【正文】 els are regression models 【1,2】and artificial neural networks 【3–5】. In this paper, we pare regression and artificial neural network models for wind turbine power curve estimation using data from the Central and South West wind farm near Fort Davis, Texas.2 The Wind Farm and the Wind Power GenerationThe Fort Davis wind farm consists of 12 turbines and two meteorological towers （met. Tower） （Fig. 1）. Data received from the wind farm can be divided into two categories. The first contains data from the two met. towers such as wind velocities and directions measured at three elevations （10, 30, and 40m）. The second contains information about turbine power generation, such as average power outputs, voltages, and currents. The two met. towers, indicated with ⊕, are the sites for measurement of wind speed and direction. Each dotted circle is the location of a wind turbine.Turbine power production depends on the energy contained in the wind. The basic measuring unit of the energy contained in the wind is wind power density [6], or power per unit of area normal to the wind azimuth, calculated as Eq. （1）, where PW is wind power density(W/m), r is air density(Kg/m), and V is horizontal ponent of the mean freestream wind velocity （m/s）.However, both wind velocity and air density are generally not constant. The hub height of the turbine is 40m above the industry standard is to relate the power to the hub height wind velocity [7]. Such a relationship implies that the velocity at the hub height and the velocity profile are known, and that the velocity profile does not change. The velocity profile is defined as the difference in velocity as a function of height from the bottom to the top of the turbine blade and is another factor which can influence turbine power production [8,9]. The hub height velocity and the velocity profile are measured by the met. towers. However,due to the limited number of the met. towers, the variable terrain,the turbines distributed over a wide range on the wind farm, andwind dynamics, the actual wind velocity and profile for each turbine are usually quite different from those obtained from the . These are some of the main reasons that the measured turbine power production versus meteorological tower wind speed does not fall on the anufacturer’s power curve as shown by . In the figure, the line represents the manufacturer’s warranted estimated output power curve for the wind turbine with 500 kW rated power, which has been adjusted especially for the Fort Davis wind farm to account for the difference in attitude with respect to sea level. The dots represent the measured wind turbine poweroutput for a met. tower 10minute average wind velocity. Which met. tower velocity to use is selected based on which direction the wind es from, ., if the wind es from the east, the measured wind speed from the east tower is used。 if the wind es from the west, the measured wind from the west tower is chosen. In Fig. 2, the large difference of turbine power production at the same wind speed, as well as high power productions at low wind speeds and low power productions at high wind speeds, implies that the wind at the turbine can be quite different from the wind at the met. towers. The air density in Eq. (1) also influences the energy contained in the wind and therefore turbine power production. However, r has less influence on turbine power production than the wind speed because the dynamic range of r is usually small and wind power is proportional to the cube of wind speed. In addition to the above factors, wind power production is also affected by other factors such as seasons of a year, time of day [1], and wind fluctuation within a certain time period. In the following parison between neural networks and regression models, the only factors considered are the 40m wind speeds and wind directions from the two met. towers. Introducing other factors would make the specification of a function for a regression model quite difficult.3 Regression Model for Wind Turbine Power Estimation Prediction by Regression Model. Regression models quantitatively describe the variability among the observations by partitioning an observation into two parts [10]. The first part of this deposition is the predicted portion having the characteristic that can be ascribed to all the observations considered as a group in a parametric framework. The remaining portion, called the residual, is the difference between the observed and the predicted values and must be ascribed to unknown sources. This can be expressed as i=1,2,3n (2) where n is the number of the observations, is ith observation,=(,……,) is the predictor variable vector related to observation , is the parameter vector, and is the error associated with ith observation. The function f is estimated by fitting a polynomial or other type of function. Fitting refers to calculating values of the parameters from a set of , the estimate , a least squares estimate of b, tries to minimize the error sum of squares shown by Eq.(3).If function f (xi ,) is linear, the regression model can be expressed as Eq. (4). This can be written as a matrix Eq. (5), where Y is a ndimensional vector and X is a n matrix. In case of the estimated regression coefficient , the predicted values are then calculated by multiplying each row in the X matrix by the column, that is. The least squares estimate of is the solution to Eq. (6), and only one function solving step is needed to get the solution. When f in Eq. (2) is a polynomial, a linear representation of Eq. (4) can still be obtained, but the number of the columns of X will be larger than the number of the predictor variables （1,2…,k）.When f is a nonlinear function, linearization (Taylor extension)of f with respect to parameters [10,11] is required for Eq. (7),where are initial values for parameter,so that techniques for Eqs. (3)–(6) can be used. These initial values may be intel