Nonlinear Observer-Based Robust Passive Control of Doubly-Fed Induction Generators for Power System Stability Enhancement via Energy Reshaping
Abstract
:1. Introduction
- The combinatorial effect of generator nonlinearities and parameter uncertainties, unmodelled dynamics, wind speed randomness, is aggregated into a perturbation, which is rapidly estimated by a nonlinear extended state observer (ESO), called sliding-mode state and perturbation observer (SMSPO) [26], in real-time. Hence, RPC can handle various types of uncertainties which is applicable to more practical cases compared to that of parameter based robust/adaptive approaches;
- RPC does not require an accurate DFIG model while only the active power and reactive power need to be measured. Thus, RPC is very easy to be implemented in practice;
- A great system damping can be injected to improve the transient responses of DFIG in various operation conditions of power systems via energy reshaping, which can provide a faster active power response when DFIG is disturbed thus the power system stability could be enhanced significantly.
2. System Modelling of DFIG-Based Wind Turbine
2.1. Wind Turbine Model
2.2. Generator Model
2.3. Shaft System Model
3. Nonlinear Observer Based Robust Passive Control
- A.1
- b0 is chosen to satisfy , where θ is a positive constant.
- A.2
- The function and are bounded over the domain of interest with , and , where γ1 and γ2 are positive constants.
4. RPC Design of DFIG for Power System Stability Enhancement
5. Case Studies
5.1. Step Change of Wind Speed
5.2. Pitch Angle Variation
5.3. Voltage Drop at Power Grid under Operation Type I
5.4. Voltage Drop at Power Grid under Operation Type II
5.5. Inter-Area Type Disturbance
5.6. Generator Parameter Uncertainties
5.7. Comparative Studies
6. Conclusions
- (1)
- A nonlinear observer is employed to estimate the aggregated effect of generator nonlinearities and parameter uncertainties, unmodelled dynamics, and wind speed randomness, which is then fully compensated in real-time by a passive controller. Hence, RPC can handle various types of uncertainties which is applicable to more practical cases compared to that of parameter based robust/adaptive approaches;
- (2)
- An extra damping is injected to improve system transient dynamics via energy reshaping, which can provide a faster active power response when DFIG is disturbed thus the power system stability could be enhanced significantly;
- (3)
- RPC does not require an accurate system model while only the measurement of active power and reactive power is required. Therefore, RPC is very easy to be implemented in practice;
- (4)
- Simulation results demonstrate that RPC can maintain a globally consistent control performance in the face of varied pitch angle, wind speed, voltage drop at power grid, and inter-area type disturbance. Compared to PID control and FLC, RPC can effectively suppress the active power and reactive power oscillation while reduce the overshoot simultaneously, such that the power system stability can be considerably enhanced. Furthermore, it just needs reasonable control costs.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Variables | |||
vwind | wind velocity | RSC | rotor side converter |
ρ | air density | PSO | particle swarm optimizer |
R | turbine radius | MPPT | maximum power point tracking |
CP | power coefficient | GGWO | grouped grey wolf optimizer |
CPmax | maximum power coefficient | SMC | sliding-mode control |
λ | tip-speed-ratio | PC | passive control |
λopt | optimal tip-speed-ratio | DG | distributed generators |
β | blade pitch angle | SMSPO | sliding-mode state and perturbation observer |
Te | electromagnetic torque | GSC | grid side converter |
Tm | mechanical torque | SPWM | sinusoidal pulse width modulation |
Qs | reactive power | LVRT | low voltage ride-through |
s | generator slip | SMIB | single machine infinite bus |
ωs | synchronous angle speed | PID | proportional-integral-derivative |
ωr | rotor angular speed | FLC | feedback linearization control |
ωb | electrical base speed | GA | genetic algorithm |
idr, iqr | dq-axis rotor current | The Control Parameters of RPC | |
ids, iqs | dq-axis stator current | k11 | SMPO sliding-mode gain of active power |
System Parameters | k12 | SMPO sliding-mode gain of active power | |
σ | leakage coefficient | α11 | SMPO gain of active power |
Rs,Rr | stator and rotor resistances | α12 | SMPO gain of active power |
Ls,Lr | stator and rotor inductances | k21 | SMPO sliding-mode gain of reactive power |
Lm | magnetizing inductance | k22 | SMPO sliding-mode gain of reactive power |
H | generator inertia | α21 | SMPO gain of reactive power |
Ht | turbine inertia | α22 | SMPO gain of reactive power |
D | damping coefficient | control gain of active power | |
Abbreviations | control gain of reactive power | ||
DFIG | doubly fed induction generator | reshaping coefficient of active power | |
RPC | robust passive control | reshaping coefficient of reactive power | |
ESO | extended state observer |
Appendix A
Appendix A.1. System Parameters
Appendix A.2. DFIG Parameter
Appendix A.3. Wind Turbine Parameters
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Active Power Control Loop | b11= −3000 | K1= 30 | = 25 | = 40 | = 400 |
k11 = 15 | k12 = 600 | = 0.2 | |||
Reactive Power Control Loop | b22 = −4500 | K2 = 15 | = 15 | = 40 | = 400 |
k21 = 15 | k22 = 600 |
Case | Step Change of Wind Speed | Pitch Angle Variation | Voltage Drop of Type I | Voltage Drop of Type II | Inter-Area Type Disturbance |
---|---|---|---|---|---|
Controller | IAE index IAEPe of active power | ||||
PID | 1.216 | 1.072 | 2.166 | 1.986 | 0.855 |
FLC | 0.389 | 0.633 | 1.459 | 1.269 | 0.516 |
RPC | 0.255 | 0.529 | 1.287 | 1.138 | 0.429 |
Controller | IAE index IAEQe of reactive power | ||||
PID | 0.752 | 0.951 | 0.896 | 0.589 | 0.917 |
FLC | 0.689 | 0.708 | 1.016 | 0.354 | 0.639 |
RPC | 0.611 | 0.895 | 0.987 | 0.317 | 0.528 |
Case (Controller) | Step Change of Wind Speed | Pitch Angle Variation | Voltage Drop of Operation Type I | Voltage Drop of Operation Type II | Inter-Area Type Disturbance |
---|---|---|---|---|---|
PID | 0.274 | 0.217 | 0.469 | 0.371 | 0.257 |
FLC | 0.209 | 0.165 | 0.388 | 0.297 | 0.226 |
RPC | 0.187 | 0.148 | 0.392 | 0.285 | 0.231 |
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Dong, J.; Li, S.; Wu, S.; He, T.; Yang, B.; Shu, H.; Yu, J. Nonlinear Observer-Based Robust Passive Control of Doubly-Fed Induction Generators for Power System Stability Enhancement via Energy Reshaping. Energies 2017, 10, 1082. https://doi.org/10.3390/en10081082
Dong J, Li S, Wu S, He T, Yang B, Shu H, Yu J. Nonlinear Observer-Based Robust Passive Control of Doubly-Fed Induction Generators for Power System Stability Enhancement via Energy Reshaping. Energies. 2017; 10(8):1082. https://doi.org/10.3390/en10081082
Chicago/Turabian StyleDong, Jun, Shengnan Li, Shuijun Wu, Tingyi He, Bo Yang, Hongchun Shu, and Jilai Yu. 2017. "Nonlinear Observer-Based Robust Passive Control of Doubly-Fed Induction Generators for Power System Stability Enhancement via Energy Reshaping" Energies 10, no. 8: 1082. https://doi.org/10.3390/en10081082