Methodology for Voltage Stability Analysis Using Hopf Bifurcation and Continuation Power Flow Simulator

Abstract

The search for the Hopf bifurcation point in power systems can be made as the load is increased by small steps, and a power flow is solved for every load until a pair of purely imaginary eigenvectors has been found (zero real part). However, a search through successive power flows is time-consuming and does not guarantee that the Hopf bifurcation point will be found. This paper proposes a methodology and strategies that mitigate these problems. To increase the possibility of finding the Hopf bifurcation point, a continuation power flow is used to stablish search paths as the loading is incremented according to a fraction of the maximum loading point of the power system. It is only at specific converged continuation power flow that the dynamic state Jacobian matrix is constructed and has its eigenvalues computed. To facilitate the understanding and application of the proposal, it is used the MATPOWER (version 7.0) computer program and two available power systems.

Keywords:

• continuation power flow
• eigen computation
• Hopf bifurcation
• matpower
• maximum transferable power
• power system loading
• PV curve
• unstable operation
• voltage stability
• voltage oscillation

Additional information

Notes on contributors

Matheus M. Roque

Matheus M. Roque received the B.S. degree in electrical engineering from the Federal University of Ceará, Fortaleza, Brazil, with an interinstitutional degree at Óbuda University, Budapest, Hungary, in 2017. In 2020 he received the M.Sc. degree in electrical engineering from the Federal University of Maranhão. In 2020, he concluded his specialization in Higher Education Teaching at Ceuma University, Maranhão, Brazil. He is currently a professor in the education network of the state of Mato Grosso do Sul, Brazil. His main research interest is electrical power systems stability.

José Eduardo O. Pessanha

José Eduardo O. Pessanha received the ScDEE degree from the Catholic University of Rio de Janeiro - Brazil (1997), MScEE from Ohio State University - USA (1991), MScEE from the Catholic University of Rio de Janeiro – Brazil (1988) and a BScEE from Santa Úrsula University (1985) - Brazil. He is currently a full Professor in the Department of Electrical Engineering at the Federal University of Maranhão, Brazil, where he is working on numerical methods, Hamiltonian formalism, power quality, power system dynamics, voltage stability and power systems restoration. Dr. Pessanha has coordinated several Research and Development Projects with Brazilian Power Systems Transmission and Distribution utilities and interinstitutional projects as well. His research interests include electric power components and systems.