Geometric Algebra, the Key Tool to Unveil Why Non-Sinusoidal Power Theories Fail

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

doi:10.1109/iceccme52200.2021.9590900

Cited by 3 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the GA framework, it is well known that it is possible to define a multiplication rule between both vectors, called geometric products. The geometric products of vectors u and i have been used extensively in technical studies to identify different power terms, [22]- [26]. The instantaneous power multivector is defined as…”

Section: Instantaneous Power Multivector / Instantaneous Current Comp...mentioning

confidence: 99%

“…In (26) pαβ is the so-named instantaneous power in the αβ plane, and qαβ is the instantaneous imaginary power in the αβ plane that constitutes the only component of the instantaneous reactive power bivector. Similarly, the zerosequence instantaneous power multivector is defined as…”

Section: E V E I E I E I E I Ementioning

confidence: 99%

“…In the same line, [25], represents the harmonics of the signal by k-vectors which are used to process the rms, phase angle, and pulsation of a sine wave. In [26], the same authors applied their proposed method to unveil the power phenomena under non-sinusoidal conditions. This approach, although original, suffers from the same limitations as in [24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of a Multidimensional Approach in the Compensation of Industrial Loads

Salmerón,

Pérez-Vallés,

Flores-Garrido

et al. 2024

IEEE Access

View full text Add to dashboard Cite

The instantaneous reactive power theory (IRPT) has long been utilized for load compensation through active power line conditioners (APLCs). IRPT effectively divides the current vector into two components: the instantaneous power current and the instantaneous reactive current. Among these components, only the former is necessary to transfer instantaneous real power to the load. However, the commonly adopted approach faces challenges when extended to multi-phase systems and their compensation strategy design. This challenge is particularly pertinent today due to the consensus that treating a three-phase system with a neutral wire as a four-conductor system is more appropriate. This paper introduces a formulation of IRPT tailored for multi-phase systems within the framework of geometric algebra (GA). GA is a mathematical structure that defines a single power variable, the instantaneous power multivector, encompassing both instantaneous real power and instantaneous reactive power within a unified mathematical entity. The current components can be directly derived from this power multivector. Additionally, this paper establishes a connection with the original p-q formulations and lays the foundations for time-instantaneous compensation (TIC) and time-average compensation (TAC). Finally, to validate the proposed model, simulation and experimental results from a three-phase four-wire industrial system using a novel approach are presented.INDEX TERMS Geometric algebra, instantaneous power multivector, instantaneous reactive power theory, multi-phase systems; load compensation.

show abstract

Section: Instantaneous Power Multivector / Instantaneous Current Comp...mentioning

confidence: 99%

Section: E V E I E I E I E I Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of a Multidimensional Approach in the Compensation of Industrial Loads

Salmerón,

Pérez-Vallés,

Flores-Garrido

et al. 2024

IEEE Access

View full text Add to dashboard Cite

show abstract

“…In both cases, an identification of the power terms collected in the frequency theories adopted up to that moment is achieved. In the same field, the works [19][20][21] can be considered, which reformulate circuit laws and electrical power within the framework of GA in an original way. However, none of these latter proposals support an extension to systems with more than one phase, which requires a new review of the matter.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous Reactive Power Theory in the Geometric Algebra Framework

2023

View full text Add to dashboard Cite

In this paper, a new approach for instantaneous reactive power analysis in the geometric algebra (GA) environment is presented. The different formulations of the instantaneous reactive power theory (IRPT) proposed, to date, have been developed in three-phase systems. There, an instantaneous power variable, and two/three reactive power variables, all handled independently, were introduced. Thanks to GA, it is possible to carry out a global treatment where an instantaneous power multivector is defined. Thus, in the same multidimensional entity all the power variables are included. From the instantaneous power multivector, the instantaneous power current and the instantaneous reactive current are determined. It should be noted that in this mathematical framework there is no limitation on the number of phases, and the extension of the IRPT to the analysis of multi-phase systems appears in a natural manner. In this study, a systematic approach with the most relevant definitions and theorems corresponding to the proposed methodology has been established. Two practical cases of five-phase and three-phase systems have been included to apply the new established formulation.

show abstract

M, The Power Definition in Geometric Algebra that Unveils the Shortcomings of the Nonsinusoidal Apparent Power S

Castro-Núñez

Londoño-Monsalve

Castro-Puche

2022

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

Geometric Algebra, the Key Tool to Unveil Why Non-Sinusoidal Power Theories Fail

Cited by 3 publications

References 20 publications

Application of a Multidimensional Approach in the Compensation of Industrial Loads

Application of a Multidimensional Approach in the Compensation of Industrial Loads

Instantaneous Reactive Power Theory in the Geometric Algebra Framework

M, The Power Definition in Geometric Algebra that Unveils the Shortcomings of the Nonsinusoidal Apparent Power S

Contact Info

Product

Resources

About