Interleaving of a Soft-Switching Boost Converter Operated in Boundary Conduction Mode

Transcription

1 Interleaving of a Soft-Switching Boost Converter Operated in Boundary Conduction Mode D. Gerber, J. Biela Power Electronic Systems Laboratory, ETH Zürich Physikstrasse 3, 8092 Zürich, Switzerland This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permission@ieee.org. By choosing to view this document you agree to all provisions of the copyright laws protecting it.

2 3374 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 Interleaving of a Soft-Switching Boost Converter Operated in Boundary Conduction Mode Dominic Gerber and Juergen Biela, Member, IEEE Abstract This paper presents the interleaved operation of a soft-switching boost converter operated in boundary conduction mode. First, the operating principle of the converter as well as the basic concept of the interleaving is presented. Then, the dynamic behavior is modeled using the z-transform to obtain a converter model that is independent of the switching frequency. With the model, the stability of the closed-loop system with a proportional integral (PI) controller is analyzed. It is shown that an adaptive PI controller can be easily implemented to achieve a minimal settling time over a wide operating range. Finally, the controller is validated with two converters with a 40-kW nominal output power and an output voltage of 3 kv. The tests at different output voltages under different load conditions show a stable interleaved operation. Index Terms Boost converter, capacitor charging, interleaving, soft switching. I. INTRODUCTION ACOMPACT and cost-effective X-ray free-electron laser system (SwissFEL) is currently built at the Paul Scherrer Institute in Switzerland [1]. This laser system requires modulators with a pulse power of 127 MW for 3 μs. The high pulse power is provided by a capacitor bank that is recharged to 3 kv by two 40-kW boost converters with a 1.25-kV input voltage between two consecutive pulses. In the considered system, two interleaved converters (Fig. 1) [2] are used to charge the capacitor bank. The interleaved operation results in a reduced input current ripple. In pulse-width modulation (PWM) controlled systems with fixed switching frequency, the interleaving can be easily controlled by shifting the PWM signals relative to each other. However, this method does not work for converters operating in boundary conduction mode (BCM) that results in a variable switching frequency. Different open-loop and closed-loop control methods for the operation in BCM have been investigated [3], [4]. However, those methods do not guarantee a soft-switched operation when the system is perturbed. In this paper, a control strategy for interleaved boost converters operated in BCM is presented. The proposed controller guarantees zero voltage switching during the Manuscript received November 27, 2014; revised February 4, 2015; accepted April 6, Date of publication May 1, 2015; date of current version October 7, The authors are with the Laboratory for High Power Electronic Systems, ETH Zurich, Zurich 8092, Switzerland ( gerberdo@ethz.ch; jbiela@ethz.ch). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPS Fig. 1. Prototype of the kV and 40-kW boost converter. interleaved operation including startup and the synchronization of the converters. The basic operation principle of the converter and the interleaving is presented in Section II. In Section III, the converter model and the controller model are introduced. Two different controllers are investigated, and the implemented controller is shown. Finally, measurements with the proposed controller and two 40-kW and 3-kV interleaved boost converters are presented. II. CONVERTER OPERATION The basic circuit of the converter including the snubber circuits is shown in Fig. 2. The details of the converter and the feedback controller are presented and analyzed in [2] and [5]. In the following, the converter operation in BCM and the interleaved operation are explained. A. Converter Operation The series-connected switches S 1a S 1n are turned ON at the beginning of interval T 1 (see Fig. 2). The input voltage V in is applied across inductor L 1, and inductor current i L starts to rise. When inductor current i L reaches the level i Lp, switches S 1a S 1n are turned OFF at the beginning of interval T 2 (peak current control). Diodes D 1a D 1n are not conducting at that time since capacitors C Sn,D1a C Sn,D1n are still charged. Inductor L 1 and snubber capacitors C Sn form a resonant circuit. Since inductor current i L is positive, the capacitors in parallel to the diodes D 1a D 1n are discharged to zero and the capacitors across the switches are charged to V out. As soon as IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

3 GERBER AND BIELA: INTERLEAVING OF A SOFT-SWITCHING BOOST CONVERTER OPERATED IN BCM 3375 Fig. 3. Interleaved inductor current waveforms. Fig. 4. Current balancing of the average inductor currents depending on inductance mismatch L = L slave L master /L master. Fig. 2. Boost converter circuit and the corresponding BCM waveforms. the voltage across the diodes reaches zero, they start to conduct (interval T 3 ). At that point of time, the difference between V out and V in is applied across L 1 and current i L decreases. At the beginning of interval T 4, i L reaches zero and the diodes stop conducting. The snubber capacitors and the inductor form again a resonant circuit. The voltage across the inductor is the difference between V out and V in. Hence, the inductor current becomes negative and the capacitors across the switches are charged to zero if the difference between V out and V in is large enough. At the end of T 4, the body diodes of the switches start to conduct. At that point of time, the switches have to be turned ON before the inductor current becomes positive and the next switching cycle starts. The operation in BCM results in a switching frequency that depends on the input and output voltage, the output power, as well as the inductance value. reference (master), whereas the other is used to adjust the phase shift (slave). In an ideal system with identical converters, the switching frequencies for both converters are identical for the same current i Lp. This is not the case in a real system because of component tolerances, temperature drifts, and so on. In BCM, nonequal inductor values result in unbalanced inductor currents. Fig. 4 shows the relative deviation of the average inductor current between the master and the slave depending on the inductor mismatch at the nominal operating point of the investigated system (Table II). The deviation is smaller if the slave s inductor is larger than the one of the master. Therefore, the converter with the smallest inductor value should be selected as the master. In order to model the interleaved operation, a general model with nonidentical converters has to be developed. III. FEEDBACK CONTROLLER In this section, the interleaving model and the controller model are derived. In addition, the optimal controller parameters are calculated. Afterward, the implemented phase shift measurement and the controller are presented. B. Interleaved Operation The inductor current waveforms for two interleaved converters are shown in Fig. 3. Since the switching frequency depends on i Lp, the phase shift ϕ = ( T n /T s,0 ) can be controlled by reducing or increasing i Lp,1 relative to i Lp,0. The phase shift can be measured by detecting the inductor current zero crossings. One converter is used as a A. System Model 1) Plant Transfer Function: The inductor current waveforms are shown in Fig. 3. It is assumed that the input and output voltage as well as i Lp,0 remain constant. The dynamic behavior of the time offset between the two inductor currents is modeled by calculating the time offset for the next switching cycle T n+1 depending on the

4 3376 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 Fig. 5. Closed-loop control system of the interleaving model. offset T n and the switching period lengths of the converters T s,0 (i Lp,0 ) and T s,1 (i Lp,1 ) T n+1 = T n T s,0 (i Lp,0 ) + T s,1 (i Lp,1 ). (1) The switching periods T s,k (i Lp,k ) can be analytically calculated by solving the differential equations describing the dynamic behavior of the converter. These expressions are nonlinear because of the resonant transitions during the time intervals T 2 and T 4. In order to simplify the model, T s,1 (i Lp,1 ) is linearized at i Lp = i Lp,0 T s,1 (i Lp,1 ) T s,1 (i Lp,0 ) + dt s,1(i Lp ) di i Lp (2) Lp ilp,0 with i Lp = i Lp,1 i Lp,0. Since the continuous offset T n is discrete in time, the z-transform is applied Z{ T n+1 }=zz{ T n }=z T(z). (3) It is assumed that i Lp,0 is constant. Hence, T s,0 (i Lp,0 ), T s,1 (i Lp,0 ), and (dt s,1 (i Lp )/di Lp ) ilp,0 are constant. Using (1) (3), one obtains T (z) = G d (z) + G p (z) I Lp (z) (4) with the disturbance transfer function G d (z) = 1 z 1 [T s,1(i Lp,0 ) T s,0 (i Lp,0 )]= 1 z 1 T s and the plant transfer function G p (z) = 1 z 1 dt s,1 (i Lp ) di Lp = 1 ilp,0 z 1 T s,1 (i Lp,0). 2) Closed-Loop Transfer Function: In this section, the closed-loop system shown in Fig. 5 is analyzed. The system model including the controller is T (z) = G c(z)g p (z) 1 + G c (z)g p (z) T G d (z) set(z)+ 1 + G c (z)g p (z) = G cl (z) T set (z) + G dis (5) where G cl (z) represents the plant closed-loop transfer function and G dis the disturbance closed-loop transfer function. B. Proportional Integral Controller Since a proportional (P) controller is not able to drive the system to the desired phase shift without a static deviation, a proportional integral (PI) controller is investigated. It is known from the control theory that a system is stable if and only if its poles are inside the unit circle of the complex plain. In the following section, the stability of the controller is investigated. Fig. 6. Settling time in cycles of the closed-loop system with PI controller. 1) Stability: The closed-loop transfer function for a PI controller G c (z) = K P + K I (z/z 1) is (K I,n + K P,n )z K P,n G cl,pi (z) = z 2 + ((K I,n + K P,n ) 2)z K P,n + 1 (6) K P,n = K P T s,1 Lp,0) (7) K I,n = K I T s,1 Lp,0). (8) Hence, the dynamic behavior of the system depends on K P,n and K I,n, providing an operating point-independent dynamic behavior. G cl,pi (z) has two poles at p 1,PI = K P,n +K I,n (K P,n + K I,n ) 2 4K I,n + 1 (9) 2 and p 2,PI = K P,n + K I,n + (K P,n + K I,n ) 2 4K I,n 2 The system is stable for and + 1. (10) 0 < K I,n < 4 2K P,n (11) 0 < K P,n < 4 K I,n. (12) 2 2) Settling Time: The settling time of the system with PI controller is shown in Fig. 6. The plot shows a minimum settling time of two switching cycles around K P,n = 1and K I,n = 1. The step response of the controller is shown in Fig. 7. The overshoot of 100% does not matter in that case since the model is a small-signal model. 3) Disturbance Transfer Function: The static controller error can be investigated by applying a unit step U(z) = (1/1 z 1 ) and using the final value theorem. The static error of the disturbance transfer function (z 1) T s G dis,pi (z) = z 2 (13) + ((K I,n + K P,n ) 2)z K P,n + 1 is lim z 1 (z 1)G dis,pi(z)u(z) = 0. (14)

5 GERBER AND BIELA: INTERLEAVING OF A SOFT-SWITCHING BOOST CONVERTER OPERATED IN BCM 3377 Fig. 7. Step response for K P,n = 1andK I,n = 1. Fig. 9. Period length T s depending on i lp at the nominal operating point. Fig. 8. Phase shift measurement. Hence, a PI controller is able to drive the system to the desired point independent of the period deviation T s. C. Phase Shift Measurement As already mentioned before, the inductor current zero crossings are used to measure T n and T s,0. However, a stable interleaved operation is only possible, when the measurement range of T n is larger than the setpoint range. Otherwise, setpoints close to the boundary of the measurement range might result in large steps in the error e = T set T n when T n exceeds the measurement range. This in turn results in an unstable operation since these large steps are not present in the real system. For the presented system, the following setpoint and measurement range are selected: T s,0 2 < T set < T s,0 (15) 2 T s,0 < T n < T s,0. (16) With this measurement range, a method is required, which is able to measure positive and negative values of T n and provides a unique T n for every switching cycle. All possible cases are shown in Fig. 8. All other cases indicate a too large deviation of the switching frequencies, which results in a controller reset. D. Linearization Since the plant transfer function is a linearized model, it has to be taken into account that the model is only an approximation of the real system behavior. Fig. 9 shows the period length depending on the peak inductor current at the nominal operating point of the presented converter. The period Fig. 10. Block diagram of the implemented controller. length shows a linear behavior at peak inductor currents bigger than 15 A. Hence, the critical operating conditions are at low peak inductor currents. E. Feedback Controller Implementation The closed-loop transfer functions G cl,p and G cl,pi show that the system dynamics depend on the product of T s,1 (i Lp,0) and the controller coefficients. Hence, the optimal controller parameters depend on the operating point. They can be calculated with K P = K P,n T s,1 (i (17) Lp,0) and K I,n K I = T s,1 (i Lp,0). (18) The term T s,1 (i Lp,0) can be calculated analytically. This means that it is possible to calculate the controller coefficients online. Since the sampling frequency of the system model is equal to the switching frequency, the integral part of the controller is sampled with the switching frequency of the converters. A block diagram of the controller is shown in Fig. 10. Since the derived model depends on the linearized system model, it is necessary to limit the controller output to assure

6 3378 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 TABLE I CONVERTER HARDWARE SPECIFICATIONS that the linearized model is a good approximation of the system dynamics. This also makes sure that the switching frequencies of both converters are close enough to each other in order to prevent one converter to skip switching cycles or switch multiple times during one switching cycle of the other converter. The slave setpoint i Lp,1 is limited after the controller output to ensure zero voltage switching (ZVS) and to avoid excessive thermal stress. IV. MEASUREMENTS In the following, the converter and the test setup are described, and the test results are presented. A. Converter 1) Semiconductors and Snubber Circuits: Since the converter is operated under ZVS conditions, MOSFETs are the best choice as semiconductor switches. However, the output voltage of 3 kv requires the series connection of multiple MOSFETs since there are no devices available with the required blocking voltage. The presented system uses 650 V MOSFETs of the type STY139N65M5. As an alternative, MOSFETs of the type IPW65R019C7 could also be used. Eight switches are connected in series, resulting in a blocking voltage of 5200 V, providing enough margin to ensure a reliable operation. Two switches are connected in parallel to reduce the conduction losses, resulting in 16 switches in total. A snubber capacitance of 11 nf is connected in parallel to each switch to ensure a voltage balancing between the switches during the switching transients. The voltage balancing of the switches is determined by two effects: 1) component tolerances of the snubber capacitances and 2) switching signal jitter of the individual MOSFETs. The voltage balancing between n capacitors connected in series is given by the capacitance values. The voltage v i of a capacitor C i in series with a capacitor C k is given by v i = C k v k. (19) C i At the beginning (T 1 in Fig. 2), all snubber capacitors are discharged. The total blocking voltage is simply the sum of all voltages v i n n C k v i = v k = v tot. (20) C i i=1 i=1 Ideally, v k is v tot /n. The resulting ratio of v k and v tot /n is v k n v tot = ni=1. (21) C k n C i The most interesting case is when v k is higher than the ideal voltage v tot /n. This occurs, when the capacitor C k is the smallest capacitor. If it is assumed that all capacitors are within C min and C max, the worst case is n = v k,max v tot n 1 + (n 1) C min C max. (22) By assuming a capacitance tolerance of ±5%, the resulting voltage imbalance is approximately 9.1% or 34 V for the presented converter. The nonsynchronous switching of the MOSFETs also results in an unequal voltage distribution of the switches. The main sources for the nonsynchronous switching are different propagation delays of the individual switching signals and gate drive circuits. The voltage difference between two switches is estimated by V = i 0 T (23) C sn,s1x where i 0 is the charging current of the snubber capacitors at the turn-off instance, T is the difference between the turn-off time instance, and C sn,s1x is the snubber capacitance in parallel to the switch. The propagation delay difference T for the presented system was measured and determined to be less than 20 ns. For a current i 0 of 100 A and a capacitance tolerance of ±5%, the resulting voltage V is 96 V. Taking the capacitance tolerance and the switching signal jitter into account, this results in a worst case blocking voltage of 505 V. The maximum blocking voltage of the MOSFETs is 650 V at a 25 C junction temperature. Since the occurring overvoltage caused by the inductance in the commutation path during the turn-off transients is small if the snubber capacitances are connected as low inductive as possible to the switches, the selected snubber capacitance values provide enough margin. Four 1200 V diodes of the type APT175DQ120BG connected in series are used at the output side. A 1-nF snubber capacitor is connected in parallel to each diode. An additional capacitor of 4 nf is connected in parallel to all diodes, resulting in an equivalent capacitance of 7 nf. This additional capacitance is used to reduce the influence of the nonlinear capacitance of the semiconductors, resulting in a wider ZVS operating range. In addition, a resistor is connected in parallel to each semiconductor to assure a balanced voltage at dc. All semiconductors are mounted on a water-cooled heat sink. Because the semiconductors are at a different electrical potential during operation, a thermally conductive insulation is required. The switching node is switched between 3 kv and 0 V at high frequencies of up to 200 khz. This leads to capacitive currents that are heating up the insulating material, reducing the voltage withstand capability [6] at high frequencies. Film materials are not suitable in this application since the small thickness results in large capacitive currents. Hence, the presented system uses thermally conductive ceramic.

7 GERBER AND BIELA: INTERLEAVING OF A SOFT-SWITCHING BOOST CONVERTER OPERATED IN BCM 3379 TABLE II SPECIFICATIONS OF THE PROTOTYPE SYSTEM. THE NOMINAL OPERATING POINT IS BOLD Fig. 11. Block schematic of the control. 2) Inductor: The inductor is split into two inductors connected in series. Four U/I cores of the type I 93/28/30 and U 93/76/30 manufactured by EPCOS are used per inductor. A litz wire with 4000 strands and a core diameter of 50 μm is used. The inductor consists of seven turns and an air gap of 5.6 mm. The inductors are air cooled by three 120-mm fans. 3) Control: The control of the converter is implemented in an field-programmable gate array. Each converter has its own control, which assures ZVS as well as several protection mechanisms. The feedback control consists of four blocks: 1) the output voltage controller; 2) the interleaving controller; 3) a master converter selector; and 4) a state machine that controls the number of operating converters (Fig. 11). The output voltage controller sets the peak inductor current of the master converter, whereas the interleaving controller sets the peak current for the slave converter. The operation of both converters is controlled by a superordinate state machine. The interleaving is disabled toward the end of the charging cycle to achieve a high repetition accuracy. In addition, the superordinate state machine features a trigger function. If the trigger function is activated, a charge retention mode is entered and the last switching cycle is suppressed. A feedback signal indicates to the superior control that the converter is ready to execute the last switching cycle. When the output voltage falls below a level where more than one switching cycle is required to reach the targeted output voltage, the capacitors are charged again until only one switching cycle is left. As soon as the superior control unit sends the trigger signal, the last switching cycle is immediately executed. This assures a defined time instance when the capacitors are fully charged, further increasing the precision of the complete system. The hardware specifications are shown in Table I. B. Test Setup The interleaved operation is tested with two 40-kW and 3-kV converters. The converter parameters are shown in Table II. The two converters are connected in parallel to an ohmic load, as shown in Fig. 12. Although the converter is designed to be operated with a capacitive load, an ohmic load has been chosen to test the interleaved operation. The interleaving works properly only when the operating point remains more or less constant. This is the case for a large capacitive load as well as for an ohmic load. Hence, an ohmic load is used since it simplifies the tests. Fig. 12. Setup for interleaving measurements. Fig. 13. Measured inductor current waveforms and phase shift at an input voltage of 1020 V, an output voltage of 2.5 kv, and an output power of 4.5 kw. C. Results The interleaved operation was successfully tested with two different ohmic loads of 1.4 and 215. The output voltages was set between 750 V and 3 kv. The operation at low output power is more critical than the operation with high output power because of the higher switching frequency and because the relative error of the linearized term is bigger at input currents close to the free-wheeling current. As an example, the measured current waveforms of the inductor current and the resulting phase shift at 2.5 kv with a 1.4-k load are shown in Fig. 13. The deviation of the setpoint during the operation can be explained by the high switching frequency and the jitter of the zero-crossing detection and the accuracy of the internal current measurement of the converter. A phase shift of 10 corresponds to a shift of approximately 200 ns at a 140-kHz switching frequency. The used current sensor has a measurement range of 100 A. An accuracy of 0.5% already corresponds to a deviation of 50 ns of the ON-time of the switch at the measured operating point. Fig. 14 shows the inductor current and the waveform at an input voltage of 1250 V and an output voltage of 3 kv after the

8 3380 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 Fig. 14. Measured inductor current waveforms and phase shift after turning ON the slave converter at an input voltage of 1250 V, an output voltage of 3 kv, and an output power of 6.5 kw. REFERENCES [1] (Mar. 2014). SwissFEL. [Online]. Available: [2] D. Gerber and J. Biela, Charging precision analysis of a 40-kW 3-kV soft-switching boost converter for ultraprecise capacitor charging, IEEE Trans. Plasma Sci., vol. 42, no. 5, pp , May [3] L. Huber, B. T. Irving, and M. M. Jovanovic, Open-loop control methods for interleaved DCM/CCM boundary boost PFC converters, IEEE Trans. Power Electron., vol. 23, no. 4, pp , Jul [4] H. Choi and L. Balogh, A cross-coupled master slave interleaving method for boundary conduction mode (BCM) PFC converters, IEEE Trans. Power Electron., vol. 27, no. 10, pp , Oct [5] D. Gerber and J. Biela, Charging precision analysis of a 40 kw, 3 kv soft-switching boost converter for ultra precise capacitor charging, in Proc. 19th IEEE Pulsed Power Conf., Jun. 2013, pp [6] W. Pfeiffer, High-frequency voltage stress of insulation. Methods of testing, IEEE Trans. Elect. Insul., vol. 26, no. 2, pp , Apr slave converter has been enabled. The phase shift is adjusted by the controller within a few cycles. The deviation after the phase shift has been adjusted is caused by the output voltage controller since it changes the setpoint of the master converter because of the doubled output power after the slave converter has been turned ON. V. CONCLUSION In this paper, the interleaved operation of a soft-switching boost converter operated in BCM is investigated. The softswitching operation as well as the interleaving concept is presented. A general model for interleaved operation is derived using the z-transform in order to obtain a switching frequencyindependent model. Afterward, the stability of the closed-loop system with a PI controller is investigated. In addition, it is shown that the dynamic behavior of the small-signal model of the system is independent of the operating point for normalized controller coefficients. An adaptive interleaving controller is presented. Finally, the controller has been implemented and successfully tested with two converters at different loads at an output voltage ranging from 750 to 3000 V. ACKNOWLEDGMENT The authors would like to thank Ampegon AG and Ampegon PPT GmbH for the construction of the converters and the tests with the 215- load. Dominic Gerber received the M.Sc. degree in electrical engineering and information technology from ETH Zurich, Zurich, Switzerland, in 2010, where he is currently pursuing the Ph.D. degree with the Laboratory for High Power Electronic Systems. He was involved in power electronics, drive systems, and high voltage technology. His current research interests include solid-state modulators, high accurate capacitor charging, and current measurement based on the Faraday effect. Juergen Biela (S 04 M 06) received the Diploma (Hons.) degree from the Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, Germany, in 1999, and the Ph.D. degree from ETH Zurich, Zurich, Switzerland, in 2006, where he is currently pursuing the Ph.D. degree with a focus on optimized electromagnetically integrated resonant converters with the Power Electronic Systems Laboratory (PES). He dealt in particular on resonant dc-link inverters with the University of Strathclyde, Glasgow, U.K., and the active control of series-connected Integrated gate-commutated thyristor with the Technical University of Munich, Munich, Germany. He joined the Department of Research, Siemens Automation and Drives, Erlangen, Germany, in 2000, where he was involved in inverters with very high switching frequencies, SiC components, and electromagnetic compatibility. He was a Post-Doctoral Fellow with PES and a Guest Researcher with the Tokyo Institute of Technology, Tokyo, Japan, from 2006 to He was a Senior Research Associate with PES from 2007 to He has been an Associate Professor of High-Power Electronic Systems with ETH Zurich since His current research interests include design, modeling, and optimization of power factor correction, dc dc and multilevel converters with an emphasis on passive components, the design of pulsed-power systems, and power electronic systems for future energy distribution.