The Use of Geometric Algebra in the Analysis of Non-sinusoidal Networks and the Construction of a Unified Power Theory for Single Phase Systems - A Paradigm Shift

Simple item page
atmire.migration.oldid1463
dc.contributor.advisorNowicki, Edwin
dc.contributor.authorCastro-Núñez, Milton
dc.date.accessioned2013-09-24T23:54:55Z
dc.date.available2013-11-12T08:00:18Z
dc.date.issued2013-09-24
dc.date.submitted2013en
dc.description.abstractThe electrical engineering scientific community since 1892 is seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. The proliferation of power electronic devices in electrical systems provides added motivation to find such a theory. Some examples of the effort regarding power definitions and measurements under non-sinusoidal conditions include four international workshops, an IEEE working group and a biannual international conference. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. In contrast to previous investigations, it is suggested here that the framework based on complex number representations in non-sinusoidal circuit analysis may in fact hamper energy flow analysis. Thus, a new circuit analysis approach is developed using geometric algebra. In a new domain – coined as the GN domain – multivectors describe circuit and power quantities, circuit quantities obey Kirchhoff’s circuit laws, it is possible to apply the superposition principle and a better sense of the flow of currents and powers in the examined circuits is shown. The power multivector results from the geometric product of the voltage and current multivectors. The power multivector allows a decomposition that accounts for the total active and non-active power, involves the well-known power terms of the sinusoidal case – reactive and active average power – and two new terms: degrading power and reactive power due to harmonic interactions. Also, the power multivector satisfies both: the principle of conservation of energy and the balance principle of reactive power. The proposed GN domain power theory is able to: 1) reveal flaws in other power theories, 2) undermines the concept that the number of reactive elements required to achieve a near unity power factor is dependent on the number of harmonics in the excitation source, and 3) shows that the traditional non-sinusoidal apparent power definition needs to be revised. Presently, no power theory has these features all together.en_US
dc.identifier.citationCastro-Núñez, M. (2013). The Use of Geometric Algebra in the Analysis of Non-sinusoidal Networks and the Construction of a Unified Power Theory for Single Phase Systems - A Paradigm Shift (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/28411en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/28411
dc.identifier.urihttp://hdl.handle.net/11023/1037
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectElectronics and Electrical
dc.subject.classificationpower theoryen_US
dc.subject.classificationpower flowen_US
dc.subject.classificationnon-sinusoidal circuit analysisen_US
dc.subject.classificationgeometric algebraen_US
dc.subject.classificationreactive poweren_US
dc.subject.classificationnon-sinusoidal apparent poweren_US
dc.subject.classificationharmonicsen_US
dc.subject.classificationpower factoren_US
dc.subject.classificationpower measurementen_US
dc.subject.classificationreactive power compensationen_US
dc.subject.classificationcurrents physical components (CPC) power theoryen_US
dc.subject.classificationnon-active poweren_US
dc.subject.classificationIEEE standard 1459en_US
dc.titleThe Use of Geometric Algebra in the Analysis of Non-sinusoidal Networks and the Construction of a Unified Power Theory for Single Phase Systems - A Paradigm Shift
dc.typedoctoral thesis
thesis.degree.disciplineElectrical and Computer Engineering
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
Files
Original bundle
Now showing 1 - 2 of 2
Thumbnail Image
Name:
ucalgary_2013_Castro-Nunez_Milton.pdf
Size:
2.56 MB
Format:
Adobe Portable Document Format
Description:
Main document (theses)
Download
Thumbnail Image
Name:
ucalgary_2013_Castro-Nunez_Milton_Figures.zip
Size:
1.7 MB
Format:
Zip files based on Chrome
Description:
Theses Figures
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
2.65 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Open Theses and Dissertations