Download Biela J. Aigner H., Parallel/Series Connection of Self

Parallel/Series Connection of Self-Sustained
Oscillating Series-Parallel Resonant Converters
H. Aigner 1 and J. Biela2
1Lorch Schweisstechnik GmbH, Im Anwender 24, 71549 Auenwald
Germany, Email: [email protected]
2Laboratory for High Power Electronic Systems, ETH Zurich
Physikstrasse 3, 8092 Zurich, Switzerland, Email: [email protected]
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Parallel/Series Connection of Self-Sustained
Oscillating Series-Parallel Resonant Converters
H. Aigner
1
1
and J. Biela2
Lorch Schweißtechnik GmbH, Im Anwender 24, 71549 Auenwald
Germany, Email: [email protected]
2
Laboratory for High Power Electronic Systems, ETH Zurich
Physikstrasse 3, 8092 Zurich, Switzerland, Email: [email protected]
Keywords
Resonant converter, Load sharing control, Series operation
Abstract
In this paper, a new interconnection concept of two (or more) series-parallel resonant converter
suitable for parallel/series connected inputs is proposed. With this connection method operation
at a wide range of operating voltages and good semiconductor utilisation is enabled. Furthermore,
the balance of the two resonant converter input voltages in case of a series connection is investigated
and a method for improving the voltage balancing is presented. The proposed concept is verified by
measurement results and the design of the converter/integrated transformer is discussed in detail.
1
Introduction
Power electronic systems for consumer or industrial applications such as welding power supplies,
often aim for an international market and therefore must be designed for a wide input voltage
range. For systems with an output power higher than a few kW often a line-to-line voltage range
from 208V to 460V must be considered during the design process. Besides the wide input voltage
range, a high efficiency and/or a compact setup are required by the customers.
There, 600V devices, which have a much better switching behaviour than 1200V devices, enable
lower switching losses and/or higher switching frequencies. The high switching frequency is especially interesting for converter systems utilising magnetic devices such as DC-DC converters, since
L Out I Out
CS1 LS1
V DC1
I S1
+
C P1
+
+
Gate Signals
Modulation
I S2
+
Gate Signals
A
I S1
CP
+
CS2 LS2
Modulation
VAB
Gate Signals
I S1
V DC2
a)
B
RL
L Out I Out
CS1 L S1
VDC1
I S2
CS2 L S2
V DC2
I S2
+
C P2
b)
RL
Gate Signals
Modulation
I S2
Fig. 1: a) Series-parallel resonant converter with independent power controllers and parallel connected outputs. Due to the tolerances of the resonant tank components, the operating frequencies of the two converters
are not identical in case a self sustained oscillation control is used [1] and independent controller/modulators
are required for the two H-bridges. b) Proposed configuration with 1 common parallel capacitor CP , so that
the two H-bridges operate at the same switching frequency and the gate signals are synchronised between the
upper and the lower H-bridge. Consequently, only 1 controller/modulator is required for both converters.
The input voltages VDC1 and VDC2 can be connected in parallel or in series for a) and b) due to the galvanic
isolation provided by the transformer.
the magnetic components shrink with increasing switching frequency resulting in a higher power
density and/or a higher efficiency at a low switching frequency.
To apply 600V devices also at high input voltages, a series connection of either the devices [2]
or of converters [3] could be performed. At the lower input voltage it is advantageous to connect
the converters/devices in parallel in order to utilise the power semiconductors better as shown in
[4] for a converter system operating in a voltage range from 200VAC . . .400VAC .
With the switchable configuration also a higher modularity could be achieved by utilising converter modules with a lower output power level and connect them in series and/or in parallel. In
case each converter has its own control unit for controlling the voltage/current at the input and/or
output, a series or a parallel connection (cf. Fig. 1a) could be relatively easily achieved [5].
In order to reduce the circuit complexity and save costs, the control could be simplified if the
power inherently balances between the parallel/series connected units as shown for example in [6].
If the converters operate synchronously at the same switching frequency, only four gate signals are
required to control the 8 switches of the two H-bridges at the input side (Fig. 1b).
This is relatively easy to achieve with conventional DC-DC converters as forward or flyback
converters, as these could be operated at the same switching frequency and the switching transients
of the converters could be synchronised [6, 7].
In welding applications a series-parallel resonant converter is very advantageous since it enables
to raise the output voltage for ignition, is short-circuit proof at the output, offers soft switching
condition and allows the possibility to utilise the transformer parasitics as resonant elements [8, 9].
These converters can be operated with a self-sustained oscillation as described in [1] and shortly
explained in section 2. With this control method the switching frequency directly depends on the
component values in the resonant tank, which could have relatively high tolerances. Consequently, a
common control of the switching devices in the two H-bridges is not possible with the configuration
shown in Fig. 1a) and balancing the output power of the parallel/series connected converter requires
an additional control.
These limitations can be overcome with the proposed series connection of the resonant tank as
shown in Fig. 1b), where the parallel capacitor Cp is used in both circuits and only one output
rectifier is required. There, the secondary windings are connected in series, so that the current in
the two primary sides is inherently synchronised and balanced as will be shown below. With this
circuit, the control by self-sustained oscillation could be directly applied and the two H-bridges
require only one control unit.
Instead of series connecting the primary sides as shown in Fig. 1b), a parallel connection as
shown in Fig. 3a) could also be utilised, which is advantageous at low mains voltages.
Because the operation of the proposed circuit connection is closely related to the operation
mode, in section 2 the operation principle of the series parallel resonant converter based on the
self sustained oscillation is discussed briefly. Thereafter, the operation of the series or parallel
connected converters is explained. There also combining the two transformers in one magnetic
component is discussed. Furthermore, the influence of component tolerances on the load sharing
is investigated. In section 3 a prototype system and measurement results validating the proposed
concept are presented.
2
Operating Principle
In the following, the operating principle of the resonant converter is shortly explained as it significantly influences the proposed connection of the DC-DC converters Fig. 1b). The operation is
based on the self-sustained oscillation above the resonance frequency of the resonant tank as proposed in [1]. There, one leg switches always at the zero crossing of the primary current IS flowing
through the series capacitor as shown in Fig. 2a), so that this leg operates at zero current switching
(ZCS) condition and could preferably be realised with IGBTs [9, 10] thus lowering system costs.
By shifting the turn off instant of the IGBTs to shortly before or after the zero crossing of current
IS the losses can be minimised for the chosen IGBT.
In the second leg, the switches always have to turn off a current. In case MOSFETs are used,
the current rapidly commutates to the relatively large output capacitance of the (Super-Junction)
MOSFETs and zero voltage switching (ZVS) conditions are achieved. Consequently, the switching
losses in both legs are very low. IGBTs are not well suited for the second leg due to their tail
current, which would result in turn off losses in spite of the ”ZVS”-condition.
The resonant oscillation in the resonant tank depends on the load and also on the component
VAB
IS
VDC
ZVS
CS1 LS1
VDC1
+
ZCS
IS
LM1
LÓut
IOut
+
Gate Signals
IR
IOut
CS2 LS2
VDC2
IS2
+
VCp
Tp/2
a)
b)
CṔ
RĹ
LM2
Gate Signals
Modulation
IS2
Fig. 2: a) Waveforms for a series-parallel resonant converter operated on the principle of the self sustained
oscillation presented in [1]. VAB is the output voltage of the H-bridge, IS the current in the series capacitor
CS , IR the current in sum of the current in the two rectifier diodes and VCp . b) Series connection of the
two the series-parallel resonant converter at the primary side, where the transformers are neglected and the
load side is transferred to the primary (indicated by the ’). Due to the missing galvanic isolation of the
transformer, the two input capacitors CDC1 and CDC2 are separated. For simplicity, the leakage inductance
of the transformer is neglected.
values CS and LS . Consequently, two series-parallel resonant converters utilising self-sustained
oscillation for control usually do not operate at the same switching frequency, even if they are
connected to the same load, due to the resonant tank tolerances. Therefore, a direct parallel/series
connection as proposed in [5] for phase-shift full-bridge converter could not directly applied for the
considered resonant converters.
2.1
Series/Parallel Connection
In order to overcome the limitations presented in the previous section, the circuit as shown in
Fig. 1b) is proposed in this paper [11]. There, the parallel capacitor CP is used by both resonant
converters. Replacing the transformers, the simplified circuit shown in Fig. 2a)b) results, where the
input capacitors providing VDC1 and VDC2 are separated as the galvanic isolation of the transformer
is not included any more in the equivalent circuit.
There, it could be seen that the two H-bridges and the two resonant tanks are connected in series,
so that the resonant current IS must flow through both resonant tanks and both H-bridges if the
magnetising current is neglected in a first approximation. Consequently, the operating frequencies
as well as the zero crossings of the resonant current of the two converters are inherently synchronised
and the H-bridges can be simply controlled by a single controller. This controller only requires one
resonant current IS1 or IS2 for controlling the circuit and synchronously triggers the respective
switches of the two H-bridges.
With the galvanic isolation provided by the transformer, the input voltages can be connected
in series or in parallel. In case of a parallel connection as shown in Fig. 3a), which is suitable for
low mains voltages, the two converter input voltages are inherently equal VDC1 = VDC2 and due to
the equal resonant tank currents IS1 ≈ IS2 the power transferred by each converter is also equal.
In case of a series connection as shown in Fig. 3b) the input current IDC of the two resonant
Table I: Difference of VDC1 and VDC2 in dependence of the component tolerances for two converters, that
are connected in series at the input.
LS1 = LS2
LS1 ±5%
CS1 ±5%
LM 1 ±5%
LS1 & CS1 ±5%
LS1 & CS1 & LM 1 ±5%
Fig. 3b) Fig. 4a)
Fig. 4b)
Voltage Difference VDC1−VDC2
≈ 0V
≈ 0V
≈ 0V
≈ 50V
≈ 10V
≈ 1.4V
≈ 24V
≈ 4.5V
≈ 0.4V
≈ 40V
≈ 7.5V
≈ 0.6V
≈ 60V
≈ 11.5V
≈ 1.8V
≈V
≈V
≈ 2.4V
C S1 LS1
VDC1
+
VDC
IDC1
CDC1
IS1
IS
L Out IOut
CP
VDC1 +
VDC
+
RL
a)
I DC2
C DC2
IS1
VDC2 +
b)
L Out IOut
IS
CP
+
IDC
IHB2
I S2
CS1 LS1
IDC1
C S2 L S2
VDC2
+
I HB1
I DC
RL
CS2 L S2
IS2
I DC2
Fig. 3: a) Parallel connection of the two the series-parallel resonant converter at the primary side. Due to
the identical resonant tank currents, which are determined by the secondary side current that is identical for
both converters due to the output series connection, the transferred power is the same for both converters.
b) Series connection of the two resonant converters at the primary side. The current IDC from the input
voltage source VDC flows through both DC capacitors CDC1 and CDC2 due to the series connection.
converters from the DC voltage source VDC is the same. Neglecting the magnetising current and/or
magnetising inductance of the two transformers in a first step, the two resonant tank currents IS1
and IS2 must be the same since the secondaries of the two transformers are connected in series
so that secondary currents of the two transformers are identical. Since the switches of the two
H-bridges are triggered synchronously, the input currents of the two H-bridges IHB1 and IHB2 are
equal. Consequently, the charging/discharging currents of the DC-link capacitors IDC1 and IDC2
are identical and with identical capacitance values CDC1 = CDC2 , the two converter input voltages
VDC1 and VDC2 are equal.
If CDC1 6= CDC2 , slightly unbalanced converter input voltages result VDC1/VDC2 ≈ C2/C1 . In
case the resonant tank component values are not exactly identical due to tolerances, only the voltage
drop across the resonant tank elements de-/increases if the magnetising inductance is neglected.
Still, the currents in the resonant tanks IS1 and IS2 are identical as they are determined by the
secondary current, so that the input voltages are still balanced even for not identical CS1 /CS2 and
LS1 /LS2 if magnetising inductances are neglected.
Considering the magnetising inductance with unidentical resonant tank component values, results in an unequal voltage drop across the magnetising inductances, since the voltage drop across
the resonant tank is not equal (assuming at the beginning: VDC1 = VDC2 ). Therefore, the magnetising currents are also not equal, resulting in slightly different resonant tank currents IS1 and
IS2 and consequently slightly different H-bridge input currents IHB1 and IHB2 . This leads to a
decreasing converter input voltage of those converter, which has a higher input current.
Due to the phase shift of the resonant tank voltage with respect to H-bridge output voltage
VAB and the synchronisation of VAB to the zero crossing of the resonant current IS1 and/or IS2
as shown in Fig. 2a), the phase of the magnetising current is usually shifted by more than 90◦
and less than 270◦ with respect to the secondary current IS . Consequently, the amplitude of
the resonant tank current slightly decreases with an increasing magnetising current. The reduced
resonant current results in a slightly smaller input current of the H-bridge/discharge current of
the input capacitor and consequently in a slightly increasing input voltage of the H-bridge. The
increasing input voltage of the H-bridge leads to an increasing magnetising current, so that in total
the input voltages are not stable and balanced any more. These considerations are true for an ideal
converter with linear inductances/transformers (without saturation/hysteresis) and ideal switches
(without loses or parasitic output capacitances).
In the real circuit with parasitics and nonlinear effects, the losses of the resonant converter
are dependent on the DC input voltage and usually increase with increasing voltage. For example
the nonlinear behaviour and the hysteresis of the magnetising inductance result in higher losses
with increasing voltage. Also the parasitic output capacitances of the switches, which are used to
achieve ZVS in case of the MOSFETs, result in slightly higher losses with increasing voltage due to
the increased circulating reactive power and non-ideal switches/conductors. In case of the IGBTs,
which switch at zero current or close to zero current, the parasitic output capacitances must be
dis-/charged directly via the switch and result in input voltage dependent switching losses.
Because of these voltage dependent losses, the unbalance of the two input voltages VDC1 and
VDC2 is limited to relatively small values – usually in the range of a few 10V as could be seen in
+
CDC1
L Out IOut
CS1 LS1
VDC1
B
A
CP
+
C DC1
L BA1
VDC
+
Coupling
VDC2
CS2 LS2
+
CDC2
LBA2
a)
CP
A
NB
VDC2
+
CDC2
B
ΦB
VDC
RL
LOut IOut
CS1 LS1
VDC1
NB
RB
+
RL
CS2 LS2
b)
Fig. 4: a) Extension of the proposed series connected resonant converters shown in Fig. 3b) by two coupled
inductors LBA1 and LBA2 for voltage balancing, which reduce the unbalance of the input voltage in case of
tolerances of the resonant components. b) An improved balancing circuit based on a small three winding
transformer. The windings on the outer legs have the same number of turns NB and the winding in the
middle leg is connected to a balancing resistor.
the second column of Table I – and the two resonant converters can be operated safely also for a
series connection at the input if the resonant tank component tolerances are not too large.
For improving the balancing of the input voltages and increasing the robustness of the input
series connection, a coupled inductor could be added to the circuit as shown in Fig. 4a). If both
resonant tank currents IS1 and IS2 are identical, the coupled inductors have no influence on the
circuit. They are like a 1:1 transformer with identical primary and secondary current, so the core
is not magnetised in the ideal case (IS1 = IS2 ).
In case of unequal currents IS1 and IS2 , the coupled inductors result in an induced voltage,
which tries to make the two currents IS1 and IS2 equal and therefore also tries to balance the input
voltages VDC1 and VDC2 . This could be nicely seen in the third column of Table I, where the input
voltage unbalance is shown for the converter system with additional inductors LBA1 and LBA2 ,
which is much smaller than the voltage unbalance of the original circuit.
However, for achieving a tight balancing in the range of a few volts even in case of larger component values tolerances, relatively large inductance values for the coupled inductors are required.
Due to the high peak value of the resonant tank current ISν , this results in large cores for the
coupled inductors and relatively high additional costs.
A more compact and cheaper solution is shown in Fig. 4b), which achieves a similar performance
as the coupled inductors as could be seen in the right column of Table I, but requires a much
smaller additional magnetic core. The balancing circuit consists of a core with two windings with
NB turns, which are for example wound around the outer legs of an E-Core. Each of these windings
is connected in parallel to one of the primary windings of the two transformers. The third winding
is wound around the middle leg of the E-core and is connected to a resistor RB . The number of
turns of this winding is adjusted to the resistance value of RB and is not critical - here it is chosen
to have also NB turns.
In normal operation, i.e. all the component values have no tolerances and VDC1 = VDC2 , the two
windings on the outer legs generate the same flux linkage amplitude but with opposite direction.
Thus, the flux generated by the left winding must also flow through the right winding and no flux
is flowing through the middle leg and no voltage is induced in the middle winding.
If the two voltages at the primary side of the transformers are different, the flux linkages
generated by the two windings are not equal any more and the difference between the two fluxes
must flow via the middle leg, which induces some voltage in the middle winding. The induced
voltage in the middle winding results in a current flow in RB that causes losses. These losses are
fed from the primary transformer voltage, which has a higher amplitude and therefore generates
a higher flux, as the surplus flux of this voltage flows via the middle leg. Due to the losses the
increase of the primary voltage and/or input DC voltage VDCν is limited.
For the considered specifications (cf. Table III), the additional losses are at most 5W for a
worst case situation with component tolerances of ±5%. By adapting the number of turns of the
winding on the middle leg, the winding on the middle leg could also be connected to some auxiliary
supply to reuse the power. However, the amount of transferred energy depends on the component
value tolerances and in case of ideal components no power is transferred. For the balancing circuit
an E19/8/5 is sufficient in case of NB = 30. With a custom core with a larger area on the outer
legs and a smaller middle leg, the balancing circuit could be made even more compact since the
flux in the middle leg is quite small.
Remark: As explained in section 2 the operation of the converter is synchronised to the zero
crossing of the resonant current. With the proposed setup only one control unit/modulator is used,
which is synchronised on one of the two resonant currents IS1 or IS2 . In the case of equal resonant
currents, it does not make a difference, which of the two resonant currents is chosen. However, due
to the influence of the magnetising current, there is a small difference in amplitude and phase of
IS1 and IS2 in the case component tolerances are included in the considerations. This could result
in slightly different operation. For example one resonant current has its zero crossing slightly after
the rising/falling edge of VAB . Usually, this small effect does not have an influence on the system
performance and could be neglected.
2.2
Component Selection
For determining the component values of the resonant tank, a fundamental frequency analysis as
presented in [12] or [13] is performed for the equivalent circuit shown in Fig. 5. There, the load
and the parallel capacitor are split in two parts, as the outputs of the two resonant converters
are connected in series. The components are furthermore transferred to the primary side of the
transformer by multiplying the inductor and the resistor by (NP /NS )2 and the capacitors by
(NS /NP )2 .
CS
VDC +
2
L´Out
2
LS
2 C´P
CS
+
2C´Out
RĹ
2
VDC +
2
LS
IS,Eq
2 C´P
R´AC
b)
a)
Fig. 5: a) Equivalent circuit for the series connected series-parallel resonant converters shown in Fig. 3b),
where the elements of the resonant tank result in the same operating frequency and duty cycle, so with
this simplified circuit the design of the resonant converter could be performed. b) By replacing the output
rectifier and the load by the resistor RAC as proposed in [12], a linear circuit results and a relatively simple
fundamental frequency analysis could be performed.
Table II: Considered design parameters for the equivalent resonant converter shown in Fig. 5.
Output Power PO
Input Voltage VDCν
Load Characteristic
Output Current IO
2.8kW
250V
20V + 0.04Ω
200A @ VO =28V
This simplified circuit is designed for providing half of the required output power at half of
the input DC voltage VDC at the nominal operating point. The load resistance for the considered
welding application is determined with the model of a welding arc, which usually is a voltage source
of 20V in series with a 40mΩ resistance (refer to Table II). Additionally, a voltage drop of 2V for
the rectifier diodes and the interconnections is considered, so that the total output voltage VOut of
the converter is 30V at nominal current and RL = (20V + 0.04ΩIN + 2V )/IN . In order to obtain
a linear circuit the rectifier and the output filter plus load resistance are replaced by an equivalent
2 2
load resistance RAC = π N /16 RL as shown in Fig. 5b). There, N is the transformer turns ratio
NP /NS and is given by the truncated value of N = 16/π 2 VDC/VOut . As the output current is
relatively high, a very low number of secondary turns is chosen – in this case NS = 1.
The operating frequency of the converter is chosen to be approximately 100kHz. To safely
achieve ZVS conditions, the resonance frequency fLs Cs , resulting for a short circuited output (i.e.
CP is inactive), is chosen to be 80kHz in order to have a safety margin. The quality factor at
nominal output power of the resonant tank including equivalent load resistance is chosen to be
QN = 2, so that the transfer ratio of the resonant tank is 1. With these assumptions the series
inductance and capacitance can be determined by
LS =
QN RAC
2πfLs Cs
and
1
.
2πfLs Cs QN RAC
CS =
(1)
100
70
90
60
80
50
20
10
a)
RL=5RNom
40
30
0
50
Voltage [V]
80
RL=2RNom
RL=RNom
60
50
70
40
60
50
150
20
30
200
Frequency [kHz]
250
300
20
b)
30
IS
40
RL=0.5RNom
100
70
VOut
VARC
50
100
150
200
Output Current [A]
250
Resonant Current IS [A]
Output Voltage [V]
The parallel capacitor transferred to the primary is chosen to be CP0 = CS / 2 , so that the
2
parallel capacitor on the secondary side is CP = N / 8 CP0 .
Based on these equations the component values given in Table III have been determined and
the output voltage as function of operating frequency as shown in Fig. 6 results.
10
300
Fig. 6: a) Output voltage of the converter system as function of operating frequency and for 4 different load
resistors. The values of the components are given in Table III. b) Output voltage of the converter system,
arc voltage (20V + 0.04mΩ IL ) and current IS through the resonant tank as function of the output current.
There, an operation at the resonance frequency of the resonant tank is assumed, so that the maximal possible
output power/current is shown. The shown operating point is 280A at nominal input voltage enabling also
full output current at reduced input voltage.
2.3
Transformer Design
So far two independent transformers and a separate series inductance LS have been assumed for the
two resonant converters. In a first step, the series inductance could be integrated in the transformer
by increasing the leakage inductance of the transformer. This is performed by adding a defined
path for the leakage flux as explained in [14], resulting in a compact and simplified converter design.
In a second step, the two transformer can be combined into one magnetic device as shown in
Fig. 7a). There, each primary winding encloses one core and the secondary winding encloses the
middle legs of both cores, i.e. the area enclosed by the secondary winding is twice the one enclosed
by the primary winding. Therefore, the transfer ratio is NP :NS × AP :AS . Such a configuration
Primary Winding 1
Midpoint
E55/21 Core
Primary Winding 1
Secondary Path for
Winding Leakage
Flux
Primary Winding 2
Space for
Secondary
Winding
Bobbins
Rectifier
Primary Winding 2
b)
a) Diodes
Fig. 7: a) Transformer setup with two separate primary windings and one secondary winding enclosing both
E-cores. The transformer is designed for an output current of 200A at 30V and uses E55/21 cores made
of N87 material. b) View of the bobbins for the transformer, where the additional path for the leakage
flux (small additional core) could be clearly seen. With the added ferrite material the leakage inductance is
adjusted, so that it is equal to the desired series inductance value.
Primary
Winding 1
IP1
j NP
RM,1
RM,2
NPIP1
NSIS
R
P1
IP2
j NP
RM,3
RM,4
R
P2
S
S
NPIP2
P2
j NS
1
P1
Primary
Winding 2
IS
Secondary
Winding
Midpoint
NSIS
IS
j NS
2
S
S
Fig. 8: Equivalent circuit of the transformer with two primary windings on two cores and one centre tapped
secondary winding enclosing both cores.
is called a matrix transformer [15, 16] and offers the advantage that the length of the secondary
winding could be reduced. Since the output current in the considered application is high, this
allows a reduction in losses.
For modelling the transformer, the equivalent circuit shown in Fig. 8 is used. It is based on
magnetic reluctances (cf. e.g. [17]) and directly links the geometrical properties of the transformer
to its magnetic and electrical behaviour. The two fluxes ΦP 1 and ΦP 2 generated by the two
primary windings add up in the secondary winding, which is split in two parts due to the midpoint
connection. The leakage inductance between the primaries and the secondary winding, which is
used as series inductance for the resonant converter, is mainly defined by Rσ1 and Rσ2 , which could
be calculated by
p
p
L1ν (L1ν − Lσν ) 2
L1ν − L1ν (L1ν − Lσν ) 2
NP
and
RM,ν =
NP .
(2)
Rσν =
L1ν Lσν
L1ν Lσν
These equations can be derived with the mesh equations set up for the magnetic circuit of a three
leg transformer, where one leg is used as leakage flux path and solving the equations for the fluxes in
the core as discussed in [17]. Based on the flux equations the related equations for the inductances
can be solved.
In the considered case, the leakage flux/inductance between the two secondary windings (turns)
is neglected, as it is relatively small and has little influence on the considerations performed in this
paper. However, this leakage inductance could have significant influence in converters with voltage
output and split secondary windings [18].
Table III: Specifications of the prototype system for the parallel connected series-parallel resonant converter.
Output Power PO
Mains Voltage Range VN
Input Voltage Range VDCν
Output Voltage Range VO
Output Current IO
Ambient Temperature
Dimensions (incl. AC/DC)
Weight (incl. AC/DC/Housing)
Efficiency (incl. AC/DC)
Resonant Tank
Transformer
2×2.8kW
208V. . .460V
254V. . .360V
20. . .100V
200A @ VO =28V
45◦ C
337x×130×211 [mm]
5.5kg
≈ 90%
Ls =58µH, Cs =68nF & Cp =700nF
E55/21 Cores, N87 Material
Prim. 13 Turns 200×100µm litz wire
Sec. 1 Turn 1470×100µm litz wire
It can be seen in the equivalent circuit, that due to the parallel connection of the two magnetic
circuits modelling the two primary windings, the currents in the two primary windings must be
identical (for the ideal circuit) due to the balance of the voltage sources modelling the magnemotive
forces (Nν Iν ). Based on the equivalent circuit shown in Fig. 5b) and the current through the
resonant tank IS,Eq , the voltage across the parallel capacitor VCp could be calculated. With VCp
the voltage across the transformer winding is given by
VP rim =
N
VCp
4
with
VCp =
0 1/(jωC 0 )
RAC
P
ILS,Eq .
0
RAC
+ 1/(jωCP0 )
(3)
With the primary voltage, the required core area could be determined by ACore = VP rim / Bmax NP ν ω.
There, Bmax is the maximal flux density in the core.
3
Measurement Results
In order to verify the proposed concept a prototype system as shown in Fig. 9a) with the specifications given in Table III has been built. The commercial version of the prototype is designed for
a nominal three-phase input voltage of 400V and operates with an input series connection of the
two resonant converter. The prototype could be easily reconfigured to work with a input parallel
connection for markets with lower mains voltages.
With this system, measurements for a series connection at the input of the two converters
has been performed. The results for operation at nominal power are given in Fig. 9b)-d), where
Secondary
Midpoint
Primary
Winding
Zoomed View
DC Link
Capacitors
VDC1 & VDC2
IS
IOut
b)
Zoomed View
IS
c)
Output is shorted
VDC1
VDC2
IOut
VDC1
VDC2
Output
Connectors
Parallel Capacitor
Transformer
200A
a)
240A
IOut
d)
Fig. 9: a) Photo of the prototype system for the welding power source with a max. output current of 200A
at 28V output voltage. Further specifications are given in Table III. Measurement results for two converters
with the specification given in Table III, which are connected in series at the input. The operating point
is IO =200A, VO =30V and VDC1 = VDC2 = 266V for b) and VDC1 = 278, VDC2 = 251V for c). In c) the
two series inductances are not identical resulting in unbalanced DC input voltages. d) DC-link voltages and
output current for a load step, from nominal output power (200A) to a short circuit at the output (very low
output power), what is a typical condition for welding power sources. As could be seen, the DC-link voltages
stay nicely balanced.
measurements for approximately identical resonant tank components resulting in balanced input
voltages and measurements for not identical series inductances are shown. Furthermore, measurement results for a load step from nominal output power to a short circuit at the output, which is
a typical operation condition for a welding power source, are given. All the results nicely match
with the predicted behaviour and show a stable operation of the two converters even in the case of
tolerances.
4
Conclusion
With the proposed circuit configuration series-parallel resonant converters operating with selfsustained oscillation can be operated with a series connection at the output and the possibility of
a parallel or a series connection at the input. In the case of a parallel connection at the input the
transferred power of the converter units balances inherently. For a series connection of the converter
inputs, a new concept is proposed which also enables an automatic balancing of the transferred
power.
Furthermore, the integration of the two transformers of the converters into a single magnetic
component and the integration of the series inductances in the transformer is explained. This allows
to reduce the losses especially on the secondary side, which conducts the high output current.
The proposed concept is verified by simulations and measurements on a prototype system, which
nicely confirm the concept.
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