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This article deals with the cost optimal commitment of power systems. System stability is often only considered after solving the commitment problem. We show by example that a cost optimization may result in a mode of operation that, while economically optimal, is unstable or has otherwise unacceptable dynamics. As a remedy, we propose to use the so-called normal vector method, which has been developed for the optimization of nonlinear dynamical systems with stability boundaries and uncertain parameters. We apply the method to a small sample power grid, where the optimization goal is to minimize the energy production costs for a given power consumption.
Stability and cost optimality of power generation and supply systems must not be considered independently from one another. Simple examples show that optimizing cost without considering stability may result in modes of operation that, while economically optimal, are unstable. We demonstrate that stability, robustness, and optimality can be considered systematically and simultaneously by combining bifurcation theory and nonlinear optimization. Essentially, the proposed method enforces a backoff distance between the optimal point of operation and operational or stability boundaries in the space of the optimization variables, where bifurcation theory is used to describe nonlinear stability boundaries.