CN111259340B - Saturation load prediction method based on logistic regression - Google Patents
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Abstract
A saturated load prediction method based on logistic regression utilizes historical load data to estimate model parameters to obtain a logistic regression load prediction model through parameter conversion; simplifying a logistic regression model; obtaining a probability model of the simplified model if Gaussian white noise is adopted; the obtained probability model and the Neyman-Fisher factorization theorem are utilized to obtain the full statistics of one parameter of the model; using the sufficient statistics of the parameter, the values of the other two parameters can be obtained using the least squares method assuming that the general solution is known; the parameter values meet the constraint conditions within a certain value range, and the parameters which obviously do not accord with the constraint formula are ignored to obtain a proper parameter range; and taking the parameter value of the optimal error value as a model parameter for all the parameters, and obtaining a final logistic model. The invention has better model prediction precision and smaller error for the existing data.
Description
Technical Field
The invention relates to a power load prediction method. In particular to a saturated load prediction method based on logistic regression, which utilizes historical load data to estimate model parameters to obtain a logistic regression load prediction model.
Background
Load prediction is one of important works of the electric power department, and accurate load prediction can bring high social benefits and economic benefits. Meanwhile, load prediction is the basis of power grid planning, and the utility and efficiency of a power grid planning project are directly affected. The load prediction has the advantages of large data information quantity, multiple uncertain factors, wide related fields, and great significance in improving the quality and speed of power distribution network planning, and can realize the rapid and accurate prediction of the load. Accurate load prediction has a great guiding effect on planning projects of government power grids.
The main method of load prediction is grey Verhulst prediction or using neural networks to implement load prediction. Compared with a neural network model, the model of logistic regression does not need a large amount of historical data, and compared with the Verhulst model, the position with higher prediction accuracy of logistic is not limited to the previous M predicted value in the whole prediction sequence. In the existing article based on logistic regression load prediction, a 3-point or 4-point method is adopted to obtain the parameters of the logistic curve, however, the method cannot avoid abnormal or erroneous data, and therefore, has room for improvement. From the theoretical and demonstration researches of domestic and foreign scholars for many years, the logistic model has very reliable identification, prediction and popularization capabilities, is simple in model form, has only three parameters in logistic equation, has very wide application fields, and can be applied to load prediction.
Disclosure of Invention
The invention aims to solve the technical problem of providing a saturated load prediction method based on logistic regression, which has better model prediction precision and smaller error for the existing data.
The technical scheme adopted by the invention is as follows: a saturation load prediction method based on logistic regression comprises the following steps:
1) Load data of a power grid are collected, and an improved logistic regression model and constraint conditions are given;
2) Determining the range of a parameter c in the logistic regression model according to the improved logistic regression model and the constraint condition;
3) Substituting each obtained c into the general solution t=m + X+ct 1 Then utilize the least square formula
Obtaining parameters a and b in a logistic regression model, and substituting the obtained results into a formula
Obtaining a parameter m in a logistic regression model;
wherein T is a matrix of Nx1,
r is the load increasing speed, t is the predicted year vector, m=1/k, k is the regional maximum saturated load, x i The reciprocal of the load y in the ith year, N is the total year of the data;
and c meets the constraint condition of the improved logistic regression model within a certain value range, and the parameter ranges of m, a and b are obtained.
4) Judging whether the calculated results m, a and b meet the constraint condition m>0，a>0，b<0, if the direct update c is not satisfied, jumping to the step 3); if yes, calculating a combination form of the model inspection indexes
Then updating c, and jumping to the step 3);
wherein, C is posterior difference test:
wherein S is 1 Is the standard deviation of historical load data, S 2 Standard deviation of the load error sequence; q is the relative residual:
Wherein->
Error->
In (1) the->
As load predicted values, x (i) is an actual load value; p is the precision:
5) Comparing all S meeting constraint conditions, substituting m, a, b=argmin S corresponding to the minimum S into the improved logistic regression model
And the method is used for predicting the maximum saturation load of the regional power grid.
According to the saturation load prediction method based on logistic regression, a logistic probability model is considered, and parameters of the model are obtained according to a Neyman-Fisher factorization theorem and historical load data estimation. The advantages are that:
1. the method can estimate the parameters of the logistic regression model according to the characteristics of the model and the historical data, and compared with a neural network model, the method does not need a large amount of historical data, and compared with a Verhulst model, the predicted value with higher prediction precision in the method is not limited to the first predicted values in the whole predicted sequence.
2. Compared with a gray Verhulst model, the method provided by the invention has better model prediction precision and smaller error for the existing data.
Drawings
FIG. 1 is a flow chart of a method of saturating load prediction based on logistic regression of the present invention;
FIG. 2a is a plot of the S-value parameter value for each iteration;
FIG. 2b is a plot of the parameter m for each iteration as a function of the number of iterations;
FIG. 2c is a plot of the parameter a for each iteration as a function of the number of iterations;
FIG. 2d is a plot of each iteration parameter b as a function of the number of iterations;
FIG. 3 is a predictive comparison graph;
fig. 4 is a graph of the prediction results of the present invention.
Detailed Description
The following describes a method for predicting saturation load based on logistic regression in detail with reference to examples and drawings.
The invention discloses a saturation load prediction method based on logistic regression, which comprises the following steps:
1) Load data of a power grid are collected, and an improved logistic regression model and constraint conditions are given; wherein,,
the improved logistic regression model is as follows:
wherein y is the load amount of the corresponding year; m=1/k, k being the regional maximum saturation load;
r is the load increasing speed of the load, y 0 Is t 0 Annual load capacity; b= -r;
the constraint conditions are as follows: m >0, a >0, b <0.
2) Determining the range of a parameter c in the logistic regression model according to the improved logistic regression model and the constraint condition; comprises calculating abs (min (M + X)), initializing c=abs (min (M) + X))+δ，
Wherein M is + Is a pseudo-inverse of M, M is a matrix of NxN, X is a matrix of Nx1, δ is an iteration step, and the ratio abs (min (M + X)) are two orders of magnitude smaller, wherein:
3) Substituting each obtained c into the general solution t=m + X+ct 1 Then utilize the least square formula
Obtaining parameters a and b in a logistic regression model, and substituting the obtained results into a formula
Obtaining a parameter m in a logistic regression model;
said formula
The derivation is as follows:
according to the general model x=m+αt b +η, where η is noise subject to a mean of 0 and variance of δ 2 The probability model for obtaining x is:
the sufficient statistics of m using the factorization theorem are:
the factorization theorem yields:
to approximate the real parameters, an unbiased estimate of m is used, namely:
the general solution t=m + X+ct 1 The derivation process of (2) is as follows:
will be
Substitution formula x=m+αt b Is obtained by:
order the
Namely: mt=x, wherein M + As pseudo-inverse matrix, M + X is a solution, ct 1 To go through, M + Is the pseudo-inverse of M, M is a matrix of NxN, and X is a matrix of Nx 1.
Let mt=0 to get t 1 Values of (2)
The method comprises the following steps:
wherein T is a matrix of Nx1,
r is the load increasing speed, t is the predicted year vector, m=1/k, k is the regional maximum saturated load, x i The reciprocal of the load y in the ith year, N is the total year of the data;
and c meets the constraint condition of the improved logistic regression model within a certain value range, and the parameter ranges of m, a and b are obtained.
4) Judging whether the calculated results m, a and b meet the constraint condition m>0，a>0，b<0, if the direct update c is not satisfied, jumping to the step 3); if yes, calculating a combination form of the model inspection indexes
Then updating c, and jumping to the step 3);
wherein, C is posterior difference test:
wherein S is 1 Is the standard deviation of historical load data, S 2 Standard deviation of the load error sequence; q is the relative residual:
Wherein->
Error->
In (1) the->
As load predicted values, x (i) is an actual load value; p is the precision:
5) Comparing all S meeting constraint conditions, substituting m, a, b=argmin S corresponding to the minimum S into the improved logistic regression model
And the method is used for predicting the maximum saturation load of the regional power grid.
Examples are given below:
and step 1, collecting load data of a power grid, and determining the range of c according to constraint conditions and actual conditions.
The load data used was [430.40,454.26,482.94,511.20,559.42,598.99,655.71,745.97,821.44,911.97,980.15,1072.38,1138.22,1153.38,1295.87 ]]The unit is (100 GW x h), the data source is the historical data of the power consumption requirement in the area governed by a certain power grid, and c is initialized>abs(min(M + X)), c is initialized to a value of 6.77×10 -4 Delta is 1.0X10 -6 The number of iterations n=700.
Step 2: and further determining the range of the parameters m, a and b according to the obtained c value and obtaining the optimal parameter value.
Substituting the value of c into the formula from small to large in sequence: t=m + X+ct 1 Wherein M is + X is a special solution and can be directly substituted into data to be obtained. And according to
And +.>
The value of a, b can be obtained from the value of c by the least square method. By the formula->
The value of m at this value of c can be obtained. Updating the value of c, c=c+δ. The number of iterations of each corresponds to m, a, b, S as shown in fig. 2a, 2b, 2c, 2 d.
Step 3: substituting the obtained m, a and b into an S formula, and substituting the optimal parameter value corresponding to S into a logistic load prediction model.
FIG. 3 is a graph of the method of the present invention in comparison to GM (1, 1) and the grey Verhulst model predictions.
By knowing the load of the year before the high speed increase period, the load result after prediction by the complete prediction model is shown in fig. 4.
Claims (3)
1. A saturation load prediction method based on logistic regression is characterized by comprising the following steps:
1) Load data of a power grid are collected, and an improved logistic regression model and constraint conditions are given; wherein,,
the improved logistic regression model is as follows:
wherein y is the load amount of the corresponding year; m=1/k, k being the regional maximum saturation load;
r is the load increasing speed of the load, y 0 Is t 0 Annual load capacity; b= -r;
the constraint conditions are as follows: m >0, a >0, b <0;
2) Determining the range of a parameter c in the logistic regression model according to the improved logistic regression model and the constraint condition; comprises calculating abs (min (M + X)), initializing c=abs (min (M) + X))+δ，
Wherein M is + Is a pseudo-inverse of M, M is a matrix of N X N, X is a matrix of N X1, δ is an iteration step, and the ratio abs (min (M + X)) are two orders of magnitude smaller, wherein:
3) Substituting each obtained c into the general solution t=m + X+ct 1 Then utilize the least square formula
Obtaining parameters a and b in a logistic regression model, and substituting the obtained results into a formula
Obtaining a parameter m in a logistic regression model;
wherein T is a matrix of Nx1,
r is the load increasing speed, t is the predicted year vector, m=1/k, k is the regional maximum saturated load, x i The reciprocal of the load y in the ith year, N is the total year of the data;
4) Judging whether the calculated results m, a and b meet the constraint condition m>0，a>0，b<0, if the direct update c is not satisfied, jumping to the step 3); if yes, calculating a combination form of the model inspection indexes
Then updating c, and jumping to the step 3);
wherein, C is posterior difference test:
wherein S is 1 Is the standard deviation of historical load data, S 2 Standard deviation of the load error sequence; q is the relative residual:
Wherein->
Error->
In (1) the->
As load predicted values, x (i) is an actual load value; p is the precision:
5) Comparing all S meeting constraint conditions, substituting m, a, b=argmin S corresponding to the minimum S into the improved logistic regression model
And the method is used for predicting the maximum saturation load of the regional power grid.
2. The method for predicting saturated loads based on logistic regression according to claim 1, wherein the formula in step 3) is
The derivation is as follows:
according to the general model x=m+αt b +η, where η is noise subject to a mean of 0 and variance of δ 2 The probability model for obtaining x is:
the sufficient statistics of m using the factorization theorem are:
the factorization theorem yields:
to approximate the real parameters, an unbiased estimate of m is used, namely:
3. the method for predicting saturated loads based on logistic regression according to claim 1, wherein the general solution t=m in step 3) + X+ct 1 The derivation process of (2) is as follows:
will be
Substitution formula x=m+αt b Is obtained by:
order the
Namely: mt=x, wherein M + As pseudo-inverse matrix, M + X is a solution, ct 1 To go through, M + Is the pseudo-inverse of M, M is a matrix of N X N, X is a matrix of N X1;
let mt=0 to get t 1 Values of (2)
The method comprises the following steps:
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