CN114266593A - Power consumption prediction method based on KPCA and linear regression - Google Patents
Power consumption prediction method based on KPCA and linear regression Download PDFInfo
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Abstract
The invention discloses a power consumption prediction method based on KPCA and linear regression, which comprises the steps of processing collected city variables in a preset time period by PCA and KPCA to obtain PCA processing variables and KPCA processing variables, dividing the PCA processing variables and the KPCA processing variables into a training set, a test set and a prediction set, then bringing the training set, the test set and the prediction set into a linear regression model, and selecting an optimal model to obtain a prediction result. The verification proves that the predicted result obtained by the method is higher in coincidence degree with the actual power consumption result, and the power predicted consumption in the occurring time period can be calculated by the method. By combining a KPCA method and a linear regression model, under the condition of less city variable samples, the power consumption condition of the prediction year or time period is predicted, the instability and uncertainty of the existing power consumption prediction model are solved, and the error between the prediction result and the actual condition is reduced.
Description
Technical Field
The invention belongs to the technical field of power data analysis, and particularly relates to a power consumption prediction method based on KPCA and linear regression.
Background
With the rapid development of the economy of China, the total electricity consumption of China is also increasing continuously. The total power consumption is taken as energy required by modern social production and resident life, and the change of the total power consumption can indirectly measure the development of national economy and the improvement of the living standard of residents. The method accurately predicts the long-term total power demand of the society, can provide guidance for the state to make an economic development strategy and implement industrial structure transformation, and is also an important basis for the state to fulfill the international obligations of energy conservation, emission reduction, low carbon and environmental protection.
Therefore, it is realistic to predict the total amount of long-term power consumption. The power consumption prediction method is various, and the main methods can be divided into three types, namely a metering economy model, a machine learning model and a bottom-up comprehensive energy system optimization model.
However, the existing power consumption prediction models have great instability and uncertainty when used for predicting long-term power consumption, and the obtained prediction result has a large error from the actual situation.
Disclosure of Invention
The application discloses a power consumption prediction method based on KPCA and linear regression, which solves the problems of poor stability and accuracy and large error between a prediction result and an actual situation in the prior art when power consumption is predicted.
The application provides an electric power consumption prediction method based on KPCA and linear regression, including:
collecting city variables of a preset time period, comprising: the total social electricity consumption, the population growth rate, the town population proportion, the nominal GDP, the resident electricity price, the coal price, the second industry added value proportion, the third industry added value proportion and the per capita employment output value;
converting the city variable into a PCA processing variable after PCA calculation;
performing dimensionality reduction processing on the city variables through a KPCA kernel function in a KPCA method to obtain a group of KPCA processing variables;
and dividing the city variables, the PCA processing variables and the KPCA processing variables into a training set, a verification set and a prediction set respectively, bringing the training set, the verification set and the prediction set into a linear regression model, calculating the mean square error of each model of the training set, the verification set and the prediction set respectively, and selecting an optimal model according to the obtained mean square error to obtain the prediction result of the total social power consumption of the year to be predicted or the time period of the year to be predicted.
In one implementation, the city variables are classified according to power characteristics, population characteristics, economic characteristics, price characteristics, industry structure characteristics, and production efficiency characteristics.
In one implementation, the PCA computing process is:
Cai＝λiai
wherein, the original independent variable is Xn × p, n is the observation times, p is the sample dimension, Cp × p is the covariance matrix of Xn × p, and λ i and ai are the eigenvalue of Cp × p and the corresponding eigenvector respectively;
if the first m principal components are taken, the principal component matrix F is calculated as follows:
P＝(aij)p*m＝(a1,a2,a3,...,am)
F＝XP
where Pp m is a matrix formed by the largest first m eigenvector of C, Fn m is a principal component having m dimensions, ithFeature vectors for city variables; specifically, ithThe main components Fi are as follows:
Fi＝Z(X1)*a1i+Z(X2)*a2i+...+Z(Xp)*api
wherein Z (X) denotes the standardization of X, a1iIs ithThe first element of the feature vector.
Further, each variable of the PCA processing variables is called a principal component, the principal component has a first principal component as an original independent variable, if the first principal component information is insufficient, a factor is added to collectively represent the original independent variable, and the COV (factor1, factor2) is satisfied as 0.
Further, the factor is a variable having the same characteristics as the first principal component.
In one implementation, the KPCA kernel function is:
with a radial basis function kernel (RBF) k (x, y) exp (-y x-y | | | non-conducting phosphor2)；
Polynomial nucleus (poly) k (x, y) ═ xTy+c)d，d∈N，c≥0；
sigmoid nucleation, k (x, y) tanh (ax)Ty+γ)；
Cosine kernel:
wherein c and d in the polynomial kernel function, gamma (gamma) in RBF, alpha (alpha) and gamma (gamma) in sigmoid kernel function are all adjustable parameters.
Further, the KPCA kernel function is any semi-positive definite symmetric function.
In one implementation, the data in the prediction set is data of a year to be predicted or a time period of the year to be predicted; the training set is data from a first time point before the current time to a second time point earlier than the first time point; the verification set is data from a third time point before the current time to a fourth time point earlier than the third time point; the fourth time point is positioned between the first time point and the second time point, or the fourth time point is the same as the first time point; the third time point is later than the first time point.
In one implementation, the step of selecting an optimal model based on the obtained mean square error comprises: at most two groups of optimal models meeting preset conditions are selected, 50% of weight is respectively given to the two groups of models, and the optimal models are obtained by adding the two groups of optimal models.
Further, the optimal model is the model with the minimum mean square error and no descending trend of the prediction set.
According to the technical scheme, the power consumption prediction method based on the KPCA and the linear regression is characterized in that PCA and KPCA dimension reduction processing is respectively carried out on collected city variables, data subjected to the PCA and KPCA dimension reduction processing are divided into three data sets in different time periods, the data sets are substituted into the linear regression model, and the optimal model is selected to reflect the prediction result. According to the invention, through a mode of combining a KPCA method and a linear regression model, the instability and uncertainty of the existing power consumption prediction model are solved, the power consumption characteristics in real life can be better reflected, and the prediction result which is more consistent with the actual situation is obtained.
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In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without any creative effort.
FIG. 1 is a flow chart of a power consumption prediction method based on KPCA and linear regression;
fig. 2 is a data processing flow chart of a power consumption prediction method based on KPCA and linear regression.
Detailed Description
The invention discloses a power consumption prediction method based on KPCA and linear regression, which comprises the steps of processing collected city variables in a preset time period by PCA and KPCA to obtain PCA processing variables and KPCA processing variables, dividing the PCA processing variables and the KPCA processing variables into a training set, a test set and a prediction set, then bringing the training set, the test set and the prediction set into a linear regression model, and selecting an optimal model to obtain a prediction result.
Referring to fig. 1, a flow chart of a power consumption prediction method based on KPCA and linear regression is shown, and the specific steps shown in fig. 1 include:
s1: collecting city variables of a preset time period, comprising: the total social electricity consumption, the population growth rate, the town population ratio, the nominal GDP, the resident electricity price, the coal price, the second industry increased value ratio, the third industry increased value ratio and the per capita employment yield value. When the method is used for predicting the total electricity consumption in a certain time period, sample data of certain city variables needs to be collected, and the preset time period is specifically formulated according to the sample data needed by the predicted time period. The preset time period can be adjusted according to the sample size of the data required by the predicted time period.
Further, in some feasible embodiments, the city variables may be classified according to power characteristics, population characteristics, economic characteristics, price characteristics, industrial structure characteristics, and production efficiency characteristics in the following table. This has the advantage that when analyzing the impact on total power usage, the impact of a particular characteristic on total power usage is typically analyzed when the city variables contained in the particular characteristic are analyzed.
| Name of variable | Abbreviations | Feature(s) |
| Electricity consumption of whole society | Elec | Electric power characteristics |
| Rate of population growth | Popu | Demographic characteristics |
| Proportion of urban population | Urban | Demographic characteristics |
| Nominal GDP | GDP | Economic features |
| Residential electricity price | ResPri | Price characteristics |
| Coal price | CoaPri | Price characteristics |
| Second industry increase in value to percentage | SecInd | Structural features of industry |
| Ratio of increase value of third production | ThiInd | Structural features of industry |
| Average employment output value | Employ | Characteristic of production efficiency |
After the prediction result of the preset time period is obtained by the method, the obtained optimal model and the characteristics of the urban variables are specifically analyzed, the closeness degree of the characteristics of the specific urban variables to the relation of the total power consumption and the sequencing of the importance levels influencing the total power consumption are obtained by combining the analysis result, and the criticality of the urban variables of the specific characteristics to the total power consumption can be more visually seen. In general, important features that affect total power usage can be divided into three categories. The first category is economic and production efficiency. The second category is demographic and price characteristics. The third category is the industry structural feature. But the results obtained will vary according to the specific situation in different cities. When a specific feature is analyzed, the respective variation trends of the city variables in the preset time period included in the feature are usually combined.
Referring to fig. 2, a data processing flow chart of a power consumption prediction method based on KPCA and linear regression is shown. The flow of the PCA processing variable and the KPCA processing variable obtained by processing the city variables in the whole method and bringing the processed variables into a regression model and the finally output model are described in detail.
S21: converting the city variable into a PCA processing variable after PCA calculation; PCA is a statistical method that transforms a set of variables that may be correlated into a set of linearly uncorrelated variables by orthogonal transformation. Firstly, Pearson correlation coefficients among variables are calculated, and the relation among the variables is analyzed. The results show that the relationship between the variables is close. In practice, the average of the absolute values of the correlation coefficients between the variables is as high as 0.81. Wherein, the absolute values of the correlation coefficients of the power consumption of the whole society, the urban population ratio, the nominal GDP, the third industry added value ratio and the per capita employment yield value are all more than 0.9, and the absolute values of the correlation coefficients of the power consumption of the whole society, the population growth rate, the resident electricity price and the coal price are all more than 0.8. Therefore, it is necessary to perform dimension reduction on the independent variables. Otherwise, the assumption of independent and equal distribution of variables in the statistical regression cannot be satisfied.
The PCA calculation process is as follows:
Cai＝λiai
wherein, the original independent variable is Xn × p, n is the observation times, p is the sample dimension, Cp × p is the covariance matrix of Xn × p, and λ i and ai are the eigenvalue of Cp × p and the corresponding eigenvector respectively;
if the first m principal components are taken, the principal component matrix F is calculated as follows:
P＝(aij)p*m＝(a1,a2,a3,...,am)
F＝XP
where Pp m is a matrix formed by the largest first m eigenvector of C, Fn m is a principal component having m dimensions, ithFeature vectors for city variables; specifically, ithThe main components Fi are as follows:
Fi＝Z(X1)*a1i+Z(X2)*a2i+...+Z(Xp)*api
wherein Z (X) denotes the standardization of X, a1iIs ithThe first element of the feature vector.
S22: performing dimensionality reduction processing on the city variables through a KPCA kernel function in a KPCA method to obtain a group of KPCA processing variables; KPCA generally defines an urban variable as X, maps the urban variable non-linearly through a kernel function phi and to a higher dimensional space phi (X), makes phi (X) linearly separable, and then performs PCA dimension reduction on phi (X). KPCA can reduce the dimensionality of samples non-linearly for processing linearly indivisible data sets.
The KPCA kernel function is as follows:
with a radial basis function kernel (RBF) k (x, y) exp (-y x-y | | | non-conducting phosphor2)；
Polynomial nucleus (poly) k (x, y) ═ xTy+c)d，d∈N，c≥0；
sigmoid nucleation, k (x, y) tanh (ax)Ty+γ)；
Cosine kernel:
wherein c and d in the polynomial kernel function comprise gamma (gamma) in the radial basis function kernel, and alpha (alpha) and gamma (gamma) in the sigmoid kernel function are adjustable parameters.
S3: the method comprises the steps of dividing initially collected city variables, PCA processing variables and KPCA processing variables into a training set, a verification set and a prediction set respectively. The data in the prediction set is data of a year to be predicted or a time period of the year to be predicted; the training set is data from a first time point before the current time to a second time point earlier than the first time point; the verification set is data from a third time point before the current time to a fourth time point earlier than the third time point; the fourth time point is positioned between the first time point and the second time point, or the fourth time point is the same as the first time point; the third time point is later than the first time point. Overall, the time point or period of the data of the training set is earlier than the time point or period of the data of the validation set. For example, the prediction set data is 2016-; the third time point of the test set is set to 2001, the fourth time point is set to 2015, and the test set is data between 2001 and 2015.
Further, the fourth point in time of the data of the validation set is between the first point in time of the data of the training set and a second point in time earlier than the first point in time, so that the data of the validation set comprises data of a part of the training set that is used as initial transition data of the validation set between the first point in time and the third point in time.
In the above practical example, the training set is data between 1980 and 2015, the test set is data between 2001 and 2015, and the test set includes data between 2001 and 2005, so that the data between 2001 and 2005 is used as an initial transition data in the test set, which facilitates to observe the amplitude ratio variation of the data between the training set and the test set, and avoids the fluctuation and the too large variation of the data variation trend of the training set and the test set due to different time periods.
S4: the city variables, PCA processing variables, and the training set, verification set, and prediction set of the KPCA processing variables are brought into the linear regression model, in the present application, the linear regression model can be selected from various types, and the following description is given by using five common types: linear regression, random forest algorithm, neural network, GBDT algorithm, and SVM algorithm. Respectively bringing the training set, the verification set and the prediction set of the city variables, the PCA processing variables and the KPCA processing variables into each linear regression model, calculating to obtain the mean square error of all the models, and counting the rising or falling trend of all the model prediction sets.
S5: and selecting an optimal model according to the obtained mean square error and the change trend of the prediction set to obtain the prediction result of the power consumption of the whole society of the year to be predicted or the time period of the year to be predicted.
Referring to the following table, taking a set of actual city variables as an example, the city variables, PCA processing variables, and KPCA processing variables are respectively divided into a training set, a verification set, and a prediction set, and are brought into a linear regression model to obtain all model results.
As can be seen from the above table, by screening all the obtained models, a model with a small mean square error and no descending trend of the prediction set is selected, and two optimal models, a polynomial Poly _ KPCA and linear regression combination model, and a cosi _ KPCA and linear regression combination model, are finally determined through comparison. And giving 50% weight to each model, and adding the two models to obtain a prediction result of the total electricity consumption of the current prediction year. The purpose of this is that if a model is selected to output the prediction result of the total power consumption of the predicted year, it will have contingency and will have a large error with the total power consumption of the actual situation. And the two optimal models are selected, and the prediction result obtained by adding the two optimal models is better matched with the total power consumption under the actual condition.
In some possible embodiments, each variable of the PCA processing variables is called a principal component, the principal component has a first principal component (factor1,1) as an original independent variable, and if the first principal component is insufficient, a second principal component is added as a factor (factor2) to jointly represent the original independent variable, for example, in all data after the PCA calculation processing, the principal component representing the population growth rate is used as an initial original independent variable, and if the information expressed by the principal component representing the population growth rate is insufficient, corresponding supplementation is required, specifically, a new principal component is introduced as a factor, and the condition of COV (factor1, factor2) 0 is satisfied. If the introduction of the new principal component or the expression information is insufficient, the introduction of other principal components is continued as new factors.
Further, the factor (factor2) is a variable having the same characteristics as the first principal component. In the above example, the principal component representing the population growth rate is used as the initial original independent variable, the factor and the initial original independent variable are intended to jointly represent a new original independent variable, the principal component with the same characteristics as the initial original independent variable is selected as the factor, and the principal component representing the proportion of the town population with the same characteristics as the population is selected as the factor because the population growth rate belongs to the population characteristics.
In some possible embodiments, the KPCA kernel function is an arbitrary semi-positive definite symmetric function. In the step of performing KPCA dimension reduction processing on the city variable, it is necessary to determine whether the selected kernel function meets a kernel criterion, that is, whether the selected kernel function is a semi-positive definite symmetric function. Because the model parameters of KPCA are adjustable, the model effect has a larger optimization space.
Further, any semi-positive definite symmetric function meeting the KPCA condition is selected as a new kernel function to be added to the KPCA method to reduce the dimensions of the city variables, or any semi-positive definite symmetric function meeting the KPCA condition is selected as a new kernel function to replace the original kernel function of the KPCA. After replacement, KPCA processing data obtained by a KPCA method is brought into an optimal model obtained by a linear regression model to meet the prediction effect.
In some possible embodiments, verification of the obtained prediction is also required. Analyzing eight variables except the power consumption of the whole society, classifying the variables with stable ascending trend and unstable changing trend along with the time, calculating the correlation coefficient between the data change of each variable and the power consumption of the whole society, and performing specific analysis by combining the self characteristics of a target city.
In the above practical example, the linear equations of the original independent variables (f1, f2, f3) and the normalized total social power consumption Elec are listed according to the two optimal models.
y＝1.156+0.580*f1-0.578*f2-0.879*f3；
y＝1.156+6.654*f1+5.691*f2+0.435*f3；
The first principal component f1 of the linear equation for the first Poly KPCA and the linear equation for the second Cosin _ KPCA shows a relatively steady growth trend, indicating a continuous increase in total electrical consumption. f2 and f3 show alternating characteristics of growth and decline to describe fluctuations in power consumption evolution. The above-mentioned f1, f2, f3 can better represent the characteristics of power consumption in real life.
Furthermore, eight variables except the total social electricity consumption analyzed by the characteristics of the city are combined, the results except the total social electricity consumption are compared with the prediction result obtained by adding the obtained optimal model, and if the match condition is better, the prediction result is proved to be more accurate.
According to the technical scheme, the power consumption prediction method based on the KPCA and the linear regression is characterized in that collected city variables in a preset time period are processed through the PCA and the KPCA to obtain PCA processing variables and KPCA processing variables, the PCA processing variables and the KPCA processing variables are divided into a training set, a test set and a prediction set and then are brought into a linear regression model, and an optimal model is selected to obtain a prediction result. The verification proves that the predicted result obtained by the method is higher in coincidence degree with the actual power consumption result, and the power predicted consumption in the occurring time period can be calculated by the method. By combining a KPCA method and a linear regression model, under the condition of less city variable samples, the power consumption condition of the prediction year or time period is predicted, the instability and uncertainty of the existing power consumption prediction model are solved, and the error between the prediction result and the actual condition is reduced.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
Claims (10)
1. A power consumption prediction method based on KPCA and linear regression is characterized by comprising the following steps:
collecting city variables of a preset time period, comprising: the total social electricity consumption, the population growth rate, the town population proportion, the nominal GDP, the resident electricity price, the coal price, the second industry added value proportion, the third industry added value proportion and the per capita employment output value;
converting the city variable into a PCA processing variable after PCA calculation;
performing dimensionality reduction processing on the city variables through a KPCA kernel function in a KPCA method to obtain a group of KPCA processing variables;
and dividing the city variables, the PCA processing variables and the KPCA processing variables into a training set, a verification set and a prediction set respectively, bringing the training set, the verification set and the prediction set into a linear regression model, calculating the mean square error of each model of the training set, the verification set and the prediction set respectively, and selecting an optimal model according to the obtained mean square error to obtain the prediction result of the total social power consumption of the year to be predicted or the time period of the year to be predicted.
2. The method of claim 1, wherein the method further comprises: and classifying the city variables according to electric power characteristics, population characteristics, economic characteristics, price characteristics, industrial structure characteristics and production efficiency characteristics.
3. The method of claim 1, wherein the PCA is calculated by:
Cai＝λiai
wherein the original independent variables are Xn × p, n is the observation times, p is the sample dimension, Cp × p is the covariance matrix of Xn × p, λiAnd aiCharacteristic values and corresponding characteristic vectors, respectively Cp × p;
if the first m principal components are taken, the principal component matrix F is calculated as follows:
P＝(aij)p*m＝(a1，a2，a3，...，am)
F＝XP
where Pp m is a matrix formed by the largest first m eigenvector of C, Fn m is a principal component having m dimensions, ithFeature vectors for city variables; specifically, ithMain component F of (2)iComprises the following steps:
Fi＝Z(X1)*a1i+Z(X2)*a2i+...+Z(Xp)*api
wherein Z (X) denotes the standardization of X, a1iIs ithThe first element of the feature vector.
4. A KPCA and linear regression based power consumption prediction method according to claim 3, characterized in that each of the PCA process variables is called principal component, the principal component has the first principal component (factor1,1) as original independent variable, if the first principal component information is insufficient, the added factors (factor2) collectively represent the original independent variables, and COV (factor1, factor2) is satisfied as 0.
5. A method for power consumption prediction based on KPCA and linear regression according to claim 4, wherein said factor (factor2) is a variable with the same characteristics as the first principal component.
6. A method for power consumption prediction based on KPCA and linear regression as claimed in claim 1, wherein said KPCA kernel function is:
with a radial basis function kernel: k (x, y) ═ exp (- γ | | | x-y | | non-conducting phosphor2)；
A polynomial kernel: k (x, y) ═ xTy+c)d，d∈N，c≥0；
sigmoid nucleation: k (x, y) ═ tanh (α x)Ty+γ)；
Cosine kernel:
wherein c and d in the polynomial kernel function, gamma (gamma) in RBF, alpha (alpha) and gamma (gamma) in sigmoid kernel function are all adjustable parameters.
7. A method for power consumption prediction based on KPCA and linear regression according to claim 6, wherein said KPCA kernel function is any semi-positive definite symmetric function.
8. A KPCA and linear regression based power consumption prediction method according to claim 1, characterized in that the data in the prediction set are data of the year to be predicted or the time period of the year to be predicted; the training set is data from a first time point before the current time to a second time point earlier than the first time point; the verification set is data from a third time point before the current time to a fourth time point earlier than the third time point; the fourth time point is positioned between the first time point and the second time point, or the fourth time point is the same as the first time point; the third time point is later than the first time point.
9. The method of claim 1, wherein the step of selecting the optimal model based on the mean square error comprises: at most two groups of optimal models meeting preset conditions are selected, 50% of weight is respectively given to the two groups of models, and the optimal models are obtained by adding the two groups of optimal models.
10. The method of claim 9, wherein the optimal model is a minimum mean square error model and no downward trend in the prediction set.
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