CN111563308B - Model generation method for representing renewable energy power probability distribution - Google Patents
Model generation method for representing renewable energy power probability distribution Download PDFInfo
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Abstract
The invention discloses a model generation method for representing renewable energy power probability distribution, which comprises the following steps: the method comprises the steps of inputting predicted data and measured data of historical output power of a renewable energy power station in a system; determining renewable energy power data required by modeling to obtain a probability density histogram or a cumulative distribution histogram; setting a renewable energy probability distribution tolerance error; determining parameters and orders of each order of a mixed form model for cutting off general distribution according to the probability density histogram or the cumulative distribution histogram based on a matlab curve fitting tool; a hybrid form model characterizing a truncated general purpose distribution of renewable energy power probability distributions is determined. The invention provides a method for modeling the randomness of renewable energy sources by cutting off a mixed form model of general distribution, which can more flexibly fit the shape of a probability distribution curve and more accurately represent the power distribution of the renewable energy sources compared with a Gaussian mixed model and other conventional distribution models.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a hybrid form model generation method for representing truncated general distribution of renewable energy power probability distribution.
Background
In recent years, with the wide grid-connected power generation of renewable energy sources such as wind power, the characteristic of output randomness of the renewable energy sources aggravates the uncertainty of the operation of a power system. In economic dispatch of a power system containing renewable energy sources, the influence of the randomness of the renewable energy sources on the standby of the system needs to be considered, namely how to describe a mathematical model of the renewable energy sources.
The actual distribution of wind power varies greatly depending on the predicted power thereof, so wind power is generally described as an actual power condition distribution model at the predicted power. When a plurality of wind power plants exist in the system, the actual power of each wind power plant is jointly distributed for the joint condition, namely the probability distribution of the actual power of all wind power plants under the condition that the predicted power of each wind power plant is known.
The Copula function is an effective method for modeling the joint conditional joint distribution of the actual power of each wind farm by considering the power correlation of multiple wind farms, and predicting the power and actual power cumulative distribution function (Cumulative Distribution Function, CDF) through all wind farms. The characterization accuracy of the Copula function method is affected by the characterization accuracy of the edge distribution of the Copula function method, and as the wind power plant prediction power, the multiple wind power plants and the power are related to the wind power plant in the geography and weather environment, the power distribution does not have obvious statistical rules, as shown in fig. 2 and 3, modeling such as Gaussian distribution, beta distribution and the like is difficult to use; because the Gaussian mixture model definition domain is unbounded, and the probability distribution function (Probability Density Function, PDF) curves of all the sub-Gaussian distributions are symmetrical, larger errors can occur during characterization; the output mode of directly using the historical data histogram often generates over-fitting due to limited data volume.
In view of this, it is desirable to provide a model that can accurately model the probability distribution of renewable energy power.
Disclosure of Invention
In order to solve the technical problems, the technical scheme adopted by the invention is to provide a model generation method for representing the probability distribution of renewable energy power, which comprises the following steps:
the method comprises the steps of inputting predicted data and measured data of historical output power of a renewable energy power station in a system; determining renewable energy power data required by modeling to obtain a probability density histogram or a cumulative distribution histogram; setting a renewable energy probability distribution tolerance error; determining parameters and orders of each order of a mixed form model of truncated general distribution according to the probability density histogram based on a matlab curve fitting tool; a hybrid form model characterizing a truncated general purpose distribution of renewable energy power probability distributions is determined.
In the method, the mixed form model for representing the truncated general distribution of the renewable energy power probability distribution specifically comprises the following steps:
the probability density function expressions of the mixed form model of the truncated general distribution are as follows:
wherein K is the mixed distribution order, K i The weight number of the ith order is 0 < k i Is less than or equal to 1α i 、β i And gamma i Parameters of the ith order truncated general distribution, respectively, - ≡ < alpha i ,β i ,γ i < + -infinity; m and n represent standardized intervals, namely defined domain intervals with PDF values of truncated general distribution strictly non-zero; when representing the actual power value of wind power, m=0, n=1; v i As a normalization coefficient, the following is given:
the cumulative distribution function expression of the hybrid form model of truncated general distribution is as follows:
in the method, the matlab curve fitting tool is a matlab self-contained cftool curve fitting tool box.
The invention provides the modeling of the randomness of the renewable energy sources by cutting off the mixed form model of the general distribution, and compared with the conventional distribution models such as the Gaussian mixed distribution model, the modeling of the renewable energy sources can be more flexible in fitting the shape of the probability distribution curve, and the power distribution of the renewable energy sources can be more accurately represented.
Drawings
FIG. 1 is a flow chart provided by the present invention;
FIG. 2 is a graph of unconditional probability of wind power for a typical wind farm provided by the present invention;
FIG. 3 is a graph of unconditional probability of wind power for another exemplary wind farm provided by the present invention;
FIG. 4 is a graph of the fitting effect of a mixed form model of truncated general distribution with the order of 3 on a wind power unconditional edge probability density histogram;
FIG. 5 is a graph of the effect of the Gaussian mixture model with the order of 3 on fitting the wind power unconditional edge probability density histogram.
Detailed Description
The invention is described in detail below with reference to the detailed description and the accompanying drawings.
As shown in fig. 1, the invention provides a model generation method for representing the probability distribution of renewable energy power, which comprises the following steps:
s1, inputting predicted data and measured data of historical output power of a renewable energy power station in a system;
s2, determining renewable energy power data required by modeling to obtain a probability density histogram or an accumulated distribution histogram; the renewable energy power data can be prediction data or actual measurement data;
s3, setting a renewable energy probability distribution tolerance error; the present embodiment may be root mean square error (Root Mean Square Error, RMSE);
s4, determining parameters and orders of each order of the mixed form model for cutting off the general distribution through a probability density histogram or an accumulated distribution histogram in the step S2 based on a curve fitting tool in matlab software. The curve fitting tool in matlab software can be a matlab self-contained cftool box or a least square method; in this embodiment, the sub-distribution of the mixed form model of the truncated general distribution, that is, the truncated general distribution model is based on the conclusion of the modeling method of the truncated general distribution model in Look-ahead economic dispatch with adjustable confidence interval based on a truncated versatile distribution model for wind power (based on the truncated general distribution model and the rolling economic dispatch of the wind power system with optimized confidence interval) proposed in the journal IEEE Transactions on Power Systems by the literature Chenghui Tang, jian Xu et al, 15june 2017. In this embodiment, the proposed hybrid form model of truncated general distribution is defined as a weighted sum of truncated general distribution models;
the model for building the probability distribution of renewable energy power by truncating the mixed form model of the general distribution is as follows:
probability density function (Probability Density Function, PDF) expressions of the hybrid form model of truncated general distribution are respectively as follows:
wherein K is the mixed distribution order, K i The weight number of the ith order is 0 < k i Is less than or equal to 1β i And gamma i Parameters of the ith truncated general distribution (Truncated Versatile Distribution, TVD), respectively, - ≡ < alpha i ,β i ,γ i < + > infinity. m and n represent standardized intervals, namely defined domain intervals with PDF values of truncated general distribution strictly non-zero, and m=0 and n=1 when representing the actual power value of wind power; v i Is a normalization coefficient:
the cumulative distribution function (Cumulative Distribution Function, CDF) expression of the hybrid form model of truncated general distribution is as follows:
s5, determining a mixed form model of truncated general distribution representing the probability distribution of renewable energy power.
In this embodiment, wind power is taken as an example, solar photovoltaic power generation is also applicable to the model of this embodiment, and compared with a gaussian mixture model, the three-point mathematical characteristic of the hybrid model of this embodiment cut-off general distribution is as follows:
1) The mixed form model of the truncated general distribution can be used for fitting the probability distribution curve shape more flexibly;
2) The mixed form model for cutting off the general distribution has a definition domain [ m, n ] which is bounded and can be customized, and is consistent with the per-unit actual renewable energy output interval;
3) The CDF function of the hybrid form model of the truncated general distribution has an expression of closed-form analysis, as shown in expression (3).
The method of the present embodiment is described below by way of specific examples:
1. parameter setting
In order to study the spatial correlation among multiple wind farms, the following wind farm groups are selected:
the U.S. kansasa wind farm group, the data source is the year round synchronization data of the National Renewable Energy Laboratory (NREL) in the united states, which comprises 14 wind farms, about 52560 sets of actual wind power history data, each obtained by a continuous prediction method corresponding to the predicted power use, and is recorded as the U.S. kansasa wind farm group.
The predicted power and the corresponding actual power data of all the wind farms studied above are per unit, i.e. within [0,1p.u. ].
2. And (5) comparing the fitting effect of the truncated general distribution mixed form model and the Gaussian mixture model on the wind power actual power unconditional probability density histogram.
A mixed form model based on truncated general distribution of the same order (l=1, 2, 3, 4) and a gaussian mixed model fit a group number of 50 wind power actual power unconditional probability density histograms. Fig. 4 and 5 show, respectively, a mixed-form model and a gaussian mixed-model curve of a truncated general distribution when the order l=3, and their respective sub-distributions (truncated general distribution and gaussian distribution). Table 1 and table 2 below list the parameters of the truncated generic distributed mixed form model and the gaussian mixed model when the order l=3, respectively, table 3 is the Root Mean Square Error (RMSE) of the truncated generic distributed mixed form model and the gaussian mixed model at different orders, wherein the RMSEs of the truncated generic distributed mixed form model are 0.3444, 0.1927 and 0.07356 when l=2, 3, 4, respectively, and the RMSEs of the corresponding gaussian mixed models are 0.6125, 0.3799 and 0.225, respectively; it can be seen that, for the wind power unconditional edge probability density histogram, the fitting effect advantage of the mixed form model of the truncated general distribution is more obvious in the mixed form model and the Gaussian mixed model of the truncated general distribution of the same order.
It is noted that the hybrid form model of truncated general distribution in fig. 4, due to its bounded domain, all PDF curves fall into the wind power per unit power interval [0,1p.u. ]. For the gaussian mixture model, 16.62% of the area exceeds the left boundary, 0p.u., and 1.36% of the area exceeds the right boundary, 1p.u.;
as shown in fig. 5. When modeling the conditional joint probability distribution of the multiple wind power plants based on Copula theory, the conditional joint probability distribution of wind power is related to edge PDF and edge CDF of each wind power plant, when modeling the wind power unconditional probability distribution based on Gaussian mixture model, CDF values at the wind power output interval boundaries, namely 0p.u. and 1p.u. power values, due to the unbounded characteristics, the situation that the CDF at 0p.u. is not 0p.u., and the CDF at 1p.u. is not 1p.u. occurs, and characterization errors of PDF and CDF accumulate when the conditional joint distribution of the Copula theory is solved, so that the accuracy of the conditional joint distribution model of the multiple wind power plants is further reduced.
TABLE 1 Mixed form model parameters of 3 rd order truncated general distribution fitting probability Density histogram
TABLE 2 3 order Gaussian mixture model parameters fitting probability Density histogram
TABLE 3 RMSE of probability Density histogram fitting of Mixed form model and Gaussian mixture model of truncated general distribution
Based on analysis of the randomness of renewable energy power, aiming at the defects of the prior art, the invention provides the randomness of renewable energy modeling through a mixed form model of truncated general distribution, and simulation verification is carried out based on actual wind power plant output data, and results show that:
compared with a Gaussian mixture model and other conventional distribution models, the mixed form model for cutting off the universal distribution can more accurately represent the renewable energy power distribution.
The present invention is not limited to the above-described preferred embodiments, and any person who is informed of structural changes made under the teaching of the present invention should fall within the scope of the present invention, regardless of whether the technical solution is the same as or similar to the present invention.
Claims (2)
1. A model generation method for characterizing a probability distribution of renewable energy power, comprising the steps of:
the method comprises the steps of inputting predicted data and measured data of historical output power of a renewable energy power station in a system;
determining renewable energy power data required by modeling to obtain a probability density histogram;
setting a renewable energy probability distribution tolerance error;
determining parameters and orders of each order of a mixed form model of truncated general distribution according to the probability density histogram based on a matlab curve fitting tool;
determining a hybrid form model of a truncated general distribution characterizing a probability distribution of renewable energy power; wherein,,
the hybrid form model for representing the truncated general distribution of the renewable energy power probability distribution specifically comprises the following steps:
the probability density function expression of the mixed form model of truncated general distribution is as follows:
wherein K is the mixed distribution order, K i The weight number of the ith order is 0<k i Is less than or equal to 1α i 、β i And gamma i Parameters of the ith order truncated general distribution, - ≡<α i ,β i ,γ i <++ infinity; m and n represent standardized intervals, namely defined domain intervals with PDF values of truncated general distribution strictly non-zero; when representing the actual power value of wind power，m＝0，n＝1；v i As a normalization coefficient, the following is given:
the cumulative distribution function expression of the hybrid form model of truncated general distribution is as follows:
2. the method of claim 1, wherein the matlab curve fitting tool is a matlab self-contained cftool curve fitting kit.
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| CN105930671A (en) * | 2016-04-29 | 2016-09-07 | 武汉大学 | Improved versatile distribution and versatile mixture distribution models characterizing wind power probability distribution |
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| CN105975751A (en) * | 2016-04-29 | 2016-09-28 | 武汉大学 | Truncated versatile distribution model representing renewable energy power probability distribution |
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| 梁海峰 ; 曹大卫 ; 刘博 ; 刘子兴 ; 郑灿 ; 李鹏 ; .风电场概率分布模型建模及误差分析.华北电力大学学报(自然科学版).2017,(03),全文. * |
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