The impacts of convex piecewise linear cost formulations on AC optimal power flow

作     者：Coffrin, Carleton Knueven, Bernard Holzer, Jesse Vuffray, Marc 

作者机构：Los Alamos Natl Lab Los Alamos NM 87545 USA Natl Renewable Energy Lab Golden CO 80401 USA Pacific Northwest Natl Lab Richland WA 99354 USA 

出 版 物：《ELECTRIC POWER SYSTEMS RESEARCH》 (电力系统研究)

年 卷 期：2021年第199卷

页      面：107191-107191页

核心收录：

学科分类：0808[工学-电气工程] 080802[工学-电力系统及其自动化] 08[工学] 

基　　金：U.S. Department of Energy's (DOE) Advanced Research Projects Agency-Energy (ARPA-e) 

主　　题：Nonlinear optimization Convex optimization Optimal power flow Piecewise linear functions 

摘      要：Despite strong connections through shared application areas, research efforts on power market optimization (e. g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.