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energies
Article
Control Method Based on Demand Response Needs
of Isolated Bus Regulation with Series-Resonant
Converters for Residential Photovoltaic Systems
Shu-Huai Zhang 1,† , Feng-Zhang Luo 1, *,† , Yi-Feng Wang 1,† , Jiang-Hua Liu 2,† , Yong-Peng He 2,†
and Yue Dong 2,†
1
2
*
†
Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China;
[email protected] (S.-H.Z.); [email protected] (Y.-F.W.)
Tianjin Research Institute of Electric Science Co., Ltd. (TRIED), Tianjin 300301, China;
[email protected] (J.-H.L.); [email protected] (Y.-P.H.); [email protected] (Y.D.)
Correspondence: [email protected]; Tel.: +86-139-2090-2432
These authors contributed equally to this work.
Academic Editor: Gabriele Grandi
Received: 24 April 2017; Accepted: 19 May 2017; Published: 27 May 2017
Abstract: Considering the effects of isolation and high efficiency, a series-resonant DC-DC converter
(L-L-C type, with two inductors and a capacitor) has been introduced into a residential photovoltaic
(PV) generation and storage system in this work, and a voltage gain curve upwarp drifting problem
was found. In this paper, the reason of upwarp drifting in the voltage gain curve is given, and a
new changing topological control method to solve the voltage regulation problem under light load
conditions is proposed. Firstly, the ideal and actual first harmonic approximation (FHA) models are
given, and this drifting problem is ascribed to the multiple peaks of higher-order resonance between
resonant tank and parasitic capacitors. Then the paper presents the pulse-frequency-modulation
(PFM) driver signals control method to translate the full-bridge LLC into a half-bridge LLC converter,
and with this method the voltage gain could easily be reduced by half. Based on this method,
the whole voltage and resonant current sharing control methods in on-line and off-line mode are
proposed. The parameters design and optimization methods are also discussed in detail. Finally,
a residential PV system platform based on the proposed parallel 7-kW full-bridge LLC converter is
built to verify the proposed control method and theoretical analysis.
Keywords: full-bridge series-resonant converter; light load; parasitic parameters; high order resonant;
residential photovoltaic system
1. Introduction
The utilization of residential photovoltaic (PV) power systems, which provide unique advantages
of flexible structures and minimal environmental pollution, has become a significant trend in renewable
energy applications [1–3]. Because of parasitic capacitance between the PV panels and ground,
addressing leakage current and meeting safety requirements are major operating concerns [4,5].
Therefore, electrical isolation of residential PV systems is currently recommended [6–8]. Additionally,
in order to make the most of PV power, high-efficiency performance is expected as well. Among
potential alternative isolated DC-DC converters, the series-resonant DC-DC converter with resonant
inductor, resonant capacitor and magnetizing inductor (we call it LLC resonant converter or LLC
below), which has been investigated to improve power conversion efficiency, has attracted interest
recently [9–13]. When the working frequency is above the main resonant frequency, LLC can
attain zero-voltage-switching (ZVS) for primary power switches. When the working frequency
Energies 2017, 10, 752; doi:10.3390/en10060752
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Energies 2017, 10, 752
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is below the main resonant frequency, LLC can both attain ZVS for primary power switches and
zero-current-switching (ZCS) for output rectifiers [14]. Additionally, the converter benefits from
a narrow switching frequency range with light load and ZVS capability, even with no load [15–19].
The comparative study between the LLC resonant converter and three other isolated DC-DC
converters was discussed in [20]. It is obvious that LLC has higher efficiency and less volume under
the same operating conditions. However, LLC resonant DC-DC converters have several problems,
as follows: (1) High voltage gain beyond regulation under light load conditions, as noted in [21].
The traditional way to solve this problem is by adopting burst mode control. Many studies on
this approach have been performed. Nevertheless, in the burst mode, the output voltage ripple
will be large, leading to lower efficiency; (2) A more serious problem under light load conditions
is the upwarp drift of the gain curve. In [22], four factors are introduced in the first harmonic
approximation (FHA) model to describe this phenomenon: metallic oxide semiconductor field effect
transistor (MOSFET) output capacitance, transformer wiring capacitance, leakage inductance at the
transformer secondary side, and junction capacitance of the rectifier diodes. The conclusion drawn is
that the junction capacitances of the rectifier diodes are the most influential factor. On the basis of this
analysis, the author proposed a method by adding parallel capacitors on the primary side. However,
during experimental verification we found that the effect of this method is unsatisfactory. On the other
hand, pulse width modulation (PWM) control can be adopted under light load conditions [23], but the
exchange between PWM and pulse frequency modulation (PFM) is complicated, and the turn-off
current will be larger; (3) In addition, because of the limited bandwidth, the dynamic performance
of LLC converters is unfavorable [24]. Different control strategies for LLC resonant converters
have been discussed. They are classified as variable-frequency operations and constant-frequency
operations [25–27]. Recently, several improved control schemes have been proposed. A mixed control
strategy in a neighborhood electric vehicle (NEV) application was proposed [28]. By combining several
control strategies, both low-frequency and high-frequency current ripples on the battery are minimized
while stability is maintained. Optimal trajectory control based on state-plane analysis can provide
very fast dynamic performance for series resonant converters [29]. Also, a Bang-Bang charge control
for LLC was proposed [24]. It is simple because it uses only the series resonant capacitor voltage and
a pair of voltage thresholds to determine the MOSFETs’ switching points. It can achieve high-loop
bandwidth and provide fast dynamic performance.
In this study, firstly in Section 2, we describe an existing residential PV power system, and analyze
the voltage regulation problem of a parallel full-bridge LLC converter in this system. In Section 3, we
discuss the ideal and actual FHA model based on previous research, and aim to analyze the reason of
the upwarp drifting in the voltage gain curve. Then, in Section 4, a new changing topological control
method to solve the voltage regulation problem at light load condition is proposed. By adapting PFM
driver signals, the full-bridge LLC converter can be changed into half-bridge LLC, and the voltage
gain could be reduced by half easily for voltage regulation. Design consideration based on the new
method is also given in this section. Based on this method, the whole voltage control methods and
simulation verifications in on-line and off-line mode are proposed in Section 5. Finally, in Section 6,
experimental results with resistive load and real household load are discussed to verify the availability
of the proposed control methods.
2. A Residential PV Power System and Problem Description
2.1. System Description
Figure 1 shows the architecture of a residential PV power system, which is composed of four
parts. The boost maximum power point tracking (MPPT) converter and the bidirectional DC-DC
converter transfer the energy from the PV and batteries to the 400 V DC bus. Compared to the systems
placing batteries at the output of PV MPPT converter, the structure in this paper can easily control
Energies 2017, 10, 752
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charging/discharging state and current of batteries with bidirectional DC/DC converter, which is
benefit for the life time and usage cost of the batteries.
Following them, a parallel full-bridge LLC converter is connected to the next 630 V DC
Energies 2017, 10, 752
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bus, which are used to supply high-frequency isolation and voltage regulation for the system.
LLC converters guarantee electrical isolation with high working frequency. As its full-load efficiency is
converters guarantee electrical isolation with high working frequency. As its full-load efficiency is
98.4% and maximum efficiency is 98.7% in experiments, efficiency is not reduced largely when energy
98.4% and maximum efficiency is 98.7% in experiments, efficiency is not reduced largely when energy
is transferred from PV and batteries to grid. At the end, a three-phase inverter is connected to the grid,
is transferred from PV and batteries to grid. At the end, a three-phase inverter is connected to the
which
supplies
the household
load.load.
The The
proposed
residential
PV power
system
cancan
be operated
in
grid, which
supplies
the household
proposed
residential
PV power
system
be operated
both
on-line
and
off-line
mode:
in both on-line and off-line mode:
(1)
In on-line
on-line mode,
mode, the
the LLC
LLC converters
converters control
control the
(1) In
the 400
400 V
V DC
DC bus
bus voltage.
voltage. The
The inverter
inverter regulates
regulates
the 630
630 V
V DC
DC bus
bus and
and harmonics
harmonics of
of the
The boost
the
the output
output currents.
currents. The
boost converter
converter adopts
adopts the
the MPPT
MPPT
algorithm.
The
bidirectional
converter
adopts
current
control
to
compensate
the
power
difference
algorithm. The bidirectional converter adopts current control to compensate the power
between household
load and PV.
difference
between household
load and PV.
(2)
In
off-line
mode,
the
LLC
resonant
converters control the 630 V DC
(2) In off-line mode,
DC bus
bus voltage.
voltage. The inverter
inverter
regulates
the
AC
output
voltage.
The
boost
converter
adopts
the
MPPT
algorithm and the
regulates the
The boost converter adopts
bidirectional converter adopts voltage control to regulate the 400 V DC bus voltage.
bidirectional
Figure 1. Architecture of residential photovoltaic
photovoltaic system.
system.
2.2. Existing Problem Description
In the proposed residential PV system, the energy generated by PV is delivered to the batteries,
little
poweris is
transmitted
to inverter
through
theresonant
LLC resonant
DC-DC converters,
when the
little power
transmitted
to inverter
through
the LLC
DC-DC converters,
when the household
household
load
is light.
The LLC converters
maywork
always
workload
at light
load condition.
So the problem
load
is light.
The
LLC converters
may always
at light
condition.
So the problem
of the
of the upturn
thevoltage
LLC voltage
gain
at high
frequencies
given
in [21]
be inescapable.
According
upturn
of the of
LLC
gain at
high
frequencies
given
in [21]
willwill
be inescapable.
According
to
to
experiments,
the
light
load
gain
is
so
high
that
the
required
voltage
(630
V
DC
or
400
V
DC)
cannot
experiments, the light load gain is so high that the required voltage (630 V DC or 400 V DC) cannot be
be restrained.
Thus,
voltage
regulation
problem
could
be described
as following:
restrained.
Thus,
thethe
voltage
regulation
problem
could
be described
as following:
(1) In
DC bus
bus voltage,
voltage, U
U400,, will
be lower than 400 V, and a steady-state
(1)
In on-line
on-line mode,
mode, the
the 400
400 V
V DC
400 will be lower than 400 V, and a steady-state
error
exists,
as
the
630
V
DC
bus
voltage
is
constant
and
with
error exists, as the 630 V DC bus voltage is constant and regulated
regulated by
by the
the following
following inverter
inverter with
closed-loop
control.
closed-loop control.
(2)
In
V DC
bus voltage,
voltage, U
U630,,will
be higher than 630 V normally. Burst mode
(2) In off-line
off-line mode,
mode, the
the 630
630 V
DC bus
630 will be higher than 630 V normally. Burst mode
is
adopted,
too
large
voltage
ripple
exists,
as
the
400
DC
bus
voltage
is stable
and
controlled
is adopted, too large voltage ripple exists, as the 400 VVDC
bus
voltage
is stable
and
controlled
by
by
the
bidirectional
DC-DC
converter,
as
shown
in
Figure
1.
the bidirectional DC-DC converter, as shown in Figure 1.
(3) Too slow voltage regulation when the load changes, and too large a voltage spike or sink when
(3) Too slow voltage regulation when the load changes, and too large a voltage spike or sink when
the load is changing suddenly.
the load is changing suddenly.
3. Ideal and Actual FHA Model
FHA modeling method is widely used due to its simple and effectiveness. In this paper, FHA
modeling process is based on previous research [30,31] and we just used it to analyze and explain the
difference between ideal and actual gain of the LLC converter.
Figure 1 shows the topology of the proposed full-bridge LLC resonant converter. The input
voltage is Uin, the output voltage is Uo. The resonant tank is formed by the resonant capacitor Cr, the
Energies 2017, 10, 752
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3. Ideal and Actual FHA Model
FHA modeling method is widely used due to its simple and effectiveness. In this paper,
FHA modeling process is based on previous research [30,31] and we just used it to analyze and
explain the difference between ideal and actual gain of the LLC converter.
Figure 1 shows the topology of the proposed full-bridge LLC resonant converter. The input
voltage is Uin , the output voltage is Uo . The resonant tank is formed by the resonant capacitor Cr ,
the resonant inductor Lr and the magnetizing inductor Lm of the transformer. The turn ratio of the
Energies 2017, 10, 752
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transformer is n:1. The switches on the primary side of the transformer (Q1 , Q2 , . . . , and Q8 ) are
MOSFETs. In the output rectifier, D1 , D2 , . . . , and D8 are the rectifier diodes. The DC voltage gain in
MOSFETs. In the output rectifier, D1, D2, …, and D8 are the rectifier diodes. The DC voltage gain in
this paper refers to the ratio of output voltage: Uo /Uin .
this paper refers to the ratio of output voltage: Uo/Uin.
3.1. Ideal FHA Model Analysis
3.1. Ideal FHA Model Analysis
Firstly, several assumptions are made here:
Firstly, several assumptions are made here:
(1) Waveforms in resonant tank are perfect sinusoidal waves under any working frequency.
(1) Waveforms in resonant tank are perfect sinusoidal waves under any working frequency.
(2) All the energy is conveyed by the fundamental component of the input voltage: uin,FHA .
(2) All the energy is conveyed by the fundamental component of the input voltage: uin,FHA.
(3)
(3) All
All the
the parasitic
parasitic parameters
parameters are
are neglected.
neglected.
(4)
(4) Figure
Figure 22 shows
shows the
the ideal
ideal equivalent
equivalent circuit
circuit of
of the
the proposed
proposed full-bridge
full-bridge LLC
LLCconverter
converterusing
usingthe
the
FHA
modeling
method
[31].
FHA modeling method [31].
Figure2.
2. Ideal
Ideal equivalent
equivalent circuit
circuit of
ofLLC
LLCresonant
resonantconverter
converter
Figure
As is known, LLC converter has two resonant frequencies, in this paper we define the higher
As is known, LLC converter has two resonant frequencies, in this paper we define the higher
resonant frequency fr1 as the main resonant frequency fr, that means: fr = fr1. fr2 is the secondary or
resonant frequency fr1 as the main resonant frequency fr , that means: fr = fr1 . fr2 is the secondary or
lower resonant frequency:
lower resonant frequency:
1
1
f r1 =
, fr 2 =
(1)
1
1
f r1 = 2π√ Lr Cr , f r2 = 2πp ( Lr + Lm )Cr
(1)
2π Lr Cr
2π ( Lr + Lm )Cr
and uin can be expressed with the Fourier series as:
and uin can be expressed with the Fourier series as:
4Uin
uin ( t ) =
⋅
4U
uin (t) =
∞
1
sin 2π Nft )
1 (
in
π · N =∑
1,3,5, N sin(2πN f t )
∞

(2)
(2)
π
N
N =1,3,5,···
t is the time parameter, N is the integer parameter for the Fourier series expansion, and f is the
t is thefrequency.
time parameter,
N is the
parameter
for the Fourier
series
expansion,
andresonant
f is the
switching
According
to integer
the above
assumptions,
the input
voltage
of LLC
switching
frequency.
According
to the above assumptions,
the input
voltage of LLC
resonant of
network
network can
be regarded
as its fundamental
component, thus
the fundamental
component
uin is:
can be regarded as its fundamental component, thus the fundamental component of uin is:
4U
uin, FHA ( t ) = in ⋅ sin ( 2π ft )
(3)
π
4U
in
uin,FH A (t) =
· sin(2π f t)
(3)
π be calculated as:
The root mean square (RMS) value of uin,FHA can
The root mean square (RMS) value of uin,FHA can2 be
as:
2Ucalculated
in
Uin, FHA (t ) =
√
π
2 2Uin
Uin,FH A (t) =
Likewise, the output voltage of the resonant network,
π can be expressed as:
∞
4U
1
Likewise, the output voltage of the resonant
network,
can be expressed as:
uro ( t ) = o ⋅ 
sin ( 2π Nft − φ )
π N =1,3,5, N
(4)
(4)
(5)
where φ is the time shift compared to the input voltage, and the fundamental component of uro is
shown as:
4U o
Energies 2017, 10, 752
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uro (t) =
∞
4Uo
1
· ∑
sin(2πN f t − φ)
π N =1,3,5,··· N
(5)
where ϕ is the time shift compared to the input voltage, and the fundamental component of uro is
shown as:
4Uo
uro,FH A (t) =
· sin(2π f t − φ)
(6)
π
The RMS value of uro,FHA can be calculated as:
Uro,FH A
√
2 2Uo
=
π
(7)
The fundamental component of the rectifier current irct can be expressed as:
irct,FH A =
√
2Irct,FH A sin(2π f t − φ)
(8)
where Irct,FHA is the RMS value of irct,FHA .
Thus the average output current Io can be obtained:
2
Io =
Ts
T
2
Z
0
√
2 2
I
|irct,FH A (t)| dt =
π rct,FH A
(9)
and the equivalent output resistance of the resonant network can be expressed as follows:
Ro,e
U
= ro,FH A =
Irct,FH A
√
2 2
π Uo
π
√
I
2 2 o
=
8
Ro
π2
(10)
In order to simplify the calculation, the equivalent output resistance in the secondary side of the
transformer can be converted to the primary side:
R0 o,e = n2 Ro,e
(11)
With all the given parameters, φ can be calculated as:
"
φ = arctan
2π f Lm n4 Ro,e 2 + (2π f Lr −
2
1
4
2π f Cr )( n Ro,e
4π 2 f 2 Lm 2 n2 Ro,e
+ 4π 2 f 2 Lm 2 )
#
(12)
The forward transfer function of the resonant network can be derived as follows:
H (s) =
Uo,FH A (s)
sL · R0 o,e
m
i
= h
Uin,FH A (s)
n (sLm + R0 o,e ) sLr + sC1 r + sLm · R0 o,e
(13)
Finally, the ideal voltage gain of the LLC resonant converter can be calculated as:
Gid =
=
n
q
Uo
Uin
=
Uo,FH A
Uin,FH A
( R0 o,e −( j2π f )
2
= k H ( j2π f )k
(14)
( j2π f )2 Lm Cr R0 o,e
2
2
3
Lr Cr R0 o,e −( j2π f ) Lm Cr R0 o,e ) +(( j2π f ) Lm −( j2π f ) Lm Lr Cr )
2
3.2. Actual FHA Model Analysis Including Parasitic Capacitors
In order to illustrate the upwarp drifting of the voltage gain curve, the junction capacitances of the
rectifier diodes and the wiring capacitance of the transformer are added. Its equivalent FHA circuit is
shown in Figure 3. Cpc represents the total parasitic capacitances of the rectifier diodes and transformer
windings. Cr_PC represents parasitic capacitance of resonant inductor, which has not been considered
Energies 2017, 10, 752
6 of 21
in former work [21]. In our LLC converter, Cr_PC = 0.2 nF. Cr_PC is so small, and the impact of the
parameter of Cr_PC can be neglected, so the parameter will not appear in the actual FHA model and
analysis in the whole article. From Figure 3, it can be obtained that the reason of the upwarp drifting
should
be ascribed
Energies 2017,
10, 752 to the high order resonance between the resonant tank and parasitic capacitors6 C
ofpc
21.
Energies 2017, 10, 752
6 of 21
Figure 3. Equivalent model of LLC resonant converter considering parasitic parameters.
Figure 3. Equivalent model of LLC resonant converter considering parasitic parameters.
3. Equivalent
of LLC
considering
parasiticas:
parameters.
AfterFigure
considering
Cpc, themodel
voltage
gainresonant
of LLCconverter
converter
can be rewritten
After considering Cpc , the voltage gain of LLC converter can be rewritten as:
′
f ⋅ Cr ⋅ B ( f )
o , e ⋅ 2πconverter
After consideringGCpcpc=, the voltage gain ofRLLC
can be rewritten as:
2
2 R0
o,e · 2π f · Cr · B ( f )
G pc = q n  A ( f ) ⋅ B ( f )  + {RR′o′ , e⋅2Aπ(ff ⋅)C⋅ 2π⋅ Bf (⋅ fC)pc + B ( f ) ⋅ 2π f ⋅ Cr } o,e
r
2
G
npc =[ A( f ) · B( f )]2 +2 R0 o,e A( f ) · 2π f · C pc + B( f ) · 2π f ·2 Cr
n  A (as:
f ) ⋅ B ( f )  + { Ro′ , e  A ( f ) ⋅ 2π f ⋅ C pc + B ( f ) ⋅ 2π f ⋅ Cr }
where A(f) and B(f) are defined
where A(f ) and B(f ) are defined as:
A ( f ) = 4π 2 f 2 Lr C r − 1
where A(f) and B(f) are defined as:
2 2
A(ABf()(ff=
C
−
π 22fff 22LLmrC
−111
44π
Cpcr −
)) ==4π
r
r
(15)
(15)
(15)
(16)
(16)
(17)
(16)
2
As shown in Figure 4, the full line
parasitic parameters with(17)
(15),
f ) 4π
=gain
4π2 2f 2fcurve
−−
1 1
B(isfB)the
LLmmCCpcpcconsidering
(17)
(=
the dash line is the ideal gain curve. The straight dot dashed line is the expected voltage gain (630 V
As shown in Figure 4, the full line is the
curve
considering parasitic parameters with (15),
the gain
gain
curve
DC/400 V DC = 1.575). Those curves are given
under
the considering
same output resistance (5 kΩ), and fr is 78.8
the dash line is the ideal gain curve. The straight dot dashed line is the expected voltage gain (630 V
kHz. Therefore, the expected voltage gain cannot be obtained under the model considering actual
DC/400
VDC
DC==1.575).
1.575).Those
Those curves
given under
same
output
resistance
(5 kΩ),
fr is
DC/400
areare
given
thethe
same
output
resistance
(5 kΩ),
andand
fr is 78.8
parasiticVparameters,
which iscurves
the same
as the under
experimental
result.
78.8
kHz.
Therefore,
the
expected
voltage
gain
cannot
be
obtained
under
the
model
considering
actual
kHz. Therefore, the expected voltage gain cannot be obtained under the model considering
parasitic
parasitic parameters,
parameters, which
which is
is the
the same
same as
as the
the experimental
experimental result.
result.
Figure 4. Voltage gain curve of full-bridge LLC converter at light load condition.
Figure
4.
gain Load
curve Conditions
of full-bridge
full-bridge LLC
LLC converter
converter at
at light
light load
load condition.
condition.
4. New Control
Method
at Light
Figure
4. Voltage
Voltage
gain
curve
of
AsControl
shown in
Figureat
3, Light
there is
an additional
Cpc in the actual FHA model, which is parallel with
4. New
New
Method
Load
Conditions
4.
Control Method
at Light
Load
Conditions
the transformer. Therefore, the reason of upwarp drifting of the voltage gain curve can be ascribed
pc in the actual FHA model, which is parallel with
As higher-order
shown in
in Figure
Figure
3, there
there is
is an
an additional
additional
to the
resonance
between
resonant
tank
parasitic
capacitors,
there is
an
As
shown
3,
CCpc
in theand
actual
FHA model,
whichand
is parallel
with
the
transformer.
Therefore,
the
reason
of
upwarp
drifting
of
the
voltage
gain
curve
can
be
ascribed
additional
resonant
bottomthe
where
the
is higher
than
the main
resonant
in
the
transformer.
Therefore,
reason
of frequency
upwarp drifting
of the
voltage
gain curve
canfrequency
be ascribedfr to
to
the
higher-order
resonance
between
parasitic
capacitors,
and
there
is an
Figure
4. But it isresonance
hard
to calculate
the
realresonant
value
Ctank
pc parasitic
dueand
to the
uncertainty
ofthere
parasitic
the
higher-order
between
resonant
tankofand
capacitors,
and
is anparameters.
additional
additional
resonant
bottom
where the
frequency
higher
main
resonant
frequency
fr in
In order
towhere
solve
thisfrequency
non-monotonic
problem
simply
andthe
effectively,
this
paper
presents
resonant
bottom
the
is higher
thanisthe
mainthan
resonant
frequency
fr in
Figure
4. But
ita
Figure
4.
But
it
is
hard
to
calculate
the
real
value
of
C
pc due to the uncertainty of parasitic parameters.
topological
method.
adapting
PFM driverofsignals,
theparameters.
full-bridge LLC converter
ischanging
hard to calculate
thecontrol
real value
of CpcBy
due
to the uncertainty
parasitic
In changed
order to into
solve
this non-monotonic
problem
andbe
effectively,
this
paper presents a
can be
half-bridge
LLC, and the
voltage simply
gain could
reduced by
half.
changing topological control method. By adapting PFM driver signals, the full-bridge LLC converter
can
changed
into half-bridge
LLC,
andMethod
the voltage gain could be reduced by half.
4.1. be
Proposed
Changing
Topological
Control
As shown
in Figure
5, a full-bridge
LLC can be simply transformed into a half-bridge LLC by
4.1. Proposed
Changing
Topological
Control Method
turning off Q3 and turning on Q4 (as shown in Figure 1) incessantly. The input voltage of resonant
in Figure
a full-bridge
LLCUcan
be simply transformed into a half-bridge LLC by
tankAs
in shown
full-bridge
LLC, 5,
uAB_F
, ranges from
in to −Uin in one period, each voltage lasts 50% of the
Energies 2017, 10, 752
7 of 21
In order to solve this non-monotonic problem simply and effectively, this paper presents
a changing topological control method. By adapting PFM driver signals, the full-bridge LLC converter
can be changed into half-bridge LLC, and the voltage gain could be reduced by half.
4.1. Proposed Changing Topological Control Method
As shown in Figure 5, a full-bridge LLC can be simply transformed into a half-bridge LLC by
Energies
2017,
7 of 21
turning
off10,
Q3752
and turning on Q4 (as shown in Figure 1) incessantly. The input voltage of resonant
tank in full-bridge LLC, uAB_F , ranges from Uin to −Uin in one period, each voltage lasts 50% of the
50%
of period,
the whole
Thus, the RMS
fundamental
harmonic
of period,
uAB_F in each
full-bridge
whole
but period.
that in half-bridge
LLC,value
uAB_Hof
, ranges
from Uin
to 0 in one
voltageLLC,
lasts
U
AB_F
,
can
be
displayed
as:
50% of the whole period. Thus, the RMS value of fundamental harmonic of uAB_F in full-bridge LLC,
1/ f
UAB_F , can be displayed as:
R 1/ f u AB _ F ⋅ dt 2 2√
0
(18)
U AB _ F = 0 u AB_F · dt=
2 U2in
U AB_F
=
=π
Uin
(18)
1/ f
1/ f
π
And
value
of fundamental
harmonic
of uAB_H
in half-bridge
LLC, UAB_H, can be displayed
Andthe
theRMS
RMS
value
of fundamental
harmonic
of u
AB_H in half-bridge LLC, UAB_H , can be
as:
displayed as:
R 1/1/f f
√
·dtdt
1
2
0  uuAB_H
⋅
AB _ H
U AB_H
=
= 2 U U=in1=
U
(19)
(19)
U AB _ H = 0 1/ f
=
U
π
2 AB_F
π in 2 AB _ F
1/ f
By adopting (10), (11) and (15), we can conclude that given the same output resistance Ro ,
By adopting (10), (11) and (15), we can conclude that given the same output resistance Ro, the
the voltage gain of the half-bridge LLC mode GH_pc is half of that of the full-bridge mode:
voltage gain of the half-bridge LLC mode GH_pc is half of that of the full-bridge mode:
11 G pc ( f , Ro )
G
( ff,,RRo ) =
GH_pc
=
(
)
2Gpc ( f , Ro )
H _ pc
o
2
(a)
(20)
(20)
(b)
Figure
signals
of the
proposed
changing
topological
LLC:LLC:
(a) Full-bridge
LLC; and
HalfFigure 5.5.Drive
Drive
signals
of the
proposed
changing
topological
(a) Full-bridge
LLC;(b)
and
(b)
bridge
LLC. LLC.
Half-bridge
To verify the above analysis, an open loop experimental based on a half-bridge LLC converter
To verify the above analysis, an open loop experimental based on a half-bridge LLC converter
has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the
has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the
actual FHA model with (15), and the dashed line is the experimental results, which are obtained by
actual FHA model with (15), and the dashed line is the experimental results, which are obtained by
changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr
changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr is
is 78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain.
78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain. Therefore,
Therefore, by utilizing the proposed changing topological control method, the expected voltage gain
by utilizing the proposed changing topological control method, the expected voltage gain can be
can be obtained under very light load condition, and even the switching frequency could be reduced.
obtained under very light load condition, and even the switching frequency could be reduced.
Compared to the full-bridge LLC, conduction loss and core loss in the half-bridge LLC increases
due to the larger RMS of the resonant current. As the switching frequency becomes lower,
and MOSFETs in switching mode decrease from 4 to 2, the turn-off loss declines largely. To conclude,
at light load condition, the fall of turn-off loss is larger than the rise of conduction loss and core loss.
Overall, the efficiency under half-bridge mode is a little higher than that under full-bridge mode.
Figure 6. Voltage gain curve of half-bridge LLC.
has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the
actual FHA model with (15), and the dashed line is the experimental results, which are obtained by
changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr
is 78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain.
Therefore, by utilizing the proposed changing topological control method, the expected voltage8gain
Energies 2017, 10, 752
of 21
can be obtained under very light load condition, and even the switching frequency could be reduced.
Energies 2017, 10, 752
8 of 21
4.2. Design Consideration Based on the New Method
As is discussed above, to track the required gain of the LLC converter in all load range, it is
important to find the required gain in full-bridge mode when load is normal. It is also important to
find the required gain in half-bridge
mode when
load is
so there
are several restrictions. In the
Figure
gain curve
curve
of light,
half-bridge
LLC.
Figure 6.
6. Voltage
Voltage gain
of
half-bridge
LLC.
following Section 4.2.1, the design procedure of the resonant tank parameters and power devices will
be discussed.
The
andLLC,
design
approach of the voltage gain and working frequency range
Compared
torequirement
the full-bridge
conduction
4.2. Design
Consideration
Based on the
New
Method loss and core loss in the half-bridge LLC increases
for
the
changing
topological
LLC
converter,
whichAs
arethe
used
to meet the
voltage gain
requirements
of
due to the larger RMS of the resonant current.
switching
frequency
becomes
lower, and
As
is
discussed
above,
to
track
the
required
gain
of
the
LLC
converter
in
all
load
range,
it
is
the whole load
range, will
be analyzed
in Section
4.2.2.
MOSFETs
in switching
mode
decrease from
4 to 2,
the turn-off loss declines largely. To conclude, at
important
to find the the
required
in full-bridge
mode
when
is normal.
It isloss
alsoand
important
to
light load condition,
fall ofgain
turn-off
loss is larger
than
the load
rise of
conduction
core loss.
4.2.1.
Resonant
Parameters
and
Rated
Operationg
Point
Design
find
the
required
gain
in
half-bridge
mode
when
load
is
light,
so
there
are
several
restrictions.
In
the
Overall, the efficiency under half-bridge mode is a little higher than that under full-bridge mode.
following Section 4.2.1, the design procedure of the resonant tank parameters and power devices will
In this paper, the design procedure of the resonant tank parameters and power devices which is
be discussed. The requirement and design approach of the voltage gain and working frequency range
presented in [31] will be adopted. As shown in Figure 7, Uin_max, Uin_min, Uout_max and Uout_min are the
for the changing topological LLC converter, which are used to meet the voltage gain requirements of
maximum and minimum of input and output voltage respectively, Pout_max is the maximum output
the whole load range, will be analyzed in Section 4.2.2.
power, n, np, ns, Lr, Lm is the turn ratio, turns of primary and secondary, resonant inductor and
excitation
inductor
of the transformer
respectively,Point
Cr is Design
the resonant capacitor, Co is the output filter
4.2.1. Resonant
Parameters
and Rated Operationg
capacitor, Rac is the effective resistive load reflected to the primary side, Gmax and Gmin are the required
In thisand
paper,
the design
procedure
of the
resonant tank
parameters
maximum
minimum
voltage
gain under
full-bridge
LLC topology,
k isand
thepower
ratio ofdevices
Lm to Lwhich
r, TD is
is
will be adopted.
As quality
shown factor
in Figure
7,resonant
Uin_max , tank,
Uin_min
,U
out_max
out_min
thepresented
dead-timeinof[31]
the bridge-arms,
Q is the
of the
fmax
and
fmin isand
the U
feasible
are
the
maximum
and
minimum
of
input
and
output
voltage
respectively,
P
is
the
maximum
out_max
maximum and minimum operating frequency under different load conditions, Ip is the current in the
output
power,
, ns ,excitation
Lr , Lm is the
turn ratio,
of primary
and
resonant inductor and
resonant
tank, n,
Im n
isp the
current
of theturns
transformer,
IQ_RMS
, Usecondary,
Q_max and PQ_max are the maximum
excitation
inductor
of the transformer
respectively,
the MOSFET
resonant capacitor,
Co isID_avg
the, output
r is
RMS current,
drain-source
voltage and
loss powerCof
each
respectively,
UD_max, filter
PD_on
capacitor,
R
is
the
effective
resistive
load
reflected
to
the
primary
side,
G
and
G
are
the
required
ac
are the maximum
average current, inverse voltage and loss power of eachmax
rectifier min
diode respectively,
maximum
and
minimum voltage gain under full-bridge LLC topology, k is the ratio of Lm to Lr , TD
Icr_RMS and U
Cr_max are the maximum RMS current and peak resonant voltage of Cr.
is theThe
dead-time
theoptimization
bridge-arms, method
Q is the quality
of the resonant
fmax and
fmin is the
design of
and
is basedfactor
on full-bridge
LLCtank,
topology,
because
the
feasible
maximum
and
minimum
operating
frequency
under
different
load
conditions,
I
is
the
current
p
efficiency of normal load range, for example 10–100%, is the main optimization objective
and
the
in
theoperating
resonant tank,
Im is the
of the
transformer,
IQ_RMS , UfQ_max
PQ_max
the
main
conditions.
Onexcitation
the othercurrent
hand, the
main
resonant frequency
r (or fr1and
) and
rated are
steady
maximum
RMS
current,
drain-source
voltage
and
loss
power
of
each
MOSFET
respectively,
I
D_avg ,
state working frequency are preset. The common setting of fr is 100 kHz, in this paper, the output
U
,
P
are
the
maximum
average
current,
inverse
voltage
and
loss
power
of
each
rectifier
diode
D_max per
D_on
power
channel is up to 4 kW, so in order to strike a balance between power efficiency and power
respectively,
Icr_RMS of
and
UCr_max
are the
RMS current and peak resonant voltage of Cr .
density, the setting
fr will
be nearly
80maximum
kHz.
Figure
full-bridge LLC
LLC converter.
converter.
Figure 7.
7. Design
Design procedure
procedure of
of the
the proposed
proposed full-bridge
The rated steady state working frequency setting needs to consider the limited peak voltage gain
under 4 kW output condition, large DC bus voltage fluctuations caused by the transient procedures
and rated conversion efficiency comprehensively.
As the rated power is 4 kW in each channel, it is hard to get a high voltage gain as in [28], because
the equivalent resistance Ro is too small to make the curve goes up. Thus, the peak voltage gain should
be guaranteed to regulate two DC bus voltage during a large disturbance.
Energies 2017, 10, 752
9 of 21
The design and optimization method is based on full-bridge LLC topology, because the efficiency
of normal load range, for example 10–100%, is the main optimization objective and the main operating
conditions. On the other hand, the main resonant frequency fr (or fr1 ) and rated steady state working
frequency are preset. The common setting of fr is 100 kHz, in this paper, the output power per channel
is up to 4 kW, so in order to strike a balance between power efficiency and power density, the setting
of fr will be nearly 80 kHz.
The rated steady state working frequency setting needs to consider the limited peak voltage gain
under 4 kW output condition, large DC bus voltage fluctuations caused by the transient procedures
and rated conversion efficiency comprehensively.
As the rated power is 4 kW in each channel, it is hard to get a high voltage gain as in [28], because
the equivalent resistance Ro is too small to make the curve goes up. Thus, the peak voltage gain should
be guaranteed to regulate two DC bus voltage during a large disturbance.
The
problem
Energies
2017,
10, 752 of gain upturn could be avoided by using the proposed changing topological control
9 of 21
method, so the limited voltage gain problem should be considered during rated operating point
presetting.
Therefore,
the rated
cangain
be achieved
the main
frequency
fr ,
point
presetting.
Therefore,
thegain
rated
can be slightly
achievedabove
slightly
aboveresonant
the main
resonant
making fullfr,use
of drop
of drop
gain curve.
wider
gain range
and higher
efficiency
frequency
making
fullscope
use of
scope It
ofcan
gainguarantee
curve. It acan
guarantee
a wider
gain range
and
near operation
higher
efficiencypoint.
near operation point.
4.2.2. Voltage
Voltage Gain
Gain and
and Working
Working Frequency
4.2.2.
Frequency Range
Range Selection
Selection
By using
usingthe
theproposed
proposedchanging
changingtopological
topological control
control method
method and
andthe
thedesign
designprocedure
procedurediscussed
discussed
By
in
Section
4.2.1,
the
voltage
gain
and
working
frequency
range
selection
are
illustrated
in
Figure8.8.
in Section 4.2.1, the voltage gain and working frequency range selection are illustrated in Figure
When
the
LLC
operates
in
full-bridge
LLC
mode,
f
is
the
voltage
gain
peak
point
under
maximum
1-Fis the voltage gain peak point under maximum
When the LLC operates in full-bridge LLC mode, f1-F
load condition,
condition, for
for example
example 4.8
4.8 kW
kW (1.2
(1.2 times
times of
isthe
theminimum
minimumvoltage
voltagegain
gain point
point
2-Fis
load
of rated
rated power),
power), ff2-F
under
selectable
minimum
load,
for
example
0.8
kW
(0.2
times
of
rated
power).
When
the
load
is
under selectable minimum load, for example 0.8 kW (0.2 times of rated power). When the load is
reduced continuously,
continuously, the
the circuit
circuit will
isthe
thevoltage
voltage gain
gain peak
peak
1-H is
reduced
will be
be changed
changed into
into half-bridge
half-bridge LLC,
LLC, ff1-H
point
under
maximum
selectable
load
condition
in
half-bridge
mode,
for
example
1.2
kW
(0.3
times
of
point under maximum selectable load condition in half-bridge mode, for example 1.2 kW (0.3 times
rated
power),
f
is
the
minimum
voltage
gain
point
without
load.
Therefore,
within
range
2,
point
of rated power),2-H
f2-H is the minimum voltage gain point without load. Therefore, within range 2, point 11
is the
the minimum
minimum frequency
frequency point
point and
and point
point 22 is
is the
the maximum
maximum frequency
frequency point
point under
under full-bridge
full-bridge LLC
LLC
is
topology,
and
within
range
1,
point
3
is
the
minimum
frequency
point
and
point
4
is
the
maximum
topology, and within range 1, point 3 is the minimum frequency point and point 4 is the maximum
frequency point
point under
under half-bridge
half-bridge LLC
LLC topology.
topology.
frequency
Figure
Figure8.8.Voltage
Voltage gain
gain and
and frequency
frequency range
range selection
selection in
in full-bridge
full-bridge and
and half-bridge LLC.
ItIt is
is necessary
necessarytoto
calculate
feasible
minimum
and maximum
frequency,
the
calculate
the the
feasible
minimum
and maximum
frequency,
to select to
theselect
operating
operating
frequency
range
and
to
ensure
a
suitable
gain
can
be
attained,
in
which
the
gain
curve
is
frequency range and to ensure a suitable gain can be attained, in which the gain curve is monotonic
monotonic
without upturn.
without upturn.
The
first-order
The first-order derivative
derivative of
of the
the half-bridge
half-bridge LLC
LLC voltage
voltage gain
gain can
can be
be described
described as:
as:
2
2
Ro′,eCr (12π2 f 2LmCpc −1) ⋅ C( f ) +D( f )  Ro′,eCrπ fB( f ) C( f ) 6π fLmCpc A( f ) +6π fLCB
r r ( f )

−


GH′ _ pc ( f1_H, Ro,Cpc ) =
3
3
2
2
2
2
2nC( f ) +D( f ) 2
nC( f ) +D( f ) 2




Ro′,e Crπ fB ( f ) D ( f ) (12π f Lr Cr C pc + 12π f LmCr C pc )
2
−
2
2
2
3
2
Ro′,e Crπ fB ( f ) D ( f ) ( C pc + Cr )
2
+
3
(21)
Energies 2017, 10, 752
G
0
H_pc
10 of 21
i
h
R0 o,e Cr 12π 2 f 2 Lm C pc − 1 · C ( f )2 + D ( f )2
R0 o,e Cr π f B( f )C ( f ) 6π f Lm C pc A( f ) + 6π f Lr Cr B( f )
f 1_H , Ro , C pc =
−
h
i3
h
i3
2
2
2n C ( f )2 + D ( f )2
n C ( f )2 + D ( f )2
2
2
R0 o,e Cr π f B( f ) D ( f ) 12π 2 f 2 Lr Cr C pc + 12π 2 f 2 Lm Cr C pc
R0 o,e Cr π f B( f ) D ( f ) C pc + Cr
−
+
h
i3
h
i3
2
2
n C ( f )2 + D ( f )2
n C ( f )2 + D ( f )2
(21)
C(f ) and D(f ) are defined as:
C ( f ) = A( f ) · B( f )
D ( f ) = 2π f · R0 o,e C pc · A( f ) + Cr · B( f )
(22)
(23)
By making G0 H_pc zero, extreme points of GH_pc are obtained. f 1_H is a local maximum value point,
and f 2_H is a local minimum value point. As shown in Figure 8, the frequency range between f 1_H and
f 2_H is the maximum feasible working area for the half-bridge LLC resonant converter, and range 1
should be contained within f 1_H and f 2_H . Similarly, the frequency range between f 1_F and f 2_F is the
maximum suitable working area for the full-bridge LLC resonant converter, and range 2 should be
contained within f 1_F and f 2_F .
In Figure 8, if Gr declines to the position of G2 , the required gain cannot be tracked with the
full-bridge LLC converter. Taking a margin of 0.1Gr into consideration, the selection of load or Ro
should satisfy the following equation:
G pc f 2_F , Ro , C pc ≤ 0.9Gr
(24)
The gain of the local maximum point f 1_F , should be larger than the required gain. Taking
a margin of 0.2Gr into consideration:
G pc f 1_F , Ro , C pc ≥ 1.2Gr
(25)
In half-bridge mode, the gain of the local maximum point f 1_H , should be larger than the required
gain Gr . If Gr rises to the position of G1 , the required gain cannot be tracked with the half-bridge LLC
converter. Taking a margin of 0.1Gr into consideration, the selection of Ro should satisfy the following
equation:
GH_pc f 1_H , Ro , C pc ≥ 1.1Gr
(26)
The gain of the local minimum point f 2_H should be smaller than the required gain Gr . Taking
a margin of 0.2Gr into consideration:
GH_pc f 2_H , Ro , C pc ≤ 0.8Gr
(27)
Considering the above design method and optimization factors, resonant tank parameters,
the voltage gain and frequency range could be calculated.
Furthermore, in order to realize fast dynamic response and good steady performance within
the whole load conditions, a new DC bus voltage control and current sharing strategy is proposed
for the parallel LLC resonant converter. By ensuring that the LLC works in full-bridge mode with
normal load and in half-bridge mode with light load, the DC bus voltage is controllable in all load
range. Meanwhile, with a dead-band controller, two resonant inductor currents can be shared evenly.
The following Section 5 will discuss the proposed control method under on-line mode and off-line
mode separately, and corresponding simulation results will be given.
5. Control of the Variable Structure LLC Converter
As shown in Figure 9, a hysteresis controller is proposed to transform the mode of the proposed
LLC converter. Pinv is the output power of the inverter, it is equal to the output power of LLC converter
when power loss of the inverter is ignored. PU is the minimum load for the full-bridge LLC converter,
and PL is the maximum load for the half-bridge LLC converter.
If the output power of inverter is above PU , LLC converter operates in the full-bridge mode.
If the output power of inverter is below PL , LLC converter operates in half-bridge mode. Otherwise,
As shown in Figure 9, a hysteresis controller is proposed to transform the mode of the proposed
LLC converter. Pinv is the output power of the inverter, it is equal to the output power of LLC
converter when power loss of the inverter is ignored. PU is the minimum load for the full-bridge LLC
converter,
PL is the maximum load for the half-bridge LLC converter.
Energies 2017,and
10, 752
11 of 21
If the output power of inverter is above PU, LLC converter operates in the full-bridge mode. If
the output power of inverter is below PL, LLC converter operates in half-bridge mode. Otherwise, the
the mode
the same.
Furthermore,
is a smaller
little smaller
order
tocontinuous
avoid continuous
U , into
mode
staysstays
the same.
Furthermore,
PL is aPLlittle
than Pthan
U, in P
order
avoid
power
power
fluctuations
around
the
transition
gap.
fluctuations around the transition gap.
Figure
Figure 9.
9. Hysteresis
Hysteresis controller
controller for
for the
the transform
transform signal
signal generation.
generation.
Energies 2017,
10, 752 Scheme in on-Line Mode
5.1. Proposed
Control
11 of 21
As
in Figure
10,inUon-Line
the reference of the 400 V DC bus voltage, IL1 and IL2 are the
5.1.illustrated
Proposed Control
Scheme
Mode
400_ref is
resonant inductor
RMS currents of each channel, f 1 andoff 2the
are400
theVworking
frequencies of each channel.
As illustrated in Figure 10, U400_ref is the reference
DC bus voltage, IL1 and IL2 are the
When
SIGNAL_FH
is
0,
the
converter
is
transformed
into
half-bridge
mode.of The
resonant inductor RMS currents of each channel, f1 and f2 are the working frequencies
each frequency
channel. of
two LLC resonant
converters
change is
ontransformed
the basis ofinto
fh_onhalf-bridge
. Then a dead
band
When SIGNAL_FH
is start
0, theto
converter
mode.
The controller
frequency is
of used
to control
the resonant
400 V DC
bus voltage.
If change
the 400onVthe
DCbasis
bus of
voltage
U400
is lower
(U400_ref
− ∆U1 ),
two LLC
converters
start to
fh_on. Then
a dead
bandthan
controller
is used
to control the
400
V DC busby
voltage.
the 400lower
V DC bus
U400 is 400
lower
(U400_ref
− ΔU1),Ifthe
the frequencies
are
increased
∆f 1 , toIf attain
gainvoltage
and higher
V than
DC bus
voltage.
U400 is
frequencies
are
increased
by
Δf
1
,
to
attain
lower
gain
and
higher
400
V
DC
bus
voltage.
If
U
400
is
higher
higher than (U400_ref + ∆U1 ), the frequencies are altered by ∆f 1 , to attain higher gain and lower voltage.
than
(U400_ref
ΔU
1), the frequencies are altered by Δf1, to attain higher gain and lower voltage. In this
In this
paper
∆f 1+ is
defined
as:
paper Δf1 is defined as: 
 −k1 · U400 − U400_re f
U400 − U400_re f ≥ ∆U1

−
k
⋅
U
−
U
U
−
U
≥
Δ
U
∆ f1 =
(28)
400 _ ref )
400 _ ref
 1 ( 400
400
1

Δf1 0= 
(28)
U400 − U400_re f < ∆U1
U 400 − U 400 _ ref < ΔU1
0
When SIGNAL_FH is 1, the gate signals of Q3 and Q4 return to normal. The LLC resonant
SIGNAL_FH
is 1, the
gatewith
signals
of Q3 and
Q4 return
to normal.
The LLC isresonant
converterWhen
operates
in full-bridge
mode
an initial
frequency
of ff_on
. The controller
similar; the
converter operates in full-bridge mode with an initial frequency of ff_on. The controller is similar; the
difference is that the step of the dead-band control scheme of DC bus voltage is ∆f 2 :
difference is that the step
control scheme
of the dead-band
is Δf2:
of DC bus voltage
 −k2 · U400 − U400_re f
−
U
U
400
400_re f ≥ ∆U1
 − k 2 ⋅ (U 400 − U 400 _ ref )
U
400 − U 400 _ ref ≥ Δ U
1
∆ f 2 = Δf =
(29)
(29)
 02 
−
U
U
400
400_re
f
U −U
< ΔU < ∆U1
0

400
400 _ ref
1
k1 and
constant,
they
are
selected
thefast
fastresponse
response
and
stability
requirements.
2 are
k1 kand
k2 are
constant,
they
are
selectedby
by considering
considering the
and
stability
requirements.
Figure 10. LLC control scheme in on-line mode.
Figure 10. LLC control scheme in on-line mode.
Simultaneously, another dead-band controller works to balance the two LLC currents. In Figure 10,
the step of Δf3 is constant and in fact very small, so the allowable error scope ΔI is 0.02|IL1 − IL2|. If
resonant inductor RMS current of first channel LLC is bigger than that of second channel LLC, and
the error is over ΔI, working frequency of first channel LLC is increased by Δf3 and working frequency
of second channel LLC is decreased by Δf3. On the contrary, the working frequency of first channel
Energies 2017, 10, 752
12 of 21
Simultaneously, another dead-band controller works to balance the two LLC currents. In Figure 10,
the step of ∆f 3 is constant and in fact very small, so the allowable error scope ∆I is 0.02|IL1 − IL2 |.
If resonant inductor RMS current of first channel LLC is bigger than that of second channel LLC,
and the error is over ∆I, working frequency of first channel LLC is increased by ∆f 3 and working
frequency of second channel LLC is decreased by ∆f 3 . On the contrary, the working frequency of first
channel LLC is decreased by ∆f 3 and the working frequency of second channel LLC is increased by
∆f 3 Otherwise, when the error between two RMS currents is over −∆I and below ∆I, which means
two resonant currents are almost balanced, this dead band controller of current sharing doesn’t work.
By use of fixed step of ∆f 3 in dead band controller, resonant currents may not be exactly the same.
However, in practical application RMS values of resonant currents need not to be identical. Also,
the dead band controller is simple and can make LLC converter more stable.
5.1.1. Transfer Conditions between Half-Bridge and Full-Bridge Mode
Assuming the efficiency of inverter is η, the output voltage of LLC converters is U630_ref ,
the equivalent output resistance for each LLC, RP could be expressed as:
RP =
2U 2 630_re f · η
Pinv
(30)
According to load range selection criteria, to make sure that the transition between half-bridge and
full-bridge mode is smooth, the LLC output resistance should satisfy Equations (24)–(27), that means:

2
 max{ R , R } ≤ 2U 630_re f ·η ≤ min{ R , R }
2_H
2_F
1_H
1_F
PL
(31)
 max{ R , R } ≤ 2U 2 630_re f ·η ≤ min{ R , R }
1_H
1_F
PU
2_H
2_F
where R1_F , R1_H are the minimum solutions to (25) and (26), and R2_F , R2_H are the maximum solution
to (24) and (27). The selection of PL and PU should meet (31).
5.1.2. Initial Working Frequency Selection
At beginning of each working mode (full-bridge or half-bridge mode), a proper initial operating
frequency is necessary to get a smooth transition performance. As is shown in Figure 10, when the
converter changes from half-bridge mode to full-bridge mode, the initial frequency ff_on is the solution
!
to the following equation:
2U 2 630_re f
, C pc = Gr
(32)
G pc f f _on ,
Pinv_rate
Pinv_rate is the rated output power of the inverter, and 2(U630_ref )2 /Pinv_rate is the corresponding
equivalent output resistance of each LLC. When the converter changes from full-bridge mode to
half-bridge mode, the initial frequency fh_on could be calculated as:
!
2U 2 630_re f
GH_pc f h_on ,
, C pc = Gr
(33)
PL
5.2. Simulation Results in On-Line Mode
In order to verify the proposed design scheme, a simulation model is fulfilled in MATLAB.
The main simulation parameters are listed in Table 1. To simplify the model and shorten the running
time of simulation, only battery is used as source here. To verify the proposed current sharing strategy,
the different resonant tank parameters of two channels are given deliberately.
To describe the current sharing result, a parameter named current unbalance factor (CUF) is
given, which can be defined as absolute value of error between two resonant RMS currents divided by
average value of two resonant RMS currents. CUF = |2(IL1 − IL2 )/( IL1 + IL2 )|.
The simulation results in on-line mode are shown in Figure 11. iBattery is the current of battery,
iA is inverter output current of phase A. u400 , u630 are the same as 400 V DC bus voltage U400 and 630
Energies 2017, 10, 752
First channel LLC Magnetizing inductor, Lm1
Second channel LLC resonant inductor, Lr2
Second channel LLC resonant capacitor, Cr2
Second channel LLC Magnetizing inductor, Lm2
400 V DC bus capacitor
630 V DC bus capacitor
AC bus voltage
228 μH
65 μH
68 nF
223 μH
200 μF
200 μF
380 V (phase to phase)
13 of 21
V DC bus
voltage U
, but u400
, u630 represent
instantaneous
values
in this
article. factor
According
To describe
the
sharing
result, a parameter
named
current
unbalance
(CUF)toisthe
630current
given,scheme,
which can
as absolute
of errorand
between
resonantbyRMS
control
u400beisdefined
controlled
by LLCvalue
converters,
u630 istwo
controlled
the currents
inverter.divided
by average value of two resonant RMS currents. CUF = |2(IL1 − IL2)/( IL1 + IL2)|.
Table
1. Simulation
The simulation results in on-line
mode
are shownParameters.
in Figure 11. iBattery is the current of battery, iA
is inverter output current of phase A. u400, u630 are the same as 400 V DC bus voltage U400 and 630 V
Value
DC bus voltage U630, but u400, uParameter
630 represent instantaneous values in this
article. According to the
control scheme, u400 isLLC
controlled
by
LLC
converters,
and
u
630
is
controlled
by
the inverter.
main resonant frequency, fr
78.8 kHz
In Figure 11a, LLC
the reference
the battery
current
s, and
secondaryof
resonant
frequency,
fr2is 3 A before 1.336.0
kHzthe two LLC resonant
channel LLC
resonant
inductor,
60 µHwith no ripple. At 1.3 s,
r1 voltage is regulated
converters operateFirst
in half-bridge
mode.
The 400
V DCLbus
First
channel
LLC
resonant
capacitor,
C
68 nFof the inverter increase
r1
the reference of battery current increases by 12 A/s, so the output currents
First channel LLC Magnetizing inductor, Lm1
228 µH
accordingly. At 1.5 s, the LLC resonant converters begin to operate in full-bridge mode, and their
Second channel LLC resonant inductor, Lr2
65 µH
frequencies are set
to ff_on
. During
this
transition,
the 400
quickly, and the
Second
channel
LLC
resonant
capacitor,
Cr2V DC bus voltage
68 recovers
nF
minimum voltage
during
the
transition
is
386
V.
After
approximately
3
s,
the
reference
of the battery
Second channel LLC Magnetizing inductor, Lm2
223 µH
current arrives at 37.5 A, and
remains
400 V
DC busunchanged.
capacitor The entire system is stable
200 µFand the 400 V DC bus
V DCFigure
bus capacitor
200 µF results at light load
voltage is flat during this 630
period.
11b shows the steady state simulation
380 V (phase to phase)
condition (half bridge mode), AC
andbus
thevoltage
400 V DC bus voltage is stable.
(a)
(b)
Figure 11. Simulation results in on-line mode: (a) transition waveforms; and (b) steady state waveforms
Figure 11. Simulation results in on-line mode: (a) transition waveforms; and (b) steady state waveforms
with light load.
with light load.
Figure 12 shows the current sharing results of LLC resonant converters with 0 to 7 kW load in
In Figure
thes,reference
ofLLC
the transforms
battery current
is 3 A before
1.3
s, figure
and the
resonant
on-line
mode.11a,
At 1.5
half-bridge
into full-bridge
LLC.
The
in two
innerLLC
box shows
converters
operatewaveforms
in half-bridge
mode.
The
400
V DCthat
bustwo
voltage
is regulated
with no ripple.
1.3 s,
detailed current
around
2.55
s. It
proves
full-bridge
LLC converters
workAt
with
theworking
reference
of batteryabove
current
by 12 A/s,
so thefroutput
therequired
invertergain
increase
frequencies
theincreases
main resonant
frequency
. This iscurrents
becauseof
the
is
accordingly.
At 1.5 above
s, the fLLC
resonant
in full-bridge
and their
achieved slightly
r, making
full converters
use of dropbegin
scopeto
ofoperate
gain curve,
as the lastmode,
paragraph
in
Section 4.2.1
values
two LLC resonant
both 9.6
A in the
box, CUF
frequencies
areshows.
set to fThe
During
thisoftransition,
the 400 Vcurrents
DC busare
voltage
recovers
quickly,
andisthe
f_on .RMS
minimum voltage during the transition is 386 V. After approximately 3 s, the reference of the battery
current arrives at 37.5 A, and remains unchanged. The entire system is stable and the 400 V DC bus
voltage is flat during this period. Figure 11b shows the steady state simulation results at light load
condition (half bridge mode), and the 400 V DC bus voltage is stable.
Figure 12 shows the current sharing results of LLC resonant converters with 0 to 7 kW load
in on-line mode. At 1.5 s, half-bridge LLC transforms into full-bridge LLC. The figure in inner box
shows detailed current waveforms around 2.55 s. It proves that two full-bridge LLC converters work
with working frequencies above the main resonant frequency fr . This is because the required gain
is achieved slightly above fr , making full use of drop scope of gain curve, as the last paragraph in
Section 4.2.1 shows. The RMS values of two LLC resonant currents are both 9.6 A in the box, CUF is
almost 0. The result indicates that in on-line mode, the proposed current sharing method can balance
currents at light and full load condition, even during load transition process.
Energies 2017, 10, 752
14 of 21
almost
0.2017,
The
result
Energies
752 indicates that in on-line mode, the proposed current sharing method can14balance
of
Energies
2017,
10,10,
752
14 21
of 21
currents at light and full load condition, even during load transition process.
almost 0. The result indicates that in on-line mode, the proposed current sharing method can balance
currents at light and full load condition, even during load transition process.
Figure 12.
12. Two
channel LLC
LLC currents
currents in
in on-line
on-line mode
mode during
during load
load transition
transition from
from 00 to
to 77kW
kWload.
load.
Figure
Two channel
Figure 12. Two channel LLC currents in on-line mode during load transition from 0 to 7 kW load.
5.3. Proposed
Proposed Control
Control Scheme
Scheme in
in Off-Line
Off-Line Mode
Mode
5.3.
5.3. Proposed Control Scheme in Off-Line Mode
In off-line
off-line mode,
mode, the
the DC
DC bus
bus voltage
voltage control
control and
and current
current sharing
sharing strategy
strategy of
of the
the LLC
LLC resonant
resonant
In
In
off-line
mode,
the
DC
bus
voltage
control
and
current
sharing
strategy
of
the
LLC
resonant
converter is
the
DC
bus
voltage
which
is controlled
by the
converter
is similar
similar to
tothe
thestrategy
strategyininon-line
on-linemode,
mode,but
but
the
DC
bus
voltage
which
is controlled
by
converter
is similar
to theisstrategy
in V
on-line
mode,
but the
DC
bus voltage
which
is bus
controlled
byU
the
LLC
resonant
converters
the
630
DC
bus
voltage
U
630, and
the
400
V
DC
voltage
400 is
the LLC resonant converters is the 630 V DC bus voltage U630 , and the 400 V DC bus voltage U400
is
LLC resonant
converters
is
the 630
V DCand
busdischarge
voltage Umanagement
630, and the 400 V DC bus voltage U400 is
controlled
by
the
forestage
storage
charge
converter.
The
architecture
in
controlled
by the
forestage
storage charge
and
managementconverter.
converter.The
The
architecture
controlled
the
forestage
charge
and discharge
discharge
management
architecture
in in
Figure
13 and
andbyparameters
parameters
of storage
the entire
entire
simulation
model are
are similar
similar with
with on-line
on-line mode,
mode,
so the
the details
details
Figure
13
of
the
simulation
model
so
13 and parameters of the entire simulation model are similar with on-line mode, so the details
areFigure
not given
given
here repeatedly.
repeatedly.
are
not
here
are
not given
here repeatedly.
Figure13.
13. LLC
LLC control
control scheme
Figure
schemein
inoff-line
off-linemode.
mode.
Figure
13. LLC
control scheme
in
off-line
mode.
SimulationResults
ResultsininOff-Line
Off-LineMode
Mode
5.4.5.4.
Simulation
5.4.
Simulation
Results in
Off-Line Mode
In Figure 14a, prior to 1 s, AC load is 50 W, and LLC converter works in half-bridge mode.
In Figure
Figure 14a, prior
prior to
to 11 s,
s, AC
AC load
load is
is 50 W,
W, and
and LLC
LLC converter works
works in
in half-bridge
half-bridge mode.
In
The
630 V DC14a,
bus voltage
is regulated
with 50
no ripple.
At 1 s,converter
the AC load changes
to 7 kW, so mode.
the
The
630
V
DC
bus
voltage
is
regulated
with
no
ripple.
At
1
s,
the
AC
load
changes
to 77 kW,
kW, so the
the
The
630resonant
V DC bus
voltage
is regulated
with
no ripple.
At 1and
s, the
AC load
changes
to
LLC
converter
begins
to work in
full-bridge
mode,
frequency
is set
initially.
During so
this
LLC
resonant
converter
begins
to
work
in
full-bridge
mode,
and
frequency
is
set
initially.
During
this
LLC
resonantthe
converter
to work
in full-bridge
and frequency
is set
During
this
transition,
630 V DCbegins
bus voltage
recovers
in 50 ms,mode,
the settling
time is 24 ms,
theinitially.
minimum
voltage
transition,
the
630
V
DC
bus
voltage
recovers
in
50
ms,
the
settling
time
is
24
ms,
the
minimum
voltage
transition,
thetransition
630 V DCisbus
recovers
in 50 voltage
ms, the is
settling
is 24 ms,
the minimum
voltage
during the
586voltage
V, and the
maximum
641 V. time
The entire
system
is stable during
during
thetransition
transition
586 V,and
andthe
the simulation
maximum
voltage islight
641
V.
The
entire
system
is stable
during
during
the
isis586
voltage
V. The
system
is stable
the transition.
Figure
14bV,shows
themaximum
resultsisat641
loadentire
condition
(half
bridgeduring
mode).the
the
transition.
Figure
14b
shows
the
simulation
results
at
light
load
condition
(half
bridge
mode).
630 V DCFigure
bus voltage
is regulated
smoothly.results at light load condition (half bridge mode). 630 V
transition.
14b shows
the simulation
630
V
DC
bus
voltage
is
regulated
smoothly.
Figure
15
shows
the
current
sharing
results of LLC resonant converters during load transition
DC bus voltage is regulated smoothly.
Figure
15
shows
the
current
sharing
results
of
LLC
resonantcurrents
converters
during
load27.0
transition
from
0 to 15
7 kW
in off-line
mode. sharing
The peakresults
valuesof
ofLLC
two resonant
resonant
are during
27.6 A and
A as
Figure
shows
the current
converters
load
transition
from
0
to
7
kW
in
off-line
mode.
The
peak
values
of
two
resonant
currents
are
27.6
A
and
27.0 A
A as
as
from 0 to 7 kW in off-line mode. The peak values of two resonant currents are 27.6 A and 27.0
Energies 2017, 10, 752
Energies 2017, 10, 752
15 of 21
15 of 21
Energies 2017, 10, 752
15 of 21
Figure 15
15shows.
shows.The
Thefigure
figure
inner
shows
detailed
current
waveforms
around
RMS
Figure
in in
inner
boxbox
shows
detailed
current
waveforms
around
1.23 s. 1.23
RMSs.values
values
of two
LLC resonant
currents
are
11.8shows
with
7 kW
load.
Theindicate
results indicate
the proposed
of
two
LLC
currents
arein11.8
A with
7AkW
load.
The
results
thataround
the that
proposed
Figure
15resonant
shows.
The
figure
inner
box
detailed
current
waveforms
1.23
s. scheme
RMS
Energies 2017, 10, 752
15 of 21
values
ofcurrents
two
LLCcurrents
resonant
currents
are 11.8
A with
7 and
kW
load.
The
results
indicate that the proposed
scheme
can
divide
evenly
during
transition
at full
load
condition.
can
divide
evenly
during
transition
and
at full
load
condition.
scheme
evenly
during
and atcurrent
full load
condition.around 1.23 s. RMS
Figurecan
15 divide
shows. currents
The figure
in inner
boxtransition
shows detailed
waveforms
values of two LLC resonant currents are 11.8 A with 7 kW load. The results indicate that the proposed
scheme can divide currents evenly during transition and at full load condition.
(a)
(a)
(b)
(b)
Figure
14.14.
Simulation
ininoff-line
off-line
mode:
waveforms;and
and(b)
(b)steady
steady
state
waveforms
Figure
14.
Simulation
results
in
(a)
transition
waveforms;
and
(b)
steady
state
waveforms
Figure
Simulationresults
results(a)
off-linemode:
mode: (a)
(a) transition
transition waveforms;
state
waveforms
(b)
with
light
load.
with
light
load.
with
light
load.
Figure 14. Simulation results in off-line mode: (a) transition waveforms; and (b) steady state waveforms
with light load.
Figure
Twochannel
channelLLC
LLCcurrents
currentsin
in off-line
off-line mode during
Figure
15.15.Two
duringload
loadtransition
transitionfrom
from0 0toto7 kW.
7 kW.
Figure
15. Two
channel
LLC
modeduring
during
load
transition
to 7 kW.
Figure
15. Two
channel
LLCcurrents
currentsin
in off-line
off-line mode
load
transition
fromfrom
0 to 70 kW.
6. Experimental
Results
6.
Results
6. Experimental
Experimental
Results
6. Experimental
Results
The
proposed
controlscheme
schemeofofthe
thefull-bridge
full-bridge LLC
LLC converters
isisverified
in a a7 7kW
residential
The
proposed
control
converters
The
proposed
control
schemeofofthe
thefull-bridge
full-bridge LLC
is verified
in ain
7 kW
residential
The
proposed
control
scheme
LLCconverters
converters
is verified
verified
in
a 7 kW
kW residential
residential
PV
system.
Figure
16
shows
the
prototype
system.
PV
Figure
16
the
prototype
PV system.
Figure
16 shows
the
prototypesystem.
system.
PV system.
system.
Figure
16 shows
shows
the
prototype
system.
Figure 16. 7 kW residential photovoltaic system hardware setup.
Figure16.
16.77kW
kWresidential
residential photovoltaic
photovoltaic system
Figure
systemhardware
hardwaresetup.
setup.
Figure 16. 7 kW residential photovoltaic system hardware setup.
Energies
Energies2017,
2017,10,
10,752
752
16
16 of
of 21
21
Design criteria and key components are listed in Table 2.
Design criteria and key components are listed in Table 2.
Table 2. Experimental parameters.
Table 2. Experimental parameters.
Parameter
Value
Parameter
Value
LLC rated power
4 kW (one
channel)
LLC main
frequency, fr1
78.8
kHz
LLC resonant
rated power
4 kW
(one
channel)
LLC
resonant
frequency,
36.0
LLCsecondary
main resonant
frequency,
fr1 fr2
78.8kHz
kHz
60
μH
LLC resonant
inductor,
Lr fr2
LLC secondary
resonant
frequency,
36.0
kHz
LLC
Lr Cr
µH
6860nF
LLCresonant
resonantinductor,
capacitor,
LLC
capacitor,
Cr Lm
nF
LLC resonant
Magnetizing
inductor,
22868μH
LLC
Magnetizing
inductor,
L
228
m
LLC MOSFET (primary side)
IPW65R045C7 (Infineon,µH
Munich, Germany)
LLC
MOSFET
(primary
side)
IPW65R045C7
(Infineon,
Munich,America)
Germany)
LLC diode rectifier (secondary side)
C4D10120E
(Cree,
Durhmorning,
LLC diode rectifier (secondary side)
C4D10120E (Cree, Durhmorning, America)
Battery voltage
100 V DC
Battery voltage
100 V DC
PV maximum power
3.5 kW
PV maximum power
3.5 kW
400
DC
bus
capacitor
200
400
VV
DC
bus
capacitor
200μFµF
630
V
DC
bus
capacitor
200
630 V DC bus capacitor
200μFµF
AC
bus
voltage
380
AC
bus
voltage
380VV(phase
(phasetotophase)
phase)
12.5
coefficient
coefficient
k 1 k1
12.5Hz/V
Hz/V
coefficient
k 2 k2
62.5Hz/V
Hz/V
62.5
coefficient
Step3,
∆f Δf
500Hz
Hz
3 3
500
Step3,
The PV
PVarrays
arrays
replaced
a chroma62150H-1000S
programmable
DCsupply
power(Chroma,
supply
The
areare
replaced
by a by
chroma62150H-1000S
programmable
DC power
(Chroma,
Taoyuan,
Taiwan)
with
PV
simulator.
The
maximum
output
power
of
the
PV
Taoyuan, Taiwan) with PV simulator. The maximum output power of the PV array simulator is 3.5array
kW.
simulator
is 3.5 kW.
The comparison
betweenand
original
waveforms and
the optimization
The
comparison
between
original waveforms
the optimization
waveforms
after usingwaveforms
proposed
after using
proposed
method
is also discussed.
Furthermore,
in order to
the availability
control
method
is also control
discussed.
Furthermore,
in order to
verify the availability
ofverify
the proposed
control
of
the
proposed
control
method
under
real
household
loads
such
as
air
conditioner,
microwave
and
method under real household loads such as air conditioner, microwave and refrigerator, experiments
refrigerator,
experiments
real household
loads are carried out.
with
real household
loads with
are carried
out.
6.1. Experimental
Experimental Results
Results in
in On-Line
On-Line Mode
Mode
6.1.
In this
this mode,
mode, the
the control
controlobject
objectisisuu400
400. Figure
with the
the original
original
In
Figure 17 shows the experimental results with
controlmethod
methodin
inon-line
on-linemode.
mode.AAsteady-state
steady-stateerror
errorofof−−25
Vexists
existsin
inuu400
400. After increasing the
the load
load
control
25 V
from 00 to
to 77 kW,
kW,there
thereisisaapulse
pulseof
of437
437VVand
andfluctuation
fluctuationduring
duringtransition.
transition. The
The settling
settling time
time is
is about
about
from
0.35 s.
s. The
The current
current balance
balance is
is out
out of
of control
control during
during transition
transitionprocess.
process.
0.35
Figure 17. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original
Figure 17. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original
control method.
method.
control
Figures 18 and 19 show the experimental results with proposed control scheme in on-line mode.
Figures
and 19
show
the experimental
results withfrom
proposed
control
in on-line
In Figure
18,18
during
the
transition
of the LLC converters
0 to 7 kW,
thescheme
fluctuation
of 400mode.
V DC
In
Figure
18,
during
the
transition
of
the
LLC
converters
from
0
to
7
kW,
the
fluctuation
of
400
V
DC
bus voltage is only −14 V, and the settling time can be neglected. The currents of the two LLC resonant
inductors are shared evenly at last, with RMS of 12.2 A and 12.0 A. The CUF is about 1.7%.
Energies 2017, 10, 752
17 of 21
bus voltage is only −14 V, and the settling time can be neglected. The currents of the two LLC resonant
inductors
are
evenly at last, with RMS of 12.2 A and 12.0 A. The CUF is about 1.7%.
Energies 2017,
10,shared
752
17 of 21
Energies 2017, 10, 752
17 of 21
Figure 18. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original
Figure
18.18.Waveforms
kW in
in on-line
on-line mode
modewith
withthe
theoriginal
original
Figure
WaveformsofofAC
ACload
load increases
increases from
from 0 to 7 kW
control method.
control
method.
control
method.
Figure 19. Waveforms of AC load transition from 7 kW to 0 in on-line mode with the new
Figure
19. Waveforms
Figure
19.
Waveforms of
of AC
AC load
load transition
transition from
from 77 kW
kW to 0 in on-line mode with the new
control scheme.
control scheme.
scheme.
control
Figure 19 shows a similar result when the AC load decreases from 7 kW to 0. For 400 V DC bus
Figure 19
19 shows aa similar
similar result
result when
when the
the AC
AC load
load decreases
decreases from 77 kW
kW to
to 0.
0. For
For 400
400 V
V DC
DC bus
bus
Figure
voltage,
the shows
maximum voltage
drop is 18 V
and the
peak value is from
422 V. What
needs
illustration
is
voltage, the
themaximum
maximumvoltage
voltagedrop
dropisis1818
V
and
peak
value
is 422
V. What
needs
illustration
is
voltage,
and
thethe
peak
value
422
V. What
needs
illustration
is that
that u630 is
controlled by inverter
and V
the
control
method
isisnot
optimized.
As space
is limited,
that
u
630 is controlled by inverter and the control method is not optimized. As space is limited,
u630although
is controlled
by inverter
control
method
notdiscuss
optimized.
As space
is limited, although
the fluctuation
of uand
630 isthe
a little
large,
we willisnot
this problem
here.
although
the
fluctuation
of
u
630 is a little large, we will not discuss this problem here.
the fluctuation of u630 is a little large, we will not discuss this problem here.
6.2. Experimental Results in Off-Line Mode
6.2. Experimental
Experimental Results
Results in
in Off-Line
Off-Line Mode
Mode
6.2.
In this mode, the control object of LLC is u630. Figure 20 shows experimental results with the
In this
thiscontrol
mode,method
the control
control
objectmode.
of LLC
LLC
630.. Figure
Figure
20 shows
shows
experimental
results
with
the
original
in off-line
Atisis
nouu630
load
condition,
the controller
works in
burstwith
mode.
In
mode,
the
object
of
20
experimental
results
the
original
control
method
in
off-line
mode.
At
no
load
condition,
the
controller
works
in
burst
mode.
The
voltage
ripple
is
about
50
V,
and
the
peak
value
is
about
693
V.
During
the
transition
from
0
to
7
original control method in off-line mode. At no load condition, the controller works in burst mode.
ThekW,
voltage
ripple
about
V,
peak
value
693
transition
in theripple
worst is
case,
the 50
maximum
voltage
is is
about
211
V. V.
The
settlingthe
time
is 0.63 s.from
The
voltage
is
about
50
V, and
and the
the
peakdrop
value
isabout
about
693
V.During
During
the
transition
from0 0toto7
the
maximum
voltage
isisabout
time
isis0.63
Figures
21case,
and
show
the experimental
results
with211
the
proposed
control
method
ins.s.off-line
7kW,
kW,ininthe
theworst
worst
case,22
the
maximum
voltagedrop
drop
about
211V.
V.The
Thesettling
settling
time
0.63
mode.
As
shown
in
Figure
21,
when
AC
load
increases
from
0
to
7
kW,
with
the
proposed
Figures
21
and
22
show
the
experimental
results
with
the
proposed
control
method
incontrol
off-line
Figures 21 and 22 show the experimental results with the proposed control method in
off-line
scheme,
the
630
V
DC
bus
voltage
declines
to
589
V
during
the
transition
and
recovers
after
21
ms.
mode. As
to 77 kW,
kW, with
with the
the proposed
proposed control
control
mode.
As shown
shown in
in Figure
Figure 21,
21, when
when AC
AC load
load increases
increases from
from 00 to
The
peak
voltage
is
642
V.
The
maximum
CUF
is
about
0.7%.
The
experimental
results
are
scheme, the
the 630
630 V
V DC
DC bus
bus voltage
voltage declines
declines to
to 589
589 V
V during
during the
the transition
transition and
ms.
scheme,
and recovers
recovers after
after 21
21in
ms.
consistent
with simulation
results.
Figure 22
shows
the experimental
waveforms with
AC load
The
peak
voltage
is
642
V.
The
maximum
CUF
is
about
0.7%.
The
experimental
results
are
in
The peak voltage is 642 V. The maximum CUF is about 0.7%. The experimental results are in consistent
variation
from
7
kW
to
2.3
kW
to
0.
The
630
V
DC
bus
voltage
fluctuation
is
only
about
10
V
during
consistent
with results.
simulation
results.
Figure
shows the waveforms
experimental
waveforms
with AC from
load
with
simulation
Figure
22 shows
the22
experimental
with
AC load variation
transition.
variation
from
7
kW
to
2.3
kW
to
0.
The
630
V
DC
bus
voltage
fluctuation
is
only
about
10
V
during
7 kW to 2.3 kW to 0. The 630 V DC bus voltage fluctuation is only about 10 V during transition.
transition.
Energies 2017, 10, 752
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2017, 10,
10, 752
752
Energies
Energies 2017, 10, 752
18 of 21
18 of
of 21
21
18
18 of 21
Figure20.
20. Waveforms
Waveforms of
of AC
AC load
loadincreases
increases from
from000toto
to777kW
kWinin
inoff-line
off-linemode
modewith
withthe
theoriginal
original
Figure
Figure
20.
Waveforms
of
AC
load
increases
from
kW
off-line
mode
with
the
original
Figure 20. Waveforms of AC load increases from 0 to 7 kW in off-line mode with the original
control
method.
control
controlmethod.
method.
control method.
Figure 21.
21. Waveforms
Waveforms of
of AC
AC load
load transition
transition from
from 00 to
to 77 kW
kW in
in off-line
off-line mode.
mode.
Figure
Figure
Figure21.
21.Waveforms
WaveformsofofAC
ACload
loadtransition
transitionfrom
from0 0toto7 7kW
kWininoff-line
off-linemode.
mode.
Figure 22.
22. Waveforms
Waveforms of
of AC
AC load
load transition
transition from
from 77 kW
kW to
to 2.3
2.3 kW
kW to
to 00 in
in off-line
off-line mode.
mode.
Figure
Figure22.
22.Waveforms
WaveformsofofAC
ACload
loadtransition
transitionfrom
from7 7kW
kWtoto2.3
2.3kW
kWtoto0 0ininoff-line
off-linemode.
mode.
Figure
6.3. Experimental
Experimental Results
Results with
with Real
Real Household
Household Load
Load
6.3.
6.3.
Experimental Results
with Real
Household Load
6.3. Experimental Results with Real Household Load
In order
order to
to verify
verify the
the availability
availability of
of the
the improved
improved control
control method
method for
for the
the residential
residential PV
PV system,
system,
In
In
order to
verify the
availability of
the improved
control method
for the
residential PV
system,
experiments
are
conducted
with
real
household
loads.
Here
the
400
V
DC
bus
voltage
and
the
630 V
V
In order to
verify
the availability
the improved
method
PVthe
system,
experiments
are
conducted
with real
real of
household
loads.control
Here the
the
400 V
Vfor
DCthe
busresidential
voltage and
and
630
experiments
are
conducted
with
household
loads.
Here
400
DC
bus
voltage
the 630
V
DC bus
bus voltage
voltage
are observed
observed
through
a real
real time
time
sampling
device,
uVSIGNAL400
SIGNAL400
represents
400the
V DC
DC
bus
experiments
are conducted
with
real household
loads.
Here device,
the 400 u
DC bus
voltage and
630bus
V
DC
are
through
sampling
represents
400
V
DC
bus voltage
are
observed through
aa real
time sampling
device, u
SIGNAL400 represents 400 V DC bus
voltage,
and
u
SIGNAL630
represents
630
V
DC
bus
voltage.
DC
bus
voltage
are
observed
through
a
real
time
sampling
device,
u
represents
400
V
DC
bus
SIGNAL400
voltage, and
and u
uSIGNAL630
SIGNAL630 represents 630 V DC bus voltage.
voltage,
represents 630 V DC bus voltage.
voltage, and uSIGNAL630 represents 630 V DC bus voltage.
6.3.1. Experimental
Experimental Results
Results with
with Air
Air Conditioner
Conditioner in
in On-Line
On-Line Mode
Mode
6.3.1.
6.3.1.
ExperimentalResults
Resultswith
withAir
AirConditioner
Conditionerinin
On-LineMode
Mode
6.3.1.
Experimental
On-Line
A 4-kW
4-kW air
air conditioner
conditioner is
is used
used as
as an
an AC
AC load
load in
in on-line
on-line mode.
mode. Figure
Figure 23
23 shows
shows the
the transient
transient
A
A
4-kWair
airconditioner
conditionerisis
usedasas
anAC
ACload
loadinin
on-linemode.
mode.Figure
Figure2323
showsthe
thetransient
transient
A
4-kW
used
an
on-line
shows
waveforms when
when the
the air
air conditioner
conditioner is
is shutdown.
shutdown. During
During this
this transition,
transition, the
the currents
currents of
of LLC
LLC and
and
waveforms
waveforms
whenslowly,
theair
airconditioner
conditioner
shutdown.
During
thistransition,
transition,
themode.
currents
LLC
and
waveforms
when
the
isisconverter
shutdown.
During
this
the
currents
ofof400
LLC
and
inverter
decline
and
the
LLC
always
works
in
full-bridge
The
V
and
inverter decline
decline slowly,
slowly, and
and the
the LLC
LLC converter
converter always
always works
works in
in full-bridge
full-bridge mode.
mode. The
The 400
400 V
V and
and
inverter
inverter
decline
slowly,
and
the
LLC
converter
always
works
in
full-bridge
mode.
The
400
V
and
630
V
630 V
V DC
DC bus
bus voltage
voltage are
are flat
flat and
and the
the entire
entire system
system is
is stable.
stable. Here
Here iiL1
L1 is current of first channel LLC
630
is current
current of
of first
first channel
channel LLC
LLC
630
V DC
bus voltage
are the
flat entire
and the
entireissystem
is stable.
Here
iL1 is
DC
bus
voltage
are
flat
and
system
stable.
Here
i
is
current
of
first
channel
LLC
resonant
resonant inductor,
inductor, and
and iA is
is inverter
inverter output
output current
current of
of phase
phase
A.
L1 A.
resonant
resonant
inductor,
and iiAA is
inverter
output
inductor,
and
iA is inverter
output
current
of current
phase A.of phase A.
Energies 2017, 10, 752
Energies 2017, 10, 752
19 of 21
19 of 21
Figure23.
23.Waveforms
Waveformswhen
when4 4kW
kWair
airconditioner
conditionershutdown
shutdownininon-line
on-linemode.
mode.
Figure
6.3.2. Experimental Results with Microwave and Refrigerator in Off-Line Mode
6.3.2. Experimental Results with Microwave and Refrigerator in Off-Line Mode
In order to verify the impact loading response ability of the proposed control method, a 1.5 kW
In order to verify the impact loading response ability of the proposed control method, a 1.5 kW
microwaveoven
ovenand
and
a 200
refrigerator
used.
Figure
shows
waveforms
during
turningmicrowave
a 200
WW
refrigerator
areare
used.
Figure
24 24
shows
thethe
waveforms
during
turning-on
on
operations
of
the
two
loads.
The
630
V
DC
bus
voltage,
phase
voltage
of
inverter
and
first
channel
operations of the two loads. The 630 V DC bus voltage, phase voltage of inverter and first channel
LLC
LLC working frequency, are observed through the same real time sampling device. Here uSIGNALA
working frequency, are observed through the same real time sampling device. Here uSIGNALA represents
represents
phasef A voltage,
fSIGNALs1 represents working frequency of first channel LLC. During this
phase
A voltage,
SIGNALs1 represents working frequency of first channel LLC. During this period,
period,
LLC
transforms
from
to full-bridge
as its
workingshows,
frequency
shows, uto630
LLC transforms from half-bridgehalf-bridge
to full-bridge
mode as itsmode
working
frequency
u630 declines
declines
555 V and
after
30 ms,
the steady
about
60 V. current
the distorted
current
555
V andto
recovers
afterrecovers
30 ms, the
steady
fluctuation
is fluctuation
about 60 V. is
The
distorted
is caused
by
is
caused
by
the
microwave
and
refrigerator,
which
don’t
have
power
factor
correction
ability.
The
the microwave and refrigerator, which don’t have power factor correction ability. The entire system
entire system is stable.
is stable.
Figure 24. Waveforms when turn on microwave oven and refrigerator in off-line mode.
Figure 24. Waveforms when turn on microwave oven and refrigerator in off-line mode.
7. Conclusions
7. Conclusions
In this work, a new method to regulate voltage for a full-bridge LLC resonant converter under
In this work, a new method to regulate voltage for a full-bridge LLC resonant converter under
light load conditions is proposed to solve the voltage gain curve upwarp drift problem. This method
light load conditions is proposed to solve the voltage gain curve upwarp drift problem. This method
transforms a full-bridge LLC resonant converter into a half-bridge LLC resonant converter by
transforms a full-bridge LLC resonant converter into a half-bridge LLC resonant converter by adapting
adapting PFM driver signals simply. Ideal and actual FHA models are analyzed based on previous
PFM driver signals simply. Ideal and actual FHA models are analyzed based on previous reference
reference method. Furthermore, a new voltage and current sharing control scheme in on-line and offmethod. Furthermore, a new voltage and current sharing control scheme in on-line and off-line mode
line mode to enhance LLC performance in a residential PV system is implemented. Based on this
to enhance LLC performance in a residential PV system is implemented. Based on this control scheme,
control scheme, the DC bus voltage is regulated smoothly in all load range, and the two LLC resonant
the DC bus voltage is regulated smoothly in all load range, and the two LLC resonant inductor currents
inductor currents are shared well.
are shared well.
Matlab simulation and experimental results, based on resistive load, are performed in the
Matlab simulation and experimental results, based on resistive load, are performed in the
laboratory. In on-line mode, steady-state error of 400 V DC bus voltage is eliminated under light load
laboratory. In on-line mode, steady-state error of 400 V DC bus voltage is eliminated under light load
conditions. During load transition from 0 to 7 kW, the 400 V DC bus voltage has a drop of 14 V in
conditions. During load transition from 0 to 7 kW, the 400 V DC bus voltage has a drop of 14 V in
simulation and stays stable in the experiments. The settling time declines from 0.35 s to almost 0 in
simulation and stays stable in the experiments. The settling time declines from 0.35 s to almost 0 in
the experiments. CUF is almost 0 in the simulation and 1.7% in the experiments. In off-line mode,
the experiments. CUF is almost 0 in the simulation and 1.7% in the experiments. In off-line mode,
burst mode is eliminated and ripple is restrained. During load transition from 0 to 7 kW, 630 V DC
bus voltage has a drop of 42 V and a rise of 11 V in simulation, while it has a drop of 41 V and a rise
Energies 2017, 10, 752
20 of 21
burst mode is eliminated and ripple is restrained. During load transition from 0 to 7 kW, 630 V DC bus
voltage has a drop of 42 V and a rise of 11 V in simulation, while it has a drop of 41 V and a rise of 12 V
in the experiments. The settling time declines from 0.63 s to 21 ms in the experiments. CUF is almost
0 in simulation and 0.7% in the experiments. Furthermore, the experimental results have also been
carried out with real household loads. The waveforms show that the improved residential PV system
can work stably with real household loads such as an air conditioner, microwave oven and refrigerator.
Acknowledgments: This research was supported by the National High Technology Research and Development
Program (863 Program) of China (Grant: 2015AA050603). The authors would also like to thank the anonymous
reviewers for their valuable comments and suggestions to improve the quality of the paper.
Author Contributions: Shu-Huai Zhang, Feng-Zhang Luo and Yi-Feng Wang proposed the control method,
completed theoretical analysis and simulation. Feng-Zhang Luo is also responsible for writing and revising
the paper. Jiang-Hua Liu, Yong-Peng He and Yue Dong helped in modifying control algorithm and
conducting experiments.
Conflicts of Interest: The authors declare no conflict of interest.
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