Design of a 5kW High Output Voltage Series-Parallel Resonant DC-DC Converter

Transcription

1 Design of a 5kW High Outut Voltage Series-Parallel Resonant DC-DC Converter Fabiana da Silveira Cavalcante and Johann W. Kolar Swiss Federal Institute of Technology (ETH) Zurich Power Electronic Systems Laboratory ETH Zentrum / ETL H16 Physikstrasse 3 CH-809 Zurich / SWITZERLAND / Euroe cavalcante@lem.ee.ethz.ch kolar@lem.ee.ethz.ch Abstract This work resents a comrehensive rocedure for designing a high outut voltage series-arallel resonant DC-DC converter. The system outut voltage control is by a combination of duty-cycle and switching frequency variation where soft-switching is reserved over the entire oerating range. The basic rincile of oeration of the converter is described and an analytical model is established which does rovide a basis for the numerical calculation of the stresses on the ower comonents. Furthermore a control strategy for minimizing the no-load conduction losses is roosed and the transient behavior in case of load stes including outut short-circuit is discussed based on digital simulations. I. INTRODUCTION The oeration of high outut voltage DC-DC converters is considerably affected by transformer non-idealities being caused by the large transformer turns ratio and/or large number of secondary turns. In articular the leakage inductance and the secondary winding caacitance do take considerable influence on the converter behavior and do otentially reduce efficiency and reliability [1]. Therefore converter toologies suitable for high-voltage alications should integrate the arasitics of the transformer into the circuit oeration. Accordingly series-arallel resonant converters are frequently emloyed for the realization of high outut voltage DC-DC converter systems. However the design of resonant converters is involved due to the large number of oerating states occurring within a ulse eriod. This aer resents a straightforward rocedure for designing a full-bridge high outut voltage series-arallel resonant DC-DC converter. The aroach is based on an extension of the first harmonic analysis roosed in []. There the converter outut ower is controlled by frequency variation at fixed duty-cycle. In contrast in the case at hand the outut ower is controlled by dutycycle variation where the oerating frequency is automatically adjusted for ensuring the commutation of one bridge leg at zero current. As the second bridge leg due to oeration above the resonance frequency commutates at zero voltage soft-switching is reserved in the entire oerating range. Furthermore in order to guarantee low losses in stand-by mode a control scheme minimizing the converter conduction and switching losses for no load oeration is roosed. Also the transient behavior for ste-like changes from rated load to no load oeration and to outut voltage short circuit is analyzed and a control concet is described which allows to maintain the converter oeration above resonance for all kinds of load changes. In the following the converter ower circuit will be described and subsequently an analytical descrition of the oerating behavior will be given based on the first harmonic concet []. Furthermore the stresses on the main ower comonents as determined by a numerical solution of the nonlinear imlicit analytical system descrition will be shown in grahical form. Furthermore results of simulations of a 5kW 3-6.5kV outut converter oerating at 50kHz at full load and 450kHz at low load will be given which fully verify the theoretical considerations. Finally a control concet guaranteeing low no-load losses and oeration above resonance also in case of highly dynamic load changes will be described. II. CIRCUIT DESCRIPTION The toology of the 5kW series-arallel resonant full-bridge DC-DC converter with imressed outut voltage oerating above resonance is shown in Fig.1. The (arasitic) caacitors C 1 C 3 serve for zero-voltage switching of ower transistors S 1 and S 3 the resonant inductor L s is formed by the transformer stray inductance in combination with an auxiliary inductor connected in series. The arallel resonant caacitor C is formed by the arasitic caacitance of the high-voltage transformer T 1 secondary winding. As freewheeling diodes D 1 D 3 the intrinsic diodes of the ower MOSFETs are emloyed; for the bridge leg realized in IGBT technology exlicit diodes D D 4 are rovided. Fig.1: Structure of the ower circuit of a series-arallel resonant DC/DC converter with imressed outut voltage; C denotes the equivalent caacitance of the secondary winding referred to the rimary /03/$ IEEE 1807

2 Fig.: Equivalent circuit of the converter circuit shown in Fig.1 for referring the outut quantities to the transformer rimary side. The rectifier circuits connected in series on the secondary side are sulied in arallel by the rimary winding. As will be shown in detail in section III the bridge leg S 1 S 3 emloying ower MOSFETs is oerating under zero voltage switching (ZVS) condition and the bridge leg S S 4 equied with IGBTs is commutating at zero current (ZCS). The equivalent circuit of the series-arallel resonant converter is deicted in Fig. where the outut quantities are referred to the transformer rimary side. There L 1 reresents the transformer magnetizing inductance the winding losses are considered by a series resistance R s. III. THEORETICAL ANALYSIS In the following oeration of the series-arallel resonant converter above resonance is assumed. There no direct current commutation from a free-wheeling diode to a ower transistor does occur and/or the (intrinsic) anti-arallel diodes of the ower MOSFETs which are characterized by a relatively slow reverse recovery behavior can be emloyed as free-wheeling diodes [3]. The voltage transfer ratio of a series-arallel resonant converter in deendency on the load and on the normalized switching frequency is deicted in Fig.3. the voltage V in is assumed to show a constant value. Furthermore the switching frequency rile of the outut voltage is neglected and the load is modeled by an equivalent resistor. The conduction states of the converter occurring within a ulse eriod are comiled in Fig.4 with reference to Fig.5. First State (t 0 t 1 ): This state begins at t 0 when the resonant current i Ls crosses zero and switch S 4 is turned on. In the revious stage S 1 was turned on under ZVS accordingly S 1 and S 4 do conduct the resonant current. The voltage v AB is ositive the resonant current is ositive sinusoid and the outut rectifier is turned off as v C decreases cosinusoidally from -V o /4n to zero and continues to increase to ositive values. The state ends when v C reaches +V o / 4n and the outut rectifier starts to conduct again. Second State (t 1 t ): In t 1 the resonant current still flows through S 1 and S 4. The voltage v C is clamed to +V o /4n and v AB is still ositive. Third State (t t 3 ): At the beginning of this state S 1 is turned off accordingly i Ls is directed to the caacitors C 1 and C 3 and charging C 1 and discharging C 3. When the voltage across C 3 reaches zero in t 3 the commutation of S 1 to D 3 is comleted. Fourth State (t 3 t 4 ): At time t 3 S 4 and D 3 are conducting. S 3 is turned on at zero voltage (ZVS). The resonant current i Ls is ositive and the inverter outut voltage v AB is zero. Immediately before the i Ls reaches zero S 4 is turned off in t 4.. Fifth State (t 4 t 5 ): As S 4 has been turned off i Ls flows through D and D 3. Accordingly we have v AB <0. When i Ls reaches zero in t 5 a half switch eriod is comleted. The system behavior for the second half switching eriod is analog to the first half eriod with relacing S 1 and S 4 by S 3 and S. Therefore the second half eriod will not be described but only the conduction states are shown in Fig.4 (cf. (t 5 t 10 )). Fig.3: Voltage transfer ratio of a series-arallel resonant converter in deendency on the load and on the normalized switching frequency f sn = f s /f o (normalization with reference to the series resonant frequency f o = (π L s C s ) -1 ); n denotes the transformer turns ratio. For low outut ower the converter characteristic is equivalent to a arallel resonant converter; for high outut ower the arasitic winding caacitance in a first aroximation can be assumed as being short-circuited by the equivalent load resistance [3] accordingly the system shows the characteristic of a series resonant converter. A. Converter Conduction States For simlifying the analysis of the converter stationary oerating behavior in the following all comonents are considered ideal and B. Design Procedure Based on First Harmonic Analysis In [] an analytical descrition of a series-arallel resonant converter with imressed outut voltage has been roosed for constant duty cycle oeration. This analytical concet will be extended to variable duty-cycle oeration and ZCS of one bridge leg and emloyed for a straightforward system design and/or for analyzing the influence of arameter variations in the following. There we assume as main secifications of the converter: outut voltage range V o = 3 6.5kV; outut current range I o = 0 00mA; outut ower range P o = 0 5kW. 1808

3 Fig.4: Conduction States of the series-arallel resonant converter within a ulse eriod (cf. Fig.5). In a first ste of the system design the comonents of the resonant circuit have to be determined under consideration of limitations caused by maximum admissible stresses on ower comonents or by arasitic comonent values. In the case at hand the converter switching frequency f s should not exceed 500kHz in order to limit the comlexity of the gate drive and control circuits and to have only a limited influence of the gate drive and signal electronics delay times on the oerating behavior; the maximum voltage stress on the (low caacitance) series caacitor C s should be lower than 1kV with resect to the caacitor technology available for high frequency high-current alications; the caacitance C /n of the arallel resonant caacitor referred to the secondary must be larger than 50F with resect to the minimum achievable winding caacitance of the high transformer emloyed in the case at hand. The rocedure for designing the resonant circuit comonents is iterative and starts from initial values for C α and n (C is the caacitance of the arallel resonant caacitor α = C /C s n denotes the transformer turns ratio). The choice of C and n is correlated via C /n 50F accordingly any values which satisfy this condition can be taken as starting values. There one has to consider that the choice of α takes a large influence on the converter oerating frequency range. For lower values of α the frequency range will be wider than for higher values. This means that the choice of α is related to the uer switching frequency limit. Following the rocedure described in [] and considering the starting values for C α and n and the effect of the outut rectifier stage we have for the rectifier conduction angle θ (cf. Fig.5) θ= tan n f C R 1 4 s o. (1) According to [] the combination of the outut rectifier the outut caacitor and the load can be reresented by an RC equivalent circuit R e C e. For the sake of clearness we will maintain notations of quantities defined in [] in the following although e.g. the variables R e and C e do not aear in the circuits resented here. With reference to [] (cf. Eqs. (17) (1) and section V in []) we have k v = sin( θ ) () β = sin( θ ) (3) kv π ω CR = (4) 4 tan( θ ) 1809

4 π D π φ = (7) where D = γ/π denotes the converter outut voltage duty cycle. Considering (7) and (6) we obtain 4 D π VAB(1) = Vin sin( ). (8) π Fig.5: Time behavior of characteristic voltages and currents and of the transistor switching functions (gate drive signals) of a series-arallel resonant converter within a ulse eriod (t 0 t 10 ). where k v is a coefficient defining the relation between V o transferred to the rimary and the amlitude of the first harmonic of the transformer rimary voltage β denotes the hase dislacement of the fundamentals of the rimary transformer voltage and current and ωc R e is a dimensionless arameter. For the AC voltage transfer ratio i.e. for the ratio of the amlitudes of first harmonics of the transformer rimary voltage and of the voltage v AB we have (cf. Eq. (34) in []) vc(1) 1 k1 = = vab(1) tan( β ) 1 [1 α ( fsn 1) (1 + )] + [ α ( fsn 1) ] ωcr ωcr (5) in deendency of θ and of the normalized switching frequency f sn = f s /f o where f o = (π L s C s ) -1 is the series resonant frequency. The time behavior of characteristic waveforms as assumed for the analysis in [] are deicted in Fig.6(a). In the case at hand (cf. Fig.6(b)) we have for the amlitude of the first harmonic of the converter outut voltage v AB 4 VAB(1) = Vin cos( φ). (6) π Furthermore according to Fig.6(b) we have for the hase dislacement φ of the first harmonic v AB(1) of the converter outut voltage v AB and of the first harmonic i Ls(1) of the inverter outut current and/or resonant circuit inut current i Ls Fig.6: Time behavior of the actual converter outut voltage of the outut voltage fundamental (shown dashed) and of the resonant current fundamental as considered for the first harmonic analysis in [] (cf. (a)) and in this aer (cf. (b)) the bridge leg comrising IGBTs is switching at the zero crossing of the resonant current i.e. at i Ls =0 (ZCS). With the relation for the inut hase angle ϕ(1) given in [] (cf. Eq.(39) in []) the duty cycle D now can be reresented as a function of the normalized switching frequency f sn and of the rectifier conduction angle θ 1 1 D = 1 tan ( α { fsn [1 + ( ω CRe+ tan( β ) )] 1} π ωc R e tan ( β ). [ ω C Re+ tan( β )] [1 +α (1 + )]) ω C R e (9) Finally also the outut voltage can be given as function of f sn and θ resulting in the voltage transfer characteristic 16 k1 π Vo = n Vin sin( D ) (10) π kv which is deicted in Fig.7 for the secifications given in section IV as a function of f sn and θ. With decreasing load and/or decreasing outut rectifier conduction angle θ the eak of the resonant characteristic shown in Fig.7 moves to higher frequencies. The converter oerating (switching) frequency which has to be adjusted accordingly in order to ensure oeration above resonance therefore shows a ronounced deendency on the load condition. The converter control scheme will be described in detail in section V. 1810

5 Fig.7: Voltage transfer characteristic of the series-arallel resonant converter in deendency of the normalized switching frequency and the rectifier conduction angle θ. Now based on the characteristics shown in Fig.7 with the starting values C = 1nF n = 15 and α = 0.4 the resonant comonents can be secified. (The starting value for n can be derived with reference to Fig.3 for assuming high outut ower where the DC gain V o /(nv in ) aroaches.5; for the given oerating conditions (V in =35V V o =3.5kV) this results in n 15). As can be seen from a finished design (cf. Fig.8(a)) the maximum duty cycle occurs in a first aroximation at the maximum outut voltage at maximum outut current i.e. at maximum outut current and rated ower (I o =00mA P o =5kW and/or V o =5kV cf. secifications given in section IV). Ideally the maximum duty cycle should be set to D = 1 the oerating oint for the maximum outut ower then would be laced at the eak of the resonant characteristic. However as for a ractical circuit a dead time has to be considered for the switch-over of an inverter bridge leg and delay times of the gate drive circuits and the signal electronics do occur we select D < 0.9 with resect to the high switching frequency. The voltage transfer characteristic (cf. Fig.7) gives a rough idea about the ossible oerating oints so it can be see that for θ = and f sn 1.35 it would be ossible to achieve V o =5kV at high outut ower. Based on (9) and (10) we obtain for oeration at 5kV/5kW θ = f sn = 1.34 and D = Substituting θ and R o = 15kΩ (equivalent to P o =5kW@V o =5kV) in (1) we have for the switching frequency f s = 50kHz. Based on this the series resonant frequency f o can be calculated and finally the inductance of the resonant inductor L s can be determined. After that the design roceeds with determining the stresses on the comonents. For the above described design of the resonant tank comonents the variables R o and θ were emloyed. However these variables do not rovide a clear reresentation of the system oerating oint. For this reason the equations which describe the system oerating behavior will be given in deendency of the outut voltage and outut current in the following. From a first harmonic analysis of the deendency of the system oerating behavior we have for a defined outut voltage V o and outut current I o Vo Q = (11) 4 n Z I θ= tan 1 s sn o π f α Q (1) θ k v = sin( ) (13) β = sin( θ) (14) kv π ω CR = (15) θ 4 tan( ) vc(1) 1 k1 = = vab(1) tan( β ) 1 [1 α ( fsn 1) (1 + )] + [ α ( fsn 1) ] ωcr ωcr (16) 1 1 D = 1 tan ( α { fsn [1 + ( ω CRe+ tan( β ) )] 1} π ωc R e tan ( β ) (17) [ ω C Re+ tan( β )] [1 +α (1 + )]) ω C R e 16 k1 π Vo = n Vin sin( D ) (18) π kv with the arameters Z s = L s /C s characteristic imedance of the series resonant circuit Q normalized load resistance f o = (π L s C s ) -1 series resonant frequency f sn = f s /f o normalized switching frequency α=c /C s. Some of the above given relations were already resented but are shown again in order to comile the whole set of equations (cf. (11)-(18)) which can be condensed into two nonlinear relations in terms of two variables i.e. in deendency of the duty-cycle and of the normalized switching frequency. So for given values of V in V o I o n α and for secified resonant circuit comonents a unique duty cycle D and unique switching frequency f sn can be determined numerically. Taking a set of values V o and I o which covers the whole oerating range the variables D and f sn can be grahically reresented as shown in Figs.8(a) and (b). Based on the solutions for D and f sn and on the time behavior of the voltages and currents shown in Fig.5 and/or Fig.6 now the stresses on all ower comonents can be calculated. There results e.g. for the eak value of the resonant inductor current fsn α Vo Î Ls = (19) n (1+ cos( θ)) Zs for the turn-off current of the ZVS bridge leg ower transistors IQoff = ÎLs sin( D π ) (0) for the eak value of the series caacitor voltage Î Ls ÛCs = (1) π Cs and for the RMS current stress on the ZVS ower MOSFETs I QRMSZVS ( D π) Î sin Ls = D π. () A grahical reresentation of (19)-() is deicted in Figs.8(c) - (f) for the arameters secified in section IV. There it can be verified that the maximum switching frequency is lower than 500kHz and the maximum voltage across the series caacitor is lower than 1 kv accordingly the design does meet the secifications. In the case of the secifications would not be met the design 1811

6 (a) (b) (c) (d) (e) (f) Fig.8: Duty cycle switching frequency and stresses on the selected ower comonents in deendency of the outut current I o and outut voltage V o. rocedure would have to be reeated with modified initial values C α and n. IV. SIMULATION RESULTS Based on the converter design described in section III digital simulations were erformed for minimum and maximum outut voltage and full load and light load condition. The resulting time behavior of the inverter outut voltage v AB of the resonant current i Ls and of the transformer magnetizing current i L1 is shown in Fig.9 for oeration at rated ower and V o =6.5kV (cf. (a)) and V o =3kV (cf. (c)). The system behavior for oeration at light load P o < 500W is deicted in Figs.9(b) (V o =6.5kV) and (d) (V o =3kV). (a) (b) Parameters as used for the simulations (cf. Fig.): V o = 3 6.5kV I o = 0 00mA P o = 0 5kW V in = 35V n = 15 C 1 C 3 = 00F R s = 100mΩ C s = 30nF C = 1nF L s = 4.3µH L 1 = 1.mH C h1 C h = 0.5µF. (c) (d) Fig.9: Digital simulation of the stationary oerating behavior; inverter outut voltage v AB (50V/div) inverter outut current i Ls (5A/div) and transformer magnetizing current i L1 (0.5A/div); time scale: 1.5µs/div. 181

7 V. CONVERTER CONTROL For system control and rotection a state machine is emloyed which is not described in detail for the sake of brevity. The turn-on and turn-off of the ZCS ower transistors is synchronized with the zero crossing of i Ls. The gate drive signals of the ZVS ower transistors are generated by comaring a constant amlitude sawtooth-shaed carrier signal s T and the controller outut voltage v c. There the sawtooth frequency has to be roerly adjusted for the different oints of oeration the amlitude of the sawtooth remains constant for all frequency variations. For generating a sawtooth with those characteristics a concet roosed in [6] is emloyed which is based on a double integrator oerating in closed loo. There the reset ulse RP is synchronized with the zero crossing of i Ls. A basic schematic of the sawtooth generator is deicted in Fig.10. (a) (b) (c) Fig.10: Control of a series-arallel resonant converter according to [6]. In the following two main asects of the converter control will be described. A. Oeration under No Load Condition According to Fig. 8(c) the amlitude of the resonant current does not change significantly with the outut ower level for higher outut voltages. That means that the conduction losses under no load condition will be almost as high as for full load. This is an inherent drawback of series-arallel resonant converter systems having a large outut voltage range. For solving this roblem the converter oeration is switched to burst mode at low load condition. There the outut voltage is maintained in a determined tolerance band around the reference value and the ower losses are reduced due to the low relative on-time of the ower transistors (cf. Fig. 11). B. Short-circuit Protection and Oeration Above Resonance The outut short-circuit and/or overcurrent rotection is of secial imortance in connection with ensuring high system reliability. In order to kee the current below a defined maximum value a current limiting mode is rovided in the state sequence. When the overload or short-circuit ceases the circuit immediately returns to normal voltage mode oeration. As mentioned before the resonant frequency of the seriesarallel resonant converter is strongly deendent on the load and one has to ensure that the circuit remains oerating above resonance and/or with lagging current as otherwise the free-wheeling diodes would be conducting current at the turn-on of the oosite ower transistor of a bridge leg. This would result in a large reverse Fig. 11: Discontinuous oeration at no load for an outut voltage reference value of V o * =6.5kV; (a) outut voltage V o (15kV/div) and the voltage v AB (500V/div); (b) transformer magnetizing current i L1 (1A/div); (c) resonant current i Ls (50A/div). recovery current and/or in excessive switching losses due to the slow reverse recovery behavior of the ower MOSFET internal diodes. According to Fig.1 oeration below resonance might occur for a large load ste. If the oerating oint changes from A to B (stelike increase of the load) the converter remains oerating above resonance. However for changing from oerating oint C to D (ste-like reduction of the load) oeration below resonance is likely to occur. Therefore in order to ensure oeration above resonance for all oerating conditions a turn-on of a ower transistor is only allowed if the oosite free-wheeling diode is not conducting current. Oeration below resonance could be revented by monitoring the olarities of the voltage v AB and of i Ls. For regular oeration the voltage v AB is always ositive or equal to zero when i Ls is ositive. For oeration below resonance for i Ls >0 v AB can be ositive or negative. So if the current goes negative and v AB is still ositive the system is oerating below resonance. In this case the ower transistors S 1 and S 4 will be turned-off but S and S 3 will not be turned-on as for regular oeration; all switches will remain in the off-state until the next zero-crossing of i Ls where S 1 and S 4 will be turned-on again restoring the regular oeration above resonance. However the roblem is alleviated in by the outut caacitor which does revent an immediate influence of the load change on the resonant circuit and does rovide time for the system control to adjust to the load condition by roerly changing the duty cycle. 1813

8 VI. CONCLUSIONS Fig. 1: Possible occurrence of oeration below resonance. The system behavior in case of changing from full load to low load is shown in Fig. 13 where the smooth transition of the control voltage v c and of the sawtooth signal s T can be observed. It is imortant to oint out that if a very faster controller is emloyed oeration below resonance could become critical again as the controller then does resond immediately to a load change. Fig. 13: Converter behavior for load change. Scales: v AB : 50V/div; i Ls : 50A/div; v c : 5V/div; s T : 5V/div This aer resents a detailed rocedure for determining the characteristic values of the ower comonents of a high outut voltage DC-DC series-arallel resonant converter. The theoretical considerations are verified by digital simulations. Furthermore the dynamic control behavior is discussed and a concet for ensuring oeration above resonance also in case of large load transients is roosed. In the course of the continuation of the research a detailed analysis of the arasitics and/or of the equivalent circuit of the highvoltage transformer will be erformed and the theoretical considerations will be verified on an exerimental 5kW laboratory model of the system. VII. REFERENCES [1] ERICKSON R.W. et al: Comarison of Resonant Toologies in High- Voltage DC Alications. IEEE Transactions on Aerosace and Electronic Systems vol. 4 no May [] IVENSKY G. KATS A. BEN-YAAKOV S.: A Novel RC Model of Caacitive-Loaded Parallel and Series-Parallel Resonant DC-DC Converters. Proceedings of the 8th IEEE Power Electronics Secialists Conference St. Louis Missouri USA vol [3] STEIGERWALD R.L.: A Comarison of Half-Bridge Resonant Converter Toologies. IEEE Transactions on Power Electronics vol. 3 no [4] GARCIA V. RICO M. SEBASTIÁN J. et al: Study of an Otimized Resonant Converter for High-Voltage Alications. Proceedings of the 3rd International Power Electronics Congress Puebla Mexico Aug [5] BARTASEH I. LIU R. LEE C.Q. et al.: Theoretical and Exerimental Studies of the LCC-Tye Parallel Resonant Converter. IEEE Transactions on Power Electronics vol. 5 no Aril [6] PINHEIRO H. JAIN P.K. JOÓS G.: Self-Sustained Oscillating Resonant Converters Oerating Above the Resonant Frequency. IEEE Transactions on Power Electronics vol. 14 no Setember 1999 [7] STEIGERWALD R.L.: Analysis of a Resonant Transistor DC-DC Converter with Caacitive Outut Filter. IEEE Transactions on Industrial Electronics vol. IE-3 no