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Published in IET Power Electronics
Received on 31st January 2010
Revised on 28th March 2011
doi: 10.1049/iet-pel.2010.0038
ISSN 1755-4535
Zero-current zero-voltage transition inverters with
magnetically coupled auxiliary circuits: analysis
and experimental results
M.L. da S. Martins1 C.M. de O. Stein1 J.L. Russi2 J.R. Pinheiro3 H.L. Hey3
1
Federal University of Technology – Parana – UTFPR, Pato Branco, PR 85503-390, Brazil
Federal University of Pampa – UNIPAMPA, Alegrete, RS 97546-550, Brazil
3
Federal University of Santa Maria – UFSM, Santa Maria, RS 97105-900, Brazil
E-mail: mlucio@utfpr.edu.br; mariolsm@gmail.com
2
Abstract: Hitherto, zero-current transition (ZCT) and zero-current zero-voltage transition (ZCZVT) inverters have provided
desirable switching conditions for main semiconductors, chiefly for minority carrier ones, by means of a current impulse that
unavoidably increases the reactive energy of the auxiliary circuit, penalising their efficiency and device ratings. This often
offsets the benefits gained by the above-mentioned soft-switching techniques. This study presents a novel family of ZCZVT
inverters that overcome this problem by using a non-resonant auxiliary circuit, which is magnetically coupled to the filter
inductor, reducing the inverter component count, and associated circuitry. The principles of operation of the ZCZVT inverter
with a magnetically coupled auxiliary circuit is presented and analysed. Experimental results from a 1 kW, 40 kHz, laboratory
prototype are used to verify the theoretical analysis and also to compare different technologies applied to the auxiliary
switches. The ZCZVT inverter with a magnetically coupled auxiliary circuit and MOSFET-based auxiliary switches presented
the highest efficiency, achieving 96% at full load, meanwhile its insulated gate bipolar transistor (IGBT)-based counterpart
reached 94.2%.
1
Introduction
Nowadays, the ever-increasing switching frequency level in
industrial power inverters (such as variable-speed drives,
AC-power sources and uninterruptible power supplies)
provides significant reduction of the physical size, weight
and cost of reactive elements and electrical performance
enhancements [1]. As semiconductors have improved over
the years, in the range of voltages above 500 V, the
insulated gate bipolar transistor (IGBT) has become
predominant. After decades of improvements and
successive generations, the IGBT still presents a strong
trade-off between on-state voltage drop and turn-off
switching time, which constrains its total power handling
capability [2].
In order to alleviate IGBT switching losses and hence to
loosen the aforementioned trade-off, soft-switching
techniques have become an attractive alternative and thus
have been continuously discussed in the past decades [3].
Owing to the IGBT turn-off switching limitations, the zerocurrent transition (ZCT) [4] and zero-current zero-voltage
transition (ZCZVT) [5] techniques appear to be the most
adequate approaches. The ZCT technique eliminates the
current and voltage overlapping completely during the turnoff of main switches, providing favourable conditions for a
minority carrier-type device to be turned off. The reverse
recovery of diodes can be significantly reduced.
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Nevertheless, voltage transitions across the semiconductors
are quite abrupt, mainly during the turn-on of main
switches, which could deteriorate the EMI performance of
the inverter.
The ZCZVT technique combines zero-current switching
turn-off conditions and zero-voltage switching turn-on
conditions for the same device, reducing IGBT losses,
smoothing the voltage and current transitions and
improving EMI performance. However, the price paid for
the favourable switching conditions is the addition of a
resonant auxiliary circuit that yields additional reactive
energy [6]. This energy is handled by the auxiliary devices
that may cause high-voltage and -current stresses, leading to
additional auxiliary circuit conduction and switching losses.
To effectively improve the inverter efficiency, it is
necessary that the auxiliary circuit losses must be smaller
than the saved main device switching losses. Hitherto, the
auxiliary circuit for ZCT and ZCZVT inverters has relied
on the operation of a resonant LC tank which produces a
huge amount of reactive energy that may offset the
inverter efficiency gain. This situation undermines the
advantages of using the aforementioned soft-switching
techniques.
To overcome the reactive energy problem that plagues the
zero-current mode soft-transition inverters, this paper presents
a novel family of ZCZVT inverters with lower auxiliary
circuit reactive energy. The improvement lies in the
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038
www.ietdl.org
replacement of the resonant tank LC by a voltage controlled
voltage source, magnetically implemented with the inductor
of the inverter output filter. In this way, as presented in [7],
coupled-filter-inductor ZCZVT inverter results in a very
compact topology, with a simple structure that allows the
linear magnetisation and demagnetisation of the auxiliary
inductor. Additionally, it allows variable timing control of
the auxiliary devices, reducing the auxiliary switches’
conduction losses. In the following sections, the principles
of operation of the ZCZVT inverter with a magnetically
coupled auxiliary circuit (ZCZVT with MCAC) is presented
and analysed. Experimental results from a 1 kW, 40 kHz
laboratory prototype are used to verify the theoretical
analysis and also to compare different technologies applied
to the auxiliary switches.
2 Magnetically coupled auxiliary circuit
ZCZVT inverters
As described in [7], a novel family of ZCZVT inverters is
generated by coupling the auxiliary circuit inductor with the
inductor of the output filter. The diagrams of the ZCZVT
inverter with magnetically coupled auxiliary circuit
(ZCZVT with MCAC) applied to one inverter leg are
shown in Figs. 1a and b. In its simplest configuration it is
comprised of a snubber capacitor (Cs), a bi-directional active
pole (Sa1 and Sa2), an inductor (La) and an auxiliary voltage
source (AVS), implemented by the secondary winding of the
coupled-filter inductor. In the auxiliary circuits of these
ZCZVT inverters, the magnetising and demagnetising
processes of the auxiliary inductor are always aided by the
Fig. 1 Auxiliary circuit of the ZCZVT inverter with magnetically
coupled auxiliary circuit
a Circuit diagram applied to one inverter leg
b Circuit diagram applied to one inverter leg with alternative connection of
the auxiliary circuit
c Detail of the N-port cantilever model of the filter-coupled-inductor
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968–978
doi: 10.1049/iet-pel.2010.0038
voltage controlled voltage source NvLm , shown in the N-port
representation for the cantilever model [8] of the coupled
inductor secondary winding (Fig. 1c). The N-port
representation for the cantilever model also comprises a
leakage inductance (LK) in the secondary branch and the
parallel connection of the current controlled current source
NiLk with the magnetising inductance (LM) in the primary
branch.
These inverters are unique in that because they are
implemented with a non-resonant auxiliary circuit, Class A
AVS [9]. Furthermore, this AVS implementation allows for
a set of advantages hitherto only presented for ZVT
inverters, such as variable timing control for the auxiliary
switches and simple design methodology.
Considering one switching period (Ts), the magnetic
implementation of the AVS consists of the use of a single
magnetic core with a primary winding (LP), forming a
closed loop with one constant voltage source and one or
more secondary winding(s) that play(s) the role of each AVS.
The location of the primary winding produces a variety of
topologies by exchanging the primary winding among the
terminals x, y, z and u of the diagram in Figs. 1a and b. If
the primary winding is connected between terminals ‘x ’ and
‘u ’ it will ensure the magnetic core demagnetising.
On the other hand, besides the two possible connection of
the auxiliary winding terminals, as shown in Figs. 1a and b,
there are three possible configurations for the secondary
winding, a single coil, named Ls (as shown in Fig. 2a), two
split coils, named Ls1 and Ls2 (see Fig. 2b) or three split
coils, named Ls1 , Ls2 and Ls3 (see Fig. 2c). Since all
configurations consist in dividing the voltage controlled
voltage source NvLm and exchanging its location in series
with the auxiliary inductor or with the auxiliary switches,
the results for each configuration will be very similar.
The simplest case is the single coil secondary winding. In
this topology (Fig. 2a), the secondary winding leakage
inductance (Lk) contributes to limiting the di/dt through the
semiconductors, keeping the auxiliary switches naturally
clamped at bus voltage. In the cases where the secondary
winding is split and connected in series with the auxiliary
switches, the leakage inductances should be minimised as
much as possible to avoid excessive overvoltage across the
auxiliary switches, which are no longer clamped at bus
voltage. Therefore the implementation of multiple coils
Fig. 2 Circuit diagrams for the three secondary winding
configurations for the ZCZVT inverters with magnetically coupled
auxiliary circuit
a Single coil (configuration 1)
b Two split coils (configuration 2)
c Three split coils (configuration 3)
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secondary windings requires more attention from the designer
and unavoidably makes necessary the use of voltage clamps
across the auxiliary switches. Aiming to make the following
analysis simpler, as well as the laboratory prototype, the
single coil secondary winding located at terminals ‘r ’ and
‘x ’, as the diagram of Fig. 1a, is chosen for the subsequent
theoretical and experimental analyses.
2.1
Principles of operation
To simplify the soft-switching auxiliary circuit analysis, all
circuit parasitic elements, such as the semiconductor
junction capacitances and stray inductances, are
disregarded. Additionally, the DC bus capacitor is assumed
to be large enough so that the bus voltage (Vi) is constant.
Besides the output load current (i0) and voltage (v0) to be
predominantly sinusoidal, because of auxiliary circuit
action, the magnetising current (iLm) and load voltage (v0)
are assumed to be constant in one switching period (Ts),
since the switching frequency ( fs) is larger than the output
current/voltage frequency ( f0). Thus, for the auxiliary
circuit analysis, magnetising current and output voltage are
defined as ILm and V0 , respectively, and it is valid only for
a switching period (Ts).
For configuration 1, assuming that load current is flowing
in a positive direction (Fig. 1a), the ZCZVT with MCAC
assumes 12 different circuit modes in one switching period
(Ts), as shown in the theoretical waveforms shown in
Fig. 3. It can be seen that the auxiliary circuit exhibits a
linear current that increases when auxiliary inductor La is
magnetised, deviating the main circuit current and also a
linear-like current when its demagnetisation takes place.
The resonant intervals are restricted to the charge and
discharge of snubber capacitor Cs , as described in the
following description. Previous to the auxiliary circuit to be
triggered, load current (I0) flows through D2 .
Mode I (t0 , t1): At instant t0 the auxiliary switch Sa1 is turned
on and the current starts to ramp up through auxiliary inductor
La . Owing to the connections of primary and secondary
coupled inductor windings, both currents increase, iLa and
i0 . As the secondary winding current rate of rise di/dt is
larger, current through main diode D2 decreases
proportionally. This mode lasts until current through diode
D2 reaches zero. This circuit mode diagram is shown in
Fig. 4a.
Mode II (t1 , t2): When diode D2 is off, capacitor Cs1 starts to
discharge. This resonant process between voltage vCs1 (vs1)
and current iLa lasts until Cs1 is fully discharged, as shown
in the circuit mode diagram depicted in Fig. 4b.
Mode III (t2 , t3): When voltage vCs1 reaches zero, current
through secondary winding is larger than primary winding
current, forcing the main diode D1 to start conducting the
difference between these two currents. This situation
enables zero-current and zero-voltage switching conditions
for S1 . This interval must last until main switch S1 is driven
into the on-state. This circuit mode diagram is shown in
Fig. 4c.
Mode IV (t3 , t4): When S1 is fully turned on, auxiliary switch
Sa1 is turned off in order to demagnetise the auxiliary inductor
La . At this instant, auxiliary diode Da2 turns on. This circuit
mode lasts until main diode D1 current reaches zero. This
circuit mode diagram is shown in Fig. 4d.
Mode V (t4 , t5): At instant t4 the primary winding current is
larger than the secondary winding current. Hence, the main
switch S1 starts conducting the current difference between
these currents. This mode lasts until secondary winding
current reaches zero and switch S1 assumes all load current,
as can be seen in Fig. 4e.
Mode VI (t5 , t6): At instant t5 current through the auxiliary
circuit is zero and the inverter operates like its hardswitched counterpart, as shown in Fig. 4f.
The description of each circuit mode for the switch S1 turnoff process is as follows.
Fig. 3 Theoretical waveforms for the ZCZVT inverter with
magnetically coupled auxiliary circuit
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Mode VII (t6 , t7): At instant t6 the auxiliary switch Sa1 is
turned on and current starts to rise up through auxiliary
inductor La in a linear fashion. This mode lasts until
primary and secondary winding currents are equal. At this
instant current through main switch S1 becomes zero, as can
be seen in the circuit diagram shown in Fig. 4g.
Mode VIII (t7 , t8): Once current through secondary winding is
larger than primary winding current, at instant t7 diode D1 is
turned on conducting the difference between these two
currents. This circuit mode enables zero-current and zerovoltage switching conditions for switch S1 . As voltage
across inductor La (secondary winding) remains positive,
current iLa continues to rise. This interval must last until
main switch S1 is driven off completely. This circuit mode
diagram is shown in Fig. 4h.
Mode IX (t8 , t9): Similar to Mode IV, when S1 is fully turned
off, the auxiliary switch Sa1 is turned off. At this instant,
auxiliary diode Da2 turns on and auxiliary inductor La
demagnetising starts. This mode lasts until main diode D1
current is zero and its circuit mode is shown in Fig. 4i.
Mode X (t9 , t10): When diode D1 is off, capacitor Cs1 starts to
charge-up in a resonant way. This circuit mode lasts until Cs1
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038
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Fig. 4 Circuit mode diagrams for the ZCZVT inverter with magnetically coupled auxiliary circuit applied to one inverter leg
a
b
c
d
e
f
g
h
i
j
k
l
Mode I (t0 –t1)
Mode II (t1 –t2)
Mode III (t2 –t3)
Mode IV (t3 –t4)
Mode V (t4– t5)
Mode VI (t5 –t6)
Mode VII (t6–t7)
Mode VIII (t7– t8)
Mode IX (t8 –t9)
Mode X (t9– t10)
Mode XI (t10–t11)
Mode XII (t11–t0)
is fully charged at bus voltage Vi , as can be seen in the
diagram of Fig. 4j.
Mode XI (t10 , t11): When voltage vCs1 reaches Vi , current iLa
decreases linearly until it becomes zero. The diagram of this
circuit mode can be seen in Fig. 4k.
Mode XII (t11 , t12): At instant t11 current through the auxiliary
circuit is zero and the inverter operates like its hard-switched
counterpart. This circuit mode diagram is shown in Fig. 4l.
Before the main switch S1 to be activated again the
auxiliary circuit is triggered, starting another switching
period. This way, instants t0 through t11 are all referred to
each switching period Ts .
2.2
Comparative voltage and current stresses
Different from the ZCT [4] and the ZCZVT inverters
previously presented in [5], whose main current waveforms
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968–978
doi: 10.1049/iet-pel.2010.0038
are shown in Figs. 5a and b, respectively, the voltage
applied through the auxiliary inductor is almost constant
during a switching period (Ts) in the ZCZVT inverter with
magnetically coupled auxiliary circuit, yielding a quite
linear current for the auxiliary inductor, switches and
diodes, as can be seen from Fig. 5c. As main
semiconductor devices (IGBTs and co-pack diodes) are
subjected to no additional stresses, they can be rated in the
same way as their hard-switched counterparts.
In contrast, from Fig. 5a it can be seen that although the
main switch suffers no additional current stress, the co-pack
diodes of the ZCT inverters proposed in [4] are subjected to
a huge current stress (grey areas). It also can be seen that
both auxiliary switches operate in a switching period,
sharing the auxiliary conduction losses (hachured areas).
In the ZCZVT presented in [5], Fig. 5b, the main switches
present a high current stress during their turn-on process. The
auxiliary switch current stress is also quite significant, and it
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Fig. 5 Main and auxiliary current waveforms for ZCT and ZCZVT inverters
a ZCT [4]
b ZCZVT [5]
c ZCZVT with MCAC
is concentrated in a single semiconductor for each output
voltage half-cycle.
Taking into account one output voltage period (T0), it also
should be addressed that the ZCZVT with MCAC presented
in Fig. 5c presents a lower current stress as the turn-on and
turn-off process of the main devices take less time.
Furthermore, as the load current varies in a sinusoidal way,
the auxiliary switch conduction interval and stress are also
proportional to a sinusoidal shape.
Table 1 presents a comparative analysis for the main
parameters of the three above-mentioned topologies. As can
be seen, the ZCT and ZCZVT inverters with magnetically
coupled auxiliary circuit present a lower device count.
However, Table 1 shows the same amount of auxiliary
devices for both inverters, when the leakage secondary
winding inductance is used as an auxiliary inductor, the
device count is lesser for the ZCZVT with MCAC.
Accounting for the main device stresses, the ZCZVT with
MCAC presents the same voltage stresses as the ZCT [4]
and ZCZVT [5]; however, its current stress is lower. On the
Table 1
Parameter
Comparative auxiliary parameter analysis
ZCT [4]
ZCZVT [5]
ZCZVT with MCAC
Number of auxiliary components (per PWM pole)
switches
2
2
2
co-pack diodes
2
2
2
capacitors
1
2
1
inductors
1
2
1
Main switches stress
IS1,2(max)
1
2
1
VS1,2 (max)
1
1
1
Main co-pack diodes stress
2IS1,2 (max)
a
k
1
2VS1,2 (max)
1
1
1
Auxiliary switches stress
√
ISa1,2(max)
a
1 + a2 − 1
ax + 1/(1 2 N )
VSa1,2 (max)
1
1
1
Auxiliary co-pack diodes stress
√
2ISa1,2(max)
a
a 2/2
ax + 1/(1 2 N )
2VSa1,2(max)
1
1
1
a ¼ Vi/(ZI0(max)); ax ¼ (1 2 kxMa)Vi/(ZxI0(max))
K ¼ I(max)/I0(max) , k . 1; kx ¼ 1 2 (va/v)2
Ma – modulation index; N – coupled-filter-inductor turns ratio;
va and v – frequencies of resonance (6)
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other hand, the auxiliary device stresses are quite dependent
on the auxiliary circuit and load current for all inverters.
Nevertheless, the ZCZVT with MCAC presents an extra
degree of freedom from the coupled-filter-inductor turns
ratio (N ) which can be used to reduce current stresses on
auxiliary devices.
2.3
Limited voltage and current transitions
Both ZCT and ZCZVT techniques presented hitherto have
relied on resonant currents to commutate the pulse-width
modulation (PWM) pole semiconductors [4, 5]. In these
topologies, to ensure that a low di/dt is applied to these
semiconductor transitions, a long resonant period must be
considered for the auxiliary resonant components. This
situation yields an exacerbated circulating energy and an
extended operating interval for the auxiliary circuit. In the
linear like currents of the auxiliary circuits of the ZCZVT
with MCAC, the low di/dt transitions are handled more
effectively, simply by choosing the proper inductance for
La , which is magnetised so that zero-current switching
(ZCS) conditions of the outgoing PWM pole switch are
enabled. This feature is very important as it allows the use
of the variable timing control, as in ZVT inverters, and has
been proved to result in better efficiency [10].
3
3.1
Design procedure and example
Design methodology
3.1.1 Auxiliary inductor and coupled-filter-inductor
turns ratio: The auxiliary inductor La controls the di/dt of
the inverter leg diodes (D1 , D2), its value can be obtained
by determining how fast the inverter leg diodes can be
turned off. However, it is difficult to determine accurately,
because the recovery characteristics of these diodes vary
among different IGBT modules. A widely adopted estimate
is to allow the current through the auxiliary inductor to
ramp up to the diode current within three times the diode’s
specified reverse-recovery time. Hence, from the expression
for the current through the auxiliary inductor for the
ZCZVT circuit mode 1 (Fig. 4a), it can be found that
La ≥
(1 − N)(Vi − NV0( max ) )
(3trr )
ILm( max )
(1)
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038
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where trr is the reverse recovery time of inverter leg diodes
(D1 , D2), N is the coupled inductor turns ratio, Vi is the bus
voltage, V0(max) and ILm(max) are the maximum load voltage
and coupled inductor magnetising current, respectively. It
must be observed that the sinusoidal load current appears
through the magnetising inductance (iLm ¼ i0), once the
primary and secondary winding currents are transferred
from one side to another during the auxiliary circuit operation.
As can be seen by (1), La depends on the value of the
coupled-filter-inductor turns ratio N, which determines
the value of the secondary voltage, affecting directly the
ZCZVT turn-on and turn-off intervals, as the secondary
current ripple as well. Expression (2) shows an approximate
value for the maximum current through auxiliary inductor
during the main switch turn-on process. It shows that the
coupled inductor turns ratio N is proportional to current
stresses
ILa (max ) |turn-on ≃
ILm( max ) 1
+
(1 − N) Za
1
Vi − V0( max )
1−N
(2)
where
La
Za =
and Ceq = Cs1 + Cs2
Ceq
(3)
Expression (4) shows an approximate value for the maximum
current through auxiliary inductor during the main switch
turn-off process. It shows that N is also proportional to
current stresses
ILa ( max ) |turn-off ≃
ILm( max )
(1 − N )
La ILm(max )
p
+
(1 − N )(Vi − V0( max ) ) 2v
(5)
where
(1 − N )
1
v = and va = La Ceq
La Ceq
(6)
La ILm( max )
(1 − N )V0( max )
(7)
It means that N must be chosen according to the compromise
between the auxiliary circuit current stresses and the loss of
duty cycle.
3.2
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968–978
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(8)
Component selection and design example
In order to illustrate the proposed design methodology described
in Section 3.1, a single-phase ZCZVT inverter with IGBT-based
technology has been analysed. The ZCZVT inverter with
MCAC specifications are given in Table 2.
The IGBT chosen for the analysis is a standard module
(SK45GB063) designed for switching applications such as
switched mode power supplies and uninterruptible power
supplies, where an output filter is required.
It is assumed that the inverter feeds a resistive load and the
output filter is a second-order (LC) low-pass filter with a cutoff frequency ( fcut ≃ 10 800 Hz) defined to ensure 5% of
THD for a standard 127 Vrms , 60 Hz sinusoidal output
voltage.
An important feature of the coupled-filter-inductor is that
its primary self-inductance plays the role of filter inductor.
In this way, as the primary winding leakage depends on
constructive features, instead of the self-inductance, the
magnetising inductance (LM) is adjusted to meet the output
filter inductor value, ensuring a high coupling factor to the
coupled-filtered-inductor.
For the SK45GB063 module a typical trr is approximately
80 ns. Thus, applying the inverter specifications, given by
Table 2, to expression (1) it can be found that
La ≥ 4.62 mH
(9)
where N was chosen equals 0.3.
From expression (8)
Ceq = Cs = 1.1 nF
(10)
where tdead was chosen equals 2 times trr .
Since the snubber capacitor incorporates the output
capacitance of the IGBT and co-pack diode, the snubber
capacitor value can be obtained by subtracting the output
capacitor value of the IGBT and co-pack diode from the
Ceq . For the SK45GB063 module a typical Coss is less than
80 pF, hence Ceq was chosen equal to 1 nF.
Auxiliary circuit semiconductor selection
The selection of power semiconductors for static or shortterm (overload) operating conditions of any application is
subject to the consideration of: (i) maximum ratings and (ii)
power dissipation (junction temperature). Under no
circumstances that might occur during any static or dynamic
operation must the maximum ratings for blocking voltage
Table 2
ZCZVT with MCAC specifications
Parameter
3.1.2 Snubber capacitor: The snubber capacitors (Cs1 ,
Cs2) are designed to control the dv/dt across the IGBTs and
co-pack diodes of the main inverter leg (PWM pole).
A good estimate is to determine the total capacitor
value by setting the resonant transient time to the inverter
4 tdead (1 − N ) 2
p
La
where tdead is the dead time of the IGBT inverter leg.
3.3
and turn-off process
DtZCZVT |turn-off ≃
Ceq = Cs = Cs1 + Cs2 =
(4)
In the same way, expressions (5) and (7) show that coupledfilter-inductor turns ratio N is proportional to the ZCZVT
intervals during main switch turn-on
DtZCZVT |turn-on ≃
dead time. Hence
bus voltage (Vi)
output voltage (Vo(rms))
switching frequency ( fs)
output filter THD (L/C)
Value
360 V
127 Vrms
40 kHz
5% (1.0 mH/20 mF)
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(Vblocking), peak current (ISa(max)), junction temperature
(TJ(max)) and safe operating area be reached.
For an IGBT switch
2
Pcond(IGBT) = Vto ISa(avg) + Rce(on) ISa(rms)
3.3.1 Blocking voltage: Since the ZCZVT inverter is
applied in DC-voltage links, which is AC-voltage supplied
via a rectifier bridge, the blocking voltage is adjusted to a
line voltage fluctuation tolerance of 10%, and thus
Vblocking = Vbus × 1.1 = 396.0 ≃ 400 V
For a MOSFET switch
2
Pcond(MOSFET) = Rds(on) ISa(rms)
where the semiconductor constants Vto , Rce(on) and Rds(on) are
defined in Table 3.
The auxiliary switch rms value is given by
(12)
ISa(rms)
where
MF
sin2 (2pf0 tk )
= ((ton × H12 ) + (toff × H22 ))
3T0
k=1
(18)
V0( max )
√
= V0(rms) 2 ≃ 180 V
I0( max ) = ILm( max ) =
P0 √
2 ≃ 11.1 A
V0(rms)
(13)
(14)
Considering a 20% output current ripple in the coupled-filterinductor because of the finite magnetising inductance, ILa(max)
can be approximated to 24 A.
The auxiliary switch average value is given by
ISa(AVG) = (H1 × BS1 + H2 × BS2)
3.3.3 Power dissipation and junction temperature:
The power dissipation of a semiconductor is directly related
to the semiconductor junction temperature, which is given by
TJ = TCASE + RthJC PLoss
= TCASE + RthJC (PCond + PSwit )
T0
≃ 668
Ts
(20)
where H1, H2, BS1 and BS2 are defined in Fig. 6a.
The turn-off switching losses for an IGBT are a function of
the maximum current (iSa) that can be defined with the aid of
Fig. 6c as follows
(15)
As power losses are dependent on device technology, the
power dissipation for an IGBT and a MOSFET is given as
described below.
Owing to the zero current turn-on of the auxiliary switches
(Sa1,2), their losses comprise conduction and turn-off
switching losses. The conduction losses are a function of
the average ISa(avg) and rms ISa(rms) current components as
follows:
MF
sin2 (2pf0 tk )
(19)
2T0
k=1
The frequency modulation ratio (MF) is defined in [11] and
given by
MF =
Table 3
(17)
(11)
3.3.2 Maximum current: The maximum auxiliary circuit
current can be given by
ILa ( max ) |turn-on = 21.1 A
(16)
PSwit(IGBT) =
MF
H1 + H2 a( sin(2pf0 tk ))b
1000To k=1
(21)
According to [12], the turn-off losses approximate zero when
snubber capacitor Cs approaches a given value (Cs ≃ 1 nF).
As can be seen in Table 3, the output capacitance (Coss) for
the IRFP360 and IRFP460 ensures that in both cases the
MOSFET losses can be approximated only by the turn-on
capacitive losses.
Auxiliary switch parameters for IGBT and MOSFET implementations
Parameter
VBreac(max) , V
I(max) , A
TJ(max) , 8C
RthJC , 8C/W
a
b
Vto
Rce(on)
Rds(on)
Coss
SK45GB063a
IRG4PC40UDb
IRFP360b
IRFP460b
600
45
150
1
0.1035
0.707
0.94 V
24 mV
–
–
600
20
150
0.77
0.0534
1.182
1.18 V
21 mV
–
–
400
20
150
0.45
–
–
–
–
0.3 V
1100 pF
500
23
150
0.45
–
–
–
–
0.5 V
870 pF
a
Semikron
International rectifier
b
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& The Institution of Engineering and Technology 2011
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038
www.ietdl.org
Fig. 7 Laboratory prototypes for the ZCZVT inverter with
magnetically coupled auxiliary
a Single-phase inverter power stage
b Different semiconductors auxiliary switch implementation
c Coupled inductor implementation
Fig. 6 Semiconductors characteristics and losses
a Normalised auxiliary circuit current stress
b Static on state voltage drop
c IGBTs switching losses
d Auxiliary switches losses for ZCZVT and main IGBT module switching
losses in hard switching mode
e Devices operating temperatures
The absolute maximum ratings datasheet parameters of
the devices SK45GB063, IRG4PC40UD, IRFP360 and
IRFP460, as well as the curve fitting constants extracted
with the aid of graphical curves [13] shown in Fig. 6d, are
shown in Table 3.
It can be seen that on-state voltage drop (Vceon) is much
higher for MOSFET IRFP460 and IRFP360, Fig. 6b, when
compared with the IGBTs, which yield higher conduction
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968–978
doi: 10.1049/iet-pel.2010.0038
losses, Fig. 6d. On the other hand, switching losses are
more predominant in the IGBTs, as can be seen in the
switching energy losses of the SK45GB063 module and the
IRG4PC40UD discrete IGBT (Fig. 6c) and estimated power
losses of the auxiliary switches (see Fig. 6d ZCZVT with
MCAC).
In order to analyse the benefits of the ZCZVT with MCAC,
the estimated losses for the ZCZVT inverter with resonant
auxiliary circuit presented in [4] have been also calculated
(see Fig. 6d ZCZVT [4]). It can be seen that the conduction
losses are predominant in the auxiliary circuit of the
ZCZVT inverter with a resonant auxiliary circuit [4], such
that only with the IRG4PC40UD is the circuit competitive
with the ZCZVT inverter with a magnetically coupled
auxiliary circuit (ZCZVT with MCAC). On the other hand,
the predominant switching losses of the ZCZVT inverter
with a magnetically coupled auxiliary circuit (ZCZVT with
MCAC) make it more efficient with MOSFET auxiliary
switches.
Considering a constant case temperature Tcase of 508C, the
estimated junction temperatures for the auxiliary switches are
shown in Fig. 6e. For all semiconductor devices, the junction
temperature does not exceed the absolute rating of 1508 (vide
Table 3). The lowest thermal resistance (RthJC) of the
MOSFETs associated with the lower losses ensures the
lowest junction temperature for the IRFP360 and IRFP460
MOSFET devices.
It is worth noticing that when compared to the main
switching losses (SK45GB063) from co-pack diode
recovery charge and IGBT switching, it can be seen that
with auxiliary devices such as SK45GB063, IRG4PC40UD
and IRFP360, the auxiliary losses are much lower, being
less than 35% of the main switching losses.
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Fig. 8 ZCZVT with MCAC experimental waveforms for a 1 kW load
a
b
c
d
e
f
Output voltage and current. Scales: vo – 100 V/div; io – 5 A/div; time – 5 ms/div
Snubber capacitor and coupled inductor primary and secondary currents. Scales: iLp – 5 A/div; iLs – 5 A/div; vCs – 100 V/div; time – 2 ms/div
Main switch turn-on. Scales: vGE – 10 V/div; vCE – 100 V/div; iC – 5 A/div; time – 500 ns/div
Main switch turn-off. Scales: vGE – 10 V/div; vCE – 100 V/div; iC – 5 A/div; time – 500 ns/div
Auxiliary switch waveforms during main switch turn-on process. Scales: vGE – 10 V/div; vCE – 100 V/div; iC – 10 A/div; time – 500 ns/div
Auxiliary switch waveforms during main switch turn-off process. Scales: vGE – 10 V/div; vCE – 100 V/div; iC – 10 A/div; time – 500 ns/div
4
Experimental results
In order to verify the theoretical analysis presented so far, a
laboratory prototype has been implemented. The prototype
inverter stage is comprised by a single-phase ZCZVT
inverter with a magnetically coupled auxiliary circuit, as
shown in Fig. 7a. The inverter main semiconductors are
implemented with two-pack IGBT modules (SK45GB063),
whereas the auxiliary switches are implemented with
discrete devices in three different ways. One auxiliary
switch implementation, named DevCon 1 (abbreviation for
Device Configuration), makes use of discrete IGBTs
(IRG4PC40UD) associated with small dissipative turn-off
snubbers, as shown in Fig. 7b. The other two
implementations make use of discrete MOSFETs (IRFP360)
associated with a reverse blocking diode (Da1) and a bypass
ultrafast power diode (Da2 , RHR740). As the reverse
blocking diode (Da1) is subjected to a very low reverse
voltage, it is implemented with a low-voltage Schottky
diode (80SQ045) in DevCon 2 (Fig. 7b) and with an
ultrafast power diode (Da1 , RHR740) in DevCon 3
(Fig. 7b). The IGBTs present lower conduction losses than
the power MOSFETs; nevertheless, their switching losses
are significantly higher. Hence, an experimental evaluation
of both technologies is appropriate. Aiming to reduce the
component count, the leakage secondary winding
inductance was adjusted to meet the auxiliary inductor
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& The Institution of Engineering and Technology 2011
value (Lk ¼ La). As defined in Section 3.2, the coupled
inductor magnetising inductance is designed to meet the
output filter inductor value (LM ¼ L). Both inductances are
presented in the coupled-inductor model of Fig. 7c.
Additionally, to reduce parasitic capacitance effects in the
auxiliary circuit, a saturable inductor implemented with
eight turns on a Toshiba ‘spike killer’ core (SA
14 × 8 × 4.5) was placed in series with the coupledinductor secondary winding.
The inverter stage operates in an open loop with a PWM
discontinuous modulation function [defined by (22)] that
permits switches S3 and S4 to commutate at the output
voltage frequency (60 Hz), maintaining the high frequency
(40 kHz) only for switches S1 and S2 , which are assisted by
the ZCZVT auxiliary circuit
VMod(PhA) = Vi − 2Vi Ma sin(u)
(22)
The main parameters of the evaluated prototype are described
in Table 4. The single-phase inverter synthesises a 127 Vrms/
60 Hz voltage that feeds a 1 kW resistive load, as can be seen
in Fig. 8a. The auxiliary circuit resonant elements are
the coupled-filter-inductor and the capacitor Cs , whose
correspondent currents and voltages are shown in Fig. 8b.
By means of these waveforms it can be seen that the
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038
www.ietdl.org
Table 4
ZCZVT prototype experimental parameters
Parameter
Vi/Vo
P0/fs
Cbus
L/C
S1 , S2 , S3 ,S4
Sa1 , Sa2
Da1
Da2
N (ns/np)
LM
La (¼Lk)
Cs (aux. capacitor)
RSn1,2/CSn1,2/DSn1,2
spike killer (Lsat)
ZCZVT with MCAC
360 VDC/127 VRMS (60 Hz)
1.0 kW/40 kHz
2000 mH
0.93 mH/2 × 20 uF
SK45GB063 (600 V/45 A)
IRG4PC40UDa (600 V/20 A)/IRFP360b,c
(400 V/23 A)
80SQ045b (Schottky)/RHR740c
RHR740
0.3 (9 turns/30 turns)
1.26 mH
5.9 mH
1.0 nF
100 Va/2.2 nFa/BYV26Ca
Toshiba–SA 14 × 8 × 4.5 (8 turns)
a
DevCon 1
DevCon 2
c
DevCon 3
b
resonant process is confined to very short intervals around the
switching transitions, ensuring very low reactive energy.
The zero-voltage and current switching conditions for main
switch S2 turn-on and turn-off can be observed in Figs. 8c and
d, respectively. It can be seen that both di/dt and dv/dt across
the main device is limited during both switching intervals.
The auxiliary switching Sa2 waveforms for the main switch
turn-on and turn-off processes are shown in Figs. 8e and f,
respectively. They show that both turn-on processes take
place with a ZCS condition and current increases in a linear
fashion through the auxiliary switch.
Fig. 9 presents an experimental comparison among the
different configurations of the auxiliary switches. It can be
seen that DevCon 1 (IGBT auxiliary switches) presented
the lowest efficiency among the ZCZVT prototypes,
achieving 94.2% of efficiency at full load. DevCon 2
(MOSFET and Schottky-based auxiliary switches) allowed
a slight efficiency gain over DevCon 1. However, DevCon
3 (MOSFET and bipolar diode-based auxiliary switches)
presented the highest efficiency, achieving 96% at full load.
Owing to the high switching frequency (40 kHz) the hardswitched prototype could not be evaluated as it proved to
be not reliable during the experimental tests. Thus, for
comparative purposes, the same specifications of the
ZCZVT inverter prototype have been used to design a
Fig. 9 Experimental efficiency curves for the tested prototypes
IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968–978
doi: 10.1049/iet-pel.2010.0038
single-phase inverter with Undeland dissipative snubber,
which replace the hard-switched inverter in the comparative.
The prototype of the Undeland inverter presented the
lowest efficiency among all experimental prototypes, which
proves that the ZCZVT inverter with magnetically coupled
auxiliary circuit is a strong candidate to replace the hardswitched and conventional ZCT and ZCZVT inverters.
5
Conclusions
In order to overcome the reactive energy problem that plagues
zero-current mode soft-transition circuits such as the ZCT and
the ZCZVT inverters, this paper presents a novel family of
ZCZVT inverters. It provides soft-switching conditions for
the main semiconductor devices by means of a non-resonant
auxiliary circuit, which is magnetically coupled to the filter
inductor. Furthermore, it allows the auxiliary inductor to be
magnetised and demagnetised from an almost constant
voltage reflected directly from the filter inductor. Besides
reducing the resonant energy from the auxiliary circuit, it
also can reduce the auxiliary circuit component count and
associated circuitry. The principals of operation of the
ZCZVT inverter with magnetically coupled auxiliary circuit
was presented and analysed. A simple design methodology is
also presented. Experimental results from a 1 kW, 40 kHz,
laboratory prototype corroborate with the reliability and
efficiency gain achieved by the proposed ZCZVT inverters.
When compared with the Undeland snubber counterpart, the
proposed ZCZVT presented an efficiency gain of 4%, which
is a considerable improvement in converter losses.
6
Acknowledgments
The authors would like to express their gratitude to
‘Coordenação de Aperfeiçoamento de Pessoal de Ensino
Superior – CAPES’ and ‘Conselho Nacional de
Desenvolvimento Cientı́fco e Tecnológico – CNPq’ (proc.
307798/2009-7, proc. 478154/2009-7 and proc. 554103/
2010-9) for fnancial support, Icotron – an EPCOS
Company, Thornton Inpec Eletrônica Ltda and Xilinx for
material support.
7
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IET Power Electron., 2011, Vol. 4, Iss. 9, pp. 968 –978
doi: 10.1049/iet-pel.2010.0038