Short-Term Power Load Point Prediction Based on the Sharp Degree and Chaotic RBF Neural Network

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 231765, 8 pages http://dx.doi.org/10.1155/2015/231765 Research Article Short-Term Power Load Point Prediction Based on the Sharp Degree and Chaotic RBF Neural Network Dongxiao Niu, Yan Lu, Xiaomin Xu, and Bingjie Li School of Economics and Management, North China Electric Power University, Beijing 102206, China Correspondence should be addressed to Yan Lu; Received 21 October 2014; Revised 9 December 2014; Accepted 16 December 2014 Academic Editor: Dan Simon Copyright © 2015 Dongxiao Niu 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. In order to realize the predicting and positioning of short-term load inflection point, this paper made reference to related research in the field of computer image recognition. It got a load sharp degree sequence by the transformation of the original load sequence based on the algorithm of sharp degree. Then this paper designed a forecasting model based on the chaos theory and RBF neural network. It predicted the load sharp degree sequence based on the forecasting model to realize the positioning of short-term load inflection point. Finally, in the empirical example analysis, this paper predicted the daily load point of a region using the actual load data of the certain region to verify the effectiveness and applicability of this method. Prediction results showed that most of the test sample load points could be accurately predicted. 1. Introduction Short-term load forecasting (STLF) plays a key role in power dispatching work. It is the foundation of power grid planning, grid control, system safety analysis, and the economic operation. The forecasting accuracy is closely related to the grid running safety and economy [1, 2]. At present, many scholars and experts have already done a lot of theoretical researches and practical simulations on shortterm load forecasting [3–20]. More common short-term load forecasting models include regression prediction model [3], time series prediction model [4], artificial neural network prediction model [5], fuzzy logic and expert system [6, 7], the wavelet analysis model [8], chaos theory [9], and combination prediction model [10–12]. Literature [13] analyzed the power factors and predicted the short-term load based on rough set method. Literature [14, 15] introduced data mining techniques for short-term load forecasting. Literature [16] proposed a novel combination prediction model for short-term load forecasting which mainly studied the weight of combination prediction model with different scenarios. Literature [17] established a combination of modified firefly algorithm and support vector regression model which was used for the STLF. Literature [18] studied the short-term forecasting of categorical changes in wind power based on Markov chain models. Literature [19] studied the short-term load forecasting based on the wavelet transform and grey model improved by PSO. Literature [20] proposed a relevance vector machine short-term load forecasting model based on nonnegative matrix decomposition. On the whole, research on short-term load forecasting has been relatively mature. The models are more complicated and intelligent. Combination forecasting model is a research trend [21]. Inflection point is usually the most concern of the dispatch staff in short-term load forecasting. How to identify and predict inflection point of short-term load is a challenge problem. At present, there is no mature solution to the short-term load forecasting of inflection point. This paper gets a load sharp degree sequence by the transformation of the original load sequence based on the algorithm of sharp degree. Then, it forecasts the load sharp degree sequence by designing and training the forecasting model of chaotic RBF neural network to realize the short-term load forecasting of inflection point. 2. Inflection Point Identification Algorithm Based on Sharp Degree Inflection point is the most important features of load curve. The inflection point in this paper is the point that 2 Mathematical Problems in Engineering Pi Therefore, in a very small load curve, the variable sharp can be defined as sharp degree of 𝛼 󵄨 󵄨󵄨 󵄨𝑃 𝑃𝑖+𝑘 󵄨󵄨󵄨 (5) sharp = 1 − ang = 1 − 󵄨󵄨 󵄨 𝑖−𝑘 󵄨 󵄨 󵄨. 󵄨󵄨𝑃𝑖 𝑃𝑖−𝑘 󵄨󵄨󵄨 + 󵄨󵄨󵄨𝑃𝑖 𝑃𝑖+𝑘 󵄨󵄨󵄨 a Pi−k Pi+k O Figure 1: Part outline figure of the load curve. changes the direction of load curve upward or downward in a certain time interval. This paper identifies the inflection point according to the sharp degree of each point on the load curve. Set the function of load curve as 𝑃 = 𝑝(𝑡), in which the independent variable 𝑡 means time and the dependent variable 𝑃 represents the load time series. Randomly select a point 𝑃𝑖 on the curve as the center. 𝑃𝑖−𝑘 is the point in front of 𝑃𝑖 a distance of 𝑘. And 𝑃𝑖+𝑘 is the point behind 𝑃𝑖 a distance of 𝑘. Define the vector 𝑘: 𝑎𝑖𝑘 = (𝑇 (𝑖) − 𝑇 (𝑖 + 𝑘) , 𝑃 (𝑖) − 𝑃 (𝑖 + 𝑘)) , 𝑏𝑖𝑘 = (𝑇 (𝑖) − 𝑇 (𝑖 − 𝑘) , 𝑃 (𝑖) − 𝑃 (𝑖 − 𝑘)) , (1) 𝑐𝑖𝑘 = (𝑇 (𝑖 − 𝑘) − 𝑇 (𝑖 + 𝑘) , 𝑃 (𝑖 − 𝑘) − 𝑃 (𝑖 + 𝑘)) . Define 𝛼, the angle of 𝑎𝑖𝑘 and 𝑏𝑖𝑘 , as the angle consisting of 𝑃𝑖−𝑘 , 𝑃𝑖 , and 𝑃𝑖+𝑘 on the load curve. Figure 1 shows the part outline figure of the load curve. The peripheral solid line is composed of load time series. The dotted line is the circular arc fitted by 𝑃𝑖−𝑘 , 𝑃𝑖 , and 𝑃𝑖+𝑘 . And 𝑂 is the center of circular arc. Usually, the value of 𝑘 is set in the range of 3– 5. For the endpoint of load curve, we will take 3 to 5 sample values forward and backward on the sample load data. On the actual curve, the points 𝑃𝑖−𝑘 , 𝑃𝑖 , and 𝑃𝑖+𝑘 can be approximately regarded as three points on the circular arc as the interval of the three points is very small [22]. Assuming that |𝑃𝑖 𝑃𝑖−𝑘 | = |𝑃𝑖 𝑃𝑖+𝑘 |, then 󵄨 󵄨 󵄨 󵄨󵄨 󵄨󵄨𝑃𝑖−𝑘 𝑃𝑖+𝑘 󵄨󵄨󵄨 /2 󵄨󵄨󵄨𝑃𝑖−𝑘 𝑃𝑖+𝑘 󵄨󵄨󵄨 /2 𝛼 sin ( ) = 󵄨󵄨 󵄨 = 󵄨󵄨 󵄨 2 󵄨󵄨𝑃𝑖 𝑃𝑖−𝑘 󵄨󵄨󵄨 󵄨󵄨𝑃𝑖 𝑃𝑖+𝑘 󵄨󵄨󵄨 󵄨󵄨 󵄨 󵄨𝑃 𝑃𝑖+𝑘 󵄨󵄨󵄨 = 󵄨󵄨 󵄨 𝑖−𝑘 󵄨 󵄨 󵄨. 󵄨󵄨𝑃𝑖 𝑃𝑖−𝑘 󵄨󵄨󵄨 + 󵄨󵄨󵄨𝑃𝑖 𝑃𝑖+𝑘 󵄨󵄨󵄨 (2) In this function, 0 < 𝛼 ≤ 180. When 𝑃𝑖−𝑘 , 𝑃𝑖 , and 𝑃𝑖+𝑘 are in a straight line, 𝛼 = 180, then 󵄨 󵄨󵄨 󵄨󵄨𝑃𝑖−𝑘 𝑃𝑖+𝑘 󵄨󵄨󵄨 𝛼 󵄨󵄨 󵄨 󵄨 󵄨 = sin ( 2 ) = sin (90) = 1. 󵄨󵄨𝑃𝑖 𝑃𝑖−𝑘 󵄨󵄨󵄨 + 󵄨󵄨󵄨𝑃𝑖 𝑃𝑖+𝑘 󵄨󵄨󵄨 (3) When the value of 𝛼 decreases tending to zero, 󵄨 󵄨󵄨 󵄨󵄨𝑃𝑖−𝑘 𝑃𝑖+𝑘 󵄨󵄨󵄨 𝛼 󵄨󵄨 󵄨󵄨 󵄨󵄨 󵄨󵄨 = sin ( 2 ) = sin (0) = 0. 󵄨󵄨𝑃𝑖 𝑃𝑖−𝑘 󵄨󵄨 + 󵄨󵄨𝑃𝑖 𝑃𝑖+𝑘 󵄨󵄨 (4) The larger the value of sharp, the smaller the value of 𝛼, and the curve would be more sharp. On the contrary, the curve would be more smooth. Because of the continuity of load, the identification of inflection point is closely related to the interval of load curve sequence and the set threshold value. Therefore, the threshold value can be set according to the load curve characteristics and actual situation. If sharp (𝑃𝑖 ) > 𝑇, the 𝑃𝑖 can be regarded as inflection point. 3. Prediction Model Based on Chaotic RBF Neural Network Artif (...truncated)