Group-Based BCU–CUEP Methods
The controlling unstable equilibrium point (controlling UEP, or CUEP) plays a key role in several applications, such as (1) the determination of the critical energy, from which an estimated critical clearing time (CCT) can be obtained, (2) the derivation of preventive control against transient instability, (3) the derivation of enhancement control for transient stability, and (4) the mode of system separations (i.e., the unstable mode) and the related diagnosis of the protection system. Nonetheless, the task of computing the controlling UEP for every power system contingency is very challenging. Several computational challenges in computing the controlling UEP are described in Chapter 12.
The BCU method computes the controlling UEP of the original model by computing the controlling UEP of an artificial reduced-state model. It has been shown that, under the boundary property or the one-parameter transversality condition, the UEP computed by the BCU method lies on the stability boundary of the original model. To check the boundary property, the boundary distance needs to be calculated, which amounts to a few time–domain simulations.
Since the boundary property is a group property, it is sufficient to compute the boundary distance of a selected contingency from a group of coherent contingencies. If the boundary distance of a UEP computed by the BCU method with respect to a contingency is 1.0, then the UEP is on the stability boundary ...