Selective transient stability-constrained optimal power flow using a SIME and trajectory sensitivity unified analysis

• A new analytic, time independent and non-heuristic transient stability constraint is proposed in terms of the mechanical powers of generators.
• A TSC-OPF is formulated where all dynamic and transient stability constraints are represented by the proposed one single stability constraint.
• The huge dimension of the TSC-OPF problem is reduced to a dimension that is equal to that of a conventional OPF model plus one.
• A non-heuristic approach is proposed to perform the preventive control of transient stability by rescheduling only a selected number of generators.
• The active power is always transferred from critical to noncritical generators having the higher impact on the system's transient stability.

A novel approach based on both single machine equivalent (SIME) and trajectory sensitivity methods is proposed to formulate a transient stability-constrained optimal power flow (TSC-OPF) in the Euclidian space, where only one single stability constraint is necessary in the optimization problem to represent all dynamic and transient stability constraints of the multi-machine system. This formulation remarkably reduces the dimension of the optimization problem to one similar to a conventional OPF, resulting in a tractable approach to the preventive control of transient stability in realistic power systems. A unified framework of time domain analysis is proposed, where the transient stability, trajectory sensitivity and SIME analyses are all combined to assess the system's stability and to compute the sensitivity coefficients of the proposed transient stability constraint. Based on these sensitivity coefficients, three non-heuristic selection criteria are proposed to perform the preventive control by rescheduling only a selected number of generators, which is the commonly accepted practice followed by the system's operators. The validity and the effectiveness of the proposed method are numerically demonstrated in the 10-machine 39-bus New England system and Mexican 46-machine 190-bus system.