Emanuel's method versus Iliovici's method for reactive power compensation in passive-active power conditioning scheme

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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“…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%

“…Equation (43) is equal to (37). Hence, also in this case, the SP is nil, as a soft switching is performed; instead, an equivalent area is absorbed by the inductor, irrespective of the value of the inductance.…”

Section: Discontinuity and Modelmentioning

confidence: 99%

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

Barcellona

Superti-Furga

2015

Circuit Theory & Apps

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“…Based on the described values of the supply voltage and the load parameters, Table 2 lists the equivalent values of the load parameters, described by the dependencies (4), (6), and (26). As a result of applying a voltage to the load terminals, the currents of individual harmonics and powers of the active (14) and reactive (15) for harmonics have been obtained. All the obtained results, increased by the RMS values or the sum, are listed in Table 3.…”

Section: Theoretical Illustrationmentioning

confidence: 99%

“…The reason for this, in addition to answering question (b), is a more significant restriction of the formula of reactive power (14) than what Czarnecki showed in [7]. Apart from the possibility of subtracting the reactive power of individual harmonics [2,7] (capacitive or inductive character), the formula for the reactive power of harmonics is not an arithmetic sum, but a weighted sum, which makes it possible to use the relationship (14) only in the area of a given harmonic and on the basis of the defined parameter; for the equivalent load, calculate the value of the reactive current as Czarnecki does in his approach. Otherwise, the apparent power resulting from the product of voltage and current of the load is always higher than the sum of reactive powers:…”

Section: Theoretical Illustrationmentioning

confidence: 99%

“…Over the years, countless scientists have attempted to describe the components of the Budeanu theory [5,[11][12][13]. The change in the description of the Budeanu theory was and is intended to improve the value of the power factor [5,11,12,14,15]. Additionally, single-phase systems are currently used to supply wireless power transmission (WPT) 2 of 18 devices [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Extension and Correction of Budeanu Power Theory Based on Currents’ Physical Components (CPC) Theory for Single-Phase Systems

Soljan

Zajkowski

2022

Energies

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In 1927, the most recognized power theory in the frequency domain was proposed by Budeanu. The second power theory in the frequency domain, which is currently catching a lot of supporters, is the approach proposed by Czarnecki. Both theories have common features in the form of the description of active power and are completely different in terms of the description and interpretation of reactive power. This article presents the possibility of using mutual elements of both approaches: thus, it is possible to interpret the physical meaning of the reactive power (reactive current) proposed by Budeanu and the power before the deformation obtained from the mathematical description.

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