Extensions, simplifications, and tests of synchronic modal equivalencing (sme)

Abstract

Dynamic equivalencing is of considerable importance in power systems. The state of the art in the transient stability context is seen in the package DYNRED, which is built on the classical coherency-based equivalencing approach. DYNRED also incorporates more recent ideas from slow-coherency/weak-coupling theory, to identify coherent groups of generators in a large model. The slow-coherency approach actually yields direct possibilities for equivalencing, although these have been explicitly addressed only for the case of low-order generator models that capture just the swing dynamics. Yet other approaches to dynamic equivalencing have been proposed in the literature. A new framework for dynamic equivalencing, termed Synchronic Modal Equivalencing (SME), was introduced. SME is motivated by slow-coherency theory, but its formulation and associated computational algorithms are more general in some important respects. Ideal synchrony of a group of generators requires the motion of each generator in the group to be a linear combination of the motions of a fixed set of basis generators in the group, when some subset of the system modes (not necessarily the slowest) is excited in a linearized model. SME keeps intact the nonlinear dynamic models of all the generators in a synchronic study group and of all the basis generators external to this group. The model of each remaining generator is replaced by a simple nondynamic linear circuit containing a dependent current source driven by the motions of the basis generators. Impedance-load buses that inter-connect only the replaced generators can be eliminated, with their effects being accounted for by the dependent current sources; the remainder of the network is left unmodified. The current paper summarizes certain extensions and simplifications of SME. The recommended SME procedure that emerges from our studies so far is described. Results are presented for tests using the simulation package EUROSTAG, and a model loosely based on the France-Spain power system. The unreduced model has 23 generators, 83 buses, and 476 state variables. After decomposition into five synchronic groups, a study group containing 6 machines is selected, along with 4 basis generators external to the study group. The resulting 10-machine equivalent matches the full model exceedingly well for disturbances in the study group. The extensions and simplifications described in this paper open the door to attempting SME on the much larger models that are of interest to industry.