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For a long time, non-sinusoidal, non-linear electric circuit analysis has been a prevalent topic. The supplementary analysis tool and domain are subjects of debate in many scientific groups, leading to a range of norms and definitions. Since its beginnings, the electric power system has advanced thanks to the development of Power Electronic devices, converters, and Renewable Energy sources. Electronic equipment has transformed the electrical system and brought industrial applications a plethora of benefits. Unfortunately, this results in distortions in the power system (voltage and current). For this, it is necessary to comprehend power flow in nonsinusoidal linear and non-linear circuit situations. Therefore, it is always necessary to use a distinct mathematical framework to examine the circuit in such a setting. Finally, an agreement on norms that adhere to well-known, established standards can be obtained under non-sinusoidal circumstances. To show the precision of geometric algebra in power flow calculations, the work presented here combines the usage of the harmonic domain and geometric algebra in circuits with disturbances for sinusoidal and non-sinusoidal excitation. [ABSTRACT FROM AUTHOR]

This paper proposes a systematic method for the identification of the load circuit parameters (say the $\boldsymbol{R}$ , $\boldsymbol{L}$ , and $\boldsymbol{C}$ elements) based only on the information of the instantaneous voltage and current measured at the point of common coupling (pcc). Geometric Algebra (GA) and concepts of differential geometry are used to produce a rigorous mathematical framework. The identification is formulated as a multidimensional geometrical problem that is solved conveniently by means of GA. Once the passive elements of the load have been identified, the active and reactive powers can be computed from first electromagnetic principles (Maxwell Equations). The theory is general and is verified with linear and nonlinear circuits. The paper shows single-phase circuits but the theory can be extended to three-phase circuits. The method is easy to program and has shown to be very robust for all tested cases. Because of its generality, the method presented will find applications beyond electric circuits. [ABSTRACT FROM AUTHOR]

In this paper, power flows in electrical circuits are modelled in a mixed time-frequency domain by using geometric algebra and the Hilbert transform for the first time. The use of this mathematical framework overcomes some of the limitations of some of the existing methodologies, in which the so-called "active current" may not lead to the lowest Root Mean Square (RMS) current under distorted supply or unbalanced load. Moreover, this current may contain higher levels of harmonic distortion compared to the supply voltage. The proposed method can be used for sinusoidal and non-sinusoidal power supplies, non-linear loads and single- and multi-phase electrical circuits, and it provides meaningful engineering results with a compact formulation. It can also serve as an advanced tool for developing algorithms in the power electronics field. Several examples have been included to verify the validity of the proposed theory. [ABSTRACT FROM AUTHOR]

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]