Comprehensive Study of Electrical Power Grid Stability Issues Using Bifurcation and Chaos Theory

In this paper, the modern nonlinear theory (bifurcation and chaos theory) is used to study the dynamics of two well-known phenomena in electric power systems named Voltage Collapse (VC) and Subsynchronous Resonance (SSR). The results showed that at specific control parameter values, the system experienced unstable conditions, which means the electric power system would totally collapse due to some increases in control parameters. So, in addition to finding such unstable conditions, we designed a linear controller to eliminate all such unstable ones.