A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter
Abstract
:1. Introduction
2. Mathematical Model
3. Lyapunov Stability Theory-Based Control Strategy
3.1. Current Control Realization
3.2. DC Voltage Control Realization
3.3. NP Voltage Balance through PWM Realization
3.4. LCL Type Output Filter Design
- (1)
- In order to ensure the output current follow the highest reference current change rate and limit the output current ripple. LT should meet: , where ΔIc is the output current ripple. fs is the switching frequency (12.8 kHz). uSNm is the amplitude of grid phase voltage. M49 is the 49th harmonic current amplitude which is chosen as 0.5 A. ω49 is the 49th harmonic angular frequency.
- (2)
- Lr and Cr resonates at fs: .
- (3)
- In order to obtain good high frequency attenuate rate and appropriate output bandwidth for NPC-SAPF, Lf, Lg and Ca should meet: Lf ≥ 5Lg and , where fm is the highest compensated frequency (2.5 kHz). Ca = Cd + Cr.
- (4)
- Larger Cd/Cr is helpful to improve the damping performance but increase the power losses [29]. Considering the harmonics characteristics of NPC-SAPF, Cd/Cr = 8 and Rd = 3 are proposed.
4. Comparison Analysis of System Stability
4.1. Stability of the Classical Feedback Control Strategy
4.2. The Proposed Control Strategy Stability
4.3. Tolerance of Inaccurate Model on Stability
5. Simulation Results
5.1. Comparisons between the Proposed Control Strategy and the Classical Feedback Control Methods
5.2. Dynamic Response of the NPC-SAPF
5.3. Steady-State Performance of the NPC-SAPF
6. Experimental Results
6.1. Dynamic Response of the NPC-SAPF
6.2. Steady-State Performance of the NPC-APF
6.3. Experimental Resultes of PR and VPI Controllers
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
References
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Parameter | Value | Parameter | Value |
---|---|---|---|
uSNabc | 220 V | Lf | 0.45 mH |
f0 | 50 Hz | Rf | 0.05 Ω |
fs | 12.8 kHz | Lg | 0.05 mH |
400 V | Lr | 70.28 μH | |
Ls | 0.02 mH | Cr | 2.2 μF |
Rs | 0.05 Ω | Cd | 17.6 μF |
C1(C2) | 4650 μF | Rd | 5 Ω |
Harmonic Order | Load Current | Grid Current | IEEE Standard 519-2014 | ||
---|---|---|---|---|---|
Amplitude (A) | Percent (%) | Amplitude (A) | Percent (%) | Maximum Percent (%) | |
1 | 22.61 | 100 | 22.77 | 100 | 100 |
5 | 5.11 | 22.59 | 0.45 | 1.97 | 4.0 |
7 | 2.45 | 10.85 | 0.64 | 2.81 | 4.0 |
11 | 1.94 | 8.60 | 0.08 | 0.34 | 2.0 |
13 | 1.28 | 5.67 | 0.24 | 1.04 | 2.0 |
17 | 1.10 | 4.87 | 0.10 | 0.45 | 1.5 |
19 | 0.78 | 3.46 | 0.17 | 0.74 | 1.5 |
23 | 0.69 | 3.06 | 0.11 | 0.48 | 0.6 |
25 | 0.50 | 2.20 | 0.09 | 0.39 | 0.6 |
29 | 0.45 | 1.98 | 0.07 | 0.31 | 0.6 |
31 | 0.32 | 1.40 | 0.06 | 0.26 | 0.6 |
35 | 0.29 | 1.29 | 0.07 | 0.31 | 0.3 |
37 | 0.20 | 0.87 | 0.05 | 0.21 | 0.3 |
41 | 0.19 | 0.85 | 0.03 | 0.13 | 0.3 |
43 | 0.12 | 0.53 | 0.05 | 0.21 | 0.3 |
47 | 0.13 | 0.60 | 0.06 | 0.26 | 0.3 |
49 | 0.07 | 0.32 | 0.03 | 0.13 | 0.3 |
THD (%) | 28.20 | 3.81 | 5.0 |
Harmonic Order | Load Current | Grid Current | ||
---|---|---|---|---|
Amplitude (A) | Percent (%) | Amplitude (A) | Percent (%) | |
1 | 22.96 | 100 | 23.03 | 100 |
5 | 5.08 | 22.10 | 0.36 | 1.56 |
7 | 2.39 | 10.41 | 0.37 | 1.61 |
11 | 1.92 | 8.36 | 0.16 | 0.69 |
13 | 1.25 | 5.44 | 0.19 | 0.83 |
17 | 1.10 | 4.79 | 0.17 | 0.74 |
19 | 0.75 | 3.27 | 0.13 | 0.56 |
23 | 0.66 | 2.87 | 0.12 | 0.52 |
25 | 0.48 | 2.09 | 0.12 | 0.52 |
29 | 0.46 | 2.00 | 0.13 | 0.56 |
31 | 0.31 | 1.35 | 0.12 | 0.52 |
35 | 0.30 | 1.31 | 0.07 | 0.30 |
37 | 0.20 | 0.87 | 0.06 | 0.26 |
41 | 0.18 | 0.78 | 0.07 | 0.30 |
43 | 0.12 | 0.52 | 0.05 | 0.22 |
47 | 0.12 | 0.52 | 0.05 | 0.22 |
49 | 0.07 | 0.30 | 0.06 | 0.26 |
THD (%) | 27.9 | 3.0 |
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Cao, Y.; Xu, Y.; Li, Y.; Yu, J.; Yu, J. A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter. Energies 2017, 10, 112. https://doi.org/10.3390/en10010112
Cao Y, Xu Y, Li Y, Yu J, Yu J. A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter. Energies. 2017; 10(1):112. https://doi.org/10.3390/en10010112
Chicago/Turabian StyleCao, Yijia, Yong Xu, Yong Li, Jiaqi Yu, and Jingrong Yu. 2017. "A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter" Energies 10, no. 1: 112. https://doi.org/10.3390/en10010112
APA StyleCao, Y., Xu, Y., Li, Y., Yu, J., & Yu, J. (2017). A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter. Energies, 10(1), 112. https://doi.org/10.3390/en10010112