## Towards a theory of voltage collapse in electric power systems.(English)Zbl 0689.93042

Summary: Several recent major power system blackouts are characterised by a progressive decline in voltage magnitude at the system buses. These events are termed ‘voltage collapses’. The mechanisms of voltage collapse are not well defined and the dynamics of the process are not well understood.
In this paper, we describe the loss of stability when a stable equilibrium point disappears in a saddle node bifurcation and present a simple model of the system dynamics after the bifurcation. The results apply generally to any generic one parameter dynamical system.
Then we use these results to propose a model for voltage collapse in power systems. The model gives an explicit mechanism for the dynamics of voltage collapse. We illustrate the model by constructing a simple power system model and simulating a voltage collapse.

### MSC:

 93C95 Application models in control theory 93C10 Nonlinear systems in control theory 37G99 Local and nonlocal bifurcation theory for dynamical systems 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations

### Keywords:

power system; voltage collapses; saddle node bifurcation
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### References:

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