Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits
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....
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/13/19/5231 |
| _version_ | 1797551552544636928 |
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| author | Diego Bellan |
| author_facet | Diego Bellan |
| author_sort | Diego Bellan |
| collection | DOAJ |
| description | 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 <i>α</i>, <i>β</i>, 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 <i>β</i> variables are always uncoupled with <i>α</i> and 0 variables, whereas coupling between <i>α</i> and 0 variables can be properly represented by an ideal transformer. Moreover, in the case of single-line switching, the <i>β</i> 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. |
| first_indexed | 2024-03-10T15:46:39Z |
| format | Article |
| id | doaj.art-51f21b5974224d2ebce88ad1eccf4be1 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T15:46:39Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-51f21b5974224d2ebce88ad1eccf4be12023-11-20T16:22:38ZengMDPI AGEnergies1996-10732020-10-011319523110.3390/en13195231Clarke Transformation Solution of Asymmetrical Transients in Three-Phase CircuitsDiego Bellan0Department of Electronics, Information and Bioengineering, Politecnico di Milano, 20133 Milan, ItalyThis 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 <i>α</i>, <i>β</i>, 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 <i>β</i> variables are always uncoupled with <i>α</i> and 0 variables, whereas coupling between <i>α</i> and 0 variables can be properly represented by an ideal transformer. Moreover, in the case of single-line switching, the <i>β</i> 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.https://www.mdpi.com/1996-1073/13/19/5231analytical methodsasymmetrical three-phase transientsClarke transformationspace vector representationtime-domain analysis |
| spellingShingle | Diego Bellan Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits Energies analytical methods asymmetrical three-phase transients Clarke transformation space vector representation time-domain analysis |
| title | Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits |
| title_full | Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits |
| title_fullStr | Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits |
| title_full_unstemmed | Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits |
| title_short | Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits |
| title_sort | clarke transformation solution of asymmetrical transients in three phase circuits |
| topic | analytical methods asymmetrical three-phase transients Clarke transformation space vector representation time-domain analysis |
| url | https://www.mdpi.com/1996-1073/13/19/5231 |
| work_keys_str_mv | AT diegobellan clarketransformationsolutionofasymmetricaltransientsinthreephasecircuits |