摘要
针对传统分形插值难以进行外推的问题,利用分形的自相似性与标度不变性将内区间的分形特性进行延拓,并由此构造了具有外推功能的分形插值算法。该算法利用内区间的迭代函数系和吸引子由特定的初始点出发进行直接搜索,并通过使迭代特定次数后获得的点集与吸引子的均方偏差不断减小的过程来逐步调整初始点的纵坐标值,而均方偏差达到最小化时的纵坐标值即可作为需要外推点的函数值。然后利用电力负荷数据的不同分形特性,将分形外推插值算法应用于电力日负荷、日峰值负荷及年用电量预测中。算例结果表明,分形外推插值算法具有较高的预测精度、较高的计算效率和良好的收敛特性。
For traditional fractal interpolation it is difficult to extrapolate. To solve this problem the fractal property of inner interval is extended outwards by self-similarity and scale invariance of fractal, and on this basis a fractal extrapolation algorithm is proposed. In this algorithm from a certain initial point the direct search is performed by use of iterated function system and attractor of inner interval, and through the process that after specified times of iteration the mean square deviation between obtained point set and attractor is ever-reduced the value of initial point on Y-axis is step-by-step adjusted; when the mean square deviation become the minimum, the corresponding value on Y-axis can be used as the function value of the point to be extrapolated. Then by use of different fractal property of power load data the proposed fractal extrapolation algorithm is applied to the forecasting of daily load, daily peak load and annual power consumption. Case study results show that the proposed algorithm possesses following advantages： more accurate forecasting results, higher calculation efficiency and good convergence property.
出处
《电网技术》
EI
CSCD
北大核心
2006年第13期49-54,共6页
Power System Technology
基金
黑龙江省自然科学基金资助项目(E0326)。
关键词
分形
外推插值
负荷预测
迭代函数系
吸引子
电力系统
fractal
extrapolation
load forecasting
iterated function system（IFS）
attractor
power system
