High Order Approximate Power Flow Solutions

This report outlines the derivation of the first-, second-, and third-order Taylor series expansions of the power flow solution; it is the Electronic Companion of the following paper:R. A. Jabr, “High-order approximate power flow solutions and circular arithmetic applications,” IEEE Transactions on Power Systems, vol. 34, no. 6, pp. 5053-5062, November 2019.The derivation is carried out in complex variables via the use of Wirtinger calculus.本报告阐述了潮流解的一阶、二阶与三阶泰勒级数展开式的推导过程，系下述论文的电子补充材料：R·A·贾布尔，《高阶近似潮流解与圆算术应用》，《IEEE电力系统汇刊》（IEEE Transactions on Power Systems），第34卷第6期，第5053-5062页，2019年11月。本次推导采用复变量结合维尔廷格微积分（Wirtinger calculus）完成。