CN113935247A - A partitioned virtual inertia estimation method considering the randomness and correlation of wind speed - Google Patents

A partitioned virtual inertia estimation method considering the randomness and correlation of wind speed Download PDF

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CN113935247A
CN113935247A CN202111302789.2A CN202111302789A CN113935247A CN 113935247 A CN113935247 A CN 113935247A CN 202111302789 A CN202111302789 A CN 202111302789A CN 113935247 A CN113935247 A CN 113935247A
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马喜平
甄文喜
姚寅
沈渭程
王臣赟
陈柏旭
董开松
朱宏毅
赵霖
魏博
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Abstract

The invention discloses a partition virtual inertia estimation method considering wind speed randomness and correlation, which comprises the following steps of: step 1: considering wake flow and time delay effects of wind speed, processing historical wind speed data by adopting a segmented aggregation approximation method, and establishing daily variation curves of the wind speed of each unit in the field; step 2: clustering the daily variation curve of the wind speed of each unit by adopting a dual-scale spectral clustering algorithm to realize the partition of the units in the field and form a plurality of clusters; and step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a nonparametric kernel density estimation method, and constructing an optimal Copula function to analyze the correlation of the wind speed between each cluster center and a wind measuring tower; and 4, step 4: and (4) considering uncertainty between wind speed and inertia, and estimating virtual inertia storage of each cluster in the wind power plant based on the internal structure and wind speed data of the actual wind power plant.

Description

Partition virtual inertia estimation method considering wind speed randomness and correlation
Technical Field
The invention belongs to the technical field of wind power generation, and particularly relates to a partition virtual inertia estimation method considering wind speed randomness and correlation.
Background
With the large-scale grid connection of wind power generation, the problems caused by the intermittency and the fluctuation of wind energy are increasingly prominent. Because the wind turbine generator is connected with the power grid through the converter, the wind turbine generator is decoupled from the frequency of the power grid, the wind turbine generator cannot directly participate in system frequency modulation, and effective inertia support cannot be provided. The available inertia of the entire power system will continue to decrease and the frequency response capability will continue to decrease. Therefore, the wind power plant with the power of 30MW or more must have a primary frequency modulation function in the detailed rules for implementation of auxiliary service management of grid-connected power plants in central China, published by the national energy agency in 2020. The frequency response of the fan is mainly realized by the technologies of virtual inertia control, droop control, primary frequency modulation and the like. With the popularization and application of the technologies, the wind turbine generator set has equivalent inertia supporting capacity. However, an accurate estimation method of the available inertia of each unit in the wind power plant is still lacking. The accurate estimation of the available inertia can provide reference for the distribution and the scheduling of the auxiliary frequency modulation output of each unit after disturbance, and also can provide theoretical support for the frequency modulation control strategy setting of the units in the region according to the reserve of the available inertia in each region.
The main influencing factors of the available inertia of the wind farm are the wind speed and the operating state in the wind farm. The wind power generation sets in the large wind power plant are large in number, the distance between the wind power generation sets is close, and certain correlation exists between the wind speeds of the wind power generation sets and the running state of the wind power generation sets. Documents, namely a wind power plant wind speed dependent model constructed by rattan Copula and a scene generation method considering the relevant relation of the Copula output of the multi-wind power plant, adopt Copula functions to analyze the relevance of wind speeds in the wind power plant. In the literature, the multi-wind-field output scene generation method considering the time-space correlation considers various wind speed influence factors, establishes a conditional Copula joint distribution function for wind power prediction, and realizes interval prediction of wind power field output. The literature, "wind power correlation analysis based on a mixed Copula function" considers the space-time correlation of wind speed, and a wind speed space-time distribution correlation model is established based on a multivariate normal distribution function and a Copula function. According to the literature, tail characteristics among fan output are considered in a wind power plant virtual inertia multi-machine cooperative control strategy considering frequency modulation capability, and a wind power output correlation analysis method based on a hybrid Copula function is provided. Research shows that the mixed Copula function has obvious advantages in representing wind speed correlation, but when constructing the mixed multi-element Copula function, related parameters are difficult to estimate, the quality of the correlation representation is influenced by weight value selection, the intermediate calculation process is complex, and for the reason, when the Copula function is used for describing the correlation between variables, the Copula function is used for calculating the correlation between the variables. On the premise of ensuring no distortion, the intermediate calculation process can be greatly simplified by selecting a single Copula function.
The current research on wind power plant inertia response focuses on virtual inertia control optimization, relatively few researches on wind power plant available inertia evaluation are carried out, and the wind power plant available inertia evaluation is evaluation of the whole wind power plant inertia. A novel method for evaluating potential help of wind capacity to system frequency stability provides an evaluation method for frequency modulation capability of a plurality of wind power plants based on the principle that rotating kinetic energy of wind turbine generators is equal. According to the literature, the probability method for evaluating comprehensive droop and inertial response of the wind power plant evaluates the joint inertial response capability of the wind power plant at a specific average wind speed by processing a Gaussian distribution model of atmospheric turbulence in blocks. On the basis, the literature, "analysis modeling of wind power plant inertia and droop response for short-term frequency regulation of a power system" comprehensively evaluates the joint frequency modulation effect of virtual inertia control and droop control. However, the wind power plants are taken as a whole by the above evaluation methods, and the distribution difference of the available inertia in the wind power plants is ignored, so that a large error may exist between the evaluation result and the actual value, and the problem of the distribution of the available inertia in the wind power plants cannot be solved.
The estimation of the available inertia of the wind farm typically uses the wind speed of a particular set of locations or the average wind speed of the wind farm to estimate the level of rotational inertia of the wind farm as a whole. An anti-intersection to copulas document proposes a load shedding model based on VSWT speed control, and deduces An inertia time constant from a single variable speed constant frequency wind generating set. However, due to the problem of computational efficiency, the model cannot accurately estimate the available inertia of the large wind farm.
Disclosure of Invention
The invention provides a partition virtual inertia estimation method considering wind speed randomness and correlation, and takes the wind speed correlation of each unit in a wind power plant, the position distribution of each unit, the running state and other factors into consideration.
The technical scheme adopted by the invention is as follows:
the partition virtual inertia estimation method considering the randomness and the correlation of the wind speed comprises the following steps of:
step 1: considering wake flow and time delay effects of wind speed, processing historical wind speed data by adopting a segmented aggregation approximation method, and establishing daily variation curves of the wind speed of each unit in the field;
step 2: clustering the daily variation curve of the wind speed of each unit by adopting a dual-scale spectral clustering algorithm to realize the partition of the units in the field and form a plurality of clusters;
and step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a nonparametric kernel density estimation method, and constructing an optimal Copula function to analyze the correlation of the wind speed between each cluster center and a wind measuring tower;
and 4, step 4: and (4) considering uncertainty between wind speed and inertia, and estimating virtual inertia storage of each cluster in the wind power plant based on the internal structure and wind speed data of the actual wind power plant.
Preferably, in step 2, the partitioning process of the wind farm is implemented as follows:
step 201: distance-based similarity metric
Set X (X) with M wind speed data1,x2,…,xM) Wherein each wind speed curve xiHas a data length of L; the Euclidean distance is the real distance between two data points in the L-dimensional space, and the wind speed curve xiAnd xjThe euclidean distance between them is defined as:
Figure BDA0003338986730000031
step 202: similarity measure based on morphological features
The morphological characteristics represent the fluctuation degree of the curve, and the information entropy is used as a measurement index of the fluctuation degree of the wind speed curve; setting a wind speed curve x in a certain time periodiThere are n possible values of x1，x2，…，xn(ii) a Probability of each possible value being p1，p2，…，pn(ii) a The wind speed curve x for that time periodiEntropy value H ofnIs defined as:
Figure BDA0003338986730000041
the size of the entropy reflects the fluctuation degree of the curve, and the larger the entropy is, the larger the fluctuation degree of the curve is; similarly, the closer the information entropy values of the two wind speed curves are, the higher the fluctuation similarity of the two curves is;
the wind speed similarity matrix of each fan is constructed by extracting similarity measurement features based on distance and form, and daily variation curves of wind speeds close to each other in distance and similar in fluctuation degree are gathered into a class by utilizing a spectral clustering algorithm, so that the partition of the wind power plant is realized.
Preferably, in step 3, after the in-field unit clustering and dimensionality reduction is performed in step 2, the whole wind power plant is divided into N unit areas, a wind speed sequence joint distribution probability histogram between each unit area and a wind measuring tower is drawn, tail characteristics and symmetry characteristics of the wind speed sequence joint distribution probability histogram are analyzed, and an optimal Copula function is selected according to a method with the minimum Euclidean distance from an empirical Copula function.
Preferably, the specific process of constructing the optimal Copula function to analyze the correlation between the wind speed of each cluster center and the anemometer tower is as follows:
step 301: first, an empirical Copula function, a random variable X, Y, and empirical distribution functions of sum F, respectively, are introducedn(x) And Hn(x) The empirical Copula function is defined as:
Figure BDA0003338986730000042
in which u, v is E [0,1 ]]；Fn(xi) When the content is less than or equal to u,
Figure BDA0003338986730000043
otherwise, the value is 0;
obtaining relevant unknown parameters of each theoretical Copula function by using a maximum likelihood estimation method; according to the formula (1), the euclidean distance squared of the theoretical Copula function and the empirical Copula function is obtained by combining the defined formula of the euclidean distance and the empirical Copula function as follows:
Figure BDA0003338986730000044
wherein P is a theoretical Copula function type,
Figure BDA0003338986730000051
reflects the squared Euclidean distance between a theoretical Copula function and an empirical Copula function,
Figure BDA0003338986730000052
the Copula function corresponding to the minimum value is an optimal Copula function;
after the optimal Copula function is selected, the binary joint probability density function between the cluster i and the anemometer tower m is as follows:
fi(vi,vm)＝Ci(uvi,vvm)f(vi)f(vm) (5)
when inertia estimation is carried out, detailed wind speed data measured by the anemometer tower are known, an optimal Copula function is established to describe the wind speed correlation between the anemometer tower and each cluster, and therefore the instantaneous wind speed probability density function of each cluster is obtained as follows:
Figure BDA0003338986730000053
preferably, in step 4, the available inertia estimation process between the partitions based on the wind speed is as follows:
according to the load shedding control mode of the wind power plant, the wind power plant is divided into a low wind speed area, a medium wind speed area and a high wind speed area;
in the low wind speed region, according to the related theory of aerodynamics, when the wind turbine runs in the MPPT operation mode, the mechanical power captured by the wind turbine can be represented by the following formula:
Figure BDA0003338986730000054
where ρ is the air density, CP maxThe wind energy capture coefficient is shown as lambda is the blade tip speed ratio, beta is the pitch angle, R is the fan blade radius, and V is the wind speed; wherein, the wind energy capture coefficient CP maxAssociated with the tip speed ratio λ and pitch angle β:
Figure BDA0003338986730000055
Figure BDA0003338986730000056
in the above formula, omega is the rotating speed of the generator; p is the number of pole pairs of the generator; g is the number of pole pairs of the gear box;
when the load shedding ratio is d%, the power value is shown in the following formula:
Figure BDA0003338986730000061
combining the two formulas to obtain:
CP-de＝(1-d％)CP max (11)
the tip speed ratio when the load shedding rate is d% can be obtained according to a bisection method, and the relation between the fan rotating speed and the wind speed when the load shedding rate is d% can be obtained through the definition of the tip speed ratio:
Figure BDA0003338986730000062
when the fan operates in a medium wind speed and constant rotating speed area, the wind speed basically reaches the upper limit, overspeed control cannot continue to act, the rotating speed of a rotor of the fan cannot obviously change along with the wind speed, but the power captured by the fan is continuously improved through variable pitch control, the rotating speed equation of the part can be approximately linearized, and the wind speed and rotating speed value (v) of two end points of a curve is obtainedn,wmax)、(vws，ws) Constructing a straight line, and obtaining a relation of the rotating speed and the wind speed as follows:
Figure BDA0003338986730000063
when the wind speed of the fan reaches the high wind speed constant power region, the rotating speed of the fan reaches the constant maximum rotating speed omegamaxIf the fan needs to be in d% load reduction operation, only the reference power P is neededrefSwitching to (1-d%) PnThe rotating speed cannot be changed;
the wind speed-rotating speed relational expression under different wind speeds is solved by utilizing the wind speed partition method, and then the rotating speed-inertia relational expression is combined, namely
Figure BDA0003338986730000064
Wherein J represents inertia, ωiAnd representing the actual rotating speed of the fan i to obtain a relation between the available inertia and the wind speed as follows:
Figure BDA0003338986730000071
preferably, the wind speed interval is divided according to the following steps: the preset load shedding target can be realized only by converting the running state of the fan from MPPT (maximum power point tracking) to a d% load shedding curve through overspeed control, and the region is called as a low wind speed region; d% load shedding rate is required to be realized through rotating speed and pitch angle control, and the d% load shedding rate is called as a medium wind speed area; the load reduction target can only be achieved through variable pitch control, and the area is called a high wind speed area.
Preferably, according to the available inertia evaluation process, the wind farm available inertia confidence interval is calculated as follows:
(1) inputting a Copula function and a wind speed-inertia relational expression;
(2) constructing a probability density function f (E) of the available inertia of each cluster, namely obtaining the probability density function according to a formula (5) and a formula (6) and combining a relational expression (15) of wind speed and inertia:
Figure BDA0003338986730000072
(2) integrating f (E) to obtain a probability distribution function phi (E) of the available inertia, i.e.
Figure BDA0003338986730000073
(3) Obtaining inertia values of a probability distribution function phi (E) corresponding to the wind turbine group at alpha/2 and 1-alpha/2 probability values by adopting a binary search-numerical integration method, and respectively recording the upper limit and the lower limit of an available inertia interval of the wind turbine group;
(4) superposing the available inertia of each cluster of the wind power plant to obtain a confidence interval of the available inertia of the full wind power plant, and analyzing the wind speed of each cluster in the cluster by using a wake effect to further obtain the distribution of the available inertia of each cluster;
(5) output available inertia E, and distribution of inertia.
The invention has the beneficial effects that:
the invention provides a wind power plant partition virtual inertia estimation method based on Copula function and clustering algorithm by considering wind power plant wind speed randomness and inter-unit wind speed correlation, and the wind power plant partition virtual inertia estimation method analyzes the internal structure and wind speed data of an actual wind power plant. And obtaining the total available inertia confidence interval of the wind power plant and the available inertia distribution of each unit. A simulation example is constructed according to the actual wind speed and output data of a wind field in Gansu, and the simulation result shows that the algorithm provided by the invention can effectively perform partition clustering on the wind power plant and the accuracy of available inertia estimation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a partitioned virtual inertia estimation method considering wind speed randomness and correlation according to the present invention.
Fig. 2 is a schematic diagram showing a simplified model of the wake effect.
Fig. 3 shows a processing flow of the wind speed data of the unit.
FIG. 4 shows a fan speed-power curve based on load shedding.
Fig. 5 shows the fan operating state.
FIG. 6 is a diagram illustrating a geographical location profile of a wind farm machine.
FIG. 7 is a graph showing cluster clustering results and daily variation curves of wind speed at the clustering center; (a) the clustered unit geographical position distribution map is obtained, and the unit with the same color is a cluster; (b) a first machine group; (c) a second machine group; (d) and (5) a cluster III.
FIG. 8 shows the histograms of wind speed distributions and the fitted probability density function for W1 and W2; (a) a central fan W1; (b) anemometer tower W2.
FIG. 9 shows a two-bin binary joint wind velocity distribution histogram.
FIG. 10 is a graph of probability density function and distribution function of Gumbel-copula; (a) a probability density function graph; (b) a distribution function graph.
FIG. 11 is a graph of a probability density function and a distribution function of Clayton-copula; (a) a probability density function graph; (b) a distribution function graph.
FIG. 12 is a graph of the probability density function and distribution function of Frank-copula; (a) a probability density function graph; (b) a distribution function graph.
FIG. 13 is a diagram showing a comparison of inertia available from an equivalent machine method and a real measurement method.
Fig. 14 shows the actual values of the available inertia and the theoretical confidence intervals of the available inertia (confidence is 90%).
FIG. 15 is a graph showing a usable inertia profile; (a) actual value of available inertia; (b) the available inertia desired value profile.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment specifically provides a partition virtual inertia estimation method considering wind speed randomness and correlation, as shown in fig. 1, including the following steps:
step 1: considering wake flow and time delay effects of wind speed, processing historical wind speed data by adopting a segmented aggregation approximation method, and establishing daily variation curves of the wind speed of each unit in the field;
step 2: clustering the daily variation curve of the wind speed of each unit by adopting a dual-scale spectral clustering algorithm to realize the partition of the units in the field and form a plurality of clusters;
and step 3: fitting wind speed probability distribution of each cluster center unit by adopting a nonparametric kernel density estimation method (solving wind speed edge distribution after fitting the probability distribution of the center units by adopting the nonparametric kernel density estimation method, providing necessary conditions for solving parameters in a Copula function later), and constructing an optimal Copula function to analyze the correlation of the wind speed between each cluster center and a anemometer tower;
and 4, step 4: and (4) considering uncertainty between wind speed and inertia, and estimating virtual inertia storage of each cluster in the wind power plant based on the internal structure and wind speed data of the actual wind power plant.
In step 1, the difference in wind speed between different units in the wind farm is mainly affected by the wake effect between the units.
The simplified wake flow model is shown in fig. 2, and the wind speed relationship between the upstream and downstream units is shown in the following formula.
Figure BDA0003338986730000101
In the formula VoThe wind speed is the wind speed blowing to the wind turbine generator set; vxThe wind speed d leaving the wind turbine set is the wind speed reduction coefficient, the size and the thrust coefficient C of the wind turbine setTThe radius R of the blades of the wind turbine generator, the distance X between adjacent wind turbine generators and the wake descent coefficient K are related. The land wind farm generally takes K as 0.075.
In a large wind power plant, there is an obvious time delay in the real-time wind condition transmitted from an upstream fan to a downstream fan, and the time delay phenomenon of the wind speed is particularly obvious under the condition of considering the wake effect. Assuming that the delay time of the wind speed from the wind farm end to the wind turbine j is tau, the wind speed of the upstream wind turbine considering the delay is:
vj(t)＝vo(t-τ)
as shown in fig. 3, when the wind speed data information amount is large, firstly, a piecewise aggregation approximation method is adopted to perform dimensionality reduction characterization on the wind speed curve. The basic form of high-dimensional data is approximately expressed by low-dimensional data, the dimension reduction processing of wind speed data can be realized, and a wind speed sequence Y with the length of n is { Y ═ Y1,y2,…,ynUsing the wind speed number series with the length of m
Figure BDA0003338986730000111
To approximate it, where m<n and m is divisible by n. Then
Figure BDA0003338986730000112
The ith element in (b) can be calculated by:
Figure BDA0003338986730000113
secondly, clustering is carried out on the wind speed change curve based on a dual-scale spectral clustering algorithm, and the specific process is as follows:
step 201: distance-based similarity metric
Set X (X) with M wind speed data1,x2,…,xM) Wherein each wind speed curve xiHas a data length of L; the Euclidean distance is the real distance between two data points in the L-dimensional space, and the wind speed curve xiAnd xjThe euclidean distance between them is defined as:
Figure BDA0003338986730000114
step 202: similarity measure based on morphological features
The morphological characteristics represent the fluctuation degree of the curve, and the information entropy is used as a measurement index of the fluctuation degree of the wind speed curve; setting a wind speed curve x in a certain time periodiThere are n possible values of x1，x2，…，xn(ii) a Probability of each possible value being p1，p2，…，pn(ii) a The wind speed curve x for that time periodiEntropy value H ofnIs defined as:
Figure BDA0003338986730000115
the size of the entropy reflects the fluctuation degree of the curve, and the larger the entropy is, the larger the fluctuation degree of the curve is; similarly, the closer the information entropy values of the two wind speed curves are, the higher the fluctuation similarity of the two curves is;
the wind speed similarity matrix of each fan is constructed by extracting similarity measurement features based on distance and form, and daily variation curves of wind speeds close to each other in distance and similar in fluctuation degree are gathered into a class by utilizing a spectral clustering algorithm, so that the partition of the wind power plant is realized.
The wind turbine clustering algorithm divides all the turbines in the farm into a plurality of turbine groups based on wind speed distribution in the farm, and establishes an available inertia evaluation model for each divided turbine group, so that the comprehensive reflection capability of the characteristics of the whole farm of the wind power plant is improved, and the accuracy of the available inertia evaluation of the whole farm is improved.
And (4) integrating the similarity measurement based on the distance and morphological characteristics, and clustering the wind speed curves of the units by using a dual-scale spectral clustering method to realize cluster grouping of the units in the field. The calculation process is as follows:
inputting: inputting wind speed data sets of each unit
Clustering:
1. determining a width parameter of a Gaussian kernel function so as to construct a similarity matrix H;
2. calculating a Laplace matrix of the similarity matrix and determining an optimal classification number k;
3. obtaining the eigenvectors corresponding to the first k maximum eigenvalues;
4. forming a feature matrix for the selected feature vectors;
5. and carrying out K-means clustering on the characteristic matrix to obtain a curve clustering result.
In step 3, the non-parametric kernel density estimation method is a non-parametric estimation method. Let { z i1,2, …, n is a sample space of a random variable z, the probability density of z is u (z), and the kernel density of u (z) is estimated as:
Figure BDA0003338986730000121
Figure BDA0003338986730000122
wherein z is a kernel density function argument; z is a radical ofiData for sample point i; l is the window width; k (delta) is a Gaussian kernel function, and delta is a kernel function argument.
After the in-field unit clustering and dimensionality reduction is carried out in the step 2, the whole wind power plant is divided into N unit areas after the in-field unit clustering and dimensionality reduction, a wind speed sequence joint distribution probability histogram between each unit area and a wind measuring tower is drawn, tail characteristics and symmetry characteristics of the histogram are analyzed, and an optimal Copula function is selected according to a method of minimizing the Euclidean distance from an empirical Copula function.
The specific process is as follows:
step 301: first, an empirical Copula function, a random variable X, Y, and empirical distribution functions of sum F, respectively, are introducedn(x) And Hn(x) The empirical Copula function is defined as:
Figure BDA0003338986730000131
in which u, v is E [0,1 ]]；Fn(xi) When the content is less than or equal to u,
Figure BDA0003338986730000132
otherwise, the value is 0;
obtaining relevant unknown parameters of each theoretical Copula function by using a maximum likelihood estimation method; according to the formula (1), the euclidean distance squared of the theoretical Copula function and the empirical Copula function is obtained by combining the defined formula of the euclidean distance and the empirical Copula function as follows:
Figure BDA0003338986730000133
wherein P is a theoretical Copula function type,
Figure BDA0003338986730000134
reflects the squared Euclidean distance between a theoretical Copula function and an empirical Copula function,
Figure BDA0003338986730000135
the Copula function corresponding to the minimum value is an optimal Copula function;
after the optimal Copula function is selected, the binary joint probability density function between the cluster i and the anemometer tower m is as follows:
fi(vi,vm)＝Ci(uvi,vvm)f(vi)f(vm) (5)
when inertia estimation is carried out, detailed wind speed data measured by the anemometer tower are known, an optimal Copula function is established to describe the wind speed correlation between the anemometer tower and each cluster, and therefore the instantaneous wind speed probability density function of each cluster is obtained as follows:
Figure BDA0003338986730000136
in step 4, the wind speed-inertia uncertainty analysis process of the wind power plant is as follows:
the wind driven generator makes the running state deviate from the maximum power point by controlling the rotation speed or the pitch angle of the wind driven generator, and then the reserved standby power control mode is the load shedding control of the fan. The load shedding control mode mainly comprises overspeed control and pitch angle control.
The available inertia estimation process between the partitions based on the wind speed is as follows:
wind speed interval division basis: as shown in fig. 4, in the area surrounded by ABB 'a', the predetermined load shedding target can be realized only by converting the operating state of the fan from MPPT to a d% load shedding curve through overspeed control, which is called as a low wind speed area; the BCB' area is limited by the maximum rotating speed of the fan, and d% load shedding rate is required to be realized through rotating speed and pitch angle control, and the area is called a medium wind speed area; in the figure, the C' D interval reaches the maximum rotating speed of 1.2p.u, and the load reduction target can be achieved only through variable pitch control, and the area is called as a high wind speed area.
TABLE 1 interval of wind speeds
Figure BDA0003338986730000141
In addition to the first three wind speed zones, as shown in fig. 5, in the startup zone, when the wind speed is below the cut-in wind speed or when the wind speed is above the cut-out wind speed: the wind speed is limited, and the wind turbine cannot normally run in a grid-connected mode or has no rotating speed reduction capacity, so that the wind turbine generator does not participate in frequency response of the power system in the wind speed area, and has no available inertia.
In the low wind speed region, according to the related theory of aerodynamics, when the wind turbine runs in the MPPT operation mode, the mechanical power captured by the wind turbine can be represented by the following formula:
Figure BDA0003338986730000142
where ρ is the air density, CP maxThe wind energy capture coefficient is shown as lambda is the blade tip speed ratio, beta is the pitch angle, R is the fan blade radius, and V is the wind speed; wherein, the wind energy capture coefficient CP maxAssociated with the tip speed ratio λ and pitch angle β:
Figure BDA0003338986730000151
Figure BDA0003338986730000152
in the above formula, omega is the rotating speed of the generator; p is the number of pole pairs of the generator; g is the number of pole pairs of the gear box;
when the load shedding ratio is d%, the power value is shown in the following formula:
Figure BDA0003338986730000153
combining the two formulas to obtain:
CP-de＝(1-d％)CP max (11)
the tip speed ratio when the load shedding rate is d% can be obtained according to a bisection method, and the relation between the fan rotating speed and the wind speed when the load shedding rate is d% can be obtained through the definition of the tip speed ratio:
Figure BDA0003338986730000154
when the wind turbine operates in a medium wind speed constant-speed area, the wind speed basically reaches the upper limit, overspeed control cannot continue to function, the rotating speed of a rotor of the wind turbine does not obviously change along with the wind speed, but the power captured by the wind turbine is continuously improved through variable pitch control, and the wind power plant available inertia evaluation method based on a mixed Copula function is based on documents]The partial rotating speed equation can be approximately linearized, and the wind speed and rotating speed value (v) passing through two end points of the curven,wmax)、 (vws，ws) Constructing a straight line, and obtaining a relation of the rotating speed and the wind speed as follows:
Figure BDA0003338986730000155
when the wind speed of the fan reaches the high wind speed constant power region, the rotating speed of the fan reaches the constant maximum rotating speed omegamaxIf necessaryD% load reduction operation is carried out on the fan, and only the reference power P is requiredrefSwitching to (1-d%) PnAnd the rotation speed does not change.
The available inertia of the fan refers to the capacity of the fan, which can participate in inertia response or primary frequency modulation response. When the frequency changes, the fan changes the output of the unit by releasing the kinetic energy of the rotor, reduces the power difference with the load and inhibits the rapid change of the frequency. Let the rotor be an object with inertia J and angular velocity ω rotation, and its rotational kinetic energy be:
Figure BDA0003338986730000161
for a single fan in a wind power plant, when inertia response is carried out, the kinetic energy of a rotor cannot be completely released, and the rotor has the limit of the lowest rotating speed, omega, in the inertia response processmin0.75 (p.u.). Therefore, if the actual rotational speed of the fan i is ωiThen, the actual available inertia of this fan is:
Figure BDA0003338986730000162
according to the equations (13) and (14), the relation between the available inertia and the wind speed is obtained as follows:
Figure BDA0003338986730000163
according to the available inertia probability evaluation process, the calculation steps of the wind power plant available inertia confidence interval are as follows:
(1) inputting a Copula function and a wind speed-inertia relational expression;
(2) constructing a probability density function f (E) of the available inertia of each cluster, namely obtaining the probability density function according to a formula (5) and a formula (6) and combining a relational expression (15) of wind speed and inertia:
Figure BDA0003338986730000164
(2) integrating f (E) to obtain a probability distribution function phi (E) of the available inertia, i.e.
Figure BDA0003338986730000171
(3) Obtaining inertia values of a probability distribution function phi (E) corresponding to the wind turbine group at alpha/2 and 1-alpha/2 probability values by adopting a binary search-numerical integration method, and respectively recording the upper limit and the lower limit of an available inertia interval of the wind turbine group;
(4) superposing the available inertia of each cluster of the wind power plant to obtain a confidence interval of the available inertia of the full wind power plant, and analyzing the wind speed of each cluster in the cluster by using a wake effect to further obtain the distribution of the available inertia of each cluster;
(5) output available inertia E, and distribution of inertia.
Example simulation
Taking a certain wind farm in Gansu as an example, a schematic layout diagram of fans in the wind farm is shown in FIG. 6: the horizontal and vertical coordinates in the figure are longitude and latitude coordinates of the position of the fan, and the lower right corner is the position of the wind measuring tower. And (3) evaluating the available inertia interval of the whole wind power plant by adopting the accurate wind speed data at the anemometer tower, and selecting the wind speed data with the height of 70m of the anemometer tower when modeling the wind speed of the fan, wherein the fan is of a uniform type, and the detailed data are shown in a table 2.
TABLE 2 wind turbine parameters
Figure BDA0003338986730000172
1.1 Cluster clustering
Clustering is carried out on the daily change curves of the wind speeds of the 33 fans by using a dual-scale spectral clustering algorithm, the clustering number is 3, and the result is shown in a figure 7 below. And obtaining the position distribution maps of the three clustered clusters by combining the positions of the clusters according to the curve clustering result.
1.2 optimal Copula function
According to the method for analyzing the cluster wind speed correlation by the Copula function, the wind speed data of a certain cluster center fan W1 and a wind measuring tower W2 are adopted for example analysis. The wind speed data is instantaneous wind speed data measured at 10-minute intervals on a certain day by the unit.
In the embodiment, nonparametric kernel density estimation method is adopted to determine wind speed edge distribution U and V of two units, and frequency histograms corresponding to wind speeds W1 and W2 are plotted as shown in FIG. 8.
From the binary distribution histogram (fig. 9), the tail of the probability density function is asymmetric, and an archimedes-Copula function can be selected to describe the relationship between the two. The parameters of three copula functions obtained by the maximum likelihood estimation method are as follows: gumbel-copula: 5.7320, respectively; clayton-copula: 4.4871, respectively; frank-copula: 20.1128.
as can be seen from the probability density function graphs (FIG. 10, FIG. 11 and FIG. 12) of the three copula functions, Gumbel-copula and Frank-copula functions have higher similarity in shape, which indicates that the two functions can be used for characterizing the correlation between the wind speeds of the two machine sets. For more accurate selection of the appropriate copula function, the above euclidean distance method is used for comparison. See table 3:
TABLE 3 correlation measurement coefficients of three copula functions and their Euclidean distances
Figure BDA0003338986730000181
Among the three, the Gumbel-Copula function has a small squared Euclidean distance, and a Clayton-Copula function can be selected in the combined distribution of the Gumbel-Copula function and the Clayton-Copula function, and can better show the relationship between the Gumbel-Copula function and the Clayton-Copula function.
1.3 available inertia confidence intervals and distributions
And describing the wind speed relativity of the three clusters by using the optimal copula function between the three clusters and the anemometer tower obtained in the step 1.2, and deducing the wind speed of each cluster by using the known anemometer tower wind speed data. And then solving the inertia of each cluster by using a wind speed-inertia relational expression. The wind speed distribution inside the cluster can be obtained by combining the wake effect and the time delay effect, and further the available inertia distribution can be obtained.
(1) Wind power plant available inertia evaluation curve based on time sequence
A wind power plant in Gansu is selected as an example, the method provided by the invention is used for evaluating the upper and lower limits of the total available inertia of the wind power plant, and the upper and lower limits are compared with historical data and actual available inertia calculated by average wind speed. The effectiveness of the method in practical application is illustrated.
And in actual operation, performing available inertia evaluation by using the historical wind speed data of 0:00-24:00 of a certain day in summer of the wind power plant M. And compares the available inertia interval estimated by the method of the invention with the available inertia curve based on the measured value. The lower graph is an available inertia change curve obtained by actually measuring the rotating speed value of the fan.
And comparing the available inertia confidence interval obtained by the method with the actual value.
Fig. 13 is a time-dependent variation curve of total available inertia of a wind farm in one day, and in combination with a 1.1 daily variation curve of wind speed, it can be seen that the use of the equivalent machine method has higher accuracy when the wind speed is higher, because when the wind speed is too high, the wind turbine enters a constant rotation speed or constant power region, and the rotation speed of the wind turbine does not change with the change of the wind speed any more, so that the rotation speeds of the units are basically consistent and are the highest rotation speeds, so the equivalent machine method works, however, as the wind speed continuously decreases, within a time period of 0.5 to 0.8 days, the accuracy of the equivalent machine method is lower, even the available inertia is 0, because many units cannot provide inertia support when the wind speed is too low. This is also the reason why the equivalent machine method cannot accurately estimate the available inertia when the wind speed is low.
FIG. 14 shows the upper and lower estimated useful inertia limits when the confidence level is 90%, and it can be seen that the probability method used herein to estimate the confidence interval of the useful inertia can better contain the actual useful inertia value, especially in the case of medium and high wind speed, but sometimes inaccurate. In 144 groups of wind speed time sequence data in one day, 10 groups with actual inertia exceeding the upper limit of a confidence interval or being lower than the lower limit of the confidence interval exist, and the error rate is 6.944%. Meanwhile, the method for solving the available inertia has good accuracy in a low wind speed interval. When the wind speed is too low, the available inertia cannot be estimated by the equivalent machine method, but the method can accurately identify the available inertia value, but also has the problem of overhigh available inertia estimation at a certain time point, and in practical application, the principle that the estimation value needs to be kept as much as possible is considered, so that the lower limit curve of the available inertia estimation has better reference value.
(2) Available spatial distribution of inertia
The distribution of the available inertia of the wind power plant is calculated by using the wind speed data of each unit of the wind power plant at the time of 10:00 of the M wind power plant and is shown in FIG. 15: fig. 15(a) is an actual value of the available inertia, and fig. 15(b) is a distribution diagram of an expected value of the available inertia obtained by the method of the present invention, which is obtained by comparing the two diagrams, and the distribution of the available inertia obtained by the method of the present invention is substantially consistent with the actual value, which cannot be realized by the equivalent machine method. The average error of the inertia distribution calculated by the method is 4.0552% by calculating the error between the theoretical value and the actual value of the available inertia of each unit. The effectiveness of the method provided by the invention in available inertia distribution estimation is fully proved. Meanwhile, dispatching personnel can master the potential of output provided by each unit when the inertia is supported according to the graph, and a basis is provided for adjusting the frequency response and the operation state of the unit.
The above description is only for the purpose of illustrating the technical solutions of the present invention and not for the purpose of limiting the same, and other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention should be covered within the scope of the claims of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims (7)

1.计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，包括以下步骤：1. the partition virtual inertia estimation method taking into account wind speed randomness and correlation, is characterized in that, comprises the following steps: 步骤1：考虑风速的尾流及时延效应，采用分段聚合近似法对历史风速数据进行处理，建立场内各机组风速日变化曲线；Step 1: Considering the wake and delay effect of wind speed, the historical wind speed data is processed by the segmented aggregation approximation method, and the daily change curve of wind speed of each unit in the field is established; 步骤2：采用双尺度谱聚类算法对各机组风速日变化曲线进行聚类，实现场内机组的分区，形成数个机群；Step 2: Use the dual-scale spectrum clustering algorithm to cluster the daily variation curve of wind speed of each unit, realize the division of the units in the field, and form several units; 步骤3：采用非参数核密度估计法对各机群中心机组风速概率分布进行拟合，构建最优Copula函数分析各机群中心与测风塔之间风速的相关性；Step 3: Use the non-parametric kernel density estimation method to fit the wind speed probability distribution of the units in the center of each cluster, and construct an optimal Copula function to analyze the correlation of wind speeds between the centers of each cluster and the wind measuring tower; 步骤4：考虑风速-惯量间的不确定性，基于实际风电场内部结构和风速数据估计风电场内各机群的虚拟惯量储备。Step 4: Consider the uncertainty between wind speed and inertia, and estimate the virtual inertia reserve of each fleet in the wind farm based on the actual wind farm internal structure and wind speed data. 2.根据权利要求1所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，在步骤2中，实现风电场的分区过程如下：2. The method for estimating the zonal virtual inertia in consideration of wind speed randomness and correlation according to claim 1, characterized in that, in step 2, the zoning process that realizes the wind farm is as follows: 步骤201：基于距离的相似性度量Step 201: Distance-based similarity measure 具有M个风速数据的集合X(x1,x2,…,xM)，其中每个风速曲线xi的数据长度为L；欧式距离为L维空间中两个数据点之间的真实距离，风速曲线xi和xj之间的欧式距离定义为:A set X(x 1 ,x 2 ,…,x M ) with M wind speed data, where the data length of each wind speed curve x i is L; Euclidean distance is the true distance between two data points in L-dimensional space , the Euclidean distance between the wind speed curves x i and x j is defined as:
Figure FDA0003338986720000011
Figure FDA0003338986720000011
 步骤202：基于形态特征的相似性度量Step 202: Similarity measurement based on morphological features 形态特征表征曲线的波动程度，采用信息熵作为风速曲线波动程度的衡量指标；设某一时间段的风速曲线xi有n种可能值，为x1，x2，…，xn；每个可能值的概率为p1，p2，…，pn；则该时间段风速曲线xi的熵值Hn定义为：The morphological characteristics represent the fluctuation degree of the curve, and the information entropy is used as a measure of the fluctuation degree of the wind speed curve; let the wind speed curve x i in a certain period of time have n possible values, which are x 1 , x 2 , ..., x n ; each The probabilities of possible values are p 1 , p 2 , ..., p n ; then the entropy value H n of the wind speed curve x i in this time period is defined as:
Figure FDA0003338986720000012
Figure FDA0003338986720000012
 熵值的大小反应了曲线的波动程度，熵值越大，曲线波动程度越大；同理，两个风速曲线的信息熵值越相近，则两条曲线的波动相似性越高；The size of the entropy value reflects the degree of fluctuation of the curve. The larger the entropy value is, the greater the degree of curve fluctuation. Similarly, the closer the information entropy values of the two wind speed curves are, the higher the fluctuation similarity of the two curves is; 通过基于距离和形态的相似性度量特征提取，构建每台风机风速的相似度矩阵，利用谱聚类算法将距离接近且波动程度相似的风速日变化曲线聚为一类，从而实现风电场的分区。Through the feature extraction of similarity measure based on distance and shape, the similarity matrix of wind speed of each wind turbine is constructed, and the diurnal variation curves of wind speed with similar distance and similar degree of fluctuation are clustered into one category by spectral clustering algorithm, so as to realize the partition of wind farms. . 3.根据权利要求2所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，在步骤3中，经过步骤2对场内机组聚类降维后，设整个风电场被分为N个机组区域，绘制各机群区域与测风塔间的风速序列联合分布概率直方图，分析其尾部特性及对称特性，根据与经验Copula函数欧式距离最小的方法选择最优Copula函数。3. The partitioned virtual inertia estimation method according to claim 2, characterized in that, in step 3, after step 2, after the clustering of units in the field is reduced, the entire wind farm is set. It is divided into N unit areas, draws the joint distribution probability histogram of the wind speed sequence between each unit area and the wind measuring tower, analyzes its tail characteristics and symmetry characteristics, and selects the optimal Copula function according to the method with the smallest Euclidean distance from the empirical Copula function. 4.根据权利要求3所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，构建最优Copula函数分析各机群中心与测风塔之间风速的相关性的具体过程如下：4. the partition virtual inertia estimation method considering wind speed randomness and correlation according to claim 3, is characterized in that, the concrete process of constructing optimal Copula function to analyze the correlation of wind speed between each cluster center and the wind measuring tower as follows: 步骤301：首先引入经验Copula函数，随机变量X、Y，经验分布函数分别为和Fn(x)和Hn(x)，经验Copula函数定义为：Step 301: First introduce an empirical Copula function, the random variables X, Y, the empirical distribution functions are and F n (x) and H n (x) respectively, and the empirical Copula function is defined as:
Figure FDA0003338986720000021
Figure FDA0003338986720000021
 式中u,v∈[0,1]；Fn(xi)≤u时，
Figure FDA0003338986720000022
否则为0；where u,v∈[0,1]; when F n (x i )≤u,
Figure FDA0003338986720000022
0 otherwise; 利用极大似然估计法求得各理论Copula函数的相关未知参数；根据式(1)，通过欧式距离的定义式，并结合理论Copula函数和经验Copula函数得到了两者的欧氏距离平方如下：The maximum likelihood estimation method is used to obtain the relevant unknown parameters of each theoretical Copula function; according to formula (1), through the definition of Euclidean distance, combined with the theoretical Copula function and the empirical Copula function, the square of the Euclidean distance of the two is obtained as follows :
Figure FDA0003338986720000023
Figure FDA0003338986720000023
 式中P为理论Copula函数类型，
Figure FDA0003338986720000024
反映了理论Copula函数与经验Copula函数间的欧式距离平方，
Figure FDA0003338986720000031
最小值所对应的Copula函数为最优Copula函数；where P is the theoretical Copula function type,
Figure FDA0003338986720000024
It reflects the square of the Euclidean distance between the theoretical Copula function and the empirical Copula function,
Figure FDA0003338986720000031
The Copula function corresponding to the minimum value is the optimal Copula function; 选出最优Copula函数之后，则机群i与测风塔m之间的二元联合概率密度函数为：After selecting the optimal Copula function, the binary joint probability density function between the cluster i and the wind tower m is: fi(vi,vm)＝Ci(uvi,vvm)f(vi)f(vm) (5)f i (vi ,v m )=C i ( u vi ,v vm )f(vi )f(v m ) (5) 当进行惯量估计时，已知测风塔测得的详细风速数据，建立最优Copula函数描述测风塔和各机群之间的风速相关性，由此得到各机群的瞬时风速概率密度函数为：When the inertia estimation is performed, the detailed wind speed data measured by the wind towers are known, and the optimal Copula function is established to describe the wind speed correlation between the wind towers and each cluster, and the instantaneous wind speed probability density function of each cluster is obtained as follows:
Figure FDA0003338986720000032
Figure FDA0003338986720000032
 5.根据权利要求4所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，在步骤4中，基于风速分区间的可用惯量估计过程如下：5. the partition virtual inertia estimation method considering wind speed randomness and correlation according to claim 4, is characterized in that, in step 4, based on the available inertia estimation process between wind speed partitions as follows: 根据风电场减载控制方式，分为低风速区、中风速区和高风速区；According to the load shedding control method of the wind farm, it is divided into low wind speed area, medium wind speed area and high wind speed area; 在低风速区，依据空气动力学相关理论，当风电机组运行于MPPT工作模式时，其捕获的机械功率可由下式表示：In the low wind speed region, according to the relevant aerodynamic theory, when the wind turbine operates in the MPPT working mode, the mechanical power captured by it can be expressed by the following formula:
Figure FDA0003338986720000033
Figure FDA0003338986720000033
 式中，ρ为空气密度，CPmax为风能捕获系数，λ为叶尖速比，β为桨距角，R为风机叶片半径，V为风速；其中，风能捕获系数CPmax与叶尖速比λ和桨距角β相关：In the formula, ρ is the air density, C Pmax is the wind energy capture coefficient, λ is the tip speed ratio, β is the pitch angle, R is the radius of the fan blade, and V is the wind speed; among them, the wind energy capture coefficient C Pmax and the tip speed ratio λ is related to the pitch angle β:
Figure FDA0003338986720000034
Figure FDA0003338986720000034
Figure FDA0003338986720000035
Figure FDA0003338986720000035
 上式中ω为发电机转速；p为发电机极对数；G为齿轮箱极对数；In the above formula, ω is the rotational speed of the generator; p is the number of pole pairs of the generator; G is the number of pole pairs of the gearbox; 当减载率为d％时，其功率值见下式：When the load shedding rate is d%, its power value is shown in the following formula:
Figure FDA0003338986720000041
Figure FDA0003338986720000041
 联合上述二式，可得：Combining the above two equations, we can get: CP-de＝(1-d％)CPmax (11)C P-de = (1-d%) C Pmax (11) 依据二分法可以求得在减载率为d％时的叶尖速比，通过叶尖速比的定义，即可得到在减载率为d％时的风机转速与风速关系：According to the dichotomy method, the tip speed ratio at the load reduction rate of d% can be obtained. Through the definition of the tip speed ratio, the relationship between the fan speed and the wind speed at the load reduction rate of d% can be obtained:
Figure FDA0003338986720000042
Figure FDA0003338986720000042
 当风机运行于中风速转速恒定区时，风速基本达到上限，超速控制已经不能继续作用，此时风机转子转速不会随风速发生明显变化，但是通过变桨控制，风机捕获的功率不断提高，可将该部分转速方程近似线性化，通过曲线两端点的风速转速值(vn,wmax)、(vws，ws)构建直线，由此得到转速与风速的关系式为：When the fan runs in the constant speed zone of medium wind speed, the wind speed basically reaches the upper limit, and the overspeed control can no longer work. At this time, the rotor speed of the fan will not change significantly with the wind speed, but through the pitch control, the power captured by the fan continues to increase. This part of the rotational speed equation can be approximately linearized, and a straight line can be constructed by the wind speed and rotational speed values (v n , w max ) and (v ws , ws ) at the two ends of the curve, and the relationship between the rotational speed and the wind speed can be obtained as follows:
Figure FDA0003338986720000043
Figure FDA0003338986720000043
 当风机风速达到高风速功率恒定区时，风机转速达到恒定最高转速ωmax，若需风机进行减载d％运行，只需要将参考功率Pref切换为(1-d％)Pn，而转速不会发生变化；When the wind speed of the fan reaches the high wind speed power constant region, the fan speed reaches the constant maximum speed ω max , if the fan needs to operate with a load reduction d%, it is only necessary to switch the reference power Pref to (1-d%)P n , while the speed will not change; 利用上述风速分区方法求解出不同风速下的风速-转速关系式，再结合转速-惯量关系式，即Using the above wind speed partitioning method, the wind speed-rotation speed relationship under different wind speeds is solved, and then combined with the speed-inertia relationship, that is
Figure FDA0003338986720000044
Figure FDA0003338986720000044
 其中，J表示惯量，ωi表示风机i的实际转速，得到可用惯量与风速的关系式，如下：Among them, J represents inertia, ω i represents the actual speed of fan i, and the relationship between available inertia and wind speed is obtained as follows:
Figure FDA0003338986720000051
Figure FDA0003338986720000051
 6.根据权利要求5所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，风速区间划分依据：只需要通过超速控制将风机运行状态从MPPT转变为d％减载曲线即可实现预定的减载目标，称这一区域为低风速区；需要通过转速和桨距角控制实现d％减载率，称为中风速区；只能通过变桨控制达到减载目标，称这一区域为高风速区。6. The partitioned virtual inertia estimation method considering wind speed randomness and correlation according to claim 5, characterized in that, the wind speed interval division basis: only need to change the fan operating state from MPPT to d% load shedding through overspeed control The predetermined load reduction target can be achieved by the curve, and this area is called the low wind speed area; the d% load reduction rate needs to be achieved through the control of the rotational speed and the pitch angle, which is called the medium wind speed area; the load reduction target can only be achieved through the pitch control , this area is called the high wind speed area. 7.根据权利要求5所述的计及风速随机性与相关性的分区虚拟惯量估计方法，其特征在于，根据可用惯量评估过程，风电场可用惯量置信区间的计算步骤如下：7. The partition virtual inertia estimation method considering wind speed randomness and correlation according to claim 5, is characterized in that, according to available inertia evaluation process, the calculation step of wind farm available inertia confidence interval is as follows: (1)输入Copula函数和风速-惯量关系式；(1) Input the Copula function and the wind speed-inertia relationship; (2)构建各机群可用惯量概率密度函数f(E)，即根据公式(5)和公式(6)并结合风速与惯量的关系式(15)，得：(2) Construct the available inertia probability density function f(E) of each fleet, that is, according to formula (5) and formula (6) and combining the relationship between wind speed and inertia (15), we can get:
Figure FDA0003338986720000052
Figure FDA0003338986720000052
 (2)对f(E)进行积分获得可用惯量的概率分布函数φ(E)，即(2) Integrate f(E) to obtain the probability distribution function φ(E) of the available inertia, namely
Figure FDA0003338986720000053
Figure FDA0003338986720000053
 (3)采用二分查找-数值积分法得到概率分布函数φ(E)在α/2和1-α/2概率值处风电机群对应的惯量值，分别将风电机群的可用惯量区间上下限记录下来；(3) Use the binary search-numerical integration method to obtain the inertia value corresponding to the wind turbine group at the α/2 and 1-α/2 probability values of the probability distribution function φ(E), and record the upper and lower limits of the available inertia interval of the wind turbine group respectively. ; (4)将风电场各机群可用惯量叠加求得全风电场的可用惯量的置信区间，同时利用尾流效应分析机群内各机组风速，进而求得各机组可用惯量的分布；(4) Superimpose the available inertia of each wind farm group to obtain the confidence interval of the available inertia of the whole wind farm, and at the same time use the wake effect to analyze the wind speed of each unit in the group, and then obtain the distribution of the available inertia of each unit; (5)输出可用惯量E，以及惯量分布。(5) Output available inertia E, and inertia distribution.
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