# The Rapid Establishment of Large Wind Fields via an Inverse Process
## 1 Introduction  
Wind power is one of the most rapidly growing renewable energies and is regarded as an appealing alternative to conventional power generated from fossil fuel. However, due to the intermittency of wind speed, large-scale wind power penetration will affect the quality of an electric grid, which makes the safe and stable operation of an electric power system a great challenge. In order to reduce the impact of large-scale wind power integration, accurate and effective wind power prediction is necessary to improve the limitations of wind power penetration [1]. As the wind power mainly depends on wind speed, most wind power prediction models will at first forecast wind speed and then convert wind speed to wind power according to certain power curves. Over the years, many methods have emerged that utilize statistical processing via local or numerical wind prediction (NWP) data for wind speed forecasts. For example, a hybrid methodology based on support vector regression is proposed for wind forecasting in [2], which shows more accurate results than those from NWP. Wind field accuracy can also be substantially improved by using the Kalman filter as a post-processing procedure [3]. With the advance of modern intelligent algorithms, statistical forecast methods have been growing strongly, as they have the advantage of suiting different topographical and historical data. However, since the majority of statistical prediction models are essentially based on local historical data, these methods may intrinsically be prone to significantuncertainty in predicting future conditions. It is desirable to establish models that can provide more assurance for forecasting. In contrast to statistical methods, physical approaches apply mechanical and thermal principles and numerical methods, such as computational fluid dynamics (CFD), to produce wind speed forecasts. Forecast methods based on physical approaches can usually provide wind speed and its associated parameters such as pressure, humidity, and temperature. Their upscaling algorithm can be based on the correlation between the representative wind farm power generation and the total power data over a certain period of measurements. There are several studies about upscaling algorithms. For example, in [4] it is proven that rough set theory is a useful tool for short-term multistep wind power prediction when combined with multiposition NWP data. A downscaled simulation framework can also be applied to carry out a multi-scale simulation of time-varying wind fields [5]. However, the calculation capacity of physical models is restricted by the complexity of its conditions as indicated by earlier studies [6], as the high number of computational grid points requires enormous computational resources and time. Therefore, any physical method will be welcome if it can yield rapid predictions based on meteorological data or real time data from other sources. Recently, a new methodology for reconstruction that employs CFD generated data and a limited number of real time measurements at distributed locations has emerged. In this methodology, CFD is used to calculate the distribution of a data set in the field so that the data set can be obtained before the prediction, which facilitates the process of reconstruction. Proper orthogonal decomposition (POD) is then used to capture dominant features of the data set and subsequent POD modes can be used to reconstruct the whole field. This methodology can meet the requirements of real-time field prediction in many situations such as underwater acoustics [7] and aerodynamic design [8]. In our previous study, we applied this method to the reconstruction of wind fields and obtained comparatively satisfactory results [9]. This method, which very often involves an inverse process, can drastically reduce the quantity of the computational work, e.g., by three or four orders of magnitude, and reconstruct velocity fields at a very fast speed, which effectively enables onsite short-term wind forecasts.