CN107657116B - Method for affine modeling of power curve of wind power plant - Google Patents
Method for affine modeling of power curve of wind power plant Download PDFInfo
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- CN107657116B CN107657116B CN201710883519.2A CN201710883519A CN107657116B CN 107657116 B CN107657116 B CN 107657116B CN 201710883519 A CN201710883519 A CN 201710883519A CN 107657116 B CN107657116 B CN 107657116B
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Abstract
The invention discloses a power curve affine modeling method for a wind power plant, which comprises the following steps: 1) carrying out wind speed affine modeling on factors influencing the input wind speed of the wind power plant in a noise element mode; 2) carrying out curve fitting on the central value of the input wind speed and output power actual measurement data by using a polynomial fitting method to obtain an affine central value curve; 3) and obtaining the relation between the output power and the input wind speed affine model through the Taylor expansion, and carrying out power curve affine modeling. The uncertain fluctuation range of the power curve is obtained on the basis of the central point, the information of the power curve is enriched, and the modeling accuracy and reliability are improved.
Description
Technical Field
The invention relates to the technical field of wind power, in particular to a power curve affine modeling method for a wind power plant.
Background
Due to uncertainty of wind speed, the wind generating set is disturbed to a large degree almost all the time, and the uncertainty is mainly reflected on space-time distribution of elements such as wind direction, average wind speed and fluctuating wind speed and is influenced by terrain, tower position, height, air density, tower shadow effect, wake effect and the like. Under the influence of a plurality of uncertain factors, the prediction of the output power of the wind power plant is increasingly concerned at home and abroad. For the prediction of wind farm power, the power curve is critical. Most wind power plants are affected seriously by wake effect due to the fact that the number of the wind power plants is large, the landform and the feature are complex, and the arrangement modes of the wind power plants are different, so that the input wind speeds of the wind power plants in the wind power plants are different to a certain extent, and the wind power plants are often in complex and variable wind conditions, so that each wind power plant does not operate according to a standard power curve given by a manufacturer. Therefore, the accurate power curve is established, and the method has important significance for evaluating the high-speed operation of wind power equipment and a wind power unit and reducing the influence of wind power fluctuation on the access power grid. At present, most of domestic and foreign researches on modeling of wind power actual measurement power curves are curve fitting of actual measurement data, wind speeds and powers obtained through fitting are in one-to-one correspondence, and influence of uncertain factors in actual operation of a wind power plant cannot be accurately reflected. The past methods for modeling power curves are mainly classified into the following methods:
1) directly applying interpolation polynomial and S-shaped curve fitting power curve to the measured data;
2) aiming at the problem of difference of wind speeds of large wind power plants with complex topography and irregular unit arrangement, a K-means clustering algorithm is utilized to perform clustering division on all wind power units of the wind power plants according to actual wind speed data, an equivalent wind speed model of the whole wind power plant is established, and then a wind speed-power model of the wind power plant based on actual measurement operation data is given;
3) by providing a single-machine optimal power curve iterative fitting algorithm for correcting wind measurement data of the wind turbine generator based on wake effect, taking the contribution rate as a termination condition to iteratively eliminate dead points to obtain an optimal power curve;
4) a wind power curve based on measured data is drawn by a proportional method, wind speeds are graded through partition fitting, then a nonparametric interval estimation method is adopted, a power probability density function of each wind speed grade is established, and an uncertain estimation interval of the wind power curve is obtained on the basis of point estimation.
Disclosure of Invention
The invention provides a power curve affine modeling method for a wind power plant, which adopts an affine concept to improve the accuracy and reliability of modeling.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for affine modeling of a power curve of a wind farm comprises the following steps:
step S1: carrying out wind speed affine modeling on factors influencing the input wind speed of the wind power plant in a noise element mode;
step S2: carrying out curve fitting on the central value of the input wind speed and output power actual measurement data by using a polynomial fitting method to obtain an affine central value curve;
step S3: and obtaining the relation between the output power and the input wind speed affine model through the Taylor expansion, and carrying out power curve affine modeling.
Further, the step S1 is specifically:
an affine model of the input wind speed is established,
where i 1, 2., n, n represents the number of noise bins, epsiloniThe representation of the noise element is represented by,
representing the actual wind speed, v0Representing the predicted wind speed, and x1 representing the noise element coefficient found by the error between the anemometer tower and the meteorological station; x2 represents the noise element coefficient obtained by the influence of the relative position of the fan on the wind speed; x3 represents the noise element coefficient found from the effect of altitude and terrain effects on the input wind speed; x4, x 5.., xi respectively represent noise element coefficients obtained by the influence of the inherent properties of the unit on the input wind speed.
Further, the step S2 is specifically:
firstly, preprocessing input wind speed and output power actual measurement data, eliminating points with large errors, dividing the wind speed into N intervals at equal intervals, solving the average data of the input wind speed and the output power distributed in each interval, and finally obtaining a central value curve by a cubic polynomial curve fitting method, wherein the central value curve is shown as a formula (2):
f(v0)＝av0 3+bv0 2+cv0+d (2)
wherein, f (v)0) Representing wind power, v, calculated from predicted wind speed0The predicted wind speed is shown, and a, b, c, d respectively represent fitting coefficients.
Further, the step S3 is specifically:
establishing an affine function relation between the output power and the input wind speed of the fan as shown in the formula (3):
wherein the content of the first and second substances,
the wind power affine is represented by the wind power affine,
represents an affine function of the wind power,
the wind speed affine model shown by the formula (1) in step S1 is substituted by the formula (3) to obtain:
in the Taylor expansion process of the affine function, the quadratic expansion term can obtain a high-order term combination of the noise element, and the high-order term combination is sorted and summarized into a new noise element according to the formula (6):
noise element ε obtained by equation (6)i+1The variation range is [ -1,1 [)]Considering the unbiased arrangement of the noise element as:
the quadratic term noise element in the formula (7) has a range of [0,1 ] after being squared]Developed by affine function of the formula (7)Noise element epsiloniThe polynomial of (a) is a specific expression of an affine function;
the affine center value is a constant term of equation (8) and is expressed as:
compared with the prior art, the invention has the beneficial effects that: the uncertain fluctuation range of the power curve is obtained on the basis of the central point, the information of the power curve is enriched, the accuracy and the reliability of modeling are improved, reference is provided for the power grid to predict the wind power output power, and meanwhile, the power flow calculation of the power system under the wind power grid connection uncertainty condition can be obtained according to the method.
Drawings
FIG. 1 is a schematic flow chart of a method for affine modeling of a power curve of a wind farm according to the present invention;
FIG. 2 is an affine model diagram according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
As shown in FIG. 1, a method for affine modeling of a power curve of a wind farm comprises the following steps:
step S1: carrying out wind speed affine modeling on factors influencing the input wind speed of the wind power plant in a noise element mode;
an affine model of the input wind speed is established,
where i 1, 2., n, n represents the number of noise bins, epsiloniThe representation of the noise element is represented by,
representing the actual wind speed, v0Representing the predicted wind speed, and x1 representing the noise element coefficient found by the error between the anemometer tower and the meteorological station; x2 denotes a fan relative position pairThe noise element coefficient obtained under the influence of the wind speed; x3 represents the noise element coefficient found from the effect of altitude and terrain effects on the input wind speed; x4, x5, xi respectively represent noise element coefficients obtained by the influence of inherent attributes of the unit such as wind shear, tower shadow effect and the like on the input wind speed;
step S2: carrying out curve fitting on the central value of the input wind speed and output power actual measurement data by using a polynomial fitting method to obtain an affine central value curve;
firstly, preprocessing actually measured data of input wind speed and output power, eliminating points with large errors, then dividing the wind speed into N intervals at equal intervals, in the embodiment, taking each wind speed interval as 0.5m/s, solving average data of the input wind speed and the output power distributed in each interval, and finally obtaining a central value curve by a cubic polynomial curve fitting method, wherein the central value curve is shown as formula (2):
f(v0)＝av0 3+bv0 2+cv0+d (2)
wherein, f (v)0) Representing wind power, v, calculated from predicted wind speed0Representing the predicted wind speed, and a, b, c and d respectively represent fitting coefficients;
step S3: obtaining the relation between output power and an input wind speed affine model through a Taylor expansion formula, and carrying out power curve affine modeling;
establishing an affine function relation between the output power and the input wind speed of the fan as shown in the formula (3):
wherein the content of the first and second substances,
the wind power affine is represented by the wind power affine,
represents an affine function of the wind power,
the wind speed affine model shown by the formula (1) in step S1 is substituted by the formula (3) to obtain:
in the Taylor expansion process of the affine function, the quadratic expansion term can obtain a high-order term combination of the noise element, and the high-order term combination is sorted and summarized into a new noise element according to the formula (6):
noise element ε obtained by equation (6)i+1The variation range is [ -1,1 [)]Considering the unbiased arrangement of the noise element as:
the quadratic term noise element in the formula (7) has a range of [0,1 ] after being squared]Developed as a noise element ε by an affine function of the formula (7)iThe polynomial of (a) is a specific expression of an affine function;
the affine center value is a constant term of equation (8) and is expressed as:
the resulting power curve affine model is shown in fig. 2.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.
Claims (1)
1. A method for affine modeling of a power curve of a wind power plant is characterized by comprising the following steps:
step S1: carrying out wind speed affine modeling on factors influencing the input wind speed of the wind power plant in a noise element mode;
step S2: carrying out curve fitting on the central value of the input wind speed and output power actual measurement data by using a polynomial fitting method to obtain an affine central value curve;
step S3: obtaining the relation between output power and an input wind speed affine model through a Taylor expansion formula, and carrying out power curve affine modeling;
wherein, the step S1 specifically includes:
an affine model of the input wind speed is established,
where i 1, 2., n, n represents the number of noise bins, epsiloniThe representation of the noise element is represented by,
representing the actual wind speed, v0Representing the predicted wind speed, and x1 representing the noise element coefficient found by the error between the anemometer tower and the meteorological station; x2 represents the noise element coefficient obtained by the influence of the relative position of the fan on the wind speed; x3 represents the noise element coefficient found from the effect of altitude and terrain effects on the input wind speed; x4, x5, xi respectively represent noise element coefficients obtained by the influence of the inherent properties of the unit on the input wind speed;
wherein, the step S2 specifically includes:
firstly, preprocessing input wind speed and output power actual measurement data, eliminating points with large errors, dividing the wind speed into N intervals at equal intervals, solving the average data of the input wind speed and the output power distributed in each interval, and finally obtaining a central value curve by a cubic polynomial curve fitting method, wherein the central value curve is shown as a formula (2):
f(v0)＝av0 3+bv0 2+cv0+d (2)
wherein, f (v)0) Representing wind power, v, calculated from predicted wind speed0Representing the predicted wind speed, and a, b, c and d respectively represent fitting coefficients;
wherein, the step S3 specifically includes:
establishing an affine function relation between the output power and the input wind speed of the fan as shown in the formula (3):
wherein the content of the first and second substances,
the wind power affine is represented by the wind power affine,
represents an affine function of the wind power,
the wind speed affine model shown by the formula (1) in step S1 is substituted by the formula (3) to obtain:
in the Taylor expansion process of the affine function, the quadratic expansion term can obtain a high-order term combination of the noise element, and the high-order term combination is sorted and summarized into a new noise element according to the formula (6):
noise obtained by the formula (6)Sound element epsiloni+1The variation range is [ -1,1 [)]Considering the unbiased arrangement of the noise element as:
the quadratic term noise element in the formula (7) has a range of [0,1 ] after being squared]Developed as a noise element ε by an affine function of the formula (7)iThe polynomial of (a) is a specific expression of an affine function;
the affine center value is a constant term of equation (8) and is expressed as:
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| CN111027229B (en) * | 2019-12-26 | 2021-12-07 | 中南大学 | Wind power curve fitting method based on sparse heteroscedastic multi-spline regression |
| CN111274701B (en) * | 2020-01-20 | 2022-06-07 | 福州大学 | Harmonic source affine modeling method adopting interval monitoring data dimension reduction regression |
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