A Trajectory-Unified Method for Constructing the Feasible Region of OPF Problems

Abstract

The feasible region plays an important role in optimal power flow (OPF) problems. However, constructing the feasible region of general optimal power flow problems is a challenging task. In this paper, a trajectory-unified (TJU) method is developed to compute the feasible region of general large-scale OPF problems. This is the first attempt, to our knowledge, to develop a numerical method to compute feasible regions of OPF problems. In addition, the projection of the computed feasible region into a desired low-dimensional sub-space is presented. By employing the proposed TJU method, we compute the feasible region of a 9-bus and the IEEE 118-bus OPF problem. It is shown that the feasible region of a power system grows in size from light-loading conditions to medium-loading conditions while it shrinks in size from medium-loading conditions to heavy-loading conditions. This discovery of a geometric property of the feasible solution asserts the observations that OPF problems are generally easy to solve during medium-loading conditions but are generally difficult to solve during heavy-loading conditions.

Keywords:

• optimal power flow
• feasible region
• power system loading conditions
• optimal power flow solutions

Additional information

Notes on contributors

Chao-Yu Xue

Chao-Yu Xue received the B.S. degree in electrical engineering from Hebei University of Technology, Tianjin, China in June 2017 and he is currently pursuing the M.S. degree in electrical engineering at Tianjin University, Tianjin, China. His current research interests include the feasible region of optimal power flow problems, and nonlinear computation and applications.

Hsiao-Dong Chiang

Hsiao-Dong Chiang received the Ph.D. degree in electrical engineering and computer sciences from the University of California at Berkeley, Berkeley, CA, USA. Since 1998, he has been a Professor in the School of Electrical and Computer Engineering at Cornell University, Ithaca, NY, USA. He holds 17 U.S. and overseas patents and several consultant positions. He is the author of two books: Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundations, BCU Methodologies, and Applications (Hoboken, NJ, USA: Wiley, 2011) and (with Luis F. Alberto) Stability Regions of Nonlinear Dynamical Systems: Theory, Estimation, and Applications (Cambridge, UK: Cambridge Univ. Press, 2015). He has served as an associate editor for several IEEE transactions and journals and is the founder of Bigwood Systems, Inc. in Ithaca, NY, USA. His current research interests include nonlinear system theory, nonlinear computation, nonlinear optimization, and their practical applications.