Guaranteed stability in optimal power generation dispatching under uncertainty

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.