Nonlinear Controllers Based on Exact Feedback Linearization for Series-Compensated DFIG-Based Wind Parks to Mitigate Sub-Synchronous Control Interaction
Abstract
:1. Introduction
2. Power System Model and PI Controller
2.1. DFIG Model
2.2. GSC Model
2.3. PI Controller
3. Feedback Linearizability of DFIG-Based Wind Park
3.1. Feedback Linearizability of DFIG
3.2. Feedback Linearizability of GSC
4. Design of Exact Feedback Linearizing Controllers
4.1. RSC Controller Design
4.2. GSC Controller Design
5. Time-domain Simulation Results and Analysis
5.1. Frequency Scanning Analysis
5.2. Eigenvalue Analysis
5.3. Time-Domain Simulations and Analysis
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Parameter | Symbol |
Voltage | v |
Current | i |
Flux linkage | ψ |
Resistance | R |
Inductance | L |
Grid voltage | e |
Stator, rotor angular frequencies | ω1, ω |
Mutual inductance | Lm |
Transmission line resistance | RL |
Transmission line inductance | LL |
Compensator capacitance | Csc |
DC-link capacitance | Cdc |
Magnitude of the stator voltage vector | Vs |
Active power, reactive power | P, Q |
Input switching signals for the grid side converter | S |
Subscripts | |
Stator, rotor | s, r |
d-axis, q-axis | d, q |
Grid side converter loop | g |
Superscripts | |
Equivalent value | ′ |
Reference value | * |
Appendix A
Parameter | Symbol | Value | Unit |
---|---|---|---|
Nominal voltage (line to line) | VL-L | 690 | V |
Nominal power | P | 100 | MW |
Stator resistance | Rs | 0.0084 | p.u. |
Rotor resistance | Rr | 0.0083 | p.u. |
Stator leakage inductance | Lls | 0.167 | p.u. |
Rotor self-inductance | Llr | 0.1323 | p.u. |
Mutual inductance | Lm | 5.419 | p.u. |
dc-link capacitance | Cdc | 10 | mF |
Nominal dc-link voltage | vdc | 1200 | V |
Compensator capacitance | Csc | 10 | mF |
Transmission line resistance | RL | 0.02 | p.u. |
Transmission line inductance | LL | 0.0016 | p.u. |
Parameter | Value |
---|---|
kg1 | 0.01 |
ki1 | 0.10 |
kg2 | 0.10 |
ki2 | 1.00 |
Appendix B
Appendix C
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Vwind (m/s) | Mode 1 EFL | PI | Mode 2 EFL | PI | Mode 3 EFL | PI |
---|---|---|---|---|---|---|
8 | −9.1 ± j629.3 | −8.0 ± j628.8 | −1.4 ± j147.7 | +1.9 ± j148.3 | −16.1 ± j94.9 | −11.5 ± j94.1 |
9 | −8.2 ± j628.9 | −7.6 ± j628.9 | −2.9 ± j145.6 | +0.7 ± j145.0 | −7.4 ± j58.2 | −6.8 ± j58.2 |
10 | −7.5 ± j627.6 | −7.3 ± j629.1 | −5.0 ± j144.2 | −0.9 ± j141.9 | −6.2 ± j22.4 | −5.7 ± j22.2 |
11 | −7.1 ± j627.0 | −6.9 ± j629.0 | −6.9 ± j143.3 | −9.9 ± j141.2 | −4.9 ± j22.0 | −4.7 ± j21.6 |
K (%) | Mode 1 EFL | PI | Mode 2 EFL | PI | Mode 3 EFL | PI |
---|---|---|---|---|---|---|
30 | −5.9 ± j524.5 | −5.5 ± j522.6 | −4.6 ± j231.1 | −2.1 ± j230.6 | −7.0 ± j95.7 | −4.3 ± j95.1 |
50 | −7.9 ± j581.3 | −6.7 ± j580.0 | −3.0 ± j173.5 | −1.5 ± j172.3 | −9.7 ± j94.5 | −6.1 ± j95.2 |
70 | −9.1 ± j629.3 | −8.0 ± j628.8 | −1.4 ± j147.7 | +1.9 ± j148.3 | −16.1 ± j94.9 | −11.5 ± j94.1 |
90 | −9.7 ± j653.1 | −8.8 ± j652.6 | +3.0 ± j111.2 | +5.8 ± j109.7 | −22.0 ± j87.6 | −16.0 ± j86.4 |
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Li, P.; Wang, J.; Xiong, L.; Wu, F. Nonlinear Controllers Based on Exact Feedback Linearization for Series-Compensated DFIG-Based Wind Parks to Mitigate Sub-Synchronous Control Interaction. Energies 2017, 10, 1182. https://doi.org/10.3390/en10081182
Li P, Wang J, Xiong L, Wu F. Nonlinear Controllers Based on Exact Feedback Linearization for Series-Compensated DFIG-Based Wind Parks to Mitigate Sub-Synchronous Control Interaction. Energies. 2017; 10(8):1182. https://doi.org/10.3390/en10081182
Chicago/Turabian StyleLi, Penghan, Jie Wang, Linyun Xiong, and Fei Wu. 2017. "Nonlinear Controllers Based on Exact Feedback Linearization for Series-Compensated DFIG-Based Wind Parks to Mitigate Sub-Synchronous Control Interaction" Energies 10, no. 8: 1182. https://doi.org/10.3390/en10081182