CN112541546A - Photovoltaic power station typical scene generation method based on multi-scene model - Google Patents
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Abstract
The invention relates to a photovoltaic power station typical scene generation method based on a multi-scene model, which comprises the following steps of firstly, obtaining historical data of output of a plurality of photovoltaic power stations under a power distribution network to form a multi-dimensional data set consisting of the historical output data of the photovoltaic power stations; then, clustering based on a local density center is carried out on the multi-dimensional set, and all data points are divided into a plurality of scenes; respectively modeling according to a plurality of scenes generated by clustering, and estimating joint probability distribution of the output of a plurality of photovoltaic power stations under each scene by using a kernel density estimation method and a Copula function; and finally, sampling the optimal Copula function under each scene by using a Latin hypercube sampling method to generate a photovoltaic output typical sample, and performing Monte Carlo probability load flow calculation on the generated sample so as to analyze the voltage quality of the power distribution network. The method can efficiently realize accurate modeling of the output of a plurality of photovoltaic power stations.
Description
Technical Field
The invention relates to a photovoltaic power station typical scene generation method based on a multi-scene model.
Background
With the gradual development of new energy, the permeability of the distributed photovoltaic power generation in a power distribution network is improved year by year. Meanwhile, the access of distributed photovoltaic brings some influences and challenges to the operation of a power distribution network, and the mismatch between the output of a photovoltaic power station and the time and space of the load can cause the problems of local voltage fluctuation, power transfer in a transformer area and the like. Considering the randomness and the volatility of the output of the photovoltaic system, the traditional deterministic power flow calculation method is difficult to meet the analysis requirement on the voltage risk of the distribution network system, and the operation state of the distribution network is usually obtained by using a probabilistic power flow algorithm. As one of widely used calculation methods, Monte Carlo-based simulation method can obtain accurate calculation results, but has the disadvantages of large calculation amount and requirement of obtaining probability load flow results through a large number of sampling samples and deterministic load flow calculation. The accuracy of the probabilistic power flow calculation using the simulation method greatly depends on the accuracy of the input variable modeling. In the calculation application such as photovoltaic access evaluation, the influence of different meteorological, illumination, social and economic factors on the output of a photovoltaic power station needs to be considered, so that a typical scene model needs to be generated to be used as a sampling object of a Monte Carlo method.
The modeling of photovoltaic output in a power distribution system still has problems to be solved at present, and on one hand, due to the fluctuation of the photovoltaic output, existing probability models such as Beta, Weibull and the like which are used traditionally cannot truly reflect the actual operation state of the existing probability models. On the other hand, in the traditional probabilistic power flow calculation, a plurality of photovoltaic power stations are still treated as independent power sources and are respectively sampled, and the correlation existing between the power stations is not utilized. In fact, in a photovoltaic high-permeability power distribution system, there are often a plurality of photovoltaic power stations in a relatively centralized range, and there are similarities in parameters, geographical locations, and operation times. The existing generation of various photovoltaic output scenes uses a single modeling method, however, the single modeling method covers all samples, and the fact that the correlation may change along with the influence of external factors such as weather, operation modes and the like is not considered. Therefore, modeling methods still have room to explore in terms of accuracy.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a photovoltaic power station typical scene generation method based on a multi-scene model and considering output correlation, and can efficiently realize accurate modeling of the output of a plurality of photovoltaic power stations.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a photovoltaic power station typical scene generation method based on a multi-scene model is characterized by comprising the following steps:
acquiring historical data of output of a plurality of photovoltaic power stations under a power distribution network, and performing data preprocessing to form a multi-dimensional data set consisting of the historical output data of the photovoltaic power stations;
clustering the multi-dimensional data set by a local density center-based clustering method, and dividing all data points into a plurality of scenes;
modeling according to a plurality of scenes generated by clustering respectively; obtaining an edge probability density function of each photovoltaic power station according to scenes by using a kernel density estimation method, constructing theoretical Copula functions in various forms for the edge probability density function of each type of scene, estimating parameters in each Copula form by using a maximum likelihood estimation method, and selecting an optimal Copula function by using an Euclidean distance method for modeling;
the optimal Copula function under each scene is sampled by utilizing a Latin hypercube sampling method, a photovoltaic output typical sample is generated, Monte Carlo probability load flow calculation is carried out on the generated sample, and therefore the voltage quality of the power distribution network is analyzed.
The technical scheme is further designed as follows: the specific steps of clustering the multi-dimensional dataset based on the local density center are as follows:
Wherein:
xirepresents the output of all photovoltaic power stations at the same moment, dcTo cut off the distance, dijIs the distance between two sample points;
and 5, removing outliers.
The method for determining the clustering center comprises the following steps:
establishing an index ρi×δiAnd setting an index threshold value, and judging the sample point of which the index is greater than the set threshold value as a clustering center.
The method for classifying the sample points comprises the following steps:
press rho to sample pointiIn descending order, for xiFind rhoiLarger than it, and a point neutralizing its distance dijNearest point xjX is a handlejIs assigned to xiThereby forming a plurality of scenes.
The method for eliminating outliers comprises the following steps:
dividing all data points in each scene into core points and outliers;
determining the boundary area of each class, and calculating cross-class point pairs xiAnd xjAverage local density of
Wherein xiIs a point within this class, xjPoints outside this class;
taking the maximum value of the average local density of all existing cross-class point pairs of a class as the upper bound of the average local density of the class; marking all the sample points once, if the local density of one sample point is smaller than the upper limit of the average local density of the class where the sample point is located, marking the sample point as an outlier, and otherwise, marking the sample point as a core point;
and (5) removing outliers.
When the optimal Copula function in each scene is sampled by using a Latin hypercube sampling method, the sampling quantity in each scene is determined in proportion according to the occurrence probability of each scene.
Compared with the prior art, the invention has the beneficial effects that:
according to the photovoltaic power station typical scene generation method based on the multi-scene model, the correlation among the output power of a plurality of photovoltaic power stations and the change of the correlation along with the external conditions are considered, and a single probability function model is improved into the multi-scene model by means of a clustering data mining method. And performing refined modeling on the data in each scene based on the joint probability distribution of the kernel density estimation and the Copula function estimation output. The accurate modeling of the output of a plurality of photovoltaic power stations can be efficiently realized. By using the method to perform subsequent probability load flow calculation, the accuracy of the calculation result can be improved, and the running speed of the program can be improved.
Drawings
FIG. 1 is an overall flowchart of a sample generation method based on a multi-scenario model according to the present invention.
FIG. 2 is a flow chart of photovoltaic output based on local density clustering;
FIG. 3 is an example of photovoltaic output clustering;
FIG. 4 is an example of the distribution of the output edge under each scenario;
FIG. 5 is a schematic diagram of construction steps of Copula function
FIG. 6 is a photovoltaic output sample generation example;
FIG. 7 is a wiring diagram of a power distribution network system used in an example probabilistic power flow calculation;
Detailed Description
The invention is described in detail below with reference to the figures and the specific embodiments.
Examples
Referring to fig. 1, a general flowchart of a sample generation method based on a multi-scenario model is shown. According to the invention, a clustering method based on a local density center is applied to output data sets of a plurality of photovoltaic power stations, and all data points are divided into a plurality of scenes, which are shown in reference to fig. 2 and 3. In this embodiment, a plurality of scenes generated by clustering are respectively modeled, and a joint probability distribution of the output of a plurality of photovoltaic power stations under each scene is estimated by using a kernel density estimation method and a Copula function, as shown in fig. 4 and 5. According to the method, a Latin hypercube sampling method is utilized to sample the model to generate a photovoltaic output typical sample, and Monte Carlo probability load flow calculation is carried out on the generated sample, so that the voltage quality of the power distribution network is analyzed, and the method is shown in a reference figure 6. The power distribution network topology used in this embodiment is shown with reference to fig. 7.
The method for generating the sample based on the multi-scenario model comprises the following steps:
step one, acquiring historical data of all photovoltaic power stations in a power distribution network, and cleaning and preprocessing the data. Assuming that the number of photovoltaic power stations accessed to the power distribution network is N, acquiring historical data of output of the N power stations to form an original data set, wherein each sample point x in the data setiThe output of all photovoltaic power stations at the same time is represented and is an N-dimensional vector. In the embodiment, historical data of two adjacent photovoltaic power stations in a certain area of Jiangsu province is selected.
And secondly, clustering the data set based on the local density center to generate a plurality of scenes, and then respectively modeling according to the scenes to form photovoltaic output multi-scene modeling. The clustering method based on the local density center solves the problems that the traditional K-Means clustering algorithm needs to depend on experience to determine parameters and is sensitive to noise and abnormal points.
Referring to fig. 2, fig. 2 is a flow chart of photovoltaic output based on local density center clustering. The Local Density Center (LDC) -based clustering method defines the local density and the distance offset of a sample as a clustering basis, and can automatically generate class numbers and clustering centers. The clustering analysis can mine the internal rules among data samples, so that the data are classified, and the method is mainly applied to the aspects of scene generation, fault screening and the like in the field of power systems. The clustering algorithm comprises the following specific steps:
firstly, assuming that the number of photovoltaic power stations accessed to a power distribution network is N, acquiring historical data of output of the N power stations to form an original data set, wherein each sample point x in the data setiThe output of all photovoltaic power stations at the same time is represented and is an N-dimensional vector.
X for each output sample pointiDefining a local density function p for each sample pointi：
Wherein:
dcfor the truncation distance, is a predetermined parameter, dijIs the distance between two sample points.
Defining the distance offset delta of each sample pointiMeaning that all local densities are greater than the sample point xiTo xiMinimum value of distance of (d):
and fourthly, determining the clustering center. The idea of determining the clustering center is that the clustering center needs to satisfy: local density ρ of the sample point itselfiLarge, i.e. the density of its surrounding points should be less than it, and the distance between a point more dense than it, i.e. the distance offset δ of the sampleiShould be as large as possible. Comprehensively considering the above conditions, establishing an index rhoi×δiAnd setting a threshold value, and judging that the point is a clustering center when the index is greater than the set threshold value.
And fifthly, classifying the rest pairs of sample points. First, press ρ for a sample pointiIn descending order, for xiFind rhoiLarger than it, and a point neutralizing its distance dijNearest point xjX is a handlejClass number of (2) is given to xi. And sequentially carrying out category assignment on all sample points according to the descending order of the local density, thereby forming a plurality of scenes.
Sixthly, removing outliers. For all data points in each scene, there are core points and outliers, which are eventually excluded.
The bounding region of each class is determined, and is composed of data points of the nature: they are at a distance dcThere are other types of points in the neighborhood of (2). Computing pairs of such cross-classes (denoted x)iAnd xj，xiPoints within the class) of the target
Taking the maximum value of the average local density of all existing cross-class point pairs of a class as the upper bound of the average local density of the class; and then marking all the sample points once, if the local density of one sample point is smaller than the upper limit of the average local density of the class in which the sample point is positioned, marking the sample point as an outlier, and otherwise, marking the sample point as a core point.
Referring to fig. 3, fig. 3 is a schematic diagram of an example of photovoltaic output clustering according to this embodiment. The photovoltaic output scenes are divided into 5 classes, i.e. 5 scenes, and the difference of the scenes may be caused by factors such as external meteorological conditions, self running modes and the like.
And step three, respectively modeling according to a plurality of scenes generated by clustering, estimating each photovoltaic output in the power distribution network by using a kernel density estimation method, and acquiring an edge probability density function of each photovoltaic power station according to the scenes. In the embodiment, a gaussian kernel function is used, and the parameter estimation adopts maximum likelihood estimation. Referring to fig. 4, fig. 4 is a schematic diagram of an example of the distribution of the output edge under each scene.
The nuclear density estimation method is a non-parametric method, a known standard form does not need to be assumed in advance in the face of any probability distribution, and therefore the method for estimating the probability distribution situation of photovoltaic output and load has a good expected effect on accuracy.
The idea of kernel density estimation is to fit the data samples using a smoothed peak function (kernel function). For n sample points (x) satisfying independent same distribution F1,x2,…xn) If the probability density function is f, the kernel density estimation function is of the following form:
where K (.) is a kernel function, h>0 is a smoothing parameter, called bandwidth, and also sees the somebody's window.
Referred to as scaled Kernel. The present invention uses a gaussian kernel function, i.e., k (x) is phi (x), which is a probability density function of a gaussian distribution.
The joint distribution function of the multi-dimensional random variables can be connected to the respective edge distribution functions using Copula functions. There are significant differences in describing random variable correlations for different Copula functional forms. The optimal Copula form is determined by adopting an Euclidean distance method and used for describing the relevant structure of the output, and a maximum likelihood method is adopted to carry out parameter estimation on the model. Referring to fig. 5, fig. 5 is a schematic diagram of a Copula function construction step.
The Copula form, parameters, Euclidean distance and occupied proportion obtained in each scene are as follows: scene 1: t-Copula function, 0.63, 0.33, 8.65% ratio; scene 2: Gumbel-Copula function, 1.28, 0.74, accounting for 25.38%; scene 3: Clayton-Copula function, 2.93, 0.81, accounting for 41.56%; scene 4: Clayton-Copula function, 3.54, 0.15, 7.39%; scene 5: Clayton-Copula function, 3.32, 0.65, based on 17.02%.
The Copula function form can connect the joint distribution function of the multidimensional random variable with respective edge distribution function, and provides a flexible method for solving the joint distribution function. For edge distribution function F1(x1),F2(x2),…,Fn(xn) There is a Copula function C that satisfies:
F1(x1)，F2(x2)，…，Fn(xn)＝C(F1(x1)，F2(x2)，…，Fn(xn))
when F is present1(x1)，F2(x2)，…，Fn(xn) When continuous, the Copula function C is uniquely determined, where F1(x1)，F2(x2)，…，Fn(xn) Is F1(x1)，F2(x2)，…，Fn(xn) To convert xi, subject to arbitrary distribution, to a uniform distribution ui＝Fi(xi)。
Commonly used Copula functions mainly include gaussian Copula function, t-Copula function, Gumbel Copula function, clayton Copula function, Frank Copula function, and the like. Different Copula functions have significant differences in describing random variable correlations. In contrast, the optimal Copula form is determined by the Euclidean distance method to describe the relevant structure of the output, the result of kernel density estimation is used as the edge distribution of random variables, and the maximum likelihood method is used for carrying out parameter estimation on the model.
And step four, sampling the optimal Copula function under each scene by using a Latin hypercube sampling method, wherein the sampling number under each scene is determined according to the occurrence probability of each scene in proportion, and then the sampling numbers are combined to generate photovoltaic output samples, the sampling number in the embodiment is set to be 1000, and the sampling number under each scene is obtained by multiplying the occurrence probability of each scene by the total sampling number in proportion. The method comprises the following two steps: and (1) sampling. And sampling each input random variable to ensure that the random distribution area can be completely covered by the sampling points. And (2) arranging. The arrangement sequence of the sampling values of the random variables is changed, so that the correlation of the sampling values of the random variables which are independent from each other tends to be minimum. Referring to fig. 6, fig. 6 is an example of photovoltaic output sample generation.
And after a photovoltaic output typical sample is obtained, carrying out Monte Carlo method probability load flow calculation by using the generated sample, and further evaluating the running state of the power distribution network containing the photovoltaic. And (4) performing power distribution network load flow calculation, taking the probability distribution of each load into consideration besides photovoltaic modeling, estimating the load by using a nuclear density estimation method, and sampling the probability distribution by using a Latin hypercube sampling method to generate a typical load sample. And (4) according to typical scenes of photovoltaic output and load samples, combining a Monte Carlo method to realize probability power flow calculation under each scene. Referring to fig. 7, fig. 7 is a wiring diagram of a power distribution network system for implementing probabilistic power flow calculation, the wiring diagram is based on an actual power distribution network in a place of Jiangsu province, wherein two distributed photovoltaic generator sets (PV1, PV2) are connected to nodes 12 and 18 of a node system.
The results of the monte carlo calculations with 4000 random samples were used as a reference. The result shows that the error between the probability load flow calculation result of the generated typical sample and the true value is about 4 percent, which is obviously lower than that of the sample generation method based on K-Means, and meanwhile, the running speed of the program is improved.
The technical solutions of the present invention are not limited to the above embodiments, and all technical solutions obtained by using equivalent substitution modes fall within the scope of the present invention.
Claims (6)
1. A photovoltaic power station typical scene generation method based on a multi-scene model is characterized by comprising the following steps:
acquiring historical data of output of a plurality of photovoltaic power stations under a power distribution network, and performing data preprocessing to form a multi-dimensional data set consisting of the historical output data of the photovoltaic power stations;
clustering the multi-dimensional data set by a local density center-based clustering method, and dividing all data points into a plurality of scenes;
modeling according to a plurality of scenes generated by clustering respectively; obtaining an edge probability density function of each photovoltaic power station according to scenes by using a kernel density estimation method, constructing theoretical Copula functions in various forms for the edge probability density function of each scene, estimating parameters in each Copula form by using a maximum likelihood estimation method, and selecting an optimal Copula function by using an Euclidean distance method for modeling;
the optimal Copula function under each scene is sampled by utilizing a Latin hypercube sampling method, a photovoltaic output typical sample is generated, Monte Carlo probability load flow calculation is carried out on the generated sample, and therefore the voltage quality of the power distribution network is analyzed.
2. The method for generating the typical scene of the photovoltaic power station based on the multi-scene model as claimed in claim 1, wherein the specific steps of clustering the multi-dimensional data set based on the local density center are as follows:
step 1, for each output sample point xiDefining a local density function p for each sample pointi：
Wherein:
xirepresents the output of all photovoltaic power stations at the same moment, dcTo cut off the distance, dijIs the distance between two sample points;
step 2, defining the distance offset delta of each sample pointi：
Step 3, determining a clustering center;
step 4, classifying the rest sample points;
and 5, removing outliers.
3. The method for generating the typical scene of the photovoltaic power station based on the multi-scene model as claimed in claim 2, wherein the method for determining the clustering center is as follows:
establishing an index ρi×δiAnd setting an index threshold value, and judging the sample point of which the index is greater than the set threshold value as a clustering center.
4. The method for generating the typical scene of the photovoltaic power station based on the multi-scene model as claimed in claim 3, wherein the method for classifying the sample points is as follows:
press rho to sample pointiIn descending order, for xiFind rhoiLarger than it, and a point neutralizing its distance dijNearest point xjX is a handlejIs assigned to xiThereby forming a plurality of scenes.
5. The method for generating the typical scene of the photovoltaic power station based on the multi-scene model as claimed in claim 4, wherein the method for eliminating the outliers is as follows:
dividing all data points in each scene into core points and outliers;
determining the boundary area of each class, and calculating cross-class point pairs xiAnd xjAverage local density of
Wherein xiIs a point within this class, xjPoints outside this class;
taking the maximum value of the average local density of all existing cross-class point pairs of a class as the upper bound of the average local density of the class;
marking all the sample points once, if the local density of one sample point is smaller than the upper limit of the average local density of the class where the sample point is located, marking the sample point as an outlier, and otherwise, marking the sample point as a core point;
and (5) removing outliers.
6. The multi-scenario model-based photovoltaic power plant typical scenario generation method of claim 1, characterized in that: when the optimal Copula function in each scene is sampled by using a Latin hypercube sampling method, the sampling quantity in each scene is determined in proportion according to the occurrence probability of each scene.
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| CN117350549B (en) * | 2023-12-04 | 2024-02-23 | 国网江苏省电力有限公司经济技术研究院 | Distribution network voltage risk identification method, device and equipment considering output correlation |
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