In most power electronics applications, the
input power supply is in the form of 50 or 60 Hz
sine wave AC voltage provided by electric utility,
that is eventually converted to a DC voltage. As
power electronic systems proliferate, AC – to –
DC rectifiers are playing an increasingly important
role.
A large majority of the power electronics
applications such as switching DC power supplies,
AC motor drives, static frequency converters, DC
servo drives, and so on, us e such uncontrolled
three – phase rectifiers [1].
The three – phase, six – pulse, full bridge
diode rectifier is a commonly used circuit
configuration. A filter LfCf is connected at the DC
side of the rectifier. In the three – phase rectifier,
the AC side inductance is assumed to be zero and
the DC side is replaced by a constant DC current
Id. The rms harmonic component I(n) of the phase
current can be determined in terms of the
fundamental frequency component I(1) as:
( ) ( )
n
I
I
n1
=
(1)
where n represents the harmonic number, n =
5,7,11,13,… To draw a conclusion, typical AC
current waveforms in the three – phase diode
rectifier circuits are far from a sinusoid. The
power factor is also very poor because of the
harmonic contents in the line current. Moreover,
these harmonic contents cause additional
harmonic losses in the utility system and may
excite electrical resonances, leading to large over
voltages [1], [2], [3], [4].
Obviously, the reduction of higher current
harmonics generated by a three – phase AC – DC
converter can be obtained as well using a PWM
rectifier [1], [5], [6].
In Figure 1 is represented a two –
quadrant frequency converter with PWM
converter at the input for monitoring and
regenerative braking in AC motor drive. When
the induction machine works like an engine,
PWM converter 1has the bill of PWM
rectifier, and if the induction machine works
like a generator, PWM converter 1 has the bill of
PWM inverter. It can be seen from the scheme
from Figure 1, that the transistors T1-T6 work
continuously.
Fig. 1. Two – quadrant frequency converter
whith PWM rectifier at the input for
monitoring and regenerative braking in
AC motor drive.
Because of rapid changes in voltages and
currents within a switching converter, PWM
rectifier equipment is a s ource of electromagnetic
interference (EMI) with other equipment as well
as with its own proper operation. The EMI is
transmitted in two forms: radiated and conducted
[1].
Even if the PWM rectifier has almost
sinusoidal currents at the entrance, it presents the
Rectifier with Near Sinusoidal Input Currents vector-controlled for
AC motor drive
IRINEL VALENTIN PLETEA1*, MARIANA PLETEA1, DIMITRIE ALEXA1
1Technical University “Gheorghe Asachi” of Iasi, Faculty of Electronics, Telecommunications and
Informations Technology, blv. Carol I, no.11, Iasi, cod 700508, ROMANIA
Abstract: This paper is presented a three – phase rectifier, which is able to assure a very low harmonic injection
in the power supply (RNSIC converter = Rectifier with Near Sinusoidal Input Currents).
Keywords: power electronics, harmonic reductions, three – phase rectifiers.
Received: April 15, 2021. Revised: January 12, 2022. Accepted: March 5, 2022. Published: April 13, 2022.
1. Introduction
WSEAS TRANSACTIONS on ELECTRONICS
DOI: 10.37394/232017.2022.13.3
Irinel Valentin Pletea, Mariana Pletea, Dimitrie Alexa
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following important disadvantages comparing to
the three-phase rectifier with diodes:
•Higher commutation loss;
•Higher cost;
•Less working safety.
In Figure 2(a) we present an AC – DC
converter generating reduced higher current
harmonics in the mains, named in what follows
for short RNSIC (Rectifier with Near Sinusoidal
Input Current) [7], [9]. Such a rectifier does not
necessitate on the AC side classic passive filters,
active filters or hybrid filters. The capacitors C1 –
C6 have the same value C and they are DC
capacitors (for example, those in the series
B25355 for Smoothing, Supporting, Discharge)
[9]. The inductors LR, LS and LT have the same
value, denoted by L, and they are connected on the
AC side. The values of L and C fulfill the
condition:
10,005,0 2≤≤
ω
LC
(2)
in order for the phase currents iR, iS and iT to
be practically sinusoidal, according to Figure
2(b). ω denotes the mains angular frequency.
Fig. 2 T hree – phase rectifier with
practically sinusoidal currents new
configuration; (b) AC current waveforms;
(c) DC current id; (d) waveform of the
capacitor current ic1
In Figure 2 (b) are presented the wave forms
of iR, iS and iT currents, and the conduction times
of the D1-D6 diodes, for a Id current of
relatively large value, as in Figure 2(c). It can
be seen that there are two or three diodes in
conduction at a certain moment of time. For an
average value of Id, in conduction can be one or
two diodes at a certain moment of time.
Of course, at small load current iL and, thus,
small current Id, in conduction can be only one
diode or none.
For the 3 cases presented above, considering
that the iR, iS and iT currents are almost sinusoidal
and have the magnitude I(1) function of the
loading resistance RL, Id current can be obtained
with the relation:
( )
1
)1(
cos1
2
3t
I
I
d
ω
π
+=
(3)
The angle ϕt1 when the D1-D6 enter in
conduction varies between the nominal value
(ϕt1)r and the maximum value equal to 180°. The
nominal value (ϕt1)r is defined for ϕ=0° and
RL/RLr=1 and it is between 45° and 60°.
There are two extreme case during RNSIC
converter functioning. In the first case, if RL = 0
(and so Vd = 0 and
1
t0ω=
), the capacitors C1 – C6
short – circuited and the angle
is
inductive. In this case, the phase currents are
sinusoidal and have maximum amplitude, equal to
Imax. In the second case, if the voltage Vd exceeds
the value
( )
m
2
3V
1 2LC−ω
, the diodes D1 – D6 do not
conduct any more and the angle
is
capacitive (and so
L
R= ∞
and
1
tω=π
). For this last
case, the phase currents are also sinusoidal and the
amplitude has a minimum value Imin.
The ratio
max
min
I
I
has the value:
( )
2
2
min
max
2
21
ω
ω
LC
LC
I
I−
=
(4)
Due to the fact that the rms currents ICRMS that
flow through the capacitors C1 – C6 have small
values as compared with Imax according to
Figure 2(d), it implies that one has to
choose (for continuous operation) capacitors
with relatively large rated capacitance CR and
rated voltage VR. The condition is better
fulfilled by the DC capacitors [7], [8].
The drive control is a standard indirect vector-
controlled algorithm. The efficiency controller
is based on Rosenbrock’s method [10],
[11], [12], [13]. Sampling input voltage and
current, the active power is computed in the
following way:
( ) ( )
∫
=Tdttitv
T
P0
1
1
(5)
2. RNSIC Converter Configuration
3. Measurement and Control Algorithm
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Irinel Valentin Pletea, Mariana Pletea, Dimitrie Alexa
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Volume 13, 2022
The rms value for the current containing
harmonics can be evaluated with:
( )
∫
=
T
dtti
T
I
0
22
1
(6)
For the input voltage, the rms value can be
calculated with:
( )
∫
=Tdttv
T
V0
22 1
(7)
and assuming no ha rmonics containing, i.e.,
sinusoidal waveform we have:
22 1
1peakpeak V
V
V
V===
(8)
The fundamental current value I1 is computed
with the described SHT method, considering the
fundamental frequency equal to 60Hz. The
power measurement algorithm is displayed in
Figure 3. The computer may calculate all
power quantities in real time, although it is
also possible to save in memory only the
following values: P1, Q1 and S and to obtain
other magnitudes using a simple electronic
spread-sheet once the drive has stopped. Because
the whole algorithm is computed digitally,
the above integrals are transformed into simple
sums, what means:
∑
=
∑
=
22
1
1
1
k
kk
i
T
I
iv
T
P
(9)
In the implemented vector-controlled drive, the
flux
Φ
is decremented by changing the flux current
reference, isd*. On the other hand, the main purpose
of the implemented power measurement algorithm
is to analyze powers in a v ector-controlled
induction motor drive when the flux is reduced in
order to decrease losses with the described
method.
Fig. 3: Power measurement algorithm
diagram.
In Figure 4 presents MATLAB model for
converter with AC motor.
Fig. 4. Matlab model for converter with
AC motor
In Figure 5 presents algorithm for control based
on vector-controlled induction motor drive.
Obtained relations:
12
AN
12
BN
12
CN
UU
= (-S1-S2)+ (2-S1-S2)
u33
UU
= (2S1-S2)+ (2S1-S2-1)
u33
UU
= (2S2-S1)+ (2S2-S1-1)
u33
(10)
Fig. 5. Matlab model for vector-controlled
induction motor drive
Fig. 6. Simulations results for current and tension.
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DOI: 10.37394/232017.2022.13.3
Irinel Valentin Pletea, Mariana Pletea, Dimitrie Alexa
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Volume 13, 2022
Fig. 7 Harmonics characteristics
[1]. N.Mohan, T.Undeland and W.Robbins:
”Power Electronics – Converter, Applications
and Design”, John Wiley & Sons Inc., 1998.
[2]. H.Akagi: “Trends in Active Power
Conditioners”, IEEE Transactions on P ower
Electronics, vol.9, no.3, 1994, pp.263-268.
[3]. D.Alexa: “Combined Filtering System
consisting of Passive Filter with capacitors in
parallel with diodes and Low – Power
Inverter”, IEE Proceedings on Electric Power
Applications, vol. 146, no.1, 1999, pp. 88-94.
[4]. D.Alexa and A.Sirbu: “Optimized combined
harmonic filtering system”, IEEE Transacions
on Industrial Electronics, vol.48, no.6, 2001,
pp.1210-1218.
[5]. B.K.Bose: “Energy, Environment, and
Advances in Power Electronics”, IEEE Trans.
On Power Electronics, vol. 15, nr.4, 2000, pp.
688 – 701.
[6]. D.W.Chung and S.K.Sul: “Minimum-Loss
strategy for three-phase PWM rectifier”,
IEEE Transacions on I ndustrial Electronics,
vol.46, no.3, 1999, pp.512-526.
[7]. D.Alexa: “ T hree – phase rectifier with
almost sinusoidal input current”, Electronics
letters, vol.37, nr. 19, 2001, pp.1148 – 1149.
[8]. D. Alexa, I.V. Pletea, T.Goras, C.Vinatoru,
E.A.Lupea, V.Palagniuc: „Two – quadrant
frequency converter having rectifier with near
sinusoidal input currents”: PCIM 2003
International Conference & Exhibition, PQ,
Nuremberg, Germany 2003.
[9]. *** Siemens Matsushita Components Guide.
Capacitors for Power Electronics, 1996.
[10]. W. Shepherd, P. Zand. Energy Flow and
Power Factor in Nonsinusoidal Circuits,
Cambridge Univ. P., Cambridge, 1979.
[11]. T.S. Key, J. Lai. IEEE and International
Harmonic Standards Impact on Power
Electronic Equipment
[12]. Design, IEEE IECON’97, pp. 430 -436, New
Orleans, LA, Nov. 1997.
[13]. K.G. Narendra, H.S. Chandrasekharaiah.
Simple method of selective harmonic
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AC-DC power system, IEE Proceedings-C,
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MA = 0.65
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55
MA = 0.3
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55
MA = 0.1
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55
MA = 0.85
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55
Moreover, the simulations results for current and
tension are presented in Figure 6. Lastly, the
harmonics characteristics are presented in Figure
7.
4. Conclusions
The adjustment of the active power
transmitted to the utilization network can
be obtained through the proper control of the
PWM inverter, without the necessity that the
induction generator has a i n PWM rectifier. The
reliability and the efficiency can be increased
while the cost can be decreased. This solution
can be applied to the system with small hydro
generators.
References
WSEAS TRANSACTIONS on ELECTRONICS
DOI: 10.37394/232017.2022.13.3
Irinel Valentin Pletea, Mariana Pletea, Dimitrie Alexa
E-ISSN: 2415-1513
22
Volume 13, 2022
Conflicts of Interest
The author(s) declare no potential conflicts of
interest concerning the research, authorship, or
publication of this article.
Contribution of individual authors to
the creation of a scientific article
(ghostwriting policy)
The author(s) contributed in the present
research, at all stages from the formulation
of the problem to the final findings
and solution.
Sources of funding for research
presented in a scientific article or
scientific article itself
No funding was received for conducting this
study.
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