Open AccessSolving OPF using linear approximations: fundamental analysis and numerical demonstration
Author(s) -
Yang Zhifang,
Zhong Haiwang,
Xia Qing,
Kang Chongqing
Publication year - 2017
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2017.1078
Subject(s) - robustness (evolution) , linear approximation , ac power , mathematical optimization , power flow , mathematics , convergence (economics) , flow (mathematics) , linear equation , computer science , voltage , power (physics) , electric power system , nonlinear system , mathematical analysis , engineering , biochemistry , chemistry , physics , geometry , quantum mechanics , economic growth , electrical engineering , economics , gene
Due to the unique advantages in computational robustness and convergence, the linear approximation approach is and will remain to be an important method to solve the optimal power flow (OPF) problem, especially for industrial applications. The DC power flow method, which is currently used in the majority of power industries, is the representative. Many studies extend the DC power flow method by including voltage magnitude, reactive power, and losses. This study provides a detailed analysis and breakdown investigation of existing linear approximations of the OPF problem. The formulation and accuracy of existing linear approximations are compared. Taking advantage of the decoupled formulation of linear approximations, the property of power flow equations is illustrated from a new perspective. Why reactive power flow equations are hard to linearise is explained theoretically. The numerical performance of existing linear approximations is demonstrated in IEEE and Polish test systems. Evidence from the theoretical analysis and numerical studies shows that the accuracy of linear approximations could be substantially improved using a mathematical transformation of the non‐linear voltage magnitude term. This finding provides a new research direction for solving the OPF problem using linear approximations.