International Journal of Bifurcation and Chaos, Vol. 28, No. 1 (2018) 1830002 (24 pages) c  World Scientific Publishing Company DOI: 10.1142/S0218127418300021 Pseudo-Pitchfork Bifurcation of Feasible Regions in Power Systems Chu-Yang Jiang Electric Power Research Institute of China Southern Power Grid, Guangzhou 510000, P. R. China School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, P. R. China jiangcy@csg.cn Hsiao-Dong Chiang School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850, USA chiang@ece.cornell.edu Received March 3, 2017; Revised October 4, 2017 Local bifurcations occur in power systems, causing changes in power system dynamic behaviors. These local bifurcations include the saddle-node bifurcation, Hopf bifurcation, and structure- induced bifurcation. This paper presents a new type of bifurcation that can occur in the optimal power flow (OPF) problem. This new type of bifurcation, termed pseudo-pitchfork bifurcation, involves bifurcations of the feasible components of the OPF problem and the disappearance of local optimal power flow solutions. The main features of this special type of bifurcation are demonstrated on several power systems with different loading condition parameters and different constraint parameters. Then the computation consideration and physical meaning of the pseudo-pitchfork bifurcation are roughly discussed. It is also demonstrated that a pseudo- pitchfork bifurcation occurring between feasible components can help us interpret the loss or birth of optimal power flow solutions and can lead to powerful numerical methods for computing high-quality optimal power flow solutions. Keywords : Optimal power flow; feasible components; local bifurcation; pseudo-pitchfork bifurcation. 1. Introduction The power system is one of the largest nonlinear physical systems in the world. It is now well rec- ognized that qualitative changes in the behavior of power systems can occur due to bifurcation phe- nomena. Pioneer work on the bifurcation analysis of power systems can be dated back to the 1970s and earlier. In the past three decades, nonlinear dynam- ical theory has become an important research sub- ject in the power system community [Chiang, 2003]. Bifurcations occur in power systems. Typical ones include the saddle-node bifurcation, Hopf bifurcation and structure-induced bifurcation. Of these three, the saddle-node bifurcation is char- acterized by the coalescence and disappearance of system operating equilibrium points. This type of bifurcation has been widely applied to power sys- tems to interpret the dynamic mechanisms of volt- age collapse [Dobson & Chiang, 1989; Chiang et al., 1990]. When a saddle-node bifurcation occurs, the system dynamics will leave the bifurcation point and move along the center manifold trajectory associated with the saddle-node point. This post- bifurcation dynamic can be used to explain the sharp decrease in voltage magnitude during voltage 1830002-1 Int. J. Bifurcation Chaos 2018.28. Downloaded from www.worldscientific.com by 107.175.207.214 on 07/15/19. Re-use and distribution is strictly not permitted, except for Open Access articles.