energies
Article
The Chaotic-Based Control of Three-Port Isolated
Bidirectional DC/DC Converters for Electric and
Hybrid Vehicles
Zheng Wang 1, *, Bochen Liu 1 , Yue Zhang 1 , Ming Cheng 1 , Kai Chu 1 and Liang Xu 2
1
2
*
School of Electrical Engineering, Southeast University, Nanjing 210096, China; bcliu@seu.edu.cn (B.L.);
yuezhang@nuaa.edu.cn (Y.Z.); mcheng@seu.edu.cn (M.C.); chukai1991@163.com (K.C.)
Aviation Key Laboratory of Science and Technology on Aerospace Electromechanical System Integration,
No. 33 Shuige Road, Jiangning District, Nanjing 210061, China; xlp1983@163.com
Correspondence: zwang@eee.hku.hk or zwang@seu.edu.cn; Tel.: +86-137-7079-6825
Academic Editor: Joeri Van Mierlo
Received: 31 July 2015; Accepted: 13 January 2016; Published: 27 January 2016
Abstract: Three-port isolated (TPI) bidirectional DC/DC converters have three energy ports and
offer advantages of large voltage gain, galvanic isolation ability and high power density. For this
reason this kind of converters are suitable to connect different energy sources and loads in electric and
hybrid vehicles. The purpose of this paper is to propose chaotic modulation and the related control
scheme for TPI bidirectional DC/DC converters, in such a way that the switching harmonic peaks
can be suppressed in spectrum and the conducted electromagnetic interference (EMI) is reduced.
Two chaotic modulation strategies, namely the continuously chaotic modulation and the discretely
chaotic modulation are presented. These two chaotic modulation strategies are applied for TPI
bidirectional DC/DC converters with shifted-phase angle based control and phase-shifted PWM
control. Both simulation and experiments are given to verify the validity of the proposed chaotic
modulation-based control schemes.
Keywords: electric and hybrid vehicles; energy conversion; bidirectional DC/DC converter;
chaotic modulation; shifted-phase angle based control
1. Introduction
With the increasing problems of emissions from oil/gas powered vehicles and the decreasing
availability of fossil fuels around the world, electric vehicles (EVs) and hybrid electric vehicles (HEVs)
are gaining widesprad attention nowadays [1,2]. EVs and HEVs not only save fossil fuel, but also
achieve low gas emissions for environmental protection [3]. Emerging renewable energy techniques
have been introduced in EVs [4]. In EVs and HEVs, the bidirectional DC/DC converter is a prominent
option to exchange power between the low-voltage energy storage device and the high-voltage DC
bus of the traction motor [5]. In Figure 1a, a bidirectional DC/DC converter is used to exchange
power between the battery and the high-voltage DC bus in series of a HEV, in such a way that the DC
link voltage is kept stable despite of voltage changes in the battery and load variation in the traction
motor [6]. Figure 1b plots the configuration of a dual-active-bridge (DAB) isolated DC/DC converter,
which is used to connect the battery and the DC bus of the traction motor [5]. Besides, the bidirectional
DC/DC converter can be used to exchange power between the battery and the grid to satisfy the
requirements of vehicle-to-grid (V2G) operation of EVs, which is shown in Figure 2 [7,8].
Energies 2016, 9, 83; doi:10.3390/en9020083
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Energies 2016, 9, 83
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Energies 2016, 9, 83
Energies 2016, 9, 83
Engine
Fuel tank
Engine
Fuel tank
Generat
or
Generat
or
Rectifier
Inverter
Rectifier
Inverter
Traction
motor
Traction
motor
DC
/DC
DC
/DC
(a)
(a)
(b)
(b)
Figure 1. Energy conversion system in series HEV with bidirectional DC/DC converter:
Figure 1. Energy conversion system in series HEV with bidirectional DC/DC converter: (a) system
(a)
system
(b) DABsystem
converter.
Figure
1. configuration;
Energy conversion
in series HEV with bidirectional DC/DC converter:
configuration; (b) DAB converter.
(a) system configuration; (b) DAB converter.
+
+
High
voltage
High
bus
voltage
bus
AC
AC
Bidirectional
rectifier
Bidirectional
rectifier
Bidirectional DC/DC
converter
Bidirectional DC/DC
converter
Bidirectional DC/DC
converter
Bidirectional DC/DC
converter
Figure 2. Electric charging system for V2G of EV.
Figure 2. Electric charging system for V2G of EV.
Figure 2. Electric charging system for V2G of EV.
-
Bidirectional DC/DC converters can be classified into isolated converters and non-isolated
Bidirectional
DC/DC converters
canusually
be classified
into topologies
isolated converters
non-isolated
converters
[9,10]. Non-isolated
converters
have simple
and fewerand
components,
but
Bidirectional
DC/DC
converters
can
be
classified
into
isolated
converters
and
non-isolated
converters
[9,10]. Non-isolated
converters
have simple
topologies
and fewer
but
they
face challenges
in high-gain
voltageusually
conversion
and galvanic
isolation.
On components,
the other hand,
converters
Non-isolated
converters
usually
have simple
topologies
and fewer
components,
they face[9,10].
challenges
in high-gain
voltage
conversion
and galvanic
isolation.
On
the
other
isolated
converters
can
achieve
wide-range
voltage
conversion
and
electric
isolation
by hand,
usingbut
they
face challenges
in can
high-gain
voltage
conversion
and conversion
galvanic
On the
other hand,
isolated
isolated
converters
achieve
wide-range
voltage
and electric
isolation
by using
high-frequency
transformers
[5,11–14].
Different
from
two-portisolation.
bidirectional
DC/DC
converters,
high-frequency
transformers
[5,11–14].
Different
fromand
two-port
bidirectional
DC/DC
converters,
multi-port
DC/DC
converters
are voltage
derived
to exchange
power
among
multiple
DC ports.
In [15],
converters
can
achieve
wide-range
conversion
electric
isolation
by using
high-frequency
DC/DC
converters
are
derived
to
exchange
power
among
multiple
ports.
[15],
amulti-port
multi-input
non-isolated
DC/DC
converter
is proposed
for
hybrid
energy
sourcesDC
in
fuel
cell In
electric
transformers
[5,11–14].
Different
from
two-port
bidirectional
DC/DC
converters,
multi-port
DC/DC
a multi-input
non-isolated
DC/DC
converter
is proposed
for
hybrid
sources
in fuel buck/boost
cell
electric
vehicles,
where
threeto
energy
sources
are connected
to a common
DCenergy
bus
through
separate
converters
are
derived
exchange
power
among
multiple
DC
ports.
In [15],
a multi-input
non-isolated
vehicles,
where
three
energythe
sources
areenergy
connected
to ain
common
DC
bus
separate
converters.
Figure
3 shows
configuration
[16],
a through
partially
isolated
multi-port
DC/DC
converter
is proposed
for system
hybrid
sources
in[15].
fuel In
cell
electric
vehicles,
wherebuck/boost
three energy
converters.
Figure is
3 shows
the to
system
configuration
in separate
[15]. In
[16],
adifferent
partiallyDC
isolated
DC/DC
converter
proposed
achieve
power
conversion
among
ports multi-port
in hybrid
sources
are
connected
to a common
DC
bus
through
buck/boost
converters.
Figure 3
DC/DC
converter
is
proposed
to
achieve
power
conversion
among
different
DC
ports
in
hybrid
vehicles.
For
this
configuration,
a
non-isolated
bidirectional
half-bridge
DC/DC
converter
is used
to
shows the system configuration in [15]. In [16], a partially isolated multi-port DC/DC
converter
vehicles.
For
this
configuration,
a
non-isolated
bidirectional
half-bridge
DC/DC
converter
is
used
between
two energy
sources,
and an
isolatedDC
dual
half-bridge
DC/DC
converter
is
is exchange
proposedpower
to achieve
power
conversion
among
different
ports
in hybrid
vehicles.
Forto
this
exchange
power between
energy
sources,
an isolated
dual
half-bridge
DC/DC
is
used
to exchange
power two
between
the
energyand
sources
and the
traction
motor.
Only converter
four active
configuration, a non-isolated bidirectional half-bridge DC/DC converter is used to exchange power
used to exchange
power
between
thetwo
energy
sources
and
theone
traction
motor.legOnly
four active
switching
devices are
needed
since the
energy
sources
share
half-bridge
on primary
side
between two energy sources, and an isolated dual half-bridge DC/DC converter is used to exchange
switching
devices are needed
since Similarly,
the two energy
sources
share
one half-bridge
leg
on primary
side
of
the high-frequency
transformer.
another
partially
isolated
multi-port
DC/DC
converter
power between the energy sources and the traction motor. Only four active switching devices are
of proposed
the high-frequency
transformer.
Similarly,half-bridge
another partially
multi-port
is
by using separate
bidirectional
DC/DCisolated
converters
for twoDC/DC
energyconverter
sources,
needed since the two energy sources share one half-bridge leg on primary side of the high-frequency
is proposed
by using separate
bidirectional
half-bridge
DC/DC
and
high controllability
is provided
for power
conditioning
[17]. converters for two energy sources,
transformer.
Similarly,
another
partially
isolated
multi-port
DC/DC converter is proposed by using
and high controllability is provided for power conditioning [17].
separate bidirectional half-bridge DC/DC converters for two energy sources, and high controllability
is provided for power conditioning [17].
2
2
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Ultracapacitor
Multiple
Input
DC/DC
Coverter
Battery
Fuel
DC/AC
Converter
Electric
Motor
FC
Figure 3. System configuration of fuel cell electric vehicles using multi-input DC/DC converter.
Figure 3. System configuration of fuel cell electric vehicles using multi-input DC/DC converter.
Different from the aforementioned multi-port converters based on two-winding transformers, a
Different from the aforementioned multi-port converters based on two-winding transformers,
three-port isolated (TPI) bidirectional DC/DC converter is proposed for three energy ports by integrating
a three-port isolated (TPI) bidirectional DC/DC converter is proposed for three energy ports by
three windings magnetically [18–20]. As an isolated DC/DC converter, the TPI bidirectional DC/DC
integrating three windings magnetically [18–20]. As an isolated DC/DC converter, the TPI bidirectional
converter has the features of high-gain voltage conversion and electric isolation [5]. The zero voltage
DC/DC converter has the features of high-gain voltage conversion and electric isolation [5]. The
transition (ZVS) condition can be achieved by the leakage inductances of transformer and parasitic
zero voltage transition (ZVS) condition can be achieved by the leakage inductances of transformer
capacitance of switching devices. Due to the reduction of switching losses with ZVS operation, the
and parasitic capacitance of switching devices. Due to the reduction of switching losses with ZVS
switching frequency of TPI bidirectional DC/DC converter is increased. Previously, several examples
operation, the switching frequency of TPI bidirectional DC/DC converter is increased. Previously,
of TPI bidirectional DC/DC converters have been given. In [18], the shifted-phase angle based control
several examples of TPI bidirectional DC/DC converters have been given. In [18], the shifted-phase
is deduced to control power for the TPI bidirectional DC/DC converter. In [19], the shifted-phase
angle based control is deduced to control power for the TPI bidirectional DC/DC converter.
angle based control is further applied for a triple-half-bridge based TPI bidirectional DC/DC converter,
In [19], the shifted-phase angle based control is further applied for a triple-half-bridge based TPI
which is used for the hybrid energy source consisting of fuel cells and super-capacitors. In [20],
bidirectional DC/DC converter, which is used for the hybrid energy source consisting of fuel cells
a decoupled power flow control scheme is proposed to mitigate the coupling effects among different
and super-capacitors. In [20], a decoupled power flow control scheme is proposed to mitigate the
ports of the TPI bidirectional DC/DC converter by linearizing the power at the operating points.
coupling effects among different ports of the TPI bidirectional DC/DC converter by linearizing the
In [21], the TPI bidirectional DC/DC converter is used to connect different batteries to a grid inverter
power at the operating points. In [21], the TPI bidirectional DC/DC converter is used to connect
for battery charging in EV. To the best of authors’ knowledge, all the previous work on TPI
different batteries to a grid inverter for battery charging in EV. To the best of authors’ knowledge,
bidirectional DC/DC converters are with fixed switching-frequency, where the peak harmonics are
all the previous work on TPI bidirectional DC/DC converters are with fixed switching-frequency,
clustered around the switching-frequency and its multiple values in spectrum. These peak switching
where the peak harmonics are clustered around the switching-frequency and its multiple values in
harmonics may induce conducted electromagnetic interference (EMI) in power converters [22].
spectrum. These peak switching harmonics may induce conducted electromagnetic interference (EMI)
Different from the fixed switching-frequency based control, the aim of this paper is to propose
in power converters [22].
chaotic modulation strategies and the related control schemes for TPI bidirectional DC/DC converters,
Different from the fixed switching-frequency based control, the aim of this paper is to propose
in such a way that the switching harmonic peaks can be suppressed in spectrum and the conducted
chaotic modulation strategies and the related control schemes for TPI bidirectional DC/DC converters,
EMI is reduced in EVs. By changing the switching frequency chaotically, the distinct switching
in such a way that the switching harmonic peaks can be suppressed in spectrum and the conducted EMI
harmonic peaks with fixed switching-frequency are broken and the power can be spread out within
is reduced in EVs. By changing the switching frequency chaotically, the distinct switching harmonic
the nearby domain in spectrum. Either the random or chaotic modulation has been studied in various
peaks with fixed switching-frequency are broken and the power can be spread out within the nearby
power converters [22–24], but those works are mainly focused on one single converter. Due to the
domain in spectrum. Either the random or chaotic modulation has been studied in various power
existence of three power converters in a TPI bidirectional DC/DC converter, the chaotic modulation
converters [22–24], but those works are mainly focused on one single converter. Due to the existence of
strategy should be designed collaboratively for the three energy ports for stable operation. Two
three power converters in a TPI bidirectional DC/DC converter, the chaotic modulation strategy should
chaotic modulation strategies, namely the continuously chaotic modulation and the discretely chaotic
be designed collaboratively for the three energy ports for stable operation. Two chaotic modulation
modulation are proposed in this paper. They are applied to the shifted-phase angle based control and
strategies, namely the continuously chaotic modulation and the discretely chaotic modulation are
the phase-shifted PWM control for the TPI bidirectional DC/DC converter. Both simulation and
proposed in this paper. They are applied to the shifted-phase angle based control and the phase-shifted
experiments are given to verify the validity of the proposed schemes.
PWM control for the TPI bidirectional DC/DC converter. Both simulation and experiments are given
to
verify the validity
of the proposed schemes.
2. Operation
Principle
2. Operation
Principle
Figure 4 shows
the topology of a TPI bidirectional DC/DC converter. The three energy sources
are connected to a three-port high-frequency transformer with full-bridge DC/DC converters.
Figure 4 shows the topology of a TPI bidirectional DC/DC converter. The three energy sources are
As shown in Figure 4, u1, u2 and u3 are converter output voltages of three ports, and i1, i2 and i3 are
connected to a three-port high-frequency transformer with full-bridge DC/DC converters. As shown
input currents of three ports. Figure 5a shows the equivalent model for the TPI bidirectional DC/DC
in Figure 4, u1 , u2 and u3 are converter output voltages of three ports, and i1 , i2 and i3 are input currents
converter. L1, L2 and L3 are leakage inductances of three ports, and Lm is the magnetic inductance.
of three ports. Figure 5a shows the equivalent model for the TPI bidirectional DC/DC converter.
L1 , L2
Figure 5b shows the simplified Y-type equivalent model without magnetic inductance. 𝐿′2 and 𝐿′3
and L3 are leakage inductances of three ports, and Lm is the magnetic inductance. Figure 5b shows
are the equivalent inductance values of L2 and L3, which are observed from port 1. After converting
the model from Y-type to Δ-type, Figure 5c is obtained. In Figure 5c, L12 is the equivalent inductance
3
Energies 2016, 9, 83
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the simplified Y-type equivalent model without magnetic inductance. L12 and L13 are the equivalent
Energies 2016, 9, 83
inductance
values of L2 and L3 , which are observed from port 1. After converting the model from
Y-type to ∆-type, Figure 5c is obtained. In Figure 5c, L12 is the equivalent inductance between port 1 and
between port 1 and port 2, L13 is the equivalent inductance between port 1 and port 3, and L23 is the
port 2, L13 is the equivalent inductance between port 1 and port 3, and L23 is the equivalent inductance
equivalent inductance between port 2 and port 3. The values of L12, L13 and L23 are deduced as shown
between port 2 and port 3. The values of L12 , L13 and L23 are deduced as shown in Equation (1):
in Equation (1):
$
L
’

’
LL212 “ 22
’
’
L
'

n2
’
 2
’
n22
’
’

’
L3
’
1
’
’
’  L '  LL33 “ n2
’
 3
’
3
’
n32
& 
L1 L12
1
L
“
L
`
L
`
(1)
1
2 L LL1'
 12
1 23
’
’
L

L

L
'

(1)

12
1
2
’
’
L' 1
’
’
’ L13 “ L1 ` L1 ` L31 L3
’
3
’

L LL'1
’
’
’
L13  L1  L3 ' 1 13 2 1

’
’
LL ' L
’
’
% L23 “ L12 ` L13 ` 2 2 3

L ' L1 '
 L23  L2 ' L3 ' 2 3
L1

S5
S7
S6
S8
S9
S11
S10
S12
i2
u2
S1
S3
Motor side
i1
Generator
side
u1
S2
S4
i3
u3
Battery
Figure 4.
4. Configuration
of TPI
TPI bidirectional
bidirectional DC-DC
DC-DC converter.
converter.
Figure
Configuration of
Based on the equivalent model in Figure 5c, the mathematical models of active power exchanged
Based on the equivalent model in Figure 5c, the mathematical models of active power exchanged
among three energy ports can be expressed in the following equations:
among three energy ports can be expressed in the following equations:
12  ˙
$  P  V1V21 '  ˆ
 12 V1 V2 12 1  φ12
’

L
’ P12
’
 “ ωL 12 φ12 1 ´ π
’
’
’
’
V1V123 ' ˆ 13  ˙

& 
(2)
 P13 V1 V31 131  φ13
(2)
 
P13
“ L13 φ13 1 ´

’
ωL13
π
’
’

ˆ
˙
’
V1 'V1 '   φ 
’
’
V22V3 3 32 1  32
32
 P12

’
% P12
 “ ωL
L23φ32  1 ´ π
23
$ P  P  P
1
12
13
’
& P1 “ P12 ` P13
(3)
PP22 “ PP12
(3)
12 
`P
P32
32
’
% PP “
´PP3232
13 
 33  PP13
where
ω ==2πf
2πfand
andf isf is
switching
frequency.
φ12
the shifted-phase
between
1 and
where ω
thethe
switching
frequency.
12 is
theisshifted-phase
angleangle
between
port 1 port
and port
2,
port
2,
φ
is
the
shifted-phase
angle
between
port
1
and
port
3,
and
φ
is
the
shifted-phase
angle
13
32
13 is the shifted-phase angle between port 1 and port 3, and 32 is the shifted-phase angle between
between
port
and
port 3, respectively.
P2 active
and P3power
are active
power
of 2port
port 2respectively.
and port 3,
port 2 and
port2 3,
respectively.
P1, P2 and P
P13 ,are
of port
1, port
and1,port3,
respectively.
From(2)
Equations
andbe
(3),observed
it can be observed
that the exchanged
power
can be controlled
From Equations
and (3), (2)
it can
that the exchanged
power can
be controlled
by the
by
the
shifted-phase
angles
between
different
energy
ports.
shifted-phase angles between different energy ports.
Energies 2016, 9, 83
5 of 19
Energies 2016, 9, 83
L1
i1
L3
i2'
L2'
i2'
L3'
i3'
L3'
i3'
u3
3
L2
2
i2'
(c)
u1
u2'
(a)
L2
3
i3'
2
u1
i3
L2'
i2'
i12
i1
uu2
3
2
1:n3
(a)
i1
i2
i3
L3
Lm
L1
L1
i12L13
i13
2
Lm
u1
L2
1:n2
1:n3
L1
u2
L13
i3
L1
u1
i1
i13
i2
i3
Energies 2016, 9, 83
i1
L2
1:n2
u2'
u3'
i3'
u2'
u3'
(c)
u1
i1
L1
u2'
u3'
u1
(b)
u3'
Figure 5. Equivalent model of TPI bidirectional DC/DC converter: (a) original equivalent model with
Figure 5. Equivalent model of TPI bidirectional DC/DC converter: (a) original equivalent model with
magnetic inductance; (b) simplified Y-type equivalent model observed from port 1 without magnetic
(b) Y-type equivalent model observed from port 1 without magnetic
magnetic
inductance; (b) simplified
inductance; (c) simplified Δ-type equivalent mode.
inductance;
(c) simplified ∆-type equivalent mode.
Figure 5. Equivalent model of TPI bidirectional DC/DC converter: (a) original equivalent model with
Figure 6 inductance;
plots the simulated
steady-state
waveforms
of observed
TPI bidirectional
magnetic
(b) simplified
Y-type equivalent
model
from port DC/DC
1 withoutconverter
magnetic with
shifted-phase
angle
based
control.
A
switching
cycle
is
divided
into
18
modes.
The
detailed
working with
inductance;
(c) simplified
Δ-type
equivalent mode.
Figure
6 plots the
simulated
steady-state
waveforms of TPI bidirectional DC/DC converter
principle
of
the
TPI
bidirectional
DC/DC
converter
is
similar
to
the
DAB
isolated
DC/DC
converter.
shifted-phase angle based control. A switching cycle is divided into 18 modes. The detailed working
Figure
6 plots the
simulated
steady-state
waveforms
of TPI bidirectional
converter
The ZVS
operation
is achieved
when
the anti-diode
is freewheeling
before theDC/DC
active switch
takeswith
the
principle of the TPI bidirectional DC/DC converter is similar′ to the DAB isolated
DC/DC converter.
′ The detailed
shifted-phase
angle
based control.
cycle isddivided
into
18dmodes.
working
current [19]. By
assuming
L12 = L13A= switching
L32 and defining
12 = 𝑢2 /V
1 and
13 = 𝑢3 /V
1, the soft-switching
The ZVS
operation
is achieved when
the anti-diode
is freewheeling
before
the active
switch takes the
principle
the TPI bidirectional
DC/DCby
converter
is similar
isolated
DC/DC converter.
operationof
conditions
can be determined
the voltage
gains dto12 the
andDAB
d13 and
shifted-phase
angles 12
1 /V and d = u1 /V , the soft-switching
current
[19].
By
assuming
L
=
L
=
L
and
defining
d
=
u
32
12 7, 13
12
1 before13
1switchTo
2 soft-switching
3
The
operation
is achieved
when
theareas
anti-diode
freewheeling
the active
takes
the
and ZVS
13. As
shown in
Figure
the grey
are theisregion
for
conditions.
extend
operation
conditions
can
be determined
by
thedefining
voltage
d/V
shifted-phase
angles
121 and
13 =and
current
[19]. By assuming
L12region,
= L13 =the
L32
and
dgains
12 =be
𝑢2′incorporated
and d
d13
/V
1,shifted-phase
the soft-switching
the soft-switching
operation
PWM
control can
in𝑢3′the
angle φ12
and φoperation
in Figure
the
grey
areas
the region
soft-switching
conditions.
Toextend
conditions
can be7,determined
by the
voltage
gainsThis
dfor
12 and
d13 and shifted-phase
angles
12
control,
and
the phase-shifted
PWM
control
isare
obtained
[25].
phase-shifted
PWM
control
scheme
13 . As shown
and

13
.
As
shown
in
Figure
7,
the
grey
areas
are
region
for
soft-switching
conditions.
To
extend
can
decrease
the
circulating
current
and
increase
the
efficiency
of
the
DC/DC
converter
[26].
the soft-switching operation region, the PWM control can be incorporated in the shifted-phase angle
the and
soft-switching
operationPWM
region,control
the PWM
control can
be incorporated
in the shifted-phase
angle
control,
the phase-shifted
is obtained
[25].
This phase-shifted
PWM control
scheme
control, and
phase-shifted
PWM
control
is obtained
[25]. Thisof
phase-shifted
control[26].
scheme
can decrease
thethe
circulating
current
and
increase
the efficiency
the DC/DCPWM
converter
can decrease the circulating current and increase the efficiency of the DC/DC converter [26].
Figure 6. Simulated steady-state waveforms of TPI bidirectional DC/DC converter.
5
Figure 6. Simulated steady-state waveforms of TPI bidirectional DC/DC converter.
Figure 6. Simulated steady-state waveforms of TPI bidirectional DC/DC converter.
5
Energies 2016, 9, 83
6 of 19
Energies 2016, 9, 83
5
5
Border of port 1
4
3
Energies 2016, 9, 83
3
Border of port 3
d12
2
5
1
Border of port 1
4 Border of port 2
0
1.2
0.9
0.6
0.3
0
φ12
3
Border of port 3
d12
3.
Border of port 1
4
d12
2
5
1
4
0
0
3
1.5
Border of port 3
Border of port 1
Border of port 2
0.3
0.6
φ12
0.9
1.2
1.5
d12
(a)
(b)
2
2
Figure 7. Soft-switching regions for TPI bidirectional DC/DC converter. (a) 13 = π/9, d13 = 1;
Border of port 3 (a) φ13 = π/9, d13
Figure 7.
Soft-switching regions for TPI bidirectional DC/DC converter.
(b) 13 = π/6, d113 = 0.6.
1
(b) φ13 = π/6, d13 = 0.6.
Border of port 2
Border of port 2
3. Chaotic Modulation
0
0
1.5
1.2
0.9
0.6
0.3
0
0
0.3
0.6
0.9
1.2
1.5
φ12
φ12
Chaotic Modulation
= 1;
Chaotic modulation strategies have already been utilized to reduce the conducted EMI for
(a)
(b)
power electronic converters and electric drives [22–24]. Due to the random-like features, chaotic
Chaotic modulation strategies have already been utilized to reduce the conducted EMI for power
Figure 7.generates
Soft-switching
regions
for TPIswitching
bidirectional
DC/DC converter.
(a) be
13 used
= π/9,toddestroy
13 = 1;
modulation
irregularly
variable
frequencies,
which could
the
electronic
converters
and= 0.6.
electric and
drives
[22–24].
Due to power
the random-like
features,
chaoticismodulation
(b) switching
13 = π/6, d13harmonics
distinct
produce
a continuous
spectrum. Chaotic
modulation
easy
generates
irregularlycompared
variabletoswitching
frequencies,
be used
to destroy
theondistinct
to implement
a truly random
source in which
practice.could
However,
the previous
studies
3.
Chaotic
Modulation
chaotic
modulation
were
focused
on
a
single
power
converter.
Different
from
that,
there
are
switching harmonics and produce a continuous power spectrum. Chaotic modulationthree
is easy to
full-bridge
in the
TPI bidirectional
DC/DC
a collaborative
chaotic
implement
compared
to a truly
random
source
in
practice.
However,
the the
previous
studies
on
Chaoticconverters
modulation
strategies
have
already
beenconverter.
utilized
toTherefore,
reduce
conducted
EMI
for chaotic
modulation
design
should beand
given
for thedrives
three energy
power
electronic
converters
electric
[22–24].ports.
Due to the random-like features, chaotic
modulation were focused on a single power converter. Different from that, there are three full-bridge
modulation
generates
irregularly variable switching frequencies, which could be used to destroy the
converters
the TPI
3.1. in
Generation
ofbidirectional
Chaotic Series DC/DC converter. Therefore, a collaborative chaotic modulation
distinct switching harmonics and produce a continuous power spectrum. Chaotic modulation is easy
design should be given for the three energy ports.
to implement
compared
to a truly
random
in practice.DC/DC
However,
the previous
studies
on
To chaoize
the switching
frequency
of source
TPI bidirectional
converter,
the chaotic
series
chaotic
modulation
were
focused
on
a
single
power
converter.
Different
from
that,
there
are
three
should be generated at first. The use of a logistic map is a simple and efficient approach to generate
3.1. Generation of Chaotic Series
full-bridge
the chaotic converters
sequence {𝑥in
𝑖 }: the TPI bidirectional DC/DC converter. Therefore, a collaborative chaotic
modulation
design
should
given for the
energy ports. DC/DC converter, the chaotic series
To chaoize the switching be
of three
TPI bidirectional
xfrequency
n  1,2,3.......
(4)
n 1  F ( A, xn )  Axn (1  xn )
should be generated at first. The use of a logistic map is a simple and efficient approach to generate
3.1. Generation of Chaotic Series
where
the control
the chaotic
sequence
{xi }:parameter A ∈ [0, 4]. Figure 8a depicts the bifurcation diagram of 𝑥𝑖 versus A of
the logistic
map.the
Theswitching
corresponding
Lyapunov
versus
A is shown
in Figure
8b. It can
be
To chaoize
frequency
of TPI exponent
bidirectional
DC/DC
converter,
the chaotic
series
seen
that
when
A
∈
[0,
1),
{𝑥
}
exhibits
the
zero
value.
When
A
∈
[1,
3),
{𝑥
}
becomes
a
fixed
value
should be generated at first. The
use of a logistic map is a simple and efficient
𝑖
xn`1 “ FpA,
xn q “ Axn p1 ´ xn q
(4)
n “ 1, 2, 3 . . . .𝑖 . . approach to generate
withchaotic
𝑥𝑖 > 0.sequence
When A is
increased, {𝑥𝑖 } begins to bifurcate with multiple values. When A > 3.57,
the
{𝑥𝑖further
}:
{𝑥𝑖 } exhibits infinite values. Besides, the boundary of these infinite values changes with the value of A.
F
( A,Figure
xn )  are
Ax8a
(1depicts
 xn ) it confirms
n  1bifurcation
,2,3that
.......it is adiagram
where the
control parameter AxnP1 [0,
4].
the
of x versus
A of
(4)
npositive,
As the corresponding Lyapunov
exponents
chaotic series. iThus,
the logistic
map.
The
corresponding
Lyapunov
exponent
versus
A
is
shown
in
Figure
8b.
It
can
be
by designing
the value
of A to be
close
to 4,
the chaotic
series the
{𝑥𝑖 } bifurcation
will be distributed
evenly
where
the control
parameter
A∈
[0, 4].
Figure
8a depicts
diagram
of 𝑥within
versus(0,A1).
of
𝑖
xi
Lyapunov exponent
seen that
P [0,The
1), corresponding
{xi } exhibits Lyapunov
the zero value.
When
3), {x
becomes
fixed
thewhen
logisticAmap.
exponent
versusA
AP
is [1,
shown
ini }Figure
8b. It acan
be value
1
0.2
with xi >seen
0. When
A isAfurther
to bifurcate
values.
When
A > 3.57,
that when
∈ [0, 1),increased,
{𝑥𝑖 } exhibits{xthe
zero value.
When A ∈with
[1, 3),multiple
{𝑥𝑖 } becomes
a fixed
value
i } begins
0 infinite
with infinite
𝑥𝑖 > 0.8
0. When
A is Besides,
further increased,
{𝑥𝑖 } begins
bifurcate
withvalues
multiple
values. When
> 3.57,
{xi } exhibits
values.
the boundary
of to
these
changes
with Athe
value of A.
{𝑥𝑖 } exhibits infinite
values. Besides,
the boundary
of theseitinfinite
values changes with the value of A.
As the corresponding
Lyapunov
exponents
are positive,
0.6
-0.2 confirms that it is a chaotic series. Thus, by
As the corresponding Lyapunov exponents are positive, it confirms that it is a chaotic series. Thus,
designing the value of A to be close to 4, the chaotic series {xi } will be distributed evenly within (0, 1).
0.4 the value of A to be close to 4, the chaotic series
-0.4 {𝑥𝑖 } will be distributed evenly within (0, 1).
by designing
0.2
1
-0.6
0.2
1
0.6
2
Parameter A
3
4
Lyapunov exponent
0
0.8 0
xi
(a)
0.4
1
-0.2
2
Parameter A
3
4
(b)
-0.4
Figure 8. Logistic map: (a) bifurcation diagram;
(b) Lyapunov exponents.
0.2
0
-0.8
00
-0.6
6
0
1
2
Parameter A
3
4
(a)
-0.8
0
1
2
Parameter A
3
(b)
Figure 8. Logistic map: (a) bifurcation diagram; (b) Lyapunov exponents.
Figure 8. Logistic map: (a) bifurcation diagram; (b) Lyapunov exponents.
6
4
Energies 2016, 9, 83
7 of 19
3.2. Chaotic-Frequency Switching Pulses
Energies 2016, 9, 83
Based
on
the chaotic series {xi }, two approaches, namely the continuously chaotic modulation
Energies
2016,
9, 83
3.2.
Switching
Pulsesare proposed to generate the chaotic pulses. As aforementioned,
and
theChaotic-Frequency
discretely chaotic
modulation
Chaotic-Frequency
Switching
Pulses
the3.2.
shifted-phase
angle
canseries
be used
regulate
the power
exchange
for TPI bidirectional
DC/DC
Based on the
chaotic
{𝑥𝑖 },to
two
approaches,
namely
the continuously
chaotic modulation
converters.
The
duty
ratio
is
kept
as
a
constant
value
of
0.5
to
ensure
the
symmetric
operation
and the
discretely
chaotic
modulation
are
proposed
to
generate
the
chaotic
pulses.
As
aforementioned,
Based on the chaotic series {𝑥𝑖 }, two approaches, namely the continuously chaotic modulation of
full-bridge
of each chaotic
port.
shows
principlethe
ofgenerate
the continuously
chaotic
modulation
strategy,
the
shifted-phase
angleFigure
can
be 9used
to regulate
power
exchange
for
TPI bidirectional
DC/DC
and the discretely
modulation
are
proposed
to
the chaotic
pulses.
As
aforementioned,
converters.
The carrier
duty
ratio
astoa regulate
constant
value
of 0.5
to of
ensure
the
symmetric
of
where
a sawtooth
wave
iskept
compared
with a the
constant
value
0.5.for
The
frequency
ofoperation
theDC/DC
sawtooth
the
shifted-phase
angle
canisbe
used
power
exchange
TPI
bidirectional
full-bridge
of
each
port.
Figure
9
shows
principle
of
the
continuously
chaotic
modulation
strategy,
carrier
wave
is
chaoized
by
using
the
chaotic
series
{x
}
as:
converters. The duty ratio is kept as a constant valuei of 0.5 to ensure the symmetric operation of
where a sawtooth
carrier
wave9 shows
is compared
with
constant
value chaotic
of 0.5. The
frequency
of the
full-bridge
of each port.
Figure
principle
of athe
continuously
modulation
strategy,
sawtooth
carrier
wave
is
chaoized
by
using
the
chaotic
series
{𝑥
}
as:
f
“
f
`
p2x
´
1q
∆
f
s with na constant 𝑖value of 0.5. The frequency of the (5)
where a sawtooth carrier wave is compared
and and
Carrier
Carrier
signalsignal
comparison
comparison
sawtooth carrier wave is chaoized by using
chaotic
series
(5)
𝑓 = the
𝑓 +
(2𝑥𝑛 −
1)𝛥𝑓{𝑥𝑖 } as:
where xn is the chaotic series, fs is the central𝑠 switching
frequency, and ∆f is the changing range of
(5)of
𝑓 = 𝑓𝑠{x+
(2𝑥 − 1)𝛥𝑓
where xfrequencies.
n is the chaotic
series,
s is the series
central
switching
frequency,
and within
Δf is the
range
switching
Since
the fchaotic
evenly
(0,changing
1), there are
infinite
i } are𝑛 distributed
switching
Since
series
distributed
evenly
(0, 1), there
𝑖 } are frequency,
values
within
thechaotic
pool ofseries,
(fs – ∆fthe
fs +central
∆f /2)
for{𝑥switching
frequencies.
where
xn isfrequencies.
the
fs/2,
is chaotic
the
switching
and
Δf is within
the changing
range are
of
infinite
values
within
the
pool
of
(f
s – Δf/2, fs + Δf/2) for switching frequencies.
Figure 10
shows theSince
principle
of the discretely
modulation
strategy.
the
switching
switching
frequencies.
the chaotic
series {𝑥𝑖 }chaotic
are distributed
evenly
withinAlso,
(0, 1),
there
are
Figure
10 within
shows
the
principle
of the
discretely
chaotic
modulation
strategy.
Also,athe
switching
infinite
values
pool
of (fthe
s – Δf/2,
fs + Δf/2) for
switching
frequencies.
pulses
are
generated
bythe
comparing
chaotic-frequency
sawtooth
carrier
wave with
constant
value
pulses
are
generated
by
comparing
the
chaotic-frequency
sawtooth
carrier
wave
with
a
constant
Figure 10 from
shows
the
principle of the
discretely
chaoticthere
modulation
strategy.
Also,for
thethe
switching
of 0.5. Different
the
continuously
chaotic
modulation,
are finite
candidates
switching
value of
Differentby
from
the continuously
chaotic modulation, there
are finite
candidates
for the
pulses
are0.5.
generated
comparing
the chaotic-frequency
carrier
wave
constant
frequencies.
As
shown in Figure
10, there
are four switchingsawtooth
frequency
values
f s1 , fwith
fs4 , and
s2 , f s3aand
switching
frequencies.
As shown
in Figure 10,chaotic
there are
four switching
values fs1, fs2,for
fs3 and
value
0.5.
Different
from
the
continuously
modulation,
therefrequency
they
are of
adopted
when chaotic
series
{xi } is located within
the domains
ofare
[0,finite
0.25),candidates
[0.25, 0.5), [0.5,the
0.75)
fs4, and they
are adopted
when
chaotic
series
{𝑥there
within
the domains
of values
[0, 0.25),
[0.25, 0. 5),
𝑖 } is located
switching
frequencies.
As
shown
in
Figure
10,
are
four
switching
frequency
f
s1, fs2, fs3 and
and [0.75, 1), respectively.
5, 0. 75) and [0.75, 1), respectively.
f[0.
s4, and they are adopted when chaotic series {𝑥𝑖 } is located within the domains of [0, 0.25), [0.25, 0. 5),
[0. 5, 0. 75) and [0.75, 1), respectively.
t
t
Switching
Switching
signalsignal
A1
A1
A2
A2
T1
T2
T3
T4
t
t
T1
T2 continuously
T3 chaotic
T4modulation.
Figure 9. Principle
of
Figure 9. Principle of continuously chaotic modulation.
Figure 9. Principle of continuously chaotic modulation.
Figure 10. Principle of discretely chaotic modulation.
Figure 10. Principle of discretely chaotic modulation.
3.3. Chaotic Modulation forFigure
TPI Bidirectional
DC/DC
Converter
10. Principle
of discretely
chaotic modulation.
3.3. Chaotic
Modulation
for full-bridge
TPI Bidirectional
DC/DC
Since there
are three
converters
inConverter
the TPI bidirectional DC/DC converter, the chaotic
3.3.switching
Chaotic Modulation
for
TPI
Bidirectional
DC/DC
Converter
modulation
should
be
applied
for
the
three
ports
collaboratively.
shown inthe
Figure
11,
Since there are three full-bridge converters in the TPI
bidirectional
DC/DCAs
converter,
chaotic
if
the
chaotic
modulation
is
applied
for
the
three
ports
independently,
the
desired
shifted-phase
angles
Since there
are threeshould
full-bridge
converters
the TPI
bidirectional
DC/DC
converter,
the chaotic
switching
modulation
be applied
for theinthree
ports
collaboratively.
As shown
in Figure
11,
be
achieved
due
to
thebe
irregular
changes
of
the
switching
frequencies.
On
the
otherinhand,
the11,
switching
modulation
should
applied
for
the
three
ports collaboratively.
As
shown
Figure
ifcannot
the chaotic
modulation
is applied
for the
three
ports
independently,
the desired
shifted-phase
angles
shifted-phase
angles
can
be
maintained
when
the
synchronously
chaotic
switching
frequencies
are
cannot
be achieved
due to
the irregular
changes
of theindependently,
switching frequencies.
On the
other hand, angles
the
if the
chaotic
modulation
is applied
for the
three ports
the desired
shifted-phase
used,be
asachieved
shown
indue
Figure
12.
Thus, notchanges
only the
of continuous
isfrequencies
provided
with
shifted-phase
angles
can
maintained
when
the
synchronously
chaoticspectrum
switching
arethe
cannot
to be
the
irregular
offeature
the switching
frequencies.
On the
other hand,
chaotic
switching
frequencies,
but
also
the
shifted-phase
angle
control
can
be
implemented.
used, as shown in Figure 12. Thus, not only the feature of continuous spectrum is provided with
chaotic switching frequencies, but also the shifted-phase angle control can be implemented.
7
7
Energies 2016, 9, 83
8 of 19
shifted-phase angles can be maintained when the synchronously chaotic switching frequencies are
used, as shown in Figure 12. Thus, not only the feature of continuous spectrum is provided with
chaotic switching frequencies, but also the shifted-phase angle control can be implemented.
Energies 2016, 9, 83
Energies 2016, 9, 83
Energies 2016, 9, 83
Figure 11.
11. Independently
Independently chaotic
Figure
chaoticmodulation.
modulation.
Figure 11. Independently chaotic modulation.
Figure 11. Independently chaotic modulation.
Figure 12. Synchronously chaotic modulation.
Figure 12. Synchronously chaotic modulation.
12.Modulation
Synchronously chaotic modulation.
4. Control Scheme Based onFigure
Chaotic
4. Control Scheme Based on Chaotic Modulation
Figure
13 shows
the on
chaotic
modulation
based control
of TPI bidirectional DC-DC converter.
Figure
12.
Synchronously
chaotic modulation.
4. Control
Scheme
Based
Chaotic
Modulation
Figure 13 shows
theofchaotic
modulation
control
of TPIthe
bidirectional
DC-DC
converter.
The closed-loop
control
DC link
voltage Uobased
in port
2 generates
shifted-phase
angle
between
The
ofchaotic
DC
link
voltage
Uo based
inthe
port
2 generates
thebidirectional
shifted-phase
angle between
Figure
shows
the
modulation
control
ofcontrol
TPI
4.closed-loop
Scheme
Based
on
Chaotic
Modulation
port
1Control
and 13
port
2,control
namely
12
. On
the
other
hand,
closed-loop
of the activeDC-DC
power
inconverter.
port 1
port
1 andthe
port
2,
namely
DC
12angle
. On
the
other hand,
the
closed-loop
control
of
the
active
power
in
port
1
The
closed-loop
control
of
link
voltage
U
in
port
2
generates
the
shifted-phase
angle
between
produces
shifted-phase
between
port
1
and
port
3,
namely

13
.The
active
power
P
i
of
port
Figure 13 shows the chaotic modulationo based control of TPI bidirectional DC-DC converter.
produces
the
shifted-phase
angle
between
port
1
and
port
3,
namely

13
.The
active
power
P
i
of
port
1 1
port
1The
and
port
2, namely
φ12of. On
other
hand,
the
closed-loop
the active
power
in port
could
beclosed-loop
calculated
by multiplying
the
converter
output
u1control
and
theofinput
current
i1 between
on port
1.
control
DC the
link
voltage
Uo in
port
2voltage
generates
the shifted-phase
angle
could
be
calculated
by
multiplying
the
converter
output
voltage
u
1
and
the
input
current
i
1
on
port
1.
Then,
switching
pulsesangle
are
generated
for
three
with
the
shifted-phase
angles
12
113, 1
produces
the
shifted-phase
between
port
1 and
port
3,
namely
φ13of.The
power
i of port
portthe
1 and
port 2, namely

12. On
the other
hand,
theports
closed-loop
control
the active
active
power
inPand
port
Then,
the
switching
are
generated
for
ports
with
the
angles
12 and 
andproduces
the
synchronously
chaotic
modulation
is three
applied
forvoltage
the
three
ports.
As
mentioned
the
could
be
calculated
bypulses
multiplying
the
converter
u1shifted-phase
and
the
input
current
i1 port
on port
the shifted-phase
angle
between
port
1output
and
port
3, namely
13.The
active
power
Piabove,
of
113, 1.
and
the
synchronously
chaotic
modulation
is
applied
for
the
three
ports.
As
mentioned
above,
the
phase-shifted
PWM
could
be
applied
for
the
isolated
DC/DC
converter
to
extend
the
soft-switching
be calculated
by multiplying
the converter
u1 and
the input current
i1 on
port
1. φ13 ,
Then,could
the switching
pulses
are generated
for threeoutput
portsvoltage
with the
shifted-phase
angles
φ12
and
phase-shifted
PWM
be applied
for thefor
DC/DC
to extend
the soft-switching
operation
region
andcould
increase
thegenerated
converter
efficiency
[25,26].
For
the
phase-shifted
PWM
control,
Then,
the
switching
pulses
are
three ports
with
the shifted-phase
angles
12 and
13, the
and
the
synchronously
chaotic
modulation
isisolated
applied
for
theconverter
three
ports.
As mentioned
above,
operation
region
increase
the
converter
efficiency
[25,26].
For the
phase-shifted
PWM
control,
the and
dutythe
ratio
D isand
added
to
the
switching
pulse
of port
1. the three
synchronously
chaotic
modulation
is applied
for
ports.
Asextend
mentioned
above,
the
phase-shifted
PWM
could
be
applied
for the
isolated
DC/DC
converter
to
the
soft-switching
the duty
ratio
D
is
added
to
the
switching
pulse
of
port
1.
phase-shifted PWM could be applied for the isolated DC/DC converter to extend the soft-switching
operation region and increase the converter efficiency [25,26]. For the phase-shifted PWM control,
operation region and increase
the converter efficiency [25,26]. For the phase-shifted PWM control,
Uo
the duty ratio D is addedU *to+ the
switching pulse
of port 1.
ϕ12
Uo
o
Controller
the duty ratio D is added
switching pulse of port 1.
Uo to the
-
1
ϕ12
Controller
1 Limitation of
Uo
amplitude
Limitationϕof
ϕ12 Phase shifted
Pi* Uo+* +
13
Controller
Controller
switching
amplitude
shifted
2 1
pulses
ϕ13 Phase
Pi* + Controller
switching
Pi
Limitation of
2
pulses
amplitude
ϕ13 Phase shifted
PPi*i +
D
Controller
switching
Uo*
Uo
+
-
Pi
D
2
pulses
Ui
D
Chaotic
modulation
Chaotic
modulation
TPI
U
o
DC-DC
TPI
converter
DC-DC
converter
Chaotic
modulation
TPI
DC-DC
U
ii
i
converter
Ui
ii
Ui
ii
Ii
Ui
Ii
Multiplier
Low pass filter
Ui
Multiplier
Ii
Low pass filter
Figure 13. Block diagram of chaotic modulation based control for TPI bidirectional DC/DC converter.
Low
pass filter
Multiplier
Figure 13. Block diagram of chaotic modulation
based control for TPI
bidirectional
DC/DC converter.
Figure
1413.
plots
the
flow chart
of digital
implementation
the bidirectional
haotic modulation
based control
Figure
Block
diagram
of chaotic
modulation
based control for
for TPI
DC/DC converter.
Figure
13.14Block
chaotic
modulation
based control
forthe
TPIhaotic
bidirectional
converter.
Figure
plotsdiagram
the periods
flowofchart
digital parameters
implementation
for
based
control
scheme.
The
switching
andofcontrol
are updated
in themodulation
PWM DC/DC
interrupt
program,
scheme.
The
switching
periods
and control
are updated
inprogram,
the modulation
PWM
interrupt
program,
which isFigure
started
the the
PWM
module
portparameters
1.
In the PWM
interrupt
the
chaotic
14by
plots
flow
chart
ofon
digital
implementation
for the haotic
basedswitching
control
which
is ΔT
started
by
the PWM
module
port
1.
In the
PWM
program,
chaotic
switching
periods
are switching
generated,
and
they
are
initially
loaded
to interrupt
the period
registers
for
the three
ports.
scheme.
The
periods
andon
control
parameters
are
updated
in
the
PWMthe
interrupt
program,
periods
ΔT
are
generated,
and
they
are
initially
loaded
to
the
period
registers
for
the
three
ports.
which
is
started
by
the
PWM
module
on
port
1.
In
the
PWM
interrupt
program,
the
chaotic
switching
After starting AD conversion, the output voltage on port 2 and the input power on port 1 are sensed,
After
starting
the output
port 2 to
and
inputregisters
power on
are sensed,
periods
ΔTAD
areconversion,
generated, and
they arevoltage
initiallyonloaded
thethe
period
forport
the 1three
ports.
After starting AD conversion, the output voltage8on port 2 and the input power on port 1 are sensed,
Energies 2016, 9, 83
9 of 19
Figure 14 plots the flow chart of digital implementation for the haotic modulation based control
scheme. The switching periods and control parameters are updated in the PWM interrupt program,
which is started by the PWM module on port 1. In the PWM interrupt program, the chaotic switching
periods ∆T are generated, and they are initially loaded to the period registers for the three ports. After
Energies
9, 83
starting
AD2016,
conversion,
the output voltage on port 2 and the input power on port 1 are sensed, which
are input to closed-loop controllers to produce the shifted-phase angles φ12 and φ13 , respectively.
which are input to closed-loop controllers to produce the shifted-phase angles 12 and 13, respectively.
Together with the duty ratio D, the values of φ12 and φ13 are loaded to the phase registers of PWM
Together with the duty ratio D, the values of 12 and 13 are loaded to the phase registers of PWM
module 2 and PWM module 3, in such a way that the corresponding switching pulses are generated.
module 2 and PWM module 3, in such a way that the corresponding switching pulses are generated.
PWM interrupt of Port 1
Update the value of
Period Register of Port 1,
2, 3
N
Is AD sampling
completed?
Y
Calculate output voltage of
Port 2 and input power of
Port 1
Generate ϕ12 and ϕ13 with
output voltage and input power
close-loop controllers and set
duty cycle D for port 1
Update the Phase
Registers of Port 1,2, 3
based on D ,ϕ12, ϕ13
Continue AD convertion,
clear TxIF and enable
global interrupt
Return
Figure 14. Flow chart of digital implementation for chaotic modulation based control for TPI
Figure 14. Flow chart of digital implementation for chaotic modulation based control for TPI
bidirectional DC/DC converter.
bidirectional DC/DC converter.
The proportional-integral (PI) controllers are used for the closed-loop control to generate the
shifted
phase angles among three
Their digital
expressions
given as: control to generate the
The
proportional-integral
(PI) ports.
controllers
are used
for the are
closed-loop
* digital expressions
*
shifted phase angles among three ports.
Their
are
given as:
12  k p1 (U o  U o )  ki1  (U o  U o )T
(6)
ÿ*
˚i )T
Pi*U
 Pqi )`
 kki 2  ( PipU
P
13 
ϕ12 “ kp1
pUk po˚2 (´
o
i1
o ´ Uo q∆T
(7)
(6)
where kp1 and ki1 are the proportional and integral coefficients
of controller for port 2, and kp2 and ki2
ÿ
˚
˚
ϕ
“
k
pP
´
P
q
`
k
pP
´
Pi q∆T
are the proportional and integral
3.
ΔT is the switching period, which (7)
p2 i of controller
13 coefficients
i
i2 for port
i
varies chaotically. To guarantee good DC output performance of the TPI bidirectional DC/DC
whereconverter,
kp1 and the
ki1 are
the proportional and integral coefficients of controller for port 2, and k and
integral coefficients should be updated according to the changing switching periods.p2
ki2 are the proportional and integral coefficients of controller for port 3. ∆T is the switching period,
which5.varies
chaotically.
To guarantee
good DC output performance of the TPI bidirectional DC/DC
Simulation
and Experimental
Verification
converter,Both
the integral
coefficients should be updated according to the changing switching periods.
simulation and experiments are given to verify the performance of the proposed
modulation strategies and control scheme. Firstly, the simulation on a 10-kW TPI bidirectional
DC/DC converter is given. The simulation parameters are listed in Table 1. Figure 15 shows the
simulated waveforms of TPI bidirectional DC/DC converter using shifted-angle based control with
fixed switching frequency. Figure 15a shows the waveforms of converter voltage u1 and current i1 of
9
Energies 2016, 9, 83
10 of 19
5. Simulation and Experimental Verification
Both simulation and experiments are given to verify the performance of the proposed modulation
scheme. Firstly, the simulation on a 10-kW TPI bidirectional DC/DC converter
is given. The simulation parameters are listed in Table 1. Figure 15 shows the simulated waveforms of
port
1, and the output
voltage
Uo of port
Figure 15b shows
waveforms
of converter
voltages
u1,
TPI bidirectional
DC/DC
converter
using2.shifted-angle
basedthe
control
with fixed
switching
frequency.
uFigure
2 and u15a
3 in shows
three ports.
The switching
period is kept
constant
at current
a value iT,
which is equal to 50 μs.
the waveforms
of converter
voltage
u1 and
1 of port 1, and the output
Energies
2016,and
9, 83control
strategies
voltage Uo of port 2. Figure 15b shows the waveforms of converter voltages u1 , u2 and u3 in three ports.
Table
Simulation
parameters
The switching period is kept constant
at a1.value
T, which
is equal to 50 µs.
Quantity
Switching frequency f
Input votage Ui
Quantity
Battery
voltage
Switching
frequency
f Ub
Input
votage
Ui
Output
voltage
Uo
Battery voltage Ub
Inductor L1
Output voltage Uo
Inductor
L2
Inductor
L1
Inductor
L
2
Inductor
L3
Inductor L3
Ratio
of
transformer
N1:N2:N3
Ratio of transformer N1 :N2 :N3
Resistor
load R
Resistor
load R
DCDC
linklink
capacitor
C
capacitor
C
Value
20 kHz
288 V
Value
V
2048
kHz
288
288VV
48 V
32.4
μH
288 V
32.4µH
μH
32.4
32.4
µH
0.9 μH
0.9 µH
6:6:1
6:6:1
8.3ΩΩ
8.3
1000
1000µFμF
Table 1. Simulation parameters.
T
T
T
300
Uo
u1
30
100
25
i1
0
0
-100
-25
-200
-50
-300
0.09212
0.09216
0.09220
0.09224
Time(s)
0.09228
i1(A)
Uo, u1(V)
200
0.09232
(a)
300
u1,u2,u3(V)
200
u2
u1
u3
100
0
-100
-200
-300
0.09212
0.09216
0.09220
0.09224
Time(s)
0.09228
0.09232
(b)
Figure 15. Simulated waveforms of shifted-phase angle control with fixed switching-frequency:
Figure 15. Simulated waveforms of shifted-phase angle control with fixed switching-frequency:
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port
port 1,
1, 22 and
and 3.
3.
Figure 16 plots the simulated waveforms with shifted-angle based control using continuously
Figure 16 plots the simulated waveforms with shifted-angle based control using continuously
chaotic modulation. The expected central switching frequency fs is set as 20 kHz and the chaotic
chaotic modulation. The expected central switching frequency fs is set as 20 kHz and the chaotic
bandwidth Δf is 2 kHz. There are infinite values for switching frequencies between 18 kHz and 20
bandwidth ∆f is 2 kHz. There are infinite values for switching frequencies between 18 kHz and
kHz. Figure 17 shows the simulated waveforms using discretely chaotic modulation, where four
20 kHz. Figure 17 shows the simulated waveforms using discretely chaotic modulation, where
different switching frequencies (18 kHz, 19.3 kHz, 20.6 kHz and 22 kHz) are used alternatively. It is
four different switching frequencies (18 kHz, 19.3 kHz, 20.6 kHz and 22 kHz) are used alternatively.
observed that the switching periods are changed irregularly in Figures 16 and 17. Although the
It is observed that the switching periods are changed irregularly in Figures 16 and 17. Although the
switching periods vary chaotically, the output DC link voltage Uo of port 2 is kept stable with the
shifted-phase angle control and chaotic modulation. Actually, no distinct difference can be observed
in the output DC link voltage Uo between the fixed frequency modulation and the chaotic modulation
strategies. It verifies that chaotic modulation only affects the high-frequency characteristics and does
not deteriorate the low-frequency operating performance of the TPI bidirectional DC/DC converter.
Energies 2016, 9, 83
11 of 19
switching periods vary chaotically, the output DC link voltage Uo of port 2 is kept stable with the
shifted-phase angle control and chaotic modulation. Actually, no distinct difference can be observed in
the output DC link voltage Uo between the fixed frequency modulation and the chaotic modulation
strategies. It verifies that chaotic modulation only affects the high-frequency characteristics and does
not deteriorate the low-frequency operating performance of the TPI bidirectional DC/DC converter.
Energies 2016, 9, 83
Energies 2016, 9, 83
T1
T2
T3
T1
T2
T3
200
300
Uo
100
200
Uo
30
u1
25
30
i1
u1
0
100
0
25
i1
i1(A) i1(A)
o, u1(V)
Uo, u1U(V)
300
-100
0
-25
0
-200
-100
-50
-25
-300
-200
0.09562
-300
0.09562
0.09566
0.09570
0.09574
Time(s)
0.09570
0.09574
(a)
Time(s)
0.09566
1,u
2,u3(V)
u1,u2u,u
3(V)
300
0.09578
-50
0.09582
0.09578
0.09582
(a)
300
200
u1
u2
200
100
u1
u2
u3
u3
100
0
0
-100
-200
-100
-300
-200
0.09562
-300
0.09562
0.09566
0.09566
0.09570
0.09574
Time(s)
0.09570
0.09574
(b)
Time(s)
0.09578
0.09582
0.09578
0.09582
(b)
Figure 16. Simulated waveforms of shifted-phase angle control with continuously chaotic modulation:
Figure 16. Simulated waveforms of shifted-phase angle control with continuously chaotic modulation:
(a)
converter
voltage,waveforms
current ofofport
1 and output
of port
2; (b) converter
voltages of
Figure
16. Simulated
shifted-phase
angle voltage
control with
continuously
chaotic modulation:
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port
1,
2
and
3.
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port 1, 2 and 3.
port 1, 2 and 3.
T1
T2
T3
T1
T2
T3
200
300
Uo
100
200
Uo
30
u1
i1
u1
i1
0
100
-100
0
25
30
0
25
-25
0
-200
-100
-300
-200
0.09562
-300
0.09562
-50
-25
0.09566
0.09566
300
2,u3(V)
u1,u2u,u1,u
3(V)
300
200
100
200
i1(A) i1(A)
o, u1(V)
(V)
Uo, u1U
300
u1
u1
0.09570
0.09574
Time(s)
0.09570
0.09574
(a)
Time(s)
0.09578
-50
0.09582
0.09578
0.09582
(a)
u2
u2
100
0
u3
u3
0
-100
-200
-100
-300
-200
0.09562
-300
0.09562
0.09566
0.09566
0.09570
0.09574
Time(s)
0.09570
0.09574
(b)
Time(s)
0.09578
0.09582
0.09578
0.09582
(b)
Figure 17. Simulated waveforms of shifted-phase angle control with discretely chaotic modulation:
(a)
converter
voltage,waveforms
current of of
port
1 and output
voltage
portdiscretely
2; (b) converter
voltages of
Figure
17. Simulated
shifted-phase
angle
controlofwith
chaotic modulation:
Figure 17. Simulated waveforms of shifted-phase angle control with discretely chaotic modulation:
port
1, 2 and 3.voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
(a) converter
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port 1, 2 and 3.
port
1, 2 and18–20
3.
Figures
show the simulated waveforms of the phase-shifted PWM controlled TPI
bidirectional
converter
using fixedwaveforms
switching frequency,
continuously
chaotic
modulation
Figures DC/DC
18–20 show
the simulated
of the phase-shifted
PWM
controlled
TPI
and
discretely
chaotic
modulation,
respectively.
The
value
of
duty
ratio
for
converter
in
port
1
is
0.75.
bidirectional DC/DC converter using fixed switching frequency, continuously chaotic modulation
It
is observed
bothmodulation,
the continuously
chaoticThe
modulation
and ratio
the discretely
chaotic
modulation
and
discretelythat
chaotic
respectively.
value of duty
for converter
in port
1 is 0.75.
produce
chaotic
waveforms
while keepingchaotic
Uo stable.
It is observed
that
both the continuously
modulation and the discretely chaotic modulation
produce chaotic waveforms while keeping Uo stable.
Energies 2016, 9, 83
12 of 19
Figures 18–20 show the simulated waveforms of the phase-shifted PWM controlled TPI
bidirectional DC/DC converter using fixed switching frequency, continuously chaotic modulation
and discretely chaotic modulation, respectively. The value of duty ratio for converter in port 1 is 0.75.
It is observed that both the continuously chaotic modulation and the discretely chaotic modulation
produce
chaotic
Energies 2016,
9, 83 waveforms while keeping Uo stable.
Energies 2016, 9, 83
T
T
u1
u1
U o, U
u1o(V)
, u1(V)
(V)
u1,u
u12,u23,u
3(V)
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
0.09562
-300
0.09562
T
T
0.02566
0.02566
T
T
i1
i1
0.02570
0.02574
0.02570Time(s)
0.02574
Time(s)
0.02578
0.02578
30
30
25
25
0
0
-25
-25
-50
-50
0.02582
0.02582
i1(A)
i1(A)
300
300
200 Uo
200 Uo
100
100
0
0
-100
-100
-200
-200
-300
0.02562
-300
0.02562
(a)
(a)
u1
u1
0.09566
0.09566
u2
u2
u3
u3
0.09570
0.09574
0.09570Time(s)
0.09574
Time(s)
(b)
0.09578
0.09578
0.09582
0.09582
(b)
Figure
18. Simulated
Figure 18.
Simulated waveforms
waveforms of
of phase-shifted
phase-shifted PWM
PWM control
control with
with fixed
fixed switching-frequency:
switching-frequency:
Figure
18. Simulated
waveforms
of phase-shifted
PWM
control
with2;fixed
switching-frequency:
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
converter
voltages
(a) converter voltage, current of port 1 and output voltage of port 2; (b)
(b) converter
voltages of
of
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
2;
(b)
converter
voltages
of
port
1,
2
and
3.
port 1, 2 and 3.
port 1, 2 and 3.
T1
T1
0.06566
0.06566
T3
T3
u1
u1
Uo
Uo
U o, U
u1o(V)
, u1(V)
u1,uu21,u32(V)
,u3(V)
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
0.09562
-300
0.09562
T2
T2
30
30
25
25
0
0
-25
-25
-50
-50
i1
i1
0.06570
0.06574
Time(s)0.06574
0.06570
Time(s)
(a)
0.06578
0.06578
i1(A)
i1(A)
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
0.06562
-300
0.06562
0.06582
0.06582
(a)
u1
u1
0.09566
0.09566
u2
u2
u3
u3
0.09570
0.09574
0.09570Time(s)
0.09574
Time(s)
0.09578
0.09578
0.09582
0.09582
(b)
(b)
Figure 19. Simulated waveforms of phase-shifted PWM control with continuously chaotic modulation:
Figure
19. Simulated
waveforms
phase-shifted
PWM voltage
control with
continuously
chaotic modulation:
(a)
converter
voltage,
current ofof
1 and output
of port
2; (b) converter
voltages of
Figure
19. Simulated
waveforms
ofport
phase-shifted
PWM control with
continuously
chaotic modulation:
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
2;
(b)
converter
of
port
1, 2 and 3.voltage, current of port 1 and output voltage of port 2; (b) converter voltages
(a) converter
voltages of
port 1, 2 and 3.
port 1, 2 and 3.
Energies 2016, 9, 83
13 of 19
Energies 2016, 9, 83
T1
T2
T3
300
Uo
30
u1
i1
100
25
0
0
-100
-25
-200
-50
-300
0.09562
0.09566
0.09570
0.09574
Time(s)
0.09580
i1(A)
Uo, u1(V)
200
0.09582
(a)
300
u1,u2,u3(V)
200
u1
u2
u3
100
0
-100
-200
-300
0.09562
0.09566
0.09570
0.09574
Time(s)
0.09578
0.09582
(b)
Figure 20. Simulated waveforms of phase-shifted PWM control with discretely chaotic modulation:
Figure 20. Simulated waveforms of phase-shifted PWM control with discretely chaotic modulation:
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port 1, 2 and 3.
port 1, 2 and 3.
Then, the experiments are carried out on a small-power laboratory prototype to verify the
Then,
the of
experiments
are
carried out
on a small-power
laboratory
prototype
to verify
performance
the proposed
modulation
strategies
and control scheme
for TPI
bidirectional
DC/DCthe
performance
of
the
proposed
modulation
strategies
and
control
scheme
for
TPI
bidirectional
DC/DC
converter. The experimental parameters are listed in Table 2. It should be noted that the rated voltage
converter.
Theofexperimental
are listed in
should energy
be noted
that the rated
voltage
and power
the prototypeparameters
are lower compared
to Table
those 2.
in It
practical
conversion
systems
of
EVs
andofHEVs,
but the are
purpose
the experiments
to verifyenergy
the validity
of the
proposed
and
power
the prototype
lower of
compared
to those inispractical
conversion
systems
of EVs
modulation
converter.
Therefore,
low-power
prototype
and
HEVs, butand
the control
purposefor
ofTPI
the bidirectional
experiments DC/DC
is to verify
the validity
of thethe
proposed
modulation
and
couldfor
still
bebidirectional
used. Power MOSFETs
(IPW65R019C7)
andthe
the low-power
driver chip prototype
HCPL3120could
are adopted
control
TPI
DC/DC converter.
Therefore,
still be for
used.
the power
switches
in the experiments.
DSPchip
TI-TMS320F28335
used asfor
thethe
digital
controller
to in
Power
MOSFETs
(IPW65R019C7)
and theThe
driver
HCPL3120 are isadopted
power
switches
implement
the
control
algorithm
and
generate
the
switching
pulses.
The
voltage
sensors
(LEM
LV25-P,
the experiments. The DSP TI-TMS320F28335 is used as the digital controller to implement the control
LEM, Beijing,
China) the
andswitching
the current
sensors
LA25-NP,
are used
to
algorithm
and generate
pulses.
The(LEM
voltage
sensors LEM,
(LEMBeijing,
LV25-P,China)
LEM, Beijing,
China)
measure
the
voltages
and
currents.
The
three-port
high-frequency
transformer
is
made
by
choosing
and the current sensors (LEM LA25-NP, LEM, Beijing, China) are used to measure the voltages and
proper magnetic cores and copper wires.
currents.
The three-port high-frequency transformer is made by choosing proper magnetic cores and
copper wires.
Table 2. Experimental parameters.
Table Quantity
2. Experimental parameters.
Value
Switching frequency f
20 kHz
Quantity
Value
Input votage Ui
50 V
Switching
frequency
f Ub
20
Battery
voltage
12kHz
V
Input votage Ui
50 V
Output voltage Uo
65
V
Battery voltage Ub
12 V
Inductor
L
1
101
μH
Output voltage Uo
65 V
Inductor
L1
101 μH
µH
Inductor
L2
206
Inductor L2
206 µH
Inductor L3
29
μH
Inductor L3
29 µH
Ratio
of transformer
5:7:1
Ratio
of transformer
N1 :N2 :NN31:N2:N3
5:7:1
Resistor
60
Resistor
load Rload R
60 Ω
Ω
DC link
C
1000 μF
µF
DC capacitor
link capacitor
C
1000
Figures21–23
21–23show
showthe
themeasured
measured waveforms
waveforms of
of TPI
TPI bidirectional
bidirectional DC/DC
Figures
DC/DCconverter
converterwith
with
shifted-phaseangle
anglecontrol
controlininexperiments.
experiments. The
The switching
asas
TT
with
fixed
shifted-phase
switchingperiod
periodisiskept
keptconstant
constant
with
fixed
switching-frequency
Figure21.
21.Different
Differentfrom
from that,
that, the
using
switching-frequency
ininFigure
the switching
switchingperiods
periodschange
changechaotically
chaotically
using
13
Energies 2016, 9, 83
14 of 19
Energies 2016, 9, 83
Energies 2016, 9, 83
T
T
T
Uo
T
u1 T
u1
i1 T
i1
Uo
u1
i1
Time(25μs/div)
Time(25μs/div)
(a)
u2(10V/div)
u2(10V/div)
uu
u3(50V/div)
u2(10V/div)
u1、uu13、
(50V/div)
1、
3(50V/div)
ip(1.88A/div)
ip(1.88A/div)
ip(1.88A/div)
Uu
u1(20V/div)
Uo、Uuo1、
(20V/div)
o、
1(20V/div)
continuously chaotic modulation in Figure 22 and using discretely chaotic modulation in Figure 23,
Energies 2016, 9, 83
continuously
chaotic modulation
in Figure 22
and usingare
discretely
chaotic
in Figure 23,the
respectively.
Although
the high-frequency
behaviors
irregular
usingmodulation
chaotic modulation,
continuously Although
chaotic modulation
in Figure 22
and using
discretely
in Figure the
23,
respectively.
the high-frequency
behaviors
are
irregularchaotic
using modulation
chaotic modulation,
output voltage of Uo in port 2 is kept stable in Figures 22 and 23. To show the improved spectrum
continuously
chaotic
modulation
in
Figure
22
and
using
discretely
chaotic
modulation
in
Figure
23,
respectively.
Although
the
high-frequency
behaviors
are
irregular
using
chaotic
modulation,
the
output voltage of Uo in port 2 is kept stable in Figures 22 and 23. To show the improved spectrum
performance,
Figure
24
plots
the
power
spectrum
of the
DC
link
current
of port
1 using
different
respectively.
Although
the
high-frequency
behaviors
are
irregular
using
chaotic
modulation,
the
output
voltage
of
U
o
in
port
2
is
kept
stable
in
Figures
22
and
23.
To
show
the
improved
spectrum
performance, Figure 24 plots the power spectrum of the DC link current of port 1 using different
modulation
strategies.
observed
clearly
that
distinct
peaky
harmonics
exist
around
4 kHz
and its
performance,
Figure
24
plots
power
spectrum
of the
DC
current
ofthe
port
1 using
different
output voltage
of Uo It
inItisport
2the
is kept
stable
in Figures
22
andlink
23.
To
show
improved
spectrum
modulation
strategies.
is observed
clearly
that
distinct
peaky
harmonics
exist
around
4 kHz
and its
multiple
frequencies
using
switching-frequency
in
Figure
24a. Differently,
the peaky
switching
performance,
Figure
24It plots
the
power
spectrum
ofin
the
DC link
of port
using
different
modulation
strategies.
isfixed
observed
clearly
that distinct
peaky
harmonics
exist
around
4 kHz
and its
multiple
frequencies
using
fixed
switching-frequency
Figure
24a.current
Differently,
the 1peaky
switching
harmonics
are
reduced
for
around
10
dB
in
spectrum
by
using
continuously
chaotic
modulation
in
modulation
strategies.
Itfor
is observed
distinct
peaky
existchaotic
around
4 kHz
and its
multiple
frequencies
using
fixed
switching-frequency
in
24a.
Differently,
the peaky
switching
harmonics
are
reduced
around
10clearly
dB in that
spectrum
byFigure
usingharmonics
continuously
modulation
in
Figure
24b24b
and
using
discretely
chaotic
ininFigure
24c.
The
reason
in
that
the
power
multiple
frequencies
using
switching-frequency
in
Figure
24a.
Differently,
the
switching
harmonics
are
reduced
for fixed
around
10 modulation
dBmodulation
in spectrum
by
using
continuously
chaotic
modulation
in of
Figure
and
using
discretely
chaotic
Figure
24c.
The
reasonlies
lies
inpeaky
that
the
power
switching
harmonics
is
spread
out
within
the
nearby
frequency
domain
in
spectrum.
harmonics
are
reduced
for
around
10
dB
in
spectrum
by
using
continuously
chaotic
modulation
in
Figure
24b
and
using
discretely
chaotic
modulation
in
Figure
24c.
The
reason
lies
in
that
the
power
of switching harmonics is spread out within the nearby frequency domain in spectrum.
Figure
24b and
using discretely
modulation
in Figure
24c.domain
The reason
lies in that the power
of
switching
harmonics
is spreadchaotic
out within
the nearby
frequency
in spectrum.
T
T Uothe nearby frequency domain in spectrum.
T
of switching harmonics is spread
out within
u1
u1
u1
u2
u2
u2
u3
u3
u3
Time(25μs/div)
Time(25μs/div)
(b)
(a)
Time(25μs/div)
(b)
Time(25μs/div)
T2
T3
Uo
u1 T1 i1 T2
i1
u1
T3
Uo
T1
u1
i1
Time(25μs/div)
Time(25μs/div)
(a)
u2(10V/div)
u2(10V/div)
u2(10V/div)
uu1、
u3(50V/div)
u1、u13、
(50V/div)
3(50V/div)
ip(1.88A/div)
ip(1.88A/div)
ip(1.88A/div)
Uuo、
u1(20V/div)
Uo、Uuo1、
(20V/div)
1(20V/div)
Figure 21. Measured waveforms of shifted-phase angle control using fixed switching-frequency:
Figure
21. Measured waveforms
using fixed switching-frequency:
(a) of shifted-phase angle control (b)
Figure
21. Measured
of shifted-phase
angle
control
using2;fixed
switching-frequency:
(a)
converter
voltage, waveforms
current of port
1 and output
voltage
of port
(b) converter
voltages of
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
2;
(b)
converter
voltages of
Figure
21.
Measured
waveforms
of
shifted-phase
angle
control
using
fixed
switching-frequency:
port 1, 2 and 3.
port 1, 2 and 3.
port
1,
2
and
3.
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
T1 T 2
T 3 Uo
port 1, 2 and 3.
u1
u1
u1
u2
u2
u2
u3
u3
u3
Time(25μs/div)
Time(25μs/div)
(b)
(a)
Time(25μs/div)
(b)
Time(25μs/div)
T1
T2
T3
Uo
u11
T
u1
Ti21
i1
T3
Uo
u1
i1
Time(25μs/div)
Time(25μs/div)
(a)
u2(10V/div)
u2(10V/div)
u2(10V/div)
uu1、
u3(50V/div)
u1、u13、
(50V/div)
3(50V/div)
ip(1.88A/div)
Uuo、
u1(20V/div)
ip(1.88A/div)
ip(1.88A/div)
Uo、Uuo1、
(20V/div)
1(20V/div)
Figure 22. Measured waveforms of shifted-phase angle control using continuously chaotic modulation:
(a)
(b)
Figure
22. Measured
waveforms
of port
shifted-phase
angle control
continuously
chaotic modulation:
(a)
converter
voltage,
current of
of
1 and output
voltageusing
of port
2; (b) converter
of
Figure
22. Measured
waveforms
shifted-phase
angle control
using
continuously
chaoticvoltages
modulation:
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
2;
(b)
converter
voltages of
Figure
22.
Measured
waveforms
of
shifted-phase
angle
control
using
continuously
chaotic modulation:
port
1,
2
and
3.
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port
1, 2 and 3.voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
(a) converter
port 1, 2 and 3.
Uo
T2
T1
T3
port 1, 2 and 3.
(a)
Time(25μs/div)
u1
u1
u1
u2
u2
u2
u3
u3
u3
Time(25μs/div)
Time(25μs/div)
(b)
Time(25μs/div)
(b)
Figure 23. Measured waveforms of shifted-phase angle control using discretely chaotic modulation:
(a)
(b)
Figure
23. Measured
shifted-phase
anglevoltage
control of
using
chaotic modulation:
(a)
converter
voltage,waveforms
current ofofport
1 and output
portdiscretely
2; (b) converter
voltages of
(a)
converter
voltage,
current
of
port
1
and
output
voltage
of
port
2;
(b)
converter
voltages of
Figure
Measured
waveforms of shifted-phase angle control using discretely chaotic modulation:
port
1, 223.
and
3.
Figure
23.
Measured
waveforms
of
shifted-phase
angle
control
using
discretely
chaotic
modulation:
port
1, 2 and 3.voltage, current of port 1 and output voltage of port 2; (b) converter voltages
(a) converter
of
(a) port
converter
current of port 1 and output voltage of port 2; (b) converter voltages of
1, 2 andvoltage,
3.
port 1, 2 and 3.
14
14
14
Energies 2016, 9, 83
15 of 19
Energies
2016, 9, 83
Energies 2016, 9, 83
(a)
(a)
(b)
(b)
(c)
(c)
Figure 24. Measured power spectrum density of shifted-phase
angle control: (a) fixed switching-frequency;
Figure 24.
Measured power spectrum density of shifted-phase angle control: (a) fixed
(b) continuously chaotic modulation; (c) discretely chaotic modulation.
Figure 24. Measured power
spectrum density
of shifted-phase
control: (a)
fixed switching-frequency;
switching-frequency;
(b) continuously
chaotic
modulation;angle
(c) discretely
chaotic
modulation.
(b)The
continuously
chaotic
modulation;
(c)
discretely
chaotic
modulation.
experimental verification is also given for the TPI bidirectional DC/DC converter with
T
u1
u1
ip
T
T
u2(10V/div)
u2(10V/div)
u1、u3(50V/div)
u1、u3(50V/div)
Uo、u1(20V/div) ip(1.24A/div)
Uo、u1(20V/div) ip(1.24A/div)
phase-shifted
PWMverification
control. The
measured
waveforms
using fixed DC/DC
switching-frequency,
The
experimental
is also
given for
the TPI bidirectional
converter with
The experimental
verification
is also
given for
the modulation
TPI bidirectional
DC/DC
converter
with
continuously
chaotic
modulation
and
discretely
chaotic
are
shown
in Figures
25–27,
phase-shifted PWM control. The measured waveforms using fixed switching-frequency,
continuously
phase-shifted
PWM
control.
The measured
waveforms
using voltage
fixed U
switching-frequency,
respectively.
The and
chaotic
modulation
schemes
can
keepare
the shown
output
o stable in port 2
chaotic
modulation
discretely
chaotic
modulation
in Figures
25–27 respectively.
continuously
chaotic
modulation
and
discretely
chaotic
modulation
are
shown
in Figures 25–27,
although they exhibit chaotic behaviors in high-frequency domain.
The
chaotic modulation
schemes
can keep
the output
voltage
Uo stable
in port
2 although
respectively.
The chaotic
modulation
schemes
can keep
the output
voltage
Uo stable
in port they
2
exhibit
chaotic
behaviors
in
high-frequency
domain.
although they exhibit chaotic
behaviors
domain.
T
T
T inUhigh-frequency
o
Uo
ip
Time(25μs/div)
(a)
u1
u1
u2
u2 u3
u3
Time(25μs/div)
(b)
Figure 25. Measured waveforms
of phase-shifted PWM control using
fixed switching frequency:
Time(25μs/div)
Time(25μs/div)
(a) converter voltage, current
2; (b) converter voltages of
(a) of port 1 and output voltage of port(b)
port 1, 2 and 3.
Figure 25. Measured waveforms of phase-shifted PWM control using fixed switching frequency:
Figure 25. Measured waveforms of phase-shifted PWM control using fixed switching frequency:
(a) converter voltage, current of port 1 and output
15 voltage of port 2; (b) converter voltages of
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
port 1, 2 and 3.
port 1, 2 and 3.
15
Energies 2016, 9, 83
16 of 19
Energies 2016, 9, 83
Energies 2016, 9, 83
T1
T2
T3
Uo
T1
T2
T3
Uo
u1
ip
u1
ip
T2
T1
T3
u2(10V/div)
u2(10V/div)
(10V/div)
u1、uu13、
(50V/div)
u32(50V/div)
u1、u3(50V/div)
ip(1.24A/div)
ip(1.24A/div)
iup(1.24A/div)
Uo、Uuo1、
(20V/div)
Uo、u1(20V/div)
1(20V/div)
Energies 2016, 9, 83
Uo
ip
u1
u1
u1
u2
u2
u1
u3
u2 u3
Time(25μs/div)
u3
(a)
(b)
Time(25μs/div)
Time(25μs/div)
(a) of phase-shifted PWM control using continuously
(b)
Figure 26. Measured waveforms
chaotic modulation:
Figure 26. Measured waveforms of phase-shifted PWM control using continuously chaotic modulation:
(a) converter
voltage,
current
of
port 1 and output
voltageusing
of Time(25μs/div)
port
2; (b) converter
voltages of
Time(25μs/div)
Figure
26. Measured
waveforms
of phase-shifted
PWM control
continuously
chaotic modulation:
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
portconverter
1, 2 and 3.voltage, current
(a) of port 1 and output voltage of port(b)
(a)
2; (b) converter voltages of
port 1, 2 and 3.
Time(25μs/div)
u1
T1
u1
ip
T2
T3
ip
Time(25μs/div)
(a)
Time(25μs/div)
Uo
u2(10V/div)
u2(10V/div)
uu23(10V/div)
u1、uu13、
(50V/div)
(50V/div)
u1、u3(50V/div)
ip(1.24A/div)
Uo、Uuo1、
(20V/div)
ip(1.24A/div)
ipu(1.24A/div)
Uo、u1(20V/div)
1(20V/div)
port 1, 2 and 3.
Figure 26. Measured waveforms of phase-shifted PWM control using continuously chaotic modulation:
Uo
T2
T1
T3
(a) converter voltage, current of port 1 and output voltage
of port 2; (b) converter voltages of
u1
Uo
T2
T1
T3
ip
u1
port 1, 2 and 3.
u
1
u2
u1
u2
u3
u2
u3
Time(25μs/div)
u3
(b)
Time(25μs/div)
(a) of phase-shifted PWM control using(b)
Figure 27. Measured waveforms
discretely chaotic modulation:
(a) converter
voltage,waveforms
current
ofofport
1 and output
portdiscretely
2; (b) converter
voltages of
Time(25μs/div)
Time(25μs/div)
Figure
27. Measured
phase-shifted
PWMvoltage
control of
using
chaotic modulation:
Figure
waveforms
of phase-shifted PWM control using
discretely chaotic modulation:
port27.
1, 2Measured
and 3.voltage,
(a) of
(b)2;
(a)
converter
current
port 1 and output voltage of port
(b) converter voltages of
(a) converter
voltage,
current of port 1 and output voltage of port 2; (b) converter voltages of
port 1, 2 and
3.
Figure
27.3.Measured waveforms of phase-shifted PWM control using discretely chaotic modulation:
portThe
1, 2 spectrum
and
comparison of DC link current in port 1 is presented among different switching
(a) converter voltage, current of port 1 and output voltage of port 2; (b) converter voltages of
strategies
for the phase-shifted
control
in Figure
Figure 28a,
thedifferent
distinct switching
The spectrum
comparison ofPWM
DC link
current
in port 28.
1 is In
presented
among
port 1, 2 and 3.
harmonics
are
observed
in
the
spectrum
using
fixed
switching-frequency.
Those
harmonic
peaks
may
strategies
for
the
phase-shifted
PWM
control
in
Figure
28.
In
Figure
28a,
the
distinct
switching
The spectrum comparison of DC link current in port 1 is presented among different
switching
introduce
the
conducted
EMI
in
EVs
and
HEVs.
By
using
chaotic
modulation,
the
switching
harmonics
are
observed
in
the
spectrum
using
fixed
switching-frequency.
Those
harmonic
peaks
may
strategiesThe
forspectrum
the phase-shifted
control
in Figure
In Figureamong
28a, the
distinct
switching
comparison PWM
of DC link
current
in port 28.
1 is presented
different
switching
harmonics the
are reduced
for around
10
dB and
in Figure
28b,c.
verifies that the
conducted the
EMIswitching
issue can
introduce
conducted
in
EVs
HEVs.
By It
using
harmonics
arefor
observed
in theEMI
spectrum
using
fixed
switching-frequency.
Those
harmonic
peaks may
strategies
the
phase-shifted
PWM
control
in Figure
28. Inchaotic
Figure modulation,
28a,
the distinct
switching
be mitigated
effectively
by using
chaotic
modulation
strategies.
As mentioned
in Section
3, the
simple
harmonics
are
reduced for
around
10 dBusing
in Figure
28b,c.
It verifies
that the
conducted
EMI
issue
can
harmonics
are observed
in the
spectrum
fixed
switching-frequency.
Those
harmonic
peaks
may
introduce
the conducted
EMI
in EVs
and HEVs.
By using
chaotic modulation,
the
switching
harmonics
Logisitc
map
is
used
to
generate
the
iterative
series
for
chaoizing
the
switching
frequency.
Therefore,
be
mitigated
effectively
by using
chaotic
modulation
strategies.
As
mentioned
in Sectionthe
3, the
simple
introduce
conducted
EMI
in
EVs
andItHEVs.
By
using
chaotic
modulation,
switching
are reduced
forthe
around
10 dB
in Figure
28b,c.
verifies
that
the
conducted
EMI issue
cancost
be mitigated
no additional
hardware
is needed
for
the proposed
chaotic
modulation,
and the
system Therefore,
is the
Logisitc
map
is
used
to
generate
the
iterative
series
for
chaoizing
the
switching
frequency.
harmonics
are reduced
for
around 10 dB
in FigureAs
28b,c.
It verifiesinthat
the conducted
EMI Logisitc
issue canmap
effectively
by
using
chaotic
modulation
strategies.
mentioned
Section
3, the simple
same
as
that
with
fixed
switching-frequency.
no
additionaleffectively
hardwareby
is using
needed
for the
proposed strategies.
chaotic modulation,
and the
system
is the
be mitigated
chaotic
modulation
As mentioned
Section
3, cost
the
simple
is used
toasgenerate
the
iterative
series
for chaoizing
the switching
frequency.inTherefore,
no additional
same
that
with
fixed
switching-frequency.
Logisitc map is used to generate the iterative series for chaoizing the switching frequency. Therefore,
hardware is needed for the proposed chaotic modulation, and the system cost is the same as that with
no additional hardware is needed for the proposed chaotic modulation, and the system cost is the
fixed switching-frequency.
same as that with fixed switching-frequency.
(a)
Figure(a)
28. Cont.
Figure 28. Cont.
(a)
Figure16
28. Cont.
Figure 28. Cont.
16
16
Energies 2016, 9, 83
17 of 19
Energies 2016, 9, 83
(b)
(c)
Figure 28. Measured power spectrum density of phase-shifted PWM control: (a) fixed switching-frequency;
Figure 28.
Measured power spectrum density of phase-shifted PWM control: (a) fixed
(b) continuously chaotic modulation; (c) discretely chaotic modulation.
switching-frequency; (b) continuously chaotic modulation; (c) discretely chaotic modulation.
6. Conclusions
6. Conclusions
In this paper, the chaotic modulation strategies and the related control schemes are presented
In TPI
thisbidirectional
paper, the chaotic
strategies
the related
control
schemes
are presented
for
DC/DCmodulation
converters, which
couldand
be used
in electric
and hybrid
vehicles.
Two
modulation strategies,
namely the continuously
chaotic
modulation
and theand
discretely
chaotic
for chaotic
TPI bidirectional
DC/DC converters,
which could
be used
in electric
hybrid
vehicles.
are proposed.
With conventional
modulation,
distinct harmonic
peaks
Twomodulation
chaotic modulation
strategies,
namely thefixed-frequency
continuously chaotic
modulation
and the discretely
exist
around
the
switching
frequency
and
its
multiple
values
in
the
spectrum,
which
may
induce
chaotic modulation are proposed. With conventional fixed-frequency modulation, distinct harmonic
conducted
EMI in
and hybrid
vehicles.
Different
from
that,in
the
switching
frequencies
of the
peaks
exist around
theelectric
switching
frequency
and its
multiple
values
the
spectrum,
which may
induce
proposed chaotic modulation strategies are changed irregularly for TPI bidirectional DC/DC
conducted EMI in electric and hybrid vehicles. Different from that, the switching frequencies of
converters. The power clustered around the switching frequency and its multiple values are thus
the proposed chaotic modulation strategies are changed irregularly for TPI bidirectional DC/DC
spread out within the nearby frequency domain, and the switching harmonic peaks are suppressed.
converters.
The power clustered around the switching frequency and its multiple values are thus
Our experiments on a small-power laboratory prototype verify that the proposed chaotic modulation
spread
out
within
the nearby
frequency
domain,
andfor
thearound
switching
harmonic
peaks
are suppressed.
strategies can reduce
the switching
harmonic
peaks
10 dB
in spectrum.
Therefore,
the
Ourconducted
experiments
on
a
small-power
laboratory
prototype
verify
that
the
proposed
chaotic
modulation
EMI induced by the high-frequency switching harmonics is mitigated effectively.
The
strategies
reducefrequency
the switching
harmonic
around
10 of
dBswitching
in spectrum.
Therefore,
averagecan
switching
is as high
as 20 kHz,peaks
and thefor
chaotic
change
frequency
will
the not
conducted
EMI
byperformance
the high-frequency
switching
harmonics
is mitigated effectively.
deteriorate
theinduced
DC output
of TPI bidirectional
DC/DC
converter.
On the
other hand,
the proposed
chaotic
strategies
TPI bidirectional
The average
switching
frequency
is as high
as 20modulation
kHz, and the
chaoticfor
change
of switchingDC/DC
frequency
converters
have
the
same
hardware
compared
to
the
conventional
fixed-frequency
modulation.
will not deteriorate the DC output performance of TPI bidirectional DC/DC converter.
The
chaotic
can be modulation
implementedstrategies
easily with
the bidirectional
digital controller.
On the
othermodulation
hand, the algorithms
proposed chaotic
for TPI
DC/DC
The
one-dimensional
logistic
map
is
used
to
generate
the
chaotic
series,
which
in
turn
generates
the
converters have the same hardware compared to the conventional fixed-frequency modulation.
irregular switching frequencies for TPI bidirectional DC/DC converters. Therefore, the proposed
The chaotic modulation algorithms can be implemented easily with the digital controller. The
strategies can provide better spectrum performance for TPI bidirectional DC/DC converters without
one-dimensional logistic map is used to generate the chaotic series, which in turn generates the
increasing the system cost.
irregular switching frequencies for TPI bidirectional DC/DC converters. Therefore, the proposed
Acknowledgments:
work
was supported
in part byfor
theTPI
National
Key Basic DC/DC
Research Program
of China
strategies
can provideThis
better
spectrum
performance
bidirectional
converters
without
(973 program) under Grant 2013CB035603, in part by the National Natural Science Foundation of China under
increasing
the system cost.
Grant 51577027, in part by the Aeronautical Science Foundation of China under Grant 20142869014, and in part
by Jiangsu Province Qin Lan Project (1116000195).
Acknowledgments: This work was supported in part by the National Key Basic Research Program of China
(973 program) under Grant 2013CB035603, in part by the National Natural Science Foundation of China under
Grant 51577027, in part by the Aeronautical Science Foundation of China under Grant 20142869014, and in part by
17
Jiangsu Province Qin Lan Project (1116000195).
Energies 2016, 9, 83
18 of 19
Author Contributions: Zheng Wang proposed the idea, designed the method and wrote the paper; Bochen Liu
designed and did the experiments; Yue Zhang and Kai Chu participated in building the experimental setup and
analyzing the data; Ming Cheng contributed verifying validity of the method.
Conflict of Interest: The authors declare no conflicts of interests.
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