Laplace-based solution for three-phase short-circuit fault in synchronous machines

Abstract

The study of synchronous machine behavior under transient conditions caused by a three-phase short-circuit fault is primarily based on two approaches: experimental analysis and simulation. Experimentally, the sudden three-phase short-circuit test applied to the machine yields a low-parameter empirical ‘short-circuit function’ that models it in a simple manner using the equivalent ‘constant voltage behind reactance’ circuit. On the other hand, fault analysis is performed through simulation using Electromagnetic Transient Programs, which are based on numerical discretization methods. However, in both cases, there is a lack of formal analytical descriptions of a generator’s transient behavior. In contrast, this paper introduces a closed-form solution using Laplace, as an alternative method for computing three-phase short-circuit faults. This deterministic appclosed-form solutionroach provides an analytical description of the machine represented by different model structures, facilitates the study of transient interactions among its windings, and enables the analysis of current components (synchronous, dc, and double frequency). Additionally, the closed-form solution is compared with a numerical integration method in terms of computational efficiency, processing time, and accuracy. This demonstrates the existence of a closed-form solution for the generator in the transient state and highlights its advantages for modeling and computation compared with current methods.