CN107527122B - Prediction method for daily coal consumption of power generation of thermal power plant - Google Patents

Prediction method for daily coal consumption of power generation of thermal power plant Download PDF

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CN107527122B
CN107527122B CN201710917256.2A CN201710917256A CN107527122B CN 107527122 B CN107527122 B CN 107527122B CN 201710917256 A CN201710917256 A CN 201710917256A CN 107527122 B CN107527122 B CN 107527122B
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杨洋
魏洪峰
王秀芹
杜晓坤
刘慧巍
张亮
杨友林
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Abstract

The invention provides a method for predicting the daily coal consumption of power generation of a thermal power plant, which comprises the following steps: acquiring the coal consumption of the thermal power plant in n days; judging whether the modeling condition of a gray GM (1,1) model is met; modeling the coal consumption of the thermal power plant on the day of power generation meeting the modeling conditions by adopting a gray GM (1,1) model; modeling the coal consumption of the power plant in the generating day within n days by adopting a gray random GM (1,1) model; predicting by using a gray random GM (1,1) model, performing data inverse transformation on an output estimation value of the gray random GM (1,1) model, and performing modeling error analysis on the gray random GM (1,1) model; judging whether the average relative error of the gray random GM (1,1) model meets the set requirement or not; calculating a residual sequence; and establishing a gray random GM (1,1) model for the residual sequence, and predicting the coal consumption of the thermal power plant on the power generation day. The method utilizes the gray random GM (1,1) model to model and predict the daily coal consumption of the thermal power plant, can more clearly disclose the internal information of the complex data, and can obtain better modeling and predicting effects.

Description

Prediction method for daily coal consumption of power generation of thermal power plant
Technical Field
The invention relates to the technical field of thermal power generation, in particular to a method for predicting the daily coal consumption of power generation of a thermal power plant.
Background
Coal is one of the important fuels consumed by thermal power plants for producing electric energy and heat energy. The modeling and prediction of the coal consumption of the thermal power plant in the generation day can timely know the consumption condition of production operation, guide the purchase, optimized allocation, storage, management and the like of the coal consumption of the thermal power plant, prevent the problems of insufficient supply of the coal consumption and the like in the process of 'coal shortage' and 'electricity shortage' in advance, and have important significance for economically and reasonably using fuel, reducing consumption and improving the coal supply guarantee capability and the economic benefit of the thermal power plant. The coal consumption of the thermal power plant in the power generation day is influenced by factors such as weather, festivals and holidays, seasons, coal price, economic forms, policies, power consumption requirements and the like, so that the whole thermal power plant has certain volatility. The gray prediction is characterized by short time sequence, less statistical data, incomplete analysis and modeling of system information, convenient operation, high modeling precision and the like, and is an effective method for processing the small sample prediction problem. At present, documents and patents for solving the problems related to modeling and predicting the coal consumption of the power generation of the thermal power plant by using a gray model are not found for a while. In view of many excellent characteristics shown by the gray system model, the method can be applied to modeling and prediction of the daily coal consumption of the power generation of the thermal power plant. The gray model can be regarded as a special case of a gray random model, most of modeling and prediction of the traditional gray system are directed at deterministic models, and an actual system is often influenced by uncertain factors such as certain interference, noise and the like. Therefore, the introduced gray random model is more extensive and is beneficial to mining and modeling the fluctuation information of the data. Because the coal consumed by the thermal power plant separately calculates the power generation consumption and the heat supply consumption, the invention utilizes the gray random model to model and predict the coal consumption of the thermal power plant in the power generation day.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for predicting the daily coal consumption of power generation of a thermal power plant.
The technical scheme of the invention is as follows:
a method for predicting the daily coal consumption of a thermal power plant comprises the following steps:
step 1, acquiring the daily coal consumption x of power generation in n days of the thermal power plant(0)；
Step 2, judging the coal consumption x of the thermal power plant in the generating day within n days(0)Whether the gray GM (1,1) model modeling condition is met: if the coal consumption of the thermal power plant in n days is x(0)The presenting increasing trend meets the modeling condition of a gray GM (1,1) model; otherwise, the model does not meet the modeling conditions of the gray GM (1,1) model, the daily coal consumption of the thermal power plant is subjected to data transformation, and a generation sequence is obtainedColumn x(1)That is, the daily coal consumption x of the thermal power plant satisfying the modeling condition of the gray GM (1,1) model after data transformation(1)；
Step 3, modeling the coal consumption amount of the thermal power plant in the generating day meeting the modeling conditions of the gray GM (1,1) model by adopting the gray GM (1,1) model, and outputting the coal consumption amount x of the thermal power plant in the generating day with the expected value of the ith day by the model(1)(i) The model output estimation value is
Figure BDA0001426037980000011
Namely the estimated value of the coal consumption of the thermal power plant on the power generation day of the ith day after data transformation, wherein i is more than or equal to 1 and less than or equal to n;
step 4, on the basis of the step 3, modeling the coal consumption of the thermal power plant in the generation day within n days by adopting a gray random GM (1,1) model, wherein the output expected value of the model is x(1)(i) The model output estimation value is
Figure BDA0001426037980000021
Step 5, predicting by using the gray random GM (1,1) model established in the step 4 to obtain a model output predicted value
Figure BDA0001426037980000022
Outputting an estimated value by a gray random GM (1,1) model
Figure BDA0001426037980000023
Performing inverse transformation on the data corresponding to the step 2 to obtain
Figure BDA0001426037980000024
Meanwhile, carrying out modeling error analysis on a gray random GM (1,1) model;
step 6, judging whether the average relative error of the gray random GM (1,1) model in the step 5 meets the set requirement: if yes, executing step 8; if not, executing step 7;
step 7, calculating residual error sequence
Figure BDA0001426037980000025
Namely the error between the estimated value and the expected value of the coal consumption of the power plant on the ith day; the residual sequence was modeled as a gray random GM (1,1), where the expected output of the model is(0)(i) (ii) a Further obtaining a residual error corrected gray random GM (1,1) model, and further correcting the prediction result of the gray random GM (1,1) model in the step 5;
and 8, predicting the daily coal consumption of the thermal power plant by using the gray random GM (1,1) model with the average relative error meeting the set requirement in the step 6 or the gray random GM (1,1) model with the residual error corrected in the step 7 to obtain a final prediction result.
The parameters in the gray GM (1,1) model are estimated using the least squares method.
The step 4 comprises the following steps:
step 4-1, taking Brownian motion and white Gaussian noise as random disturbance, introducing a random factor into a gray GM (1,1) model and forming a gray random GM (1,1) model;
step 4-2, establishing a gray random GM (1,1) model;
and 4-3, estimating a parameter sigma in the gray random GM (1,1) model, and carrying out numerical solution on the gray random GM (1,1) model.
Modeling error analysis is carried out on the gray random GM (1,1) model, and the gray random GM (1,1) model is calculated by adopting relative errors and average relative errors;
relative error
Figure BDA0001426037980000026
Average relative error
Figure BDA0001426037980000027
Wherein i is more than or equal to 1 and less than or equal to n.
Has the advantages that: gray models have been widely used in the modeling and prediction of various types of small sample data. In fact, in the deterministic process, random factors interfere, and in some cases, the influence of the random factors cannot be ignored and may play a substantial role in the interference of the system. Because of the immeasurable and complex nature of stochastic factor interference, stochastic models that are abstracted from real problems are generally more complex than model-specific. Under the influence of various factors, the daily coal consumption data of the thermal power plant presents certain fluctuation. The method utilizes the gray random GM (1,1) model to model and predict the daily coal consumption of the thermal power plant, can more clearly disclose the internal information of the complex data, and can obtain better modeling and predicting effects. The gray random GM (1,1) model provided by the invention has the characteristics of simple parameters, clear physical significance, convenience in solving and the like. In the solving process, a gray GM (1,1) model is used for solving two parameters, and then an optimization algorithm and a numerical algorithm of a random differential equation are used for solving a third parameter.
The gray GM (1,1) model can be seen as a special case of the gray random GM (1,1) model. The gray random model is also suitable for small sample data, can effectively mine fluctuation information in complex data, has the characteristics of strong model expansibility, flexible application, wide application range, high model modeling precision and the like, can be widely applied to modeling, predicting, analyzing and controlling problems of thermal power plants and other industrial data, and can also be applied to related problems of small sample complex system analysis, data mining, model optimization and improvement and the like.
Drawings
FIG. 1 is a diagram of modeling data of daily coal consumption in thermal power plant according to an embodiment of the present invention;
FIG. 2 is a graph of modeling results of a gray GM (1,1) model and a gray random GM (1,1) model in an embodiment of the present invention;
FIG. 3 is a graph of the gray GM (1,1) model and gray random GM (1,1) model predictions for an embodiment of the present invention;
fig. 4 is a flowchart of a method for predicting coal consumption of a thermal power plant on a power generation day according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to the following embodiments.
Taking the prediction of coal consumption of a certain thermal power plant on a power generation day as an example, the method for predicting coal consumption of a thermal power plant on a power generation day is implemented, and as shown in fig. 4, the method comprises the following steps:
step 1, acquiring the daily coal consumption x of power generation in n days of the thermal power plant(0)；
The coal quantity for daily power generation consumption of the thermal power plant is the coal quantity in a furnace (in a bunker) measured by a metering device plus or minus the difference of the coal storage bunkers at the beginning of the last day of the day, and the coal quantity for daily power generation consumption of the thermal power plant within n days is recorded as x(0)＝(x(0)(1),x(0)(2),…,x(0)(n))，x(0)(n) the coal consumption of the thermal power plant on the nth day; the data of the coal consumption of a certain thermal power plant on a power generation day is shown in the attached figure 1.
Step 2, judging the coal consumption x of the thermal power plant in the generating day within n days(0)Whether the gray GM (1,1) model modeling condition is met: if the coal consumption of the thermal power plant in n days is x(0)The presenting increasing trend meets the modeling condition of a gray GM (1,1) model; otherwise, the model does not meet the modeling condition of a gray GM (1,1) model, data transformation is carried out on the coal consumption of daily power generation of the thermal power plant, for example, fractional order accumulation generation transformation is carried out, and a generation sequence x is obtained(1)That is, the daily coal consumption x of the thermal power plant satisfying the modeling condition of the gray GM (1,1) model after data transformation(1)，x(1)＝(x(1)(1),x(1)(2),…,x(1)(n)), as the output expectation, x, of the gray GM (1,1) model(1)(n) is the generation sequence x(1)The coal consumption of the thermal power plant on the nth day after the data conversion;
step 3, modeling the coal consumption amount of the thermal power plant in the generating day meeting the modeling conditions of the gray GM (1,1) model by adopting the gray GM (1,1) model, and outputting the coal consumption amount x of the thermal power plant in the generating day with the expected value of the ith day by the model(1)(i) The model output estimation value is
Figure BDA0001426037980000046
Namely the estimated value of the coal consumption of the thermal power plant on the power generation day of the ith day after data transformation, wherein i is more than or equal to 1 and less than or equal to n;
the coal quantity x of daily power generation consumption of the thermal power plant meeting the gray GM (1,1) model modeling condition(1)＝x(0)Or generating the sequence x(1)Estimating parameters in a gray GM (1,1) model by using a least square method;
the gray GM (1,1) model is:
Figure BDA0001426037980000041
wherein, a and b are respectively the development coefficient and the gray effect amount of a gray GM (1,1) model. Let z(1)＝(z(1)(1),z(1)(2),...,z(1)(n)),z(1)(1)＝x(1)(1),
Figure BDA0001426037980000042
The gray GM (1,1) model matrix form is expressed as:
Figure BDA0001426037980000043
estimating parameters a and b by using a least square method to satisfy [ a b]T＝(BTB)-1BTY, wherein:
Figure BDA0001426037980000044
Y＝[x(1)(2)-x(1)(1) x(1)(3)-x(1)(2)...x(1)(n)-x(1)(n-1)]T。
calculated in this embodiment, a is-0.0225 and b is-0.1829. The results of modeling the gray GM (1,1) model are shown in fig. 2.
Step 4, on the basis of the step 3, modeling the coal consumption of the thermal power plant in the generation day within n days by adopting a gray random GM (1,1) model, wherein the output expected value of the model is x(1)(i) The model output estimation value is
Figure BDA0001426037980000045
Wherein i is more than or equal to 1 and less than or equal to n;
step 4-1, considering Brownian motion and white Gaussian noise as random disturbance, introducing a random factor into a gray GM (1,1) model and forming the gray random GM (1,1) model, wherein the gray GM (1,1) modelMiddle parameter-a is rewritten as
Figure BDA0001426037980000051
Figure BDA0001426037980000052
Is white gaussian noise, e.g., b (t) is standard brownian motion;
one standard brownian motion is a random variable that satisfies the following three conditions:
(1)B(0)＝0；
(2) for s is more than or equal to 0 and less than T and less than or equal to T,
Figure BDA0001426037980000053
wherein N (0,1) represents a normally distributed random variable having zero mean and variance;
(3) for 0 ≦ s < T < u < v ≦ T, the increments B (T) -B(s) and B (v) -B (u) are independent.
Step 4-2, establishing a gray random GM (1,1) model, wherein the mathematical form is dx (t) ═ ax (t) dt + bdt + sigma x (t) dB (t);
4-3, estimating a parameter sigma in the gray random GM (1,1) model by using an optimization algorithm, and carrying out numerical solution on the gray random GM (1,1) model;
the parameter sigma in the gray random GM (1,1) model is estimated by using an optimization algorithm, and a fitness function in the optimization algorithm can be selected according to the needs of actual problems, such as:
Figure BDA0001426037980000054
the numerical algorithm of the classical stochastic differential equation is: Euler-Maruyama method, Milstein method, R-K method, etc. The method adopts a Euler-Maruyama method to carry out numerical solution on a gray random GM (1,1) model. The general form of the autonomous random differential equation is given by the time between 0 and T
dx(t)＝f(x(t))dt+g(x(t))dB(t)),0≤t≤T
Where x (0) is an initial value, f and g are continuously measurable functions, f is a drift coefficient, g is a diffusion coefficient, and B (t) is standard Brownian motion. The following form of integration can be written
Figure BDA0001426037980000055
For a positive integer L, the Euler-Maruyama method is adopted, then
xj＝xj-1+f(xj-1)Δt+g(xj-1)(B(τj)-B(τj-1)),j＝1,2,...,L
Wherein,
Figure BDA0001426037980000056
xjto approximate substitute xτj. For convenience, let Δ t be Rt and R be an integer of 1 or more, the increment of brownian motion can be expressed as
Figure BDA0001426037980000057
The results of modeling the gray random GM (1,1) model are shown in FIG. 2.
Step 5, predicting by using the gray random GM (1,1) model established in the step 4 to obtain a model output predicted value
Figure BDA0001426037980000061
Wherein i is more than or equal to 1, and i is an integer. Will be provided with
Figure BDA0001426037980000062
Performing inverse transformation on the data corresponding to the step 2 to obtain
Figure BDA0001426037980000063
Meanwhile, carrying out modeling error analysis on a gray random GM (1,1) model;
to pair
Figure BDA0001426037980000064
In other words, two parts of data are included: model output estimation value and model output prediction value
Figure BDA0001426037980000065
Is carried out corresponding to step 2Is inversely transformed to obtain
Figure BDA0001426037980000066
Wherein,
Figure BDA0001426037980000067
the estimated value of the coal consumption of the power generation day of the i-th thermal power plant obtained by applying a gray random GM (1,1) model,
Figure BDA0001426037980000068
the method is a predicted value of the coal consumption of the power plant on the (n + 1) th day obtained by applying a gray random GM (1,1) model,
Figure BDA0001426037980000069
the method is a predicted value of the coal consumption of the power plant on the (n + 2) th day obtained by applying a random gray model.
Calculating a gray random GM (1,1) model by using indexes such as relative error, average relative error and the like to perform modeling error analysis, wherein the relative error deltaiAnd average relative error
Figure BDA00014260379800000610
Are respectively defined as
Figure BDA00014260379800000611
Wherein i is more than or equal to 1 and less than or equal to n.
The grey GM (1,1) model and the grey random GM (1,1) model are modeled for error analysis as shown in tables 1 and 2.
TABLE 1 Gray GM (1,1) model modeling error analysis
Figure BDA00014260379800000612
TABLE 2 Gray random GM (1,1) model modeling error analysis
Figure BDA00014260379800000613
Step 6, judging whether the average relative error of the gray random GM (1,1) model in the step 5 meets the set requirement: if yes, executing step 8; if not, executing step 7;
step 7, calculating residual error sequence
Figure BDA00014260379800000710
Namely the error between the estimated value and the expected value of the coal consumption of the power plant on the ith day; the residual sequence was modeled as a gray random GM (1,1), where the expected output of the model is
Figure BDA0001426037980000071
And further obtaining a residual error corrected gray random GM (1,1) model, and further correcting the prediction result of the gray random GM (1,1) model in the step 5.
The conventional residual error correction method in the field of classical gray models is to establish a GM (1,1) model for a residual error sequence, such as Zhou Yin, application of a residual error gray prediction model in logistics demand prediction [ J ]. railway transportation and economy, 2007,29(11):59-61, Liu Si Feng and the like. The invention establishes a gray random GM (1,1) model for a residual sequence, wherein the residual sequence is expressed as:
Figure BDA0001426037980000072
the model output estimation value obtained by using the gray random GM (1,1) model for the residual sequence is
Figure BDA0001426037980000073
The predicted value of model output obtained by using a gray random GM (1,1) model for the residual sequence is
Figure BDA0001426037980000074
The residual modified gray random GM (1,1) model outputs an estimate of
Figure BDA0001426037980000075
The residual modified gray random GM (1,1) the model outputs a predicted value of
Figure BDA0001426037980000076
And 8, predicting the daily coal consumption of the thermal power plant by using the gray random GM (1,1) model with the average relative error meeting the set requirement in the step 6 or the gray random GM (1,1) model with the residual error corrected in the step 7 to obtain a final prediction result.
And according to the requirement of the actual problem on the precision, predicting the daily coal consumption of the thermal power plant by using a gray random GM (1,1) model or a residual error corrected gray random GM (1,1) model. When the gray random GM (1,1) model is used for predicting the daily coal consumption of the power generation of the thermal power plant, the result is
Figure BDA0001426037980000077
When the residual error corrected gray random GM (1,1) model is used for predicting the daily coal consumption of the power generation of the thermal power plant, the result is
Figure BDA0001426037980000078
In the embodiment, the modeling result of the coal consumption of the thermal power plant on the day of power generation obtained by the gray random GM (1,1) model meets the set requirement, so residual correction is not performed. The results of the gray random GM (1,1) model prediction compared to the gray GM (1,1) model results are shown in FIG. 3. The grey GM (1,1) model and the grey random GM (1,1) model prediction error analysis are shown in tables 3 and 4.
TABLE 3 Gray GM (1,1) model prediction error analysis
Figure BDA0001426037980000079
TABLE 4 Gray random GM (1,1) model prediction error analysis
Figure BDA0001426037980000081
。

Claims (3)

1. A method for predicting the daily coal consumption of a thermal power plant is characterized by comprising the following steps:
step 1, acquiring the daily coal consumption x of power generation in n days of the thermal power plant(0)；
Step 2, judging the coal consumption x of the thermal power plant in the generating day within n days(0)Whether the gray GM (1,1) model modeling condition is met: if the coal consumption of the thermal power plant in n days is x(0)The presenting increasing trend meets the modeling condition of a gray GM (1,1) model; otherwise, the modeling condition of the gray GM (1,1) model is not satisfied, data transformation is carried out on the coal consumption of the thermal power plant in daily power generation, and a generation sequence x is obtained(1)That is, the daily coal consumption x of the thermal power plant satisfying the modeling condition of the gray GM (1,1) model after data transformation(1)；
Step 3, modeling the coal consumption amount of the thermal power plant in the generating day meeting the modeling conditions of the gray GM (1,1) model by adopting the gray GM (1,1) model, and outputting the coal consumption amount x of the thermal power plant in the generating day with the expected value of the ith day by the model(1)(i) The model output estimation value is
Figure FDA0002620285160000011
Namely the estimated value of the coal consumption of the thermal power plant on the power generation day of the ith day after data transformation, wherein i is more than or equal to 1 and less than or equal to n;
wherein the gray GM (1,1) model is:
Figure FDA0002620285160000012
dx(1)＝-ax(1)dt+bdt
a and b are respectively the development coefficient and the gray action amount of a gray GM (1,1) model, and t is a time variable;
step 4, on the basis of the step 3, modeling the coal consumption of the thermal power plant in the generation day within n days by adopting a gray random GM (1,1) model, wherein the output expected value of the model is x(1)(i) The model output estimation value is
Figure FDA0002620285160000013
Step 4-1. Considering Brownian motion and white Gaussian noise as random disturbance, introducing a random factor into a gray GM (1,1) model and forming a gray random GM (1,1) model; wherein the parameter-a in the gray GM (1,1) model is rewritten as
Figure FDA0002620285160000014
Figure FDA0002620285160000015
Is white gaussian noise, b (t) is standard brownian motion;
step 4-2, establishing a gray random GM (1,1) model with a mathematical form of dx(1)＝-ax(1)dt+bdt+σx(1)dB(t)；
4-3, estimating a parameter sigma in the gray random GM (1,1) model, and carrying out numerical solution on the gray random GM (1,1) model;
step 5, predicting by using the gray random GM (1,1) model established in the step 4 to obtain a model output predicted value
Figure FDA0002620285160000016
Outputting an estimated value by a gray random GM (1,1) model
Figure FDA0002620285160000017
Performing inverse transformation on the data corresponding to the step 2 to obtain
Figure FDA0002620285160000018
Meanwhile, carrying out modeling error analysis on a gray random GM (1,1) model;
step 6, judging whether the average relative error of the gray random GM (1,1) model in the step 5 meets the set requirement: if yes, executing step 8; if not, executing step 7;
step 7, calculating residual error sequence
Figure FDA0002620285160000019
Namely the error between the estimated value and the expected value of the coal consumption of the power plant on the ith day; will be residual errorThe sequence establishes a gray random GM (1,1) model, where the expected output of the model is(0)(i) (ii) a Further obtaining a residual error corrected gray random GM (1,1) model, and further correcting the prediction result of the gray random GM (1,1) model in the step 5;
wherein, the model output estimation value obtained by using a gray random GM (1,1) model for the residual sequence is
Figure FDA0002620285160000021
The predicted value of model output obtained by using a gray random GM (1,1) model for the residual sequence is
Figure FDA0002620285160000022
The residual modified gray random GM (1,1) model outputs an estimate of
Figure FDA0002620285160000023
The residual error corrected gray random GM (1,1) model outputs a predicted value of
Figure FDA0002620285160000024
Wherein M is an integer of 1,2, 3.
And 8, predicting the daily coal consumption of the thermal power plant by using the gray random GM (1,1) model with the average relative error meeting the set requirement in the step 6 or the gray random GM (1,1) model with the residual error corrected in the step 7 to obtain a final prediction result.
2. The method according to claim 1, characterized in that the parameters in the grey GM (1,1) model are estimated using the least squares method.
3. The method of claim 1, wherein the performing modeling error analysis on the gray random GM (1,1) model comprises calculating a relative error and an average relative error of the gray random GM (1,1) model;
relative error
Figure FDA0002620285160000025
Average relative error
Figure FDA0002620285160000026
Wherein i is more than or equal to 1 and less than or equal to n.
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