Electrical three phase circuit analysis using quaternions

Brasil, Victor do Prado; Filho, Anesio de Leles Ferreira; Ishihara, J.Y.

doi:10.1109/ichqp.2018.8378813

Cited by 11 publications

(7 citation statements)

References 16 publications

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“…In this paper, we extend the previous work of [10] for quaternion power analysis, highlighting the relation between power and load. In [10], the quaternionic power for a load was described in terms of quaternionic impedance but only for a balanced load in Y configuration. Here, we study the quaternionic power for a general (balanced and unbalanced) load in ∆ configuration.…”

Section: Introductionsupporting

confidence: 56%

“…Using these definitions, in [10] a three-phase series RLC balanced circuit is analysed and the power quaternion for the Y load is obtained.…”

Section: E Inversementioning

confidence: 99%

“…The authors of [9] analyze a single-phase RLC circuit. In [10], it is pointed out that quaternion characterization of three-phase quantities serves as a link between the usual time and frequency domains. More specifically, with quaternions, it is possible to define three-phase electrical quantities analogously to singlephase's with phasors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Three-phase Quaternion Power in Three-wire Systems

Komeno¹,

Filho²,

Ishihara³

et al. 2024

RE&PQJ

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Instantaneous power theory has a central role in power systems analysis. Among mathematical settings used for the development of this theory, quaternion algebra has been used for describing electrical variables in recent works. In this context, this paper aims to describe three-phase power in a quaternion framework. We analyze quaternion power for balanced and unbalanced delta loads, comparing the expressions obtained to the usual expressions of complex power. The quaternion power expression obtained also makes it natural to introduce a decomposition of the unbalanced load in terms of a balanced component and an unbalanced load with null average power. It is also shown that delta unbalanced loads are equivalent to time-varying balanced loads. The results obtained extend the power systems theory in the quaternion domain and emphasize the advantages of using this framework.

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Section: Introductionsupporting

confidence: 56%

“…Using these definitions, in [10] a three-phase series RLC balanced circuit is analysed and the power quaternion for the Y load is obtained.…”

Section: E Inversementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Three-phase Quaternion Power in Three-wire Systems

Komeno¹,

Filho²,

Ishihara³

et al. 2024

RE&PQJ

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“…Fully capturing the evolution of state vector estimation error terms requires close scrutiny of the ACF impact on state vector estimation errors. This is achieved through formulating (38) in a network-wide format as (39) where {P n ,Q n ,G n } are the block-diagonal matrices…”

Section: Proof Of Propositionmentioning

confidence: 99%

“…Impact of the ACF on state vector estimation error terms can now be rigorously formulated using the expressions in (22) and (39) culminating in the network-wide regressive expression for state vector estimation error given by…”

Section: Proof Of Propositionmentioning

confidence: 99%

Quaternion-Valued Distributed Filtering and Control

Talebi

Werner

Mandic

2020

IEEE Trans. Automat. Contr.

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This work presents a unified framework for filtering and control of quaternion-valued state vector processes through multi-agent networked systems. To achieve this goal, the filtering problem in sensor networks is revisited, where a distributed Kalman filtering algorithm for filtering/tracking quaternionvalued state vector processes is developed. The distributed quaternion Kalman filter is formulated to mirror the operations of an optimal centralized approach in a fashion that will allow each agent to retain a Kalman style filtering operation and an intermediate estimate of the state vector. The work includes a comprehensive performance analysis of the developed distributed quaternion Kalman filtering algorithm, resulting in a closedform expression for the second-order error moment. More importantly, due to the comprehensive framework for fusion of the covariance information and drawing upon concepts from the conducted performance analysis, a duality between the developed distributed Kalman filter and decentralized control is established. This essentially extends the duality between Kalman filtering and linear quadrature regulators to the quaternion domain and distributed setting. The theoretical concepts in this work are verified via simulations. Index Terms-Qauternion-valued filtering and control, sensor networks, distributed Kalman filtering, decentralized control.

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