a high-efficiency isolated hybrid series resonant ... · under high-input conditions, the converter...

A High-efficiency Isolated Hybrid Series Resonant Microconverter for Photovoltaic Applications

Xiaonan Zhao

Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science In

Electrical Engineering

Jih-Sheng Lai, Chair Khai D. T. Ngo

Dong S. Ha

November 20, 2015 Blacksburg, VA

Keywords: Microconverter; photovoltaic, high-efficiency; isolated dc-dc converter; hybrid operation; series resonant converter; PWM

Copyright © 2015, Xiaonan Zhao

A High-Efficiency Isolated Hybrid Series Resonant

Microconverter Photovoltaic Applications

Xiaonan Zhao

ABSTRACT Solar energy as one type of the renewable energy becomes more and more popular

which has led to increase the photovoltaic (PV) installations recently. One of the PV

installations is the power conditioning system which is to convert the maximum available

power output of the PV modules to the utility grid. Single-phase microinverters are

commonly used to integrate the power to utility grid in modular power conditioning

system. In the two-stage microinverter, each PV module is connected with a power

converter which can transfer higher output power due to the tracking maximum power

point (MPP) capability. However, it also has the disadvantages of lower power conversion

efficiency due to the increased number of power electronics converters. The primary

objective of this thesis is to develop a high-efficiency microconverter to increase the output

power capability of the modular power conditioning systems.

A topology with hybrid modes of operation are proposed to achieve wide-input

regulation while achieving high efficiency. Two operating modes are introduced in details.

Under high-input conditions, the converter acts like a buck converter, whereas the

converter behaves as a boost converter under low-input conditions. The converter operates

as the series resonant converter with normal-input voltage to achieve the highest efficiency.

With this topology, the converter can achieve zero-voltage switching (ZVS) and/or zero-

current switching (ZCS) of the primary side MOSFETs, ZCS and/or ZVS of the secondary

iii

side MOSFETs and ZCS of output diodes under all operational conditions. The

experimental results based on a 300 W prototype are given with 98.1% of peak power stage

efficiency and 97.6% of weighted California Energy Commission (CEC) efficiency

including all auxiliary and control power under the normal-input voltage condition.

iv

To my parents, Yanmin Zhao

Cuiqing Xu

v

Acknowledgements

First, I would like to first thank my academic and career advisor, Dr. Jih-Sheng Lai,

for all of his guidance and support and affording me the opportunity to work under him in

the Future Energy Electronics Center (FEEC).

I also would like to thank Dr. Khai D. T. Ngo and Dr. Dong S. Ha for serving on

my committee, also for their interests, suggestions and comments throughout my pursuit

of this degree.

I am very grateful to have the opportunity to work in the FEEC and developed

precious friendship with all of colleagues. The insight and knowledge I have gained from

discussions with all of these colleagues have been absolutely invaluable. I would like to

thank Mr. Gary Kerr, Dr. Thomas LaBella, Dr. Cong Zheng, Dr. Baifeng Chen, Dr.

Michael Choe, Dr. Qingqing Ma, Dr. Zaka Ullah Zahid, Mr. Wei-han Lai, Mr. Seungryul

Moon, Mr. Jason Dominic, Mr. Lanhua Zhang, Mr. Rui Chen, Mr. Bo Zhou, Miss. Rachael

Born, Mr. Chih-Shen Yeh and Miss. Yu Wei for their help and supports. Also I would like

to thank visiting scholars Dr. Zhong-Yi Lin, Dr. Yu-Cheng Liu, Dr. Ruixiang Hao, Dr.

Zhiling Liao, Dr. Yan Li and Dr. Xueshen Cui for their help.

I would like to thank my parents, Yanmin Zhao and Cuiqing Xu, for their

continuous love, support, and encouragement with every venture that I undertake life.

Thanks for all of my friends for their support and encouragement. They have afforded me

has kept me focused and helped me realize not only my academic goals, but also my goals

in all aspects of life.

vi

Table of Contents

Chapter 1 Introduction ............................................................................. 1

1.1 Overview of Photovoltaic Power Conditioning Systems........................................ 1

1.2 State-of-Art Isolated High Step-up DC-DC Converter ........................................... 6

1.3 Research Objectives and Thesis Outline............................................................... 10

Chapter 2 Proposed Isolated Hybrid Series Resonant Microconverter Topology and Operations ........................................................................... 12

2.1 Overview of Proposed Topology and Operations ................................................. 12

2.2 Buck Mode ............................................................................................................ 17

2.2.1 Principle of Operation ................................................................................. 17

2.2.2 Duty Cycle Derivation ................................................................................ 26

2.3 Boost mode ........................................................................................................... 29

2.3.1 Principle of Operation ................................................................................. 29

2.3.2 Duty Cycle Derivation ................................................................................ 37

2.4 Summary ............................................................................................................... 40

Chapter 3 Power Stage Design Procedure and Experimental Results .. 43

3.1 Power Stage Design Procedure ............................................................................. 43

3.1.1 Transformer Design .................................................................................... 43

3.1.2 Resonant Tank Design ................................................................................ 48

3.1.3 MOSFETs and Diodes Selection ................................................................ 51

3.2 Experimental Results ............................................................................................ 53

3.2.1 Prototype Design Summary ........................................................................ 53

vii

3.2.2 Converter Operations Verification .............................................................. 56

3.2.3 Experimental results of MOSFETs Soft-Switching .................................... 58

3.2.4 Converter Efficiency ................................................................................... 61

3.3 Loss Breakdown Analysis..................................................................................... 62

3.4 Summary ............................................................................................................... 63

Chapter 4 Conclusions and Future Work ............................................ 65

4.1 Conclusions ........................................................................................................... 65

4.2 Future Work .......................................................................................................... 66

viii

List of Figures

Figure 1.1. Model of PV cell .............................................................................................. 2

Figure 1.2. P-V and I-V curves of PV cell .......................................................................... 2

Figure 1.3. PV Power conditioning system: (a) centralized inverters and (b) multiple string inverters. ....................................................................................................... 3

Figure 1.4. PV power conditioning system: (a) Single-stage microinverter, (b) Two-stage microinverter.................................................................................................. 4

Figure 1.5. Flyback topology: (a) without clamp circuit, (b) with clamp circuit ............... 7

Figure 1.6. (a) Traditional LLC topology (b) One of modified LLC topology with wide-input regulation .............................................................................................. 8

Figure 2.1. Researched isolated series resonant converter topology ................................ 12

Figure 2.2. Main steady-state waveforms of two operating modes: (a) under normal-input condition (30 V), (b) Buck mode (under 33 V input condition), (c) Boost mode (under 27 V input condition). ...................................................................... 15

Figure 2.3. Equivalent duty cycle definition of Buck mode operation ............................. 17

Figure 2.4. Steady-state waveforms of Buck mode with 33 V input voltage, 380 V output voltage and 300 W output power. .............................................................. 18

Figure 2.5. Operating periods of Buck mode .................................................................... 19

Figure 2.6. State-plane trajectory of resonant tank operating in Buck mode ................... 20

Figure 2.7. (a) State-plane trajectory of interval [t0 - t1], (b) Equivalent circuit of interval [t0 - t1]. ...................................................................................................... 21

Figure 2.8. (a) State-plane trajectory of interval [t2 – t3]. (b) Equivalent circuit of interval [t2 – t3]. ..................................................................................................... 22

Figure 2.9. (a) State-plane trajectory of interval [t5 – t6]. (b) Equivalent circuit of interval [t5 – t6]. ..................................................................................................... 24

Figure 2.10. (a) Equivalent circuit of interval [t7 – t8], (b) State-plane trajectory of interval [t7 – t8]. ..................................................................................................... 25

Figure 2.11. State-plane trajectory of Buck mode ............................................................ 27

Figure 2.12. The voltage conversion ratio, M, curves in Buck mode versus dbuck ............ 29

ix

Figure 2.13. Steady-state waveforms of Boost mode with 27 V input voltage, 380 V output voltage and 300 W output power. .............................................................. 30

Figure 2.14. Operating periods of Boost mode ................................................................. 31

Figure 2.15. State-plane trajectory of resonant tank operating in Boost mode................. 32



Figure 2.18. (a) State-plane trajectory of interval [t4 – t5], (b) Equivalent circuit of interval [t4 – t5]. ..................................................................................................... 35


Figure 2.20. Equivalent duty cycle dboost definition .......................................................... 37

Figure 2.21. State-plane trajectory of Boost mode ........................................................... 38

Figure 2.22. The voltage conversion ratio, M, curves in Boost mode versus dboost .......... 40

Figure 2.23. Curves of voltage conversion ratio M .......................................................... 42

Figure 3.1. Specific power loss for several frequency/flux density combinations as a function of temperature of Ferroxcube 3C95 [48]. ............................................... 44

Figure 3.2. Equivalent circuit of primary-side MOSFETs and magnetizing current during the first dead time period in Boost mode................................................... 45

Figure 3.3. Simplified circuit of circuit in figure 3.2, (a) initial state, (b) end state. ........ 46

Figure 3.4. Winding structure of transformer ................................................................... 47

Figure 3.5. Resonant inductor currents and resonant capacitor voltages with different resonant tanks operating in Buck mode under the operating condition of 100 kHz switching frequency, 35 V input voltage, 380 V output voltage and 300 W power levels. .................................................................................................... 50

Figure 3.6. Resonant inductor currents and resonant capacitor voltages with different resonant tanks operating in Boost mode under the operating condition of 100 kHz switching frequency, 25 V input voltage, 380 V output voltage and 300 W power levels. .................................................................................................... 50

Figure 3.7. Photograph of hardware prototype ................................................................. 55

x

Figure 3.8. Experimental test setup................................................................................... 55

Figure 3.9. Operation waveforms under 30.4 V input and 300 W output ........................ 56

Figure 3.10. Buck mode operation with 33 V input and 300 W output ............................ 56

Figure 3.11. Boost mode operation with 27 V input and 300 W output ........................... 57

Figure 3.12. ZVS of primary side MOSFET S1 under normal-input condition. ............... 58

Figure 3.13. ZVS of primary side MOSFET S1 during Boost mode under 27 V input condition. .............................................................................................................. 59

Figure 3.14. ZCS of primary side MOSFET S1 under normal-input condition. ............... 59

Figure 3.15 Turn-on and turn-off transition of primary side MOSFETs during Buck mode under 33 V input condition. ........................................................................ 60

Figure 3.16. ZCS of primary side MOSFET S1 during Boost mode under 27 V input condition. .............................................................................................................. 60

Figure 3.17. ZVS of secondary MOSFET S5 under normal-input condition. ................... 61

Figure 3.18. Measured converter efficiency ..................................................................... 62

Figure 3.19. Calculated breakdown of converter loss under 30 V input, 225 W output power condition. ................................................................................................... 64

xi

List of Tables

Table 1.1. Summary of topologies from literature review .................................................. 9

Table 3.1. Transformer Parameters ................................................................................... 48

Table 3.2. Different resonant tanks analysis. .................................................................... 48

Table 3.3. A summary of power stage components loss under normal-input condition............................................................................................................................... 63

1

Chapter 1

Introduction

1.1 Overview of Photovoltaic Power Conditioning Systems

Due to the limited quantity of fossil fuels, the demand of renewable energy is

steadily increasing each year [1]. Solar as one type of the renewable energy has been fast

growing because of its great potential of installations and price decreasing. The world’s

cumulative PV capacity has achieved 102 GW in the year 2012 and would be expected to reach

288 GW in 2017 [2], and, in the past 3 years alone, the average cost of installing utility-

scale solar in the United States (US) has come down from approximately $3.24 per watt to

$1.55 per watt [3].

The power conditioning system (PCS) converting PV modules output power to

utility grid is an important portion in the PV installations [4], [5]. The PCS must ensure

that the PV modules operate at the maximum power point (MPP) so that utility grid can

capture the maximum available power. Maximum power point tracking (MPPT) is

necessary for PV modules because of their non-linear output characteristics. Figure 1.1

shows the simplified model of a single PV cell and Figure 1.2 shows the P-V, I-V

characteristics of the PV cell. These nonlinear I-V characteristics can vary drastically

depending on the PV cell material, solar irradiance, temperature, module shading, etc. [6].

For the PCS, the MPPT capability is significant to make sure to convert the maximum

output power to utility grid.

2

pvIdI sRshI

shR

Figure 1.1. Model of PV cell

Figure 1.2. P-V and I-V curves of PV cell

Depending on different levels of MPPT implementation for PV modules, there are

three main categories of PV power conditioning system architectures: centralized, string,

and modular [7]-[9].

With centralized PCS as shown in Figure 1.3(a), a large number of PV strings in

parallel are connected with one high-power grid-connected inverter. Each PV string is

composed of tons of modules in series, generating high output voltage. This grid-connected

inverter tracks the maximum power point of the entire array of modules. The centralized

PCS used with conventional ac grid and is easy to maintain due to only single power

electronics converter. However, there are also some limitations. The major disadvantage is

its low MPPT efficiency. The inverter can only track the MPP of entire array of modules

because of the only power electronics converter, which will cause the some of the PV

modules cannot operate at the MPP. MPPT efficiency will be lower than the case that each

PV modules operates at its own MPP. Another disadvantage is the high DC input voltage

3

requiring high voltage cables which is hard to maintain and also has the potential of safety

problems.

Utility Grid Utility Grid

PV module

PV module PV module

PV modulePV module PV module

PV module

PV module PV module

PV module

PV module

PV module

DC

AC

DC

AC

DC

AC

(a) (b)

Figure 1.3. PV Power conditioning system: (a) centralized inverters and (b) multiple string inverters.

The secondary PCS type is the string inverters as shown in Figure 1.3(b) which are

also used with the conventional ac utility grid. Several PV modules connected in series to

form a PV string and each string is connected with a grid-tie inverter. The string inverter

system has more power electronics converters compared with centralized inverter system.

Therefore string inverter systems are more expensive and more complicated to maintain.

However, the MPPT efficiency is improved. If one PV string is partial shading, it cannot

affect the MPP of entire PV arrays because each PV string has its own MPPT capability.

4

In addition, the PV arrays output voltage is lower so it can eliminate the cost of high voltage

DC cabling. But it still exists the problem of mismatch loss between PV modules.

Utility Grid

DC

AC

DC

AC DC

AC

DC

AC

DC

DC

DC

DC

PV module PV module PV module PV module

(a) (b)

Figure 1.4. PV power conditioning system: (a) Single-stage microinverter, (b) Two-stage microinverter

In order to overcome the problem of mismatch loss between PV modules existing

in conventional centralized and string inverter systems, the third type of PCS architecture

is the developed which is modular system as shown in Figure 1.4. Each PV module has its

own power electronics converter which tracks the MPP of each individual PV module.

Compared with traditional centralized and string inverter systems, the modular

power conditioning system is more attractive due to their superior MPPT, scalability, and

fault tolerance [9]. Each module has its own power electronics converter generating

maximum available power by performing MPPT individually. Therefore, it has the

advantage of reducing the impact of shading, debris or snow covering the PV modules. The

modular PCS can be the easiest way to install and upgrade because installations can be

scaled by one module and one converter. Another advantageous feature of modular

5

systems is that the residents can adopt this configuration. Although the installation costs

of modular systems are higher because there are more power electronics converters, they

are still very attractive due to the advantages analyzed above.

Power electronics converter in modular PCS configuration is also called

microinverter. Microinverter can be classified as two groups: single-stage microinverter as

pictured in Figure 1.4(a) and two-stage microinverter as pictured in Figure 1.4(b). Single-

stage microinverter converts the PV module voltage directly to ac, while two-stage

microinverter will boost PV module voltage to standard dc bus voltage and the second

stage converts the dc power to ac. There is an intermediate dc-dc converter named

microconverter between the PV module and inverter stage responsible for MPPT [8] in

two-stage microinverter system.

Compared with single-stage microinverter, two-stage microinverter is more

attractive in terms of inverter lifespan. Since electrolytic capacitors which accelerates the

degradation by high temperatures are widely used in the single-stage microinverter to

eliminate the input double line frequency ripple. Electrolytic capacitors have to be avoided

to use in order to prolong lifespan of microinverter. In a two-stage microinverter system,

input double line frequency can be rejected by applying some control strategies on the

microconverter stage without any electrolytic capacitors, for example, proportional-

resonant controller, on the dc-dc microconverter stage [49], [50].

Other than the capability of MPPT, one of the basic requirements for PCS is to

provide galvanic isolation between the modules and the grid. In the US, the metal frames

of the PV modules are required to be grounded to the utility earth ground according to

National Electric Code requirements [10]. The purpose is to guarantee the safety of

6

personnel who install and maintain the module. Without the isolation of PCS, there is the

potential ground loop through power converter, grid, ground and the parasitic capacitances

that exist between the PV cells and the metal frame of the module, which will cause large

ground leakage currents. These large leakage currents can cause severe electromagnetic

interference (EMI) problems and other grid power quality problems like increasing grid

current total harmonic distortion (THD) [11].

In conclusion of the analysis above, the isolated dc-dc converter serving as the

front-end dc-dc stage in the two-stage microinverter system is worth to research. The

motivations of this thesis are to research a new isolated microconverter focusing on high

efficiency and wide-input regulation to make sure the MPPT capability.

1.2 State-of-Art Isolated High Step-up DC-DC Converter

This section will give a review of existing isolated dc-dc converter topologies

serving as the micoconverter. There are two types topologies of isolated dc-dc stage: high

boost ratio voltage-fed converter [12] and current-fed converter [13]-[16]. They can also

be classified into other two groups: PWM converter [17]-[23] and resonant converter [24],

[25].

The most commonly converter used in the microinverter system is the flyback

topology in the past 30 years. The flyback topology as shown in Figure 1.5(a) has long

been attractive because of its relative simplicity circuit and low cost [17]. Flyback

converter can also regulate the output voltage over wide-input range by simply

implementing the PWM operation. A drawback to the use of the flyback is the relatively

high voltage and current stress suffered by its switching components. High peak and RMS

current stress is a particular problem for flyback when operating in discontinuous

7

conduction mode (DCM). In addition, high tum-off voltage of primary switch which

requires the use of a RCD clamp to limit the switch voltage excursion. Unfortunately, in

this scheme the energy stored in the transformer leakage is dissipated in the clamp resistor,

hurting the converter efficiency. Another disadvantage is the low utilization of the

magnetic components resulting large size and lower power density.

Vin

S1

VoLm

1:nD1

Vin

S1

VoLm

1:nD1

S2

CoCo

Cclam p

(a) (b)

Figure 1.5. Flyback topology: (a) without clamp circuit, (b) with clamp circuit

Then active clamp flyback has been introduced in an attempt to absorb the main

switch turn off voltage spike and achieve the soft-switching [17]-[20] as shown in Figure

1.5(b). The efficiency of active clamp flyback is higher compared with flyback converter.

There are other modified flyback circuits aiming to increase the converter efficiency [21]-

[23]. Although all of these converters can improve the efficiency limitations of the

traditional flyback converter, they all either add additional components or control

complexity.

Lm

1 n

S1

S2

S3

S4

LrCr

S5

S6

S7

S8

(a)

8

Lm

1 n

S1

S2

S3

S4

LrCr

S5

S6

S7

S8

1 n

S9

S10

S11

S12

(b)

Figure 1.6. (a) Traditional LLC topology (b) One of modified LLC topology with wide-input regulation

Considering the main efficiency limitation factor for the flyback converter is the

switching loss on the both main switch and output diode, resonant converter is an attractive

choice. One of the most popular isolated high step-up resonant converter is the series

resonant converter for its high efficiency. It directly transfers power to the load for the

majority of the switching cycle, always achieves zero-voltage switching (ZVS) and low

current switching of the primary side switches, and also realizes zero-current switching

(ZCS) of the output side switches [26]-[28]. The advantage of high efficiency is ideal for

PV application. However, for the traditional series resonant converter, it is suitable for

fixed-input and fixed-output voltage application since it doesn’t have capability of wide-

input regulation. The highest efficiency operating points are at the conditions that switching

frequency is at or slightly lower than the resonant frequency [29].

The other topology is the LLC converter which is shown in Figure 1.6(a) with the

regulation capability under certain operating range [30]. However, LLC converters can

achieve high efficiency and high power density only if operating around the resonant

frequency because of the low circulating currents. The efficiency drops a lot when the

9

switching frequency is far away from the resonant frequency, which results in narrow input

voltage range and limited voltage regulation capability. This limitation previously kept the

LLC topology from being used on PV microinverters, for which a very wide-input voltage

range is typically expected. Several pieces of research have been conducted to mitigate the

problem of the conventional LLC converter [31]-[39]. Some of these revised topologies

operate with variable frequency controller to achieve wide-input regulation [31], [32],

however, when the converter is operating far from its series resonant frequency, the light-

load efficiency is poor due to large circulating currents. Some of these topologies added a

lot more components and one of them is shown in Figure 1.6(b) [37]. Although they can

achieve high efficiency with wide-input range regulation. They are suffering the

complexity and cost. Table 1.1 summarized the advantages and drawbacks of these

topologies.

Table 1.1. Summary of topologies from literature review

Converter Advantages Disadvantages Flyback

converter Wide-input regulation capability; Simple structure; Low cost.

High voltage and current stresses of the main switch; Hard switching; Poor magnetic utilization; Low efficiency.

Flyback derived

converters

Wide-input regulation capability; Improved efficiency.

Add more components or control complexity. High cost Poor magnetic utilization.

Serires resonant covnerter

High efficiency operating at or slightly below the series resonant frequency; Soft-switching.

Lack of capability of wide-input regulation.

LLC and modified LLCs

Wide-input regulation capability; High efficiency operating near the resonant frequency.

Low efficiency operating far from its resonant frequency and light loads; Modified LLCs suffer complex control, or extra components.

10

1.3 Research Objectives and Thesis Outline

The target of this research is to study a new isolated dc-dc converter implementing

in the frond-end dc-dc stage of the two stage microinverter. There are several critical

requirements that the converter should focus on.

(1) The specifications of the microconverter are 15-55 V input voltage and 380 V

output voltage which requires the converter should be high step-up.

(2) The converter should provide galvanic isolation.

(3) The converter should have the capability of wide-input regulation.

(4) The most important characteristic is high efficiency.

(5) Low cost and high power density are also the two of requirements that should

be considered.

To achieve the goals listed above, this thesis covers analysis and design of a high

efficiency microconverter. The thesis outline is as follows:

Chapter 1 presents the application background. Three types of PV power

conditioning system with advantages and drawbacks are introduced. This chapter also

gives the existing topologies in literature.

Chapter 2 explores a new topology with hybrid modes of operation based on the

highly-efficient series resonant converter. This chapter also introduces the different

operating modes in details.

Chapter 3 describes the power stage design considerations and procedures. A 300

W prototype is built to validate the analysis in chapter 2. In this chapter, steady-state

waveforms of different operating modes are shown as well as switches soft-switching

waveforms. The efficiency and loss are analyzed and matched with experimental results.

11

Finally, Chapter 4 provides a summary of the work and proposes future research

work.

12

Chapter 2 Proposed Isolated Hybrid Series Resonant Microconverter Topology and Operations

2.1 Overview of Proposed Topology and Operations

For the majority of the time, PV modules operate at the normal output voltage. The

microconverter should optimize the highest efficiency at this condition to convert the

maximum available power. Therefore, the designed converter operates as the series

resonant converter working at, or slightly below, the series resonant frequency with

normal-input voltage to achieve the highest efficiency. To achieve the wide-input

regulation, the converter should be operated with different operating modes under the

different input voltage condition, since the pure series resonant converter can only operate

at fixed-input and fixed-output condition.

Lm

1 n

S1

S2

S3

S4

Lr Cr

Rth

Vth

+

vin

-

Cin

S5 S6

Do1 Do2

iLr

iLmvCr

+ -+vpri-

Co RL

+Vo-

Figure 2.1. Researched isolated series resonant converter topology

The topology of researched isolated series resonant converter is shown in Figure

2.1. The transformer primary side is connected with a full-bridge comprised of S1-S4 which

13

also can be replaced by the half-bridge and the push-pull topologies. For the transformer, n

is the turns ratio and Lm is the magnetizing inductance. For the transformer secondary side,

resonant inductor Lr and resonant capacitor Cr make up the series resonant tank where Lr is

total inductance value of the leakage inductance of the transformer and the external inductor.

Two output diodes Do1, Do2 and two secondary switches S5, S6 is connected with the series

resonant tank.

Under the high-input conditions, the converter operates as a buck converter so

that it can buck the high-input voltage to standard output dc bus voltage. There are two

ways to achieve the buck function in pervious literatures: (1) phase shift control of the

primary side full bridge [40]-[43], (2) variable frequency control of the primary side full

bridge [44], [45]. In this thesis, the phase shift modulation is utilized. The entire converter

should be the hybrid buck series resonant converter: buck function is performed by the

transformer primary side while series resonant operation is performed by series resonant

tank. It is referred to “Buck mode” during the description of the following sections of this

thesis. When input voltage is normal voltage, phase shift angle between two legs is 180

degrees and the converter operates a pure series resonant converter as shown in Figure

2.2(a). When input voltage is higher than normal voltage, the range of phase shift angle

between two legs are 0 to 180 degrees. The steady-state waveforms under 33 V input-

voltage condition are shown in Figure 2.2(b).

Under the low-input conditions, the converter needs a way to boost the low-input

voltage to the standard dc bus output voltage. This is performed by two switches of the

transformer secondary side turning on at the same time during a short period to short

14

0

0

0

0

0

0

1,4G

5,G 6G

1, 2Do Doi i

1tot 2t t3 t4

vpri

iLr, iLm

vCr

(a)

0

0

0

0

0

0

41,G G

5,G 6G

, LLr mi i

1, 2Do Doi i

1tot t2 t3 t4t5 t6t7 t8 t9t10

vpri

vCr

(b)

15

0

0

0

0

0

0

1,4G

5,G 6G

priv

Crv

, LLr mi i

1, 2Do Doi i

1tot 2t 3t t4 t5 t6 t7 t8

(c)

Figure 2.2. Main steady-state waveforms of two operating modes: (a) under normal-input condition (30 V), (b) Buck mode (under 33 V input condition), (c) Boost mode (under 27

V input condition).

secondary side circuit. This is the same mechanism as the traditional PWM boost converter

at the period of turning on the main switch. To simplify naming conventions, this mode of

operation will be referred to as “Boost mode”. The main steady-state waveforms of the

“Boost mode” which are under 27 V input-voltage condition is shown in Figure 2.2(c).

The angular frequency of resonant tank is defined in equation (2.1) and the

impedance of resonant tank is defined in (2.2), while θ is the angular displacement of the

resonant tank.

1r

r rL Cω = (2.1)

rr

r

LZC

= (2.2)

16

trωθ = (2.3)

The switching frequency, fs, is selected to be equal to the resonant frequency, fr, as

defined in (2.4).

12s r

r r

f fL Cπ

= = (2.4)

In order to simplify the analysis of the converter, the following assumptions are

made:

1. The output capacitor Co is large enough so that the output voltage Vo can be

considered constant during a switching period Ts.

2. Co is much larger than the resonant capacitors Cr.

3. Parasitic output capacitances of MOSFETs, Coss, is treated as a constant capacitor

during dead time period analysis.

17

2.2 Buck Mode

2.2.1 Principle of Operation

As mentioned in the section 2.1, the modulation method of input side full bridge is

phase shift. To simplify the steady-state analysis of Buck mode operation, the phase angle

between the two switching legs, φ, will be translated to an equivalent duty cycle, dbuck. As

shown in Figure 2.3, the effective duty cycle is the period when input voltage is applied to

the primary winding of the transformer. The equivalent duty cycle is expressed in (2.5).

The range of phase shift angel φ is 0 to 180 degree corresponding 0 to 0.5 equivalent duty

cycle.

360buck od ϕ= (2.5)

The main steady-state waveforms of Buck mode is shown in Figure 2.4 and

operating periods of the Buck mode are shown in Figure 2.5. The state-plane trajectory of

Effective duty cycle

dbuck

Figure 2.3. Equivalent duty cycle definition of Buck mode operation

18

the resonant tank, composing of resonant inductor current, iLr and resonant capacitor

voltage, vCr, is shown in Figure 2.6.

G1,G4

G5,G6

vpri

iLr, iLm

vCr

iDo1, iDo2

vds2, ids2

vds4, ids4

vds6, ids6

0

0

0

0

0

0

0 t0 t1t2 t3 t4t5 t6t7t8 t9t0

Figure 2.4. Steady-state waveforms of Buck mode with 33 V input voltage, 380 V output voltage and 300 W output power.

Interval [t0-t1]: At time t0, the beginning of a switching period, the current through

Lr is zero and the voltage across Cr is at minimum value, Point A1 in the state-plane

trajectory presents this beginning point as shown in Figure 2.6.

( ) 00 =tiLr (2.6)

19

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

iLr

S5 S6

+ vpri - Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

iLr

S5 S6

+ vpri - Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

iLr

S5 S6

Co

Do1 Do2

(a)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

(b)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

+ vpri - Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

- vpri + Co

Do1 Do2

(c) (d)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

(e) (f)

(g) (h)

(i) (j)

RL RL

RLRL

RL RL

RL RL

RL RL

Figure 2.5. Operating periods of Buck mode

( )0Cr crv t v= −∆ (2.7)

20

The average voltage of the resonant capacitor Cr is zero and the Crv∆ is defined as

the voltage ripple across the resonant capacitor Cr, expresses in (2.8).

ro

socr CV

TPv4

=∆ (2.8)

A1

B1

A2

B2

in onV V−0oV−

Lr ri Z

Crv

Figure 2.6. State-plane trajectory of resonant tank operating in Buck mode

During [t0-t1], S1, S4 and S6 turn on. The input voltage is applied across the

transformer primary winding. Resonant inductor Lr and resonant capacitor Cr are resonant

during this period. The converter delivers the energy to the load through Do1 and S6 as

shown in Figure 2.5(a). The equivalent circuit of this interval is pictured in Figure 2.7(b).

Here, the operating point moves along the trajectory path from A1 to B1 as shown Figure

2.7(a). The current through Lr and voltage across Cr are expressed in the time domain in

(2.9) and (2.10) respectively, where r1 is the radius of the trajectory path and is given in

(2.11), and the center is located at (nVin-Vo, 0) .

( ) ( )( )10sinLr r

r

ri t t tZ

π ω= − − (2.9)

21

( ) ( ) ( )( )1 0coscr in o rv t nV V r t tπ ω= − + − − (2.10)

1 in o Crr nV V v= − + ∆ (2.11)

At time t0, there is a certain delay turning on the switch S6 to allow the body diode

conduct firstly which can allow S6 ZVS turn on.

S4 and S6 turn off at time t1. The magnetizing current reflected in the transformer

secondary winding is expressed in (2.12).

( )1 4in buck s

Lmm

nV d Ti tL

= (2.12)

A1

B1

in onV V−0

Lr ri Z

Crv

r1Lr Cr

VonVin

+ -

iLr

vCr

(a) (b)

Figure 2.7. (a) State-plane trajectory of interval [t0 - t1], (b) Equivalent circuit of interval [t0 - t1].

Interval [t1 - t2]: At time t1, S4 and S6 turn off. During this interval, the converter

enters a dead time period as shown in Figure 2.5(b). The power is also transferred from

input to output directly while the body diode of S6 is forced to turn on. During this short

time period, the magnetizing current is at its peak value and is expressed in (2.12). The

transformer primary side current including iLr and im acting as a current source, discharges

the parasitic output capacitance of S3 and charges the parasitic output capacitance of S4.

22

When the output capacitance of S3 is fully discharged, the body diode conducts until

S3 is turned on at t2. S3 will achieve ZVS turn-on at t2.

Interval [t2 – t3]: At time t2, S3 turns on under ZVS condition as described in the

interval [t1-t2].

A1

B1

A2

0oV−

Lr ri Z

Crv

Lr Cr

Vo

+ -

iLr

vCr

(a) (b)

Figure 2.8. (a) State-plane trajectory of interval [t2 – t3]. (b) Equivalent circuit of interval [t2 – t3].

During this time period, both S1 and S3 are on so the primary winding of the

isolation transformer is shorted. There is no voltage applied in the windings of the

transforner. For the transformer secondary side, the power is continuously delivered to

output by Do1 and body diode of S6 as shown in figure 2.5(c). The state-plane trajectory

draws from point B1 to A2 as shown in Figure 2.8(a). The equivalent circuit of the resonant

tank during this time period is shown in Figure 2.8(b). The center point of this path located

at the origin (-Vo, 0) and the radius is expressed in (2.15). The equations of iLr and vcr are

given in (2.13) and (2.14), respectively, where β is the initial angle which will be calculated

in the section 2.2.2.

( ) ( )( )22sinLr r

r

ri t t tZ

β ω= − − (2.13)

( ) ( )( )2 2cosCr o rv t V r t tβ ω= − + − − (2.14)

β r2

23

2 o crr V v= + ∆ (2.15)

Interval [t3 – t4]: At time t3, the resonant current reaches to zero entering the

discontinuous conduction mode (DCM) as shown in Figure 2.5(d). The trajectory path

stays at point A2. When designing the resonant tank parameters and switching frequency,

it is critical to make sure the DCM operation to guarantee ZCS of output diodes Do1, body

diode of S6 and primary side MOSFETs S1. During this time period, iLr remains at zero and

vcr remains at its maximum value.

Interval [t4 - t5]: At t4, S1 turns off and the converter enters another dead time

period as shown in Figure 2.5(e). During this short period, the magnetizing current

remaining at its maximum value acts as a current source and discharges the parasitic output

capacitance of S2 while charging parasitic output capacitance of S1. Since the value of the

magnetizing current is dependent on dbuck, ZVS turn on of S2 is conditional based on the

operating conditions.

Interval [t5 – t6]: At time t5, the current through Lr is zero and the voltage across Cr

is at maximum value. Point A2 in the state-plane trajectory presents this beginning point

as shown in Figure 2.6(a).

During [t5-t6], S2, S3 and S5 turn on. The voltage across the primary winding of the

transformer is input voltage. The converter delivers the energy to the load through Lr, Cr,

Do2 and S5 as shown in Figure 2.5(f). The equivalent circuit of this interval is pictured in

Figure 2.9(b). Here, the operating point moves along the trajectory path from A2 to B2 as

shown Figure 2.9(a). The current through Lr and voltage across Cr are expressed in the

time domain in (2.16) and (2.17), respectively, where r1 is the radius of the trajectory path

and is given in (2.11), and the center is located at (-nVin+Vo, 0).

24

( ) ( )( )15sinLr r

r

ri t t tZ

π ω= − − − (2.16)

( ) ( ) ( )( )1 0cosCr in o rv t nV V r t tπ ω= − + − − − (2.17)



S3 and S5 turn off at time t6. The magnetizing current is expressed in (2.18).

( )6 4in buck s

Lmm

nV d Ti tL

= − (2.18)

A2

B2

in onV V− + 0

Lr ri Z

Crv

Lr Cr

nVin

- +

iLr

vCr Vo

(a) (b)

Figure 2.9. (a) State-plane trajectory of interval [t5 – t6]. (b) Equivalent circuit of interval [t5 – t6].

Interval [t6 – t7]: At time t6, S3 and S5 turn off. During this interval, the converter

enters a dead time period as shown in Figure 2.5(g). The power is also transferred from

input to output directly while the body diode of S5 is forced to turn on. During this short

time period, the magnetizing current is at its negative peak value and is expressed in (2.18).

The transformer primary side current including iLr and iLm acting as a current source

discharges the parasitic output capacitance of S4 and charges the parasitic output

capacitance of S3.

r1

25

When the output capacitance of S4 is fully discharged, the body diode conducts until

S4 is turned on at t7. S4 will achieve ZVS turn-on at t7.

Interval [t7 – t8]: At time t7, S4 turns on under ZVS condition as described in the

interval [t6-t7].

A1

B2

0oV

Lr ri Z

Crv

Lr Cr

Vo

- +

iLr

vCr

(a) (b)

Figure 2.10. (a) Equivalent circuit of interval [t7 – t8], (b) State-plane trajectory of interval [t7 – t8].

During this time period, both S2 and S4 are on so the primary winding of the

isolation transformer is shorted. There is no voltage applied in the windings of the

transforner. For the transformer secondary side, the power is continuously delivered to

output by Do2 and body diode of S5. The state-plane trajectory draws from point B2 to A1

as shown in Figure 2.10(b). The equivalent circuit of the resonant tank during this time

period is shown in Figure 2.10(a). The equations of iLr and vcr are given in (2.19) and

(2.20), respectively, where β is the initial angle which will be calculated in the section

2.2.2.

( ) ( )( )27sinLr r

r

ri t t tZ

β ω= − − − (2.19)

( ) ( )( )1 2 7coscr o rv t V r t tβ ω= − − − (2.20)

β r2

26

Interval [t8 – t9]: At time t8, the resonant current reaches to zero entering the

discontinuous conduction mode (DCM). The trajectory path stays at point A1. When

designing the resonant tank parameters and switching frequency, it is critical to make sure

the DCM operation to guarantee ZCS of output diodes Do2, body diode of S5 and primary

side MOSFETs S2. During this time period, iLr at remains zero and vcr remains at its

minimum value.

Interval [t9 – t10]: At t9, S2 turns off and the converter enters another dead time

period. During this short period, the magnetizing current remaining at its minimum value

acts as a current source and discharges the output capacitance of S1 while charging that of

S2. Since the value of the magnetizing current is dependent on dbuck, ZVS turn on of S1 is

conditional based on the operating conditions.

2.2.2 Duty Cycle Derivation

To derive the relationship between equivalent duty cycle and voltage conversion

ratio of the Buck mode, the state-plane trajectory curve can help to solve the derivation by

transferring to geometrical analysis as shown in Figure 2.11. Using the standard form for

the equation of a circle, the trajectory of arc A1B1 is defined in (2.21) and the trajectory of

arc B1A2 is defined in (2.22). The radius of the two resonant period trajectory paths, r1

and r2, as well as the centers of the paths are dependent on both the output power level and

the votlage conversion ratio.

( ) ( )2 2 21cr in o r Lrv nV V Z i r− + + = (2.21)

( ) ( )2 2 22cr o r Lrv V Z i r+ + = (2.22)

27

A1

B1

A2

B2

in onV V−0oV−

Lr ri Z

Crv

Figure 2.11. State-plane trajectory of Buck mode

The intersection of the two circles occurs at point B1, which stands for t1 in time

domain (2.23).

( )( ) ( )( ) ( )( ) ( )( ) 2

2 2 2 22 21 1 1 1 1cr in o r Lr cr o r Lrv t nV V Z i t r v t V Z i t r− + + − = + + − (2.23)

The resonant inductor current and resonant capacitor voltage at point B1 from arc

A1B1 can be present as (2.24) and (2.25) respectively based on the steady-state analysis in

section 2.2.1. The angle β is calculated as (2.26). The resonant capacitor voltage at point

B1 from arc B1A2 is expressed in (2.27).

( ) ( )11 1sinLr r

r

ri t tZ

ω= (2.24)

( ) ( ) ( )1 1 1coscr in o rv t nV V r tω= − − (2.25)

( ) ( )1 11 11

2 2

sin sin sinr Lrr

Z i t r tr r

β ω− − = =

(2.26)

( ) ( )1 2 coscr ov t V r β= − + (2.27)

1 buck st d T= (2.28)

Combined with equation (2.23) to (2.27)

( )12 cr o

cr crin

v Vv t vnV∆

= − ∆ (2.29)

r2 r1 β

28

The relationship between equivalent duty cycle and voltage conversion ratio as

expressed in (2.30) is derived from (2.27), (2.28) and (2.29).

( ) ( )( )

21

2

2 1 4 1cos

4 1o s o r

o s o rbuck

r s

P T M M V C MP T M V C M

dT

π

ω

− − + −− + − = (2.30)

Voltage conversion ratio M is defined in (2.31) where n is the transformer turns

ratio.

o

in

VMnV

= (2.31)

The votlage conversion ratio, M, of the converter operating in Buck mode versus �� are plotted for different output powers and different resonant tank parameters in

Figure 2.12(a) and Figure 2.12(b) respectively. The lines are the curves based on the

calculation results, while x marks are simulation validation.

(a) With different output powers

29

(b) With different resonant tank impedances

Figure 2.12. The voltage conversion ratio, M, curves in Buck mode versus dbuck

2.3 Boost mode

2.3.1 Principle of Operation

The main steady-state waveforms of Boost mode is shown in Figure 2.13 and

operating periods of the Buck mode are shown in Figure 2.14. The state-plane trajectory of

the resonant tank, composing of resonant inductor current, iLr and resonant capacitor

voltage, vCr, is shown in Figure 2.15.

Interval [t0-t1]: At time t0, the beginning of a switching period, the current through

Lr is zero (2.32) and the voltage across Cr is at minimum value (2.33). Point A1 in the state-

plane trajectory presents this beginning point as shown in Figure 2.10.

( ) 00 =tiLr (2.32)

( )0Cr crv t v= −∆ (2.33)

30

G1,4

G5,G6

vpri

iLr, iLm

vCr

iDo1, iDo2

vds2, ids2

vds4, ids4

vds6, ids6

0

0

0

0

0

0

0

t0 t1 t2 t3t4 t5 t6 t7t0

Figure 2.13. Steady-state waveforms of Boost mode with 27 V input voltage, 380 V output voltage and 300 W output power.

The average voltage of the resonant capacitor Cr is zero and the Crv∆ is defined as

the voltage ripple across the resonant capacitor Cr, expresses in (2.34).

4o s

crin r

P TvnV C

∆ = (2.34)

31

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

iLr

S5 S6

+ vpri - Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

iLr

S5 S6

+ vpri - Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

(a)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

(b)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

- vpri + Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

- vpri + Co

Do1 Do2

(c) (d)

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

Lm

1 n

S1

S2

S3

S4

Lr Cr

Vin

S5 S6

Co

Do1 Do2

(e) (f)

(g) (h)

- vpri +

- vpri +

+ vpri -

+ vpri -

RL RL

RLRL

RL RL

RL RL

Figure 2.14. Operating periods of Boost mode

During [t0-t1], S1, S4 and S6 turn on while S5 keeps turning on state from the previous

switching cycle. The voltage across the primary winding of the transformer is input voltage,

and Lr and Cr are resonant during this period as shown in Figure 2.14(a). The secondary

winding of transformer and resonant tank are short circuit by turning on the S5 and S6 at

the same time. Lr is charged almost linearly acting as a conventional boost inductor. The

equivalent circuit of this interval is pictured in Figure 2.16(a). Here, the operating point

32

moves along the trajectory path from A1 to B1 as shown Figure 2.16(b). The current

through Lr and voltage across Cr are expressed in the time domain in (2.35) and (2.36),

respectively, where r1 is the radius of the trajectory path given in (2.37), and the center is

located at (��, 0) .

Crv

B1

A1A2

B2

Lr ri Z

in onV V−

innV

0

Figure 2.15. State-plane trajectory of resonant tank operating in Boost mode

Crv

B1

A1

Lr ri Z

innV

0

Lr Cr

nVin+ -

iLr

vCr

(a) (b)


( ) ( )( )10sinLr r

r

ri t t tZ

π ω= − − (2.35)

( ) ( ) ( )( )1 0coscr in rv t nV r t tπ ω= + − − (2.36)

1 in Crr nV v= + ∆ (2.37)

At time t0, similar as Buck mode, there is a certain delay turning on the switch S6

to allow the body diode conduct firstly which can allow S6 ZVS turn on.

33

Crv

B1

A2

Lr ri Z

in onV V− 0

Lr Cr

nVin+ -

iLr

vCr Vo

β

(a) (b)


Interval [t1-t2]: S5 turns off at time t1. The input voltage is still applied in the

primary winding of transformer. For the transformer secondary side, the energy is

transferred to the load directly through resonant tank composing of Lr and Cr, Do1 and S6

as shown in Figure 2.14(b). The equivalent circuit of this interval is pictured in Figure

2.17(a). Here, the operating point moves along the trajectory path from B1 to A2 as shown

Figure 2.18(b). The current through Lr and voltage across Cr are expressed in the time

domain in (2.38) and (2.39), respectively, where r2 is the radius of the trajectory path given

in (2.40), and the center is located at (nVin-Vo, 0) while β is the initial angle of this interval.

( ) ( )( )21sinLr r

r

ri t t tZ

β ω= − − (2.38)

( ) ( ) ( )( )2 1coscr in o rv t nV V r t tβ ω= − + − − (2.39)

2 in o Crr nV V v= − + + ∆ (2.40)

At time t2, the current through resonant inductor reaches to zero, so Do1 achieves

ZCS turn off.

Interval [t2 – t3]: At time t2, the resonant current reaches to zero and the converter

enters the discontinuous conduction mode (DCM) as shown in figure 2.14(c). The

34

trajectory path stays at point A2 since the resonant inductor current keeps zero and resonant

capacitor voltage is at its maximum value. It is critical to make sure the DCM operation to

guarantee ZCS of output diodes Do1, and primary side MOSFETs S1 and S4.

Interval [t3 – t4]: At t3, S1 and S4 turn off under ZCS conditions and the converter

enters a dead time period. The magnetizing inductor is continuously charged from t0 to t3

since input voltage is applied in the transformer primary winding. The magnetizing current

reaches to its peak value as expressed in (2.41). At this point, the magnetizing current

appears as a current discharging the parasitic output capacitances of S2 and S3 while

charging those of S1 and S4. As long as the magnetizing inductance is designed

appropriately, the voltages across S2 and S3 can reach zero before t4, which will allow S2

and S3 to achieve ZVS turn on.

( ) ( )m

sinLmLm L

TnVtiti443 == (2.41)

Interval [t4-t5]: At time t4, S2, S3 and S5 turn on while S6 keeps turn-on state from

the previous interval. The voltage across the primary winding of the transformer is input

voltage. Lr and Cr are resonant during this period as shown in Figure 2.14(e). The

secondary winding of transformer and resonant tank are short circuit by turning on the S5

and S6 at the same time. Lr is charged almost linearly acting as a conventional boost

inductor. The equivalent circuit of this interval is pictured in Figure 2.18(b). Here, the

operating point moves along the trajectory path from A2 to B2 as shown Figure 2.18(a).

The current through Lr and voltage across Cr are expressed in the time domain in (2.42)

and (2.43).

( ) ( )( )14sinLr r

r

ri t t tZ

ω= − − (2.42)

35

( ) ( ) ( )( )1 4coscr in rv t nV r t tω= − + − (2.43)



CrvA2

B2

Lr ri Z

innV−

0

Lr Cr

nVin

+ -

iLr

vCr

Figure 2.18. (a) State-plane trajectory of interval [t4 – t5], (b) Equivalent circuit of interval [t4 – t5].

Lr Cr

nVin

+ -

iLr

vCr VoCrv

A1

B2

Lr ri Z

in onV V− +0β

(a) (b)


Interval [t5-t6]: S6 turns off at time t1. The input voltage is still applied in the

primary winding of transformer. The secondary side, the converter begins to transfer to the

load directly through resonant tank composing of Lr and Cr, Do2 and S5 as shown in Figure

2.14(f). The equivalent circuit of this interval is pictured in Figure 2.19(a). Here, the

operating point moves along the trajectory path from B2 to A1 as shown Figure 2.19(b).

The current through Lr and voltage across Cr are expressed in the time domain in (2.44)

and (2.45), respectively.

36

( ) ( )( )25sinLr r

r

ri t t tZ

β ω= − − − (2.44)

( ) ( ) ( )( )2 5coscr in o rv t nV V r t tβ ω= − + − − − (2.45)

At time t6, the current through resonant inductor reaches to zero, so Do2 achieves

ZCS turn off.

Interval [t6 – t7]: At time t6, the resonant current reaches to zero and the converter

enters the discontinuous conduction mode (DCM) as shown in figure 2.14(g). The

trajectory path stays at point A1 for the resonant inductor current is zero and resonant

capacitor voltage is at its maximum value. It is critical to make sure the DCM operation to

guarantee ZCS of output diodes Do2, and primary side MOSFETs S2 and S3.

Interval [t7 – t8]: At t7, S2 and S3 turn off under ZCS conditions and the converter

enters a dead time period. The magnetizing inductor is continuously charged from t4 to t7.

The magnetizing current reaches to its negative peak value as expressed in (2.46). At this

point, the magnetizing current appears as a current discharging the parasitic output

capacitances of S1 and S4 while charging those of S2 and S3. Once again, as long as the

magnetizing inductance is designed appropriately, the voltages across S1 and S4 can reach

zero before t8, which will allow S1 and S4 to achieve ZVS turn on.

( ) ( )7 8 4in s

Lm Lmm

nV Ti t i tL

= = − (2.46)

37

2.3.2 Duty Cycle Derivation

In order to derive the relationship between duty cycle and voltage conversion ratio

of Boost mode, the equivalent duty cycle needs to be defined firstly. As shown in Figure

2.20, the duty cycle of S5 and S6 includes two parts, drec and dboost. drec is fixed at 0.5 which

is the same as primary side switches. drec is responsible for energy delivery while dboost is

responsible to boost voltage. Only dboost should be considered when deriving the

relationship between duty cycle dboost and voltage conversion ratio M.

Next, a closer looks needs to be taken at the trajectory curve, similar as Buck mode.

Since the trajectory curve is symmetrical, only arc A1B1 and arc B1A2 will be considered

here. As shown in Figure 2.21, the trajectory curve with additional geometrical lines and

initial angle is present. Using the standard equations of circles, the trajectory of arc A1B1

is defined in (2.47) and the trajectory of arc B1A2 is defined in (2.48). The radius of the

two resonant period trajectory paths, r1 and r2, as well as the centers of the paths are

dependent on both the output power level and the voltage conversion ratio.

( ) ( )2 2 21cr in r Lrv nV Z i r− + = (2.47)

Figure 2.20. Equivalent duty cycle dboost definition

dboost

drec

G1

G2

G5

G6

38

( ) ( )2 2 22cr in o r Lrv nV V Z i r− + + = (2.48)

Crv

B1

A1A2

Lr ri Z

in onV V−

innV

0β

r1r2

Figure 2.21. State-plane trajectory of Boost mode

The intersection of the two circles occurs point B1, which stands for t1 in time

domain.

( )( ) ( )( ) ( )( ) ( )( ) 2

2 2 2 22 21 1 1 1 1cr in r Lr cr in o r Lrv t nV Z i t r v t nV V Z i t r− + − = − + + − (2.49)

The resonant inductor current and resonant capacitor voltage at point B1from arc

A1B1 can be present as (2.50) and (2.51) respectively based on the interval [t0-t1] analysis.

The angle β is calculated as (2.52). The resonant capacitor voltage at point B1 from arc

B1A2 is expressed in (2.53).

( ) ( )11 1sinLr r

r

ri t tZ

ω= (2.50)

( ) ( ) ( )1 1 1coscr in rv t nV r tω= − (2.51)

( ) ( )1 11 11

2 2

sin sin sinr Lrr

Z i t r tr r

β π π ω− − = − = −

(2.52)

( ) ( )1 2 coscr in ov t nV V r β= − + (2.53)

Where 1 boost st d T= (2.54)

39

Combined with equation (2.49) to (2.53).

( )12 in cr

cr cro

nV vv t vV

∆= − + ∆ (2.55)

The equivalent duty cycle can be derived as (2.56) from (2.51), (2.54) and (2.55).

( )21

2 2

4 2cos

4o r o s

o r o sboost

r s

V C PT M MV C PT M

dTω

− + − + = (2.56)

The voltage conversion ratio, M, of the converter operating in Boost mode versus

dboost curves are plotted for different output powers and different resonant tank parameters

in Figure 2.22(a) and Figure 2.22(b) respectively. The lines are the curves based on the

calculation results, while x marks are the simulation validation.

(a) With different output power levels

40

(b) With different resonant tank impedances

Figure 2.22. The voltage conversion ratio, M, curves in Boost mode versus dboost

2.4 Summary

To achieve high efficiency over a wide-input range for PV applications, a hybrid

series resonant DC-DC converter is proposed in this paper. Two operating modes are united

to allow the converter operating in a wide range. The curves of voltage conversion ratio

are shown in the Figure 2.23 with different output power levels and different resonant tank

parameters. The most efficient operating point occurs at the intersection point between two

operating modes. Under this operating point, the input voltage is defined as normal-input

voltage. When input is higher than normal-input voltage, converter operates at Buck mode.

Converter operates at Boost mode under low-input conditions. The converter operates in

the fixed frequency during different operating modes. The converter can achieve high

41

efficiency over wide-input range because the converter achieves zero-voltage switching

(ZVS) and/or zero-current switching (ZCS) of the primary-side MOSFETs, ZCS and/or

ZVS of the secondary-side MOSFETs and ZCS of output diodes under all operational

conditions.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.5

1

1.5

2

d

M

Normal input

Low input

High input

Boost Mode

Buck Mode

dbuck drec+dboost

Po=300 WPo=150 WPo=30 W

(a) with different output power levels

42

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.5

1

1.5

2

d

M

Normal input

Low input

High input

Boost Mode

Buck Mode

dbuck drec+dboost

Zr=106Zr=53Zr=26.5

(b) with different resonant tank impedances

Figure 2.23. Curves of voltage conversion ratio M

43

Chapter 3

Power Stage Design Procedure and

Experimental Results

3.1 Power Stage Design Procedure

This section will illustrate the detailed design of each critical component of power

stage. The design process will optimize the converter at most efficient operating point

which is under normal-input voltage condition.

3.1.1 Transformer Design

The transformer turns ratio is designed based on the most efficient operating point.

As mentioned in chapter 2, the converter acts as a pure series resonant converter and

achieves highest efficiency under normal-input voltage condition. The transformer turns

ratio should be selected to get the desired output voltage based on the normal-input

condition, as expressed in (3.1).

_

o

in normal

VnV

= (3.1)

Now that the transformer’s turns ratio has been selected, the next steps are to select

the core size, shape and material [46], [47]. Considering that the microinverters set up on

the rooftop with PV panels, the ambient temperature will vary greatly depending on

geographical locations, weather, and seasons. Therefore, it is important to select a core

material that has a relatively flat temperature curve such as Ferroxcube 3C95 [48].

44

Figure 3.1. Specific power loss for several frequency/flux density combinations as a function of temperature of Ferroxcube 3C95 [48].

The number of turns will be selected based on the peak ac flux density, ΔB. If the

flux φ is divided by Ac, the cross-sectional area of the core which is available from the core

datasheet, the flux density is got in (3.2).

c

BAφ

∆ = (3.2)

Combined with Faraday’s law, ΔB can be calculated as shown in (3.3) for Buck

mode and (3.4) for Boost mode where the unit for ΔB is Tesla (T), Ac is in cm2, and n1

is the transformer primary side turns number.

12in buck s

buckc

V d TBn A

∆ =

(3.3)

c

sinboost An

TVB14

=∆

(3.4)

45

It is important to calculate ΔB for all operating conditions to make sure the core

will not saturate. Further, the turns number selection should also minimize the core loss

and winding loss. An approximation of the core loss density for any combination of

operating temperature (T) in [ºC], frequency (f) in [Hz] and flux density (B) in [T] can be

obtained from the following empirical fit formula (3.5):

x yv m sP C f B= ∆ (3.5)

Equation (3.5) can be seen from the Ferroxcube 3C95 datasheet, where Cm, x and y

are coefficients. All of these parameters can be obtained from the core material datasheet.

The winding loss equation is shown in (3.6), where ipri is the RMS current through

transformer primary winding and Rpri and Rsec are the DCR of the windings.

2 2_ sec( )pri

wind T pri pri

iP i R R

n= + (3.6)

The next step is to determine magnetizing inductance of the primary winding of

transformer. During the dead time of Boost mode, the magnetizing inductance of

transformer and the length of dead time can be designed properly to ensure ZVS of the

primary side switches under all input voltage conditions. The detailed analysis is presented

in the following part.

IDT

Coss Coss

CossCoss

0

0 0

0Vin Vin

Vin Vin

Figure 3.2. Equivalent circuit of primary-side MOSFETs and magnetizing current during the first dead time period in Boost mode.

46

Ceq

0

Vin

Ceq

Vin

0

IDT IDT

(a) (b)

Figure 3.3. Simplified circuit of circuit in figure 3.2, (a) initial state, (b) end state.

As mentioned in Chapter 2, during the dead time, the magnetizing current acts as a

current source to charge and discharge the parasitic output capacitances of primary side

MOSFETs. During the first dead time period, the output capacitances of S1 and S3 are

charged and the output capacitances of S2 and S4 are discharged as shown in Figure 3.2.

Coss1 and Coss4 are in series and Coss2 and Coss3 are in series to make up two 0.5Coss while

these two 0.5Coss are in parallel. Therefore the equivalent output capacitance is equal to the

parasitic output capacitance of one MOSFET. At the beginning of the dead time, the

voltage across the current source is Vin while it is –Vin at the end of the dead time. The

simplified circuit is shown in Figure 3.3. Based on the capacitor charge balance, the current

value to charge and discharge the capacitance can be expressed in (3.7), where td is the

length of dead time.

_ min2 in

DT eqd

VI Ct

= (3.7)

The magnetizing current in the transformer reflected to the primary side is

expressed in (3.8) as derived in Chapter 2.

m

sinDT L

TVnI4

2

= (3.8)

The magnetizing current should be larger than the current that charging and

discharging capacitors to ensure ZVS of primary side MOSFETs during Boost mode.

47

Combined equations (3.7) and (3.8), the relationship between magnetizing inductance,

length of dead time and parasitic output capacitance can be derived in (3.9).

2

8d

ms oss

n tLf C

≤ (3.9)

It can be seen in (3.9) that a tradeoff needs to be made between the magnetizing

inductance and dead time. The length of dead time affects the length of time that is used

for transferring power to load. If the dead time is two long, the MOSFETs conduction time

will be too short resulting in high RMS current values and high conduction loss. On the

other hand, magnetizing inductance affects the circulating current. The lower magnetizing

inductance will result in higher circulating current which will hurt the efficiency especially

under the light load conditions. The selected magnetizing inductance can be manufactured

by adjusting the thickness of gap.

With all the designed procedures above, the transformer parameters are listed in

Table 3.1 and the winding structure is shown in Figure 3.4, where the red dots are the cross-

section of the primary winding and green dots are the cross-section of the secondary

winding.

Figure 3.4. Winding structure of transformer

15 AWG25 AWG

48

Table 3.1. Transformer Parameters

3.1.2 Resonant Tank Design

To design the resonant tank Lr and Cr, the waveforms of the inductor current and

capacitor voltage are explored firstly. Three cases of resonant tank are demonstrated here.

The parameters of these resonant tanks are listed in Table 3.2. Figure 3.5 shows the

resonant network waveforms operating in the Buck mode while Figure 3.6 shows the

resonant network waveforms operating in the Boost mode.

Table 3.2. Different resonant tanks analysis.

For all three cases operating in Buck mode, the input voltage is 35 V, the output

voltage is 380 V, output power is 300 W, and the switching frequency is 100 kHz. It can

clearly be seen that the larger the resonant inductor, the shorter the DCM period, and the

lower the converter RMS currents. For all three cases operating in Boost mode, the input

Parameter Value Core Shape RM14/ILP

Core Material Ferroxcube 3C95

Turns ratio, n 12.5

Primary winding, n1 4 turns, 16 AWG

Secondary winding, n2 50 turns, 25 AWG

Leakage inductance, Llk 31.6 uH

Primary side magnetizing inductance 15.6 uH

Secondary side magnetizing inductance 2.41 mH

Case Lr (uH) Cr (nF) Zr fr (kHz)

Case1 168.8 15 106.08 100 Case2 84.4 30 53.04 100 Case3 42.2 60 26.52 100

49

voltage is 25 V, the output voltage is 380 V, output power is 300 W, and the switching

frequency is 100 kHz. The larger the resonant inductor, the longer boost period, the shorter

the DCM period, and the lower the conveter RMS currents.

During both operation of Buck and Boost modes, a larger Lr directly correlates to

lower RMS currents in the converter’s MOSFETs, diodes resonant capacitors, and isolation

transformer which will be benefit to the efficiency. Ideally, the larger Lr, the higher

efficiency will be reached. However, if Lr is too large, there maybe have some violations.

(1) The converter will operate in the CCM mode under some conditions and cannot

guarantee ZCS of the output diodes and converter’s MOSFETs.

(2) The Cr is too small and the voltage across the Cr will be super high.

(3) Practicality of the transformer and external inductor design is also a limitation.

Now that the voltage across the resonant capacitor is one of the constraints, resonant

capacitor is designed firstly. To guarantee the proper operation of the converter, the voltage

across this resonant capacitor should be lower than output voltage for all operating

conditions. Based on the steady-state analysis in Chapter 2, the resonant capacitor voltage

of Buck and Boost modes should be satisfied (3.10) and (3.11) respectively.

4o s

Cr oo r

P TV VV C

∆ = < (3.10)

4o s

Cr oin r

P TV VnV C

∆ = < (3.11)

50

Figure 3.5. Resonant inductor currents and resonant capacitor voltages with different resonant tanks operating in Buck mode under the operating condition of 100 kHz

switching frequency, 35 V input voltage, 380 V output voltage and 300 W power levels.

Figure 3.6. Resonant inductor currents and resonant capacitor voltages with different resonant tanks operating in Boost mode under the operating condition of 100 kHz

switching frequency, 25 V input voltage, 380 V output voltage and 300 W power levels.

Lr=42.2uH Lr=84.4uH Lr=168.8uH

Cr=60nF Cr=30nF Cr=15nF

Time base:10us/div

Lr=42.2uH Lr=84.4uH Lr=168.8uH

Cr=60nF Cr=30nF Cr=15nF

Time base:10us/div

51

Once the value for the resonant inductor is decided by the equations (3.10) and

(3.11), the resonant inductor which is the total of the transformer leakage inductance and

the external inductor can be chosen according to (3.12).

21

2rr r

LC ω

= (3.12)

When selecting the material of resonant capacitor, there are tips should be followed.

(1) The voltage across the capacitor is ac which requires the capacitor can work in ac

circuit. (2) The capacitor material should have a low temperature coefficient. (3) The

capacitor should have low ESR so that the power dissipation is minimized. In conclusion

of requirements above, the NP0/C0G ceramic capacitors is a good choice.

3.1.3 MOSFETs and Diodes Selection

The principle of MOSFETs and diodes selection is based on the voltage and current

stresses and the tradeoff between MOSFETs and diodes conduction and switching loss

[46].

For the primary side full bridge, the voltage stresses of the MOSFETs are the

maximum input voltage as expressed in (3.13).

maxmax1234 −− = inds VV (3.13)

The conduction loss as expressed in (3.14) can be calculated based on the RMS

current through the MOSFETs and the Rdson of the MOSFETs, where Rdson is the

MOSFET’s drain-source on-resistance.

dsonrmsscond RiP 212341234 −= (3.14)

As analyzed in chapter 2, the primary side MOSFETs S1-4 can achieve ZVS and

ZCS during Boost mode, so there are no turn-on and turn-off loss on switches S1-4. The

52

only switching loss is from the gate turn-on charging as calculated in (3.15), where Qg is

the gate charge of the MOSFET, Vaux is the power supply of the gate driver.

1234 2s

sw boost g auxfP Q V− = (3.15)

During Buck mode, switches S1 and S2 will have turn-off switching loss, and S3 and

S4 have turn-on switching loss. Before turning on the switches S1 and S2, the parasitic output

capacitance needs to be discharged firstly. The switching loss equation is shown in (3.16).

The switches S3 and S4 turn off under the moment that certain current presents in the

MOSFET, so the switching loss can be expressed in (3.17), where tf is the turn-off time of

the MOSFET and ioff is the turn off current.

( )212 2

ssw buck oss in g aux

fP C V Q V− = + (3.16)

( )34 2s

sw buck in off f g auxfP V i t Q V− = + (3.17)

For the output diode Do1 and Do2, the voltage stresses are the output voltage as

expressed in (3.18).

12Do oV V= (3.18)

Since the output diodes Do1 and Do2 can be ensure ZCS under entire operating

range, there is no reverse recovery of the output diodes. The loss on the Do1 and Do2 are

only caused by forward voltage and parasitic resistors in the diodes as shown in (3.19). id-

ave is the average current through output diode and id-rms is the RMS current in equation

(3.19). For the output diodes selection, the smaller forward voltage, the less loss.

acrmsdavedfcondd RiiVP 2−−− += (3.19)

53

For the secondary side switches S5 and S6, the voltage stresses are the output voltage

which is the same as output diodes as expressed in (3.20).

56 maxds oV V− = (3.20)

As mentioned in the chapter 2, the secondary side switches S5 and S6 achieve both

ZVS and ZCS during operating in Buck mode. Even though S5 and S6 achieve ZVS, they

still need to discharge the parasitic output capacitance before the body diode conducts. The

conduction and switching loss are calculated in (3.21) and (3.22). Vaux2 is the power supply

of the S5 and S6 gate driver.

256 56cond s rms dsonP i R−= (3.21)

( )256 22

ssw buck oss o g aux

fP C V Q V− = + (3.22)

During Boost mode, switches S5 and S6 will lose ZCS but still achieve ZVS. The

switches S5 and S6 turn off under the moment that certain current presents in the MOSFETs.

Therefore the switching loss can be expressed in (3.23), where tf is the turn-off time of the

MOSFET and ioff is the turn off current.

( )256 22

ssw boost oss o in off f g aux

fP C V V i t Q V− = + + (3.23)

3.2 Experimental Results

3.2.1 Prototype Design Summary

A 300 W prototype with a 30 V normal-input voltage was built to verify the

converter operations. The input voltage range of the converter was designed to handle 15-

55 V, with a maximum power point range of 22-36 V with normal output voltage of 380

V. The nominal input voltage of 30 V was designed to accommodate standard 60-cell PV

54

modules. The detailed specifications are shown in Table 3.2. The normal-input voltage is

30.4 V since the transformer turns ratio is 12.5. The Buck mode occurs when the input

voltage is above the 30.4 V while the Boost mode occurs when the input voltage is below

the 30.4 V. The 380 V output voltage is to be designed for the 120 V ac or 240 V ac

inverters. Texas Instrument’s TMS320F28026 Digital Signal Processor (DSP) was used

for control implementation and modulation.

For the experimental setup as shown in Figure 3.8, the input of the converter is

connected to a variable voltage DC power supply in series with a 2 Ohms resistor which

can acts as a PV module. The output of the converter is connected to a DC Electronic Load

with constant voltage mode. The electronic load is fixed to 380 V.

A summary of specifications are given in Table 3.3 and a summary of the power

stage parameters for the hardware prototype are given in Table 3.4. Figure 3.7 shows the

hardware prototype, whose dimensions are 4.95 inches length, 2.1 inches width and 0.9

inches height.

Table 3.3. Specification of hardware prototype

Specifications

Vin 15-55 V

Vmpp 22-36 V

Vin-nom 30 V

Vo-nom 380 V

Po 30-300 W

55

Table 3.4. Parameters of power stage

Power Stage

fs 110 kHz

Cr 23.5 nF

Lr 90 uH

Cin 88 uF

Co 1.2 uF

S1-S4 Infineon BSC016N06NS

S5, S6 ROHM SCT2120AF

Do1, Do2 NXP BYV29B-500

Figure 3.7. Photograph of hardware prototype

microconverterVth Vo

Rth

Electronic DC load

Figure 3.8. Experimental test setup.

4.95’’ 4.95’’

2.1’’

4.95’’

Input side Output side Transformer

External inductor

Output diodes

Input side full bridge

Input capacitor

Output capacitor

56

3.2.2 Converter Operations Verification

The steady state waveforms of the converter operating under 30.4 V with 300 W

output are shown in Figure 3.9. In Figure, the green curve is the voltage across primary

winding of transformer, vpri and the blue curve is the resonant current , iLr. It can be seen

that the voltage across the transformer primary side is the square waveform which indicates

that the phase angel between two primary switching legs is 180 degree. The resonant

current is a pure sinusoidal waveform because the switching frequency is equal to the

resonant frequency.

Figure 3.9. Operation waveforms under 30.4 V input and 300 W output

Figure 3.10. Buck mode operation with 33 V input and 300 W output

vpri: 50 V/div

iLr: 2 A/div

Time base: 5 us/div

vpri: 50 V/div

iLr: 5 A/div

Time base: 2 us/div

57

The steady state waveforms of the converter operating in Buck mode with 33 V

input and 300 W output are shown in Figure 3.10. In Figure, the grey curve is the voltage

across primary winding of transformer, vpri and the green curve is the resonant current , iLr.

The phase angle between two legs can be observed from vpri. The resonance begins at the

high voltage vpri and ends at the vpri is shorted. When S1 and S4 are on at the same time

resulting no voltage applied in the transformer windings, there is no energy transfer to the

load. The small circulating current during the DCM period is due to resonant between Lr

and parasitic output capacitances of secondary side MOSFETs and diodes.

Figure 3.11. Boost mode operation with 27 V input and 300 W output

The steady state waveforms of the converter operating in Boost mode with 27 V

input and 300 W output are shown in the Figure 3.11. In Figure, the voltage across primary

winding of transformer, vpri and the resonant current , iLr are shown as well. The resonant

inductor is charged near linearly at the beginning of the switching cycle since the secondary

side switches S5, S6 turns on at this period. The resonance begins at one of the secondary

side switches turns off and the energy is transferred to the load during this period. The

resonance ends at the resonant current reaches to zero. After that, the converter runs into

vpri: 20 V/div

iLr: 2 A/div

Time base: 5 us/div

58

DCM period. The small circulating current during the DCM period is due to the resonance

between Lr and parasitic output capacitances of secondary side MOSFETs and didoes.

3.2.3 Experimental results of MOSFETs Soft-Switching

Now that the basic converter operations have been verified, soft-switching of the

primary and secondary side MOSFETs will be explored in this section.

Figure 3.12 shows ZVS transition waveforms of the MOSFET S1 operating under

normal-input voltage. The red waveform is the drain-to-source voltage of S1 and green

waveform is the gate-to-source voltage of S1. The gate signal is given after that the drain-

to-source voltage drops to zero. It is clear to see that the load conditions don’t affect ZVS

of primary side MOSFETs. Figure 3.13 shows ZVS transition waveforms of the MOSFET

S1 operating in Boost mode. The red waveform is the drain-to-source voltage of S1 and grey

waveform is the gate-to-source voltage of S1 while the green waveform is the resonant

current.

vds1: 10 V/div vds1: 10 V/div

vgs1: 5 V/div vgs1: 5 V/div

Time base: 100 ns/div

Figure 3.12. ZVS of primary side MOSFET S1 under normal-input condition.

Light load: Po=30 W Full load: Po=300 W

59

Figure 3.13. ZVS of primary side MOSFET S1 during Boost mode under 27 V input condition.

When the resonant current reaches to zero under normal-input voltage condition,

the primary side MOSFETs turn off with ZCS as shown in Figure 3.14. The red waveform

is the drain-to-source voltage of S1 and blue waveform is the current through transformer

primary winding. When the converter operates in Boost mode, the DCM operation is to

ensure ZCS of the primary side MOSFETs, as shown in Figure 3.16. Before S1 turns off,

the converter operates in the DCM period and the current through the switch is zero. In

Figure 3.16, the red waveform is the drain-to-source voltage of S1 and the green waveform

is the resonant current.

Figure 3.14. ZCS of primary side MOSFET S1 under normal-input condition.

vds1: 20 V/div

vds1: 10 V/div vgs1: 5 V/div

iLr: 2 A/div


ipri: 5 A/div

Time base: 1 us/div

60

Figure 3.16. ZCS of primary side MOSFET S1 during Boost mode under 27 V input condition.

Figure 3.15 shows the bottom switches S2, S4 turn-on and turn-off transition during

Buck mode. Bottom switch S2 achieve ZVS by the magnetizing current but lose ZCS. For

the bottom switch S4, ZCS is realized but it cannot achieve ZVS under most of the Buck

mode operating range, especially under the small duty cycle condition. Since the

magnetizing current is not large enough to fully discharge the parasitic output capacitance.

vds1: 10 V/div

iLr: 2 A/div


vds2: 20V/div vgs2:10V/div


vds2: 50 V/div

vds4: 50 V/div

iLr: 2A/div Time base: 2 us/div

Figure 3.15. Turn-on and turn-off transition of primary side MOSFETs during Buck mode under 33 V input condition.

61

Figure 3.17. ZVS of secondary MOSFET S5 under normal-input condition.

Because the current direction through secondary side switches S5 and S6 is from the

source terminal to drain terminal, the gate signal can be controlled to have a fixed short

time delay to make the body diode conduct firstly. Therefore, during both Buck and Boost

modes, S5 and S6 achieve ZVS under entire operating range. Figure 3.17 shows the turn on

transition of S5 under normal-input condition, where the red waveform is the drain-to-

source voltage of S5, green waveform is the gate drive and the grey one is the resonant

current. The similar waveforms can be observed when converter operates in Buck and

Boost modes.

3.2.4 Converter Efficiency

The efficiency of the proposed converter is tested for different input voltages and

output power levels. The experimental efficiency curves under the 28 V, 30 V and 32 V

input voltage conditions are shown in Figure 3.18. These loss measurements consist of all

system loss including control, sensing, and other auxiliary loss. The converter’s peak

efficiency is 98.1 % and the CEC efficiency at the nominal 30 V input is 97.6 %. Under

the heavy load conditions, efficiency under 27 V input condition is less than 0.5 % lower

than that under 30 V input condition while the efficiencies are almost same under the light

load conditions. The CEC efficiency at the 27 V input condition in 97.3 %. However, the

vds5: 200 V/div vgs5: 10 V/div

iLr: 2 A/div Time: 100 ns/div

62

efficiency under the light loads condition in Buck mode drops a lot. The CEC efficiency in

under 32 V input condition is 96.7 %.

Figure 3.18. Measured converter efficiency

Voltage measurements were made using Fluke 287 digital multimeters with have a

dc voltage accuracy of 0.025 % for the input voltage, 0.03 % for the output voltage, and

currents are measured with Fluke 289 digital multimeters with a dc current accuracy of

0.05 % for both the input and output currents.

3.3 Loss Breakdown Analysis

Although some of the loss equations have been presented in the section 3.1, this

section will give a summary of the power stage loss under the most efficiency operating

point as shown in the table 3.3. In addition to the power stage loss, additional auxiliary loss

such as sensing, control, and gate driver quiescent current loss need to be taken into

consideration in order to complete the loss analysis.

63

Table 3.3. A summary of power stage components loss normal-input condition.

S1-4 conduction loss 21234 14cond s rms dsonP i R−=

S1-4 switching loss 1234 2sw s g auxP f Q V=

S5,6 conduction loss 256 52cond s rms dsonP i R−=

S5,6 switching loss ( )256 2sw s oss o g auxP f C V Q V= +

Do1, Do2 loss 22( )d f d ave d rms acP V i i R− −= + Transformer core loss 14

_ 1000x y RM

core T m s TmP C f B= ∆ *

Transformer winding loss 2 2_ sec( )pri

wind T pri pri

iP i R R

n= +

External resonant inductor core loss 8_ 1000

x y RMcore I m s inductor

mP C f B= ∆ *

External resonant inductor winding loss 2_ ( )pri

wind I esr

iP R

n=

Resonant capacitor loss 2( )prirC c

iP r

n=

* ΔB is calculated in equation (3.3) and (3.4). mRM14 is the mass of RM14 core in grams;

mRM8 is the mass of RM8 core in grams.

Figure 3.19 shows the calculated breakdown loss analysis with 30 V input and 225

W output according to the calculation in Table 3.3. The loss analysis example is chosen

under this operating condition is due to the 75 % load condition takes 53 % weight of the

CEC efficiency. Most of loss are from the transformer and output diodes and other loss,

where the other loss are including the DSP control, sensing and other auxiliary power.

3.4 Summary

In this chapter, a detailed design procedure for power stage, including transformer

design, resonant tank design, and MOSFETs and diodes selection is presented. The design

is target to optimize the efficiency at the most efficient operating point. A 300 W prototype

is built based on the design procedure to validate the analysis in chapter 2. Two operating

64

modes are verified as well as soft-switching. Converter efficiency is tested with different

input voltages and different power levels. The converter’s peak efficiency is 98.1 % and

the CEC efficiency at the nominal 30 V input is 97.6 %. Most of loss are from the

transformer and output diodes and other loss, where the other loss are including the DSP

control, sensing and other auxiliary power, under 30 V input and 225 W output operating

condition.

Figure 3.19. Calculated breakdown of converter loss under 30 V input, 225 W output power condition.

W

65

Chapter 4

Conclusions and Future Work

4.1 Conclusions

Solar energy will be more and more important in the future due to the limitation of

the traditional fuels. To utilize the solar energy, one of the most important way is the

module power conditioning system because it owns the highest MPPT efficiency and

another reason is that it can be set up on the rooftop for residents. Therefore high efficiency

microinverter which can convert the energy from PV panel to the grid will contribute

significantly to solar utilization. This thesis studied a new isolated dc-dc converter served

as the frond-end dc-dc stage of the two stage microinverter. The main contents are as

following.

A topology with hybrid modes of operation are proposed to achieve the wide-input

regulation capability while achieving high efficiency. The converter operates as the series

resonant converter with normal-input voltage to achieve the highest efficiency. The

converter acts like a buck converter under the high-input conditions, whereas the converter

behaves as a boost converter under the low-input conditions. Besides the capability of

wide-input regulation, the converter also provides galvanic isolation. The hardware

prototype can reach to 98.1% of peak power stage efficiency and 97.6% of weighted CEC

efficiency including all auxiliary and control power under the 30V input voltage condition.

Since with this topology and modulation, the converter can achieve zero-voltage switching

(ZVS) and/or zero-current switching (ZCS) of the primary-side MOSFETs, ZCS and/or

66

ZVS of the secondary-side MOSFETs and ZCS of output diodes under all operational

conditions.

4.2 Future Work

Due to the time limitation, the previous work was focused on topology efficiency

optimization. Next steps, controllers of each operating mode should be designed as well as

a smooth transition method. A series work on the system integrations need to be explored,

including soft-start, MPPT and double line frequency ripple rejection. All of these issues

are very important for a micoconverter performance.

Further efforts can be done to improve the microconverter efficiency. The

magnetics components have chances to be improved if the proximity effect and fringing

effect are to be further explored. On the other hand, the wide-bandgap semiconductor can

be utilized in the primary side. Since they have much smaller parasitic capacitance, it will

be easier to achieve ZVS and lower loss from the gate charge.

67

References

[1] B. K. Bose, "Global Warming: Energy, Environmental Pollution, and the Impact of Power Electronics," IEEE Ind. Electron. Mag., vol. 4, no. 1, pp. 6-17, Mar. 2010.

[2] “Global market outlook for photovoltaics, 2013-2017,” www.epia.org. [3] The Business Council for Sustainable Energy, "2014 Sustainable Energy in America

Factbook", 2014. Availabe: http://www.bcse.org [4] J.-S. Lai, "Power conditioning systems for renewable energies," in Proc. IEEE Int.

Conf. on Elect. Mach. and Syst. (ICEMS), 2007, pp. 209-218. [5] J.-S. Lai, "Power conditioning circuit topologies," IEEE Ind. Electron. Mag., vol. 3,

no. 2, pp. 24-34, Jun. 2009. [6] W. Xiao, A. Elnosh, V. Khadkikar, and H. Zeineldin, "Overview of maximum power

point tracking technologies for photovoltaic power systems," in Proc. IEEE Annu. Conf. Ind. Electron. Soc. (IECON), 2011, pp. 3900-3905.

[7] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, "A review of single-phase grid-

connected inverters for photovoltaic modules," IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1292-1306, Sept./Oct. 2005.

[8] F. Blaabjerg, Z. Chen, and S. B. Kjaer, "Power electronics as efficient interface in

dispersed power generation systems," IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1184-1194, Sept. 2004.

[9] Q. Li and P. Wolfs, "A Review of the Single Phase Photovoltaic Module Integrated

Converter Topologies With Three Different DC Link Configurations," IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1320-1333, May. 2008.

[10] J. Wiles, "Photovoltaic Power Systems and the National Electric Code: Suggested

Practices," Southwest Technology Development Institute, Mar. 2001. [11] O. Lopez, R. Teodorescu, F. Freijedo, and J. DovalGandoy, "Leakage current

evaluation of a singlephase transformerless PV inverter connected to the grid," in Proc. IEEE Appl. Power Electron. Conf. and Expo. (APEC), 2007, pp. 907-912.

[12] Aurora Micro datasheet from http://www.power-one.com. [13] P. L. Chapman et al. “Multi-stage power inverter,” U.S. Patent 0275196 A1, Nov. 1,

2012.

http://www.epia.org

http://www.bcse.org

http://www.power-one.com

68

[14] P. L. Chapman et al. “Multi-stage power inverter,” U.S. Patent 0275196 A1, Nov. 1, 2012. [15] P. L. Chapman et al. “Power converter with reverse recovery avoidance,” U.S.

Patent0155128 A1, Jun. 21, 2012. [16] S. Jiang, D. Cao Y. Li, and F.-Z. Peng, “Grid-connected boost-half-bridge photovoltaic

microinverter system using repetitive current control and maximum power point tracking,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4711-4722, Nov. 2012.

[17] Texas Instruments, "Under the Hood of Flyback SMPS Designs", User's Guide

SLUP261, 2011. Availabe: http://www.ti.com [18] R. Watson, F. C. Lee, and G. C. Hua, "Utilization of an active-clamp circuit to

achieve soft switching in flyback converters," IEEE Trans. Power Electron., vol. 11, no. 1, pp. 162-169, Jan. 1996.

[19] W. Yu, B. York, and J.-S. Lai, "Inductorless forward-flyback soft-switching

converter with dual constant on-time modulation for photovoltaic applications," in Proc. IEEE Energy Convers. Congr. Expo., 2012, pp. 3549-3555.

[20] T. LaBella, B. York, C. Hutchens, and J.-S. Lai, "Dead time optimization through

loss analysis of an active-clamp flyback converter utilizing GaN devices," in Proc. IEEE Energy Convers. Congr. Expo., 2012, pp. 3882-3889.

[21] L. Jong-Jae, J.-M. Kwon, K. Eung-Ho, and B.-H. Kwon, "Dual Series-Resonant

Active-Clamp Converter," IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 699-710, Feb. 2008.

[22] B. R. Lin, Y. S. Huang, and J. J. Chen, "Soft switching active-clamped dual-series

resonant converter," Power Electronics, IET, vol. 3, no. 5, pp. 764-773, 2010. [23] G. Spiazzi, D. Tagliavia, and S. Spampinato, "DC-DC flyback converters in the

critical conduction mode: a re-examination," in Proc. IEEE IAS Annual Conf. , 2000, pp. 2426-2432 vol.4.

[24] C. Rodriguez, and G. A. J. Amaratunga, “Long-lifetime power inverter for photovoltaic

AC modules,” IEEE Trans. Power Electron., vol. 55, no. 7, pp. 2593-2601, Jul. 2008. [25] C. Rodriguez, “Power conditioning unit,” U.S. Patent 0033463 A1, Feb. 9, 2012. [26] C. Q. Lee, K. Siri, "Analysis and Design of Series Resonant Converterby State-Plane

Diagram," in IEEE Transactions on Aerospace andElectronic Systems, vol.AES-22, no.6, pp.757-763, Nov. 1986.

[27] T. LaBella, W. Yu, J.-S. Lai, M. Senesky, and D. Anderson, "A Bidirectional Switch

Based Wide-Input Range High-Efficiency Isolated Resonant Converter for Photovoltaic Applications," IEEE Trans. Power Electron., VOL. 29, NO. 7, JULY 2014

http://www.ti.com

69

[28] C. Zheng, J. -S. Lai, R. Chen, E. W. Faraci, Z. U. Zahid, B. Gu, L. Zhang, G. Lisi, and D. Anderson, “High-Efficiency contactless power transfer system for electric vehicle battery charging application”, IEEE Journal of Emerging and Selected Topics in Power Electronics., vol. 3, pp. 65-74, Mar. 2015

[29] Y. Ren, M. Xu, J. Sun, and F. C. Lee, "A family of high power density unregulated

bus converters," IEEE Trans. Power Electron., vol. 20, no. 5, pp. 1045-1054, Sept. 2005.

[30] B. Yang, F. C. Lee, A. J. Zhang, and G. Huang, "LLC resonant converter for front

end DC/DC conversion," in Proc. IEEE Appl. Power Electron. Conf. and Expo. (APEC), 2002, pp. 1108-1112 vol.2.

[31] R. Beiranvand, B. Rashidian, M. R. Zolghadri, and S. M. H. Alavi, "A Design

Procedure for Optimizing the LLC Resonant Converter as a Wide Output Range Voltage Source," IEEE Trans. Power Electron., vol. 27, no. 8, pp. 3749-3763, Aug. 2012.

[32] F. Musavi, M. Craciun, D. S. Gautam, W. Eberle, and W. G. Dunford, "An LLC

Resonant DC-DC Converter for Wide Output Voltage Range Battery Charging Applications," IEEE Trans. Power Electron., vol. 28, no. 12, pp. 5437-5445, Dec. 2013.

[33] H. Hu, X. Fang, F. Chen, Z. J. Shen, and I. Batarseh, "A Modified High-Efficiency

LLC Converter With Two Transformers for Wide-input Range Applications," IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1946-1960, Apr. 2013.

[34] B.-G. Chung, K.-H. Yoon, S. Phum, E.-S. Kim, and J.-S. Won, "A novel LLC

resonant converter for wide-input voltage and load range," in Proc. IEEE Int. Conf. on Power Electron. and ECCE Asia (ICPE & ECCE), 2011, pp. 2825-2830.

[35] Z. Liang, R. Guo, J. Li, and A. Q. Huang, "A High-Efficiency PV Module-Integrated

DC/DC Converter for PV Energy Harvest in FREEDM Systems," IEEE Trans. Power Electron., vol. 26, no. 3, pp. 897-909, Mar. 2011.

[36] B. York, W. Yu, and J.-S. Lai, "An Integrated Boost Resonant Converter for

Photovoltaic Applications," IEEE Trans. Power Electron., vol. 28, no. 3, pp. 1199-1207, Mar. 2013.

[37] H.-D. Gui, Z. Zhang, X.-F. He, and Y.-F. Liu, "A high voltage-gain LLC micro-

converter with high efficiency in wide-input range for PV applications," in Proc. IEEE Appl. Power Electron. Conf. and Expo. (APEC), 2014, pp. 637-642.

[38] Y. Gu, L. Hang, Z. Lu, Z. Qian, and D. Xu, "Voltage doubler application in isolated

resonant converters," in Proc. IEEE Annu. Conf. Ind. Electron. Soc. (IECON), 2005, pp. 1184-1188.

70

[39] B. Yang, R. Chen, and F. C. Lee, "Integrated magnetic for LLC resonant converter," in Proc. IEEE Appl. Power Electron. Conf. and Expo. (APEC), 2002, pp. 346-351 vol.1.

[40] K. D. T. Ngo, "Analysis of a series resonant converter pulse width-modulated or

current-controlled for low switching loss," IEEE Trans. Power Electron., vol. 3, no. 1, pp. 55-63, Jan. 1988.

[41] L. Corradini, D. Seltzer, D. Bloomquist, R. Zane, D. Maksimovic, and B. Jacobson,

"Minimum Current Operation of Bidirectional Dual-Bridge Series Resonant DC/DC Converters," IEEE Trans. Power Electron., vol. 27, no. 7, pp. 3266-3276, Jul. 2012.

[42] Y. Lu, E. K. W. Cheng, and S. L. Ho, "Quasi Current Mode Control for the Phase-

Shifted Series Resonant Converter," IEEE Trans. Power Electron., vol. 23, no. 1, pp. 353-358, Jan. 2008.

[43] Y.-K. Lo, C.-Y. Lin, M.-T. Hsieh, and C.-Y. Lin, "Phase-Shifted Full-Bridge Series-

Resonant DC-DC Converters for Wide Load Variations," IEEE Trans. Ind. Electron., vol. 58, no. 6, pp. 2572-2575, Jun. 2011.

[44] Charette, A., AI Haddad, K. , Simard, R., Rajagopalan, V.," Variable Frequency and

Variable Phase Shift Control of Dual Series Resonant Converter for Utility Interface", 14 Annual Conference of Industrial Electronics Society, 1988. IECON '88. Volume: 3 Pages: 563 - 568,

[45] Aboushady, A.A., Ahmed, K.H., Finney, S.J., and Williams, B.W., “Steady-state

analysis of full-bridge series resonant converter with phase-shift and frequency control,” in Power Electronics, Machines and Drives (PEMD 2010), 5th IET International Conference on, 2010, pp 1-6.

[46] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed.

New York: Springer, 2001. [47] W. T. McLyman, Transformer and Inductor Design Handbook, Fourth ed. Boca

Raton: CRC Press, 2011. [48] Ferroxcube, 3C95 Material specification datasheet, Sept. 2008. [49] B. Gu, J. Dominic, J. Zhang, L. Zhang, B. Chen, and J. -S. Lai, “Control of electrolyte

free microinverter with improved MPPT performance and grid current quality,” in Proc. of IEEE APEC 2014, pp.1788-1792, Mar. 2014.

[50] X. Zhao, L. Zhang, R. Born, J.-S. Lai, “Solution of Input Double-Line Frequency

Ripple Rejection for High-Efficiency High-Power Density String Inverter in Photovoltaic Application”, in Proc. of IEEE APEC 2016, Mar. 2016.

a high-efficiency isolated hybrid series resonant ... · under high-input conditions, the converter...

Documents