Limitations of assigning general critical values to voltage stability indices in Voltage-Stability-Constrained optimal power flows

The representation of system stability in Optimal Power Flow (OPF) models is a challenging task, which, in some cases, might render such representation impractical. The use of Voltage Stability Indices (VSIs) to monitor how close a system is to voltage collapse may be a very straightforward approach to overcoming those difficulties. However, when the voltage collapse is associated with a single generator encountering one of its reactive power generation limits, VSIs are difficult to be predicted. Nevertheless, assigning a general critical value to VSIs could be considered. Thus, this paper proposes the analysis of such consideration by modeling and solving a Voltage-Stability-Constrained OPF (VSC-OPF) problem in the context of electricity markets. The Voltage Stability Constraint (VSC) was implemented by means of the Minimum Singular Value (MSV), which is based on the Singular Value Decomposition (SVD) of the power flow Jacobian matrix, and the Tangent Vector Norm (TVN), which is based on the Tangent Vector (TV) to the bifurcation manifold of the power flow equations. The consideration of assigning an absolute critical value to these VSIs was verified with a small 6-bus test system. Results show that such consideration is too conservative, which may lead to inadequate price signals in the context of VSC-OPFs applied to electricity market clearing.