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A High-Efficient LLCC Series-Parallel Resonant Converter 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 anyway. Furthermore, the module-integrated 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]. I. INTRODUCTION 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 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 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 transformer. 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. II. DESIGN OF RESONANT TANK ELEMENTS 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 = 697 2 2 π vPV and Vout = 2 π Vdstr (2) ωs = 2π f s = I in = Vout = Vin 1 Ls Cs and ωp = 2π f p = 1 LpCp P 1 ⎛⎜ ω ωp ⎞⎟ + jreff Vout − reff Vout ωp Lp ⎜⎝ ωp ω ⎟⎠ (3) (4) (5) reff 2 2 ⎡ 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 698 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: 699 TABLE I. TARGET QUANTITIES FOR THE IMPLEMENTATION OF THE RESONANT TANK Ls/Lp 1 Ls/Cs 77 µH/µF ωs/ωp 0.5 reff 0.13 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: 2 L = N pri AL (6) 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 implementation. IV. EXPERIMENTAL RESULTS 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. CONSTRUCTION OF THE TRANSFORMER-INDUCTOR DEVICE 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 tank. 700 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. REFERENCES [1] [2] [3] [4] Figure 11. LLCC characteristics at the border to hard swicthing operation for minimum vPV = 27.5 V and corresponding maximum P = 144 W [5] 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. 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