Mathematical Problems in Engineering

Volume 2015, Article ID 897952, 10 pages

http://dx.doi.org/10.1155/2015/897952

## “Section to Point” Correction Method for Wind Power Forecasting Based on Cloud Theory

^{1}School of Economics and Management, North China Electric Power University, Beijing 102206, China^{2}College of Electrical Engineering, Hunan University, Changsha 410006, China

Received 11 September 2014; Revised 11 November 2014; Accepted 21 November 2014

Academic Editor: Davide Spinello

Copyright © 2015 Dunnan Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

As an intermittent energy, wind power has the characteristics of randomness and uncontrollability. It is of great significance to improve the accuracy of wind power forecasting. Currently, most models for wind power forecasting are based on wind speed forecasting. However, it is stuck in a dilemma called “garbage in, garbage out,” which means it is difficult to improve the forecasting accuracy without improving the accuracy of input data such as the wind speed. In this paper, a new model based on cloud theory is proposed. It establishes a more accurate relational model between the wind power and wind speed, which has lots of catastrophe points. Then, combined with the trend during adjacent time and the laws of historical data, the forecasting value will be corrected by the theory of “section to point” correction. It significantly improves the stability of forecasting accuracy and reduces significant forecasting errors at some particular points. At last, by analyzing the data of generation power and historical wind speed in Inner Mongolia, China, it is proved that the proposed method can effectively improve the accuracy of wind speed forecasting.

#### 1. Introduction

Wind power is a critical component of new energy. It can be grid connected with some advantages like safety, reliability, nonpollution, and being fuel-free, which has undergone rapid growth worldwide in recent years. China also attaches great significance to the development of wind energy resources. However, as the scale of wind power keeps expanding, the large scale of wind power grid connected proposed a severe challenge to the security and stability of the grid because of the constant changing of wind output with wind speed. In order to improve the reliability of wind power consumption, the accuracy of wind power prediction is very important [1].

There are mainly two wind power forecasting methods at present. One is to forecast wind power by wind speed according to the wind power formula [2–4]. The other is to make statistical prediction based on historical data by adding meteorological factors (wind speed, wind direction) as auxiliary forecasting [5, 6]. Regarding the first method, the wind power depends on the wind speed of wind power station, which is mainly influenced by the forecasting accuracy of wind speed. However, the wind speed is changing irregularly and the wind power and wind speed are both quantitative data. It is difficult to establish the exact correlation between the wind power and wind speed. In the second method, the overreliance on historical data leads to the lower forecasting accuracy when the catastrophe point occurs.

Most of the current methods can only forecast the “point to point” wind power. These methods establish a causal model between the wind power and wind speed about each point in time based on historical data, that is, to forecast the wind power at particular time point according to the wind speed of the same time point.

References [7, 8] forecasted the wind speed of wind turbines based on physical method with the data of wind speed and its direction, taking into account topographic change and wake effect. And the method proposed is capable of forecasting the wind power output by considering wind power curve. However, it has significant influence on the wind power forecasting accuracy, because some numerical weather prediction (NWP) values cannot provide accurate values at some catastrophe points. It has significant influence on the wind power prediction accuracy. Reference [9] derived the causality equation between the wind speed and wind power based on the grey theory. Similarly, this kind of approach also leads to a significant error at the catastrophe points. By building autoregressive moving average (ARMA) model to predict wind speed, the paper results show that when the wind speed experienced a large shock, the deviation shocks accordingly. Besides, the longer the forecasting, the greater the deviation. So this method is more suitable for the ultra-short-term wind speed forecasting [10]. References [11–13] established the association between the wind speed and wind power through intelligent algorithms. The results show that the forecasting accuracy is higher for a smooth sequence, while forecasting accuracy is not very satisfactory when data catastrophe points occur. In the “point to point” approach proposed above we usually present different degrees of trend inertia when forecasting the catastrophe points, which therefore affect the forecasting accuracy.

Therefore, there are mainly two ways to improve the accuracy of wind power forecasting, which is of great significance: first, how to establish an accurate association between wind speed and wind power; second, how to ensure the stability of the catastrophe points forecasting.

To this end, we use the “section to point” correction method of the wind power forecasting model to improve the forecasting accuracy. Firstly, the improved correlation between the wind speed and wind power is presented. To a large extent, the stability of forecasting accuracy can be greatly enhanced by reducing errors at catastrophe points.

#### 2. Cloud Theory

##### 2.1. Cloud Model

Dr. Li has proposed a cloud that depicts uncertainty concept of natural language on the basis of randomness and fuzziness [14]. It makes uncertain transformation between qualitative concept expressed by natural language and quantitative expression.

If is a quantitative universe represented with an accurate value, is a qualitative concept in , and quantitative value ,* x* is a stochastic realization of qualitative concept , and the certainty degree of to is a random number with stability. Then, the distribution of in universe is called Cloud.

First, all maps from to interval are a one-to-many transformation. The membership degree of to is a probability distribution but not a fixed value, whose graphic looks like a cloud rather than a distinct curve. Second, cloud consists of lots of droplets, and every droplet is a quantitative concept transformed from a qualitative concept. One droplet may be insignificant, but specification of cloud at different times may make a difference. Therefore, the whole figure of the cloud reflects quantitative concept characteristics. Similarly, the distribution of droplets looks like clouds in the sky, and we cannot see clear boundary nearby but we can see a cloud at distance. That is why we name the figure as cloud. Third, Mathematical Expected Curve of a cloud is its membership degree curve from the point of fuzzy set theory. Fourth, the thickness of the cloud is uneven. It is thicker at waist because droplets are scattered, while it is thinner at top and in the bottom, because droplets are concentrated there. The thickness of cloud reflects the randomness of membership degree. Thus, close to or far from the concept center means the randomness of the membership degree is small, while, as for droplets neither near nor far from concept center, the randomness of the membership degree is big.

Cloud is an uncertain transformation model between qualitative concept and quantitative value. Cloud model generally uses three numerical characteristics, Expectation Ex, Entropy En, and Excess Entropy He, to represent a concept as a whole, as shown in Figure 1.