CN110264006B - Wind power probabilistic prediction method based on chaotic firefly algorithm and Bayesian network - Google Patents
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Abstract
The invention discloses a wind power probabilistic prediction method based on a chaotic firefly algorithm and a Bayesian network, which comprises the following steps: 1, acquiring wind speed, wind direction, air temperature and wind power actual power data, preprocessing the data, and selecting training set and test set data; 2, performing empirical mode decomposition on the wind power original data to make the wind power time sequence more stable; 3, constructing a Bayesian network model to obtain an initial prediction interval; 4, calculating the range of interval change amplitude, and obtaining the optimal interval change amplitude by using a chaotic firefly algorithm; and 5, performing chaotic search near the optimal interval change amplitude to obtain a final prediction interval. The method can measure the uncertainty of the wind power through the construction prediction region, thereby providing effective reference for power scheduling decision.
Description
Technical Field
The invention relates to the technical field of wind power generation, in particular to a wind power prediction model method based on EMD decomposition, a Bayesian network and a chaotic firefly algorithm.
Background
In recent years, with the development of socio-economic, the demand for energy is increasing, fossil energy is gradually facing the risk of exhaustion, and the use of a large amount of fossil fuel brings about a serious pollution problem. In order to cope with the problems of fuel energy and environmental pollution, renewable energy is widely used. Among them, wind energy has been rapidly developed and applied over the past decades as a clean, renewable, most potentially exploited source of energy. With the gradual expansion of the scale of wind power generation, wind power occupies a greater and greater proportion in a power system. The weak controllability of wind power caused by the intermittency and uncertainty of wind power brings great challenges to the safe and stable operation of the power system. In order to reduce the risk of wind power network access, reduce the construction cost of system reserve capacity and help the power department to make an accurate scheduling scheme, reliable, timely and accurate wind power prediction becomes a problem which needs to be solved urgently at present.
Wind power generation is affected by factors such as weather factors, unit faults and data misloading, so that the collected data often has abnormal values and missing values, and certain trouble is brought to wind power prediction. Meanwhile, the wind power data has large volatility, and if the data is not subjected to certain technical processing, the prediction result obtained by directly predicting the data is often poor. However, the current research generally aims at processing abnormal values and missing values existing in a data set, no targeted countermeasures are provided for strong fluctuation of wind power data, and the accuracy of a prediction result often does not reach an ideal level.
At present, the methods for wind power prediction at home and abroad mainly include a physical method based on numerical weather forecast, a statistical method based on time series historical data and a prediction method of the mixture of the two methods. Generally speaking, a prediction mode which can simultaneously consider numerical weather physical data and time series historical data for wind power prediction can remarkably improve the prediction accuracy, but how to effectively combine data of two components and predict the data is a problem which is difficult to solve in the past. Researchers have achieved excellent research results in the field of point prediction of wind power prediction for decades, and prediction accuracy has already approached an ideal level. However, due to the uncertainty of wind energy and the inherent defects of the model, the traditional deterministic point prediction method has the problems that point prediction errors cannot be eliminated, the uncertainty of the result cannot be measured, the fluctuation range of the wind power cannot be given, and the like.
In the current method for carrying out probabilistic prediction on wind power, most models are optimized by using an evolutionary algorithm, but the traditional evolutionary algorithm has strong global searching capability and can effectively improve the convergence speed of the models, but the traditional evolutionary algorithm generally has the defects of low later-stage convergence speed, early maturity of the models and easy falling into local optimal solution. The operation time of the algorithm is long in wind power prediction, and the time availability requirement cannot be met; the prediction precision is not high, and the requirement of accuracy usability cannot be met.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a wind power probabilistic prediction method based on a chaotic firefly algorithm and a Bayesian network, and can provide effective reference for power scheduling decision by measuring the uncertainty of the wind power through a construction interval.
The invention adopts the following technical scheme for solving the technical problems:
the invention relates to a wind power probabilistic prediction method based on a chaotic firefly algorithm and a Bayesian network, which is characterized by comprising the following steps of:
step 1.1, collecting historical data of wind speed to form an original wind speed sequence, and filling missing values and abnormal values and normalizing the original wind speed sequence to obtain a preprocessed wind speed sequence which is recorded asV=[v1,v2,...vi,...,vN],viI is more than or equal to 1 and less than or equal to N, and N is the total number of samples, wherein the wind speed data of the ith time point in the preprocessed wind speed sequence V is the wind speed data of the ith time point;
acquiring historical data of wind directions to form an original wind direction sequence, and performing missing value and abnormal value filling and normalization processing on the original wind direction sequence to obtain a preprocessed wind direction sequence which is recorded as F ═ F1,f2,...fi...fN],fiWind direction data of the ith time point in the preprocessed wind direction sequence F are obtained;
collecting historical data of air temperature to form an original air temperature sequence, and performing missing value and abnormal value filling and normalization processing on the original air temperature sequence to obtain a preprocessed air temperature sequence which is marked as T ═ w1,w2,...wi,...wN],wiThe temperature data of the ith time point in the preprocessed temperature sequence T is obtained;
acquiring actual power historical data of wind power to form an original wind power sequence, and filling missing values and abnormal values and normalizing the original wind power sequence to obtain a preprocessed wind power sequence which is recorded as P ═ P1,p2,...,pi,...,pN],piWind power data of the ith time point in the wind power sequence P after the pretreatment is obtained;
dividing a data set consisting of the preprocessed wind speed sequence, wind direction sequence, air temperature sequence and wind power sequence into training set data and test set data;
step 1.2, carrying out empirical mode decomposition on the preprocessed wind power sequence P to obtain a data set consisting of k IMF components and a margin; the k IMF components are denoted as Is the jth IMF scoreAmount of, and is the jth IMF componentThe wind power decomposition value of the ith time point;
step 2, constructing a Bayesian network model by using training set data:
step 2.1, the jth IMF componentWind power decomposition value of the ith time pointAnd the wind speed data v of the ith time pointiWind direction data fiAnd gas temperature data wiAs an influence factor in the bayesian network model, the jth IMF component is addedWind power decomposition value of the (i + 1) th time pointAs an output node, thereby constructing a Bayesian network model;
step 2.2, respectively calculating the conditional probability of the output node corresponding to each influence factor when the influence factors take different values according to historical data, thereby obtaining a conditional probability table;
step 2.3, obtaining the jth IMF component according to the conditional probability table and the Bayesian network modelPower resolution value of the (i + 1) th time pointAnd taking a power interval corresponding to the highest point on the probability distribution curve as the jth IMF componentWind power decomposition value of the (i + 1) th time pointThe initial prediction interval of (1);
step 2.4, repeating the steps 2.1 to 2.3, so as to obtain an initial prediction interval of the power decomposition value of the (i + 1) th time point in the k IMF components, taking the sum of the initial prediction intervals of the power decomposition value of the (i + 1) th time point in the k IMF components as the wind power prediction interval of the (i + 1) th time point, and recording the sum as the wind power prediction interval of the (i + 1) th time point
Step 3, obtaining an optimal interval amplitude variation range by using a chaotic firefly algorithm:
step 3.1, predicting the interval according to the wind power of the (i + 1) th time pointDetermining the median of the prediction interval of the (i + 1) th time pointWherein,the predicted value is used as the wind power predicted value of the (i + 1) th time point;
predicting the wind power of the (i + 1) th time pointLower limit of (2)Wind power predicted value divided by (i + 1) th time pointThe lower ratio of the (i + 1) th time point is recorded asThereby obtaining the lower limit ratios of the N time points, and selecting the maximum value and the minimum value in the lower limit ratios of the N time points as the lower limit ratio betalowThe variation range of (a);
predicting the wind power of the (i + 1) th time pointUpper limit of (2)Wind power predicted value divided by (i + 1) th time pointThe upper ratio of the time points at i +1 is recorded asThereby obtaining the upper limit ratios of the N time points, and selecting the maximum value and the minimum value in the upper limit ratios of the N time points as the upper limit ratio betahighThe variation range of (a);
lower limit ratio betalowAnd an upper limit ratio betahighThe method is used as a parameter to be optimized in the chaotic firefly algorithm, and two corresponding variation ranges are used as the variation ranges of the population;
step 3.2, initializing the population:
setting a compression operator as g, a population scale as M, a current evolutionary algebra as T, and a maximum evolutionary algebra as TmaxThe current chaotic search frequency is D, and the maximum chaotic search frequency is DmaxThe absorption factor of light intensity is gamma, gamma belongs to [0,1 ]]Maximum attraction ω0Step size factor eta, eta is equal to [0,1 ]];
When the initialization t is 0, M random numbers are generated in the variation range of the population and are used as M firefsInitial position of firefly, wherein the initial position of the nth firefly at the t-th evolutionary iteration is recorded asThe initial position of the mth firefly isN is more than or equal to 1 and less than or equal to M, M is more than or equal to 1 and less than or equal to M, wherein,the nth firefly is in a lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the nth firefly at the t evolution iteration is the upper limit ratio betahighThe random number in the variation range of (a),the mth firefly is in the lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the mth firefly at the tth evolution iteration is the upper limit ratio betahighRandom number in the variation range of (2), the initial position of the firefly population is recorded as
Step 3.3, calculating the fluorescence brightness of the firefly:
the luminance of the nth firefly in the t evolution iteration is constructed by using the formula (1)And the luminance of the mth firefly in the tth evolutionary iteration is obtained according to the formula (1)
In the formula (1), u is a confidence level,the average bandwidth of the prediction interval of the nth firefly in the t evolution iteration is obtained by the formula (2),the predicted interval coverage rate of the nth firefly in the t evolution iteration is obtained by the formula (3),to predict the interval coverageIs obtained by the formula (4), and lambda is the predicted interval coveragePenalty factor when confidence level mu is not reached;
in the formula (2), R is a wind power true value sequence P ═ P1,p2,...,pi,...,pN]The difference between the maximum value and the minimum value in (b),the lower bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (5),the upper bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (6);
in the formula (3), bn,i+1Is the Boolean constant of the (i + 1) th time point of the nth firefly, if the real value p of the wind power of the (i + 1) th time pointi+1The prediction interval range of the (i + 1) th time point of the nth firefly in the t evolution iterationIn the interior, then order b n,i+11 is ═ 1; otherwise, let bn,i+1=0;
In the formulae (5) and (6),predicting the median of the interval for the (i + 1) th time point of the nth firefly;
according to the initial position and the fitness function of the fireflies, the fitness value of each firefly is used as the initial fluorescence brightness of the fireflyThe fluorescence brightness of the t-th evolution iterationMinimum value ofIs marked asWherein,for the t-th iteration of evolution, the firefly populationIs located at the optimum position in the (c),to an optimum positionIs determined by the first component of (a),to an optimum positionA second component of (a); let Igmin(Xgbest) Is the global optimum fitness value after t evolutionary iterations, andmake global optimum position
Step 3.4, the firefly position moves:
according to the light intensity absorption factor gamma and the maximum attraction omega0Obtaining the mutual attraction degree omega of the mth firefly and the nth firefly; if it isThe mth firefly moves toward the nth firefly according to the mutual attraction degree omega; and obtaining the updated position of the mth firefly and using the updated position as the position of the mth firefly in the (t + 1) th evolution iteration and recording the position as the updated positionOtherwise, the nth firefly moves towards the mth firefly according to the mutual attraction omega; and obtaining the updated position of the nth firefly and using the updated position as the position of the nth firefly in the (t + 1) th evolution iteration, and recording the position as the position of the nth fireflyThereby obtaining the updated positions of all the fireflies and forming a firefly population during the (t + 1) th evolutionary iteration;
step 3.5, obtaining the brightness of each individual in the firefly population during the t +1 th evolution iteration by using the formula (1), and comparing the brightness among the firefly individuals, so as to find out the fitness value of the firefly with the minimum brightness in the firefly population during the t +1 th evolution iteration, and recording the fitness value as the fitness valueWherein,the optimal position in the firefly population after the t +1 th evolutionary iteration;
if the global optimum fitness valueThen will beIs assigned to XgbestThereby updating the global optimum position Xgbest(ii) a Otherwise, the global optimal position XgbestKeeping the same;
step 3.6, the optimal position in the firefly population during the t +1 th evolution iterationLocal search is performed nearby:
initialization d ═ 0, at [ -1,1 [ ]]Randomly generating q-dimension chaotic variable in d-th chaotic search in intervalq represents a dimension, and q is 1, 2;
the optimal position of the t +1 th evolution iterationAssigning to the optimal coordinate y in the d-th chaotic search(d)And q is 1,when q is equal to 2, the reaction is carried out, for the optimal coordinate y in the d-th chaotic search(d)The q-th component of (a);
step 3.7, chaotic search is carried out by using the logistic mapping shown in the formula (7) to obtain chaotic variables during the d +1 th chaotic search
In the formula (7), s is a constant and is more than 0 and less than or equal to 2;
step 3.8, obtaining the optimal coordinate y in the d +1 th chaotic search by using the formula (8)(d+1)Q component of
In formula (8), when q is 1, xq,maxAs the first component of the initial position of the firefly populationMaximum value of (1), xq,minAs the first component of the initial position of the firefly populationMinimum value of (1); when q is 2, xq,maxSecond component of initial position of firefly populationMaximum value of (1), xq,minSecond component of initial position of firefly populationMinimum value of (1); g(t)For the compression operator after the t-th evolutionary iteration, the method is obtained by using the formula (9):
in formula (9), L is a constant greater than 0;
step 3.9, if D is less than DmaxIf so, assigning d +1 to d, and returning to the step 3.7; otherwise, obtaining the optimal coordinate sequence through chaotic searchAnd proceeds to step 3.9.1;
step 3.9.1, calculating the fitness value of the optimal coordinate sequence using equation (1)Finding the minimum fitness value in the fitness values of the optimal coordinate sequence and recording the minimum fitness value as Imin(ybest) Wherein, ybestFor the optimal coordinate sequenceThe optimal position of (1);
step 3.9.2 if the global optimum fitness valueThen pass throughUpdating the global optimal position; otherwise, let the global optimum position XgbestKeeping the same;
step 3.10, if T is less than TmaxAssigning t +1 to t and returning to the step 3.3; otherwise, the global optimal position X in the firefly population is obtainedgbestObtaining the optimal solution of the fitness functionAnd
step 4, according to the optimal solutionAndrespectively calculating the optimal lower bound of the prediction interval of the (i + 1) th time pointThe (i + 1) th time pointIs optimally upper bound of the prediction intervalAnd by an optimal lower bound of the prediction intervalAnd an optimal upper boundAnd forming a final prediction interval, and substituting the test set data into the Bayesian network model so as to complete the probabilistic prediction of the wind power.
Compared with the prior art, the invention has the beneficial effects that:
1. the empirical mode decomposition adopted by the invention is a self-adaptive data processing and mining method, and can be used for carrying out stabilization processing on data, so that the wind power is more stable, and the fluctuation of the wind power is reduced.
2. The method utilizes the Bayesian network prediction model to carry out probabilistic interval prediction to overcome the defects of low reliability, complex calculation and the like of the existing prediction method, and improves the prediction quality of the wind power.
3. According to the method, the cleaned wind power data is combined with the chaotic firefly algorithm and the Bayesian network method, a prediction model is constructed, the optimal interval amplitude variation range is obtained, and a certain reference is provided for resource scheduling personnel.
4. Aiming at the problem of wind power probabilistic prediction, the invention provides a novel chaotic firefly algorithm, which carries out chaotic search near the optimal solution solved by the firefly algorithm, improves the global optimization capability of the chaotic firefly algorithm, and solves the problem that the chaotic search cannot be carried out in a negative value interval by carrying out the chaotic search by using logistic mapping, thereby improving the prediction quality of the probabilistic interval and facilitating a decision maker to carry out scientific and reasonable decision.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a block diagram of a bayesian network of the present invention.
Detailed Description
In this embodiment, a wind power probabilistic prediction method based on a chaotic firefly algorithm and a bayesian network, as shown in fig. 1, includes: acquiring wind speed, wind direction, air temperature and wind power actual power data, and preprocessing the data; EMD decomposition is carried out on the actual wind power, and the fluctuation of the wind power is reduced; establishing a Bayesian network model to obtain an initial prediction interval; and calculating the range of the interval change amplitude, obtaining the optimal interval change range when the fitness function is optimal by using the chaotic firefly algorithm, thereby obtaining a final prediction interval, and analyzing and evaluating a prediction result. Specifically, the method comprises the following steps:
step 1.1, collecting historical data of wind speed to form an original wind speed sequence, and performing missing value and abnormal value filling and normalization processing on the original wind speed sequence to obtain a preprocessed wind speed sequence which is recorded as V ═ V1,v2,...vi,...,vN],viThe wind speed data of the ith time point in the wind speed sequence V after pretreatment, i is more than or equal to 1 and less than or equal to N, and N is the total number of samples;
acquiring historical data of wind directions to form an original wind direction sequence, and performing missing value and abnormal value filling and normalization processing on the original wind direction sequence to obtain a preprocessed wind direction sequence, wherein the preprocessed wind direction sequence is marked as F ═ F1,f2,...fi...fN],fiWind direction data of the ith time point in the preprocessed wind direction sequence F;
collecting historical data of the air temperature to form an original air temperature sequence, and performing missing value and abnormal value filling and normalization processing on the original air temperature sequence to obtain a preprocessed air temperature sequence which is marked as T ═ w1,w2,...wi,...wN],wiThe temperature data of the ith time point in the preprocessed temperature sequence T are obtained;
gather reality of wind-powered electricity generationThe power historical data form an original wind power sequence, and the original wind power sequence is subjected to missing value and abnormal value filling and normalization processing, so that a preprocessed wind power sequence is obtained and is marked as P ═ P1,p2,...,pi,...,pN],piWind power data of the ith time point in the wind power sequence P after pretreatment;
dividing a data set consisting of the preprocessed wind speed sequence, wind direction sequence, air temperature sequence and wind power sequence into training set data and test set data;
step 1.2, carrying out empirical mode decomposition on the preprocessed wind power sequence P to obtain a data set consisting of k IMF components and a margin; wherein k IMF components are denoted as Is the jth IMF component, and is the jth IMF componentThe wind power decomposition value of the ith time point;
step 2, constructing a Bayesian network model by using training set data:
step 2.1, the jth IMF componentWind power decomposition value of the ith time pointAnd the wind speed data v of the ith time pointiWind direction data fiAnd gas temperature data wiAs an influence factor in the bayesian network model, the jth IMF component is addedWind power decomposition value of the (i + 1) th time pointAs output nodes, thereby constructing a Bayesian network model, as shown in FIG. 2;
step 2.2, respectively calculating the conditional probability of the output node corresponding to each influence factor when the influence factors take different values according to historical data, thereby obtaining a conditional probability table;
step 2.3, obtaining the jth IMF component according to the conditional probability table and the Bayesian network modelPower resolution value of the (i + 1) th time pointAnd taking a power interval corresponding to the highest point on the probability distribution curve as the jth IMF componentWind power decomposition value of the (i + 1) th time pointThe initial prediction interval of (1);
step 2.4, repeating the steps 2.1 to 2.3, so as to obtain an initial prediction interval of the power decomposition value of the (i + 1) th time point in the k IMF components, taking the sum of the initial prediction intervals of the power decomposition value of the (i + 1) th time point in the k IMF components as the wind power prediction interval of the (i + 1) th time point, and recording the sum as the wind power prediction interval of the (i + 1) th time point
Step 3, obtaining an optimal interval amplitude variation range by using a chaotic firefly algorithm:
step 3.1, predicting the interval according to the wind power of the (i + 1) th time pointDetermining the median of the prediction interval of the (i + 1) th time pointWherein,the predicted value is used as the wind power predicted value of the (i + 1) th time point;
predicting the wind power of the (i + 1) th time pointLower limit of (2)Wind power predicted value divided by (i + 1) th time pointThe lower ratio of the (i + 1) th time point is recorded asThereby obtaining the lower limit ratios of the N time points, and selecting the maximum value and the minimum value in the lower limit ratios of the N time points as the lower limit ratio betalowThe variation range of (A) is [0.4,1.2 ]];
Predicting the wind power of the (i + 1) th time pointUpper limit of (2)Wind power predicted value divided by (i + 1) th time pointAs a firstThe upper ratio of the i +1 time points is recorded asThereby obtaining the upper limit ratios of the N time points, and selecting the maximum value and the minimum value in the upper limit ratios of the N time points as the upper limit ratio betahighThe variation range of (A) is [0.8,1.8 ]];
Lower limit ratio betalowAnd an upper limit ratio betahighThe method is used as a parameter to be optimized in the chaotic firefly algorithm, and two corresponding variation ranges are used as the variation ranges of the population;
step 3.2, initializing the population:
setting a compression operator as g, a population scale as M, a current evolutionary algebra as T, and a maximum evolutionary algebra as TmaxThe current chaotic search frequency is D, and the maximum chaotic search frequency is DmaxThe absorption factor of light intensity is gamma, gamma belongs to [0,1 ]]Maximum attraction ω0Step size factor eta, eta is equal to [0,1 ]];
When the initialization t is 0, generating M random numbers in the variation range of the population and taking the random numbers as the initial positions of M fireflies, wherein the initial position of the nth fireflies in the t evolution iterationThe initial position of the mth firefly isN is more than or equal to 1 and less than or equal to M, M is more than or equal to 1 and less than or equal to M, wherein,the nth firefly is in a lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the nth firefly at the t evolution iteration is the upper limit ratio betahighThe random number in the variation range of (a),the mth firefly is in the lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the mth firefly at the tth evolution iteration is the upper limit ratio betahighRandom number in the variation range of (2), the initial position of the firefly population is recorded as
Step 3.3, calculating the fluorescence brightness of the firefly:
the luminance of the nth firefly in the t evolution iteration is constructed by using the formula (1)And the luminance of the mth firefly in the tth evolutionary iteration is obtained according to the formula (1)
In the formula (1), u is a confidence level,the average bandwidth of the prediction interval of the nth firefly in the t evolution iteration is obtained by the formula (2),the predicted interval coverage rate of the nth firefly in the t evolution iteration is obtained by the formula (3),to predict the interval coverageIs obtained by the formula (4), and lambda is the predicted interval coveragePenalty factor when confidence level mu is not reached;
in the formula (2), R is a wind power true value sequence P ═ P1,p2,...,pi,...,pN]The difference between the maximum value and the minimum value in (b),the lower bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (5),the upper bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (6);
in the formula (3), bn,i+1Is the Boolean constant of the (i + 1) th time point of the nth firefly, if the real value p of the wind power of the (i + 1) th time pointi+1The prediction interval range of the (i + 1) th time point of the nth firefly in the t evolution iterationIn the interior, then order b n,i+11 is ═ 1; otherwise, let bn,i+1=0;
In the formulae (5) and (6),predicting the median of the interval for the (i + 1) th time point of the nth firefly;
according to the initial position and the fitness function of the fireflies, the fitness value of each firefly is used as the initial fluorescence brightness of the fireflyThe fluorescence brightness of the t-th evolution iterationMinimum value of (1) is notedWherein,for the t-th iteration of evolution, the firefly populationIs located at the optimum position in the (c),to an optimum positionIs determined by the first component of (a),to an optimum positionA second component of (a); let Igmin(Xgbest) Is the global optimum fitness value after t evolutionary iterations, andmake global optimum position
Step 3.4, the firefly position moves:
according to the light intensity absorption factor gamma and the maximum attraction omega0Obtaining the mutual attraction degree omega of the mth firefly and the nth firefly according to the formula (7);
in the formula (7), the reaction mixture is,is the distance between firefly m and firefly n in the population at the t iteration, and has:
in the formula (9), the reaction mixture is,the position of the mth firefly in the (t + 1) th evolution iteration;
in the formula (10), the compound represented by the formula (10),the position of the nth firefly in the t +1 evolution iteration;
step 3.5, obtaining the brightness of each individual in the updated firefly population by using the formula (1), and comparing the brightness of the firefly individuals, so as to search the fitness value of the firefly with the minimum brightness in the t +1 th evolution iteration in the updated population The optimal position in the firefly population after the t +1 th evolutionary iteration;
if the global optimum fitness valueThen will beIs assigned to XgbestThereby updating the global optimum position Xgbest(ii) a Otherwise, the global optimal position XgbestKeeping the same;
step 3.6, the optimal position in the firefly population during the t +1 th evolution iterationLocal search is performed nearby:
initialization d ═ 0, at [ -1,1 [ ]]Randomly generating within the intervalQ-dimension chaotic variable in d chaotic searchesq represents a dimension, and q is 1, 2;
the optimal position obtained by the firefly algorithm in the t +1 th evolution iterationAssigning to the optimal coordinate y in the d-th chaotic search(d)And q is 1,when q is equal to 2, the reaction is carried out, for the optimal coordinate y in the d-th chaotic search(d)The q-th component of (a);
step 3.7, chaotic search is carried out by using the logistic mapping shown in the formula (11) to obtain chaotic variables during the d +1 th chaotic search
In the formula (11), s is a constant and is more than 0 and less than or equal to 2;
step 3.8, obtaining the optimal coordinate y in the d +1 th chaotic search by using the formula (12)(d+1)Q component of
In the formula (12), the reaction mixture is,when q is 1, xq,maxAs the first component of the initial position of the firefly populationMaximum value of (1), xq,minAs the first component of the initial position of the firefly populationMinimum value of (1); when q is 2, xq,maxSecond component of initial position of firefly populationMaximum value of (1), xq,minSecond component of initial position of firefly populationMinimum value of (1); g(t)For the compression operator after the t-th evolutionary iteration, the method is obtained by using the formula (13):
in formula (13), L is a constant greater than 0;
step 3.9, if D is less than DmaxIf so, assigning d +1 to d, and returning to the step 3.7; otherwise, obtaining the optimal coordinate sequence through chaotic searchAnd proceeds to step 3.9.1;
step 3.9.1, calculating the fitness value of the optimal coordinate sequence using equation (1)Finding the minimum fitness value in the fitness values of the optimal coordinate sequence is recorded as Imin(ybest) Wherein, ybestFor the optimal coordinate sequenceThe optimal position of (1);
step 3.9.2 if the global optimum fitness valueThen pass throughUpdating the global optimal position; otherwise, let the global optimum position XgbestKeeping the same;
step 3.10, if T is less than TmaxAssigning t +1 to t and returning to the step 3.3; otherwise, the global optimal position X in the firefly population is obtainedgbestObtaining the optimal solution of the fitness functionAnd
step 4, substituting the test set data into the Bayesian network model to obtain the wind power prediction interval of the (i + 1) th time pointOptimal solution obtained according to step 3.10Andrespectively calculating the optimal lower bound of the prediction interval of the (i + 1) th time pointOptimal upper bound of prediction interval of i +1 th time pointAnd by an optimal lower bound of the prediction intervalAnd an optimal upper boundAnd forming a final prediction interval, and substituting the test set data into the Bayesian network model so as to complete the probabilistic prediction of the wind power.
According to the invention, the EMD decomposition, the chaotic firefly algorithm and the Bayesian network are combined, the EMD decomposition enables the wind power to be more stable, the establishment of a model is facilitated, environmental factors influencing wind power generation can be considered through the Bayesian network model, the wind power prediction is closer to the reality, the chaotic firefly algorithm is used, the prediction interval is more accurate, and the model can provide a certain reference in the aspect of resource scheduling.
Claims (1)
1. A wind power probabilistic prediction method based on a chaotic firefly algorithm and a Bayesian network is characterized by comprising the following steps:
step 1, acquiring wind speed, wind direction, air temperature and wind power actual power data and carrying out data preprocessing:
step 1.1, collecting historical data of wind speed to form an original wind speed sequence, and performing missing value and abnormal value filling and normalization processing on the original wind speed sequence to obtain a preprocessed wind speed sequence which is recorded as V ═ V1,v2,...vi,...,vN],viI is more than or equal to 1 and less than or equal to N, and N is the total number of samples, wherein the wind speed data of the ith time point in the preprocessed wind speed sequence V is the wind speed data of the ith time point;
acquiring historical data of wind directions to form an original wind direction sequence, and performing missing value and abnormal value filling and normalization processing on the original wind direction sequence to obtain a preprocessed wind direction sequence which is recorded as F ═ F1,f2,...fi...fN],fiWind direction data of the ith time point in the preprocessed wind direction sequence F are obtained;
collecting historical data of air temperature to form an original air temperature sequence, and performing missing value and abnormal value filling and normalization processing on the original air temperature sequence to obtain a preprocessed air temperature sequence which is marked as T ═ w1,w2,...wi,...wN],wiThe temperature data of the ith time point in the preprocessed temperature sequence T is obtained;
acquiring actual power historical data of wind power to form an original wind power sequence, and filling missing values and abnormal values and normalizing the original wind power sequence to obtain a preprocessed wind power sequence which is recorded as P ═ P1,p2,...,pi,...,pN],piWind power data of the ith time point in the wind power sequence P after the pretreatment is obtained;
dividing a data set consisting of the preprocessed wind speed sequence, wind direction sequence, air temperature sequence and wind power sequence into training set data and test set data;
step 1.2, carrying out empirical mode decomposition on the preprocessed wind power sequence P to obtain a data set consisting of k IMF components and a margin; the k IMF components are denoted as Is the jth IMF component, and is the jth IMF componentThe wind power decomposition value of the ith time point;
step 2, constructing a Bayesian network model by using training set data:
step 2.1, the jth IMF componentWind power decomposition value of the ith time pointAnd the wind speed data v of the ith time pointiWind direction data fiAnd gas temperature data wiAs an influence factor in the bayesian network model, the jth IMF component is addedWind power decomposition value of the (i + 1) th time pointAs an output node, thereby constructing a Bayesian network model;
step 2.2, respectively calculating the conditional probability of the output node corresponding to each influence factor when the influence factors take different values according to historical data, thereby obtaining a conditional probability table;
step 2.3, obtaining the jth IMF component according to the conditional probability table and the Bayesian network modelPower resolution value of the (i + 1) th time pointAnd taking a power interval corresponding to the highest point on the probability distribution curve as the jth IMF componentWind power decomposition value of the (i + 1) th time pointThe initial prediction interval of (1);
step 2.4, repeating the steps 2.1 to 2.3, so as to obtain an initial prediction interval of the power decomposition value of the (i + 1) th time point in the k IMF components, taking the sum of the initial prediction intervals of the power decomposition value of the (i + 1) th time point in the k IMF components as the wind power prediction interval of the (i + 1) th time point, and recording the sum as the wind power prediction interval of the (i + 1) th time point
Step 3, obtaining an optimal interval amplitude variation range by using a chaotic firefly algorithm:
step 3.1, predicting the interval according to the wind power of the (i + 1) th time pointDetermining the median of the prediction interval of the (i + 1) th time pointWherein,the predicted value is used as the wind power predicted value of the (i + 1) th time point;
predicting the wind power of the (i + 1) th time pointLower limit of (2)Wind power predicted value divided by (i + 1) th time pointThe lower ratio of the (i + 1) th time point is recorded asThereby obtaining the lower limit ratios of the N time points, and selecting the maximum value and the minimum value in the lower limit ratios of the N time points as the lower limit ratio betalowThe variation range of (a);
predicting the wind power of the (i + 1) th time pointUpper limit of (2)Wind power predicted value divided by (i + 1) th time pointThe upper ratio of the time points at i +1 is recorded asThereby obtaining the upper limit ratios of the N time points, and selecting the maximum value and the minimum value in the upper limit ratios of the N time points as the upper limit ratio betahighThe variation range of (a);
lower limit ratio betalowAnd an upper limit ratio betahighThe method is used as a parameter to be optimized in the chaotic firefly algorithm, and two corresponding variation ranges are used as the variation ranges of the population;
step 3.2, initializing the population:
setting a compression operator as g, a population scale as M, a current evolutionary algebra as T, and a maximum evolutionary algebra as TmaxThe current chaotic search frequency is D, and the maximum chaotic search frequency is DmaxLight intensity ofAbsorption factor gamma, gamma is in the range of 0,1]Maximum attraction ω0Step size factor eta, eta is equal to [0,1 ]];
When the initialization t is 0, generating M random numbers in the variation range of the population and taking the random numbers as the initial positions of M fireflies, wherein the initial position of the nth fireflies in the t evolution iterationThe initial position of the mth firefly isN is more than or equal to 1 and less than or equal to M, M is more than or equal to 1 and less than or equal to M, wherein,the nth firefly is in a lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the nth firefly at the t evolution iteration is the upper limit ratio betahighThe random number in the variation range of (a),the mth firefly is in the lower limit ratio beta in the t evolution iterationlowThe random number in the variation range of (a),the mth firefly at the tth evolution iteration is the upper limit ratio betahighRandom number in the variation range of (2), the initial position of the firefly population is recorded as
Step 3.3, calculating the fluorescence brightness of the firefly:
the luminance of the nth firefly in the t evolution iteration is constructed by using the formula (1)And the luminance of the mth firefly in the tth evolutionary iteration is obtained according to the formula (1)
In the formula (1), u is a confidence level,the average bandwidth of the prediction interval of the nth firefly in the t evolution iteration is obtained by the formula (2),the predicted interval coverage rate of the nth firefly in the t evolution iteration is obtained by the formula (3),to predict the interval coverageIs obtained by the formula (4), and lambda is the predicted interval coveragePenalty factor when confidence level mu is not reached;
in the formula (2), R is a wind power true value sequence P ═ P1,p2,...,pi,...,pN]The difference between the maximum value and the minimum value in (b),the lower bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (5),the upper bound of the prediction interval of the (i + 1) th time point of the nth firefly in the t evolution iteration is obtained by the formula (6);
in the formula (3), bn,i+1Is the Boolean constant of the (i + 1) th time point of the nth firefly, if the real value p of the wind power of the (i + 1) th time pointi+1The prediction interval range of the (i + 1) th time point of the nth firefly in the t evolution iterationIn the interior, then order bn,i+11 is ═ 1; otherwise, let bn,i+1=0;
In the formulae (5) and (6),predicting the median of the interval for the (i + 1) th time point of the nth firefly;
according to the initial position and the fitness function of the fireflies, the fitness value of each firefly is used as the initial fluorescence brightness of the fireflyThe fluorescence brightness of the t-th evolution iterationMinimum value of (1) is notedWherein,for the t-th iteration of evolution, the firefly populationIs located at the optimum position in the (c),to an optimum positionIs determined by the first component of (a),to an optimum positionA second component of (a); let Igmin(Xgbest) Is the global optimum fitness value after t evolutionary iterations, andmake global optimum position
Step 3.4, the firefly position moves:
according to the light intensity absorption factor gamma and the maximum attraction omega0Obtaining the mutual attraction degree omega of the mth firefly and the nth firefly; if it isThe mth firefly moves toward the nth firefly according to the mutual attraction degree omega; and obtaining the updated position of the mth firefly and using the updated position as the position of the mth firefly in the (t + 1) th evolution iteration and recording the position as the updated positionOtherwise, the nth firefly moves towards the mth firefly according to the mutual attraction omega; and obtaining the updated position of the nth firefly and using the updated position as the position of the nth firefly in the (t + 1) th evolution iteration, and recording the position as the position of the nth fireflyThereby obtaining the updated positions of all the fireflies and forming a firefly population during the (t + 1) th evolutionary iteration;
step 3.5, obtaining the brightness of each individual in the firefly population during the t +1 th evolution iteration by using the formula (1), and comparing the brightness among the firefly individuals, so as to find out the fitness value of the firefly with the minimum brightness in the firefly population during the t +1 th evolution iteration, and recording the fitness value as the fitness valueWherein,the optimal position in the firefly population after the t +1 th evolutionary iteration;
if the global optimum fitness valueThen will beIs assigned to XgbestThereby updating the global optimum position Xgbest(ii) a Otherwise, the global optimal position XgbestKeeping the same;
step 3.6, the optimal position in the firefly population during the t +1 th evolution iterationLocal search is performed nearby:
initialization d ═ 0, at [ -1,1 [ ]]Randomly generating q-dimension chaotic variable in d-th chaotic search in intervalq represents a dimension, and q is 1, 2;
the optimal position of the t +1 th evolution iterationAssigning to the optimal coordinate y in the d-th chaotic search(d)And q is 1,when q is equal to 2, the reaction is carried out, for the optimal coordinate y in the d-th chaotic search(d)The q-th component of (a);
step 3.7, chaotic search is carried out by using the logistic mapping shown in the formula (7) to obtain chaotic variables during the d +1 th chaotic search
In the formula (7), s is a constant and is more than 0 and less than or equal to 2;
step 3.8, obtaining the optimal coordinate y in the d +1 th chaotic search by using the formula (8)(d+1)Q component of
In formula (8), when q is 1, xq,maxAs the first component of the initial position of the firefly populationMaximum value of (1), xq,minAs the first component of the initial position of the firefly populationMinimum value of (1); when q is 2, xq,maxSecond component of initial position of firefly populationMaximum value of (1), xq,minSecond component of initial position of firefly populationMinimum value of (1); g(t)Compressing the operator after the t-th evolution iteration and obtaining the result by using an equation (9):
in formula (9), L is a constant greater than 0;
step 3.9, if D is less than DmaxIf so, assigning d +1 to d, and returning to the step 3.7; otherwise, obtaining the optimal coordinate sequence through chaotic searchAnd proceeds to step 3.9.1;
step 3.9.1, calculating the fitness value of the optimal coordinate sequence using equation (1)Finding the minimum fitness value in the fitness values of the optimal coordinate sequence and recording the minimum fitness value as Imin(ybest) Wherein, ybestFor the optimal coordinate sequenceThe optimal position of (1);
step 3.9.2 if the global optimum fitness valueThen pass throughUpdating the global optimal position; otherwise, let the global optimum position XgbestKeeping the same;
step 3.10, if T is less than TmaxAssigning t +1 to t and returning to the step 3.3; otherwise, the global optimal position X in the firefly population is obtainedgbestObtaining the optimal solution of the fitness functionAnd
step 4, according to the optimal solutionAndrespectively calculating the optimal lower bound of the prediction interval of the (i + 1) th time pointOptimal upper bound of prediction interval of i +1 th time pointAnd by an optimal lower bound of the prediction intervalAnd an optimal upper boundAnd forming a final prediction interval, and substituting the test set data into the Bayesian network model so as to complete the probabilistic prediction of the wind power.
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