序列运算理论及其应用

SEQUENCE OPERATION THEORY AND ITS APPLICATIONS

为了更好地处理电力系统中的各种不确定性因素 ,文中从数学的高度建立了一套序列运算理论。提出了任意两个定义在非负区间上的离散序列之间的卷和运算、卷差运算、交积运算、并积运算 ,研究了它们的交换律、结合律、分配律等运算性质 ;与代数中的 1 ,0 ,∞相对应 ,提出了单位序列、零序列和无穷序列的概念 ,得到了它们的特殊性质。最后分析得到 ,这几种序列运算分别相当于代数中的加法、减法、乘法等运算。序列运算这一研究成果具有普遍的指导意义 ,可望在电力系统和其他领域发挥积极的作用 ,目前已经实现了适合于综合资源规划和电力市场的新的随机生产模拟算法 。

A new general and good mathematical approach named sequence operation theory (SOT) is firstly established for the purpose of dealing with the uncertainty factors in power systems. Four type of discrete sequence operations named addition type convolution (ATC), subtraction type convolution (STC), AND type product (ATP) and OR type product (OTP) respectively, are proposed in this paper. It is interesting to find that ATC, ATP and OTP operations satisfy commutative law, associative law and distributive law. Furthermore, the concept and definition of unit sequence, zero sequence, infinite sequence are presented along with their special features. After detail analysis of these operations, a very useful result is obtained that ATC, STC and ATP operation can be respectively treated as addition, subtraction and multiplication in arithmetic. SOT is a general mathematical theory. It could be expected to have wide application in power system and other research fields. Success applications have been achieved in power system probabilistic production cost simulation and uncertainty analysis of electricity price.