HIGH EFFICIENCY LLC RESONANT CONVERTER WITH DIGITAL CONTROL
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1 HIGH EFFICIENCY LLC RESONANT CONVERTER WITH DIGITAL CONTROL ADRIANA FLORESCU, SERGIU OPREA Key words: LLC resonant converter, High efficiency, Digital control. This paper presents the theoretical analysis and practical implementation of an LLC resonant converter using fully digital control. The power train specific operation, together with a simplified approach for, determines the small-signal (control to output) transfer function is also presented. The SIMPLIS/Simetrix simulator is used for the verification of the theoretical results. An experimental prototype is developed using a commercially available Digital Signal Controller (dspic33fj6gs50) in order to validate the proposed theoretical model.. INTRODUCTION As the demands for high power applications increase, the designer must select the suitable converter topology that meets the design expectations in terms of high efficiency, high operating frequency, large variation of the input and output voltages and low electromagnetic interferences (EMI). The resonant converters represent a good option because of their inherently high efficiency across wide input and output operating voltages range and low EMI [, ]. During the period , traditional PWM converters were limited to operating frequencies around 0 50 khz due to the low speed of the power switching devices that produce excessive losses during transitions between states. The reduced switching frequency solves the problem of high switching losses but increase the dimensions of the power train components (inductors, transformers and capacitor and, consecutively, the price of the converter. At the begining of 980 s the resonant converters were developped. The basic idea of a resonant converter is their command of the power switches, either when their voltage is zero (ZVS) or their current is zero (ZCS) thus greatly reducing the associated switching losses. The currents/voltages waveforms on a resonant converter are close to the sinusoidal ones, which represents a major benefit, compared with the rectangular Politehnica University of Bucharest, Splaiul Independenţei 33 Bd., 06004, Bucharest, adriana.florescu@upb.ro. MICROCHIP Technology, Bucharest, Romania, sergiu.oprea@microchip.com. Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 58,, p. 83 9, Bucarest, 03
2 84 Adriana Florescu, Sergiu Oprea waveform of the classical converters that causes electromagnetic interferences (EMI) during the commutation process. The reduced switching losses allow the resonant converters to achieve high efficiency at considerable higher switching frequencies than the classical hard switched topologies. As the name indicates, the LLC resonant converter includes two inductances (LL) and a capacitor (C). The two inductors together with the capacitor form a resonant tank that will create a quasi-sinusoidal current or voltage waveform through, or across the switching network elements. The high efficiency of the LLC resonant converter at high input voltages recommends this topology for off-line (AC/DC) applications. Specific applications of the LLC resonant converters include LCD/TVs sets, laptop s chargers, highpower LED lighting, HID/HPS lamp ballast and applications that require high efficiency and high-power density. The power range for LLC resonant converters is between 80W up to more than kw and their maximum efficiency exceeds 85%.. ANALYSIS, MODELING AND DESIGN OF THE LLC CONVERTER.. OPERATION OF THE RESONANT LLC CONVERTER The power train of the half-bridge LLC converter is presented Fig.. The input 30 Vac grid voltage is converted into V in = 34 Vdc using a bridge rectifier (not represented in Fig. ) that supplies the switch network represented by switches Q and Q which transform the continuous voltage into a rectangular waveform one. The resonant tank includes the capacitor C r, the inductance L r and the magnetizing inductance L m of the T transformer (with a turn ratio of n:) considered ideal. The transformer drives the output rectifier that can be a simple diode bridge or a synchronous one in order to improve the efficiency at high output currents. The rectified signal is filtered by the output capacitor, C out and applied to the load, R load. The transformer provides the galvanic isolation necessary for the AC/DC conversion applications. Fig. The half-bridge LLC converter power train scheme and the equivalent resonant network scheme.
3 3 High efficiency LLC resonant converter with digital control 85 The Simetrix/SIMPLIS simulator is used to simulate the circuit. The schematic and the associated waveforms are presented in Fig.. Fig. The Simetrix/SIMPLIS simulation scheme and the associated waveforms. The control of the LLC converter requires variable switching frequency. The Duty Cycle is kept constant, 50%, and a small amount of Dead Time is inserted between the two states in order to prevent the shoot-through phenomenon. The DC gain factor of the LLC converter can be developed by analysis (continuous time Laplace domain) of the equivalent network schematic (Fig. ). The Fourier analysis for the rectangular signal at the output of the switching network gives: Vdc Vdc vsw( t) = + sin( k ω t). () π k k =,3,5 The resonant tank will filter the DC component and the high order harmonics. Using the First Harmonic Approximation [4] on the equivalent schematic, the transfer function of the resonant tank is: rectifier, ( RMS) n Rload ( s = sw,( RMS ) in V L) H ( =, () V n Z where n is the transformer s transformation ratio and: where: Zin = + s Lr + n Rload ( s Lm). (3) s Cr The LLC converter DC gain, M, is given by (4): M ( f sw ) = n H ( =, (4) λ (λ + ) + Q ( fn ) fn fn
4 86 Adriana Florescu, Sergiu Oprea 4 f r = π Lr Cr = resonant frequency, (5) Lr Z 0 = = characteristic impedance, (6) Cr π Zout Pout Q = = quality factor, 8 n Vout (7) Lr λ = = inductances rapport, Lm (8) f f sw fn = = normalized frequency. (9) r The DC gain can now be plotted using Matlab or any other tool. A family of curves that represent the DC gain M versus the switching frequency is represented in Fig. 3. Fig. 3 The DC gain, M and the operating regions of the LLC converter. The LLC converter exhibits multi-resonant behavior regarding the operating point. Fig. 3 presents the operating regions as a function of switching frequency. The region is in general used for operation of the LLC converter because the ZVS soft transition occurs only in this region. The ZCS transition is present in region but the RMS currents through the switches are high. The operation point of the LLC converter is, in general, kept near the resonant frequency in the right part of the DC gain peak. The controller will vary the switching frequency to maintain constant the output voltage. As the M curve indicates the frequency variation is inverse proportional with the output voltage; when the frequency increases the output voltage decreases. The controler must ensure that the variation
5 5 High efficiency LLC resonant converter with digital control 87 of the switching frequency is constrained to certain limits (i.e. to avoid EMI problem... SMALL SIGNAL ANALYSIS In order to develop a control system for the LLC converter it is necessary to determine the small-signal (control to output) characteristics of the LLC converter. The presence of high order harmonics may affect the accuracy of the small-signal model if the state-space average method is applied. The Extended Describing Function method or the Phasor Method can be used with good accuracy, but they led to extensive computation in order to develop the small-signal model. In this paper a simplified methodology is described in order to obtain the small-signal, control to output transfer function of the LLC converter. The schematic used to determine the open loop transfer function is presented in Fig. 4. Fig. 4 The open loop control schematic and the associated Bode plots (SIMPLIS simulation). The LLC converter is a multi-resonant one and the small signal transfer function will depends on the operating region. In order to derive the control to output characteristic it is necessary to make some initial assumptions that will greatly simplify the analysis: the converter operates only in region (ZVS), the switching frequency is much higher than the frequency of the perturbation signal (f SW >> f C ), the Dead Time is small compared with the switching period (T SW ) and the output smoothing filter has a time constant much higher than the switching frequency. Also the self resonant frequency of the resonant tank is much higher that the perturbation signal frequency. All these assumptions are easily achievable in a practical implementation of the LLC converter. The harmonics of the rectangular signal produced by the switching network will impact the accuracy of this simplified analysis. However, as shown in [5], the effect of these high order harmonics is minimal. A more general method of analysis for circuits in presence of high order harmonics is given in [6]. The simplified small signal circuit is presented in Fig. 5. The impedance of the resonant tank components must be evaluated at the operating switching frequency of the LLC converter (f sw ).
6 88 Adriana Florescu, Sergiu Oprea 6 Fig. 5 The equivalent simplified small signal circuit of the LLC converter. The transfer function is now: ωsw * Lm n * ( Rload ( + Resr)) Uout( s * Cout ) H ( = =, (0) Uin( + ωsw * Lm n * ( Rload ( + Resr)) ωsw * Cr s * Cout H s + n Re ch out esr ( = GM C R, () ZRL + n s + ZRL ( Rech + Resr) + n Rech Resr Cout RL ech where G M is the modulator gain, n is the transformer s transformation ratio and: R ech Z ω C The modulator gain is given by: Z + n R ωsw Lm = Rload, () n RL = + ωswlr. (3) sw r G V f M = in GVCO, (4) sw where V in is the input voltage, G vco is the Voltage Controlled Oscillator gain (Hz/V) and fsw is the total frequency variation of the VCO that theoretically maintain constant the output voltage if the input varies from 0 to V in max. Determining the modulator gain is not a trivial task, because this parameter depends on both the input voltage and the operating point of the converter. Also, the variation of the modulator gain with the input voltage diminishes the line regulation performance of the LLC converter. Worst case scenario (i.e. high input voltage and low output power or low input voltage and high output power) analysis must be performed in order to avoid unwanted effects coming from the variation of the modulator gain.
7 7 High efficiency LLC resonant converter with digital control 89 The Bode plots for the switching and proposed model (from SIMPLIS simulation) are presented in Fig. 6. Note that the 80 phase shift, present on the switching model, is coming from the modulator (VCO). The simplified model predicts correctly the position of the dominant pole and the gain of the system up to more than one 0 th of the switching frequency. The simplified model does not include the Right Half Plane Zero (RHPZ) or any other high order effects of this converter. However, these effects occur at high frequencies well beyond the typical crossover frequency for a front-end converter. Fig. 6 The Bode plots for the switching and the proposed model..3. IMPLEMENTATION OF THE DIGITAL CONTROLLER The proposed simplified model is validated by practical implementation of the LLC converter using a 6 bit DSC (Digital Signal Controller). The Microchip s dspic33fj6gs50 6 bit high performance DSC was chose for this task. After inspection of the Bode plots, a PI controller is proposed for the control of the LLC converter due to its simplicity. The analytical expression of a continuous time PI controller is: T u( t) Kp e( t) + Ki e( t) )dt, (5) = 0 where K p and K i are the proportional respectively the integral gains and e(t) is the error signal. The Laplace transformation of (5) gives: U ( = Kp * E( + Ki E(, (6) s HR( = Kp ( + K K i p ) s = K p s + ωpi ωpi, (7) s
8 90 Adriana Florescu, Sergiu Oprea 8 Ki where ω pi = is the zero of the PI controller. Kp The transfer function of the compensated system is: Hs( = H( HR(, (8) where H( is the control to output transfer function of the LLC (). The transfer function of the proposed PI controller is: s + HR( = (9) s The Bode plots of the compensated LLC converter are depicted in Fig. 7. Crossover frequency is 9 khz and the phase margin exceeds 80. The simulations were done at half of the full load. A degradation of the phase margin parameter is expected to occur at various conditions across the entire operating range of the converter. Fig. 7 The Bode plots of the compensated converter. The PI transfer function is converted to Z domain using the backward Euler method [3] z s =, (0) Ts z z HR ( z) = Ts. () 800 z The Equation () can be now directly implemented in the DSC. In order to fulfill the minimal distortion criteria (THD < 3 %) the control loop must run at a frequency higher than 00 khz, 0 th time higher than the crossover frequency of the system [3]. The pre-warping technique is not used for this implementation. The resolution of the DSC is 0 bit led to about 60 db dynamic range. The PWM generator resolution is bit and the dead time generator resolution is.04 ns. The
9 9 High efficiency LLC resonant converter with digital control 9 resonant tank current is monitored in order to detect an over-current condition. The DSC and the additional circuitry are placed on the secondary side of the converter (low voltage side) and the signals are separated by transformers..4. EXPERIMENTAL RESULTS The practically implemented LLC converter prototype has the following electrical parameters: V in = 60V 340V, V out = V, I out(max) = 0A. The resonant frequency is 00 khz and the maximum operating frequency is 70 khz. The typical waveforms of the LLC resonant converter are presented in Figs. 8 and 9. The ZVS transition can be maintained across the entire operating domain. Fig. 8 The typical waveforms. Fig. 9 The ZVS transitions. Fig. 0 The measured efficiency (%) vs. output current (A). 3. CONCLUSIONS This paper presents a highly efficient LLC resonant converter employing fully digital control. A detailed description of the LLC resonant converter power train and the digital controller are presented. A simplified method for the analysis of the small signal transfer function of the LLC converter is presented together with the simulations of the switching model. The analysis of the LLC resonant converter cannot be decoupled from its operating conditions set by the load and input voltage. This fact complicates the design of the LLC converter. However, due
10 9 Adriana Florescu, Sergiu Oprea 0 to its high performance, the LLC converter becomes widely accepted in front end applications. A prototype of the digitally controlled LLC converter implemented with a commercially available DSC (dspic33fj6gs50) [7] is also presented. The experimental results validate the proposed theoretical model. The measured efficiency exceeds 87% for medium to high output powers. A further refinement must include the operation of this converter together with a Power Factor Corrector circuit (PFC) in order to meet the IEC regulations regarding the harmonic content of the input current. Received on January 8, 03 REFERENCES. F. Constantinescu, A.G. Gheorghe, M. Nitescu, The energy balance error for circuit transient analysis, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 55, 3, pp , 00.. A.G. Gheorghe, F. Constantinescu, M. Nitescu, A new algorithm for envelope following analysis, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 56,, pp. 9 36, Buso, P. Mattaveli, Digital Control in Power Electronics, Morgan and Claypool Publishers, J.-W. Huang, S.-C. Wang, Y.-H. Liu, Design of a digitally-controlled LLC resonant converter, International Conference on Information and Electronics Engineering, Bangkok, Thailand, Bo Yang, Topology Investigation of Front End DC/DC Power Conversion for Distributed Power System, PhD dissertation, Virginia Tech University, F.I. Hănţilă, M. Maricaru, R.M. Ciuceanu, L. Corlan, Harmonic Analysis of Circuits with Nonlinear Resistive Elements, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 57, 4, pp , * * *, dspic33fj06gs0/x0 and dspic33fj6gsx0/x04 Data Sheet, Microchip Inc., 009.
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