CN113935247B - Partition virtual inertia estimation method considering wind speed randomness and correlation - Google Patents
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Abstract
The invention discloses a partitioned virtual inertia estimation method considering wind speed randomness and correlation, which comprises the following steps: step 1: considering the wake flow and time delay effect of wind speed, adopting a sectional aggregation approximation method to process the historical wind speed data, and establishing a wind speed daily change curve of each unit in the field; step 2: clustering wind speed daily variation curves of all units by adopting a double-scale spectral clustering algorithm, and partitioning the units in the field to form a plurality of clusters; step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a non-parameter kernel density estimation method, and constructing an optimal Copula function to analyze the relevance of the wind speed between each cluster center and the anemometer tower; step 4: and (3) taking uncertainty between wind speed and inertia into consideration, and estimating virtual inertia reserves of each cluster in the wind power plant based on the internal structure of the actual wind power plant and wind speed data.
Description
Technical Field
The invention belongs to the technical field of wind power generation, and particularly relates to a partitioned virtual inertia estimation method considering wind speed randomness and correlation.
Background
With large-scale grid connection of wind power generation, the problems caused by the intermittence and fluctuation of wind energy are increasingly remarkable. Because the wind turbine generator is connected with the power grid through the converter, the wind turbine generator is decoupled from the power grid frequency, the wind turbine generator cannot directly participate in system frequency modulation, and effective inertia support cannot be provided. The available inertia of the whole power system is continuously reduced, and the frequency response capability is continuously reduced. Therefore, the national energy agency in the "national regional grid-connected power plant auxiliary service management implementation rule" issued in 2020 requires that 30MW and above wind farms have a frequency modulation function. The frequency response of the fan is mainly realized by virtual inertia control, sagging control, primary frequency modulation and other technologies. With the popularization and application of the technologies, the wind turbine generator set has equivalent inertia supporting capacity. However, an accurate estimation method for the available inertia of each unit in a wind farm is still lacking. The accurate estimation of the available inertia can provide reference for distribution and scheduling of auxiliary frequency modulation output of each unit after disturbance, and can also provide theoretical support for frequency modulation control strategy setting of 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 power plant are the wind speed and the running state in the wind power plant. The number of wind power units in the large wind power plant is large, the distance between the wind power units is relatively close, and certain correlation exists between wind speed and running state of the wind power units. The document 'adopts rattan Copula to construct a wind power plant wind speed dependent model' and 'considers a scene generation method of a multi-wind power plant output Copula correlation', adopts a Copula function to analyze the correlation of wind speeds in a field. The literature, namely a multi-wind power plant output scene generation method considering space-time correlation, considers various wind speed influence factors, establishes a condition Copula joint distribution function of wind power prediction, and realizes the interval prediction of wind power plant 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 multi-element normal distribution function and the Copula function. The literature, namely a wind power plant virtual inertia multi-machine cooperative control strategy considering frequency modulation capability, considers tail characteristics among fan output and provides a wind power output correlation analysis method based on a hybrid Copula function. Research shows that the mixed Copula function has obvious advantages in the aspect of representing the wind speed correlation, but when the mixed multi-component Copula function is constructed, the correlation parameters are difficult to estimate, the advantages and disadvantages of the correlation representation are influenced by the selection of the weight values, the intermediate calculation process is complex, and the Copula function is used for describing the correlation among variables. On the premise of ensuring no distortion, the single Copula function is selected to greatly simplify the intermediate calculation flow.
Current research on wind farm inertia response focuses on virtual inertia control optimization, and available inertia evaluation of wind farms is relatively few in research and is an evaluation of overall inertia of wind farms. The literature 'a new method for evaluating potential help of wind capacity to system frequency stability' provides a method for evaluating frequency modulation capability of a plurality of wind farms based on the principle that rotational kinetic energy of wind turbines is equal. The literature, namely a probability method for evaluating comprehensive sagging and inertial response of a wind farm, evaluates the combined inertial response capability of the wind farm at a specific average wind speed through a Gaussian distribution model of atmospheric turbulence processed in a blocking mode. On the basis, the literature 'analytical modeling of wind farm inertia and droop response for short-term frequency regulation of a power system' comprehensively evaluates the combined frequency modulation effect of virtual inertia control and droop control. However, the wind farm is taken as a whole by the evaluation method, so that the distribution difference of the available inertia in the wind farm is ignored, 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 farm cannot be solved.
Assessment of wind farm usable inertia a wind farm's overall rotational inertia level is typically estimated using the wind speed of a particular location unit or the average wind speed of the wind farm. The literature An introduction to copulas proposes deriving the inertia time constants from a single variable speed constant frequency wind turbine generator set based on a load shedding model for VSWT speed control. However, the model cannot accurately estimate the available inertial quantity of the large wind power plant due to the problem of calculation efficiency.
Disclosure of Invention
The invention provides a partitioned virtual inertia estimation method for taking wind speed randomness and relativity into consideration factors such as relativity of wind speeds of all units in a wind power plant, position distribution and running state of all units and the like.
The technical scheme adopted by the invention is as follows:
the partitioned virtual inertia estimation method considering wind speed randomness and correlation comprises the following steps:
Step 1: considering the wake flow and time delay effect of wind speed, adopting a sectional aggregation approximation method to process the historical wind speed data, and establishing a wind speed daily change curve of each unit in the field;
Step 2: clustering wind speed daily variation curves of all units by adopting a double-scale spectral clustering algorithm to realize the partitioning of the units in a field and form a plurality of clusters;
Step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a non-parameter kernel density estimation method, and constructing an optimal Copula function to analyze the relevance of the wind speed between each cluster center and the anemometer tower;
step 4: and (3) taking uncertainty between wind speed and inertia into consideration, and estimating virtual inertia reserves of each cluster in the wind power plant based on the internal structure of the actual wind power plant and wind speed data.
Preferably, in step 2, the partitioning process of the wind farm is implemented as follows:
step 201: distance-based similarity measure
A set X (X 1,x2,…,xM) of M wind speed data, wherein the data length of each wind speed curve X i is L; the Euclidean distance is the true distance between two data points in L-dimensional space, and the Euclidean distance between wind speed curves x i and x j is defined as:
Step 202: similarity measurement 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 i with n possible values in a certain time period as x 1,x2,…,xn; the probability of each possible value is p 1,p2,…,pn; the entropy value H n of the time period wind speed curve x i is defined as:
The magnitude 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 daily variation curves with close distances and similar fluctuation degrees are gathered into one type by utilizing a spectral clustering algorithm through similarity measurement feature extraction based on the distances and the forms, so that the partition of the wind power plant is realized.
Preferably, in step 3, after the in-field unit is clustered and dimension reduced in step 2, the whole wind power plant is divided into N unit areas, a wind speed sequence joint distribution probability square chart between each unit area and a wind measuring tower is drawn, tail characteristics and symmetrical characteristics of the wind power plant are analyzed, and an optimal Copula function is selected according to a method with the minimum Euclidean distance from the empirical Copula function.
Preferably, the specific process of constructing the optimal Copula function to analyze the correlation of wind speed between each cluster center and the anemometer tower is as follows:
Step 301: first, an empirical Copula function, random variable X, Y, was introduced, the empirical distribution function being the sum F n (x) and H n (x), respectively, the empirical Copula function being defined as:
wherein u, v E [0,1]; f n(xi) is less than or equal to u, Otherwise, 0;
Obtaining related unknown parameters of each theoretical Copula function by using a maximum likelihood estimation method; according to formula (1), the Euclidean distance square of the two is obtained by combining a theoretical Copula function and an empirical Copula function by the definition formula of Euclidean distance as follows:
Where P is the theoretical Copula function type, Reflects the square of the Euclidean distance between the theoretical Copula function and the empirical Copula function,/>The Copula function corresponding to the minimum value is the 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, knowing detailed wind speed data measured by a wind measuring tower, establishing an optimal Copula function to describe wind speed correlation between the wind measuring tower and each cluster, thereby obtaining an instantaneous wind speed probability density function of each cluster as follows:
Preferably, in step 4, the process of estimating the available inertial quantity based on the wind speed partition 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 aerodynamic correlation theory, when the wind turbine generator is operated in the MPPT working mode, the captured mechanical power can be represented by the following formula:
Wherein ρ is air density, C P max is wind energy capture coefficient, λ is tip speed ratio, β is pitch angle, R is fan blade radius, and V is wind speed; wherein the wind energy capture coefficient C P max is related to the tip speed ratio λ and the pitch angle β:
omega in the above formula is the rotation speed of the generator; p is the pole pair number of the generator; g is the pole pair number of the gear box;
when the load shedding rate is d%, the power value is as follows:
The two formulas are combined to obtain:
CP-de＝(1-d％)CP max (11)
According to the dichotomy, the tip speed ratio when the load shedding rate is d percent can be obtained, and the relationship between the fan rotating speed and the wind speed when the load shedding rate is d percent can be obtained through the definition of the tip speed ratio:
When the fan runs in a constant region of the wind speed and the rotating speed, the wind speed basically reaches the upper limit, overspeed control cannot be continuously performed, at the moment, the rotating speed of the rotor of the fan cannot be obviously changed along with the wind speed, but the captured power of the fan is continuously improved through variable pitch control, the partial rotating speed equation can be approximately linearized, and a straight line is constructed through wind speed rotating speed values (v n,wmax)、(vws,ws) of two end points of a curve, so that the relation between the rotating speed and the wind speed is obtained as follows:
When the wind speed of the fan reaches a constant area of high wind speed power, the rotating speed of the fan reaches a constant maximum rotating speed omega max, if the fan is required to perform load shedding d% operation, only the reference power P ref is required to be switched into (1-d%) P n, and the rotating speed is not changed;
Solving a wind speed-rotating speed relation under different wind speeds by using the wind speed partitioning method, and combining the rotating speed-inertia relation to obtain
Wherein J represents inertia, omega i represents the actual rotation speed of the fan i, and a relation between the available inertia and wind speed is obtained as follows:
Preferably, the wind speed interval division is based on: the preset load shedding target can be realized only by converting the running state of the fan from MPPT to d% load shedding curve through overspeed control, and the area is called as a low wind speed area; d% load shedding rate, called a medium wind speed zone, is required to be achieved through rotation speed and pitch angle control; the load reduction target can be achieved only through pitch control, and the area is called a high wind speed area.
Preferably, according to the available inertial amount evaluation process, the calculation steps of the wind farm available inertial amount confidence interval are as follows:
(1) Inputting a Copula function and a wind speed-inertia relation;
(2) Constructing an available inertia probability density function f (E) of each cluster, namely, according to a formula (5) and a formula (6) and combining a relation (15) of wind speed and inertia, and obtaining the inertia probability density function:
(2) Integrating f (E) to obtain a probability distribution function phi (E) of the available inertia, i.e
(3) Obtaining inertia values corresponding to the wind turbine groups at the alpha/2 and 1-alpha/2 probability values of the probability distribution function phi (E) by adopting a binary search-numerical integration method, and respectively recording the upper limit and the lower limit of the available inertia interval of the wind turbine groups;
(4) Superposing the available inertia of each cluster of the wind power plant to obtain a confidence interval of the available inertia of the whole wind power plant, and analyzing the wind speed of each unit in the clusters by utilizing wake effect to obtain the distribution of the available inertia of each unit;
(5) The available inertia E is output, as well as the inertia profile.
The invention has the beneficial effects that:
according to the method, wind speed randomness of a wind power plant and wind speed correlation among units are considered, a method for estimating virtual inertia of a wind power plant partition based on Copula functions and a clustering algorithm is provided, and the internal structure and wind speed data of an actual wind power plant are analyzed. And obtaining a total available inertial measurement confidence interval of the wind power plant and available inertial measurement distribution of each unit. According to the actual wind speed and output data of a certain Gansu wind farm, a simulation example is constructed, and simulation results show that the algorithm provided by the invention can effectively perform partition clustering on the wind farm and can estimate the accuracy of the available inertial quantity.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a partitioned virtual inertia estimation method of the present invention that accounts for wind speed randomness and correlation.
FIG. 2 is a simplified model schematic of wake effects.
FIG. 3 shows a process 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 shows a wind farm motor geographical location profile.
FIG. 7 shows cluster clustering results and a cluster center wind speed daily variation curve; (a) The clustered machine set geographic position distribution map is that the machine sets with the same color are a cluster; (b) cluster one; (c) cluster two; (d) Cluster III.
FIG. 8 shows the histograms of W1 and W2 wind speed distributions and the fitted probability density function; (a) a central fan W1; (b) anemometer tower W2.
FIG. 9 shows a two-unit binary combined wind velocity distribution histogram.
FIG. 10 is a graph showing probability density and distribution functions of Gumbel-copula; (a) a probability density function map; (b) a distribution function graph.
FIG. 11 is a graph showing the probability density function and distribution function of Clayton-copula; (a) a probability density function map; (b) a distribution function graph.
FIG. 12 is a graph showing probability density and distribution functions of Frank-copula; (a) a probability density function diagram; (b) a distribution function graph.
FIG. 13 is a graph showing the comparison of available inertial amounts of the equivalent machine method and the actual measurement method.
Fig. 14 shows the actual value of the available inertial amount and the theoretical confidence interval of the available inertial amount (the confidence is taken to be 90%).
FIG. 15 shows a usable inertial mass distribution map; (a) actual values of available inertial quantity; (b) a profile of available inertial mass expected values.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the 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 invention, as 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 made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment specifically provides a partitioned virtual inertia estimation method considering wind speed randomness and correlation, as shown in fig. 1, comprising the following steps:
Step 1: considering the wake flow and time delay effect of wind speed, adopting a sectional aggregation approximation method to process the historical wind speed data, and establishing a wind speed daily change curve of each unit in the field;
Step 2: clustering wind speed daily variation curves of all units by adopting a double-scale spectral clustering algorithm to realize the partitioning of the units in a field and form a plurality of clusters;
Step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a non-parameter kernel density estimation method (after fitting the probability distribution of the center unit by adopting the non-parameter kernel density estimation method, solving the wind speed edge distribution, providing necessary conditions for solving parameters in a Copula function, and constructing an optimal Copula function to analyze the relevance of wind speed between each cluster center and a anemometer tower;
step 4: and (3) taking uncertainty between wind speed and inertia into consideration, and estimating virtual inertia reserves of each cluster in the wind power plant based on the internal structure of the actual wind power plant and wind speed data.
In step 1, the difference of wind speeds among different units in the wind farm is mainly influenced by wake effects among the units.
The simplified wake model is shown in fig. 2, and the wind speed relationship between the upstream and downstream units is shown in the following formula.
Wherein V o is the wind speed blowing to the wind turbine generator; v x is the wind speed d leaving the wind turbine, and the magnitude of the V x is the wind speed reduction coefficient, and the V is related to the thrust coefficient C T of the wind turbine, the radius R of the wind turbine blade, the distance X between adjacent wind turbines and the wake flow reduction coefficient K. The land wind farm typically takes k=0.075.
In a large wind farm, there is significant time delay in the transfer of real-time wind conditions from an upstream fan to a downstream fan, and the time delay phenomenon of wind speed is particularly significant with wake effects taken into account. Assuming that the delay time of wind speed from the wind farm end to the fan j is tau, the upstream fan wind speed considering delay is:
vj(t)＝vo(t-τ)
As shown in FIG. 3, when the wind speed data information amount is large, the wind speed curve is firstly subjected to dimension reduction characterization by adopting a piecewise aggregation approximation method. The basic form of the high-dimensional data is approximately represented by the low-dimensional data, the dimension reduction processing of the wind speed data can be realized, and for a wind speed array Y= { Y 1,y2,…,yn } with the length of n, a wind speed array with the length of m is used It is approximately expressed, where m < n and m is divisible by n. Then/>The i-th element of (b) can be calculated by the following formula:
Secondly, clustering wind speed change curves based on a double-scale spectral clustering algorithm, wherein the specific process is as follows:
step 201: distance-based similarity measure
A set X (X 1,x2,…,xM) of M wind speed data, wherein the data length of each wind speed curve X i is L; the Euclidean distance is the true distance between two data points in L-dimensional space, and the Euclidean distance between wind speed curves x i and x j is defined as:
Step 202: similarity measurement 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 i with n possible values in a certain time period as x 1,x2,…,xn; the probability of each possible value is p 1,p2,…,pn; the entropy value H n of the time period wind speed curve x i is defined as:
The magnitude 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 daily variation curves with close distances and similar fluctuation degrees are gathered into one type by utilizing a spectral clustering algorithm through similarity measurement feature extraction based on the distances and the forms, so that the partition of the wind power plant is realized.
The wind turbine generator system clustering algorithm divides all the turbine generator systems in the wind power plant into a plurality of turbine generator system groups based on wind speed distribution in the wind power plant, and establishes available inertial quantity assessment models for the divided sub-turbine generator system groups respectively, so that comprehensive reflecting capacity of the whole characteristics of the wind power plant is improved, and accuracy of the available inertial quantity assessment of the whole wind power plant is improved.
And combining the proposed similarity measurement based on the distance and morphological characteristics, clustering the wind speed curves of the units by using a double-scale spectral clustering method, and grouping the clusters of the units in the field. The calculation process is as follows:
Input: inputting wind speed data set of each unit
Clustering:
1. determining width parameters of a Gaussian kernel function so as to construct a similarity matrix H;
2. Calculating a Laplacian matrix of the similarity matrix and determining an optimal classification number k;
3. Solving the feature vectors corresponding to the first k maximum feature values;
4. constructing a feature matrix for the selected feature vector;
5. and carrying out K-means clustering on the feature 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 i |i=1, 2, …, n } be the sample space of the random variable z, the probability density of z is u (z), then the kernel density of u (z) is estimated as:
Wherein z is a kernel density function argument; z i is the data for sample point i; l is window width; k (delta) is a Gaussian kernel function, and delta is a kernel function argument.
After the dimension reduction of the in-field unit cluster in step 2, the whole wind power plant is divided into N unit areas, a wind speed sequence joint distribution probability orthogram between each unit area and a wind measuring tower is drawn, tail characteristics and symmetrical characteristics of the wind power plant are analyzed, and an optimal Copula function is selected according to a method with the minimum Euclidean distance with the empirical Copula function.
The specific process is as follows:
Step 301: first, an empirical Copula function, random variable X, Y, was introduced, the empirical distribution function being the sum F n (x) and H n (x), respectively, the empirical Copula function being defined as:
wherein u, v E [0,1]; f n(xi) is less than or equal to u, Otherwise, 0;
Obtaining related unknown parameters of each theoretical Copula function by using a maximum likelihood estimation method; according to formula (1), the Euclidean distance square of the two is obtained by combining a theoretical Copula function and an empirical Copula function through the definition formula of the Euclidean distance, and is as follows:
Where P is the theoretical Copula function type, Reflects the square of the Euclidean distance between the theoretical Copula function and the empirical Copula function,/>The Copula function corresponding to the minimum value is the 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, knowing detailed wind speed data measured by a wind measuring tower, establishing an optimal Copula function to describe wind speed correlation between the wind measuring tower and each cluster, thereby obtaining an instantaneous wind speed probability density function of each cluster as follows:
in step 4, the wind farm wind speed-inertia uncertainty analysis process is as follows:
The wind driven generator makes its running state deviate from the maximum power point by controlling its rotating speed or pitch angle, and the control mode of the standby power is the load shedding control of the fan. The load shedding control mode is mainly divided into overspeed control and pitch angle change control.
The available inertial estimation process based on wind speed partition is as follows:
Wind speed interval division basis: as shown in fig. 4, in the area surrounded by ABB 'a', the preset load shedding target can be realized only by converting the running state of the fan from MPPT to d% load shedding curve through overspeed control, and the area is called a low wind speed area; the BCB' area is limited by the highest rotating speed of the fan, and d% load shedding rate, called as a medium wind speed area, is required to be realized through the control of the rotating speed and the pitch angle; in the graph, the section C' D reaches the maximum rotating speed of 1.2p.u, and the load shedding target can be achieved only through pitch control, so that the section is called a high wind speed area.
TABLE 1 wind speed interval
In addition to the first three wind speed zones, as shown in FIG. 5, when the start zone, wind speed is below the cut-in wind speed or the wind speed is above the cut-out wind speed: the wind speed is limited by the wind speed condition, and the fan cannot normally run in a grid connection mode or has no rotation speed reducing capability, so that the wind turbine generator does not participate in the frequency response of the power system in the wind speed region, and no inertia is available.
In the low wind speed region, according to the aerodynamic correlation theory, when the wind turbine generator is operated in the MPPT working mode, the captured mechanical power can be represented by the following formula:
Wherein ρ is air density, C P max is wind energy capture coefficient, λ is tip speed ratio, β is pitch angle, R is fan blade radius, and V is wind speed; wherein the wind energy capture coefficient C P max is related to the tip speed ratio λ and the pitch angle β:
omega in the above formula is the rotation speed of the generator; p is the pole pair number of the generator; g is the pole pair number of the gear box;
when the load shedding rate is d%, the power value is as follows:
The two formulas are combined to obtain:
CP-de＝(1-d％)CP max (11)
According to the dichotomy, the tip speed ratio when the load shedding rate is d percent can be obtained, and the relationship between the fan rotating speed and the wind speed when the load shedding rate is d percent can be obtained through the definition of the tip speed ratio:
When the wind speed basically reaches the upper limit when the wind turbine runs in the constant region of the wind speed and the overspeed control cannot be continuously performed, the rotation speed of the wind turbine rotor cannot be obviously changed along with the wind speed, but the captured power of the wind turbine is continuously improved through the variable pitch control, the partial rotation speed equation can be approximately linearized according to the literature [ the wind power plant available inertial energy assessment method based on the mixed Copula function ], and a straight line is constructed through wind speed rotation speed values (v n,wmax)、 (vws,ws) of two end points of a curve, so that the relation between the rotation speed and the wind speed is obtained as follows:
When the wind speed of the fan reaches a constant area of high wind speed power, the rotating speed of the fan reaches a constant maximum rotating speed omega max, if the fan is required to perform load shedding d% operation, the reference power P ref is only required to be switched into (1-d%) P n, and the rotating speed is not changed.
The usable inertia of a fan refers to the capacity of the fan to participate in an inertia response or primary frequency modulation response. When the frequency is changed, 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 rotating at inertia J and angular velocity ω, the rotational kinetic energy of which is:
For a single fan in a wind power plant, the kinetic energy of the rotor cannot be completely released when inertia response is performed, and in the inertia response process, the rotor has the limit of the minimum rotation speed, ω min =0.75 (p.u.). Therefore, if the actual rotation speed of the fan i is ω i, the actual available inertia of the fan is:
according to equations (13) and (14), the relation between the available inertia and wind speed is obtained as follows:
According to the above-mentioned available inertial probability evaluation process, the calculation steps of the wind farm available inertial confidence interval are as follows:
(1) Inputting a Copula function and a wind speed-inertia relation;
(2) Constructing an available inertia probability density function f (E) of each cluster, namely, according to a formula (5) and a formula (6) and combining a relation (15) of wind speed and inertia, and obtaining the inertia probability density function:
(2) Integrating f (E) to obtain a probability distribution function phi (E) of the available inertia, i.e
(3) Obtaining inertia values corresponding to the wind turbine groups at the alpha/2 and 1-alpha/2 probability values of the probability distribution function phi (E) by adopting a binary search-numerical integration method, and respectively recording the upper limit and the lower limit of the available inertia interval of the wind turbine groups;
(4) Superposing the available inertia of each cluster of the wind power plant to obtain a confidence interval of the available inertia of the whole wind power plant, and analyzing the wind speed of each unit in the clusters by utilizing wake effect to obtain the distribution of the available inertia of each unit;
(5) The available inertia E is output, as well as the inertia profile.
Calculation example simulation
Taking a Gansu wind farm as an example, a schematic diagram of the arrangement of fans in the wind farm is shown in fig. 6: in the figure, the abscissa is the longitude and latitude coordinate of the position where the fan is located, and the lower right corner is the position of the anemometer tower. And (3) carrying out the available inertial measurement interval assessment of the whole wind power plant by adopting accurate wind speed data at the wind measuring tower, and selecting the wind speed data of the wind measuring tower at the height of 70m when carrying out wind speed modeling of the wind turbine, wherein the wind turbine is of a unified model, and the detailed data are shown in Table 2.
TABLE 2 wind turbine parameters
1.1 Cluster clustering
And clustering the wind speed daily variation curves of 33 fans by using a double-scale spectral clustering algorithm to obtain a clustering number of 3, wherein the result is shown in the following figure 7. And simultaneously, obtaining three clustered cluster position distribution diagrams according to curve clustering results and combining unit positions as follows.
1.2 Optimal Copula function
According to the method for analyzing the correlation of the cluster wind speeds by the Copula function, the wind speed data of a central fan W1 and a wind measuring tower W2 of a certain cluster are adopted for carrying out calculation analysis. The wind speed data is the instantaneous wind speed data measured by the unit at intervals of 10 minutes.
In the embodiment, a non-parameter kernel density estimation method is adopted to determine wind speed edge distribution U and V of two sets, and meanwhile frequency histograms corresponding to W1 and W2 wind speeds are drawn as shown in figure 8.
As can be derived from the binary distribution histogram (fig. 9), the probability density function tails are asymmetric, and the archimedes-Copula function can be used to describe the relationship between the two. The parameters of the three copula functions are obtained by using a maximum likelihood estimation method: gumbel-copula:5.7320; clayton-copula:4.4871; frank-copula:20.1128.
From the three copula function probability density function graphs (fig. 10, 11 and 12), it can be seen that gummel-copulla has a higher similarity in shape with the Frank-copula function, indicating that both functions can be used to characterize the correlation between wind speeds of two sets. In order to more accurately select the appropriate copula function, the comparison is made using the euclidean distance method described above. See table 3:
TABLE 3 three copula function correlation metrics and Euclidean distance thereof
Among the three, the Gumbel-Copula function has smaller square Euclidean distance, and the Clayton-Copula function can be selected in the joint distribution of the Gumbel-Copula function and the Gumbel-Copula function, and the function can better show the relation between the Gumbel-Copula function and the Clayton-Copula function.
1.3 Available inertial confidence interval and distribution
The wind speed correlation of the wind speed correlation is described by utilizing the optimal copula function between the three clusters and the anemometer tower obtained in the step 1.2, and the wind speed data of the known anemometer tower are used for deducing the wind speed of each cluster. And then solving the inertia of each cluster by using a wind speed-inertia relation. The wake flow effect and the time delay effect are combined to obtain the wind speed distribution inside the cluster, so that the available inertial energy distribution is obtained.
(1) Time sequence-based wind power plant available inertial measurement evaluation curve
And (3) taking a certain Gansu wind power plant as an example, evaluating the upper limit and the lower limit of the total available inertial quantity of the wind power plant by using the method provided by the invention, and comparing with the actual available inertial quantity calculated by using historical data and using average wind speed. The effectiveness of the method in practical application is demonstrated.
In actual operation, the wind speed historical data of the wind farm M on a certain day in summer from 0:00 to 24:00 is used for carrying out available inertial measurement assessment. And comparing the available inertial measurement interval estimated by the method with an available inertial measurement curve based on the measured value.
The comparison of the available inertial measurement confidence interval and the actual value obtained by the method.
Fig. 13 is a graph of the total available inertial amount of the wind farm over time in one day, combined with a graph of the wind speed daily variation in 1.1, it can be seen that the equivalent machine method has higher accuracy when the wind speed is higher, because when the wind speed is too high, the fan enters a constant rotation speed or constant power area, and the rotation speed of the fan does not change along with the change of the wind speed, so that the rotation speeds of all units are basically consistent and are the highest rotation speeds, so that the equivalent machine method only works, however, as the wind speed continuously decreases, the accuracy of the equivalent machine method is lower, even the available inertial amount is 0 in 0.5-0.8 days, because many units cannot provide inertial support when the wind speed is too low. This is also why the equivalent machine method does not accurately evaluate the available inertia at low wind speeds.
Fig. 14 shows the upper and lower limits of the available inertial measurement unit when the confidence level is 90%, and it can be seen from the graph that the probability method is adopted to evaluate the available inertial measurement unit, so that the available inertial measurement unit can better contain the actual available inertial measurement unit, and particularly has better accuracy in the case of medium and high wind speeds, but also has inaccurate places. In 144 groups of wind speed time sequence data on one day, 10 groups of actual inertia exceed the upper limit of the confidence interval or are lower than the lower limit of the confidence interval, and the error rate is 6.944%. Meanwhile, the solution provided by the invention has good accuracy in a low wind speed region by using an inertial measurement method. When the wind speed is too low, the equivalent machine method cannot evaluate the available inertia, but the method can accurately identify the available inertia value, but the problem that the available inertia value at a specific time point is too high is also solved, and in practical application, the principle that the evaluation value needs to be kept as much as possible is considered, and the lower limit curve of the available inertia value evaluation has better reference value.
(2) Spatial distribution of available inertial energy
The available inertia distribution of the wind power plant is calculated by using wind speed data of each unit of the wind power plant at the moment 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 inertial quantity, fig. 15 (b) is a graph of expected value of the available inertial quantity obtained by the method of the present invention, and the graph is compared with the two graphs, so that the available inertial quantity distribution obtained by the method of the present invention is basically consistent with the actual value, which cannot be achieved by the equivalence machine method. The average error of inertia distribution calculated by the method is 4.0552% by calculating the error of the theoretical value and the actual value of the available inertia of each unit. The effectiveness of the method provided by the invention in the estimation of the available inertial mass distribution is fully demonstrated. Meanwhile, a dispatcher can grasp potential of each unit for providing output when the inertia is supported according to the graph, and a basis is provided for adjusting frequency response and unit operation states.
The foregoing is merely illustrative of the present invention and not restrictive, and other modifications and equivalents thereof may occur to those skilled in the art without departing from the spirit and scope of the present invention.
Claims (3)
1. The partition virtual inertia estimation method considering the randomness and the relativity of the wind speed is characterized by comprising the following steps:
Step 1: considering the wake flow and time delay effect of wind speed, adopting a sectional aggregation approximation method to process the historical wind speed data, and establishing a wind speed daily change curve of each unit in the field;
Step 2: clustering wind speed daily variation curves of all units by adopting a double-scale spectral clustering algorithm, and partitioning the units in the field to form a plurality of clusters;
Step 3: fitting the wind speed probability distribution of each cluster center unit by adopting a non-parameter kernel density estimation method, and constructing an optimal Copula function to analyze the relevance of the wind speed between each cluster center and the anemometer tower;
Step 4: taking uncertainty between wind speed and inertia into consideration, and estimating virtual inertia reserves of each cluster in the wind power plant based on the internal structure of the actual wind power plant and wind speed data;
In step 2, the partitioning process for implementing the wind farm is as follows:
step 201: a distance-based similarity measure;
A set X with M wind speed data (X 1,x2, X M), wherein the data length of each wind speed profile x i is L; the Euclidean distance is the true distance between two data points in L-dimensional space, and the Euclidean distance between wind speed curves x i and x j is defined as:
（1）
Step 202: similarity measurement 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; let x i be the wind speed curve for a certain period of time, with n possible values, be x 1,x2,X n; the probability of each possible value is p 1,p2,/>P n; the entropy value H n of the time period wind speed curve x i is defined as:
（2）
The magnitude 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 method comprises the steps of constructing a similarity matrix of wind speeds of each fan through similarity measurement feature extraction based on distance and morphology, and gathering wind speed daily change curves with similar distances and similar fluctuation degrees into one type by utilizing a spectral clustering algorithm so as to realize the partition of a wind power plant;
In the step 3, after the in-field unit cluster is subjected to dimension reduction in the 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 symmetrical 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 with the empirical Copula function;
The specific process of constructing the optimal Copula function to analyze the correlation of wind speed between each cluster center and the anemometer tower is as follows:
Step 301: first, an empirical Copula function is introduced, random variables x and y, and empirical distribution functions are respectively F n (x) and H n (y), and the empirical Copula function is defined as:
（3）
In the middle of ；/>Time,/>=1, Otherwise 0;
obtaining related unknown parameters of each theoretical Copula function by using a maximum likelihood estimation method; according to formula (1), the Euclidean distance square of the two is obtained by combining a theoretical Copula function and an empirical Copula function by the definition formula of Euclidean distance as follows:
（4）
Where P is the theoretical Copula function type, Reflects the square of the Euclidean distance between the theoretical Copula function and the empirical Copula function,/>The Copula function corresponding to the minimum value is the optimal Copula function;
after the optimal Copula function is selected, the binary joint probability density function between the cluster k and the anemometer tower m is:
（5）
When inertia estimation is carried out, knowing detailed wind speed data measured by a wind measuring tower, establishing an optimal Copula function to describe wind speed correlation between the wind measuring tower and each cluster, thereby obtaining an instantaneous wind speed probability density function of each cluster as follows:
（6）；
Also included in step 4 is the process of estimating the available inertial energy based on the wind speed partition 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 aerodynamic correlation theory, when the wind turbine generator is operated in the MPPT working mode, the captured mechanical power can be represented by the following formula:
（7）
In the method, in the process of the invention, Is air density/>For maximum wind energy capture coefficient,/>For tip speed ratio,/>Is pitch angle, R is fan blade radius,/>Is the wind speed; wherein the wind energy capture coefficient/>Speed ratio with tip/>And pitch angle/>Correlation:
（8）
（9）
omega in the above formula is the rotation speed of the generator; p is the pole pair number of the generator; g is the pole pair number of the gear box;
when the load shedding rate is d%, the power value is as follows:
（10）
the joint formula (7) and formula (10) can be obtained:
（11）
according to the dichotomy, the tip speed ratio when the load shedding rate is d percent can be obtained, and the relationship between the fan rotating speed and the wind speed when the load shedding rate is d percent can be obtained through the definition of the tip speed ratio:
（12）
When the fan runs in the medium-speed rotating speed constant region, the wind speed basically reaches the upper limit, overspeed control cannot be continuously performed, at the moment, the rotating speed of the rotor of the fan cannot be obviously changed along with the wind speed, but the captured power of the fan is continuously improved through variable pitch control, a rotating speed equation of the fan running in the medium-speed rotating speed constant region can be approximately linearized, and a straight line is constructed through wind speed rotating speed values (v n,wmax)、(vws,ws) of two end points of a curve, so that the relation between the rotating speed and the wind speed is obtained as follows:
（13）
When the wind speed of the fan reaches a constant area of high wind speed power, the rotating speed of the fan reaches a constant maximum rotating speed omega max, if the fan is required to perform load shedding d% operation, only the reference power P ref is required to be switched into (1-d%) P n, and the rotating speed is not changed;
solving a wind speed-rotating speed relation under different wind speeds by using the wind speed partitioning method, and combining the rotating speed-inertia relation to obtain
（14）
Wherein J represents inertia, omega i represents the actual rotation speed of the fan i, and a relation between the available inertia and wind speed is obtained as follows:
（15）。
2. The partitioned virtual inertia estimation method according to claim 1, wherein the wind speed interval division is based on: the preset load shedding target can be realized only by converting the running state of the fan from MPPT to d% load shedding curve through overspeed control, and the area is called as a low wind speed area; d% load shedding rate, called a medium wind speed zone, is required to be realized through control of the rotating speed and the pitch angle; the load shedding target can be achieved only through pitch control, and the area is called a high wind speed area.
3. The partitioned virtual inertia estimation method according to claim 1, wherein the calculation step of the wind farm available inertial confidence interval according to the available inertial estimation process is as follows:
(1) Inputting a Copula function and a wind speed-inertia relation;
(2) Constructing an available inertia probability density function f (E) of each cluster, namely, according to a formula (5) and a formula (6) and combining a relation (15) of wind speed and inertia, and obtaining the inertia probability density function:
（16）；
(2) Integrating f (E) to obtain a probability distribution function ϕ (E) of available inertia, i.e
（17）；
(3) Obtaining inertia values corresponding to the wind turbine groups at the alpha/2 probability values and the 1-alpha/2 probability values of the probability distribution function ϕ (E) by adopting a binary search-numerical integration method, and respectively recording the upper limit and the lower limit of the available inertia interval of the wind turbine groups;
(4) Superposing the available inertia of each cluster of the wind power plant to obtain a confidence interval of the available inertia of the whole wind power plant, and analyzing the wind speed of each unit in the clusters by utilizing wake effect to obtain the distribution of the available inertia of each unit;
(5) The available inertia E is output, as well as the inertia profile.
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