Voltage Stability Constrained Optimal Power Flow Considering PV-PQ Bus Type Switching: Formulation and Convexification

PV-PQ switching of generator buses when hitting reactive power limits is an important factor in voltage stability. This article establishes the formulation and convexification of voltage stability constrained optimal power flow (VSC-OPF) considering PV-PQ switching that co-optimizes generation dispatch and bus type profile. The conventional power flow Jacobian is intractable to be adopted since it has a variable size under PV-PQ switching. To solve this issue, a big-M-parameterized constant-size power flow Jacobian is constructed which explicitly considers PV-PQ switching. It is proved that this new Jacobian has the same minimum eigenvalue as the conventional Jacobian, which enables us to propose a more tractable VSC-OPF by enforcing a lower bound for the constant-size Jacobian minimum eigenvalue. Further, a linear approximation of the voltage stability constraint is constructed by combining smoothing, relaxation and eigen-sensitivity techniques. Finally, we establish an semi-definite programming formulation for VSC-OPF considering PV-PQ switching, which can be efficiently solved by outer linearization algorithm. The proposed formulation and convexification techniques are extendable to include more general PV-PQ switching actions triggered by hitting the capability curve of converter-interfaced generators. The proposed method is verified via numerical tests on the IEEE 118-bus system. Comparing to the VSC-OPF under a predefined bus type profile, our method finds out the optimal bus type profile that helps to achieve a lower-cost solution and higher precision in voltage stability assessment.