LLCC
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 LLCC converter with voltage-source output. Instead of the resonant elements, ratios of them, e.g. the ratio of inductances L s
/ L p 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 L s
/ L p is only a function of geometry, this design parameter is directly considered by geometry. Experimental results demonstrate the high efficiency.
A.
I.
Application Concept
I
Institute for Power Electronics and Electrical Drives (ISEA)
RWTH Aachen University
Jaegerstr. 17-19, 52066 Aachen, Germany
E-mail: di@isea.rwth-aachen.de
NTRODUCTION
• 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 anyway. Furthermore, the module-integrated converter concept only shows two power stages. Most solutions show more, or higher effort [2].
A highly efficient dc-dc converter is proposed as module integrated converter for photovoltaic applications, where PV voltage v
PV
, in the tens of volts, is boosted to a dc-distribution line voltage of V dstr
= 700 V, as indicated in Fig. 1.
• 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].
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:
• 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 V dstr
.
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].
978-1-4244-4783-1/10/$25.00 ©2010 IEEE 696

Figure 2. Single-phase LLCC -type Series-Parallel Resonant Converter
The DC-AC converter controls the dc-distribution voltage to a constant value of V dstr
= 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.
η euro
= 0 .
03 η
5%
+ 0 .
06 η
10%
+ 0 .
13 η
20%
+ 0 .
1 η
30%
+ 0 .
48 η
50%
+ 0 .
2 η
100%
(1)
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:
• Controllability: Due to the nature of parallel resonance the converter can be controlled by a small operation
• 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. frequency variation [6],[7],[8]. A wide input voltage range
Often series-parallel resonant converters are found comprising a current-source output. Due to high output voltage of V dstr
= 700 V, a voltage source dc-link is installed to minimize the stresses for the parallel resonant components L p and C p
[5]. The rectifier is realized as voltage doubler, reducing the ratio of secondary side numbers of turns on the transformer.
This paper focuses on the most important parts of the design of the five degrees of freedom of the resonant tank, i.e. r eff
, C s
, L s
, L p and C p
.
II.
v
D
PV,max
= 2 v
ESIGN OF
PV,min
is designed.
R
ESONANT
T
ANK
E
LEMENTS
• Resonant-pole principle: The resonant tank, consisting of the four elements C s
, L s
, L p and C p
, 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.
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.
• Low diode stress: The parallel capacitance C p
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.
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.
• 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”
η euro
. Latter takes the regular existence of reduced solar irradiation into account. It is defined as the weighted sum (1), with η x% being the efficiency of the converter operating at x% of nominal load.
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 : V in
=
2
π
2 v
PV and V out
=
π
2
V dstr
(2)
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ω s
= 2 π f s
=
1
L s
C s and ω p
= 2 π f p
=
1
L p
C p
(3)
I in
=
P r eff
V out
+ j r eff
V out
1
ω p
L p
ω
ω p
−
ω p
ω
(4)
V out
V in
=
⎢
⎣
⎡
⎢
1 +
L s
L p
⎝
1 +
ω
ω s
2
2 p
−
ω
ω s
2
2
−
ω
ω 2 p
2 r eff
⎟
⎤
⎟
⎦
⎞
⎠
⎥
⎥
2
+
P 2 r 4 eff
V 4 out
L s
C s
⎛
⎜⎜
ω
ω s
−
ω
ω s
⎞
⎟⎟
2
(5)
ω =
It can be read from (5) that for an operation frequency of
ω s
, i.e. converter operation in the Load Independent Point, the voltage ratio is independent of transferred power P and equals the effective transformer ratio r eff
. Regrouping the five degrees of freedom to the new five parameters r eff
L s
/ L p
and L s
/ C s
, ω s
, ω s
/ ω p
,
allows to visualize the voltage transfer function using normalized quantities. An exemplary plot is given in
Fig. 3.
Figure 4. Resonant current I in v
PV
(clamped to 8 A) @
=35V, P =167W r eff
=0.11, ω s
/ ω p
=0.1,
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 L s
/ L p
and L s
/ C s
. In that case the same would happen as illustrated in Fig. 3, i.e. that 167 W cannot be transferred at v
PV
= 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 @ r
L s
/ C s eff
=0.1,
= 12µH/µF
ω s
/ ω p
=0.25, L s
/ L p
=0.5 and
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:
• I in
is reduced for minimum L s
/ L p
, see Fig. 4
• I in
is reduced for maximum L s
/ C s
, see Fig. 4
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 I in
using (4), the operation frequency is necessary. Since the latter calculation is of 8 carried out numerically. th
ω using (5)
order, it is
Figure 5. Consecutive design steps of the resonant-tank parameters
L s
/
At zero power, (5) indicates that there is no dependence on
C s
. Thus, L s
/ L p
is minimized first for the operation points at zero power. As second step L s result is still a function of
/ C r s eff
is maximized for the specified maximum power levels as function of v
and ω s
/ ω
PV
. Since the p
, multiple
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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/m 2 and 25°C, the module shows its terminal behavior being characterized by a maximum power point P at the MPP voltage v
STC,MPP
= 35 V. Since P ( v
PV
MPP
P ( v
PV
)
= 167 W
) is linked to both the PV-characteristics and the converter transfer function, v
PV,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 respectively is illustrated in Fig.7.
C p
. The significant deviation between exact simulation, FHA and eFHA
Figure 6. Voltage conversion gain and resulting characteristic v
PV,STC
with
PV module connected @ STC, r eff
L s
/ C s
=0.05,
= 25µH/µF
ω s
/ ω p
=0.25, L s
/ L p
=2 and
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
PV,STC
goes through the load independent point, but also has its maximum power point P
MPP to the constant power characteristic P =167 W. v
PV,STC is approaching the constant power characteristic P =0 W respectively. In Fig. 6.b it is visualized, that on the one hand v
= 167 W when v
PV,STC
tangents
Figure 7. Comparison of FHA, eFHA and exact simulations @ f s
=200 kHz, r eff
=0.12, ω s
/ ω p
=0.167, L s
/ L p
=1 and L s
/ C s
= 36µH/µF
The derived design method identified results in a design given in Tab. 1:
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TABLE I.
L s
/ L p
T ARGET QUANTITIES FOR THE IMPLEMENTATION OF THE
RESONANT TANK
L s
/ C s
ω s
/ ω p r eff
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 ω s
. Operation frequency and covers this load independent point. By now, all quantities are related to this parameter such that ω s
ω varies
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 2 pri
A
L
(6)
Figure 8. Frequency dependent loss contributors and their sum
Thus, the important related parameter L s
/ L p
, being both defined for the primary side, neither depend on primary side- nor on secondary side number of turns ( the parameter important for the resonant operation only a function of material and geometry. Hence, the remaining parameter r values by choosing N eff pri
N pri
and N sec
). Hence,
L s
/ L p
is
can be set at the end to quasi arbitrary
and N sec
. This coherence is important e.g. in the design of contactless energy transmission systems using rotating transformers [14].
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 kHz is identified for the implementation.
IV.
E
XPERIMENTAL
R
ESULTS
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.
III.
C
ONSTRUCTION OF THE
T
RANSFORMER
-I
NDUCTOR
D
EVICE
The most critical parameter in the design and construction of the transformer-inductor device is the parameter
Furthermore, r eff
L s
/ L p
.
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 v
PV
= 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 d v out
/d t . 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 tank.
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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.
R
EFERENCES
Figure 11. LLCC characteristics at the border to hard swicthing operation for minimum v
PV
= 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. of v
The overall efficiency is characterized for the MPP voltage
PV
= 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.
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PCIM , May 1998
[2] C. P. Dick, “Multi-resonant converters as photovoltaic moduleintegrated maximum power point tracker,” PhD-thesis at Institute for
Power Electronics and Electrical Drives, RWTH Aachen University , to be published in 2010
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25, no. 4, pages 634-643, July 1989.
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Industry Applications , vol. 29, pages 126-135, January 1993.
[5] R. L. Steigerwald, “A comparison of half-bridge resonant converter topologies,” IEEE Transactions on Power Electronics , vol. 3, no. 2, pages 174-182, April 1988.
[6] R. P. Severns, “Topologies for three-element resonant converters,”
IEEE Transactions on Power Electronics , vol. 7, no. 1, pages 89-98,
January 1992.
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Power Electronics Association, 1997.
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European Conference on Power Electronics and Applications 2007 , pages 1-10, September 2007.
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
η euro
= 96 %
[12] Ramesh Oruganti, Fred C. Lee, “Resonant Power Processors: Part 1 -
State Plane Analysis,” Industry Applications Society Annual Meeting,
1984, Conference Record of the 1984 IEEE , pages 860-867, 1984.
[13] K. Venkatachalam, C. R. Sullivan, H.A.T. Tacca ”Accurate pediction of ferrite core loss with nonsinusoidal waveforms using only steinmetz parameters,” Workshop on Computers in Power Electronics, 3-4 June
2002 Page(s):36 – 41, June 2002
[14] D. Hirschmann, C.P. Dick, S. Richter, R. De Doncker, “Design of a
Contactless Rotary Energy Transmission for an Industrial Application,”
(7) , PESC 08 - IEEE 39th
Annual, June 15-19 Pages 4314-4319, Rhodes, Greece including control losses, could be demonstrated at rated power of 167 W.
V.
C
ONLUSIONS AND
F
UTURE
W
ORK
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
701