CN106548256B - Method and system for modeling time-space dynamic correlation of wind power plant - Google Patents
Method and system for modeling time-space dynamic correlation of wind power plant Download PDFInfo
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Abstract
The invention discloses a method and a system for modeling space-time dynamic correlation of a wind power plant.A mixed Copula function for describing the space-time dynamic correlation between wind speed and active power output of a wind driven generator is constructed, and a parameter estimation value and a corresponding weight coefficient of each sub-Copula function in the mixed Copula function are obtained according to a historical measured wind speed sample of the wind power plant; the wind power output distribution function with correlation is obtained through the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator, the space-time dynamic correlation between the wind speed of the wind power plant and the output power of the wind driven generator can be more accurately described, and the matching degree with the actual wind speed of the wind power plant is improved.
Description
Technical Field
The invention relates to the technical field of wind power generation, in particular to a method and a system for modeling a time-space dynamic correlation of a wind power plant.
Background
Wind power generation is one of the fastest renewable energy sources developed in recent years due to mature technology and good economical efficiency. By 2015, the installed capacity of wind power put into operation in China reaches 1 hundred million kilowatts, and the annual average power generation of wind power accounts for more than 3% of the total power generation in China, and reaches 1900 hundred million kilowatt-hours. At present, wind power in China mainly adopts a centralized large-scale development mode, wherein the installed capacity of wind power in areas where large wind power bases such as Hebei, Mondon, Mongolian, Gansu Jiquan, Jilin, Jiangsu coastal areas, Shandong coastal areas and the like are located reaches 7900 ten thousand kilowatts, and the installed capacity of wind power at sea reaches 500 thousand kilowatts. However, in the wind power base, due to the fact that the geographic positions are close to each other and are located in the same wind zone, the wind speeds close to the wind power plant have certain correlation, when the wind speed correlation is strong, the characteristics of increasing and decreasing of output among the wind power plants obviously cause certain hidden dangers to the operation of the power system, and operators often relieve the operation pressure of the power system at certain economic cost; and when the wind speed has negative correlation, the complementary characteristic of the output between the wind power plants obviously slows down the operating pressure and risk of the power system. Therefore, wind farms within a wind base cannot be considered as independent individuals and their correlation models must be established.
In the following four documents:
[1]Li X,Du D J,Pei J X,et al.Probabilistic load flow calculation withLatin hypercube sampling applied to grid-connected induction wind powersystem[J].Transactions of the Institute of Measurement and Control,2013,35(1):56-65.
[2] dungwei, lie happy, shao hua, etc. probabilistic load flow calculation and impact analysis considering wind speed dependence [ J ] grid technology, 2012,36(4):45-50.
[3] Yanghuang, Wangshuang, Yidexin, etc. the power system considering the output correlation of multiple wind power plants is randomly optimized and dispatched [ J ] the power automation equipment, 2013,33(1): 114-.
[4] Lijunfang, Zhang Yifang, Liu Yi Fang, etc. the alternating current probability trend risk assessment considering random variable correlation [ J ] high voltage technology, 2010,36(2):519 one 524.
Document [1] performs random load flow calculation based on the monte carlo simulation method MCSM, only considering the random characteristic of wind speed, how the wind speeds are related, and does not discuss deeply. Document [2] considers the wind speed dependence of wind farms, but does not discuss the structure of the wind speed in depth, but only assumes that there is a linear correlation between the wind speeds. Documents [3-4] introduce Copula functions for the complexity of the structure related to wind speeds, but only select a certain Copula function for description according to an empirical formula. Such as: document [3] adopts a Gumbel Copula function, which can only reflect the tail-up characteristic of the wind speed and cannot reflect the tail-down characteristic of the wind speed; document [4] uses a normal Copula function, which is only applicable to describe the symmetric correlation characteristic of wind speed.
Disclosure of Invention
At least one of the objectives of the present invention is to provide a method and a system for modeling a time-space dynamic correlation of a wind farm, which can more accurately describe the time-space dynamic correlation of the wind speed of the wind farm and the output power of a wind turbine generator, and improve the matching degree with the actual wind speed of the wind farm, in view of the problems in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for modeling a spatio-temporal dynamic correlation of a wind power plant comprises the following steps:
acquiring a first parameter probability density function of the wind speed according to a historical measured wind speed sample of the wind power plant;
obtaining a probability density function of active power output of the wind driven generator according to a relation function of wind speed and output power of the wind driven generator;
constructing a hybrid Copula function describing space-time dynamic correlation between wind speed and active power output of a wind driven generator, and acquiring a parameter estimation value and a corresponding weight coefficient of each sub-Copula function in the hybrid Copula function according to a historical measured wind speed sample of a wind power plant;
and acquiring a wind power output distribution function with correlation through the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator.
Preferably, the first parametric probability density function is: weibull distribution, Rayligh distribution, Γ distribution, or Gumbel distribution probability density function.
Preferably, when the first parametric probability density function is a Weibull distribution, the first parametric probability density functionNumber of
Wherein: v is the wind speed, k is the shape parameter of Weibull distribution, and the characteristic of the wind speed distribution is reflected; and c is a scale parameter of Weibull distribution, and reflects the average wind speed of the area where the wind power plant is located.
Preferably, the wind speed v and the output power P of the wind power generatorwThe relationship function of (1) is:
Preferably, the probability density function of the active power output of the wind driven generator
Preferably, the hybrid Copula function is characterized in that
Preferably, the number n of the sub Copula functions is 3, and C is the corresponding value1,C2,C3Gumbel Copula function, Frank Copula function, Clayton function, respectively.
Preferably, the historical measured wind speed sample of the wind power plant is a wind speed sample of the same time period of each day in a preset number of days.
A system for modeling spatio-temporal dynamic correlation of a wind farm, comprising, connected by a network:
the sample storage module is used for storing historical measured wind speed samples;
the probability distribution calculation module is used for acquiring a first parameter probability density function of the wind speed according to a historical measured wind speed sample of the wind power plant; obtaining a probability density function of active power output of the wind driven generator according to the relation between the wind speed and the output power of the wind driven generator;
the hybrid Copula function construction module is used for constructing a hybrid Copula function for describing space-time dynamic correlation between wind speed and active power output of the wind driven generator, and acquiring a parameter estimation value and a corresponding weight coefficient of each sub Copula function in the hybrid Copula function according to a historical measured wind speed sample of the wind power plant; and
and the probability distribution model establishing module is used for acquiring a wind power output distribution function with correlation according to the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator so as to describe the wind power correlation of the wind power plant.
In summary, due to the adoption of the technical scheme, the invention at least has the following beneficial effects:
constructing a hybrid Copula function describing space-time dynamic correlation between wind speed and active power output of a wind driven generator, and acquiring a parameter estimation value and a corresponding weight coefficient of each sub-Copula function in the hybrid Copula function according to a historical measured wind speed sample of a wind power plant; the wind power output distribution function with correlation is obtained through the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator, the space-time dynamic correlation between the wind speed of the wind power plant and the output power of the wind driven generator can be more accurately described, and the matching degree with the actual wind speed of the wind power plant is improved.
Drawings
FIG. 1 is a flowchart of a method for modeling spatiotemporal dynamic correlation of a wind farm according to an embodiment of the present invention;
FIG. 2 is a graph of a wind turbine output as a function of wind speed according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a system for modeling spatiotemporal dynamic correlation of a wind farm according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and embodiments, so that the objects, technical solutions and advantages of the present invention will be more clearly understood. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example one
And obtaining the probability distribution model of the output of the wind driven generator by combining the relation between the wind speed and the output power of the wind driven generator through the probability distribution model of the wind speed, thereby determining the wind power random model of the wind power plant.
As shown in fig. 1, a method for modeling a spatiotemporal dynamic correlation of a wind farm disclosed in an embodiment of the present invention includes the following steps:
step 101: according to a historical measured wind speed sample of a wind power plant, a first parameter probability density function of the wind speed is obtained
The probability distribution model of the wind speed is the basis of wind energy resource analysis, a large number of documents are available in recent years for researching the probability distribution of the wind speed, different theoretical distributions are adopted for fitting the wind speed, and the main theoretical distributions are as follows: weibull (Weibull) distribution, rayleigh (rayleigh) distribution, Gamma (Gamma) distribution, gunn (gunbel) distribution, and the like. Among them, Weibull (Weibull) distribution is often used in wind energy calculation, and not only has simple form but also can be well fitted with actual wind speed distribution. The invention describes the randomness of wind speed using a two-parameter Weibull (Weibull) distribution. The expression for the two-parameter Weibull (Weibull) distribution probability density function is:
in the formula: v is the wind speed; k is a shape parameter and reflects the characteristics of wind speed distribution; and c is a scale parameter which reflects the average wind speed of the wind power place in the region.
Based on historical measured wind speed data, estimated values of k and c can be obtained through parameter estimation, and therefore a probability distribution model of the wind speed is determined.
Step 102: obtaining the probability density function of the active power of the wind driven generator according to the relation between the wind speed and the output power of the wind driven generator
The output power of the wind driven generator is mainly influenced by the wind speed, a probability distribution model of the wind speed is determined, and a random model of the wind power output can be deduced according to the relation between the wind speed and the output power of the wind driven generator. For example, as shown in fig. 1, the output power of the wind turbine is expressed as:
in the formula: prThe rated power of the wind driven generator; v. ofciTo cut into the wind speed; v. ofrRated wind speed; v. ofcoCutting out the wind speed;
experimental data statistics shows that the wind speed is between the cut-in wind speed and the rated wind speed in most of time, and the output power of the wind driven generator and the wind speed are in an approximate linear relation as shown in the formula (2), so that the probability density function of the active power output of the wind driven generator is as follows:
step 103: constructing a hybrid Copula function describing the spatio-temporal dynamic correlation between wind speed and active power output of a wind turbine
According to the Copula theory, the relevant structure information of the random variable is obtained, and the most basic method is to determine the joint probability distribution function of the random variable. When the correlation structure of the random variable is complicated, it is difficult to obtain a certain functional expression. The Copula function is used as a connection function, can establish the relation between the joint distribution and the edge distribution, and provides an indirect way for measuring the correlation.
According to the multivariate Sklar theorem, the distribution function F is carried out on any N edges1(u1),F2(u2),....,FN(uN) There is a Copula function C that satisfies:
F(u1,u2,....uN)＝C(F1(u1),F2(u2),...,FN(uN)) (4)
when F is present1(u1),F2(u2),....,FN(uN) Continuous, Copula function C (F)1(u1),F2(u2),...,FN(uN) Will be uniquely determined; f (u) in the formula (4)1,u2,....uN) Is an edge distribution function of F1(u1),F2(u2),....,FN(uN) The joint cumulative distribution function of (a).
The partial derivatives of the two sides of the formula (4) can be obtained:
wherein f, c, fiAre respectively F, C, FiA density function of (a); c can be expressed as:
from equation (5), the joint probability density distribution function f (u)1,u2,....uN) Can be expressed as the product of Copula function and edge probability density function of univariate. Therefore, the correlation structure between random variables can be embodied by the corresponding Copula function.
The selection of Copula function is a prerequisite for correlation analysis. Since the types of Copula functions are many, and different Copula functions are suitable for different situations, a suitable Copula function is finally determined according to the characteristics of the correlation by analyzing the correlation characteristics of the historical measured data of the wind speed.
Construction of hybrid Copula function
Different Copula functions exhibit different correlation structures. In real life, various correlation characteristics can be shown between random variables, and all the characteristics cannot be embodied by using a single Copula function. For example, a normal Copula function is more suitable for describing a symmetric structure between variables, and a Clayton function is more sensitive to only the tail-end correlation. Therefore, in order to overcome the inherent defect of a single Copula function, a plurality of Copula functions are combined and optimized to construct a mixed Copula function:
in the formula: ci(u1,u2,···,un,θi) As a function of sub-Copula, thetaiIs a corresponding parameter; omegai∈[0,1]Is a weight coefficient;
because the characteristics of various Copula functions are integrated by the mixed Copula function, the mixed Copula function can be better matched with the actually measured data, and the model is more accurate.
In a preferred embodiment, the present invention constructs a hybrid Copula function using an archimedes Copula function. I.e., the hybrid Copula function has the form:
in the formula: c1,C2,C3Gumbel Copula function, Frank Copula function, Clayton function, respectively. By changing the weight coefficient in equation (8), the correlation structure of different input random variables can be satisfied.
Step 104: obtaining a wind power output distribution function with correlation through the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator
In a preferred embodiment, the historical measured wind speed sample of the wind farm is a wind speed sample of the same time period for each day within a preset number of days. For example, historical data for a certain period of time in 24 periods of wind speed of the wind farm for the past year may be input; the method comprises the steps of constructing a time-interval hybrid Copula function, performing parameter estimation by using a maximum Expectation (EM) algorithm to obtain the time-interval hybrid Copula function, further obtaining a wind power output distribution function with correlation in a time interval according to the relation between wind speed and output power of a wind driven generator, describing the wind power correlation in the time interval of a wind power plant, and further providing dynamic optimization power flow or dynamic optimization scheduling service.
Example two
Taking the wind speed of a certain time period of the wind power plant as an example, the correlation of the wind speed is analyzed by constructing a hybrid Copula function. Based on historical measured data of wind speed of a wind power plant in a certain period of time, parameter estimation is carried out on the mixed Copula function by using a maximum expectation algorithm to obtain a parameter estimation value thetaiAnd corresponding weight coefficient omegaiAs shown in table 1 below:
TABLE 1
In order to quantitatively evaluate the accuracy of the correlation model of the wind power plant, the accuracy of the established model is evaluated by using a relative error index epsilon and an Average Mean Square (ARMS) index ξ of the sum of variances.
In the formula PwfFor simulating the obtained total active power of wind powerPower, PwrIs the actual value. PwfiAnd PwriRespectively are the values of the ith point on the accumulation distribution curve of the analog value and the actual value, and N is the number of the sampling points.
Obtaining a simulation value of wind speed based on a mixed Copula function model, obtaining active power output of a wind power plant according to a formula (2), calculating indexes epsilon and ξ by using formulas (9) and (10), and comparing the indexes with a result obtained by a single Copula function model, wherein the result is shown in table 2:
TABLE 2
According to the quantitative analysis result in the table 2, compared with a single Copula function, the relative error index epsilon and the ARMS index ξ obtained through calculation are smaller and are more matched with the actual wind speed of the wind power plant, so that the wind power plant space-time dynamic correlation modeling method disclosed by the embodiment of the invention is based on the wind power plant space-time dynamic correlation modeling obtained through the mixed Copula function, has higher precision compared with a method based on the single Copula function, and is more accurate in description of the actual wind speed correlation structure.
EXAMPLE III
As shown in fig. 3, a system for modeling wind speed probability distribution according to an embodiment of the present invention includes: the system comprises a sample storage module, a probability distribution calculation module, a hybrid Copula function construction module and a probability distribution model building module, wherein the sample storage module is connected through a local area network, a wireless access network or the like or a network bus interface and is provided with a central processing unit and an operating memory.
The sample storage module is used for storing historical measured wind speed samples;
the probability distribution calculation module is used for acquiring a first parameter probability density function of the wind speed according to a historical measured wind speed sample of the wind power plant; obtaining a probability density function of active power output of the wind driven generator according to the relation between the wind speed and the output power of the wind driven generator;
the hybrid Copula function construction module is used for constructing a hybrid Copula function for describing space-time dynamic correlation between wind speed and active power output of the wind driven generator, and acquiring a parameter estimation value and a corresponding weight coefficient of each sub Copula function in the hybrid Copula function according to a historical measured wind speed sample of the wind power plant; and
and the probability distribution model establishing module is used for acquiring a wind power output distribution function with correlation according to the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator so as to describe the wind power correlation of the wind power plant.
The above embodiments are only for illustrating the preferred embodiments of the present invention and not for limiting the present invention. Various alterations, modifications and improvements will occur to those skilled in the art without departing from the spirit and scope of the invention.
Claims (6)
1. A method for modeling a spatio-temporal dynamic correlation of a wind farm, characterized by comprising the following steps:
acquiring a first parameter probability density function of the wind speed according to a historical measured wind speed sample of the wind power plant; obtaining a probability density function of active power output of the wind driven generator according to a relation function of wind speed and output power of the wind driven generator;
constructing a hybrid Copula function describing space-time dynamic correlation between wind speed and active power output of a wind driven generator, and acquiring parameter estimation values and corresponding weight coefficients of each sub Copula function in the hybrid Copula function by using a maximum expectation algorithm according to a historical measured wind speed sample of a wind power plant; wherein the hybrid Copula function is:
wherein, Ci(u1，u2，…，un，θi) Is a Copula subfunction, thetaiIs a parameter estimation value; omegaiAre corresponding weight coefficients, ωi∈[0，1]And is
n is the number of the sub Copula functions, and n is 3; corresponding sub-Copula function C1、C2、C3Gumbel Copula function, Frank Copula function and Clayton function; the parameter estimation values of the three sub Copula functions are respectively: 13.35, 37.95, 29.58; the weight coefficients of the three sub Copula functions are respectively: 0.27, 0.31, 0.42; acquiring a wind power output distribution function with correlation according to the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator; the historical measured wind speed sample of the wind power plant is a wind speed sample in the same time period of each day in preset days.
2. The method of claim 1, wherein the first parametric probability density function is: weibull distribution, Rayligh distribution, Γ distribution, or Gumbel distribution probability density function.
3. The method of claim 1, wherein when the first parametric probability density function is a Weibull distribution,
first parameter probability density function
Wherein: v is the wind speed, k is the shape parameter of Weibull distribution, and the characteristic of the wind speed distribution is reflected; and c is a scale parameter of Weibull distribution, and reflects the average wind speed of the area where the wind power plant is located.
4. Method according to claim 1, wherein said wind speed v is related to the wind generator output power PwThe relationship function of (1) is:
wherein the content of the first and second substances,
Prthe rated power of the wind driven generator; vciTo cut into the wind speed; vrRated wind speed; vcoTo cut out the wind speed.
5. The method of claim 3, wherein the probability density function of the wind turbine active power output
6. A system for modeling spatio-temporal dynamic correlations of a wind farm, the system comprising, connected by a network:
the sample storage module is used for storing historical measured wind speed samples;
the probability distribution calculation module is used for acquiring a first parameter probability density function of the wind speed according to a historical measured wind speed sample of the wind power plant; obtaining a probability density function of active power output of the wind driven generator according to the relation between the wind speed and the output power of the wind driven generator;
the hybrid Copula function construction module is used for constructing a hybrid Copula function for describing space-time dynamic correlation between wind speed and active output of the wind driven generator, and acquiring a parameter estimation value and a corresponding weight coefficient of each sub Copula function in the hybrid Copula function by using a maximum expectation algorithm according to a historical measured wind speed sample of the wind power plant; and
the probability distribution model establishing module is used for acquiring a wind power output distribution function with correlation according to the constructed hybrid Copula function and the relation between the wind speed and the output power of the wind driven generator so as to describe the wind power correlation of the wind power plant;
the historical measured wind speed sample of the wind power plant is a wind speed sample in the same time period of each day in preset days;
wherein the hybrid Copula function is:
wherein, Ci(u1，u2，…，un，θi) Is a Copula subfunction, thetaiIs a parameter estimation value; omegaiAre corresponding weight coefficients, ωi∈[0，1]And is
n is the number of the sub Copula functions, and n is 3; corresponding sub-Copula function C1、C2、C3GumbelCopula function, Frank Copula function and Clayton function respectively; the parameter estimation values of the three sub Copula functions are respectively: 13.35, 37.95, 29.58; the weight coefficients of the three sub Copula functions are respectively: 0.27, 0.31, 0.42.
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