Unified Analysis of Isolated
Bidirectional Converters
for Battery Charging
Simone Buso, Giorgio Spiazzi
University of Padova - DEI
Outline
Introduction
Review of Considered Converter Topologies
Single-Phase Dual Active Bridge (DAB)
Single-Phase Series Resonant DAB (SR-DAB)
Three-Phase Dual Active Bridge (DAB)
Three-Phase Series Resonant DAB (SR-DAB)
Interleaved Boost with Coupled Inductor (IBCI)
Unified Analysis
Soft-switching conditions
Transferred Power Calculation
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Introduction
ZIN
IOUT
+
+
+
ZOUT
+
+
VIN
VOUT
V2
V1
-
-
-
ISOLATED DC-DC
(STAGE #1)
DC-LINK
VBATT
-
CURRENT SOURCE
(STAGE #2)
Focus on the isolated stage
(V1 = high voltage port, V2 = low voltage port)
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Isolated Bidirectional Topologies
topologies with reduced switch count
Flyback
Cuk
Sepic
….
topologies with dual bridge (or half-bridge or push-pull)
configuration
Dual Active Bridge (DAB)
Interleaved Boost with Coupled Inductors (IBCI)
….
topologies with dual bridge configuration and high
frequency resonant networks
Series Resonant DAB (SR-DAB)
….
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Reduced Switch Count Topologies
High voltage and/or current stress on active components
Limited soft-switching operation
Transformer leakage inductance requires suitable snubber
circuits
Example: bidirectional Cuk converter
u1 Ld
+
C1
i1
+
ug
L1
S1
u2
+
C2
i2
L2
S2
Lm
+
Co uo Ro
-
1:n
Switch overvoltage!
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Dual Active Bridge (DAB)
Single-phase:
i1
S1aH
i2
S1bH
iL
L
S2aH
SS2bH
V1
V2
n:1
S1aL
S1bL
S2aL
S2bL
Simple phase-shift modulation
Extended soft-switching operation
Exploitation of transformer leakage inductance
Optimum design for constant port voltages V1 and V2
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Dual Active Bridge (DAB)
Three-phase:
S1aH
i1
S1bH
S1cH
va1
V1
L
S2bH
S2cH
i2
va2
iLb
vb1
S1bL
L
S1cL
iLc
V2
vb2
o1 o2
vc1
S1aL
iLa
S2aH
L
vc2
n:1
S2aL
S2bL
S2cL
Simple phase-shift modulation
Extended soft-switching operation
Exploitation of transformer leakage inductance
Optimum design for constant port voltages V1 and V2
Reduced input and output current ripples
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Series Resonant Dual Active Bridge
(SR-DAB)
Single-phase:
i1
i2
S1aH
S1bH
iL C
S2aH
L
S2bH
vC
V1
V2
n:1
S1aL
S1bL
S2aL
S2bL
Same characteristics as single-phase DAB
Higher degree of freedom (two parameters: L and C)
Inherent protection against transformer saturation (with
C split between primary and secondary)
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Series Resonant Dual Active Bridge
(SR-DAB)
Three-phase:
S1aH
i1
S1bH
S1cH
va1
V1
S2aH
L
S2bH
S2cH
i2
va2
iLb C
vb1
S1bL
L
S1cL
iLc C
V2
vb2
o1 o2
vc1
S1aL
iLa
C
L
vc2
n:1
S2aL
S2bL
S2cL
Same characteristics as three-phase DAB
Higher degree of freedom (two parameters: L and C)
Inherent protection against transformer saturation (with
C split between primary and secondary)
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Interleaved Boost with Coupled
Inductors (IBCI)
CCL
CCL
VCL
VCL
Lm
ia
ima
S2aH S2bH
i1
ns
ib
S1bH
np
i2
V2
S1aH
L iL
ns
V1
np
Lm
imb
S2aL S2bL
S1aL
S1bL
Simple phase-shift modulation
Extended soft-switching operation
Exploitation of mutual inductor leakage inductance
Duty-cycle control of port 2 switches for variable port
voltages V1 and V2
Reduced port 2 current ripple (low-voltage high-current
port)
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Unified Analysis
All the aforementioned topologies control the power
transfer between the two ports by modulating the voltage
applied to a current shaping impedance
iL
vA
Z
vB
For DAB and IBCI topologies, Z is a simple inductor while
for SR-DAB topologies Z is a series resonant L-C tank
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Phase-Shift Modulation
Example: power transfer from vA to vB
vA
VA
Single-phase DAB
-VA
iL
ϕ
L
2πfswt
π
vB
vA
2π
VB
vB
-VB
2πfswt
π
2π
iL(π) = - iL(0)
iL
iL(ϕ)
π
VA > VB
2π
2πfswt
iL(0)
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Phase-Shift Modulation
vA and vB are square wave voltages of amplitudes VA and
VB, respectively
VA = V1
VB = nV2
The power transfer between ports 1 and 2 is controlled
through the phase-shift angle ϕ
0 ≤ ϕ ≤ π/2
-π/2 ≤ ϕ ≤ 0
vA
vA
P
P
vB
vB
Inductor current has a piecewise linear behavior (DAB)
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Plus Phase-Shift Modulation
D > 0.5
2π(1-D)
IBCI converter
iL
S2aL
L
S2aH
S2bH
θ
VA
vA(θ)
vA
θ
S2bL
θ
vB
VB
vB(θ)
S1aH= S1bL
θ
S1aL= S1bH
Case A:
ϕ
0 < ϕ < π(D-1/2)
Case B:
ϕ−π(D-1/2)
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
θ6
2π
π(D-1/2) < ϕ < π/2
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Plus Phase-Shift Modulation
IBCI converter
2π(1-D)
S2aL
S2aH
S2bH
θ
S2bL
θ
VA
vA(θ)
0 ≤ θ ≤ θ1
vA = 0
θ
VB
vB(θ)
S1aH= S1bL
ϕ
Lm
ϕ−π(D-1/2)
ia
π(3/2-D)-ϕ
π(D-1/2)
ima
S1bH
i1
np
ns
i2
0
θ1 θ2
θ3
π
θ4 θ5
V
2
v B = − V1
θ
S1aL= S1bH
ib
npθ
6
Lm
imb
L iL
ns
V1
2π
S2aL S2bL
S1aL
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Plus Phase-Shift Modulation
IBCI converter
2π(1-D)
S2aL
S2aH
S2bH
θ
S2bL
θ
VA
vA(θ)
θ
VB
vB(θ)
θ1 ≤ θ ≤ θ2
ns
v A = (Vg − Vg + VCL )
np
ns
=
VCL = VA
np
C
v B = − V1
S1aH= S1bL
θ
S1aL= S1bH
CL
ϕ
VCL
ϕ−π(D-1/2)
Lm
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
ia
π
ima
θ6
ib
i1
np
θ4i2 θ5
V2
S1bH
S2bH
ns
2π
L iL
ns
V1
np
Lm
imb
S2aL
S1aL
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Plus Phase-Shift Modulation
IBCI converter
2π(1-D)
S2aL
S2aH
S2bH
θ
S2bL
θ
VA
vA(θ)
θ
VB
vB(θ)
θ2 ≤ θ ≤ θ3
ns
v A = (Vg − Vg + VCL )
np
ns
=
VCL = VA
np
C
v B = V1
S1aH= S1bL
θ
S1aL= S1bH
CL
ϕ
VCL
ϕ−π(D-1/2)
Lm
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
ia
π
ima
θ6
ib
S1aH
S1bH
i1
np
θ4i2 θ5
V2
S2bH
ns
2π
L iL
ns
V1
np
Lm
imb
S2aL
S1aL
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S1bL
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Plus Phase-Shift Modulation
IBCI converter
2π(1-D)
S2aL
S2aH
S2bH
θ
S2bL
θ
VA
vA(θ)
θ3 ≤ θ ≤ π
vA = 0
θ
VB
vB(θ)
S1aH= S1bL
ϕ
Lm
ϕ−π(D-1/2)
ia
π(3/2-D)-ϕ
π(D-1/2)
ima
S1aH
θ1 θ2
θ3
π
θ4 θ5
V
2
i1
ns
ib
S1bH
np
i2
0
v B = V1
θ
S1aL= S1bH
npθ
6
Lm
imb
L iL
ns
V1
2π
S2aL S2bL
S1aL
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S1bL
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Plus Phase-Shift Modulation
vA is a three-level voltage of amplitude VA while vB is a
square wave voltage of amplitude VB
VgD = (VCL − Vg )(1 − D ) ⇒
VA =
ns
n V
VCL = s 2
np 1 − D
np
VCL =
Vg
1− D
VB = V1
The duty-cycle of port 2 switches is controlled so as to
obtain the condition VA=VB
The power transfer between ports 1 and 2 is controlled
through the phase-shift angle ϕ
0 ≤ ϕ ≤ π/2
-π/2 ≤ ϕ ≤ 0
vA
vA
P
P
vB
vB
Inductor current
has a piecewise linear behavior
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Plus Phase-Shift Modulation
D > 0.5
IBCI converter
iL
2π(1-D)
S2aL
L
S2aH
S2bH
vB
θ
VA
vA(θ)
vA
θ
S2bL
θ
vB(θ)
VB
S1aH= S1bL
θ
S1aL= S1bH
Power flow
iL(θ)
I0
I1
I2
ϕ
Case A:
0 < ϕ < π(D-1/2)
(VA = VB)
θ
I4 = -I1
π(D-1/2)-ϕ
π(D-1/2)+ϕ
0 θ1
θ2
θ3
π θ4 θ5
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θ6
2π
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Plus Phase-Shift Modulation
D > 0.5
IBCI converter
iL
2π(1-D)
S2aL
L
S2aH
S2bH
θ
VA
vA(θ)
vA
θ
S2bL
θ
vB
VB
vB(θ)
S1aH= S1bL
θ
S1aL= S1bH
Power flow
I2
iL(θ)
I1
Case B:
I0
π(D-1/2) < ϕ < π/2
(VA = VB)
θ
I4 = -I1
ϕ
ϕ−π(D-1/2)
I5 = -I2
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
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θ6
2π
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Phase-Shift Modulation in ThreePhase Converters
va1
V1
vb1
θ
vc1
θ
Phase a voltages
(Hp: symmetry)
θ
vo1
2V1/3
V1/3
ϕ < π/3
θ
vao1 = vA
2V1/3
V1/3
θ
nvao2 = vB
2nV2/3
S1aH
nV2/3
i1
ϕ
π/3
2π/3
S1cH
va1
V1
π/3-ϕ
0
θ
S1bH
vb1
S1aL
S1bL
L
iLb
L
o1
vc1
π
iLa
S1cL
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iLc
L
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Phase-Shift Modulation in ThreePhase Converters
Decoupled phase behavior (perfect symmetry)
vA and vB are six-step voltage waveforms
The power transfer between ports 1 and 2 is controlled
through the phase-shift angle ϕ
0 ≤ ϕ ≤ π/2
-π/2 ≤ ϕ ≤ 0
vA
vA
P
P
vB
vB
Two different situations (power from port 1 to port 2):
0 ≤ ϕ ≤ π/3
π/3 ≤ ϕ ≤ π/2
Inductor current has a piecewise linear behavior (DAB)
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Systematic Steady-State Analysis
The analytical determination of the current waveforms
requires a systematic method for complex topologies (e.g.
three-phase resonant DAB).
The outcome is the mathematical expression of phase
currents as a function of phase-shift and other design
parameters.
In addition, soft switching conditions can be analyzed in
detail by extracting current values at the moment of
switch commutations.
iL
vA
General case:
Z
vB
v Z v A − vB
υ=
=
VN
VN
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VB
k=
VA
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Systematic Steady-State Analysis
The half switching period is divided into m subintervals. For each
subinterval (i = 1÷m), the values of the current shaping
impedance state variables xi at the end of the interval are
calculated, in normalized form, as a function of their value xi-1 at
the beginning, i.e.:
xi = M i xi −1 + N i υi
We can iterate, obtaining
 m −1

x m = M m ,1x 0 +  ∑ M m, i +1N i υi  + N m υm = M m,1x 0 + F
 i =1

j
where
M j,i = ∏ M k
j≥i
k =i
and υ is a column vector containing m υi elements, i.e.
υ = [υ1 υ2 L υm ]
T
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Systematic Steady-State Analysis
Exploiting the waveform symmetry, we can write:
x m = M m ,1 x 0 + F = − x 0
from which the initial state variable values are found:
x 0 = (− I − M m ,1 ) F
−1
that can be used to derive the current waveform expressions
and to discuss soft-switching conditions
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Example: IBCI
Base variables:
Base voltage:
VN = V A
Base impedance:
ZN = ωswL
Base current:
IN = VN/ZN
Base power:
PN = VN2/ ZN
The half switching period is subdivided into 4
subintervals (m = 4).
Two situations has to be considered:
Case A: 0 < ϕ < π(D-1/2)
Case B: π(D-1/2) < ϕ < π/2
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Example: IBCI
i=
1
2
υ
δ
υ
A
k
ϕ
-k
B
k
1

π D − 
2

1+k
3
δ
1

π D −  − ϕ
2

1

ϕ − π D − 
2

VA
vA(θ)
4
υ
δ
υ
1-k
2π(1 − D )
-k
1-k
3

π − D  − ϕ
2

-k
δ
1

π D − 
2

1

π D − 
2

2π(1-D)
θ
VB
vB(θ)
S1aH= S1bL
θ
S1aL= S1bH
Case B
ϕ
ϕ−π(D-1/2)
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
θ6
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2π
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Example: IBCI
Defining j(θ) = i(θ)/IN as the normalized inductor
current:
Ji = Ji−1 + υiδi
Comparing with:
for
i = 1,K, m
xi = M i xi −1 + N i υi
Mi = 1

Ni = δi
for
i = 1,K, m
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Example: IBCI
From: x 0 = (− I − M m ,1 ) F
−1
the normalized initial inductor current value is:
1 4
J0 = − ∑ υiδi
2 i=1
For both cases A and B we have:
π

J0 = − π(1 − D ) + k  − ϕ 
2

For plus phase-shift modulation k = 1:
1

J0 = π D −  − ϕ
2

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Example: SR-DAB
Base variables:
Base voltage:
VN = V A
Base impedance:
Z N = Zr
Base current:
IN = VN/ZN
Base power:
PN = VN2/ ZN
Base frequency:
ωN = ωr
iL
vA
L
Zr =
C
1
ωr =
LC
Z
vB
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Example: SR-DAB
υ
C
uC
L
iL
Current shaping impedance state variables:

θ
θ
θ
 jL (θ) = υ sin f  − UC0 sin f  + JL 0 cos f 

 n
 n
 n

u (θ) = υ1 − cos θ   + U cos θ  + J sin θ 
C0
 f 
 f  L0  f 

 C
 n 
 n
 n

Normalized state variable vector:
 jL 
x= 
uC 
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Example: SR-DAB
The half switching period is subdivided into 2
subintervals (m = 2).
i=1
i =2
υ
1+k
δ
ϕ
υ
1-k
δ
π−ϕ
VA
vA(θ)
θ
VB
vB(θ)
θ
ϕ
0
θ1
π
θ2
2π
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Example: SR-DAB
Current shaping impedance state variables:


 δi 
 δi  
 δi  
 cos  − sin  
 sin  
 JLi  
fn 
fn    JLi−1  


 fn  υ
=
+
i
U    δ 
U  






δ
δ
 Ci   sin i  cos i    Ci−1  1 − cos i  
f 
f 
f 
 n
 n 
  n

{
{
Matrix M
Matrix N
for i = 1,2

π
 π 
 cos  − sin  
 fn 
 fn  
Mm,1 = M2,1 = 
π
π 
 sin  cos  
 fn  
  fn 
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Example: SR-DAB
Matrix F:

π  
π
 π − ϕ 
 sin    sin  − 2 sin
 
 fn   + 
 fn 
 fn  k
F=

 π  
 π − ϕ
π 
 − cos  − 1
1 − cos    2 cos
 fn   
 fn 
 fn  

Initial conditions:
−1

π
π 
 − 1 − cos 
sin  
fn 
fn  



x0 =
F


π
π


− 1 − cos  
 − sin 
 fn 
 fn  

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Example: SR-DAB
Initial conditions:

 

 π − ϕ
ϕ
 
 − sin 
sin
 π  

 − sin   
1
fn 
fn 
k 



+
x0 =
fn   


π
 π − ϕ
 ϕ  
 π  

 − cos   
1 + cos  
0
 1 + cos  − cos
 fn  
 fn 
 fn 
 fn   

  π − ϕ
π
 ϕ 
− sin  + k sin
 − sin 
fn 
fn 
fn 




JL 0 (ϕ) =
π
1 + cos 
 fn 
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Example: Three-Phase DAB
vao1 = vA
2V1/3
V1/3
θ
nvao2 = vB
2nV2/3
nV2/3
θ
ϕ
π/3-ϕ
0
π/3
2π/3
π
The half switching period is subdivided into 6
subintervals (m = 6).
Two situations has to be considered:
Case A: 0 < ϕ < π/3
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Example: Three-Phase DAB
and SR-DAB
vao1 = vA
2V1/3
V1/3
θ
nvao2 = vB
2nV2/3
nV2/3
θ
ϕ
ϕ−π/3
0
π/3
2π/3
π
The half switching period is subdivided into 6
subintervals (m = 6).
Two situations has to be considered:
Case B: π/3 < ϕ < π/2
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Example: Three-Phase DAB
and SR-DAB
i=
A
B
1
υ
1+ k
3
2
δ
ϕ
υ
1− k
3
3
δ
π
−ϕ
3
1+ 2k
π 1+ k
ϕ−
3
3
3
υ
2−k
3
2+k
2π
−ϕ
3
3
vao1 = vA
4
δ
ϕ
ϕ−
5
υ
2(1 − k )
3
π
−ϕ
3
2−k
3
2π
− ϕ 1− k
3
3
π
3
δ
υ
1− 2k
3
6
δ
υ
δ
ϕ
1− k
3
π
−ϕ
3
1− 2k
3
2π
−ϕ
3
ϕ−
π
3
2V1/3
V1/3
θ
nvao2 = vB
2nV2/3
nV2/3
Case B
θ
ϕ
ϕ−π/3
0
π/3
2π/3
π
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Soft-switching conditions
Single phase DAB: port 1
i1
S1aH
S1bH
iL
vA
VA
-VA
L
ϕ
V1
2πfswt
π
2π
vB
S1aL
VB
2πfswt
S1bL
-VB
π
2π
Power flow
π
jL (0) = −ϕ ⋅ k − (1 − k ) ≤ 0
2
π1 
ϕ ≥  − 1
2k 
iL(π) = - iL(0)
iL
iL(ϕ)
π
2π
2πfswt
iL(0)
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Soft-switching conditions
Single phase DAB: port 2
vA
VA
i2
S2aH
S2bH
-VA
iLs
ϕ
V2
2πfswt
π
2π
vB
VB
n:1
S2aL
S2bL
-VB
2πfswt
π
2π
Power flow
π
jL (ϕ) = ϕ − (1 − k ) ≥ 0
2
π
ϕ ≥ (1 − k )
2
iL(π) = - iL(0)
iL
iL(ϕ)
π
2π
2πfswt
iL(0)
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Soft-switching conditions
Single phase DAB
Port 1:
Port 2:
π1 
ϕ ≥  − 1
2k 
π
ϕ ≥ (1 − k )
2
For a power flow from port 1 to port 2 the phase-shift
interval is 0 ≤ ϕ ≤ π/2. Thus, if k ≥ 1 the soft switching
condition is satisfied for any ϕ value and for both
bridge switches.
The same consideration holds for a power flow from
port 2 to port 1 where voltages vA and vB are swept
and k’ = 1/k. Now, if k’ ≥ 1 (k ≤ 1) the soft switching
condition is satisfied for any ϕ value.
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Soft-switching conditions
Single phase DAB
i1
S1aH
S1bH
V1
S1aL
iL
L
Port 1:
Port 2:
π1 
ϕ ≥  − 1
2k 
π
ϕ ≥ (1 − k )
2
S1bL
For a bidirectional power flow, if k = 1
the soft switching condition is satisfied
for any ϕ value between –π/2 and π/2.
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Soft-switching conditions
Single phase SR-DAB converter: port 1
i1
NORMALIZED WAVEFORMS
i2
S1aH
S1bH
iL C
S2aH
L
S2bH
vC
V1
4
α LH
π
3.2
JL1(ϕ
ϕ)
2.4
V2
1.6
0.8
n:1
S1aL
S1bL
S2aL
S2bL
)
0
− 0.8
− 1.6
Power flow
− 2.4
JL0(ϕ
ϕ)
− 3.2
 π    π − ϕ
 ϕ 
− sin  + k sin
 − sin 
fn    fn 
fn 


JL 0 (ϕ) =
<0
π
1 + cos 
 fn 
−4
0
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0.667
1
θ
π
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Soft-switching conditions
Single phase SR-DAB converter: port 2
i1
NORMALIZED WAVEFORMS
i2
S1aH
S1bH
iL C
S2aH
L
S2bH
vC
V1
4
α LH
π
3.2
JL1(ϕ
ϕ)
2.4
V2
1.6
0.8
n:1
S1aL
S1bL
S2aL
S2bL
)
0
− 0.8
− 1.6
Power flow
ϕ
 π − ϕ
π
sin  − sin
sin 

fn 
fn 
fn 



JL1(ϕ) =
k>0
+
π
π
1 + cos 
1 + cos 
 fn 
 fn 
− 2.4
JL0(ϕ
ϕ)
− 3.2
−4
0
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0.667
1
θ
π
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Soft-switching conditions
Single phase SR-DAB converter
i1
NORMALIZED WAVEFORMS
i2
S1aH
S1bH
iL C
S2aH
L
S2bH
vC
V1
4
α LH
π
3.2
JL1(ϕ
ϕ)
2.4
V2
1.6
0.8
n:1
S1aL
S1bL
S2aL
S2bL
)
0
− 0.8
− 1.6
Power flow
− 2.4
JL0(ϕ
ϕ)
− 3.2
Worst case: ϕ = 0
π
sin  
fn 

J L 0 (0 ) = J L1 (0 ) =
(k − 1)
π
1 + cos 
 fn 
−4
0
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0.667
1
θ
π
K=1
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Soft-switching conditions
Interleaved Boost with Coupled Inductors
CCL
CCL
VCL
VCL
Lm
ia
ima
S2aH S2bH
i1
ns
ib
S1bH
np
i2
V2
S1aH
L iL
ns
V1
np
Lm
imb
S2aL S2bL
S1aL
S1bL
Power flow
Let’s analyze the port 1 switch commutations first
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Soft-switching conditions
S1aH
D > 0.5
S1bH
S2aL
i1
ns
L iL
ns
S2aH
S2bH
V1
S1bL
Case A: 0 < ϕ < π(D-1/2)
θ
S2bL
θ
VA
vA(θ)
S1aL
2π(1-D)
θ
vB(θ)
VB
S1aH= S1bL
θ
S1aL= S1bH
iL(θ)
J1 = J0 + kϕ
π
= − π(1 − D ) + k ≥ 0
2
I0
I1
I2
ϕ
θ
I4 = -I1
π(D-1/2)-ϕ
π(D-1/2)+ϕ
k ≥ 2(1 − D)
0 θ1
θ2
θ3
π θ4 θ5
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θ6
2π
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Soft-switching conditions
S1aH
D > 0.5
S1bH
S2aL
i1
ns
L iL
2π(1-D)
S2aH
S2bH
ns
V1
θ
VA
vA(θ)
S1aL
θ
S2bL
θ
S1bL
VB
vB(θ)
Case B: π(D-1/2) < ϕ < π/2
S1aH= S1bL
1 


J2 = J1 + (1 + k )ϕ − π D − 
2 


π
= ϕ − (1 − k ) ≥ 0
2
I2
iL(θ)
I1
I0
θ
I4 = -I1
ϕ
ϕ−π(D-1/2)
I5 = -I2
π(3/2-D)-ϕ
π(D-1/2)
2
k ≥ 1− ϕ
π
θ
S1aL= S1bH
0
θ1 θ2
θ3
π
θ4 θ5
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θ6
2π
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Soft-switching conditions
S1aH
S1bH
i1
ns
S1aL
L iL
ns
S1bL
Case A: 0 < ϕ < π(D-1/2)
k ≥ 2(1 − D)
Case B: π(D-1/2) < ϕ < π/2
2
k ≥ 1− ϕ
π
V1
Case B is included in case A!
Same condition holds for reversed power flow
k = 1 is used to minimize the inductor
current crest factor
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Soft-switching conditions
Interleaved Boost with Coupled Inductors
CCL
CCL
VCL
VCL
Lm
ia
ima
S2aH S2bH
i1
ns
ib
S1bH
np
i2
V2
S1aH
L iL
ns
V1
np
Lm
imb
S2aL S2bL
S1aL
S1bL
Power flow
For port 2 switch commutations we have to analyze the
currents ia and ib which depend also on duty-cycle:
ia = ima +
ns
iL
np
ib = imb −
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ns
iL
np
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Soft-switching conditions
IBCI
D > 0.5
CCL
S2aL
VCL
Lm
ia
ima
ib
vA(θ)
np
vB(θ)
VB
imb
θ
VA
θ
S1aH= S1bL
θ
S1aL= S1bH
S2aL S2bL
Case A: 0 < ϕ < π(D-1/2)
θ
S2bL
S2bH
np
Lm
S2aH
S2bH
i2
V2
2π(1-D)
iL(θ)
I0
I1
I2
ϕ
ib (θ2 ) = Impk
ns
− I2 ≥ 0
np
θ
I4 = -I1
π(D-1/2)-ϕ
π(D-1/2)+ϕ
0 θ1
θ2
θ3
π θ4 θ5
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θ6
2π
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Soft-switching conditions
IBCI
D > 0.5
CCL
S2aL
VCL
Lm
ia
ima
ib
vA(θ)
np
vB(θ)
VB
imb
θ
VA
θ
S1aH= S1bL
θ
S1aL= S1bH
S2aL S2bL
Case A: 0 < ϕ < π(D-1/2)
θ
S2bL
S2bH
np
Lm
S2aH
S2bH
i2
V2
2π(1-D)
iL(θ)
I0
I1
I2
ϕ
ib (θ3 ) = Imvl
ns
− I3 ≤ 0
np
θ
I4 = -I1
π(D-1/2)-ϕ
π(D-1/2)+ϕ
0 θ1
θ2
θ3
π θ4 θ5
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θ6
2π
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Soft-switching conditions
IBCI
D > 0.5
CCL
S2aL
VCL
Lm
ia
ima
2π(1-D)
S2aH
S2bH
S2bH
np
θ
S2bL
θ
VA
vA(θ)
θ
i2
V2
ib
np
Lm
VB
vB(θ)
imb
S1aH= S1bL
Case B: π(D-1/2) < ϕ < π/2
θ
S1aL= S1bH
S2aL S2bL
I2
iL(θ)
I1
I0
ib (θ1 ) = Impk
ns
− I1 ≥ 0
np
θ
I4 = -I1
ϕ
ϕ−π(D-1/2)
I5 = -I2
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
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θ6
2π
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Soft-switching conditions
IBCI
D > 0.5
CCL
S2aL
VCL
Lm
ia
ima
2π(1-D)
S2aH
S2bH
S2bH
np
θ
S2bL
θ
VA
vA(θ)
θ
i2
V2
ib
Lm
VB
vB(θ)
np
imb
S1aH= S1bL
Case B: π(D-1/2) < ϕ < π/2
θ
S1aL= S1bH
S2aL S2bL
I2
iL(θ)
I1
I0
ib (θ3 ) = Imvl
ns
− I3 ≤ 0
np
θ
I4 = -I1
ϕ
ϕ−π(D-1/2)
I5 = -I2
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
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θ6
2π
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Soft-switching conditions
Considerations:
CCL
CCL
VCL
VCL
Lm
ia
ima
S2aH S2bH
i1
ns
ib
S1bH
np
i2
V2
S1aH
L iL
ns
V1
np
Lm
imb
S2aL S2bL
S1aL
S1bL
The active clamp operation requires the clamp current to
have zero average value. This means that the upper
switch current must reverse polarity during their
conduction interval (help soft-switching)
A non negligible magnetizing inductor ripple helps to
satisfy the soft-switching conditions especially at low
power levels
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Normalized Transferred Power
Single-phase DAB
iL
vA
VA
L
-VA
ϕ
vA
vB
2π
VB
Power flow
2πfswt
π
2π
iL(π) = - iL(0)
iL
iL(ϕ)
π
π
1
= ∫ jL (θ)dθ
π0
π
vB
-VB
P(ϕ)
Π (ϕ) =
PN
2πfswt
2π
2πfswt
iL(0)
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Normalized Transferred Power
Single-phase DAB
NORMALIZED TRANSFERRED POWER
1
iL
L
0.8
vA
vB
0.6
Π ( φ)
0.4
Power flow
 ϕ
Π (ϕ) = kϕ1 − 
 π
0.2
0
0
0
0
VB
k=
VA
0.25
0.5
0.75
φ
1
1
π
NORMALIZED PHASE-SHIFT ANGLE
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Normalized Transferred Power
Single-phase DAB
NORMALIZED TRANSFERRED POWER
1
iL
L
Πmax
0.8
vA
vB
0.6
Π ( φ)
0.4
Power flow
0.2
Π max
π
π
= Π  = k
4
2
0
0
0
0
0.25
0.5
0.75
φ
1
1
π
NORMALIZED PHASE-SHIFT ANGLE
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Normalized Transferred Power
Single-phase SR-DAB
NORMALIZED TRANSFERRED POWER
1
iL
L
C
0.9
0.8
vC
vA
vB
0.7
0.6
Π ( ϕ )0.5
Power flow
P(ϕ)
Π ( ϕ) =
PN
0.4
0.3
0.2
0.1
0
0
0.125
0.25
0.375
0.5

 π − 2ϕ  
 cos
 
NORMALIZED PHASE-SHIFT ANGLE
2fn  
2kfn 

=
−1

π 
 π 

 cos

2fSpiazzi
 S. Buso, G.

n
60/66
- University
of Padova - DEI
ϕ
π
Normalized Transferred Power
Single-phase SR-DAB
NORMALIZED TRANSFERRED POWER
1
iL
L
C
0.8
vC
vA
Πmax
0.9
0.7
vB
0.6
Π ( ϕ )0.5
Power flow
Π max
π
= Π 
2




2kfn 
1
=
− 1
π 
 π  
 
 cos
 2fn  

0.4
0.3
0.2
0.1
0
0
0.125
0.25
0.375
0.5
ϕ
π
NORMALIZED PHASE-SHIFT ANGLE
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Normalized Transferred Power
2π(1-D)
IBCI
iL
θ
L
θ
VA
vA(θ)
θ
vA
vB
VB
vB(θ)
θ
I2
iL(θ)
Power flow
I1
I0
ϕ
θ3
1
Π (ϕ) = ∫ jL (θ)dθ
πθ
1
θ
I4 = -I1
ϕ−π(D-1/2)
I5 = -I2
π(3/2-D)-ϕ
π(D-1/2)
0
θ1 θ2
θ3
π
θ4 θ5
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θ6
2π
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Normalized Transferred Power
NORMALIZED TRANSFERRED POWER
0.6
IBCI
0.55
iL
0.5
L
0.45
0.4
0.35
vA
vB
(
)
Π ϕ , Dtest 0.3
0.25
0.2
0.15
0.1
Power flow
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ϕ
π
NORMALIZED PHASE-SHIFT ANGLE
1


for 0 ≤ ϕ ≤ π D - 
2kϕ(1 − D)
2

Π (ϕ) = 
2
kϕ1 − ϕ  − kπ D − 1  for π D - 1  ≤ ϕ ≤ π
  π 
2
2
2


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Normalized Transferred Power
NORMALIZED TRANSFERRED POWER
Three-phase DAB
iL
0.8
L
0.6
vA
vB
Power flow
Π ( ϕ )0.4
0.2
0
π
 2 ϕ 
ϕ 3 − 2π  ϕ ≤ 3
Π (ϕ) = 
2
ϕ
π π
π
ϕ −
−
≤ϕ≤

π 18 3
2
0
0.125
0.25
0.375
0.5
ϕ
π
NORMALIZED PHASE-SHIFT ANGLE
S. Buso, G. Spiazzi - University of Padova - DEI
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Normalized Transferred Power
Three-phase SR-DAB
iL
L
NORMALIZED TRANSFERRED POWER
C
0.8
vC
vA
0.7
vB
0.6
0.5
Power flow
Π 1( ϕ )0.4
0.3
0.2
0.1
No closed form
expression for Π(ϕ)
0
0
0.083
0.167
0.25
0.333
0.417
0.5
ϕ
π
S. Buso, G. Spiazzi - University of Padova - DEI
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Conclusions
Different isolated bidirectional topologies, belonging to
the family of dual active bridge structures, have been
considered
A unified analysis has been carried out to calculate the
steady-state current waveform responsible for the power
transfer
Soft-switching conditions have been investigated for each
converter topology
The transferred power and its relation with the phaseshift angle has been calculated
S. Buso, G. Spiazzi - University of Padova - DEI
66/66