CN106651020B - Short-term power load prediction method based on big data reduction - Google Patents

Short-term power load prediction method based on big data reduction Download PDF

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CN106651020B
CN106651020B CN201611165569.9A CN201611165569A CN106651020B CN 106651020 B CN106651020 B CN 106651020B CN 201611165569 A CN201611165569 A CN 201611165569A CN 106651020 B CN106651020 B CN 106651020B
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张淑清
杨振宁
张航飞
马灿
李盼
宿新爽
李军锋
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Yanshan University
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Abstract

The invention provides a short-term power load prediction method based on big data reduction, which comprises the following steps: the method comprises the steps of firstly removing redundant data and bad data in big data by using a Lasso principle, and then performing dimensionality reduction and feature extraction on environment factor variables by using Principal Component Analysis (PCA). The extracted feature vectors and the simplified processed historical load data are used as the input of an Elman neural network for training and prediction. The method of the invention obviously improves the prediction precision and speed of the short-term power load.

Description

Short-term power load prediction method based on big data reduction
Technical Field
The invention relates to the technical field of power load prediction, in particular to a short-term power load prediction method based on big data reduction.
Background
The power load prediction is one of the important work of a power supply department and is a precondition for ensuring the reliable power supply and the safe operation of a power system. The accurate load prediction can economically and reasonably arrange the start and stop of the generator set in the power grid, and the economic benefit and the social benefit are improved. In the face of the rapid development of the smart power grid, the influence factors of the power load are increased, the data are exponentially increased, the characteristic of large data multidimensional is gradually formed, and the traditional data analysis mode cannot meet the requirement. How to efficiently and accurately predict the power load with the characteristics becomes a key problem to be solved at present. In the current short-term power load prediction model, a BP neural network which is widely applied identifies a dynamic network by using a static feedforward network, changes a dynamic time modeling problem into a static space modeling problem so as to enable the prediction precision to be low, and needs a large amount of sample data during training so as to enable the prediction speed to be slow, which can cause the operation cost of power to be greatly increased, namely the current short-term load prediction method can not completely meet the requirements of an intelligent power grid in the face of the characteristics of large data of power loads. Therefore, we propose a short-term power load prediction method based on big data reduction.
Disclosure of Invention
The invention aims to provide a short-term power load prediction method based on big data reduction, which can obviously improve the prediction precision and speed of short-term power load in an intelligent power grid.
In order to achieve the purpose, the following technical scheme is adopted, and the method comprises the following steps:
step 1, selecting a load sequence of n sampling points of the same type of dates before a forecast day, wherein the sampling point of each date is 48 points, namely sampling is performed every 30 min;
step 2, acquiring load-influencing related weather factor data of n dates of the same type and prediction days;
step 3, carrying out high-dimensional data reduction on the acquired original power load and the acquired big data of the related weather factors by utilizing a minimum absolute value contraction (Lasso) principle, and removing bad data to obtain a useful load sequence;
step 4, performing dimensionality reduction and feature extraction on weather environment factor variables through Principal Component Analysis (PCA) to obtain environment feature factors;
and 5, establishing an Elman dynamic neural network short-term power load prediction model, training and predicting by taking the extracted feature vector and historical load data as input of the Elman dynamic neural network, and predicting the load value at each moment of the (n + 1) th day by an Elman method.
The relevant weather factor load data in step 2 comprises: the method comprises the following steps that 10 weather factor data are input as simulation data in sunny days (X1), cloudy days (X2), rainy days (X3), the highest air temperature (X4), the lowest air temperature (X5), air pressure (X6), humidity (X7), radiation (X8), wind speed (X9), cloud cover (X10) and the like;
the principle of minimum absolute value shrinkage (Lasso) in step 3) is as follows:
carrying out data mining on the big load data by using a Lasso algorithm, and eliminating redundant data, thereby providing simple and effective characteristic data for a load prediction algorithm; the Lasso method is a compression estimation method, and a more refined model is obtained by constructing a penalty function, so that the model compresses a plurality of coefficients, and the coefficients are set to be zero, thereby keeping the characteristic of subset contraction;
a linear regression model is set:
y＝α+β1x1+β2x2+…+βpxp+ (1)
wherein α is a constant term, β1,β2,…βpIs a regression coefficient; is a random perturbation term; (x)i1,xi2,...,xip；yi) N is n sets of observations of the variables, which are satisfied
Figure BDA0001182402160000031
Wherein j is 1, 2.. multidot.p;
the Lasso estimate of the constant term and regression coefficients is defined as:
Figure BDA0001182402160000032
the specific process of data dimension reduction is as follows:
(a) constraint conditions are as follows:
Figure BDA0001182402160000033
s is a penalty function;
(b) order to
Figure BDA0001182402160000034
Representation βjLeast squares estimation of (1) then
Figure BDA0001182402160000035
(c) When the value of s is continuously increased, the data entering the regression model are increased, and when a certain value is reached, all the data enter the regression model; when the s value is reduced to a certain degree, the estimated values of some regression coefficients are 0, and the model provides a variable with the coefficient of 0, so that the purpose of reducing the dimension is achieved.
In the step 4, the principal component analysis mainly aims at performing dimensionality reduction processing on weather data in power load prediction, extracting multi-weather-factor characteristic indexes, and using the multi-weather-factor characteristic indexes and historical load data as modeling objects together, so that the established characteristic quantities comprehensively represent the influence of each factor on the power load and can simplify a prediction model;
assuming n samples, each sample has p variables, forming an n × p data matrix
Figure BDA0001182402160000036
The specific process is as follows:
(a) data normalization-raw data index is normalized to valid data between [0,1 ];
Figure BDA0001182402160000037
(b) calculating a matrix of correlation coefficients
Figure BDA0001182402160000041
Where rij (i, j ═ 1,2, …, p) is the correlation coefficient between original variables xi and xj, and is calculated by the following formula:
Figure BDA0001182402160000042
because R is a real symmetric matrix (i.e., rij — rji), only the upper or lower triangular elements need to be computed;
(c) computing eigenvalues and eigenvectors
First, the eigen equation | λ I-R | ═ 0 is solved, and the eigenvalue λ is usually found by the jacobian methodi(i-1, 2, …, p) and arranged in order of magnitude, i.e. λ1≥λ2≥…,≥λpNot less than 0; then, the corresponding characteristic values lambda are respectively obtainediCharacteristic vector a ofi(i＝1,2,…,p)；
(d) Calculating principal component contribution rate and accumulated contribution rate
Carrying out comprehensive evaluation and weighted summation on m main components
f＝w1z1+w2z2+…+wmzm(7)
In the formula, wi is the contribution ratio of the main component, and the calculation formula is as follows:
Figure BDA0001182402160000043
the contribution rate represents the percentage of the ith principal component in the original index information amount, so that the proportion of the first principal component should be the maximum, and then gradually decreases. The cumulative variance contribution of the first m principal components is:
Figure BDA0001182402160000051
in order to achieve the purpose of reducing dimension, the accumulated contribution rate of the current m principal components reaches more than 85%, and the previous p evaluation indexes can be replaced by the previous m principal components;
(e) and (3) constructing a new sample matrix, defining: calculating sample values of each main component according to the formula (12) and the formula (13) by taking x1, x2, … and xP as original variable indexes, and z1, z2, … and zm (m is less than or equal to p) as new variable indexes;
Figure BDA0001182402160000052
Figure BDA0001182402160000053
in step 5, the specific prediction method is as follows:
the Elman neural network is characterized in that a carrying layer is added in a hidden layer of a BP feedforward network and serves as a one-step delay operator to achieve the purpose of memorizing, and the Elman neural network has the function of dynamic characteristics by storing internal states, so that the system has the characteristics of adapting to mutation events;
the nonlinear state space expression of the Elman network is:
Figure BDA0001182402160000054
in the formula, k is the number of times of neural network training; y is an n-dimensional output vector; x is a hidden layer neuron output vector; u is an input vector; xc is a feedback state vector; w3 is the connection weight from the middle layer to the output layer; w2 is the input layer to middle layer connection weight; w1 is the connection weight of the receiving layer to the middle layer. g is the transfer function of the output neuron, and is the linear combination of the intermediate layer outputs; f is the transfer function of hidden layer neuron, often adopting s function;
the Elman network also adopts a BP algorithm to correct the weight, and the learning index function adopts an error square sum function:
Figure BDA0001182402160000061
in the formula (I), the compound is shown in the specification,
Figure BDA0001182402160000062
a target input vector is obtained.
Compared with the prior art, the method has the following advantages:
1. redundant data and bad data in the big data of the smart power grid can be removed by using the Lasso principle, so that the data is more effective and simplified;
2. and introducing Lasso-PCA to perform dimensionality reduction processing on meteorological data in power load prediction, extracting multiple weather factor characteristic quantities, and using the characteristic quantities and historical load data together as modeling objects, so that the established characteristic quantities comprehensively represent the influence of each factor on the power load, can simplify prediction input data, and meanwhile, a dynamic Elman neural network prediction model is adopted, so that the accuracy and the speed of power load prediction are obviously improved.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
FIG. 2 is a diagram of the Elman neural network structure of the method of the present invention.
FIG. 3 is a graph showing the results of principal component analysis of 10 environment variable factors by the method of the present invention.
FIG. 4 is a graph comparing predicted load curves to actual load curves under different methods.
Fig. 5 is a comparison graph of prediction error under different methods.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
as shown in fig. 1, the present invention provides a short-term power load prediction method based on big data reduction, comprising the following steps:
1) selecting a load sequence of 48 points (sampling every 30 min) for predicting n days of the same type;
2) acquiring load factor data influencing n dates of the same type and prediction dates;
3) carrying out high-dimensional data reduction on the acquired original power load and the acquired big data of the related weather factors by using a minimum absolute value contraction (Lasso) principle, and removing bad data to obtain a useful data set;
4) performing dimensionality reduction and feature extraction on the environment factor variable through Principal Component Analysis (PCA) to obtain an environment feature factor;
5) and establishing an Elman dynamic neural network short-term power load prediction model, and training and predicting by taking the extracted feature vectors and historical load data as the input of the Elman neural network.
As shown in fig. 2, the Elman neural network is generally divided into 4 layers: input layer, intermediate layer (hidden layer), receiving layer and output layer. The connection of the input, hidden and output layers is similar to a feed-forward network, with the elements of the input layer acting only for signal transmission and the elements of the output layer acting for linear weighting. The transfer function of the hidden layer unit can adopt a linear or nonlinear function, the carrying layer is used for memorizing the past state of the hidden layer and is used as the input of the hidden layer unit together with the network input at the next moment, so that the network has a dynamic memory function, and the purpose of dynamic modeling is achieved.
Application example:
a PCA-Elman prediction model is established based on power load data of a certain province to predict the daily load of the region, and 10 related environmental factor data such as power load data (y) of the region in 2004 from 3 month 1 to 3 month 8, sunny days (X1), cloudy days (X2), rainy days (X3), highest air temperature (X4), lowest air temperature (X5), air pressure (X6), humidity (X7), radiation (X8), wind speed (X9), cloud cover (X10) and the like are selected as simulation data. During prediction, the data of the previous 7 days are used as training samples, the load sequence of every previous 3 days is used as an input vector, the load sequence of the 4 th day is used as a target vector, 4 groups of training samples are obtained according to the rule to carry out sample training on the model, and finally the data of the 8 th day is used as a test sample of the network to verify the accuracy of the network model.
The prediction process is performed according to the flow chart described in fig. 1. And performing bad data processing on the input load sequence by using a Lasso principle to enable the input data to be accurate and simple, then performing dimensionality reduction processing on meteorological data in power load prediction by using PCA, extracting multiple weather factor characteristic quantities, using the multiple weather factor characteristic quantities and simplified historical load data as modeling objects together, and inputting the modeling objects into an Elman neural network model to perform load prediction. The structure of the Elman neural network is shown in figure 2.
For example, fig. 3 is a result diagram of principal component analysis performed on 10 environment variable factors, and the obtained first 3 principal component cumulative variance contribution rates can reach above 85% by arranging the principal component eigenvalues from large to small, which illustrates that the first 3 principal components almost contain information of all influencing factors, and a new factor is selected according to the principle that the contribution rate is greater than 85% (the eigenvalue is greater than 1), and the first 3 eigenvalues are selected and corresponding eigenvectors are calculated to be used as the input of the dynamic neural network.
As shown in fig. 4 and 5, the comparison graphs of the predicted load curve and the actual load curve under different methods and the comparison graph of the prediction error under each method are respectively shown, and the method has higher accuracy in predicting the short-term power load compared with other prediction methods.
As described above, the method firstly eliminates redundant data and bad data in big data by using the Lasso principle, and then performs dimensionality reduction and feature extraction on environment factor variables through Principal Component Analysis (PCA). The extracted feature vectors and the simplified processed historical load data are used as the input of an Elman neural network for training and prediction, and finally, a more accurate prediction result compared with the previous prediction method is obtained. The method provides a new idea for the short-term load prediction of the power system under the smart grid.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.

Claims (5)

1. A method for short-term power load forecasting based on big data reduction, the method comprising the steps of:
step 1, selecting a sampling point load sequence of n same-type dates before a forecast date; the sampling point for each date is 48 points, namely sampling once every 30 min;
step 2, acquiring load-influencing related weather factor data of n dates of the same type and prediction days;
step 3, carrying out high-dimensional data reduction on the acquired original power load and the acquired big data of the related weather factors by utilizing a minimum absolute value contraction (Lasso) principle, and removing bad data to obtain a useful load sequence;
step 4, performing dimensionality reduction and feature extraction on weather environment factor variables through Principal Component Analysis (PCA) to obtain environment feature factors;
and 5, establishing an Elman dynamic neural network short-term power load prediction model, training and predicting by taking the extracted feature vector and historical load data as input of the Elman dynamic neural network, and predicting the load value at each moment of the (n + 1) th day by an Elman method.
2. The big data reduction-based short-term power load forecasting method of claim 1, wherein: the related weather factor load data comprises sunny day X1, cloudy day X2, rainy day X3, highest air temperature X4, lowest air temperature X5, air pressure X6, humidity X7, radiation X8, wind speed X9 and cloud cover X10, and the 10 weather factor load data are input as simulation data.
3. The method as claimed in claim 1, wherein the minimum absolute value shrinkage (Lasso) principle in step 3 is as follows:
a linear regression model is set:
y＝α+β1x1+β2x2+…+βpxp+ (1)
wherein α is a constant term, β1,β2,…βpIs a regression coefficient; is a random perturbation term; (x)i1,xi2,...,xip；yi) N is n sets of observations of the variables, which are satisfied
Figure FDA0002525753460000021
Wherein j is 1, 2.. multidot.p;
the Lasso estimate of the constant term and regression coefficients is defined as:
Figure FDA0002525753460000022
the specific process of data dimension reduction is as follows:
(a) constraint conditions are as follows:
Figure FDA0002525753460000023
s is a penalty function;
(b) Order to
Figure FDA0002525753460000024
Representation βjLeast squares estimation of (1) then
Figure FDA0002525753460000025
(c) When the value of s is continuously increased, the data entering the regression model are increased, and when a certain value is reached, all the data enter the regression model; when the s value is reduced to a certain degree, the estimated values of some regression coefficients are 0, and the model provides a variable with the coefficient of 0, so that the purpose of reducing the dimension is achieved.
4. The method as claimed in claim 1, wherein in step 4, assuming n samples, each sample has p variables, a data matrix of n x p order is formed
Figure FDA0002525753460000026
The specific process is as follows:
(a) data normalization-raw data index is normalized to valid data between [0,1 ];
Figure FDA0002525753460000027
(b) calculating a matrix of correlation coefficients
Figure FDA0002525753460000031
In the formula, rij(i, j ═ 1,2, …, p) as the original variable xiAnd xjThe calculation formula of the correlation coefficient between the two is as follows:
Figure FDA0002525753460000032
since R is a real symmetric matrix (i.e., R)ij＝rji) So only the upper triangle element or the lower triangle element needs to be calculated;
(c) computing eigenvalues and eigenvectors
First, the eigen equation | λ I-R | ═ 0 is solved, and the eigenvalue λ is usually found by the jacobian methodi(i-1, 2, …, p) and arranged in order of magnitude, i.e. λ1≥λ2≥…,≥λpNot less than 0; then, the corresponding characteristic values lambda are respectively obtainediCharacteristic vector a ofi(i＝1,2,…,p)；
(d) Calculating principal component contribution rate and accumulated contribution rate
Carrying out comprehensive evaluation and weighted summation on m main components
f＝w1z1+w2z2+…+wmzm(7)
In the formula, wiThe calculation formula is as follows:
Figure FDA0002525753460000033
the contribution rate represents the percentage of the ith principal component in the original index information quantity, so that the proportion of the first principal component is the maximum, and then the first principal component gradually decreases; the cumulative variance contribution of the first m principal components is:
Figure FDA0002525753460000041
in order to achieve the purpose of reducing dimension, the accumulated contribution rate of the current m principal components reaches more than 85%, and the previous p evaluation indexes can be replaced by the previous m principal components;
(e) and (3) constructing a new sample matrix, defining: note x1，x2，…，xpIs an index of a primary variable, z1，z2，…，zm(m is less than or equal to p) is a new variable index, and each sample value of each main component is calculated according to the formula (12) and the formula (13);
Figure FDA0002525753460000042
Figure FDA0002525753460000043
5. the method as claimed in claim 1, wherein in step 5, the specific prediction method is as follows:
the nonlinear state space expression of the Elman network is:
Figure FDA0002525753460000044
in the formula, k is the number of times of neural network training; y is an n-dimensional output vector; x is a hidden layer neuron output vector; u is an input vector; x is the number ofcIs a feedback state vector; w is a3Connecting the weight from the middle layer to the output layer; w is a2Connecting the weight from the input layer to the middle layer; w is a1The connection weight from the receiving layer to the middle layer; g is the transfer function of the output neuron, and is the linear combination of the intermediate layer outputs; f is the transfer function of hidden layer neuron, often adopting s function;
the Elman network also adopts a BP algorithm to correct the weight, and the learning index function adopts an error square sum function:
Figure FDA0002525753460000051
in the formula (I), the compound is shown in the specification,
Figure FDA0002525753460000052
a target input vector is obtained.
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