Geometric algebra: a multivectorial proof of Tellegen's theorem in multiterminal networks

Castilla, M.; Bravo, Juan Carlos; Ordóñez, Manuel

doi:10.1049/iet-cds:20070245

Cited by 25 publications

(19 citation statements)

References 5 publications

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“…Therefore, the total load current can be expressed as . Finally, if and then the total load current which equals the current through the supply source is (14) The values of and are therefore given by (15) …”

Section: A Generic Overview Of the Power Theorymentioning

confidence: 99%

Advantages of Geometric Algebra Over Complex Numbers in the Analysis of Networks With Nonsinusoidal Sources and Linear Loads

Castro-Núñez

Castro-Puche

2012

IEEE Trans. Circuits Syst. I

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An alternative circuit analysis technique is used to study networks with nonsinusoidal sources and linear loads. In contrast to the technique developed by Steinmetz, this method is supported by geometric algebra instead of the algebra of complex numbers, uses multivectors in place of phasors and is performed in the domain instead of the frequency domain. The advantages of this method over the present technique involve: determining the flow of current and power quantities in the circuit, validating the results using the principle of conservation of energy, discerning and revealing other forms of reactive power generation, and the ability to design compensators with great flexibility. The power equation is composed of the active power and the -power representing the nonactive power. All the -power terms are sorted into reactive power terms due to phase shift, reactive power terms due to harmonic interactions and degrading power terms which determine the new quantity called degrading power. This decomposition shows that estimating these quantities is intricate. It also displays the power equation's functionality for power factor improvement. The geometric addition of power quantities is not pre-established but results from applying the established norm and yields the new quantity called net apparent power.Index Terms-Compensator design, harmonics, power factor, power flow, reactive and apparent power.

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Section: A Generic Overview Of the Power Theorymentioning

confidence: 99%

Advantages of Geometric Algebra Over Complex Numbers in the Analysis of Networks With Nonsinusoidal Sources and Linear Loads

Castro-Núñez

Castro-Puche

2012

IEEE Trans. Circuits Syst. I

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“…Moreover, power formulas have been given first in Clifford frequency domain and then in time domain. Further, a non-active power multivector has been developed, which condenses all power information and obeys the usual conservation law [16]. In this sense, it bridges the gap between frequency domain and time domain.…”

Section: Discussionmentioning

confidence: 99%

Considerations on the non-active power using geometric algebra

Castilla

Bravo

Montañó³

et al. 2011

2011 International Conference on Power Engineering, Energy and Electrical Drives

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Abstract-Several approaches have been developed to define the non-active power concept under nonsinusoidal situations in electrical systems. Nevertheless, these contributions do not provide a complete and satisfactory solution to the non-active power reversibility between frequency domain and time domain. This paper presents a non-active power multivector concept, based on an original vector space frequency-domain approach that bridges the gap between both domains. The suggested correspondence can provide a convenient descriptive language to reconcile Fryze's instantaneous non-active power with Budeanu´s deactive-power. To clarify this correspondence, a basis example is considered. IndexTerms-Non-active power, apparent power, instantaneous power, multivector, geometric algebra.

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“…Despite the application of GA to circuit analysis and power theory has a very short history some relevant advances have been made in this area from different perspectives [27][28][29][30][31][32][33][34][35].…”

Section: The System Modelmentioning

confidence: 99%

Geometric Objects: A Quality Index to Electromagnetic Energy Transfer Performance in Sustainable Smart Buildings

Bravo

Castilla

2018

Symmetry

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Sustainable smart buildings play an essential role in terms of more efficient energy. However, these buildings as electric loads are affected by an important distortion in the current and voltage waveforms caused by the increasing proliferation of nonlinear electronic devices. Overall, buildings all around the world consume a significant amount of energy, which is about one-third of the total primary energy resources. Optimization of the power transfer process of such amount of energy is a crucial issue that needs specific tools to integrate energy-efficient behaviour throughout the grid. When nonlinear loads are present, new capable ways of thinking are needed to consider the effects of harmonics and related power components. In this manner, technology innovations are necessary to update the power factor concept to a generalized total or a true one, where different power components involved in it calculation, properly reflect each harmonic interaction. This work addresses an innovative theory that applies the Poynting Vector philosophy via Geometric Algebra to the electromagnetic energy transfer process providing a physical foundation. In this framework, it is possible to analyse and detect the nature of disturbing loads in the exponential growth of new globalized buildings and architectures in our era. This new insight is based on the concept of geometric objects with different dimension: vector, bivector, trivector, multivector. Within this paper, these objects are correlated with the electromagnetic quantities responsible for the energy flow supplied to the most common loads in sustainable smart buildings. Besides, it must be considered that these phenomena are characterized by a quality index multivector appropriate even for detecting harmonic sources. A numerical example is used to illustrate the clear capabilities of the suggested index when it applies to industrial loads for optimization of energy control systems and enhance comfort management in smart sustainable buildings.

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Geometric algebra: a multivectorial proof of Tellegen's theorem in multiterminal networks

Cited by 25 publications

References 5 publications

Advantages of Geometric Algebra Over Complex Numbers in the Analysis of Networks With Nonsinusoidal Sources and Linear Loads

Advantages of Geometric Algebra Over Complex Numbers in the Analysis of Networks With Nonsinusoidal Sources and Linear Loads

Considerations on the non-active power using geometric algebra

Geometric Objects: A Quality Index to Electromagnetic Energy Transfer Performance in Sustainable Smart Buildings

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