A High-Efficient LLCC Series-Parallel Resonant Converter

A High-Efficient LLCC Series-Parallel Resonant
Christian P. Dick, Furkan K. Titiz, Rik W. De Doncker
Institute for Power Electronics and Electrical Drives (ISEA)
RWTH Aachen University
Jaegerstr. 17-19, 52066 Aachen, Germany
E-mail: [email protected]
Abstract—A high efficient LLCC-type resonant dc-dc converter
is discussed in this paper for a low-power photovoltaic
application. Emphasis is put on the different design mechanisms
of the resonant tank. At the same time soft switching of the
inverter as well as the rectifier bridge are regarded. Concerning
the design rules, a new challenge is solved in designing a LLCCconverter with voltage-source output. Instead of the resonant
elements, ratios of them, e.g. the ratio of inductances Ls/Lp is
considered as design parameters first. Furthermore, the derived
design rule for the transformer-inductor device fits directly into
the overall LLCC-design. Due to the nature of transformers, i.e.
the relation of the inductances Ls/Lp is only a function of
geometry, this design parameter is directly considered by
geometry. Experimental results demonstrate the high efficiency.
Lifetime: The critical component of the system
exposed to harsh environment at the module is the
module-integrated converter. In comparison to singlephase AC-modules, no low frequency energy
buffering passives as electrolytic capacitors are
applied [1]. Furthermore, the effort for the converter
functionality at the module is minimized. Only
maximum power point tracking (MPPT) and safety
features are realized at high efficiency, also reducing
costs. Thus, a potentially high lifetime is achieved.
Costs: All grid-related functionalities like grid current
control, disconnection from the grid in case of
failures, metering etc. are only implemented once in a
central unit, which is necessary at least for metering
converter concept only shows two power stages. Most
solutions show more, or higher effort [2].
Flexibility: All kinds of modules can be connected via
a specific module-integrated converter. With the high
step-up ratio a high-frequency transformer will be part
of the topology. Thus, also classical thin-film modules
can be connected to ground to avoid deterioration
coming from small leakage currents in case of a
negative bias voltage. The system concept can be
combined with classical string or central converter
concepts. In case only parts of the PV-generator suffer
from shading, these specific modules might be
connected via a module-integrated converter [2].
Safety: The proposed system concept in Fig. 1 allows
grounding of the dc-distribution wires for the
installation and for maintenance work on the building
facade. The module-integrated converters are
programmed to operate only at a certain range of Vdstr.
Latter is a major safety improvement compared to
classical string or central converter concepts using a
dc-distribution, carrying the short circuit photovoltaic
dc-current when being grounded [2].
A. Application Concept
A highly efficient dc-dc converter is proposed as module
integrated converter for photovoltaic applications, where PV
voltage vPV, in the tens of volts, is boosted to a dc-distribution
line voltage of Vdstr = 700 V, as indicated in Fig. 1.
Figure 1. Parallel module-integrated converter concept
The advantages of this kind of parallel converter concept
with central dc-ac converter, compared to other moduleintegrated solutions, are as follows:
978-1-4244-4783-1/10/$25.00 ©2010 IEEE
Figure 2. Single-phase LLCC-type Series-Parallel Resonant Converter
The DC-AC converter controls the dc-distribution voltage
to a constant value of Vdstr = 700 V. Thus, the moduleintegrated dc-dc converter is clamped to a fixed voltage of the
distribution line and performs MPPT by maximization of the
output current.
B. Fundamentals on LLCC-type Converter
The critical component, exposed to the harsh environment
in the application, is the module-integrated converter itself.
Efficiency is maximized to maximize energy output and to
reduce operation temperature enhancing lifetime. The singlephase LLCC-type series-parallel resonant converter as
depicted in Fig. 2 is chosen, since this converter potentially
shows high efficiency. It is operated at 50% duty cycle and
180° phase shift of the inverter legs. The converter is
controlled by small variation of the operation frequency f. The
topology suits the requirements for the following reasons:
Low turn-off currents: Due to the nature of the
resonance, the load-resonant current comes down
before the turn-off instant. Thus, high frequencies can
be achieved resulting reduced component size.
Resonant-pole principle: The resonant tank, consisting
of the four elements Cs, Ls, Lp and Cp, is designed to
show an inductive behavior for the input MOSFET
bridge at operation frequency. Thus, the resonant pole
principle is applied resulting in zero-voltage switching
[3],[4]. Additional capacitive snubbers are installed
across the MOSFETs.
Low diode stress: The parallel capacitance Cp is the
sum of the parasitic capacitances of the diode, the
transformer, and an external capacitor. It acts as a
snubber for the rectifier diodes, since the diode’s
voltage slopes are limited.
High part-load efficiency: Due to the nature of the
series resonance, the rms-current in the resonant tank
is reduced significantly at part-load, reducing
component stress at reduced load [5]. This is a major
advantage in photovoltaic applications, since part-load
efficiency has major impact on “European Efficiency”
ηeuro. Latter takes the regular existence of reduced
solar irradiation into account. It is defined as the
weighted sum (1), with ηx% being the efficiency of the
converter operating at x% of nominal load.
η euro = 0.03η 5% + 0.06η10% + 0.13η 20% + 0.1η 30% + 0.48η 50% + 0.2η100% (1)
Controllability: Due to the nature of parallel resonance
the converter can be controlled by a small operation
frequency variation [6],[7],[8]. A wide input voltage
range vPV,max = 2vPV,min is designed.
Often series-parallel resonant converters are found
comprising a current-source output. Due to high output
voltage of Vdstr = 700 V, a voltage source dc-link is installed to
minimize the stresses for the parallel resonant components Lp
and Cp [5]. The rectifier is realized as voltage doubler,
reducing the ratio of secondary side numbers of turns on the
This paper focuses on the most important parts of the
design of the five degrees of freedom of the resonant tank, i.e.
reff, Cs, Ls, Lp and Cp.
Optimization is carried out in all steps for high efficiency
at the boundary conditions of the specifications in all
operational points. In this first step the choice of the
components is qualified with the goal of minimum apparent
power in the resonant tank, i.e. minimum rms-currents when
using voltage-source inverter and rectifier as given in Fig.2.
A. Converter Design Rules based on First Harmonic
Approximation (FHA)
Minimum currents in the resonant tank are the key to high
efficiency. This can be directly read from the loss models of
the different components as, on-state MOSFET losses,
resonant capacitor losses and copper losses of the transformerinductor device.
For the minimization of rms-currents, FHA is used as
converter model to derive design rules. Here, the design
method of a previous work on LLC-type resonant converters
[9],[10] is extended to LLCC-type converters. Under classical
ac-operation, i.e. describing the pulsed voltage waveforms
only with their fundamental component in (2) [5], the FHA
converter model is given by (4) and (5), with the definition of
resonant frequencies in (3):
FHA : Vin =
2 2
and Vout =
ωs = 2π f s =
I in =
Ls Cs
and ωp = 2π f p =
1 ⎛⎜ ω ωp ⎞⎟
+ jreff Vout
reff Vout
ωp Lp ⎜⎝ ωp ω ⎟⎠
⎡ L ⎛ ω 2 ω 2 ω 2 ⎞⎤
P2 L ⎛ ω ω ⎞
⎢1 + s ⎜⎜1 + s2 − s2 − 2 ⎟⎟⎥ + 4 4 s ⎜⎜ − s ⎟⎟
ωp ⎠⎦⎥ reff Vout Cs ⎝ ωs ω ⎠
⎣⎢ Lp ⎝ ωp ω
It can be read from (5) that for an operation frequency of
Figure 4. Resonant current Iin (clamped to 8 A) @ reff =0.11, ωs/ωp=0.1,
vPV=35V, P=167W
ω = ωs, i.e. converter operation in the Load Independent Point,
the voltage ratio is independent of transferred power P and
equals the effective transformer ratio reff. Regrouping the five
degrees of freedom to the new five parameters reff, ωs, ωs/ωp,
Ls/Lp and Ls/Cs allows to visualize the voltage transfer function
using normalized quantities. An exemplary plot is given in
Fig. 3.
Fig. 4 furthermore indicates a non reachable area, representing
that the specific operation point cannot be driven at even more
extreme values of the parameters Ls/Lp and Ls/Cs. In that case
the same would happen as illustrated in Fig. 3, i.e. that 167 W
cannot be transferred at vPV = 20 V. Thus, in a good converter
design the resonant tank limits the operation capability of the
converter to the specified operation region. If the converter
would be capable to transfer more power than necessary, rmscurrents are increased in the specified operation region.
With the knowledge on how and in which direction to vary
parameters, the design procedure in Fig. 5 is developed as
described below.
Figure 3. Voltage conversion gain @ reff =0.1, ωs/ωp=0.25, Ls/Lp=0.5 and
Ls/Cs = 12µH/µF
At an operation frequency around the series resonant
frequency, the resonant tank is inductive resulting in ZVS of
the MOSFET bridge. In this example it is observed, that zero
power can be transferred at high input voltages, but 190 W
cannot be transferred at low PV input voltages of only 20 V.
With the boundary condition of being capable to operate the
PV-module in all its possible operation points, now
parameters can be varied to minimize rms-currrents. As
proposed in [9],[10] for LLC-type converters, it is figured out:
Iin is reduced for minimum Ls/Lp, see Fig. 4
Iin is reduced for maximum Ls/Cs, see Fig. 4
Figure 5. Consecutive design steps of the resonant-tank parameters
This coherence was evaluated numerically using FHA and
later on also using a circuit simulator for a variety of operation
points. Only one operation point is illustrated in Fig. 4. For the
calculation of Iin using (4), the operation frequency ω using (5)
is necessary. Since the latter calculation is of 8th order, it is
carried out numerically.
At zero power, (5) indicates that there is no dependence on
Ls/Cs. Thus, Ls/Lp is minimized first for the operation points at
zero power. As second step Ls/Cs is maximized for the
specified maximum power levels as function of vPV. Since the
result is still a function of reff and ωs/ωp, multiple
combinations are iterated. The resonant current can easily be
calculated using (4).
B. Visualization of MPP-tracking Capability by Frequency
Variation using FHA
In the application of a photovoltaic module-integrated
converter, the irradiation and temperature operation point is in
interaction with the LLCC-converter transfer function. As
indicated before, the converter should perform tracking the
maximum power by variation of operation frequency. For one
example at standard test conditions (STC), i.e. at 1000 W/m2
and 25°C, the module shows its terminal behavior P(vPV)
being characterized by a maximum power point PMPP = 167 W
at the MPP voltage vSTC,MPP = 35 V. Since P(vPV) is linked to
both the PV-characteristics and the converter transfer function,
vPV,STC can be calculated as a function of ω. For the purpose of
visualization an extreme set of parameters is used for the
determination of the characteristics in Fig. 6.
Varying the operation frequency ω, the MPP can be
tracked for example using a simple hill climbing algorithm
aiming at maximum converter output current with operation
frequency as parameter.
C. Fast Numerical Design Procedure based on Derived
Design Rules
Since FHA is only an approximation, simulations based on
exact calculations were used for the design. With the above
derived knowledge of how to design the parameters to the
limits, only a few simulations have to be carried out, following
the procedure in Fig. 5. Thus, a fast design is established.
Exact simulations were used since an analytical model
could not be derived, even when looking at the extended First
Harmonic Approximation (eFHA) [11] or the State Plane
Analysis [12]. The latter ones either have an approximation
included again, or are derived for LLCC converters with
current-source output. The analytic description of the given
converter with voltage-source output always shows the
challenge of describing the rectifier in the discontinuous
conduction mode due to snubbering with Cp. The significant
deviation between exact simulation, FHA and eFHA
respectively is illustrated in Fig.7.
Figure 6. Voltage conversion gain and resulting characteristic vPV,STC with
PV module connected @ STC, reff =0.05, ωs/ωp=0.25, Ls/Lp=2 and
Ls/Cs = 25µH/µF
Fig. 6.a indicates that for small and large frequency values,
the operation point moves to a short- or open circuit of the
module, both resulting in zero power and the fact that vPV,STC
is approaching the constant power characteristic P =0 W
respectively. In Fig. 6.b it is visualized, that on the one hand
vPV,STC goes through the load independent point, but also has
its maximum power point PMPP = 167 W when vPV,STC tangents
to the constant power characteristic P =167 W.
Figure 7. Comparison of FHA, eFHA and exact simulations @ fs=200 kHz,
reff =0.12, ωs/ωp=0.167, Ls/Lp=1 and Ls/Cs = 36µH/µF
The derived design method identified results in a design
given in Tab. 1:
77 µH/µF
D. Operation Frequency
Out of the set of five degrees of freedom only four are
determined yet, see Tab. 1. The remaining parameter is the
series-resonant frequency ωs. Operation frequency ω varies
and covers this load independent point. By now, all quantities
are related to this parameter such that ωs is still free to choose.
For gaining maximum efficiency the frequency dependent loss
mechanisms quantified based on different loss models like the
Improved Generalized Steinmetz Equation [13]. Results are
depicted in Fig. 8.
Figure 9. Transformer-inductor device
This structure allows to independently design the leakage
and the main flux path. However, there is a potential to be
tapped to optimize the device. Since increased field strength
leads to proximity losses in the windings close to the airgaps,
the combination of outer ferrite cores with inner low- or
medium-µ materials seem to gain higher efficiencies. A
distributed airgap material, especially metal-powder
composites, would even show better performance in theory,
but the necessary thin plates of such material were not
available to the authors.
In every magnetic component the inductances referred to
the primary side are given by:
L = N pri
Thus, the important related parameter Ls/Lp, being both
defined for the primary side, neither depend on primary sidenor on secondary side number of turns (Npri and Nsec). Hence,
the parameter important for the resonant operation Ls/Lp is
only a function of material and geometry. Hence, the
remaining parameter reff can be set at the end to quasi arbitrary
values by choosing Npri and Nsec. This coherence is important
e.g. in the design of contactless energy transmission systems
using rotating transformers [14].
Figure 8. Frequency dependent loss contributors and their sum
The reduction of copper and core losses of the
transformer-inductor device are traced back to the reduction of
material at higher frequencies. An optimum series resonant
target frequency of 215 kHz is identified for the
The proposed converter is constructed and measurements
are presented here. Measurements visualizing the basic
operation and the controllability by frequency variation are
depicted in Fig. 10.
The most critical parameter in the design and construction
of the transformer-inductor device is the parameter Ls/Lp.
Furthermore, reff is integrated into the component. All other
parameters can be adjusted afterwards, maybe leading to an
overall increased or decreased converter operation frequency.
However, not meeting the design requirement from Tab. 1
would mean additional losses coming from increased
component stress due to increased rms-currents in the resonant
tank. It has to be noted that leakage inductance is in the same
order of magnitude as the main inductance. Thus, a leakage
path must allow a high leakage flux and a reluctance in the
main magnetic path has to limit the main inductance. This
functionality is realized with a setup with multiple airgaps
using ferrite core material as depicted in Fig. 9.
Figure 10. Exemplary LLCC characteristics at vPV = 35 V
The inductive behavior of the resonant tank leads to the
intended zero-voltage switching, i.e. that there is some small
current in the resonant tank remaining at the switching instant.
Furthermore, the soft commutation of the diodes can be
identified by the limited dvout/dt. At low power levels, see Fig.
10.a, the remaining current in the resonant tank results in a
triangular shape. From the conduction time of the diodes it can
be read, that mainly reactive power circulating in the resonant
Concerning the design goal of limiting the transferrable
power to the specifications at low input voltages Fig. 11
shows the border to hard-switching operation.
distributed airgap material. However, such thin plates
consisting of brittle metal-powder composites were not
available to the author yet.
Figure 11. LLCC characteristics at the border to hard swicthing operation for
minimum vPV = 27.5 V and corresponding maximum P = 144 W
As seen in Fig. 10.c, considerably higher power levels can
be transferred at increased input voltage.
The overall efficiency is characterized for the MPP voltage
of vPV = 35 V. Due to a design for European efficiency, see (1)
with emphasis on a high part-load efficiency, Fig. 12 depicts
the results including error propagation through the accuracy of
the measurement equipment.
Figure 12. Measurements for European efficiency
An efficiency drop in the higher power level is tolerated
and wanted, since part load efficiency was optimized in the
numerical optimization using the design procedure based on
FHA. A European efficiency of
ηeuro = 96%
including control losses, could be demonstrated at rated
power of 167 W.
The design of a highly efficient LLCC series-parallel
resonant converter is presented together with experimental
results for a photovoltaic application. Design rules on the
design of the resonant tank elements are motivated and
qualified. The method leads to the high efficiency for a wide
specified input region. In a future step the leakage path in the
transformer-inductor device should be substituted by a
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