Analysis and Design of a 500 W DC Transformer

Transcription

1 University of Colorado, Boulder CU Scholar Electrical, Computer & Energy Engineering Graduate Theses & Dissertations Electrical, Computer & Energy Engineering Spring Analysis and Design of a 500 W DC Transformer Tadakazu Harada University of Colorado at Boulder, tadakazu_harada@mail.toyota.co.jp Follow this and additional works at: Part of the Electrical and Electronics Commons Recommended Citation Harada, Tadakazu, "Analysis and Design of a 500 W DC Transformer" (2014). Electrical, Computer & Energy Engineering Graduate Theses & Dissertations This Thesis is brought to you for free and open access by Electrical, Computer & Energy Engineering at CU Scholar. It has been accepted for inclusion in Electrical, Computer & Energy Engineering Graduate Theses & Dissertations by an authorized administrator of CU Scholar. For more information, please contact cuscholaradmin@colorado.edu.

2 Analysis and Design of a 500 W DC Transformer by Tadakazu Harada B.S., Tokyo University of Agriculture and Technology, 2006 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Master of Science Department of Electrical, Computer, and Energy Engineering 2014

3 This thesis entitled: Analysis and Design of a 500 W DC Transformer written by Tadakazu Harada has been approved for the Department of Electrical, Computer, and Energy Engineering Dragan Maksimovic Robert W.Erickson Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline.

4 iii Abstract: Tadakazu Harada (M.S., Electrical, Computer, and Energy Engineering) Analysis and Design of a 500W DC Transformer Thesis directed by Prof. Dragan Maksimovic Fuel consumption and environmental concerns motivate new engineering developments in the automotive industry. Vehicle electrification techniques, such as drivetrain hybridization and replacements of various mechanical components with electronic components require highly efficient switched-mode power converters. Analysis and design of a DC transformer (DCX) converter configuration are addressed in this thesis, including component design and efficiency optimization techniques. A 500 W prototype converter is constructed and tested in two operating modes: as a full-bridge DCX or as a dual active bridge DCX. It is shown that the DCX converter has the potential to achieve small size and high efficiency over wide ranges of operating conditions.

5 iv Acknowledgements I would like to thank my thesis advisor, Professor Dragan Maksimovic, for his support and encouragement. I did not have enough knowledge about power electronics before starting my studies at the University of Colorado at Boulder. Thanks to my advisor s support, I was able to keep up my motivation and to gain valuable knowledge in the area. Additionally, I would like to thank Professors Robert Erickson and Khurram Afridi, who have helped me learn and better understand analysis, modeling and design techniques in power electronics. I am grateful to the Colorado Power Electronics Center (CoPEC) and Toyota Motor Corporation, and I would like to acknowledge my fellow CoPEC students Hua Chen, Hyeokjin Kim, Beom Seok Choi, and Fan Zhang for their help and support, which I will never forget. Finally, I would like to thank my family for their support throughout my graduate studies and throughout my life.

6 Contents Chapter 1 Introduction Hybrid System Toyota Hybrid System Power Control Unit Intelligent Power Module Selection of DC-DC Converters Soft Switching Technology Three-Level Converter Proposed DC-DC Converter Architecture Power Stage Design of DC Transformer and Dual Active Bridge Semiconductor Device Loss Model Transformer Loss Model Core Loss Eddy Currents in Winding Conductors Copper Loss Accurate Prediction of Ferrite Core Loss with Nonsinusoidal Waveform Transformer and Tank Inductor Design Optimization DC Blocking Capacitor...21

7 vi 3 State Plane Analysis Review of State Plane Analysis State Plane Analysis Applied to the Dual Active Bridge Primary ZVS Condition in DAB DAB State Plane Solution Analysis of DAB Operation Modes Mode1 : Operation with β > 0 and Primary ZVS Mode2 : Operation with β > 0 and Hard-Switched Primary Mode3 : Operation with β < 0 and Soft-Switched Primary Experimental Results Experimental Results Device Loss Analysis Phase-Shift Optimization in DAB Analysis of Optimal Efficiency Trajectory Experimental Results: Conversion Ratio and Efficiency Summary and Future Work DAB Design and Component Selection State Plane Analysis of DAB Converter Conclusion Future Work...51 Bibliography...53

8 Tables Table 2.1 DAB Transformer Implementation Details Correspondence table with DAB...21

9 Figures Figure 1.1 Toyota Hybrid System Structure of the 3 rd generation PCU (Power Control Unit) Buck-boost SAZZ boost converter Coupled-inductor converters Three level boost converter with IGBT Proposed composite converter system architecture Operating modes Switching loss simulation model MOSFET energy loss of the simulated data Transformer loss analysis Current waveform of tank inductor Dual active bridge converter Experimental waveforms of the prototype Time-domain waveforms and state planes State plane of the DAB in Mode State plane of the DAB in Mode State plane of the DAB in Mode3...36

10 ix 3.5 Prototype DAB converter Comparison between theory and experiments in the state plane Loss analysis of full bridge DCX and DAB DCX Characteristics of reverse diode and MOSFET loss analysis Optimize phase shift between primary and secondary Prototype experimental waveforms of the DAB Efficiency contours of DAB Comparison of analytical Prototype experimental waveforms of the full bridge and DAB DCX Prototype experimental switching transitions...51

11 1 Chapter 1 Introduction Rising numbers of vehicles in the world cause increased air pollution induced by CO 2 emissions. Therefore, automotive industries focus on improvements of fuel efficiency technologies. Typical technologies for gasoline mileage improvement include reductions in size and weight of the vehicle, improvements in engine efficiency and powertrain components, reductions in air resistance, and increased vehicle electrification, including use of high-efficiency switching power converters. It is expected that auxiliary electric power consumption in vehicles will increase up to 2 kw to 3 kw in the future, because mechanical components will be replaced by electronic components [1]. For example, the electric power steering system using a drive motor operated from 12V increased the steering load capabilities [2]. The impact of the total power loss in the electricity consumption can not be ignored in future. Furthermore, drivetrain electrification techniques, such as hybridization, can lead to substantial improvements in fuel economy. These approaches also rely on high-efficiency power electronics components. In this chapter, hybrid vehicle systems are reviewed, and the need for high-efficiency, small-size boost DC-DC converter is identified. This provides motivation for the work presented in this thesis, which is focused on analysis and design of a DC transformer (DCX) converter, which can be used as a building block in automotive applications.

12 2 1.1 Hybrid system In recent years, environmentally conscious vehicles, such as hybrid vehicles (HV), fuel cell vehicles (FCV), and electric vehicles (EV), have been developed to reduce the effects on the environment. In particular, HV s have spread most rapidly across the world. The basic HV system is reviewed in the following section Toyota Hybrid system A popular hybrid system is the Toyota Hybrid System II (THS-II) shown Fig. 1.1 [3]. This system consists of two motors, two inverters, and a boost DC-DC converter. The bus voltage is boosted by the DC-DC converter from 200 V obtained from a nickel-metal hydride battery voltage to 650 V [3]. The driving motor output is 60kW. The boost DC-DC converter power rating is 25kW. The high voltage can reduce the size of motor and improve the system efficiency. Additionally, the bus voltage can be controlled depending on the load conditions. Figure 1.1: Toyota Hybrid System

13 Power Control Unit In the 3 rd generation Toyota hybrid system, the maximum voltage of the boost converter increased from 500 V to 650 V. Therefore, the volume of the power control unit, which is 11.2 liters, is reduced by 37% compared to the previous model. The power control unit (PCU) which consists of the inverters for the generator and the motor, and the boost DC-DC converter, is shown in Figure1.2. A water cooling system has been employed in the PCU. Figure 1.2: Structure of the 3 rd generation PCU (Power Control Unit) [4]

14 Intelligent Power Module Intelligent power module (IPM) of Fig. 1.2 consists of the high voltage power module and the control circuit which contains the gate drivers. The power module is implemented using Insulated Gate Bipolar Transistors (IGBT) and Free Wheeling Diodes (FWD). An important issue facing the design of the power module for automotive applications is related to the thermal management. The thermal design affects the size of device, thereby reducing cost. Therefore, the water cooling system is applied to the IPM. The most important issue facing the design of a high power hybrid system is the size of the boost DC-DC converter between the battery and the inverters. In particular, the boost converter requires a large capacitor and a large inductor. One approach to reducing the size of the capacitor and the inductor is to increase the switching frequency. However, as the switching losses increase with increasing switching frequency, it becomes difficult to keep the converter efficiency high. As a result, there is a tradeoff in the selection of switching frequency. In this thesis, the design goal of small size and high efficiency is addressed through considerations of converter topology and soft-switching techniques. 1.2 Selection of DC-DC Converter Candidate DC-DC converter topologies in a hybrid system are reviewed in this section Soft Switching Technology An approach to improving the DC-DC converter efficiency is to attempt to mitigate some of the switching losses. Soft switching techniques include zero-voltage switching (ZVS) or zero-current switching (ZCS). In a ZVS transition, a switch is turned on at a time when the voltage across its terminals is approximately zero, so that turn-on switching losses are ideally zero. In a similar manner, ZCS can be described as a

15 5 switching transition when a switch is turned off at a time when the switch current is approximately zero, so that turn-off switching losses are ideally zero. One soft switching circuit is the snubber-assisted zero-voltage transition/zero-current transition (SAZZ) converter described in [5] and shown in Fig The main switches Sm1, Sm2, and the reactor L1 are the same as in the conventional boost converter. The auxiliary snubber circuit is implemented as the auxiliary active switches Sa1, Sa2, Diode D1-4, capacitors C1, C2 and reactor L2. In general, soft switching approaches usually adopt auxiliary circuits to achieve soft switching. However, there are additional conduction and switching losses in the auxiliary circuit. Figure 1.3: Buck-boost SAZZ boost converter [5] Another approach is based on the interleaving converter modules, i.e. operating converter modules in parallel, with appropriate phase shifts between the modules, as shown in Fig. 1.4 [6]. This approach can reduce the input and the output capacitor voltage ripples, thereby allowing reduced capacitor. Additionally, the switching frequency of the switches in a two-phase interleaved converter is one half of the inductor current frequency, so that the switching losses can be reduced. A disadvantage of this approach is that additional transformer introduces additional size and loss.

16 6 Figure 1.4: Interleaved coupled-inductor converters [6] Three-Level Converter Three-level converters ([7], [8]) can significantly reduce inductor size. The inductor current ripple compared to the traditional boost converter is significantly reduced. The voltage stress of the switching devices is also one half of the voltage stress in the conventional boost converter. As a result, the switching loss of each device is reduced. Lower-voltage devices, e.g. 600V MOSFETs can be applied in the threelevel converter even though the output voltage exceeds 600 V. The MOSFET switches have potentials to reduce switching losses further. However, an extra capacitor is needed with large RMS current rating, which implies increased capacitor size.

17 7 Figure 1.5: Three level boost converter with IGBTs; MOSFET switches can also be used in this configuration Proposed DC-DC Converter Architecture A new boost composite converter architecture consisting of a boost converter, a buck converter, and a DC transformer (DCX) as shown in Fig. 1.6 has recently been introduced [9].The system allows 600V MOSFETs to be used as switches, with advantages in terms of low on resistance and low switching loss. The DCX behaves in a manner similar to an ideal transformer, where the primary and secondary winding voltages and currents are related by the number of turns. The DCX can achieve very high efficiency, but the voltage conversion ratio between the primary and the secondary is fixed. Based on the hybrid system, the output voltage can be controlled by demand of power from the motor in a range from 200 V to 650 V. Therefore, a candidate boost DC-DC system needs to be able to adjust the conversion ratio M = V out V in. The boost converter together with the DCX can be configured to allow adjustment of V out. In this case, the system conversion ratio is M = N DCX + M boost. However, when a system

18 8 conversion ratio M less than N DCX + 1 is required, the DCX should be shut down, and the boost module should produce the required output voltage. In this transition from the operating mode with only the boost module to the operating mode with the DCX and the boost module together, an abrupt voltage change may occur. One approach to mitigate the voltage discontinuity is to control the DCX output voltage. Another buck converter is added before the DCX, so that the DCX input voltage can be controlled smoothly. In this architecture, the system conversion ratio is given by M = M buck N DCX + M boost. This system can efficiently achieve boost function over the required ranges of input and output voltages by selecting the appropriate operating mode. Figure 1.6: Proposed composite converter system architecture [9]

19 9 Figure 1.7: Operating modes in the composite converter The DCX module is a key component in the composite system architecture. In the rest of this thesis, analysis and design of a scaled (500W) DCX prototype are addressed, together with experimental results comparing the DCX efficiency under various operating conditions.

20 10 Chapter 2 Power Stage Design of DC Transformer and Dual Active Bridge In general, a DC-DC converter consists of capacitors, magnetics, and semiconductor devices. Ideally, the converter efficiency is 100%. However, losses exits under real operating conditions. The efficiency of a converter is defined as η = V outi out V in V in (2.1) In general, the converter is designed to maximize converter efficiency to the extent possible, and to conform to requirement specifications, which include ranges of input and output voltages, as well as output power. The DC-DC converter configuration considered in this chapter is the DC transformer introduced in Chapter Semiconductor Device Loss Model Although the DC transformer can achieve zero-voltage switching, it still has some switching loss. The switching loss can be estimated based on simulations of detailed device models, or by empirical observations. With zero-voltage switching, the switching loss is estimated as P swq,soft 0.5P swq,hard (2.2) where P swq,hard is the transistor hard-switching loss.

21 11 The soft switching loss of the rectifier diode is approximated using the following empirical model P swq,soft αv D I D t rr f s (2.3) where V D is the voltage across diode, I D is the current through diode,t rr is the recovery time of the diode, and f s is the switching frequency. In the considered DCX prototype, the resulting losses are modeled with α = The device model of Infineon IPW65R660CFD CoolMOS is provided on the Infineon website [10]. The simulation circuit is shown in Fig The gate drive voltage is 10V. The circuit is simulated with different voltage and current values, and the energy loss during the switching transition is extracted. The hard-switching loss of the body diode is approximated as the energy loss during high side MOSFET turn-on transition, and switching loss of the transistor is approximated as the energy loss during high side MOSFET turn-off transition. Figure 2.1: Switching loss simulation model The switching loss model of the MOSFET and the body diode are given by E sw_mosfet = K sw_mosfet (I in + I) a M(V out ) b M (2.4) P sw_body_diode = K swd (I L I L ) a DV b D (2.5)

22 12 The parameters in equations (2.6) and (2.7) are calculated by using Matlab curve fitting tool. K sw_mosfet = 11.01E 7, a M = 1.905, b M = (2.6) K sw_d = 28.7E 5, a D = , b D = (2.7) The simulation data and the switching model are compared in Fig. 2.2.

23 13 (a) (b) Figure 2.2: Energy loss based on simulation data compared with the loss predicted by the model, for (a), MOSFET and (b) diode.

24 Transformer Loss Model Core Loss The core loss P fe can be approximated based on the core material datasheet. B = λ 2nA c (2.8) P fe = K fe ( B) β A c l m (2.9) where λ is the core primary flus linkage, A c is the equivalent core cross-section area, n is the primary number of turns, and l m is the equivalent core magnetic path length. The waveform of flux density B is triangular in the DCX converter, so B can be decomposed into a series of sinusoidal waveform by Fourier series expansion, f(x) = π 2 n=1 8 sin ( nπ 2 ) sin(nx) n 2 (2.10) Eddy Currents in Winding Conductors Eddy currents cause additional power losses in winding conductors. The length δ is the skin depth. The resistivity σ is Ωcm at room temperature. The skin effect can be modeled by calculating the effective area of copper, where the skin depth δ is given by δ = ρ πμf (2.11)

25 15 A layer of winding conductors consists of n l turns. The layer can be approximately modeled as a foil, where the winding porosity η increases the effective resistivity and therefore increases the effective skin depth, δ = δ η (2.12) The winding porosity η is given by η = π 4 d n l l w (2.13) φ is defined as the ratio of the effective foil conductor thickness h to the effective skin depth δ. φ = h δ = η π d 4 δ (2.14) Copper Loss Copper loss includes both DC and AC components. DC copper loss is given by the DC current in the winding. The DC copper loss is 2 P Cu_DC = I rms R (2.15) When multiple conductors are packed into layers, the magnetomotive force may increase from layer to layer, and the corresponding eddy currents may increase significantly. This effect is known as the proximity effect [11]. Interleaving the winding between primary and secondary layers in the transformer can reduce the copper losses due to the proximity effect. The basic analysis of interleaving the winding is reviewed here based on [12]. The quantity m is the ratio of the magnetomotive force F(h). m = F(h) F(h) F(0) (2.16)

26 16 For a 1:2 transformer, if we interleave the primary and secondary winding layers in the secondary/primary/secondary manner, the magnetomotive force will cancel each other, and the result is equivalent to a single layer winding. In the DCX prototype, Litz wire, which consists of many thin strands of wire, is applied in the designs of the reactor and the transformer. The Litz wire can reduce the losses associated with the skin and proximity effects. However, in Litz wire, the current among the strands is actually not evenly distributed. To model this effect, we assume all the strands are packed in a square. Therefore for a total of N strands, the equivalent number of layers in the primary is N primary. If we define M = N primary m (2.17) then the ac loss to dc loss ratio F R can be found by the classical Dowell s equation F R = P pri P pri,dc = φ [G 1 (φ) (M2 1)(G 1 (φ) 2G 2 (φ))] (2.18) The functions G 1 (φ) and G 2 (φ) are G 2 (φ) = G 1 (φ) = sinh(2φ) + sin(2φ) cosh(2φ) cos(2φ) (2.19) sinh(φ) cos(φ) + cosh(φ) sin(φ) cosh(2φ) cos(2φ) (2.20) The waveform of input current I in is an approximately square-wave waveform, and therefore I in can be described by Fourier series expansion, f(x) = n=1 4 π 1 sin{(2n 1)x} 2n 1 (2.21)

27 17 The total copper loss is given by P cu_primary = I in 2 2 R pf R (2.22) Where I in is the amplitude of each harmonic according to Fourier expansion in (2.22) Accurate Prediction of Ferrite Core Loss with Nonsinusoidal Waveforms Section has shown methods for Fourier analysis applied to the calculation of core loss. The generalized Steinmetz equation (GSE) [13] provides a more accurate prediction of core losses in the presence of nonsinusoidal waveforms, P fe (t) = k 1 db dt α B(t) β α (2.23) The GSE approach takes into account only the instantaneous flux density. The improved generalized Steinmetz equation (igse) [14,15] considers the flux density over a period. P fe (t) = k i db dt α ( B) β α (2.24) where ΔB is the peak-to-peak flux density. The equations for time-average loss are P fe = 1 T T k i db dt ( B) β α dt 0 k i = (2π) α 1 k fe 2π 0 cos θ α 2 β α dθ (2.25) (2.26)

28 Transformer and Tank Inductor Design Optimization A designer makes an effort to minimize the loss and the size of the magnetics, and there are variable design parameters such as core materials, core shape, number of turns, wire size. A useful method for the examination of magnetics design is the K g method [16]. This approach can optimize the wire size of the windings for minimized copper loss. K g σl2 2 I max B2 max RK (2.27) u K g = A c 2 W A (MLT) (2.28) where (MLT) is the mean-length-per-turn of the winding. The expression for K g is a function of the core components. In (2.27), the quantities I max, B max, L, K u, R, and ρ are given specifications. The quantity K g which refers to magnetics core datasheet is made large enough to satisfy (2.27). One should note that the K g method strictly applies only to the design of inductors with negligible core or proximity losses. The core material TSF-50ALL from TSC international is chosen to implement the DAB converter transformer. 50ALL is a flat-line material, which means that the material properties such as core loss, permeability, and saturation flux density, do not change much as temperature varies. A winding fill factor K u = 0.4 is assumed given the PQ core shape and Litz wire used for the windings. The designer will optimize the total power loss between core and copper losses in magnetic device. A large number of turns in the devices can reduce the core loss and peak flux density, but longer primary and secondary windings also increase winding resistance and conduction losses. In this tradeoff, Fig. 2.3 shows the result of total power loss with the PQ35/35 core. Copper loss is linearly-increasing depending on the number of primary turns, because of the increasing winding resistance. In contrast, increasing the number of turns results in lower peak ac flux density, so that the core loss is reduced, as shown by (2.25). The primary number of turns to minimize total loss at 300W output power is around 57 turns. For the prototype construction, the number of turns selected was somewhat lower, 44 turns, because of practical limitations imposed by the core window area, and the fact that further benefits of increasing

29 19 the number of turns to the theoretically optimal value are relatively small. More turns cannot provide a significant benefit. Table 2.1 summarizes the DAB transformer design. Figure 2.3: Core loss, copper loss and total loss vs. the number of turns in the primary at 300W output power Table 2.1: DAB Transformer Implementation Details Core material Core shape Winding Turns Air gap Core loss Copper loss TSF-50ALL PQ Primary : Litz wire 330 strands #44 Secondary : Litz wire 175 strands #44 Primary : 44 Secondary : mm W@300W 0.85 W@300W

30 20 Simulation of the DAB circuit is performed in LTspice. The trapezoidal (near square wave) inductor current minimizes the rms current, which reduces the copper loss in both the transformer and the inductor. The copper loss is calculated by the root-mean-square current I rms through the tank inductor. The inductor current waveform at 300 W output power is plotted in Fig for 3 different inductance values. In this thesis, the tank inductor is optimized at 300 W, and the inductance of 40 H is chosen, which results in the desirable trapezoidal current waveform. The tank inductor is implemented using a PQ20/16 core, as documented in Table 2.1 (a) (b) Figure 2.4: Current waveform of tank inductor at (a) 60 H, (b) 40 H, and (C) 35 H. I(L3) is the current of the inductor on the primary side. I(L2) is the secondary-side current. (c)

31 21 Table 2.2: Specified tank inductor design Core material TSC 50ALL Core shape PQ Winding #16 AWG Turns 9 Air gap 0.127mm Inductance 40uH Core loss 1.02 W@300W Copper loss W@300W 2.4 DC Blocking Capacitor The behavior of the dual active bridge (DAB) circuit of Fig. 2.4 converter is studied in the following chapter. At this point, the choice of the DC blocking capacitor is addressed. In practical implementation, the switches may not operate with exact 50%duty cycles. The duty cycle mismatch may result in a DC voltage presented across the transformer. This voltage may cause the transformer magnetizing current to increase, which reduces efficiency, and may even result in core saturation. To prevent this, a DC blocking capacitor is required to remove the DC voltage from transformer. However, this extra DC blocking capacitor introduces an extra resonance with the transformer magnetizing inductance. The resonant frequency between the magnetizing inductance of transformer L M and DCblocking capacitor C block is 1 f 0 = 2π L M C (2.29) block When the blocking capacitor is 1.2μF, the resonant frequency is 1.89kHz in Fig. 2.6(a). The inductor current loses the sharpness in the waveform. Therefore, a circuit is required to prevent high-q resonance. In the case of the blocking capacitor 50μF, the resonant frequency is 293kHz as illustrated by the waveforms in Fig. 2.6(b).

32 22 Figure 2.5: Dual active bridge converter (a) 1.2uF DC Blocking Capacitor (b) 50uF DC Blocking Capacitor Figure 2.6: (a)(b) Experimental waveforms of the prototype where the upper waveform is the tank inductor current [1.0A/div], the secondary waveform is the drain-to-source voltage of a bridge switch [50V/div], and the lower waveforms is the gate signal.

33 23 Chapter 3 State Plane Analysis State plane presents a useful mathematical tool to analysis of switched second order systems with resonance. On the state plane, the states of the system (capacitor voltage and inductor current) are normalized and plotted against each other. If a proper normalization factor is chosen, and if it is assumed that the system losses can be neglected, the state trajectory is composed of only circular and linear segments. The state-plane trajectory graphically represents the behavior of switched resonant circuits. As a result, we can analyze the boundary condition of soft switching from a geometric viewpoint. Based on the work presented in [17], the state plane analysis is reviewed in this chapter, and applied to the DAB converter. 3.1 Review of State Plane Analysis In state plane analysis [18,19], a normalized approach is an effective method for analyzing resonant circuit behavior. First, suitable base voltage and base current are selected for normalization of the converter waveforms. The base voltage is V base = V g (3.1)

34 24 The base current follows from this selection as I base = V base R 0 (3.2) R 0 = L l C p (3.3) ω 0 = 1 L l C p (3.4) The notation for normalized unit-less waveforms is defined by m p (t) = V p(t) V base (3.5) j l (t) = i l(t) I base (3.6) The DCX has behavior equivalent to that of an ideal transformer, where the turns ratio of the transformer equals to the voltage conversion ratio of the converter, n 2 n 1 = V out V g (3.7) The ratio n 1 n 2 is equal to the turns ratio n t. The conversion ratio is then defined as M N = V out n t V g, and equations describing normalized voltage and current waveforms are given by m p (t) = J pk sin ω 0 t (M N 1) cos ω 0 t 1 (3.7) j l (t) = J pk cos ω 0 t (M N 1) sin ω 0 t (3.8) It follows that (m p (t) + 1) 2 + j l (t) = J 2 pk + (M N 1) 2 (3.9)

35 25 which represents a circle in the state plane. The radius of the circle is, r 1 = J 2 pk + (M N 1) 2 (3.10) The circle shows how the energy is ringing between the inductor and the capacitor. The center of the circle is at (m p, j l ) = ( 1,0). The correlation can be visualized as geometric parameters of the m p (t) j l (t) state plane trajectory. 3.2 State Plane Analysis Applied to the Dual Active Bridge The benefit associated with the use of state plane analysis is a simplification of resonant interval solutions. The state planes of the DAB converter for both the primary and the secondary resonances are shown in Fig. 3.1 [20]. Fig. 3.1 (a) shows the gate-drive waveforms, and the corresponding primary and secondary voltages. The system variables and their corresponding normalized quantities are listed in Table 3.2. The state plane trajectory is composed of both linear and circular segment, because the DAB converter operates with resonant intervals (Ⅰ&Ⅲ) and non-resonance intervals (Ⅱ&Ⅳ). Because DAB is a multi-resonant converter, the state plane of the DAB converter has m p j l state plane, which describes the behavior of inductor of current and primary voltage, as well as m s j s state plane, which describes the behavior of inductor of current and secondary voltage. In this section, the converter conversion ratio is considered to be approximately M N = 1. m s (t) = v s(t) V out (3.11) j s (t) = i l (t) n t R o V out (3.12)

36 26 where a prime ( ) indicates the normalization of the secondary parameters. (R o ) 2 = n t 2 L l C s (3.13) which represents the secondary capacitance C s and the tank inductance reflected through the transformer turns ratio to the secondary side in normalization Primary ZVS Condition in DAB The trajectory of the state plane for the primary side transition is in the counter-clockwise direction, while the trajectory of the state plane for the secondary is in the clockwise direction. In the primary side transition, the counter-clockwise direction indicates that the magnitude of inductor current is decreasing while the DAB converter primary side commutes. Therefore, sufficient inductor energy is necessary to achieve primary ZVS, while the secondary ZVS condition is independent of the energy stored in the inductor at the starting point of resonant transition. If the inductor energy is large enough to charge/discharge all four primary-side switch capacitances C p across the input voltage, ZVS can be accomplished, 1 2 L li pk 2 > 4 2 C pv g 2 (3.14) This equation simplifies to I pk > 2V g C p L l (3.15)

37 27 A minimum power P min at which primary ZVS will be achieved can be calculated. From the primary state plane of Fig. 3.1, full ZVS is achieved if the radius of the resonance r 1 > 2, where r 1 is found in (3.8). M N can be approximated as 1. In this case, the ZVS condition in the normalized state plane is given by J pk > 2 (3.16) For the secondary, ZVS is always achieved. Table 3.2: Correspondence table with DAB between time domain and primary state plane Time Domain i l (t) v p (t) v s (t) v g I 1 I 2 I pk t 1 t 2 t 3 t 4 Primary State Plane j l (t) m p (t) m s (t) 1 j 1 j 2 J pk α β δ ζ

38 28 (a) (b)

39 29 (c) (d) Figure 3.1: Time-domain waveforms of the resonant transition of the primary and secondary (a) in the DAB converter, the DAB schematic (b), primary (c) and secondary (d) state planes DAB State Plane Solution Subinterval I: In subinterval I, ZVS is achieved during resonant transition of the primary full bridge in the primary state plane of Fig. 3.1 (c). The length of the transition can be expressed by the resonant angle α. t 1 = α ω 0 (3.17)

40 30 The angle α is solved form the state plane by noting that the resonant radius r 1 = J pk. Therefore, the angle α is given by α = sin 1 ( 2 J pk ) (3.18) Fig. 3.1 (c) is applied to use geometric approach to finding the inductor current at the end of subinterval I. J 1 can be solved by the triangle theorem between r 1 and the m p axis. Subinterval II: The transition of subinterval II is linear in both primary and secondary, because v p and v s are constant. The inductor voltage is V g + V out n t = 2V g during the course of the subinterval. Therefore, t s can be represented by t 2 = L l 2V g (I 1 + I 2 ) (3.19) Normalizing by multiplying both side by ω 0, and (3.3) and (3.4) is applied to (3.19) β = 1 2 (J 1 + J 2 ) (3.20) Subinterval III: The transition of subinterval III in the secondary state plane takes the same behavior of subinterval I in the primary state plane. The same approach of (3.18) can be applied to and the initial current is calculated by geometrical arguments. δ = sin 1 ( 2 J pk ) (3.21) J 2 = J pk 2 4 (3.22)

41 31 (3.18) is reflected to the secondary state plane. δ = n t C s C p sin 1 ( C s C p 2n t J pk ) (3.23) and the initial current J 2 = J pk 2 4n t C s C p (3.24) Subinterval IV: In the transition of subinterval IV, the segments in both primary and secondary may draw straight line. The sum of the four subintervals should be equal to half-period the switching period, t 1 + t 2 + t 3 + t 4 = T s 2 (3.25) The normalization of subinterval IV as ς = t 4 ω 0 is given by ς = π F α β δ (3.26) 3.3 Analysis of DAB Operation Modes In order to control the optimal efficiency trajectory for DAB, the state plane analysis of previous section have to consider converter operation with V out n t V g. The DAB operation modes have some boundaries which are determined by the magnitude of phase shift and the dead times. Furthermore, there are ZVS boundaries of both primary and secondary side devices. A new approach is developed for the more general case. In this section, M N is defined as a variable. M N = V out n t V g (3.27)

42 Mode 1: Operation with β > 0 and primary ZVS In Mode 1, the subinterval II has length greater than 0, and the peak current I pk is sufficient to achieve ZVS. When β is assumed to be close to 0, the primary state plane trajectory is shown Fig Figure 3.2: The DAB converter in Mode 1 in the normalized primary state plane By analysis of the state plane geometry, the average output current can be found. First, two triangles relating the radius r 1 give the value of J 1 J 1 = J pk 2 4M N (3.28) The conduction angle of the primary resonance is given by α = cos 1 (1 (J pk J 1 ) J pk 2 + 2(1 M N ) 2) (3.29)

43 33 The waveform of the current is linear during intervals II and IV, therefore the time interval can be solved by the slope of the current, which are normalized to obtain t 2 = L l I 1 + I 2 V g + V out n t (3.30) t 4 = L l I pk I 2 V g V out n t (3.31) β = J 1 + J M N (3.32) ς = J pk J 2 1 M N (3.33) The switching period is T s = 2(t α + t β + t γ ), which remains the same as in the simplified case considered previously π F = α + β + ς (3.34) with F = f s f 0. Finally, by applying charge balance to the output capacitor and integrating the charge transferred to the output, the average output current can be found as J = i 0 I base = F n t π (2 + J p + J 2 2 ς + J p J 2 β) 2 (3.35) Mode 2: Operation with β > 0 and hard-switched primary As the current I pk available to achieve ZVS of primary devices decreases, the energy stored in the inductor also decreases. As a result, hard switching of the primary devices will occurs. The boundary

44 34 condition of ZVS for the primary-side devices is found from the state plane of Fig If the radius of the resonance r 1 < 1 + M N, the condition is substituted into (3.28) J pk < 4M N (3.36) Figure 3.3: The DAB converter in Mode 2 as normalized state plane At the end of the resonant transition, the primary devices are hard-switched. The state plane of operation is shown in Fig M 1 is defined as the normalized voltage at the end of the resonant interval. Below J 1 = 0, M 1 is found by examining the triangle formed between r 1 and m p axis as M 1 = J pk 2 + (1 M N ) 2 M N (3.26) Equations (3.32), (3.33), and (3.34) are unchanged, and the equations for and J are given by α = cos 1 (1 J pk 2 + (1 + M 1 ) 2 2(M 1 M N ) 2 ) (3.27) J out = F n t π (1 + M 1 + J pk + J 2 ς J β) (3.28)

45 Mode 3: Operation with β < 0 and primary soft-switched primary In Mode 3, the primary devices are operated with ZVS. Because the power flow still remains positive, the secondary devices are hard-switched during the dead time of the primary devices. The state plane for Mode 3 is shown in Fig To ensure consistency with the other operation mode, two new angles are defined as γ = α + β (3.29) = β (3.30) Furthermore, (1 M 2 ) is the normalized value of the voltage v p when the secondary devices are switched. The equations for γ and J become and from two radii γ = cos 1 (1 (J pk + J 2 ) 2 + (1 + M 2 ) 2 2(1 M N ) 2 + 2J pk 2 ) (3.31) = cos 1 (1 (J 1 + J 2 ) 2 + (1 M 2 ) 2 2(M N M 2 ) 2 + 2J 2 2 ) (3.32) J 2 2 = (1 M N ) 2 + J pk 2 (M 2 + M N ) 2 (3.33) J 1 2 = (1 M N ) 2 + J (M N M 2 ) 2 (3.34) the equation for the ζ interval is modified ζ = J pk + J 1 1 M N (3.35)

46 36 The normalization of switching frequency is defined as before, F = f s f 0. The normalized switching period equation becomes Finally, the averaging of the output current yields π F = γ + φ + ζ = α + ζ (3.36) J out = F n t π (2M 2 + J pk J 1 ζ) 2 (3.37) Figure 3.4: State plane of the DAB in Mode Experimental Results The proposed DAB converter was constructed with the transformer, as described in Table 2.1, and 40 H tank inductor, as described in Table 2.2, implemented on the transformer primary. Infineon

47 37 IPW65R660CFD CoolMOS devices are used for all primary and secondary transistors. Four MOSFETs are used for each bridge. Fig. 3.5 shows the 500 W prototype converter. The analytical and the measured state plane trajectories are compared in Fig The measured data come from oscilloscope waveform. There are surges in the state plane in Fig. 3.7 (a) and (f). Since the 40 H tank inductor is designed for trapezoidal current waveform at 300 W, the inductor current in interval IV has a positive slope under the conditions away from 300 W. Figure 3.5: Prototype DAB converter

48 38 (a) (b) (c) (d) (e) (f) Figure 3.6: Comparison between theory and experiments in the primary state plane trajectories at (a) 300- W, (c) 400 W, and (e) 500 W. The secondary state plane trajectories are (b) 300 W, (d) 400 W, and (f) 500 W.

49 39 Chapter 4 Experimental Results Analysis and design of the DAB converter prototype are presented in Chapter 3, focusing on the 300 W operating point. However, the vehicle application presents the converter with a range of operating points. The loads vary widely and rapidly. Therefore, the operation of the DAB converter should be considered across a wide range of output power levels. The converter should be able to accomplish high efficiency under all conditions. One approach to extending converter operation to a wide range of output powers is to use the converter phase shift as a control variable. According to the load power requirements, the phase shift between the primary and the secondary full bridge needs to be optimized. In this chapter, efficiency analysis of the DAB is compared to experimental measurements obtained in the prototype converter. Additionally, a control method of the optimized phase shift is described and tested in experiments. 4.1 Loss Analysis The full bridge DCX and DAB DCX converter prototype is implemented using eight MOSFET transistor. Both of the circuit topologies are exactly same. In the full bridge DCX, only the primary MOSFETs are actively controlled, while the secondary-side MOSFETs are kept off. The secondary-side body diodes perform the rectification function. In the DAB case, both the primary-side and the secondaryside MOSFETs are actively controlled, with a phase shift between the two bridges used as a control variable.

50 40 A comparison between the full bridge DCX and the DAB DCX converter loss at 200 W is given in Fig This loss analysis includes both the primary and secondary transistor device and magnetic component loss. A difference between the full bridge DCX and DAB DCX is the conduction loss on secondary side. The full bridge DCX has diode conduction and switching losses due to secondary MOSFET intrinsic body diodes. In the DAB DCX, the MOSFET conduction losses compared to the full bridge DCX increase because the output current flows through the MOSFET on-resistance on the secondary. The total device losses of the DAB DCX can be reduced. To verity this, a comparison of characteristics of reverse diode with MOSFET is shown in Fig. 4.2 (a). The plot of intrinsic body diode conduction is obtained from the datasheet specification of the forward characteristics of the body diode, while the plot of MOSFET conduction drop is linear because the MOSFET on-resistance is constant. The analytical predictions of P Diode_Conduction and P MOSFET_Conduction are given by P Diode_Conduction = 2I D (V F + I d R d ) (4.1) P MOSFET_Conduction = 2I d 2 R on (4.2) These relationships can be converted to conduction losses in the devices in Fig. 4.2 (b). The total device loss in a wide load range can be improved by the secondary MOSFET conduction. The DAB DCX will otherwise exhibit the same behavior of the full bridge DCX across the full load range. Therefore, both full bridge DCX and DAB DCX are capable of achieving the same performance in the full load range.

51 Loss [W] Diode Pcond Diode Psw MOSFET Pcond MOSFET Psw Ind Cu Ind Fe Transformer Cu Transformer Fe 0 Full Bridge Dual Active Bridge Figure 4.1: Loss analysis of full bridge DCX and DAB DCX at 200W

52 42 (a) (b) Figure 4.2: In (a), characteristics of body diode and MOSFET loss analysis of full bridge DCX and DAB DCX. In (b), the secondary-side conduction losses are compared.

53 Efficiency [%] Phase-Shift Optimization in DAB If primary and secondary dead times are constant with normalized values α 0 and δ 0, the total phase shift is [21] Φ ab = α + β + δ (4.3) Analysis of DAB operating modes presented in Chapter 3 indicates that a controller must adjust both the converter primary dead time α and the total phase shift Φ ab to the specified values at each output power. Fig. 4.3 shows the efficiency of DAB as a function of phase-shift time t 2. Example waveforms are given in Fig For the optimal controller, the optimized dead time to maximize the efficiency is nonlinear, and a controller requires measurements of the output power to find the appropriate dead time for each power. By the use of voltage sensing at the input port and output port, a controller can calculate the conversion ratio M N Phase Shift [ns] Figure 4.3: Efficiency as a function of phase shift between primary and secondary at 300 W

54 44 (a) Phase shift 233 ns (b) Phase shift 266 ns (c) Phase shift 300ns Figure 4.4: Experimental waveforms of the DAB converter prototype operating at 300W with dead time α

55 Analysis of Optimal Efficiency Trajectory In order to maximize converter efficiency across a full range of operating points, a prototype DAB converter is examined. Losses are calculated to produce the analytical efficiency contour plots of Fig. 4.6 (a), while the experimental efficiency contour is plotted in Fig. 4.6 (b). The analysis model considers only the square-wave approximated waveforms of the inductor current. Therefore, the analytical efficiency contour plot does not match the experimental efficiency contour when the DAB is operated with extreme phase shift so that the inductor current becomes a triangle wave. However, the optimal trajectories in the experiment are similar to the presented analytical predictions. On this trajectory, the primary dead time α may be approximated as constant. The optimal trajectories show a linear relationship between Φ ab and M N. M N = KΦ ab + C (4.4) The dead times t 1 and t 3 are constants. Therefore, the controller can adjust only t 2 by sensing values for V g and V out. The optimal trajectories for the power range 350 W P out is nonlinear. Therefore, nonoptima phase shift can lead to significantly reduced DAB DCX efficiency, while potential gains with phase shift optimization are relatively small. One approach to maintain high efficiency is to switch to full bridge DCX operation at full load.

56 46 (a) (b) Figure 4.5: Efficiency contours of the DAB converter based on (a) experimental results and (b) analytical efficiency predictions. The blue line indicates the highest efficiency trajectory.

57 Efficiency [%] Experimental Results: Conversion Ratio and Efficiency Conversion ratio and efficiency are measured experimentally using Fluke 45 multimeter to measure input current and output voltage, and Agilent 34411A mutlimeter for output current and input voltage. A comparison between the experimental efficiencies and the predicted efficiencies is given in Fig The phase shift in the DAB DCX is manually optimized. Gate-drive losses are not included in measured or calculated efficiency values, but are estimated to be approximately 173 mw for the full bridge DCX and approximately 216 mw for the DAB DCX. The DAB DCX analytical efficiency prediction is slightly better than Full Bridge DCX. However, the DAB DCX experimental efficiency at 100 W is not as good as the prediction. The green waveforms indicate the inductor current in Fig In the DAB DCX, the inductor current flows through secondary MOSFETs. As a result, the inductor current waveform becomes a triangle wave. On the other hand, the full bridge DCX at 100 W features discontinuous conduction modes of operations. As a result, the full bridge DCX operates with lower RMS currents and lower losses at light load Pout [W] Full Bridge Exp DAB Exp Full Bridge Cal DAB Cal Figure 4.6: Comparison of analytical calculated (analytical) efficiency and experimentally measured efficiency for the prototype operates as the full-bridge DCX, or as the DAB DCX.

58 48 (a) (b) Figure 4.7: Prototype experimental waveforms of the full bridge DCX (a), and the DAB DCX converter (b), operating at 100W.

59 49 Chapter 5 Summary and Future Work This thesis focuses on analysis and design of a DC transformer (DCX) DC-DC converter, which exhibits high efficiency, and small size suitable for automotive applications. The DCX is a building block in a new DC-DC converter architecture described in [9]. This work details the analysis, design, control method, and implementation of zero-voltage switching in the DCX operated as a dual active bridge (DAB) converter. Additionally, from the 500 W prototype DAB converter, techniques for component selection, converter design, and optimal efficiency trajectory are examined. Contributions of the thesis are summarized as follows. 5.1 DAB Design and Component Selection A loss model of the DAB converter which exhibits optimal efficiency at 300W output power is proposed. Design parameters for optimization of converter efficiency include transformer design and tank inductance value. The proposed optimization indicates that the converter tank inductance is selected to place the ZVS boundary at a target operating power. The ZVS boundary condition is defined by the tank inductor stored energy which is required to commutate the primary-side switches with zero-voltage switching (ZVS). Therefore, the optimal tank inductance is related with the primary device selection and converter operating point.

60 State Plane Analysis of DAB Converter Motivated by the simplified analysis, the sate plane analysis techniques presented in [20, 21] are reviewed in Chapter 3. This approach can visualize all resonant intervals in two dimensions, and derive the ZVS boundary condition from a geometric viewpoint. The resulting converter solution can be applied to achieve high efficiency design. First, the direct analysis of ZVS intervals yields the ZVS boundary condition in terms of the output power level. Second, the ZVS condition can be used to program optimal phase-shift between primary and secondary at each output power. 5.3 Conclusions Through comparisons between the full bridge DCX and the DAB DCX, it is found that the DAB DCX can improve the efficiency if MOSFET conduction loss is significantly lower than the intrinsic body diode conduction loss. Additionally, a high step-down DAB converter can be expected to significantly improve efficiency because the secondary-side devices conduct the high secondary currents. The detailed state plane analysis is extended to analyze the converter across different operating modes. The loss model is used to solve for a method of varying the output power. The converter needs to response to changes in output power so that the highest efficiency can be achieved at each power level. It is shown how it is possible to track the optimal phase shift through sensing the input voltage and the output voltage. This optimal trajectory is slightly modified to obtain a proposed trajectory over the full load range. In this case, non-optimum phase shift can lead to significantly reduced DAB DCX efficiency, while potential gains with optimum phase shift are relatively small. One approach to maintaining high efficiency is to switch from the DAB DCX to the full bridge DCX. At very light loads, DAB DCX efficiency is reduced because of additional conduction and switching losses. The primary switching transitions are shown in Fig The additional switching losses are accrued by full or partial hard switching.

61 51 (a) (b) (c) (d) Figure 5.1: Prototype experimental switching transitions of the full bridge DCX (a) (b), and the DAB DCX converter operating at 100 W (c) (d). 5.4 Future Work Further research has been identified in the process of completing this thesis. First, this thesis relied on the assumption of a linear value C p which can be used to model the parasitic energy storage behavior of the transistor devices. However, the actual behavior of this parasitic element is nonlinear, which affects resonant transitions. Therefore, using the equivalent linear capacitors model developed in [22] can improve accuracy in the state plane analysis of DAB converter. Second, the state plane analysis of the full bridge DCX considers only an ideal semiconductor model. This model could be improved considerably. The switching circuit analysis technique based on the non-ideal diode characteristics, reverse recovery and junction capacitance, can be applied to state plane analysis of the full bridge DCX as in [23].