interleaved buck converter
TRANSCRIPT
Interleaved Buck Converter
Scientific Project
Supervised by: Dr. Philippe Dularue
Studied by:
Felicia WHYTE Siyamak SARABI
Master of Electrical
Engineering for Sustainable Development
University Lille 1 February, 2013
outline
• What is interleaved buck converter
• Formulation in average model
• EMR representation for IBC
• Simulation in PSIM
• Simulation in MATLAB
• Comparison between two simulation
• Conclusion
What is interleaved buck converter
• It is a DC to DC buck converter which has a coupled component. This coupling leads to have less inductance for the same single inductor case
Notations
Formulation in average model
• Applying KVL:
• (V1= α1E; V2 = α2E; V1’= -V2’)
• V2 – V1 – V2’ + V1’ = 0
• α2E – α1E + 2V1’ = 0
• V1’ = (α1
− α2)E
2
• Output Voltage, U
• U = V1 – V1’
• U = α1E – (α
1 − α
2)E
2
• U = (α1
+ α2)E
2
• U = αE
Formulation in average model
• Inductor 1
• VL1 = L11
𝑑𝑖1
𝑑𝑡 + ri1 - Lµ
𝑑𝑖2
𝑑𝑡
• VL1 = V1 - U
• In Laplace domain
• VL1 = L11𝑠i1+ ri1 - Lµ𝑠i2
• i1 = - i2
•𝑖
1
VL1 =
1
𝐿11+Lµ 𝑠+𝑟
• Inductor 2
• VL2 = L22
𝑑𝑖2
𝑑𝑡 + ri2 - Lµ
𝑑𝑖1
𝑑𝑡
• VL2 = V2 - U
• In Laplace domain
• VL2 = L22𝑠i2+ ri2 - Lµ𝑠i1
• i1 = - i2
•𝑖
2
VL2
= 1
𝐿22+Lµ 𝑠+𝑟
EMR representation for IBC
2/3
m_chop
Scope5
Scope3
Scope2
Scope1
U
IL11
IL22
U_1
IL11 + IL22
U_2
Monophysical coupling
(ex series circuit)1
E
I_1
I_2
E_1
I
E_2
Monophysical coupling
(ex series circuit)
E2
IL2
Input Tuning
V1
I2
Monophysical
Conversion
(eg. Chopper)1
E1
IL1
Input Tuning
V1
I1
Monophysical
Conversion
(eg. Chopper)U I RES
LOAD
V1
U
IL2
IL22
Inductor 2
V1
U
IL1
IL11
Inductor 1I UES
Electrical SourceIL11 + IL22
I R
U
U1
Capacitor
E
U
Simulation in PSIM©
Results
0
50
100
150
200
250
300
350
E1 U1
0
-100
-200
100
200
I(M1_1) I(M1_2)
0 0.001 0.002 0.003 0.004 0.005 0.006
Time (s)
0
50
100
150
200
I(R1)
𝐿1 = 100 𝑚𝐻 𝐿2 = 100 𝑚𝐻 𝐿12 = 99 𝑚𝐻 𝑟1 = 𝑟2 = 5𝑚Ω C = 100 μ𝐹 𝐸 = 300 𝑉 𝑈 = 200 𝑉 𝑅 = 2 𝑡𝑜 50 Ω
Continuous and discontinuous mode
0 0.001 0.002 0.003 0.004 0.005 0.006
Time (s)
0
50
100
150
200
250
300
350
I(R1) ILL
Load DC current Inductors Current
𝐼𝑅 > ∆𝑖𝐿 𝐶𝐶𝑀 (𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑀𝑜𝑑𝑒) 𝐼𝑅 < ∆𝑖𝐿 𝐷𝐶𝑀 (𝐷𝑖𝑠𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑀𝑜𝑑𝑒)
0.00355 0.0036 0.00365 0.0037
Time (s)
0
10
20
30
I(R1) ILL
0.00395 0.004 0.00405 0.0041
Time (s)
0
5
10
15
20
25
I(R1) ILL
CCM DCM
Constant duty cycle
K1
K2
K1
K2
K1
K2
Same Switching
1/3 lag Switching
Complementary Switching
t
t
t
t
t
t
0 0.001 0.002 0.003
Time (s)
0
100
200
300
U1 U2
Results
• Results for ideal switches
Less ripple in case of 1/3 lag switching compared to same switching
0 0.001 0.002 0.003
Time (s)
0
-50
50
100
150
200
I(M1_1) I(M2_1)
In Case of complementary switching Out put is always half of the input
and it is independent from duty cycle
Results
• Impacts of capacitor to the output current • No DC current pass through the capacitor • It is acting as a smooth element to remove ripple from the load current
0
50
100
150
200
250
300
350
Sum of coupled inductor currents
0
50
100
150
200
250
300
350
Currrent before Capacitor
0
-100
-200
100
200
300
Capacitor Currrent
0 0.001 0.002 0.003 0.004 0.005 0.006
Time (s)
0
50
100
150
200
Resistor Current
• Impact of the capacitor to the transient response
Results
C=100 uFτripple= cte
C=10 uFτripple= cte
Simulation in MATLAB
2/3
m_chop
Scope5
Scope3
Scope2
Scope1
U
IL11
IL22
U_1
IL11 + IL22
U_2
Monophysical coupling
(ex series circuit)1
E
I_1
I_2
E_1
I
E_2
Monophysical coupling
(ex series circuit)
E2
IL2
Input Tuning
V1
I2
Monophysical
Conversion
(eg. Chopper)1
E1
IL1
Input Tuning
V1
I1
Monophysical
Conversion
(eg. Chopper)U I RES
LOAD
V1
U
IL2
IL22
Inductor 2
V1
U
IL1
IL11
Inductor 1I UES
Electrical SourceIL11 + IL22
I R
U
U1
Capacitor
E
U
Results
Inductors Currrents
Results
conclusion
• Both structural (PSIM) and functional (Matlab-Simulink), produced similar results, with the Simulink outputs being smoother, with less ripples
• No real difference was observed in the results obtained when
perfect components were used, instead of ideal switches. One of the differences between the two is that perfect components are able to highlight phenomena which ideal switches are not able to.
• The average model provides a macroscopic view of the system and facilitates the simulation of the dynamics of the system without performing many complex operations.