Abstract
Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. Using the framework based on complex algebra in non-sinusoidal circuit analysis (frequency domain), the verification of the energy conservation law is only possible in sinusoidal situations. In this case, reactive energy turns out to be proportional to the energy difference between the average electric and magnetic energies stored in the loads and its cancellation is mathematically trivial. However, in industrial architecture, apparent power definition of electric loads (non-sinusoidal conditions) is inconsistent with the energy conservation law. Up until now, in the classical complex algebra approach, this goal is only valid in the case of purely resistive loads. Thus, in this paper, a new circuit analysis approach using geometric algebra is used to develop the most general proof of energy conservation in industrial building loads. In terms of geometric objects, this powerful tool calculates the voltage, current, and apparent power in electrical systems in non-sinusoidal, linear/nonlinear situations. In contrast to the traditional method developed by Steinmetz, the suggested powerful tool extends the concept of phasor to multivector-phasors and is performed in a new Generalized Complex Geometric Algebra structure (CGn), where Gn is the Clifford algebra in n-dimensional real space and C is the complex vector space. To conclude, a numerical example illustrates the clear advantages of the approach suggested in this paper.
Highlights
Most of the harmonic problems affecting electrical distribution networks in industrial architecture are generated within the building
This is partly due to the proliferation of linear and nonlinear loads connected to the circuits in the building; air conditioning, computers, CCTV, servers, adjustable speed drive (ASD), and other electronic equipment, are the main sources of problems
The quickest way to approach the construction of geometric algebra (GA) is through its familiarity with the concept of vector space Vn spanned by orthonormal basis vectors {σ1, σ2, σ3 ...σn }
Summary
Most of the harmonic problems affecting electrical distribution networks in industrial architecture are generated within the building. The correct answer is based on the fact that, in sinusoidal conditions and with linear and/or nonlinear loads, the traditional apparent power definition is erratic, except for resistive loads This is a direct consequence of having only magnitudes for currents and voltages in a circuit branch instead of an expression composed by signed quantities; with this limitation, network analysis involving all the harmonics simultaneously cannot even be performed. In contrast to classical versions, our representation of apparent power considers the net flow of all the power components representing source–load interactions This new vector space seems suitable for developing a theory more useful to generalize and to interpret energy conservation in the linear/nonlinear loads of industrial buildings, and to solve the problem of quantification of losses in the complex case of industrial architecture
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