Abstract
This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.
Highlights
For more than a century, the steady-state operation of AC electrical circuits has been analysed in the frequency domain using complex numbers
geometric algebra (GA) was applied in order to analyse and solve symmetric and balanced three-phase electrical circuits that operate under sinusoidal and non-sinusoidal conditions
The Argand diagram σ1-σ2 was used to depict vectors, while the scalar-bivector one was introduced in order to depict impedances/admittances and power components
Summary
For more than a century, the steady-state operation of AC electrical circuits has been analysed in the frequency domain using complex numbers. Castilla and Bravo [19,20] made improvements to former theories and presented an alternative formulation, called generalized complex geometric algebra This theory can be used to perform power calculations, but cannot solve electrical circuits in the GA domain. GA is applied to analyse and solve three-phase electrical circuits under sinusoidal and non-sinusoidal conditions This can be seen as a relevant improvement compared to previous theories based on GA that only addressed single-phase electrical systems. It is possible to define a new power concept based on geometrical principles that take the interaction of voltage and current harmonics of different frequency into account This is not possible using phasors based on complex algebra;. It establishes basic principles for the compensation of non-active current that allow for the optimisation of energy losses in power transmission lines
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