CN106251238B - Wind power plant modeling sequence discretization step length selection and model error analysis method - Google Patents
Wind power plant modeling sequence discretization step length selection and model error analysis method Download PDFInfo
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Abstract
A wind power plant modeling sequence discretization step length selecting and model error analyzing method comprises the steps of firstly fitting a fan equivalent power characteristic curve to obtain actual output under the condition that the whole wind power plant has no limit output; then selecting a proper sequence discretization step length, obtaining a probabilistic sequence of wind power plant output by using a sequence operation theory, describing wind power plant output probability distribution by using a Weibull function, and estimating parameters by using a maximum likelihood estimation method; and finally, analyzing and evaluating the error of the output probability density function of the wind power plant by using a sequence operation theory and a random sampling method. The method can establish an accurate model of the probability distribution of the wind power plant, reduces the influence of factors such as the terrain of the wind power plant, the limited output and the like on the wind power plant, and can provide reference for the planning and the operation of the power system. And finally, verifying the effectiveness of the method provided by the invention based on a calculation example of historical data of a certain wind power plant.
Description
Technical Field
The invention provides a method for selecting a discretization step length of a wind power plant modeling sequence and analyzing a model error aiming at the research of the output characteristic of the current wind power plant, and belongs to the technical field of data processing.
Background
In recent years, new energy power generation, particularly wind power generation, has been rapidly developed at home and abroad. Because wind power has intermittence, randomness and fluctuation, the influence of large-scale wind power access to a power grid on a power system is increasingly prominent. The accurate wind power plant output model is established, a basis can be provided for researches such as wind power plant wind-fire ratio selection and microgrid economic dispatching, and the method has important practical significance.
The research of the wind power plant output model is mainly divided into two types at present. One is to establish a deterministic model to obtain the specific output of the wind power plant, and because the actual output of the wind power plant is influenced by various factors, the model is difficult to establish, and the result error is large. And the other method is to establish a probability distribution model to obtain a probability density function of the output of the wind power plant. Compared with a deterministic model, due to the uncertainty of the wind power, the establishment of the probability distribution model has more practical significance, the probability density function can be given, the existing error can be given, the reliability is higher, and the application field is wider. Therefore, the invention provides a method for selecting the sequence discretization step length in wind power plant modeling, and the method is used for carrying out error analysis on the model and providing a reference basis for planning and operating the power system.
Disclosure of Invention
For wind power output, establishing an accurate output probability distribution model has important significance for a power system. The invention aims to provide a new method for establishing a probability distribution model and analyzing a model error aiming at the defects of the existing model so as to provide a more reliable basis for planning and operating a power system.
The problem of the invention is realized by the following technical scheme:
a wind power plant probability distribution model modeling and model error analysis method comprises the steps of firstly, fitting to obtain a fan equivalent power characteristic curve, and accordingly obtaining the actual output under the condition that the whole wind power plant has no limit output; then selecting a proper sequence discretization step length, and obtaining a probabilistic sequence of the output of the wind power plant by using a sequence operation theory so as to obtain a probability distribution function of the wind power plant; and finally, analyzing and evaluating the error of the output probability density function of the wind power plant.
The wind power plant probability distribution model modeling and model error analysis method comprises the following steps:
a. based on the historical wind speed of a typical day and the power data of the corresponding fan under the condition of unlimited output, obtaining a fan equivalent power characteristic curve by using least square fitting, and further obtaining the actual output under the condition of unlimited output of the whole wind power plant;
b. selecting a proper sequence discretization step length, obtaining a probabilistic sequence of wind power plant output by using a sequence operation theory, describing wind power plant output probability distribution by using a Weibull function, and estimating parameters by using a maximum likelihood estimation method;
c. and analyzing and evaluating the error of the output probability density function of the wind power plant by using a sequence operation theory and a random sampling method.
The method for selecting the discretization step length of the wind power plant modeling sequence and analyzing the model error comprises the following specific steps of:
①, selecting an initial discretization step length q to be 0.001, and obtaining a probabilistic sequence value F (i) of the wind power plant output by using a sequence operation theory;
②, let i be 1, interpolate the data of the i-th and i + 2-th sequences, and find the value F (i + 1)' of the i + 1-th sequence by using the interpolation function, so as to obtain the smoothing coefficient of the i + 1-th sequence:
③ sequentially making i equal to 2, 3, 4 … …, N-2, and obtaining the smoothing coefficients corresponding to the sequence values according to the method of ② in the step, thereby obtaining the overall smoothing coefficient of the probabilistic sequence:
④, q is q + Δ q, Δ q is 0.001, under the condition that q can be divided by 1, the overall smoothing coefficient of the corresponding probabilistic sequence is sequentially obtained according to steps ② and ③, and the process is ended when q is 0.1, the threshold value of the overall smoothing coefficient of the probabilistic sequence is determined to be 0.3, and the minimum q value smaller than the threshold value is selected as the final discretization step size.
The method for selecting the discretization step length of the wind power plant modeling sequence and analyzing the model error comprises the following specific steps of carrying out error analysis on a wind power output probability distribution function:
the method provided by the invention adopts a sequence operation theory and a random sampling method, provides a reliability index, and analyzes and evaluates the error of the output probability density function of the wind power plant.
①, selecting a proper sequence discretization step length q, and obtaining a probabilistic sequence F (i) of wind power output by using a sequence operation theory;
② random sampling method is adopted to select N groups of wind power plant output values and corresponding probability value data, and the number N of data selection in each sequence discrete intervaliThe following formula should be satisfied:
Ni＝N×F(i) (3)
③, giving an error delta of the probability density function, calculating a probability density function value f (x; lambda, k) · (1 +/-delta) corresponding to the error, and counting the frequency sigma of the wind farm output value selected in the step ② and the corresponding probability value within a given error range, wherein the sigma is the reliability of the wind farm output probability density function when the error is delta, and the larger the sigma is, the more accurate the probability density function is.
Drawings
FIG. 1 is a flow chart of a wind farm output probability distribution model study;
FIG. 2 is a wind farm output distribution fitting effect;
FIG. 3 is a fitting curve of equivalent power characteristics of a 3MW wind turbine;
FIG. 4 is a wind farm output distribution histogram;
FIG. 5 is a wind farm output probability density distribution graph;
FIG. 6 is a wind farm output cumulative probability density distribution graph;
FIG. 7 is a wind farm output probability density function error plot.
Detailed Description
The invention provides a method for selecting the discretization step length of a wind power plant modeling sequence and analyzing the model error, so that a more accurate wind power plant combing probability distribution model can be established, and a basis is provided for planning and operating a power system better. The implementation of the method mainly comprises the following parts: firstly, fitting to obtain a fan equivalent power characteristic curve, and further obtaining the actual output under the condition that the whole wind power plant has no limit output; then selecting a proper sequence discretization step length, and obtaining a probabilistic sequence of wind power plant output by using a sequence operation theory to obtain a probability density function of wind power output; and finally, analyzing and evaluating the error of the output probability density function of the wind power plant.
The invention obtains the output of the wind power plant by using the equivalent power characteristic of the fan and adopting a method from wind speed to power. The actual output of the fan is affected by factors such as terrain, so the actual power characteristic of the fan is not completely consistent with that given by factory shipment. In consideration of the influence of the network side limited output, the method adopts the historical wind speed of a typical day and the power data corresponding to the situation that the fan has no limited output to fit the equivalent power characteristics of the fan, so that the actual output which can be generated under the situation that the wind power plant has no limited output can be obtained. In addition, a selection rule of the sequence discretization step length is provided, and the model error is further reduced. And selecting Weibull distribution to describe the power distribution fitting effect of the wind power plant according to the comparison of different distribution functions on the power distribution fitting effect of the wind power plant. Compared with the existing wind power plant model building method, the method provided by the invention has higher accuracy.
The specific implementation mode of fitting the fan equivalent power characteristic curve is as follows:
and selecting a plurality of groups of typical daily wind speeds and power data corresponding to the fan under the condition of unlimited output to perform equivalent power characteristic curve fitting, wherein the fitted function form is shown as a formula (4). The power data are from wind turbines which are in different geographical positions and wind speeds and have no limit output condition. The fitting is performed using the least squares method and the objective function is as in equation (5).
In the formula, vc，vNRespectively cut-in and rated wind speed, v, of the fan0To cut out the wind speed.
In the formula, pwActual output data under the condition of unlimited output of the fan; and p (v) fitting a force value for the fan.
The specific implementation mode of selecting the appropriate sequence discretization step length in the invention is as follows:
①, selecting an initial discretization step length q to be 0.001, and obtaining a probabilistic sequence value F (i) of wind power output;
②, let i be 1, interpolate the data of the i-th and i + 2-th sequences, and find the value F (i + 1)' of the i + 1-th sequence by using the interpolation function, so as to obtain the smoothing coefficient of the i + 1-th sequence:
③ sequentially making i equal to 2, 3, 4 … …, N-2, and obtaining the smoothing coefficients corresponding to the sequence values according to the method of ② in the step, thereby obtaining the overall smoothing coefficient of the probabilistic sequence:
④, q is q + Δ q, Δ q is 0.001, under the condition that q can be divided by 1, the overall smooth coefficient of the corresponding probabilistic sequence is sequentially obtained according to steps ② and ③, and the process is ended when q is 0.1, the threshold value of the overall smooth coefficient of the probabilistic sequence is determined to be 0.3, and the minimum q value smaller than the threshold value is selected as the optimal discretization step size.
The specific implementation method for fitting the wind power plant output probability distribution function is as follows:
currently, some research results propose to describe the wind farm output probability distribution by using a weibull distribution, a normal distribution or a beta distribution. The distribution functions are used for fitting the actually-generated probabilistic sequence of the wind power plant, and the fitting effect is shown in the attached figure 2. It can be seen that the fitting effect of the weibull function on the output probability distribution of the wind farm is obviously better than that of the other two distribution functions, therefore, the output probability distribution of the wind farm is fitted by selecting two parameters weibull distribution, and the distribution functions have the following forms:
in the formula, λ > 0 is a scale parameter, also called a scale parameter; and k is more than 0 and is a shape parameter, and describes the shape of the wind power plant output probability density function.
And (3) carrying out maximum likelihood estimation on the parameters of the Weibull distribution in the formula (8) to obtain a probability density distribution function of the output of the wind power plant.
The specific implementation mode of the invention for carrying out error analysis on the wind power output probability distribution function is as follows:
①, selecting a proper sequence discretization step length q, and obtaining a probabilistic sequence F (i) of wind power output by using a sequence operation theory;
② random sampling method is adopted to select N groups of wind power plant output values and corresponding probability value data, and the number N of data selection in each sequence discrete intervaliThe following formula should be satisfied:
Ni＝N×F(i) (9)
③, giving an error delta of the probability density function, calculating a probability density function value f (x; lambda, k) · (1 +/-delta) corresponding to the error, and counting the frequency sigma of the wind farm output value selected in the step ② and the corresponding probability value within a given error range, wherein the sigma is the reliability of the wind farm output probability density function when the error is delta, and the larger the sigma is, the better the fitting of the probability density function is.
By utilizing the probability distribution function error analysis method provided by the invention, the integrity and the interval error analysis of the probability distribution function can be carried out, the integral accuracy of the wind power plant output probability distribution function and the main interval of generating errors are reflected, and thus, a reliable basis is provided for the planning and the operation of a power system.
Example analysis
The method is verified by adopting 2011-material 2013 historical data (sampling interval 15min) of a wind power plant with installed capacity of 48MW, and the fan capacity of the wind power plant is 3 MW.
According to the method provided by the invention, the equivalent power characteristic of the wind turbine of the wind power plant is obtained through fitting, and the expression is shown as a formula (10).
And obtaining the actual output of the wind power plant according to the historical wind speed data and the equivalent power characteristics of the wind turbine. And calculating, and taking the sequence discretization step length q as 0.02 to obtain a distribution histogram of the wind power plant output probabilistic sequence, namely the graph shown in figure 4. Equation (11) is the weibull distribution function to which the resulting wind farm output meets.
And (3) carrying out integral error analysis on the output probability distribution function of the wind power plant, wherein the given errors are respectively 10%, 20% and 30%, and the reliability of the probability density function in the corresponding error range is obtained, as shown in Table 1. The higher the reliability is, the better the fitting of the output probability density function of the actual wind power plant is.
TABLE 1 reliability of probability density function in different error ranges
Table 2 shows the reliability calculation results of different intervals of wind power output, taking the 20% error as an example. As can be seen from Table 2, the reliability of the probability density function in the range of the output value [0, 0.2] of the wind power plant is the minimum, which shows that the fitting degree in the range of the interval is poor, the actual output distribution rule of the wind power plant has large fluctuation, and in the system operation process, the importance is increased; the reliability in the range of the (0.4, 0.6) and the (0.8, 1) interval is higher, which shows that the fitting degree of the probability density function in the two intervals is better, the output probability distribution rule of the wind power plant is stronger, and the wind power plant has more reference value.
The effectiveness of the wind power plant model building and error analysis method provided by the invention is verified by an example.
Reliability of different power intervals within 220% error range of table
Claims (1)
1. The method for selecting the discretization step length of the wind power plant modeling sequence and analyzing the model error is characterized in that the actual output under the condition of unlimited output of the wind power plant is obtained by using the historical wind speed data of the wind power plant and the equivalent power characteristic curve of a fan; then selecting a proper sequence discretization step length to obtain a probabilistic sequence of the wind power plant output, and fitting to obtain a wind power plant output probability distribution function; finally, analyzing and evaluating errors of the output probability density function of the wind power plant by using a sequence operation theory and a random sampling method;
the process of obtaining the actual output under the condition of unlimited output of the wind power plant by using the historical wind speed data of the wind power plant and the equivalent power characteristic curve of the fan is as follows:
selecting a plurality of groups of typical daily wind speeds and power data corresponding to the condition of unlimited output of the fan to perform equivalent power characteristic curve fitting, wherein the fitting function form is shown as the following formula:
in the formula, vc，vNRespectively cut-in and rated wind speed, v, of the fan0Cutting out the wind speed; a is0，a1，a2，a3The coefficient is the equivalent power characteristic function of the fan; pNRated power for the fan;
the power data come from wind turbines which are located at different geographical positions and different wind speeds and have no limit output condition;
fitting was performed using the least squares method, and the objective function is shown below:
in the formula, pwActual output data under the condition of unlimited output of the fan; p (v) fitting a force value for the fan;
the process of selecting a proper sequence discretization step length is as follows:
①, selecting an initial discretization step length q to be 0.001, and obtaining a probabilistic sequence value F (i) of wind power output;
②, let i be 1, interpolate the data of the i-th and i + 2-th sequences, and find the value F (i + 1)' of the i + 1-th sequence by using the interpolation function, so as to obtain the smoothing coefficient of the i + 1-th sequence:
③, sequentially making i 2, 3, 4.. and N-2, respectively obtaining smoothing coefficients corresponding to the sequence values according to the method of step ②, thereby obtaining a probabilistic sequence overall smoothing coefficient:
④, q is q + Δ q, Δ q is 0.001, under the condition that q can be divided by 1, the overall smooth coefficient of the corresponding probabilistic sequence is sequentially obtained according to steps ② and ③, and the process is ended when q is 0.1;
selecting Weibull distribution to fit the output probability distribution of the wind power plant; the distribution function form of the contribution probability distribution is as follows:
in the formula, λ is a scale parameter, also called a scale parameter; k is a shape parameter and describes the shape of the wind power plant output probability density function;
carrying out maximum likelihood estimation on a parameter x of Weibull distribution to obtain a density probability distribution function of the output of the wind power plant;
the process of analyzing and evaluating the error of the wind power plant output probability density function comprises the following steps: firstly, selecting a proper sequence discretization step length q, and obtaining a probabilistic sequence F (i) of wind power output by using a sequence operation theory; then, selecting N groups of wind power plant output and corresponding probability value data by adopting a random sampling method, wherein the number N of the selected data in each sequence discrete intervaliThe following formula should be satisfied:
Ni＝N×F(i)
finally, giving an error delta of the probability density function, calculating a probability density function value f (x; lambda, k) · (1 +/-delta) corresponding to the error, and counting to obtain the output values of the N groups of selected wind power plants and the frequency sigma of the corresponding probability value in a given error range; and sigma is the reliability of the wind power plant output probability density function when the error is delta, and the larger sigma is, the better the fitting of the probability density function is.
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