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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
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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.
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To my parents, Yanmin Zhao
Cuiqing Xu
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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.
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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
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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
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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
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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 2.16. (a) Equivalent circuit of interval [t0 – t1], (b) State-plane trajectory of interval [t0 – t1]. ..................................................................................................... 32
Figure 2.17. (a) Equivalent circuit of interval [t1 – t2], (b) State-plane trajectory of interval [t1 – t2]. ..................................................................................................... 33
Figure 2.18. (a) State-plane trajectory of interval [t4 – t5], (b) Equivalent circuit of interval [t4 – t5]. ..................................................................................................... 35
Figure 2.19. (a) Equivalent circuit of interval [t5 – t6], (b) State-plane trajectory of interval [t5 – t6]. ..................................................................................................... 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
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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
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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
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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.
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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
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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
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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
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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.
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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
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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
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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)
At time t5, there is a certain delay turning on the switch S5 to allow the body diode
conduct firstly which can allow S5 ZVS turn on.
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)
Figure 2.16. (a) Equivalent circuit of interval [t0 – t1], (b) State-plane trajectory of interval [t0 – t1].
( ) ( )( )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)
Figure 2.17. (a) Equivalent circuit of interval [t1 – t2], (b) State-plane trajectory of interval [t1 – t2].
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)
At time t4, there is a certain delay turning on the switch S5 to allow the body diode
conduct firstly which can allow S5 ZVS turn on.
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)
Figure 2.19. (a) Equivalent circuit of interval [t5 – t6], (b) State-plane trajectory of interval [t5 – t6].
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
Time base: 500 ns/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
Time base: 500 ns/div
vds2: 20V/div vgs2:10V/div
Time base: 200 ns/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
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