CN108764528A - A kind of Daily treatment cost interval prediction method of allowed for influencing factors analysis - Google Patents
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Abstract
The invention discloses a kind of Daily treatment cost interval prediction methods of allowed for influencing factors analysis, first, the trend curve of load data is extracted using median filtering method, then principal component analysis is carried out to impact factor and trend term load, several principal components are integrated out as input, trend term load realizes the trend term prediction of load as output in support vector machines；Then trend term is subtracted from load curve, obtains random entry, and interval prediction is carried out using Markov model to random entry；Then trend term predicted value is added with random entry forecast interval to get to the forecast interval value of load；The upper and lower envelope of historical load curve is extracted using cubic spline interpolation, point in sampling originally carries out Markov interval prediction, the upper and lower limit of forecast interval and upper and lower envelope are compared, calculate error, finally the error is added in original forecast interval to get to final forecast interval.Prediction result of the present invention is stablized, and precision of prediction is high.
Description
Technical Field
The invention relates to the technical field of energy prediction, in particular to a daily maximum load interval prediction method based on influence factor analysis.
Background
Because various uncertain factors are contained in the power system, decision-making work necessarily faces risks to a certain degree, and uncertainty of power demand must be considered during decision-making. The results of traditional deterministic prediction methods do not reflect the uncertainty of the demand, and interval prediction can meet this objective requirement. The result of the interval prediction is not a simple deterministic value, but an interval, and the interval corresponds to a certain level of probability confidence level, which can describe the possible range of future prediction results. According to the interval prediction result, a power system decision maker can better recognize uncertainty and risk factors which may exist in future loads when performing production planning, system safety analysis and other work, so that a more reasonable decision can be made in time. Therefore, the method has important theoretical significance and practical value for analyzing the change rule of the load of the power system, researching the prediction method of the power load interval and realizing the uncertainty prediction of the power load.
The current interval prediction method has the following defects:
1. the calculation is complex;
2. the hypothesis is strong;
3. the calculation time is long.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a daily maximum load interval prediction method based on influence factor analysis, so that the load of a power distribution area can be accurately predicted in the middle period.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the daily maximum load interval prediction method based on influence factor analysis is characterized by comprising the following steps
Downloading historical load data to obtain a historical load curve;
finding out a trend curve of the historical load curve by using a median filtering method to obtain a trend item load;
carrying out principal component analysis on the influence factors and the trend item loads in the power system, integrating a plurality of principal components, taking the plurality of principal components as input and the trend item loads as output, and realizing the trend item prediction of the loads on a support vector machine;
subtracting the trend item load from the historical load curve to obtain a random item; averagely dividing the curve of the random item into a plurality of regions according to the maximum and minimum amplitude as the upper and lower limits, and calculating a transition probability matrix, wherein the region with the maximum transition probability is the prediction region of the random item;
carrying out interval prediction on the random item by using a Markov model to obtain a trend item prediction value of the load;
and adding the predicted value of the trend item of the load and the prediction interval of the random item to obtain an original prediction interval.
The method further comprises the following steps:
extracting upper and lower envelope lines of the historical load curve by a cubic spline interpolation method;
comparing the upper limit and the lower limit of the original prediction interval with the upper envelope line and the lower envelope line, and calculating an error;
and adding the error into the original prediction interval to obtain a final prediction interval.
The impact factors include the area covered by the load, and the industrial/commercial/residential power consumption ratio.
The process of analyzing the main components of the influence factors and the trend item loads in the power system and integrating a plurality of main components is as follows:
the first step is as follows: assuming that n samples and p variables are provided, the observation data matrix is:
wherein X is an observation data matrix, XijIs the value of the jth variable for the ith sample.
The second step is that: calculating a matrix of correlation coefficients for the samples
Assuming that the original data is still represented by X after normalization, the correlation coefficient of the normalized data is:
wherein r isijIs the correlation coefficient of the ith variable and the jth variable.
The third step: calculating characteristic value (lambda) of correlation coefficient matrix R by using Jacobian method1,λ2,…,λp) And the corresponding featuresEigenvector ai＝[ai1,ai2,…,aip]，i＝1，2，…，p；
The fourth step: selecting important principal components, and writing a principal component expression;
the first k principal components are selected according to the magnitude of the accumulated contribution rate of each principal component, wherein the contribution rate refers to the proportion of the variance of a certain principal component to the total variance, namely the proportion of a certain characteristic value to the total characteristic value, namely
Wherein λ isiIs the characteristic value of the ith variable.
The larger the contribution rate is, the stronger the information of the original variable contained in the principal component is; the selection of the number k of the principal components is mainly determined according to the accumulated contribution rate of the principal components, and the accumulated contribution rate is required to reach more than 85 percent;
the principal component expression is as follows:
Zi＝ai1×x1+ai2×x2+…+aip×xp
wherein Z isiIs the ith main component, xjIs the jth variable, aijIs the feature vector of the jth variable in the ith principal component.
Compared with the prior art, the invention has the beneficial effects that:
1. the prediction result is stable, and the prediction precision is high;
2. the prediction method is a data-driven and self-adaptive method, and the prediction result does not depend on the prior knowledge of a user;
3. the invention has simple, visual and easy operation;
4. the method has strong guiding significance on the actual situations of power grid dispatching, planning and the like.
Drawings
FIG. 1 is a flowchart of a daily maximum load interval prediction method based on impact factor analysis according to the present invention;
fig. 2 is a graph of ideal forecast results and actual data.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and detailed description.
Example (b):
as shown in fig. 1, the method for predicting the daily maximum load interval based on the impact factor analysis provided in this embodiment specifically includes the following steps:
1) and finding out a trend curve of the historical load curve by using a median filtering method to obtain a trend item load, and subtracting the trend item load from the historical load curve to obtain a random item. Assuming that the history curve f (t), t is 1,2, …, N and the trend curve is M (t), then
Where 2d +1 is the window length.
2) Carrying out principal component analysis on the influence factors (including the area covered by the load, the industrial/commercial/residential electricity utilization ratio and the like) and the trend item load to integrate a plurality of principal components;
the first step is as follows: assuming that n samples and p variables are provided, the observation data matrix is:
wherein X is an observation data matrix, XijIs the value of the jth variable for the ith sample.
The second step is that: calculating a matrix of correlation coefficients for the samples
Assuming that the original data is still represented by X after normalization, the correlation coefficient of the normalized data is:
wherein r isijIs the correlation coefficient of the ith variable and the jth variable.
The third step: calculating characteristic value (lambda) of correlation coefficient matrix R by using Jacobian method1,λ2,…,λp) And corresponding feature vector ai＝[ai1,ai2,…,aip]，i＝1，2，…，p；
The fourth step: selecting important principal components, and writing a principal component expression;
however, because the variance of each principal component is decreased and the amount of information contained is also decreased, in the actual analysis, the first k principal components are selected according to the magnitude of the cumulative contribution rate of each principal component, instead of selecting p principal components, where the contribution rate refers to the proportion of the variance of a principal component to the total variance, and actually, the proportion of a feature value to the total feature value, that is, the proportion of the feature value to the total feature value
Wherein λ isiIs the characteristic value of the ith variable.
The larger the contribution rate is, the stronger the information of the original variable contained in the principal component is; the selection of the number k of the principal components is mainly determined according to the accumulated contribution rate of the principal components, and the accumulated contribution rate is generally required to reach more than 85 percent, so that the comprehensive variables can be ensured to include most of information of the original variables;
the principal component expression is as follows:
Zi＝ai1×x1+ai2×x2+…+aip×xp
wherein Z isiIs the ith main component, xjIs the jth variable, aijIs the feature vector of the jth variable in the ith principal component.
3) Taking the principal component and the historical load data at the time t-1 as input, taking the historical load data at the time t as output, and training a model; based on the trained model, taking principal components and load data immediately before the prediction point as input, and predicting by the model to obtain a trend item prediction result of the load;
4) and averagely dividing the random item curve into 3 intervals according to the maximum and minimum amplitude as the upper limit and the lower limit, and calculating a transition probability matrix, wherein the interval with the maximum transition probability is the prediction interval of the random item.
Wherein omega1，Ω2，Ω3Represents interval 1, interval 2, interval 3.
The transition probability matrix can be expressed as
Wherein A isij(i-1, 2, 3; j-1, 2,3) indicates the probability that the value S (t-1) at the previous time is located in the i interval and the value S (t) at the next time is located in the j interval. Namely:
wherein, BijAnd (t) judging whether the value S (t-1) at the previous moment is in the interval i and the value S (t) at the next moment is in the variable of the interval j, if so, the value is 1, and if not, the value is 0.
If the load value of the day before the forecast is in the ith interval, forecasting the load random term interval S of the dayΩ(t) is Ai1,Ai2,Ai3The interval in which the maximum value of (1) is located.
5) The sum of the predicted value of the trend item of the load and the prediction interval of the random item is an original prediction interval.
Wherein,for trend term prediction, SΩ(t) a load random term interval of the prediction day,is the original prediction interval.
6) Finding out the upper and lower envelope lines y (t) ═ y (y) of the load curve by a Cubic Spline Interpolation (Spline Interpolation for short), which is a process of obtaining a curve function set by solving a three-bending moment equation set mathematically through a smooth curve of a series of shape value points)l(t)yh(t)]；
7) And calculating the error between the upper envelope line and the lower envelope line and the upper limit and the lower limit of the original prediction interval.
8) The sum of the original prediction interval and the error is the final prediction interval.
In the prediction model, the prediction accuracy of the prediction method is evaluated in terms of both accuracy and precision.
1. Accuracy of
If the actual value of the predicted point falls between the upper limit and the lower limit of the prediction result, the prediction is accurate.
Accuracy c is defined as follows:
where m is the total number of predictions.
2. Accuracy of measurement
Adjusting the distance proportion:
the distance proportion is adjusted downwards:
taking the average absolute value, standard deviation, maximum value and minimum value of the up/down distance proportion as evaluation standards, and respectively marking the evaluation standards asstd(D1)，D1max，D1minAndstd(D2)，D2max，D2min。
among the eight indexes, the smaller the value is, the smaller the threshold value between the predicted value and the true value is, the more stable the prediction is, and the accuracy of the prediction is embodied.
From the above analysis, it can be seen that there is a mutual constraint relationship between accuracy and precision, and a model with high accuracy will inevitably result in low precision, while a model with high precision will be limited in accuracy. How to make a trade-off selection between the two requires analysis of the specific situation.
Fig. 2 is a graph of ideal forecast results and actual data. As can be seen from the figure, in most cases, the true value is located between the upper limit and the lower limit of the prediction interval, and the accuracy is extremely high. The upper limit and the lower limit of the prediction interval are well fit with the fluctuation condition of a real curve, the error is small, and the accuracy is high.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.
Claims (4)
1. The daily maximum load interval prediction method based on influence factor analysis is characterized by comprising the following steps
Downloading historical load data to obtain a historical load curve;
finding out a trend curve of the historical load curve by using a median filtering method to obtain a trend item load;
carrying out principal component analysis on the influence factors and the trend item loads in the power system, integrating a plurality of principal components, taking the plurality of principal components as input and the trend item loads as output, and realizing the trend item prediction of the loads on a support vector machine;
subtracting the trend item load from the historical load curve to obtain a random item; averagely dividing the curve of the random item into a plurality of regions according to the maximum and minimum amplitude as the upper and lower limits, and calculating a transition probability matrix, wherein the region with the maximum transition probability is the prediction region of the random item;
carrying out interval prediction on the random item by using a Markov model to obtain a trend item prediction value of the load;
and adding the predicted value of the trend item of the load and the prediction interval of the random item to obtain an original prediction interval.
2. The impact factor analysis-based daily maximum load interval prediction method of claim 1, further comprising:
extracting upper and lower envelope lines of the historical load curve by a cubic spline interpolation method;
comparing the upper limit and the lower limit of the original prediction interval with the upper envelope line and the lower envelope line, and calculating an error;
and adding the error into the original prediction interval to obtain a final prediction interval.
3. The method for predicting the daily maximum load interval based on the impact factor analysis as claimed in claim 1 or 2, wherein the impact factors include the area covered by the load and the industrial/commercial/residential power consumption ratio.
4. The daily maximum load interval prediction method based on impact factor analysis according to claim 1 or 2, wherein the main component analysis is performed on the impact factors and the trend item loads in the power system, and the process of integrating a plurality of main components is as follows:
the first step is as follows: assuming that n samples and p variables are provided, the observation data matrix is:
wherein X is an observation data matrix, XijIs the value of the jth variable for the ith sample.
The second step is that: calculating a matrix of correlation coefficients for the samples
Assuming that the original data is still represented by X after normalization, the correlation coefficient of the normalized data is:
wherein r isijIs the correlation coefficient of the ith variable and the jth variable.
The third step: calculating characteristic value (lambda) of correlation coefficient matrix R by using Jacobian method1,λ2,…,λp) And corresponding feature vector ai＝[ai1,ai2,…,aip]，i＝1，2，…，p；
The fourth step: selecting important principal components, and writing a principal component expression;
the first k principal components are selected according to the magnitude of the accumulated contribution rate of each principal component, wherein the contribution rate refers to the proportion of the variance of a certain principal component to the total variance, namely the proportion of a certain characteristic value to the total characteristic value, namely
Wherein λ isiIs the characteristic value of the ith variable.
The larger the contribution rate is, the stronger the information of the original variable contained in the principal component is; the selection of the number k of the principal components is mainly determined according to the accumulated contribution rate of the principal components, and the accumulated contribution rate is required to reach more than 85 percent;
the principal component expression is as follows:
Zi＝ai1×x1+ai2×x2+…+aip×xp
wherein Z isiIs the ith main component, xjIs the jth variable, aijIs the feature vector of the jth variable in the ith principal component.
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Application publication date: 20181106 |