Boundary properties of the BCU method for power system transient stability assessment

The BCU method has been confirmed as an important on-line tool for direct transient stability assessment of power systems. The boundary property, which guarantees the controlling UEP of the original model and that of the reduced-state model, is a key issue in the BCU method. Instead of one-parameter transversality conditions proposed earlier, analytical results on the boundary property will be explored. We have applied the self-indexing energy function and the structural stability to analyze boundary properties of simple power systems. We have shown that, under certain mild conditions, the original system and the reduced-state system share the same UEPs on stability boundaries. Numerical studies confirm theoretical developments.

I. Introduction

A boundary of stability region based controlling unstable equilibrium point (BCU) method has been reported as an important on-line tool for direct transient stability assessments of power systems in literature [1]–[3], [8]. The boundary property, which guarantees the controlling UEP of the original model and that of the reduced-state model is a key issue of the BCU method. It has been shown that if the one-parameter transversality conditions of a parametrized system are satisfied, finding the controlling unstable equilibrium points (UEP) of the original model can be achieving by finding the controlling UEP of the reduced-state model. However, because of the complexity of practical power system models, the one-parameter transversality conditions may not be always satisfied. The violation of the one-parameter transversality conditions may cause incorrectness in the BCU method when computing the controlling UEP. [6], [7] discussed several counter examples show that the BCU method may fail to give correct stability assessments. [5] argued that lightly damped systems in [6] are rare and typical faults tend to move the power system in directions where the BCU method works.