# Vasile Mircea POPA

## 34-6 PIERDERILE PE LINIA DE ALIMENTARE A UNUI CONSUMATOR TRIFAZAT LEGAT ÎN TRIUNGHI

THE SUPPLY LINE LOSS OF A THREE-PHASE LOAD IN DELTA CONNECTION
The electrical power system usually operated in a symmetrical three-phase steady state mode. But, there are certain situations that can cause non-symmetrical operations. The presence of the unbalanced three-phased loads induce the apparition of the non-symmetrical systems involving currents and voltages as well the extra-loss within the supply wire. In this work we present a mathematical proof in Mathcad of additional losses in the electrical energy transmission line working under non-symmetrical conditions. Was considered a simplified model in delta connection, but the obtained result generalizes to complex electrical circuits. Finally, we show the conclusions and references.
Keywords: three-phase load, delta connection, active power, electrical energy transmission line, supply line loss, unbalanced functioning regime, mathematical proof in the Mathcad of additional losses under unbalanced conditions
Cuvinte cheie: receptor trifazat, conexiune în triunghi, putere activă, linie de transport a energiei electrice, pierderi pe linia de alimentare, regim dezechilibrat de funcţionare, demonstraţie matematică în mediul Mathcad a pierderilor suplimentare în regim dezechilibrat

Descarcare text

## THE SUPPLY LINE LOSS OF A  THREE-PHASE LOAD IN STAR CONNECTION

The electrical power system usually operated in a symmetrical three-phase steady state mode. But, there are certain situations that can cause non-symmetrical operations. The presence of the unbalanced three-phased loads induce the apparition of  the non-symmetrical systems involving currents and voltages as well the extra-loss within the supply wire. In this work we present a mathematical proof in Mathcad of additional losses in the electrical energy transmission line working under non-symmetrical conditions. Was considered a simplified model in star connection, but the obtained result generalizes to complex electrical circuits. Finally, we  show the conclusions and references.

Keywords: three-phase load, star connection, active power, electrical energy transmission line, supply line loss, unbalanced functioning regime, mathematical proof in the Mathcad of additional losses under unbalanced conditions

Cuvinte cheie: receptor trifazat, conexiune în stea, putere activă, linie de transport a energiei electrice, pierderi pe linia de alimentare, regim dezechilibrat de funcţionare, demonstraţie matematică în mediul Mathcad a pierderilor suplimentare în regim dezechilibrat

Descărcare text

## 29-52 ASPECTE PRIVIND PIERDERILE PE LINIA DE ALIMENTARE A UNUI CONSUMATOR TRIFAZAT DEZECHILIBRAT

ASPECTS REGARDING THE SUPPLY LINE LOSS OF A
The electrical power system normally operated in a symmetrical threephase
steady state mode. However, there are certain situations that can cause
non-symmetrical operations. The presence of the unbalanced three-phased
loads determines the apparition of the non-symmetrical systems involving
currents and voltages as well the extra-loss within the supply wire. In this paper
we present a mathematical proof in Mathcad of additional losses in the electrical
energy transmission line working under non-symmetrical conditions. Was
considered a simplified model, but the obtained result generalizes to complex
electrical circuits. Finally, we draw the conclusions and we indicate the
references.
Keywords: receiver phase, active power, symmetric components,
power transmission line, power line losses, unbalanced mode of operation
mathematical proof of additional losses under unbalanced
Cuvinte cheie: receptor trifazat, putere activă, componente simetrice,
linie de transport a energiei electrice, pierderi pe linia de alimentare, regim
dezechilibrat de funcţionare, demonstraţie matematică a pierderilor
suplimentare în regim dezechilibrat

Descărcare text

## 27-42 O PRIVIRE MATEMATICĂ ASUPRA PIERDERILOR PE LINIA DE TRANSPORT ÎN REGIM DEFORMANT

A MATHEMATICAL APPROACH TO THE LOSSES OF TRANSMISSION LINE UNDER NON-SINUSOIDAL REGIME
In this paper we present a mathematical proof of additional losses in the electrical energy transmission line due to superior harmonics. The proof is based on the Cauchy – Buniakovski – Schwarz inequality, a very important inequality in mathematics. Was considered a simplified model, but the obtained result generalizes to complex electrical circuits. At the beginning of the paper there was a more general overwiev of the issue of technological losses in power transmission line. Finally, we draw the conclusions and we indicate the references.
Keywords: electricity transmission line, transmission line losses, deforming operating system, mathematical proof of additional losses under deforming
Cuvinte cheie: linie de transport a energiei electrice, pierderi pe linia de transport, regim deformant de funcţionare, demonstraţie matematică a pierderilor suplimentare în regim deformant

Descarcare text

## 25-51 ANALIZA PUTERILOR COMPLEXE ALE UNUI RECEPTOR TRIFAZAT

THE COMPLEX POWERS ANALYSIS OF A THREE-PHASE
This paper presents the real unbalanced load and the powers
absorbed by it. It is considered the impedances with negative real part, in other
words generalized impedances. Also, taking into consideration the calculation
symmetrical components of impedances, a three-phase impedance system may
be divided into two parts: a balanced part and an unbalanced part. Afterwards,
the complex powers absorbed are calculated for the direct, inverse and
homopolar sequences. Then the diagram of the complex powers is deduced for
the real unbalanced load and are presented the conclusions. The bibliography
can be found at the end of the paper.
Keywords: three-phase, power complex receiver, generalized
impedance, symmetrical components, calculation of symmetrical components
Attenuation, the powers
Cuvinte cheie: receptor trifazat, putere complexă, impedanţă
generalizată, componente simetrice, componente simetrice de calcul ale
impedanţelor, diagrama puterilor
Descarcare text

## 25-50 ANALIZA PUTERILOR ACTIVE ALE UNUI RECEPTOR TRIFAZAT

THE ACTIVE POWERS ANALYSIS OF A THREE-PHASE LOAD
In this paper we consider a three-phase load and the absorbed powers
by it. We define the real unbalanced load, which has a balanced part and an
extremely unbalanced part. Using the complex power absorbed by the threephase
load, we make the actiwe powers analysis of it. Also, we construct the
energetical diagrams about the active powers circulation and are presented the
conclusions. In the end of the paper we indicate the references.
Keywords: three-phase, power complex receiver, active power,
generalized symmetrical components, impedance, calculation of symmetrical
components Attenuation, energy diagrams
Cuvinte cheie: receptor trifazat, putere complexă, putere activă,
impedanţă generalizată, componente simetrice, componente simetrice de calcul
ale impedanţelor, diagrame energetice
Descarcare text

## 19-50 ASPECTE PRIVIND RECEPTOARELE GENERALIZATE ÎN ELECTROTEHNICĂ

ASPECTS REGARDING THE GENERALIZED
This paper presents the generalized loads in electrotechnics and a
extremely unbalanced loads. It is considered the impedances with negative real
part, in other words generalized impedances. Also, taking into consideration the
calculation symmetrical components of impedances, a three-phase impedance
system may be divided into two parts: a balanced part and an unbalanced part.
We have a clear representation in impedance’s complex plane. The
bibliography can be found at the end of the paper.
symmetrical components, symmetrical components impedance calculation
Cuvinte cheie: receptor trifazat, receptor dezechilibrat real, impedanţă
generalizată, componente simetrice, componente simetrice de calcul ale impedanţelor

50 ASPECTE PRIVIND RECEPTOARELE

## 23-44 ASPECTE COMPARATIVE PRIVIND PUNTEA DE DIODE AVÂND O SARCINĂ COMPLEXĂ

COMPARATIVE ASPECTS REGARDING THE
In this paper we consider a three-phase ideal diode-bridge fed by a
non-symmetrical voltage system and with a complex load. Using an analytical
method we obtain the Fourier coefficients of serial development for the
harmonic currents on both of the DC and AC sides. To demonstrate the
usefulness of the analytical method, the results obtained by the analytical
method are compared with those obtained by the simulation method, which
gives accurate results. The paper considers a three-phase diode-bridge under
four particular non-symmetrical supply conditions. The values obtained by the
analytical method are near to those obtained by using digital simulation
(maximum relative error 1.1% in DC side and 2.6% in AC side). Finally, we
draw the conclusions and we indicate the references.
Cuvinte cheie: punte de diode, alimentare nesimetrică, sarcină complexă,
simulare pe calculator, compararea rezultatelor obţinute
Keywords: bridge diode, food ne symmetrical, complex power,
computer simulation, comparison of the results obtained

23-44 ASPECTE COMPARATIVE PRIVIND PUNTEA

## 21-40 METODĂ ANALITICĂ PENTRU STUDIUL PUNŢII DE DIODE AVÂND O SARCINĂ COMPLEXĂ

THE DIODE-BRIDGE WITH A COMPLEX LOAD
Commonly, three-phase diode bridge rectifiers are often used to
convert AC input into a DC voltage. It is well known that they generate large
amounts of harmonic currents in DC and AC sides.The paper proposes an
analytical method for calculating the harmonic currents of a three-phase diodebridge
under non-symmetrical supply conditions and with a complex load. We
are considering a three-phase ideal diode-bridge fed by a non-symmetrical
voltage system: ea(x) = Easin(x-x1), eb(x) = Ebsin(x-x2) and ec(x) = Ecsin(x-x3).
Performing those calculations we obtain the Fourier coefficients of serial
development for the harmonic currents on both the DC and AC sides. The
equations for the harmonic currents are derived, taking into account the effects
of the DC and AC side impedances. All the calculations are conducted only by
algebraic calculation with high accuracy. The proposed method can be easily
extended to the harmonic analysis of three-phase thyristor-bridge with nonsymmetrical
supply conditions and a complex load.
Cuvinte cheie: punte de diode, alimentare nesimetrică, sarcină complexă,
analiză armonică
Keywords: bridge diode, symmetrical power, complex task, harmonic
analysis

40 METODĂ ANALITICĂ PENTRU STUDIUL PUNŢII