DUAL BRIDGE LLC RESONANT CONVERTER WITH FREQUENCY ADAPTIVE PHASE-SHIFT MODULATION CONTROL FOR WIDE VOLTAGE GAIN RANGE

Transcription

1 DUAL BRIDGE LLC RESONANT CONVERTER WITH FREQUENCY ADAPTIVE PHASE-SHIFT MODULATION CONTROL FOR WIDE VOLTAGE GAIN RANGE S M SHOWYBUL ISLAM SHAKIB ELECTRICAL ENGINEERING UNIVERSITI OF MALAYA KUALA LUMPUR, MALAYSIA meshakib07@gmail.com MUTSUO NAKAOKA ELECTRICAL ENGINEERING UNIVERSITI OF MALAYA KUALA LUMPUR, MALAYSIA mlm17319@st.oit.ac.jp SAAD MEKHILEF ELECTRICAL ENGINEERING UNIVERSITI OF MALAYA KUALA LUMPUR, MALAYSIA saad@um.edu.my Abstract This paper presents an isolated DB LLC resonant converter with frequency adaptive phase-shift modulation control which overcomes the unity gain problem of conventional DB converter. The proposed control maintains the Zero Voltage Switching (ZVS) to all switches under all operating voltage and load variations. The control proposed for this circuit based on two control variables: switching frequency and phase-shift angle of the secondary switches. The Switching frequency changes with the load in such a way that, it is secured ZVS to the primary side for all phase-shift angles. To do so, the voltage gain becomes independent of the loaded quality factor. On the other hand, the phase-shift angle in between two bridges is used to regulate the output voltage and power flows of the converter. However these two variables control is beneficial for reducing conduction losses and switch turn-on losses throughout the wide voltage and load operation. Experimental results of a 1-kW prototype converter with V input and 48V output are presented to verify all theoretical analysis and characteristics. Keywords DB, LLC resonant converter, frequency adaptive phase shift modulation control (FAPSM), Zero-Voltage-Switching (ZVS). I. INTRODUCTION In DC micro grid, the Energy storage systems (ESSs) should have bidirectional DC-DC converter to store the excess energy and release it when the renewable energy sources are unable to generate sufficient energy or during the peak demand of energy consumption. Besides, voltage variation in the DC bus is wide, so the voltage gain range of bidirectional DC-DC converter should be as wide as possible. Dual active bridge (DAB) has drawn lots of interest in the energy storage systems due to having the bi-directional capability with high-efficiency, high-power density, and reliability [1]-[3]. The voltage gain of DAB is limited to unity to maintain ZVS for all load variations [4], [ 5]. It also suffers from high circulating current in the secondary side and high turn-off losses. In order to extend the gain range with ZVS or minimize the circulating energy further, some control strategies were proposed in [1], [3],[6]. However, these control strategies cannot overcome all the disadvantages at a time. The resonant version of DAB is called DAB resonance converter (DABRC) has the same performance with improved efficiency [6]-[9]. In [7] and [8], a dual bridge series resonance converter with fixed frequency phase-shift control has been proposed and analyzed using modified fundamental harmonic approximation approach. The voltage gain of this converter has to be limited to unity to maintain the ZVS over the wide load range, and the circulating current in the lowvoltage side is high as well. As a result, the efficiency is degraded, especially when the voltage gain deviates from the unity. Therefore, the converter becomes unsuitable for wide input voltage applications. A bi-directional DAB LLC converter for energy storage systems has been proposed in [6]. This converter operated at a constant frequency, but the duty ratio is different based on desired voltage gain. An extra inductor is added to make the topology symmetrical in any operating modes, which increases the power loss and cost for the system. The gain is still limited to maintain the high conversion efficiency. It is also operated in the capacitive slope region which is suitable for ZCS realization. II. STEADY STATE ANALYSIS The conventional DB LLC resonant converter with active rectifier is shown in Fig. 1. The power is transferred from input to the load with the aid of resonant tank components, C r, L r, and L m. Based on the Fundamental Harmonic Approximation (FHA), the AC-equivalent two-port model is /17/$ IEEE 2265

2 derived as shown in Fig. 2. All the inductors, capacitors, diodes, switches and the high-frequency transformer are assumed to be ideal in the model. Fig. 3 shows the steady-state waveforms of the converter where all the switches in both primary and secondary side have the constant duty cycle of 0.5. Generally, The phase-shift angle between primary and secondary switches is used to control the power flow and output voltage regulation [7],[8]. If the phase-shift angle is greater than zero i.e. > 0, power flows from the primary side to the secondary side, otherwise (i.e < 0) power flows in the reverse direction. Only the forward power flow is analyzed in this paper. The parameters which are transferred to the primary side are denoted by superscript ( / ). The following parameters are normalized for the DB LLC resonant converter: V base =, Zbase = = = = ; I base = (1) Where, is the angular series resonance frequency. The normalized switching frequency can be defined as Fig. 1. DB LLC resonant converter. (2) Where, = 2f s and f s is the switching frequency. The normalized reactances of the resonant tank can be expressed as = F ; = ; = (3) Fig. 2. AC-equivalent circuit of DB LLC resonant converter. Where, K = is defined as inductance ratio. In Fig. 2, the input of the resonant tank is a square wave voltage which is generated by the primary switching network. It is assumed that the higher order harmonics of the inverter output voltage are absorbed by the resonance tank components except the fundamental one, V r1.n (t). It can be defined by the (4), based on the Fourier decomposition. Following that the voltage across the transformer or the equivalent output voltage of the transformer referred to the primary is also a square wave voltage whose fundamental component can be expressed in (5), where is the controlled phase shift between primary and secondary switches. V r1.n (t) = V r1.n.r = (4) V t1.n (t) = V t1.n.r = (5) Where, V r1.n.r = and Vt1.N.R = fundamental RMS voltage of V r and V t. are the normalized Fig. 3. Key operating waveforms of DB LLC resonant converter. Due to the approximation of fundamental component of the input voltage, the current in the resonant tank would also be a sinusoidal function. Thus, the normalized fundamental 2266

3 components of resonant current (I r1.n (t)) can be defined in (6), where is the phase difference between V r1.n (t) and I r1.n (t). In a similar manner, the normalized fundamental transformer current (I t1.n (t)) can be expressed in (7), where is the phase angle with respect to V t1.n (t). I r1.n (t) = I r1.n.r (6) where, I r1.n.r is the normalized fundamental RMS resonant current. = (12) = (13) The equivalent input impedance of the two port network shown in Fig. 2 can be calculated as follows Z in.n = = j ( ) + I t1.n (t) = I t1.n.r (7) where, I t1.n.r is the normalized fundamental RMS transformer current. It can be seen from Fig. 2 that the output DC current I / o.n would be equal to the average value of I t1.n (t) after being actively rectified at angle Solving (8), yields to I / o.n = = It1.N.R cos () (8) Where, A = Q ( )2 Z in.n < = B = - ( )2 Q cot + ( )2 (F- ) C = ( )2 + ( )2 - (14) = (15) I t1.n.r = There is a phase difference in between transformer voltage and current due to the active control of the secondary switches. So, AC-equivalent resistance (R ac = 8R L/ / 2 or 2 R L/ /8 depending on the type of filter) to represent the secondary side circuit including HF transformer, the rectifier circuit, output filter and load is no longer valid to analyze the converter equivalent circuit. The current on the secondary side always remains in continuous conduction mode and maintain a phase difference, with respect to transformer secondary voltage. However, the circuit, including HF transformer, active rectifier, output filter and load can be represented by equivalent impedance instead of R ac. From the (5) and (9), it can be expressed as the ratio of transformer voltage and current in phasor form. cos Where = ( ) is the phase angle of the quality factor which can be expressed as follows Q = (9) (10) and Q is the = (11) Where, P o is the output power delivered to the load. From the AC-equivalent circuit, the phase angle and can be calculated in terms of controllable phase shift, and normalized switching frequency as follows A. Converter DC Voltage Gain From the equivalent circuit in Fig. 2, the voltage gain can be simplified as follows = G = (16) It is seen that, when = 0 0, the operation of the DB LLC resonant converter is the same as a conventional LLC resonant converter with diode rectifier and equivalent load can be seen as a resistor [6]. B. Reverse Power The reverse energy persists in the converter when the phase difference between transformer voltage and current occurs. It increases the conduction losses due to the part of the energy are transferred back and forth between output and input side. The ratio of reverse power to the output power can be calculated for the proposed converter as follows [6], [9], (17) III. DESIGN The design is focused on ensuring constant output voltage with wide input voltage and load variations. The prime issues 2267

4 of the design objectives are to increase the gain range and maintain ZVS operation from 20% load to full load. The specifications of the designed example are as follows: Input voltage, V in = V, Output voltage, V o = 48V, Output power, P o = 1-kW. C. ZVS Turn-on in the Primary Side Switches It should be noted that the ZVS turn-on for the primary side switches can be secured if the resonant converter will operate with inductive slope region. In this region, the resonant current becomes inductive with respect to inverted square voltage. It can be assumed that the ZVS turn-on will be occurred in the primary side switches if the input impedance of the converter represents inductive. In order to secure the ZVS turn-on, the phase angle () of the input impedance should be positive ( i.e > 0 ). It can be expressed by (15) as, >0 (18) In Fig. 4, describes the variations of and G with respect to for different Q values. The value of normalized frequency (F) and inductor ratio (K) has been chosen arbitrarily in the Fig. 4 to find out the ZVS turn-on range with regards to wide load variations (i.e Q) and control variable.it is seen that goes to the negative value when the voltage gain more than unity at light load conditions [8]. So, it can be assumed that ZVS turnon will be lost in the primary side switches if G is larger than one especially at light load conditions. Thus, for the fixed frequency single phase-shift modulation (SPM) control based converter, voltage gain is limited to unity to maintain ZVS turn-on in the primary side switches at light load conditions. Fig. 4. Plots of and G with respect to for the fixed switching frequency (F = 1.2), and K (K=0.6) A new control variable can be added with SPM control scheme to overcome the aforementioned drawback. Equation (18) is the function of Q, F and respectively. As a function of both F and, the ZVS turn-on range can be increased by manipulating those control variables with respect to loaded conditions. This could be helpful to mitigate the problem of unity gain with ZVS turn-on for the fixed frequency SPM control based converter. To do so, (18) can be expressed as follows after some manipulation. > (19) To satisfy the requirements of ZVS turn-on in the primary side, solving (19) at the extreme condition (i.e = 45 0 ) yields to > (20) The above equation defines the relationship between normalized frequency and the loaded quality factor. So, the switching frequency can be calculated in each load condition to secure ZVS turn-on in the primary bridge within allowable phase-shift angle. Fig. 5. Plots of and G with respect to at different Q and F values respectively According to (20), the frequency is selected sequentially with the load changes. Fig. 5 describes the variations of and G, as compared to both phase shift angle and switching frequency for different Q values. In this technique f s increases with decreasing load i.e. f s changes until the becomes positive for all variations. Multiples plot have been depicted in Fig. 5, for different Q and F values and all are following the same path. Thus, it is also confirmed from the Fig. 5, that the frequency selection minimized the effect of Q values on converter voltage gain (G) i.e. the converter gain becomes independent on load conditions. D. Selection of Quality factor at Full Load In order to minimize the reactive components, RMS currents and total operating switching frequency variations, full load quality factor (Q) should be chosen wisely. Q is proportional to the size of inductive components and inversely proportional to the size of the capacitive components. Although, Q is expected to be small to get the small inductive components including magnetic cores, but, the operating frequency range will be higher under all loads due to the selection of small full load Q value. So, based on the discussion above, Q = 2.5 at full load is selected. 2268

5 E. Voltage Gain Selection Fig. 5 describes the G with respect to where the maximum gain is limited to the numerical value 2. G increases linearly with and becomes flat when close to In high voltage gain operation, the RMS resonant current of the converter increases at a constant rate when G rises from the unity. The converter draws extremely high RMS current for slightly increasing G in that region where G changes slowly with. In addition, it is seen from (17) that reverse power increases with increasing resulting high circulating current in the converter. Thus the high RMS current and reverse power limits the voltage gain. So, the maximum voltage gain (G max) is chosen as 1.8 for this converter to minimize the enormous value of RMS current and reactive power from the converter circuit. So, the transformer turns ratio is calculated as follows reverse energy will be more due to the high value of especially at light load condition. This reverse energy will increase the conduction losses which are responsible for reducing the efficiency. Thus, the choice of high K value is not reasonable, otherwise efficiency will be degraded. n = = = 15 : 4 (21) The minimum voltage gain is obtained as, G min = = 0.9 (22) F. ZVS Turn-on in the Secondary Side Switches The ZVS turn-on in the secondary side switches can be realized by evaluating the phase angle between transformer voltage and current. It would be secured, if the transformer current is capacitive with respect to the transformer square voltage. Thus, to maintain the ZVS turn-on in the secondary side, should be positive. From (16), it can be written as, If is positive, (23) can be further simplified as follows K > (24) Fig. 6 shows the DC voltage gain G and versus phase-shift angle with different K. The voltage gain remains unchanged with different K when phase-shift angle varies from 0 0 to 90 0, which means the DC voltage gain of the converter is independent of the inductor ratio K. For the similar inductor ratio (K), the phase angle at full load has the narrow ZVS turn-on range than 20% load. Thus, it can be assured that if becomes positive for full load condition, ZVS turn-on will be secured for the rest of the load conditions. It is observed that a small L m (i.e large K) is useful to extend the ZVS turn-on range on the secondary side. But with large K value, the Fig. 6. Plots of and G with respect to at different K values The inductor ratio K can be calculated by (24) at extreme condition like Q = 2.5 (i.e: full load), G min = 0.9 and F = as follows, K > > (25) Finally with the help of (1), (2), (3) and (11) resonant tank elements are calculated as follows: L r = C r = (26) (27) L m = (28) The design specifications of the proposed converter are summarized in Table I. TABLE I. SPECIFICATIONS OF THE DESIGNED CONVERTER Parameter - Symbol Value - Unit Input voltage, V in V Output voltage, V o 48 V Resonant Inductor, L r μh Resonant Capacitor, C r nf Parallel Inductor, L m 5.61 mh Rated load Resistance (full load) IV. EXPERIMENTAL RESULTS A prototype converter is built and tested in the laboratory to verify the designed converter. It is designed for maximum 1-kW power throughput with MOSFET bridges, running from V DC supplies. The resonant frequency can be chosen high to reduce the parasitic effects in the circuit. N95 material based ferrite core (PQ 50/50) is used to build the HF 2269

6 transformer. An auxiliary inductor is added with HF transformer leakage inductors to get the desired resonant inductor. With the proper design, the resulted magnetizing inductance is set to 5.61 mh. HEXFET MOSFET IRFR 4620PbF and MOSFET IPP200N15N3G are adopted as the primary and secondary switches respectively. Fig. 7 and 8 show the experimental waveforms of the designed converter at full load of 1-kW for 400V and 200V input respectively. The measured resonant currents in both cases are sinusoidal because of the converter operated with a frequency which is close to resonance frequency. The current waveforms show that the ZVS turn-on in both bridges is well achieved at the full load. The voltage and current stresses across the resonant tank components are higher at 200V than 400V operation. Fig. 9. Measured voltage and current waveforms under 400V input, 48V output and 20% load condition Vr (100 V/div), Ir (4A/div) V r I r I t V t V t (200V/div), I t (4A/div) 2μs/div I 2 V cr V cr (100V/div), I 2 (12A/div) 2μs/div Fig. 10. Measured voltage and current waveforms under 200V input, 48V output and 20% load condition Fig. 7. Measured voltage and current waveforms under 400V input, 48V output and full load condition V r (100 V/div), I r (15A/div) V r I r V t I t I 2 V t (200V/div), I t (15A/div) 5μs/div V cr V cr (500V/div), I 2 (50A/div) 5μs/div Fig. 8. Measured voltage and current waveforms under 200V input, 48V output and full load condition The efficiency of the converter under 400V and 200V on different load conditions is shown in Fig. 11. The efficiency becomes higher all over the load range at 400V due to the minimization of reverse energy and turn-on losses in both bridges. In contrast, efficiency is degraded at 200V due to the high value of RMS resonant current and reverse energy. Thus the efficiency is decreasing gradually in boost operation with increasing conduction losses. Calculated efficiency is slightly more than the measured value due to the series resistance and other parasitic components of practical circuitry. FAPSM control scheme minimizes the RMS resonance current further with decreasing load which leads the higher efficiency at light load conditions even higher than the full load efficiency. So, the variation of efficiency from 20% load to full load for constant input voltage is narrow. Fig. 9 and 10 show the voltage and current waveforms of the proposed converter at the minimum load of 200W for 400V and 200V input respectively. It is seen that the resonance currents are little bit deviated from the sinusoidal shape because the converter is operated at a frequency which is far away from the resonant frequency. Like the full load operation, the component stresses become high at minimum input voltage operation. The current waveforms show that the ZVS turn-on of all switches is achieved at minimum load conditions. Efficiency (%) V input 200 V input 400 V input (Measured) 200 V input (Measured) Load (%) Fig. 11. Measured efficiency of the proposed LLC resonant converter 2270

7 V. CONCLUSION In this paper, a frequency adaptive phase shift modulation control for a dual bridge LLC resonant DC/DC converter is proposed. This control strategy makes the converter operating at a wide voltage gain range with ZVS turn-on over wide load conditions. It overcomes the narrow voltage gain limitation of dual bridge LLC resonant converter. Due to the two independent control variables, the voltage gain becomes independent of Q and K values. The proposed control also reduces the reverse energy at light load condition that improves the light load efficiency as well. The measured efficiency during maximum input voltage operation is about 97.86% even at 20% of full load condition. The performance of the proposed LLC resonant converter is experimentally verified with V input and 48V output converter prototype. ZVS turn-on is verified through experiment results for wide input and load range. All the switches maintain ZVS turn-on which reduces the switching losses and improves the efficiency of the converter. For the maximum and minimum input voltage condition, the measured efficiency is 96.5% and 92% respectively for the full load condition. Therefore, the designed converter becomes a good candidate for variable input and constant output voltage applications. [8] L. Xiaodong, "A LLC-Type Dual-Bridge Resonant Converter: Analysis, Design, Simulation, and Experimental Results," IEEE Transactions on Power Electronics, vol. 29, pp , [9] H. Bai and C. Mi, "Eliminate Reactive Power and Increase System Efficiency of Isolated Bidirectional Dual-Active-Bridge DC-DC Converters Using Novel Dual-Phase-Shift Control," IEEE Transactions on Power Electronics, vol. 23, pp , ACKNOWLEDGMENT This work was supported by the High Impact Research of University of Malaya-Ministry of higher education of Malaysia under Project UM.C/HIR/MOHE/ENG/17 and Postgraduate Research Grant (PPP) Project No. PG A. REFERENCES [1] D. Costinett, D. Maksimovic, and R. Zane, "Design and Control for High Efficiency in High Step-Down Dual Active Bridge Converters Operating at High Switching Frequency," IEEE Transactions on Power Electronics, vol. 28, pp , [2] S. P. Engel, N. Soltau, H. Stagge, and R. W. D. Doncker, "Dynamic and Balanced Control of Three-Phase High-Power Dual-Active Bridge DC- DC Converters in DC-Grid Applications," IEEE Transactions on Power Electronics, vol. 28, pp , [3] F. Krismer and J. W. Kolar, "Efficiency-Optimized High-Current Dual Active Bridge Converter for Automotive Applications," IEEE Transactions on Industrial Electronics, vol. 59, pp , 2012 [4] A. K. Jain and R. Ayyanar, "PWM control of dual active bridge: comprehensive analysis and experimental verification," in Proc. 34th Annual Conference of IEEE Industrial Electronics, IECON, 2008, pp [5] H. Zhou and A. M. Khambadkone, "Hybrid Modulation for Dual- Active-Bridge Bidirectional Converter With Extended Power Range for Ultracapacitor Application," IEEE Transactions on Industry Applications, vol. 45, pp , [6] J. Tianyang, Z. Junming, W. Xinke, S. Kuang, and W. Yousheng, "A Bidirectional LLC Resonant Converter With Automatic Forward and Backward Mode Transition," IEEE Transactions on Power Electronics, vol. 30, pp , [7] X. Li and A. K. S. Bhat, "Analysis and Design of High-Frequency Isolated Dual-Bridge Series Resonant DC/DC Converter," IEEE Transactions on Power Electronics, vol. 25, pp ,