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
Date
2013-09-24
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Abstract
The 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.
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Electronics and Electrical
Citation
Castro-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/28411