CN110110912B - Photovoltaic power multi-model interval prediction method - Google Patents
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Abstract
The invention provides a photovoltaic power generation seasonal multi-model interval prediction method based on an extreme learning machine and kernel density estimation, which comprises the steps of firstly, analyzing indexes such as output power, power deviation, power change rate and the like of a photovoltaic power station, and showing that photovoltaic output and fluctuation show obvious seasonal distribution characteristics according to results; establishing a deterministic prediction model of photovoltaic output in different seasons by using an extreme learning machine neural network; and secondly, fitting the error distribution of deterministic prediction by a nonparametric nuclear density estimation method to obtain a photovoltaic power prediction interval meeting a certain confidence level. The method can describe the possible fluctuation range of the photovoltaic power under different confidence levels, provides a way for evaluating the reliability of the prediction interval, and provides support for the photovoltaic power station in the aspects of risk evaluation and system reliability analysis.
Description
Technical Field
The invention relates to a photovoltaic power generation seasonal multi-model interval prediction method based on an extreme learning machine and kernel density estimation, and belongs to the field of photovoltaic power generation prediction.
Background
Photovoltaic power generation is rapidly developed and is one of the most promising energy sources. By the end of 2017, the global photovoltaic power generation installed capacity is increased by 102GW, and the accumulated installed capacity reaches 405 GW. The photovoltaic power generation is influenced by uncontrollable meteorological and environmental factors, the output of the photovoltaic power generation has large fluctuation and randomness, and the grid connection of a large-scale photovoltaic power generation system influences the stability of a power grid, the power quality of the power grid and the operation and the dispatching of a power system. The accurate photovoltaic power generation power prediction can effectively improve the safety and stability of the operation of the power grid, so that the access rate of photovoltaic power generation is improved.
At present, research in the field of photovoltaic power prediction mainly focuses on deterministic prediction, but a deterministic prediction method cannot effectively describe distribution of prediction errors, and a system can not decide a reserved standby system based on photovoltaic deterministic prediction in scheduling operation, so that the system is constrained in practical engineering application.
In addition, the photovoltaic output has obvious periodicity and nonlinearity, and the distribution characteristics of the photovoltaic output are different under different weather conditions in different seasons, so that the mapping relation to be fitted by the photovoltaic power generation power prediction model has obvious difference under different weather conditions, and the accurate prediction of the power generation power under various different weather conditions is very difficult by adopting a single model.
Disclosure of Invention
The invention aims to provide a photovoltaic power generation power season multi-model interval prediction method based on an extreme learning machine and kernel density estimation, so that the fluctuation range of photovoltaic power is accurately estimated, and richer uncertain information is provided for power grid enterprises in the aspects of risk assessment and system reliability analysis.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a photovoltaic power multi-model interval prediction method comprises the following steps:
s1, collecting historical operation data, historical environment data and numerical weather forecast data of a photovoltaic power station;
s2, analyzing distribution characteristics of photovoltaic output and fluctuation thereof according to collected historical data of the photovoltaic power station, and classifying the photovoltaic output and the fluctuation thereof according to seasons; theoretical power P of photovoltaic power plant based on the data collected in step S1th(t) and the actual power Pr(t) calculating the power deviation PeAnd rate of change of power λ:
Pe=Pth(t)-Pr(t)
according to the calculation result, the output power P and the power deviation P of the photovoltaic power station are statistically analyzedeObtaining the obvious seasonal distribution characteristics of the power change rate lambda and the change trend and probability distribution characteristics in one year, and classifying the data collected in the step S1 according to seasons based on the statistical analysis result;
s3, utilizing limit according to classified dataThe learning machine establishes a seasonal prediction model, S31. establishing a deterministic prediction model for each season using an extreme learning machine for training data divided according to seasons, for a training sample (x)i,yi),xi∈Rp,yi∈Rp,i=1,2,…,N,xiInput data representing a model, yiTo predict target data, RPSetting an extreme learning machine containing L hidden layer nodes for model input and output sample sets, wherein an extreme learning machine model with a stimulus function f (x) can be expressed as
Wherein: beta is alConnecting weight vectors between the first hidden layer node and the output neuron; omegai=[ωi1,ωi2,…,ωiL]TIs the weight connecting the l-th hidden node and the input node; blThe deviation of the first hidden layer node is shown; omegai·xiForm omegaiAnd xiInner product of (d);
s32, applying the test data divided according to seasons to the deterministic prediction model trained in the step S31 to obtain deterministic prediction power, and calculating deterministic prediction error
e=Pfore-Pprac
Wherein: pforeA photovoltaic power certainty prediction value is obtained; ppracActual measurement of photovoltaic power;
s33, dividing the deterministic prediction power data into proper power levels, setting the length delta P of each power level to be 1000W, and setting the maximum value P of the powermax10000W, minimum value PminWhen 0, the number of segments K is:
K=[(Pmax-Pmin)/ΔP]+1
and is divided into
Dk=[Pmin+(k-1)ΔP,Pmin+kΔP]
Wherein: k is 1,2, …, K;
s34, fitting the prediction error e by adopting kernel density estimation, wherein the probability density function is
Wherein: k (x) is a kernel function; e.g. of the typejIs a prediction error sample; h is the window width; j is the total number of prediction error samples;
s35, after the probability density function of the prediction error is obtained through the method in the step S34, the cumulative probability distribution function is obtained, the cumulative probability density distribution function is set to be F (delta), wherein delta is a random variable representing the prediction error,is an inverse function of F (delta) and represents a boundary value of a prediction error interval, whereinIs the cumulative probability of prediction error, the actual power PpracThe confidence interval satisfying a confidence level of 1- α is:
[Pfore+G(α1),Pfore+G(α2)]
wherein: alpha is alpha2-α11-alpha, taking the symmetrical probability interval, i.e. alpha1=α/2,α2=1-α/2;
And S4, photovoltaic power interval prediction is achieved through a seasonal prediction model.
Furthermore, the historical operating data comprises historical power data of the photovoltaic power station, the historical environmental data comprises historical irradiance, environmental temperature, humidity and wind speed data corresponding to the photovoltaic power station, and the numerical weather forecast data comprises numerical weather forecast irradiance, environmental temperature, humidity and wind speed data of the location of the photovoltaic power station.
Further, the step S4 includes:
s41, inputting numerical weather forecast data into the deterministic prediction model in the step S31 to obtain deterministic prediction power;
and S42, substituting the predicted power into the confidence interval formula of the step S35 according to the power grade divided by the step S33, and obtaining the photovoltaic power prediction interval.
The photovoltaic power multi-model interval prediction method has the advantages that:
1. the multi-model prediction method based on the seasonal characteristics provides possibility for improving the adaptability of the model under different operating conditions, and can obtain better prediction accuracy.
2. The interval prediction method can quantify the variation of the prediction result caused by uncertain factors, give the upper and lower limits of the range of the predicted power in the predicted time period, provide a confidence interval under a certain confidence level, has comprehensive prediction information, and has more significance for risk management and supply and demand balance of the power market.
3. The non-parameter estimation method does not need to make any hypothesis, the function form and the parameters of the non-parameter estimation method are unknown, and the non-parameter estimation method is more consistent with the real distribution of random variables than the parameter estimation method, wherein the kernel density estimation method has the advantages of high fitting accuracy, intuition, understandability, convenience in implementation and the like.
Drawings
FIG. 1 is a flow chart of a photovoltaic power multi-model interval prediction method
FIG. 2 is a photovoltaic output power trend graph
FIG. 3 is a diagram of a trend of deviation of photovoltaic power
FIG. 4 is a trend graph of photovoltaic power change rate
FIG. 5 is a photovoltaic power distribution diagram in a typical season
FIG. 6 is a photovoltaic power deviation profile for a typical season
FIG. 7 is a photovoltaic power rate of change profile for a typical season
FIG. 8 is a diagram of a network structure of an extreme learning machine
FIG. 9 is a diagram showing a probability density distribution diagram of each power level in spring
FIG. 10 is a graph showing probability density distribution of each power level in winter
FIG. 11 is a graph comparing deterministic prediction performance of two models
FIG. 12 is a diagram of seasonal multi-model power prediction intervals
FIG. 13 is a graph of annual single model power prediction interval
Detailed Description
In order that those skilled in the art can better understand the present invention, the following technical solutions are further described with reference to the accompanying drawings and examples.
A photovoltaic power multi-model interval prediction method based on extreme learning machine and kernel density estimation is disclosed, a flow chart is shown in figure 1, and the method comprises the following specific steps:
s1, collecting historical operation data, historical environment data and numerical weather forecast data of the photovoltaic power station.
The historical operation data comprises historical power data of the photovoltaic power station, the historical environment data comprises historical irradiance, environment temperature, humidity and wind speed data corresponding to the photovoltaic power station, and the numerical weather forecast data comprises numerical weather forecast irradiance, environment temperature, humidity and wind speed data of the location of the photovoltaic power station. Selecting the data of a new energy electric power system national key laboratory photovoltaic empirical test power station of North China Power university in 2017 years all the year, wherein the power station consists of a photovoltaic power generation system with the capacity of 250Kw, a solar energy meteorological station, a photovoltaic power station monitoring system and a numerical weather forecasting system, and the data sampling time is 15 minutes.
S2, analyzing distribution characteristics of photovoltaic output and fluctuation thereof according to collected historical data of the photovoltaic power station, and classifying the photovoltaic output and the fluctuation thereof according to seasons, wherein the method specifically comprises the following steps:
s21, according to the data collected in the step S1, theoretical power P of the photovoltaic power station is obtainedth(t) and the actual power Pr(t) calculating the power deviation Δ P and the power change rate λ.
ΔP=Pth(t)-Pr(t)
The power deviation describes the weakening effect of the shadow, cloud cover shielding, weather change and temperature on the photovoltaic output on the basis of the outer envelope line of the photovoltaic output, and the physical meaning of the power deviation is the difference value of the actual output and the theoretical output of the photovoltaic power station and reflects the attenuation degree of the photovoltaic output.
The power change rate describes the relative change amplitude of the photovoltaic output within a certain time period (15min), and reflects the intensity of the photovoltaic output fluctuation in a short time.
And S22, according to the calculation result of the step S21, statistically analyzing the change trend and the probability distribution characteristic of the photovoltaic power station output power P, the power deviation delta P and the power change rate lambda in one year to obtain obvious seasonal distribution characteristics of the photovoltaic power station output power P, the power deviation delta P and the power change rate lambda.
As shown in fig. 2, 3 and 4, the most important factor determining the photovoltaic power generation is the magnitude of solar irradiance received by the photovoltaic module, the overall solar irradiance is strong in spring and summer, and weak in autumn and winter, so that the variation trend of the photovoltaic power generation in one year presents an obvious seasonal distribution characteristic, the photovoltaic output is high in spring and summer, and the photovoltaic output is low in autumn and winter; the power deviation generated in summer is maximum and is decreased progressively from summer to spring and autumn, and the power deviation is minimum in winter, and the power deviation has obvious seasonal difference; the power change rate shows obvious regularity along with the change of seasons, the power change rate is larger in autumn and winter, and is smaller in spring and summer, which shows that the power generation power fluctuates more severely in autumn and winter.
The seasonal characteristics of the variables such as the photovoltaic power generation power, the power deviation, and the power change rate are counted, as shown in table 1. The photovoltaic power and the power deviation value are larger in spring and summer and smaller in autumn and winter, which are consistent with the seasonal variation trend of solar irradiance in one year, and the overall variation trend of the power variation rate is opposite to the former two indexes, which shows that the power generation power difference value is larger between the seasons in autumn and winter, and the power variation rate is increased. The change of the characteristic value shows that the photovoltaic power generation power and the fluctuation thereof can also show seasonal trends under the influence of factors such as weather and weather in different seasons.
TABLE 1 seasonal characteristics of photovoltaic output power fluctuations
And carrying out probability analysis on the photovoltaic power, the power deviation, the power change rate and other variables in four seasons of spring, summer, autumn and winter respectively. As shown in fig. 5, when the power is 0, the corresponding probability is the ratio of the small power such as sunrise and sunset to the total day duration of the night no-power duration, so that the longest night time in winter can be obtained, the shortest night time in summer can be obtained, the spring is slightly longer in autumn, the opposite is obtained for the corresponding photovoltaic power generation duration, and the night time has a great influence on the photovoltaic power generation power. Fig. 6 and 7 show that the probability of large power deviation (>4000W) is the largest in summer, and the power change rate distribution is the most concentrated; and the power deviation in winter is mainly concentrated below 2000W, and the power change rate distribution is dispersed, which shows that the output fluctuation is most severe in a short time in winter. The probability distribution of photovoltaic output fluctuation in different seasons has obvious difference.
And S23, classifying the data collected in the step S1 according to seasons based on the statistical analysis result in the step S22.
S3, establishing a seasonal prediction model according to the classified data, and specifically comprising the following steps:
s31, establishing a deterministic prediction model for each season by using an Extreme Learning Machine (ELM) according to training data divided according to seasons, and performing prediction on training samples (x)i,ti),xi∈Rp,ti∈Rp,i=1,2,…,N,xiInput data set, t, representing a modeliFor predicting the target data set, the extreme learning machine model with L hidden nodes and the excitation function f (x) can be expressed as
Wherein: beta is aiConnecting weight vectors between the ith hidden node and the output neuron; omegai=[ωi1,ωi2,…,ωiN]TIs the weight connecting the ith hidden node and the input node; biThe deviation of the ith hidden layer node is shown; y isjIs the jth nodeThe output value of (d); omegai·xjForm omegaiAnd xjThe inner product of (d).
The extreme learning machine is a novel single-hidden-layer forward neural network, compared with the traditional neural network, the output weight of the network can be analyzed through one-step calculation, the generalization capability and the learning speed of the network are greatly improved, the extreme learning machine has strong nonlinear fitting capability, the calculated amount and the search space are also greatly reduced, and the network structure is shown in fig. 8. Aiming at the difference of the spring, summer, autumn and winter sections, the number L of hidden layer nodes of the model is respectively set to 410, 220, 300 and 260.
S32, applying the test data divided according to seasons to the deterministic prediction model trained in the step S31 to obtain deterministic prediction power, and calculating deterministic prediction error
e=Pfore-Pprac
Wherein: pforeA photovoltaic power certainty prediction value is obtained; ppracActual measurement of photovoltaic power;
s33, dividing the deterministic predictive power data into proper power levels, and assuming that the length delta P of each power level is 1000W, and the maximum power P ismax10000W, minimum value PminIf 0, the number of segments N is:
N=[(Pmax-Pmin)/ΔP]+1
and is divided into
Di=[Pmin+(i-1)ΔP,Pmin+iΔP]
Wherein: 1,2, …, N;
it is guaranteed that enough samples are available for probability statistics for each power level, since too few sample points do not reflect the actual distribution of prediction errors well. Therefore, the intervals with adjacent power grade distribution and less sample points are merged, so that the number of the sample points in the merged new interval meets the requirement. Thus, the spring samples are divided into 8 power levels, with the remaining seasons being 7 power levels, based on the number of deterministic predicted power samples.
S34, fitting the prediction error e by adopting kernel density estimation, wherein the probability density function is
Wherein: k (x) is a kernel function; e.g. of the typeiIs a prediction error sample; h is the window width; and N is the total number of samples.
S35, after the probability density function of the prediction error is obtained through the method in the step S34, the cumulative probability distribution function is obtained, the cumulative probability density distribution function is set to be F (delta), wherein delta is a random variable representing the prediction error,is an inverse function of F (delta), and represents a boundary value of a prediction error interval with probabilityThe actual power PpracThe confidence interval satisfying a confidence level of 1- α is:
[Pfore+G(α1),Pfore+G(α2)]
wherein: alpha is alpha2-α11-alpha, taking the symmetrical probability interval, i.e. alpha1=α/2,α2=1-α/2。
In fig. 9, prediction errors of spring power levels are unimodal distribution, but distribution forms are obviously different, while fig. 10 includes unimodal and multimodal distributions, which shows that prediction error probability distributions under different power levels are obviously different, and prediction error probability distributions under different seasons under the same power level are also obviously different. The method is feasible according to the segmented fitting method in different seasons, and can well describe the prediction error probability distribution corresponding to the prediction power of each grade.
S4, photovoltaic power interval prediction is achieved through a seasonal prediction model, and the method specifically comprises the following steps:
s41, inputting numerical weather forecast data into the deterministic prediction model in the step S31 to obtain deterministic prediction power.
And evaluating the deterministic prediction effect of the seasonal multi-model and the annual model by adopting the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE).
Wherein:the photovoltaic power predicted value is obtained; x is the actual value of the photovoltaic power; n is the number of samples.
MAE expresses the accuracy of prediction by measuring the average distance between the predicted value and the actual value, and RMSE represents the standard deviation of a sample, so that the stability of prediction can be quantified. The smaller the MAE and RMSE values, the better the prediction.
Comparing the seasonal multi-model with the annual single model power prediction method, the deterministic prediction power and the actual power distribution obtained are shown in fig. 11. Seasonal multi-model predictions are more densely distributed, i.e., closer to actual power values, than annual single models.
Table 2 shows the deterministic prediction error and accuracy for two prediction methods, which can be concluded as follows:
(1) in terms of average absolute error and root mean square error, the seasonal multi-model power prediction method is smaller than a single model all year around;
(2) the prediction precision of the seasonal multi-model is higher than 95%, and the model has better prediction performance than a single model all the year round.
TABLE 2 comparison of deterministic prediction performance of seasonal multi-models to annual models
And S42, substituting the predicted power into the confidence interval formula in the step S35 according to the corresponding grade to obtain the photovoltaic power prediction interval.
And evaluating an uncertainty prediction result by adopting a prediction interval coverage rate (PICP) and a prediction interval average bandwidth (PINAW).
Wherein: n is a radical ofiIs the number of predicted samples; κ is a boolean value, and κ is 1 if the prediction target value is included in the upper and lower limits of the section prediction, otherwise κ is 0. The index reflects the probability that the actual observed value falls in the upper and lower boundaries of the prediction interval, and the larger the value is, the more target values fall in the prediction interval, and the better the prediction effect is.
Wherein: and R is the variation range of the prediction target value. The index evaluates the capability of the prediction result for gathering uncertain information, and at a certain PICP time, if the PINAW value is smaller, the prediction interval is narrower, and the prediction effect is better. The method avoids the problems that the prediction interval is too wide due to the fact that reliability is simply pursued, effective uncertainty information of the prediction value cannot be given, and decision value is lost.
And selecting data of 2 days in each season in the verification sample to compare and analyze with the annual model, and respectively giving photovoltaic power prediction intervals of different confidence levels of the selected sample under the seasonal multi-model and the annual single model in fig. 12 and fig. 13. Under the same confidence level, the prediction results of the seasonal multi-model can have narrower upper and lower limits of an interval while the photovoltaic time series change is ensured to be tracked.
The prediction evaluation indexes of the two models are calculated respectively, and the PICP and PINAW indexes obtained under different confidence levels are shown in Table 3.
TABLE 3 comparison of uncertainty prediction performance between seasonal multi-models and annual models
Under the same confidence level, the seasonal multi-model prediction method PICP is obviously superior to a year-round single model, and PINAWs are smaller than the year-round single prediction model. The invention can obtain a narrower prediction interval while ensuring that more points fall in the prediction interval, has more accurate prediction result and provides more accurate selection basis for decision makers.
The above examples are merely representative of preferred embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, various changes, modifications and substitutions can be made without departing from the spirit of the present invention, and these are all within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (3)
1. A photovoltaic power multi-model interval prediction method is characterized by comprising the following steps:
s1, collecting historical operation data, historical environment data and numerical weather forecast data of a photovoltaic power station;
s2, analyzing distribution characteristics of photovoltaic output and fluctuation thereof according to collected historical data of the photovoltaic power station, and classifying the photovoltaic output and the fluctuation thereof according to seasons; theoretical power P of photovoltaic power plant based on the data collected in step S1th(t) and the actual power Pr(t) calculating the power deviation PeAnd rate of change of power λ:
Pe=Pth(t)-Pr(t)
according to the calculation result, the output power P and the power deviation P of the photovoltaic power station are statistically analyzedeThe characteristic of the change trend and probability distribution of the power change rate lambda in one year is compared to obtain the characteristic of obvious seasonal distribution of the power change rate lambda in order to solve the problem of the influence of the power change rate lambda on the power change rate lambda in the whole yearClassifying the data collected in the step S1 according to seasons based on the statistical analysis result;
s3, establishing a seasonal prediction model by using an extreme learning machine according to the classified data, S31, establishing a deterministic prediction model for each season by using the extreme learning machine according to the training data divided according to the seasons, and establishing a deterministic prediction model for a training sample (x)i,yi),xi∈Rp,yi∈Rp,i=1,2,…,N,xiInput data representing a model, yiTo predict target data, RPSetting an extreme learning machine containing L hidden layer nodes for model input and output sample sets, wherein an extreme learning machine model with a stimulus function f (x) can be expressed as
Wherein: beta is alConnecting weight vectors between the first hidden layer node and the output neuron; omegai=[ωi1,ωi2,…,ωiL]TIs the weight connecting the l-th hidden node and the input node; blThe deviation of the first hidden layer node is shown; omegai·xiForm omegaiAnd xiInner product of (d);
s32, applying the test data divided according to seasons to the deterministic prediction model trained in the step S31 to obtain deterministic prediction power, and calculating deterministic prediction error
e=Pfore-Pprac
Wherein: pforeA photovoltaic power certainty prediction value is obtained; ppracActual measurement of photovoltaic power;
s33, dividing the deterministic prediction power data into proper power levels, setting the length delta P of each power level to be 1000W, and setting the maximum value P of the powermax10000W, minimum value PminWhen 0, the number of segments K is:
K=[(Pmax-Pmin)/ΔP]+1
and is divided into
Dk=[Pmin+(k-1)ΔP,Pmin+kΔP]
Wherein: k is 1,2, …, K;
s34, fitting the prediction error e by adopting kernel density estimation, wherein the probability density function is
Wherein: k (x) is a kernel function; e.g. of the typejIs a prediction error sample; h is the window width; j is the total number of prediction error samples;
s35, after the probability density function of the prediction error is obtained through the method in the step S34, the cumulative probability distribution function is obtained, the cumulative probability density distribution function is set to be F (delta), wherein delta is a random variable representing the prediction error,is an inverse function of F (delta) and represents a boundary value of a prediction error interval, whereinIs the cumulative probability of prediction error, the actual power PpracThe confidence interval satisfying a confidence level of 1- α is:
[Pfore+G(α1),Pfore+G(α2)]
wherein: alpha is alpha2-α11-alpha, taking the symmetrical probability interval, i.e. alpha1=α/2,α2=1-α/2;
And S4, photovoltaic power interval prediction is achieved through a seasonal prediction model.
2. The prediction method of claim 1, wherein the historical operating data comprises historical power data of the photovoltaic power station, the historical environmental data comprises historical irradiance, ambient temperature, humidity and wind speed data corresponding to the photovoltaic power station, and the numerical weather forecast data comprises numerical weather forecast irradiance, ambient temperature, humidity and wind speed data of the location of the photovoltaic power station.
3. The prediction method according to claim 1, wherein the step S4 includes:
s41, inputting numerical weather forecast data into the deterministic prediction model in the step S31 to obtain deterministic prediction power;
and S42, substituting the predicted power into the confidence interval formula of the step S35 according to the power grade divided by the step S33, and obtaining the photovoltaic power prediction interval.
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