微机保护实用快速开平方算法

Fast SQRT algorithm of microcomputer protection

对于被开方数为两数平方和形式的开方运算,传统简化开方算法精度不高,不能满足工程需要。提出了一种利用泰勒级数展开式求取近似平方根的算法,利用泰勒级数推导出计算公式,选取一次多项式作为近似值带入该公式得到平方根。重点分析了一次多项式系数的选取原则和方法。通过分析系数在不同范围内取值时的最大误差,得到误差最小的一次多项式系数。理论分析表明,提出的算法与传统算法计算量相当,但精度能提高4倍以上,最大误差不超过0.05%,满足微机保护装置需求。

A new square root algorithm is proposed to improve the precision of the traditional simplified algorithm when the radicand is the sum of two squares. Taylor series is introduced to derive the formula which uses the first polynomial as the approximate value. The principle and method of selecting the coefficients of the polynomials is analyzed. The coefficients of the first polynomial with minimal error is obtained based on the analysis of maximal error when the coefficient is distributed in different scopes. The results of theoretical analysis show that the computation complexity of proposed algorithm is similar to the traditional method, but the precision is increased by 4 times. The maximal error is below the 0.05% and it meets the requirement of microprocessor protection.