【正文】 ? ? ? ?1 1dx a x bdt ?? 它的差分方程是 ? ? ? ? ? ? ? ?01x k az k b??。而且，不管是發(fā)展系數(shù) a 還是控制變量 b 都由 ??? ?1zk值確定。 第三步： 構建累加矩陣 B 和系數(shù)向量 nx 。目標函數(shù)定義為最小 平均絕對百分比誤差 ，如下： ? ?1m innkM A P E e k?? ? 且， ? ? ? ? ? ? ? ? ? ?? ? ? ?000? 100%x k x kekxk??? ? ?? ?0xk為原始數(shù)據(jù)， ? ?? ?0?xk為預測值， n 是該數(shù)列的維數(shù)。 遺傳算法是 一個隨機搜索算法 ， 模擬自然選擇與演化 。在 數(shù)值函數(shù)優(yōu)化 方面，改進的十進制編碼法相對于 二進制編碼 法擁有很大的優(yōu)勢。 我們利用改進的十進制碼 代表性方法來 尋找 在灰色 GM（ 1， 1）模型中 最佳系數(shù) 的 ? 值。擁有高度地適應度 F（ ? ?,ik? ）的個體 ? ?,ik? 逐代衍化和發(fā)展。 第五步： 交叉和變異 ：編碼和交叉是相關的； 我們利用了十進制碼 表示法，因此 我們提出了一種新的交叉算子 “ 單點線性算術交叉 ”。 ② 位在左側的交叉可以通過以下計算算法 ： a： 基因分析 ： ? ?* 1 *ik ik ikz z z??? ? ? ? ?* 1 *jk jk jkz z z??? ? ? b：交換后基因： ? ?* 1 *ik ik jkz z z??? ? ? ? ?* 1 *jk jk ikz z z??? ? ? 中英文資料 8 ? ?0,1?? 稱為交叉系數(shù)，每次根據(jù)隨機的交叉系統(tǒng)來選擇。每當進行 變異操作 時， r會被 隨機 的 挑選 。 中英文資料 9 第四章．負荷預測案例 在本章，我們試著對 GM（ 1， 1） 關于改進的遺傳算法 進行性能評估。接著，我們可以算出 a 和 b，然后我們利 用 GM（ 1， 1） IGA 來預測第 m+1 天中的第 j 點的負荷，于中英文資料 10 是我們可以得到 ? ?1jXm?，最后第 m+1 天地 24 個預測值構成了這個負荷數(shù)據(jù)序列? ?? ?1 1 , 2 , , 2 4jx m j? ? ?。 設置模擬殘差 ? ?? ?0xk為 ? ? ? ? ? ? ? ? ? ?00?k x k x k? ??， k=1， 2，?， n 設置模擬的相對剩余為 ? ? ? ? ? ? ? ?0 ,k k x k??? k=1， 2，?， n 設置 ??0x 平均值為 ? ? ? ?011 nkx x kn ?? ? 設置 ??0x 的方差為 ? ? ? ?? ?2021 11nkS x k xn ???? 設置殘差平均值為 ? ?11 nk kn???? ? 設置殘差方差為 ? ?? ?222 11nkSkn ?????? 因此， GM（ 1， 1） IGA 的校驗值如下： 1).平均相對誤差為 ? ?11 nk kn? ???? 2).均方差 率為 12c S S? 3).小誤差概率為 ? ?? ?10 .6 7 4 5p p k S??? ? ? 4).關聯(lián)度為 ? ? ? ?11s s s s s s? ? ? ? ? ? ? ? 其中， ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ?1 0 0 0 021112nks x k x x n x??? ? ? ?? 中英文資料 11 ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ?1 0 0 0 02 ? ? ? ?11nks x k x x n x??? ? ? ?? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ?1 0 0 0 021? ?1 2nks s x k x x n x n??? ? ? ? ?? 根據(jù)上述公式 ， GM（ 1， 1） IGA 的指標的校驗值見表 1。兩種模型的偏差值如下， GM（ 1， 1）的平均誤差為 %，然而， GM（ 1， 1）IGA 的平均誤差為 %。 GM（ 1， 1） IGA 的特點是簡單、易于開 發(fā)，因此，它在電力系統(tǒng)中作為一個輔助工具來解決預測問題是適宜的。 Energy Systems, Vol 18. No 1,pp1926 1996. [13] Edmund, . Heng Dipti Srinivasan A. C. Liew. “Short Term Load Forecasting Using Geic Algorithm And Neural Networks”.IEEE Catalogue No: 98EX137 pp576581 [14] Chew, . , Lin, . , and Chen, ., The Grey Predictor Control in Inverted 中英文資料 15 Pendulum System, Journal of China Institute of Technology and Commerce, ,pp. 1726, 1995 [15] J. Grey Syst., “Introduction to grey system theory,” , ,pp. 1–24, 1989 Application of Improved Grey Prediction Model for Power Load Forecasting [Abstract] Although the grey forecasting model has been successfully utilized in many fields, literatures show its performance still could be improved. For this purpose, this paper put forward a GM (1, 1)connection improved geic algorithm (GM (1, 1)IGA) for shortterm load forecasting (STLF). While Traditional GM (1,1) forecasting model is not accurate and the value of parameter ? is constant, in order to solve this problem and enhance the accuracy of shortterm load forecasting (STLF), the improved decimalcode geic algorithm (GA) is applied to search the optimal ? value of grey model GM (1, 1). What’s more, this paper also proposes the onepoint linearity arithmetical crossover,which can greatly improve the speed of crossover and mutation. Finally, a daily load forecasting example is used to test the GM (1, 1)IGA model and traditional GM (1, 1) model, results show that the GM (1, 1)IGA had better accuracy and practicality. Keywords: Shortterm Load Forecasting, Grey System,Geic Algorithm, Onepoint Linearity Arithmetical Crossover. 1. Introduction 中英文資料 16 Daily peak load forecasting plays an important role in all aspects of economic, reliable, and secure strategies for power system. Specifically, the shortterm load forecasting (STLF) of daily electricity usage is crucial in unit mitment, maintenance, power interchange and task scheduling of both power generation and distribution facilities. Shortterm load forecasting (STLF) aims at predicting electric loads for a period of minutes, hours, days or weeks. The quality of the shortterm load forecasts with lead times ranging from one hour to several days ahead has a significant impact on the efficiency of operation of any power utility, because many operational decisions, such as economic dispatch scheduling of the generating capacity, unit mitment, scheduling of fuel purchase as well as system security assessment are based on such forecasts [1]. Traditional shortterm load forecasting models can be classified as time series models or regression models [2,3,4]. Usually, these techniques are effective for the forecasting of shortterm load on normal days but fail to yield good results on those days with special events [5,6,7]. Furthermore, because of their plexities, enormous putational efforts are required to produce acceptable results. The grey system theory, originally presented by Deng[8,9,10], focuses on model uncertainty and information insufficiency in analyzing and understanding systems via research on conditional analysis, forecasting and decision making. The grey system puts each stochastic variable as a grey quantity that changes within a given range. It does not rely on statistical method to deal with the grey quantity. It deals directly with the original data, and searches the intrinsic regularity of data[11]. The grey forecasting model utilises the essential part of the grey system , grey forecasting can be said to define the estimation done by the use of a grey system, which is in between a white system and a blackbox system. A system is defined as a white one if the information in it is known