Abstract
This work deals with the use of the Clarke transformation for the theoretical derivation of circuit models for the analysis of asymmetrical transients in three-phase circuits. Asymmetrical transients occur when only one or two phases of a three-phase power system are involved in a switch operation. Such a condition is critical from a theoretical viewpoint since the Clarke transformation is based on the assumption of circuit symmetry between the three phases. If the symmetry assumption is not met, the equivalent circuits in the transformed variables α, β, and 0 are not uncoupled. The literature concerning numerical approaches for asymmetrical transient analysis is very rich, but a comprehensive and rigorous analytical investigation of circuit models within the framework of the Clarke transformation is still lacking. Contrary to numerical approaches, analytical solutions provide deeper insight into the phenomenon and allow for theoretical interpretation and better understanding of the transient behavior. The proposed circuit models show that the β variables are always uncoupled with α and 0 variables, whereas coupling between α and 0 variables can be properly represented by an ideal transformer. Moreover, in the case of single-line switching, the β variables have no transient, i.e., they keep the steady-state behavior. Transient properties can be readily and effectively observed by representing the trajectory of the space vector on the complex plane. All the analytical results have been checked numerically through the Simulink (Matlab R2020a, The MathWorks, Inc., Natick, MA, USA) implementation of a specific three-phase circuit introduced to illustrate the main theoretical issues.
Highlights
Transformation methods for circuit analysis of three-phase power systems have a long and important history in electrical engineering
When three-phase power systems come into play, system matrices show a specific symmetrical structure originating from the common assumption of circuit symmetry between the three phases
As far as transient analysis of three-phase circuits is concerned, the Clarke transformation is the natural candidate since it operates in the time domain [10,11,12,13]
Summary
Transformation methods for circuit analysis of three-phase power systems have a long and important history in electrical engineering. As far as transient analysis of three-phase circuits is concerned, the Clarke transformation is the natural candidate since it operates in the time domain [10,11,12,13]. A general methodology for the analysis of three-phase symmetrical transients based on the Clarke transformation and the related concept of space vector has been recently published [14]. Asymmetrical transients originate from a switch operation of one or two phases in a specific section of a three-phase circuit. The proposed analytical approach provides theoretical insight into the comprehension of asymmetrical transients by explaining the role of each Clarke modal circuit in the determination of the time-domain phase variables.
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