Model-Based Current Sharing Approach for DCM Interleaved Flyback Micro-Inverter
Abstract
:1. Introduction
2. Working Principle and Dynamic Modeling
2.1. Working Principle
2.2. Accurate Dynamic Model in DCM Operation
- The DC side decoupling capacitor Cpv is large enough to neglect the current ripple across the Cpv;
- The equivalent series resistances (ESR) of the inductances in primary/secondary side of transformer and the output filter are considered. The transformer leakage inductance is ignored.
2.3. Comparisons between the Accurate Dynamic Model and the Existing Model
2.3.1. The Proposed Fourth-Order Model
2.3.2. The Third-Order Model Based on Single-Phase Flyback Converter
2.3.3. The Second-Order Model Based on Average Small Signal
3. Current Controller Using Sliding Mode Control
4. Simulation
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Cpv | input capacitor | mF |
Vpv | PV voltage | V |
n | the transformer turns ratio | - |
Lm1, Lm2 | the primary magnetizing inductances of the transformer | uH |
im1, im2 | the primary currents of the transformer | A |
is1, is2 | the secondary currents of the transformer | A |
Lf | the filter inductor | uH |
Cf | filter capacitor | uH |
Rp1, Rp2 | ESRs of the primary magnetizing inductance | Ω |
Rs1, Rs2 | ESRs of the secondary magnetizing inductance | Ω |
Rf | ESR of the output filter inductor | Ω |
iac | output current | A |
iac_ref | the reference of iac | A |
fs | switching frequency | kHZ |
fg | frequency of gird | HZ |
Vg | grid voltage | V |
P0 | rated power | W |
D | main MOSFET duty cycle | - |
, | the average and small signal of x in one switching period | - |
H | the number of steady-state subinterval | - |
Ak and Bk | steady state equations in k-interval | - |
di(i = 1, …, k) | k-interval duty cycle | - |
revised matrix | - | |
nL | the number of inductor | - |
don_1, don_2 | duty cycles of switches Q1 and Q2 when they are on | - |
doff_1, doff_2 | the time intervals from turn-off of switches Q1 and Q2 to the decreasing to zero of transformer inductor currents | - |
ADCM, BDCM, WDCM | The coefficient matrixes of the proposed model | - |
Gdt4, Gdt3_1, Gdt3_2, Gd2 | The transfer functions of the proposed fourth-order model, the reduced to third-order model, the third-order model based on single-phase flyback converter and second-order model | - |
a2 ~ a0, b3 ~ b0, c1 ~ c0, , j2 ~ j0, f2 ~ f0, h2 ~ h0 | the coefficients of Gdt4, Gdt3_1, Gdt_2 and Gd2 | - |
e1 e2 | tracking errors of Flyback1 and Flyabck2 | A |
α | current sharing error | A |
I1ref, I2ref | the primary current references of Flyback1 and Flyback2 converters | A |
S | the sliding surface | - |
λ | sliding coefficient | - |
ρ | observer gain matrix | - |
coefficient matrix for limiting integral gain | - | |
K | positive definite feedback gain matrix | - |
kp,smc, ki,smc | proportional and integral of sliding mode law | - |
Appendix A.
- a2 ~ a0:
- b3 ~ b0:
- c1 ~ c0:
- j2 ~ j0:
- f2 ~ f0:
- h2 ~ h0:
Appendix B. Robustness of the Proposed SMC
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Interval | Switch Q1 | Switch Q2 | Diode 1 | Diode 2 |
---|---|---|---|---|
1 | ON | OFF | OFF | ON |
2 | ON | OFF | OFF | OFF |
3 | OFF | OFF | ON | ON |
4 | OFF | ON | ON | OFF |
5 | OFF | ON | OFF | OFF |
6 | OFF | OFF | OFF | OFF |
7 | ON | ON | OFF | OFF |
Parameters | Value | Parameters | Value |
---|---|---|---|
CPV | 11 mF | Rp1, Rp2 | 0.15 Ω |
Lm1, Lm2 | 6 μH | Rs1, Rs2 | 0.05 Ω |
Cf | 0.68 μF | Rf | 0.29 Ω |
Lf | 600 μH | Vg | 220 V |
n | 6 | fg | 50 Hz |
fs | 100 kHz | P0 | 250 W |
Parameters | Value | Parameters | Value | Parameters | Value |
---|---|---|---|---|---|
Lm1 | 5.8 μH | Rp1 | 0.15 Ω | Rs1 | 0.051 Ω |
Lm2 | 6.2 μH | Rp2 | 0.18 Ω | Rs2 | 0.085 Ω |
Ls1 | 216 μH | Ls2 | 223 μH | - | - |
Controller | Pout | Case 1 | Case 2 | ||
---|---|---|---|---|---|
α | THDs | α | THDs | ||
the proposed SMC | 200 W | 0.001 | 2.97% | 0.01 | 3.44% |
PI controller | 200 W | 0.01 | 6.43% | 0.32 | 6.85% |
the proposed SMC | 150 W | 0.001 | 2.45% | 0.05 | 2.83% |
PI controller | 150 W | 0.005 | 6.58% | 0.318 | 6.87% |
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Share and Cite
Dong, M.; Tian, X.; Li, L.; Song, D.; Wang, L.; Zhao, M. Model-Based Current Sharing Approach for DCM Interleaved Flyback Micro-Inverter. Energies 2018, 11, 1685. https://doi.org/10.3390/en11071685
Dong M, Tian X, Li L, Song D, Wang L, Zhao M. Model-Based Current Sharing Approach for DCM Interleaved Flyback Micro-Inverter. Energies. 2018; 11(7):1685. https://doi.org/10.3390/en11071685
Chicago/Turabian StyleDong, Mi, Xiaoyu Tian, Li Li, Dongran Song, Lina Wang, and Miao Zhao. 2018. "Model-Based Current Sharing Approach for DCM Interleaved Flyback Micro-Inverter" Energies 11, no. 7: 1685. https://doi.org/10.3390/en11071685
APA StyleDong, M., Tian, X., Li, L., Song, D., Wang, L., & Zhao, M. (2018). Model-Based Current Sharing Approach for DCM Interleaved Flyback Micro-Inverter. Energies, 11(7), 1685. https://doi.org/10.3390/en11071685