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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.

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 [

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 [

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 [

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.

Dr. Li has proposed a cloud that depicts uncertainty concept of natural language on the basis of randomness and fuzziness [

If

First, all maps from

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

Cloud numerical characteristics.

Expectation Ex: it is the expectation of cloud entropy in domain space. Generally speaking, it is a dot that can best represent qualitative concept or a most typical sample of quantified concept.

Entropy En: it is the uncertain measure of qualitative concept. When the entropy is larger, the numerical range that can be accepted by the concept becomes larger, which means the concept is vaguer.

Hyper Entropy He is entropy of Entropy En, which reflects dispersion of droplets. The larger Hyper Entropy He is, the larger its dispersion, membership degree, and thickness are.

We can see that the fuzziness and randomness are integrated by three digital features of cloud model into mutual maps of qualitative and quantitative concepts.

Normal cloud model is generally applied to express language value; its Mathematical Expected Curve is as follows:

Generation algorithm of normal cloud is as follows:

calculate

If three eigenvalues (Ex, En, He) of normal cloud is given.

Above algorithm can be applied to generate normal cloud consists of an arbitrary number of droplets. Cloud generated by this algorithm normally has uneven thickness, so these three eigenvalues can depict the whole figure of the cloud and no more definition is required to define waist, top and bottom of the cloud.

Generation algorithm can be realized not only by software, but also by hardware, which is named cloud generator; four cloud generators are proposed in this paper.

It is a map from qualitative aspect to quantitative aspect, which is on the basis of the numerical characteristics of the cloud (Ex, En, He). Some 2-

The schematic diagram of forward cloud generator.

Following is the algorithm.

Generate a normal random number

Generate a normal random number

Calculate certainty degree

Repeat steps

It is a model that realizes conversion from quantitative value to qualitative concept. It can convert an amount of accurate values to qualitative concepts represented by the numerical characteristics (Ex, En, He), as shown in Figure

Schematic diagram of backward cloud generator.

Following is the algorithm (a backward algorithm without need of the certainty degree information).

On the basis of

Then calculate the first-order central absolute moment

The sample variance

The expected value is calculated as

Given a quantitative value

Schematic diagram of

Following is the algorithm.

Generate normal random number

Calculate the certainty degree as (

Given a certainty degree

Schematic diagram of

Following is the algorithm.

Generate forward random number

Calculate quantitative value

Single condition and single rule generator can be formally represented as

Rule generator.

First of all, the quantitative values of the wind speed and wind power are converted to qualitative concepts which can be expressed by nature language based on cloud transformation and backward cloud generator of cloud theory [

Flowchart of wind power forecasting.

In this paper, the principle of improving forecasting accuracy is mainly reflected by the following two aspects.

Based on cloud theory, enhance the relevance between data and decrease the information loss.

According to two consecutive years of Inner Mongolia Wind Power sampling data, this paper selects twenty data dots to calculate the wind speed forecasting value and the wind power value, respectively. As shown in Figure

As quantitative data, if the reasoning formula between the wind speed and wind power is deduced by numeric values, correlation results will be inaccurate under the influence of invisible factors. In this paper, quantitative and qualitative data can be transformed effectively based on cloud theory. Then accurate association rules considering invisible factors are constructed by data mining. In this paper, the construction of forecasting model and the calculation of the “section to point” correction coefficient are both based on cloud theory. This is the guarantee of improving prediction accuracy in this paper.

With the help of change discipline of the adjacent time, the “section to point” correction can slow down tendency inertia caused by the wind speed catastrophe.

Processed by cloud synthesization, the wind speed and wind power data contain both the characteristics of current trends and change laws of historical data. Based on this, correction coefficient calculated by this model can restrain prediction fluctuation and significantly improve forecasting, especially when the wind speed changes abruptly. Like a “sword,” the “section to point” correction in this paper can improve forecasting accuracy effectively.

First, transform [

The first step of the wind power forecasting consists of cloud transformation and concept abstracting. Then, cloud generator is built based on association rules mining from similar cloud concepts. So, wind power eigenvalue can be forecasted after inputting the wind speed data.

The

The principle of “section to point” correction is correcting the forecasted value of the wind power by cloud model, through synthesization of change rules between wind speed and wind power.

Data near the forecasting point is taken as basic sequence in this paper. The step is taken as

As can be seen from Figure

Prediction comparison of relative error between wind speed and power.

Flowchart of power eigenvalue prediction.

Rules of cloud reasoning

Cloud synthesization.

As shown in Figure

Prediction comparison between section to point and point to point.

Before correction, the data of the wind speed and wind power must be processed as follows.

The wind speed change rate: the formula is shown as follows:

In formula (

Elastic coefficient, which means the effect of the wind speed while the wind power changes: the formula is shown as follows:

In formula (

Divide historical data.

A sequence is constructed according to these two types of data mentioned based on the historical data:

The process of “correction step” are shown in Figure

Through backward cloud generator, three characteristic numbers

Then, three characteristic numbers

Step of “section to point” correction.

If current vector is

In formula (

By comparing the number of

Three characteristic numbers (Ex, En, He) are generated by cloud synthesization.

Change rate of the wind speed and the elastic coefficient based on cloud generator forecasted, which are used to obtain the value of the correction coefficient:

In formula (

The forecasted value of wind power can be carried out through multiplying the wind power eigenvalue by the correction coefficient.

In order to verify the effectiveness of forecasting model proposed in this paper the wind speed and wind power data for daily load forecasting are provided by a wind power station in Inner Mongolia with a period of 60 days in 2013. Among the data, the first 30 days are used for history database matching, and the last 30 days are taken as forecasted comparative data. Figure

Historical data for wind speed and power.

Seven qualitative clouds are obtained after cloud transformation and concept abstracting on the basis of the wind power data in 2013. Its eigenvalues are shown in Table

Table

Eight qualitative clouds are obtained after cloud transformation and concept abstracting based on the wind speed data in 2013, whose eigenvalues are shown in Table

Table

The a priori algorithm is applied to mining the association rules between historical wind speed and wind power. 8 rules that can satisfy the constraint of the minimum support threshold and the minimum confidence threshold are determined. The rules are shown in Table

Take average wind speed 6.2 (m/s) of the 30th day as input value; then the corresponding 8th class qualitative cloud would be activated. The cloud which has the highest membership degree is taken as the forward rule. Also, Wind speed 6.2 (m/s) corresponding to the qualitative concept of “Slightly fast 2” will be drawn. According to the 5th rule, wind power cloud which is named “high” is taken as the backward rule. Current period wind power eigenvalue can be calculated based on mining associated rules, and the value is 1238.4 (MW). This wind power eigenvalue also can be taken as forecasting value. Figure

When the wind power eigenvalue is taken as a predictive value, forecasting precision is improved slightly comparing with forecasting value by the model ARMA (“point-to-point” model). But the maximum errors of them are bigger, which means both of them cannot make effective inhibition of fluctuation at the catastrophe point. Therefore, the forecasted value at the catastrophe point should be corrected, which is the second step “section to point” correction. The steps are as follows.

Eigenvalue of the qualitative concept of wind power.

Ex | En | He | |
---|---|---|---|

Rather low | 135 | 25 | 7.1 |

Low | 530 | 132 | 9.3 |

Slightly low | 900 | 121 | 5.2 |

Moderate | 1200 | 80 | 6.2 |

Slightly high | 1530 | 70 | 8.5 |

High | 1965 | 60 | 10.2 |

Rather high | 2290 | 50 | 12.3 |

Eigenvalue of the qualitative concept of wind speed.

Ex | En | He | |
---|---|---|---|

Rather slow | 1.2 | 0.33 | 0.02 |

Slow | 2.3 | 0.2 | 0.03 |

Slightly slow | 3.2 | 0.3 | 0.06 |

Moderate 1 | 4.1 | 0.25 | 0.04 |

Moderate 2 | 5.0 | 0.32 | 0.03 |

Slightly fast | 6.2 | 0.23 | 0.03 |

Fast | 7.4 | 0.27 | 0.04 |

Rather fast | 9.0 | 0.29 | 0.05 |

Association rules after mining.

Rules | Wind speed | Wind power |
---|---|---|

Rule 1 | Rather slow | Rather low |

Rule 2 | Slow | Low |

Rule 3 | Slightly slow | Slightly low |

Rule 4 | Moderate 1 | Moderate |

Rule 5 | Moderate 2 | Slightly high |

Rule 6 | Slightly fast | High |

Rule 7 | Fast | Rather high |

Rule 8 | Rather fast | Rather high |

Comparison table of relative error (%).

Maximum | Minimum | Mean | |
---|---|---|---|

ARMA | 42.32 | 0.51 | 16.59 |

Power eigenvalue | 37.84 | 0.63 | 12.87 |

Cloud chart after the wind power concept retrieval.

Cloud chart after the wind speed concept retrieval.

Prediction comparison chart.

(1) According to 5-day wind speed and wind power data close to the forecasting point, the first sequence of the elasticity coefficient can be concluded as

These two sequences above can obtain two clouds by backward cloud generator. Then, they are synthesized to produce new forecasting clouds. By setting up rules generator, it can be predicted that the elastic coefficient is 0.67. Similarly, forecasting value of the wind speed change rate is 1.65.

(2) According to the change rate of the wind speed and the elastic coefficient of forecasting value, correction coefficient is 1.12. Finally, the forecasting value of corrected power is 1387.0 (MW). The result of the first step is shown in Figure

The average relative error and the maximum relative error are reduced after being corrected, and the forecasting accuracy has improved. Particularly for catastrophe point forecasting, the volatility of forecasting value is reduced, which is of great importance for wind power grid security. Figure

As can be seen from Table

Comparison table of relative error after correction (%).

Maximum | Minimum | Mean | |
---|---|---|---|

ARMA | 42.32 | 0.51 | 16.59 |

Power eigenvalue | 37.84 | 0.62 | 12.87 |

After correction | 26.21 | 0.32 | 10.87 |

Comparison table of relative error in mutation points (%).

1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|

ARMA | 42.32 | 39.21 | 32.42 | 36.23 | 33.24 |

Model in this paper | 14.21 | 25.32 | 26.21 | 25.23 | 12.57 |

Prediction comparison after correction.

Comparison chart in mutation points.

As a “point to point” forecasting model, forecasting results of ARMA are subject to the trend of adjacent time. Moreover, huge error occurs when encountering wind speed catastrophe points. Compared with ARMA, the average relative error of this model is reduced by 3.72% in terms of prediction accuracy. The improvement of prediction accuracy is shown in the following two aspects.

First, it realizes the transformation between quantitative data and qualitative data based on cloud theory. And it builds an accurate correlation between wind speed and wind power, which reduces the average relative error by 3.72%.

Second, catastrophe points forecasting realizes the “section to point” correction and the current forecasting correction by cloud synthesization and historical data. It reduces the trend inertia at catastrophe points and reduces the average relative error by 2%. Particularly at catastrophe points, the reduction can reach up to 11.63%.

Model proposed in this paper will improve the accuracy of prediction as historical data continuously accumulates. Given more historical data, it will be capable of attaining sequences with higher similarity from adjacent data in a broader space-time. Due to limited data in this paper, cloud reasoning and sequence analyzing are only applied to wind speed data which has significant influence on wind power. If meteorological data are added, the prediction accuracy could be further improved.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was financially supported by the National Natural Science Foundation of China (71401055). And the authors would like to thank all projects partners for their contribution.