The integral method to calculate the power states in electrical circuits

Hartman, M.

doi:10.1109/cpe.2009.5156032

Cited by 3 publications

(7 citation statements)

References 8 publications

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“…In particular, the form proposed in [36] appears as (19). In addition, both [34,36] recognize the representativeness on the v-i plane.…”

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

“…Recently, the idea in [33] has been discussed and proposed again in [36,37]. In particular, the form proposed in [36] appears as (19).…”

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

“…Recently, the idea in [33] has been discussed and proposed again in [36,37]. In particular, the form proposed in [36] appears as (19). In addition, both [34,36] recognize the representativeness on the v-i plane.…”

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

“…Equation (40) is equal to (36). Hence, it is possible to claim that the SP is in this case nil, as a soft switching is performed; instead, an area equivalent to the missing SP is generated by the capacitor.…”

Section: Discontinuity and Modelmentioning

confidence: 99%

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Swept area theory: an approach in nonlinear and switched network analysis

Barcellona

Superti-Furga

2015

Circuit Theory & Apps

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In this work, according to the concept of 'area' on the v-i plane, a new approach called swept area theory, under both nonlinear continuous and discontinuous conditions, is developed. Novel conservative functions, such as area velocity and closed area over time (CAT), involved in this theory, are proposed. An analysis is carried out, by means of these functions, over nonlinear R, L, and C elements and over the ideal switch. In addition, jump discontinuities are discussed in detail. The CAT is related to the harmonic reactive powers and under sinusoidal steady state becomes proportional to the classical reactive power. A balance rule concerning harmonic reactive powers over nonlinear resistor under continuous conditions is obtained and discussed as a novel interesting result. This aspect impacts on a possible expanded definition of reactive power under distorted conditions. Thanks to the switching power, a novel quantitative relation between hard-switching commutations and CAT is obtained, with both theoretical and applicative relevance. More explanation is presented through a demonstration that shows how an ideal switch and power converters can become sources of reactive power. Issues of principle regarding the ideal switch model with respect to the real one are another important result of this work.So far, only time-invariant nonlinear networks have been dealt with, whereas time-variant networks are usually considered by means of switches. The general problem and solution methods of switched networks are presented in [19][20][21][22][23]. Classical issues in the presence of switching are network solution and inconsistent initial conditions. Network solution (with related problems of uniqueness of solution and stability) is fulfilled by several methods, of which one of the main is the complementarity approach, where switching is basically external constraint to a time-invariant multiport [24]. Inconsistent initial conditions, caused by switching, imply discontinuities on state variables and impulsive behavior on some voltages or currents, as addressed in depth in [25,26]. Nevertheless, as a whole, it appears to lack general principles as well as applications of generalized power in the field of switched networks; a notable exception is the 'connection energy' [27].Another important aspect that appeared previously is the 'area' on the v-i plane. From this idea in [28], a conservative function was proposed, called 'mean generalized content' (MGC), which is balanced and under periodical continuous steady-state conditions is invariant on nonlinear resistors. Therefore, the MGC could be seen as a generalization of the reactive power in distorted conditions [29]. In [30], the MGC was extended to circuits with ideal switches. In that paper, the definition of switching power (SP) was introduced, and a relationship between switching and reactive power was outlined.Following the aforementioned area approach, this paper intends to develop the swept area theory (SAT), which widely uses the concepts of trajectory and area on ...

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“…In particular, the form proposed in [36] appears as (19). In addition, both [34,36] recognize the representativeness on the v-i plane.…”

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

“…Recently, the idea in [33] has been discussed and proposed again in [36,37]. In particular, the form proposed in [36] appears as (19).…”

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

Section: Matching With Some Results Presented In Literaturementioning

confidence: 99%

Section: Discontinuity and Modelmentioning

confidence: 99%

See 2 more Smart Citations

Swept area theory: an approach in nonlinear and switched network analysis

Barcellona

Superti-Furga

2015

Circuit Theory & Apps

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“…Thus, within the area of the power theory in a single‐phase circuit, we have at present the following propositions:Depenbrock's concept distinguishing a basic harmonic and some others in nonsinusoidal waveforms; on this distinction the definition of power was based. This concept is contained in the latest IEEE Std 1459 (2010);the concept proposed by Czarnecki (2008), called current's physical components (CPC), which constitutes the original development of the concept proposed by Fryze (1932, 1966) as well as Shepherd and Zakikhani (1972); andthe concept proposed by Tenti and Mattavelli, called conservative power theory (CPT) (Tenti et al , 2010) which is the original development of the concept of Fryze and Iliovici (Hartman, 2010; Iliovici, 1925). The aim of the author is to show the properties of Czarnecki's concept, especially to emphasize its limitation in elimination of scattered current in single‐phase circuits with nonsinusoidal voltage and current waveforms and reactive linear load, time invariant (LTI).…”

Section: Introductionmentioning

confidence: 99%

Reflections on current components according to CPC concept in a single phase circuit with nonsinusoidal voltage and current waveforms and LTI load

Hartman

2012

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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PurposeThe purpose of this paper is to show the limitation of current physical components (CPC) concept in a practical application.Design/methodology/approachThe study proposes using the sum of active and scattered currents in the compensation procedure of the reactive current according to Czarnecki's concept as well as in scattered current elimination, to get the optimal energy transfer from the source supply to the load.FindingsThe results show that CPC concept can be apply only when supply circuit voltage does not consist of interharmonics or/and subharmonics. It can also be shown that elimination of particular harmonics of the scatter current cannot be applied in practice due to the change of active power in the circuit. Only complete elimination of scatter current, e.g. by an active filter is possible without any change of active power.Practical implicationsThe paper provides new information about CPC practical implementation.Originality/valueThis paper presents new features of CPC concept.

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Reflections on current components according to CPC concept in a single phase circuit with nonsinusoidal voltage and current waveforms and LTI load

Hartman

2011

2011 7th International Conference-Workshop Compatibility and Power Electronics (CPE)

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The integral method to calculate the power states in electrical circuits

Cited by 3 publications

References 8 publications

Swept area theory: an approach in nonlinear and switched network analysis

Swept area theory: an approach in nonlinear and switched network analysis

Reflections on current components according to CPC concept in a single phase circuit with nonsinusoidal voltage and current waveforms and LTI load

Reflections on current components according to CPC concept in a single phase circuit with nonsinusoidal voltage and current waveforms and LTI load

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