can be ignored, taking into account the strength of the hidden factor.
1) Determining the parameter expression of the synthesis factor FOU equation, wherein the process is as follows:
a. in this section, the OU process is extended to use time series analysis and weather data to model the effect of weather on line load forecasts. The Brown process of mass friction is introduced, and the penetration process of particles at random speed is described. This process can be classified as a smooth gaussian-markov process, which is the underlying assumption for many statistical processes in time series analysis. In the OU process, brownian motion is applied to calculate uncertainty associated with meteorological data in the line load forecast. An ITO random differential equation is applied to solve the OU process.
Based on the ITO random differential equation, a mathematical model of the IFOU process can be established by considering the line load time sequence.
Figure BDA0002785601300000051
Where this random differential equation is designated as the IFOU procedure. In this equation, the effect of weather data is modeled using brownian motion vectors. K is used for explaining the number of hidden factors, including wind speed, air temperature and parameters
Figure BDA0002785601300000052
Is the k-ththIntensity of the sub-brownian motion.
The FOU equation model of the synthesis factor includes two terms describing the line load prediction curve. A first model deterministic evaluation of line load time series data. In other words, the term is determined by considering the transposed dynamic transfer vector ΨtTo determine the line load time series XtHow it varies around the mean vector mu. Wherein the vector Ψt∈R1×dAnd μ e Rd×1The relation between the past line load and the predicted point is reflected. In the second term of the IFOU process, the concealment factor is described by multiple brownian motions. The k independent brownian motion is used to model k different hidden factors (wind speed, air temperature) that are evolved into the observed line load time series predictions.
b. According to the formula (1), the ITO solution formula is eΨt(xt- μ). Equation (1) can be restated as:
d(eΨt(xt-μ))＝eΨtΨ(Xt-μ)dt+eΨtdxt (2)
then, taking the interval [ s; t ], integrating the ITO on both sides of equation (2) to obtain equation (3), as shown in equation (4) by simplification:
Figure BDA0002785601300000061
Figure BDA0002785601300000062
therefore, a load prediction value x is obtained based on the observation time span value d and the statistical characteristics of the line history and weather datat。
Dynamic transfer vector ΨtAnd the mean vector mu, by observation
Figure BDA0002785601300000063
And calculating and updating. Considering (4), xn-dX ofnThe predicted value is equal to:
xn＝e-ψδxn-1+(I-e-ψδ)μ+εn (5)
in the formula, the parameter epsilonnThe calculation is as follows:
Figure BDA0002785601300000064
the first term of equation (6) is used to determine the Ψ, μ vector. However, in evaluating the hiding factor strength, the parameter ε is considerednI.e. assuming { epsilonnAs having a zero mean.
c. Parameters specified by the hiding factor strength are used to explain the effect of weather data on improved line load forecastingAnd (6) sounding. The mathematical model of the hidden factor strength is shown in equation (7). In this equation, the first term calculates the contribution of the kth concealment factor to the total line load value. q. q.sc、qrAnd q issRespectively, the heat rejected by convection, radiation to the surrounding air and the heat gained by solar radiation. Mathematical models of these parameters can be found in the IEEE thermal equilibrium equations. The term is calculated using the predicted value of the concealment factor. In addition, the second term determines the degree of influence of the line load associated with the kth concealment factor, which is not taken into account by the general line load time series model.
Based on a gaussian brownian motion prediction model, factors in the S range can be predicted. The difference of observed values of different time scales is considered, the Gaussian Brown motion model is improved, and the accuracy of the model for predicting the time sequence under the fluctuation condition is improved. The model is expressed as:
Figure BDA0002785601300000071
Figure BDA0002785601300000072
Figure BDA0002785601300000073
wherein N istIs the Poisson process, explaining the fluctuation of the hidden factor.
Figure BDA0002785601300000074
And
Figure BDA0002785601300000075
the expected value of the concealment factor, the standard deviation of the concealment factor value and the upper bound of the fluctuation are determined separately. In addition, dwtIs the value of Wiener usage. (8) Is calculated based on the ITO random differential equation (9). According to the equation, based on predictions
Figure BDA0002785601300000076
The first term defined determines the trend of the hidden factor curve. The deviation and fluctuation of the hidden factor value are determined according to the second term and the last term of the equation given in (4), respectively.
d. The deviation and fluctuation of the hiding factor value are determined from the second and last terms of the equation given in (9), respectively. The algorithm flow is as follows:
Figure BDA0002785601300000077
Figure BDA0002785601300000081
the following steps are described: the first step, collecting historical meteorological data obtained by meteorological department: (
Figure BDA0002785601300000082
Wind speed, air temperature),
Figure BDA0002785601300000083
The predicted value of,
Figure BDA0002785601300000084
And
Figure BDA0002785601300000085
is started. In the second stage a brownian process is set for each concealment factor.
Figure BDA0002785601300000086
And
Figure BDA0002785601300000087
the variables are updated according to the gradient method for each hidden factor. The purpose of the update step is to reduce the Root Mean Square Error (RMSE) of the concealment factor prediction.
2) Optimized line load prediction model
First, the proposed model is tested using a data set. Then, evaluating a Gaussian Brownian motion model calculation method for predicting the wind speed and the air temperature hidden factor; however, in line load prediction, the error of the predicted hidden factor value can be ignored by considering the strength of the hidden factor; finally, the performance of the model was evaluated.
The invention discloses a distribution network line load prediction method based on solution of an Onstein-Ulnbeck process, and provides an IFOU equation of which an OU equation is expanded into a comprehensive factor. However, after the OU equation is extended to the FOU equation of the synthesis factor, it can determine hidden factors and describe the effect of these hidden factors on the line load curve estimation. A new parameter update method is proposed, applying covariance matrices and maximum likelihood estimation to assign deterministic parameters of FOU equations for synthesis factors. The samples of the factor indicating process are updated to minimize the prediction error.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (2)

1. A distribution network line load prediction method based on solution of an Ornstein-Ulnbeck process is characterized by comprising the following specific steps:
1) after data are collected and preprocessed, applying an Ornstein-Ulnbek equation of a mixed factor to the solution of weather and time series information;
2) substituting the weather data into an oenstein-ulench equation of the mixed factor, determining hidden factors through the oenstein-ulench equation of the mixed factor, and describing the influence of parameters of the hidden factors on the estimation of the line load curve;
3) training parameters under different conditions, and finding out the hidden factor strength of each cluster by training and updating the selection range of hidden factors, the certainty of the parameters and the sampling selection of the hidden factors so as to minimize the line load prediction error;
4) testing the proposed model by using a data set, and evaluating a Brown prediction method for predicting wind speed and air temperature hidden factors;
5) and (4) introducing the parameters obtained in the step into an Ornstein-Ulnbek equation of the mixed factor to be solved, and obtaining a predicted value of the line load.
2. The distribution network line load prediction method based on the oenstein-ulnbek process solution according to claim 1, characterized in that a mathematical model of the oenstein-ulnbek equation of the mixed factors is established based on ITO random differential equation, taking into account the line load time sequence, see formula 1.
Figure FDA0002785601290000011
k is the number of hidden factors, and is determined as 2 in the equation definition, and the parameters mainly take into account the influence of temperature and wind speed
Figure FDA0002785601290000012
Is the k-ththIntensity of hidden factor, line load time series XtMean vector μ, vector Ψt∈R1×d，μ∈Rd×1And the parameter d represents the observation time span value.
According to equation (1), let ITO solve equation eΨt(xtμ), the partial derivative is calculated for equation (1), the influence term is constant, the partial derivative is 0, and equation (1) can be restated as:
d(eΨt(xt-μ))＝eΨtΨ(Xt-μ)dt+eΨtdxt (2)
then, taking the interval [ s; t ], integrating the ITO on both sides of equation (2) to obtain equation (3), as shown in equation (4) by simplification:
Figure FDA0002785601290000021
Figure FDA0002785601290000022
load prediction value x is obtained based on observation time span value d and statistical characteristic line of line history and weather datat；
Dynamic transfer vector ΨtWith the mean vector μ, by observation xn,
Figure FDA0002785601290000026
Calculation and update are performed taking into account (4), xn-dX ofnThe predicted value is equal to:
xn＝e-ψδxn-1+(I-e-ψδ)μ+εn (5)
in the formula, the parameter epsilonnThe calculation is as follows:
Figure FDA0002785601290000023
the first term of equation (6) is used to determine the psi, mu vector,
the mathematical model of the hidden factor strength is shown in equation (7):
Figure FDA0002785601290000024
Figure FDA0002785601290000025
Figure FDA0002785601290000031
wherein N istIs a Poisson process, explains the fluctuating distribution of the concealment factor,
Figure FDA0002785601290000032
and
Figure FDA0002785601290000033
the expected value of the concealment factor, the standard deviation of the concealment factor value and the upper bound, dw, of the fluctuation are determined separatelytIs the value of Wiener usage.
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Application publication date: 20210319