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A solution of optimal power flow with voltage stability constraints

A competitive electricity market often requires the separation of transmission and generating services; therefore, the transmission system operator does not have an impact on short and long term generation patterns. At the same time, the transmission operator needs to accommodate various transactions and generation patterns. In the desire to accommodate market-based transactions, the transmission operator is very much interested in quantifying the various stability margins (voltage, dynamic, etc.) and in determining the level of robustness of the transmission system. In the case of voltage stability, the index of robustness used is the difference from the current operating condition to an infeasible point. Particularly relevant is the amounts of additional reactive load that can be accommodate before the system experience a voltage collapse. In this paper, the authors propose a development of OPFs based on a primal-dual nonlinear interior-point method, which can handle maximum loadability constraint under contingency state. The developed OPF can solve the optimal operating point while keeping enough loadability margin under contingency state. In order to demonstrate the advantage of the proposed methods, the OPFs are applied to several test systems under various operating conditions.