Theorems of compensation and Tellegen in non‐sinusoidal circuits via geometric algebra

Castro-Núñez, Milton; Londoño-Monsalve, Deysy; Castro-Puche, Róbinson

doi:10.1049/joe.2019.0048

Cited by 9 publications

(9 citation statements)

References 29 publications

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“…• Castro-N ú ñez. This theory was developed by Castro Núñez in the year 2010 [18], and then extended and refined in several later works [5,15,19,20]. A relevant contribution of this work consists on the resolution of electrical circuits by using GA (without requiring complex numbers).…”

Section: Geometric Algebra For Power Flow Analysismentioning

confidence: 99%

“…A relevant contribution of this work consists on the resolution of electrical circuits by using GA (without requiring complex numbers). Also, a multivector called geometric apparent power that is conservative and fulfils the Tellegen theorem is defined [20]. As in Menti and Castilla-Bravo proposals, the results are presented only for single-phase systems.…”

Section: Geometric Algebra For Power Flow Analysismentioning

confidence: 99%

“…This feature cannot be applied in other power theories based on GA since, in general, A † = A for any k-vector A with k > 1 [18]. In (20), several terms of engineering interest can be identified. On the one hand, the scalar term M 0 = u•i matches the active power P , and it will be called active geometric power, or M a .…”

Section: B Power Flow In Gamentioning

confidence: 99%

“…In this section, the current consumed by a load is decomposed by using the proposed power theory. Simplifying (20) and taking into account that for any vector a −1 = a/ a 2 :…”

Section: Current Decomposition In Gamentioning

confidence: 99%

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Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

et al. 2021

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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.

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Section: Geometric Algebra For Power Flow Analysismentioning

confidence: 99%

Section: Geometric Algebra For Power Flow Analysismentioning

confidence: 99%

Section: B Power Flow In Gamentioning

confidence: 99%

“…In this section, the current consumed by a load is decomposed by using the proposed power theory. Simplifying (20) and taking into account that for any vector a −1 = a/ a 2 :…”

Section: Current Decomposition In Gamentioning

confidence: 99%

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Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

et al. 2021

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“…As explained in previous studies [62], [63], [177], GA applied to sinusoidal, non-sinusoidal, linear, and nonlinear circuits is a promising technique to describe the power flow in terms of the energy conservation principle. The decomposition of the current into in-phase and quadrature components I = I c + a has contributed to the development of methods for quadrature RMS current compensation [65]. However, Montoya et al [178] found inconsistencies in the power formulation and reformulated the power theory based on GA (GAPoT) to correct such inconsistencies and shortcomings and define the total current through a decomposition considering the active current suggested by Fryze.…”

Section: B Electrical Engineeringmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

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Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.INDEX TERMS Geometric algebra, Clifford algebra, quaternion algebra, screw theory, signal processing, electrical engineering and power systems, geometric and quantum computing, image processing, computer vision, graphic engineering, artificial intelligence, machine learning, neural networks, control engineering, robotics, biomedical engineering, and biotechnology.

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Current survey of Clifford geometric algebra applications

Hitzer

Hildenbrand

2022

Math Methods in App Sciences

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Theorems of compensation and Tellegen in non‐sinusoidal circuits via geometric algebra

Cited by 9 publications

References 29 publications

Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Current survey of Clifford geometric algebra applications

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