Control Design of LCL Type Grid-Connected Inverter Based on State Feedback Linearization
Abstract
:1. Introduction
2. Single Closed-Loop Controller Design Based on State Feedback Linearization
2.1. Model of the Three-Phase Three-Leg Grid-Connected Inverter
2.2. Single Closed-Loop Control Strategy Based on State Feedback Linearization
- for all 0 ≤ j ≤ m, for all k ≤ ri − 1, for all 0 ≤ i≤ m and for all x in a neighborhood of x0.
- the m × m matrix E(X) is nonsingular at .
2.3. Parameters Design of Current Single Closed Loop Controller
- Stability conditions of the system
- 2.
- Restrictive conditions of dipoles parameters
- 3.
- Cut-off frequency of the closed loop system
- 4.
- Closed loop amplitude frequency characteristic at zero frequency
3. Design of Double Closed Loop Controller Based on Reduced Order State Feedback Linearization
3.1. State Feedback of Inverter Side Inductance and Filter Capacitor Subsystem
3.2. State Feedback of Grid-Side Inductance Subsystem
3.3. Parameters Design of Double Closed Loop Controller
4. Simulations and Experiments
4.1. Simulation and Experimental Environment
- Based on Equations (17)–(20), selecting the cut-off frequency of the open-loop transfer function as 750 Hz, the single closed-loop control system parameters can be designed as: k3 = 5000, k2 = 107π, k1 = 200k2, k0 = 104k2. At this time, the corresponding phase margin is Pm = 45°, and the closed-loop bandwidth is 1 kHz.
- Similarly, the parameters of the double closed loop control system can be designed as: k0 = 2 × 10−4, k1 = 108, k2 = 5 × 103, k3 = 102k3. Then, the corresponding open loop cut-off frequency is 680 Hz, phase margin is Pm = 43°, and closed-loop bandwidth is 1 kHz.
4.2. Steady State Control Performance
4.3. Dynamic Control Performance
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
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Variables | Symbols | Value |
---|---|---|
DC Bus Voltage | udc | 650 V |
Grid Voltage | ug | 380 V |
Grid-side inductor | L2 | 0.2 mH |
Inverter side inductor | L1 | 0.3 mH |
Filter capacitor | C | 20 uF |
Switching frequency | f | 10 kHz |
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Yang, L.; Feng, C.; Liu, J. Control Design of LCL Type Grid-Connected Inverter Based on State Feedback Linearization. Electronics 2019, 8, 877. https://doi.org/10.3390/electronics8080877
Yang L, Feng C, Liu J. Control Design of LCL Type Grid-Connected Inverter Based on State Feedback Linearization. Electronics. 2019; 8(8):877. https://doi.org/10.3390/electronics8080877
Chicago/Turabian StyleYang, Longyue, Chunchun Feng, and Jianhua Liu. 2019. "Control Design of LCL Type Grid-Connected Inverter Based on State Feedback Linearization" Electronics 8, no. 8: 877. https://doi.org/10.3390/electronics8080877