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Enhancing grid stability: a hybrid control strategy for DFIG-based wind turbines to mitigate sub-synchronous oscillations

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Abstract

The global development of wind energy conversion systems is continually evolving, and it has emerged as a crucial element in the functioning of electrical grids across most nations. The doubly fed induction generator (DFIG), which is the most widely used wind turbine, has received considerable attention. Nonetheless, the incorporation of DFIG-based wind turbines into power grids equipped with series compensation renders them susceptible to sub-synchronous resonance (SSR). Within the realm of static SSR, two crucial factors contribute to this phenomenon: the induction generator effect (IGE) and torsional interactions (TI). This study examines the potential use of stability boosting supplementary controllers (SBSC) along with voltage source converter based FACTS devices to mitigate steady-state SSR under weak grid conditions. SBSC consists of a sub-synchronous resonance damping controller (SSRDC) and an inertia-based controller (IBC), which are incorporated into the conventional back-back controller of the DFIG. The SSRDC uses an appropriate input control signal that is highly appreciable for mitigating the IGE effects of SSR and is provided in the best location of the rotor-side converter and grid-side converter. IBC is introduced to suppress the multi-mass drive train TI that occurs owing to the influence of the mechanical dynamics in the electrical network. Variable compensation in the transmission line is effectively provided with the help of a static synchronous series compensator. The controller parameters of the SBSC and flexible AC transmission system (FACTS) devices are optimized using particle swarm optimization. Small-signal stability investigations for the proposed hybrid controllers involve employing the eigenvalue method, and verification of these findings is conducted through time-domain analysis. To substantiate the superior performance of the proposed hybrid controller strategy, an experimental validation is conducted.

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Abbreviations

DFIG:

Doubly fed induction generator

IGE:

Induction generator effect

SBSC:

Stability boosting supplementary controllers

IBC:

Inertia-based controller

TI:

Torsional interactions

VSC:

Voltage source converter

SSRDC:

Sub-synchronous resonance damping controller

RSC:

Rotor side converter

GSC:

Grid side converter

SSSC:

Static synchronous series compensator

FACTS:

Flexible AC transmission systems

PSO :

Particle swarm optimization

SSO:

Sub-synchronous oscillations

TCSC :

Thyristor controlled series compensator

GCSC :

Gate controlled series compensator

WF :

Wind farms

SCR:

Short circuit ratio

RPDC :

Reactive power damping controller

APDC :

Active power damping controller

\(\rho \) :

Air density

\({V}_{{\text{w}}}\) :

Wind speed

λ:

Blade tip speed radio

\(\beta \) :

Pitch angle of wind turbine

\({A}_{{\text{r}}}\) :

Area flounced by the rotor

\({k}_{{\text{ps}}},\) \({k}_{{\text{is}}}\) :

Proportional and Integral constants of speed controller

\({k}_{{\text{pp}}}\), \({k}_{{\text{ip}}}\) :

Proportional and Integral constants of power controller

\({\omega }_{r}, {\omega }_{m}\) :

DFIG rotor speed and turbine rotation speed

\({P}_{{\text{e}}},{T}_{{\text{e}}},{T}_{{\text{m}}}\) :

Electromagnetic power, Electromagnetic torque and mechanical torque

\({P}_{{\text{ref}}},{T}_{{\text{ref}}}\) :

Reference value of electromagnetic power and torque

\({H}_{{\text{t}}},{H}_{{\text{g}}}\) :

Inertia constant of turbine and generator

\({B}_{{\text{t}}}\), \({B}_{{\text{g}}}\) :

Frictional damping coefficient of turbine and generator

\({T}_{{\text{ls}}},{T}_{{\text{hs}}}\) :

Torque of low-speed and high-speed shaft

\({K}_{{\text{sh}}}, {D}_{{\text{sh}}}\) :

Shaft spring and damping constants

\({n}_{{\text{t}}},{n}_{{\text{g}}}\) :

Teeth of gear of the wind turbine and generator

\({\theta }_{s}\) :

Torsion angle of the drive train

\({f}_{s} ,{ f}_{n}\) :

Synchronous frequency and natural frequency of the system

\({X}_{c},\) \({X}_{L}\) :

Reactance of series capacitor and inductive reactance offered by the transmission line and transformer ( \({X}_{l}+{X}_{T} )\)

\({R}_{{\text{r}}}\) :

Rotor resistance

\({K}_{{\text{SSRDC}}}\) :

Gain of SSRDC

\({T}_{1{\text{SSRDC}}}, {T}_{2{\text{SSRDC}}}\) :

Time constants of the lead-lag block of the phase-shifter in SSRDC

\({n}_{{\text{p}}}\) :

Number of pole pairs

\({i}_{{\text{qs}}},{i}_{{\text{ds}}}{,i}_{{\text{qr}}},{i}_{{\text{dr}}}\) :

Stator and rotor current under qd-axis

\({\phi }_{k}\),\({\psi }_{k}\) :

Left and right eigenvector associated with the SSO mode

\({c}_{j}\) :

Row of C corresponding to the system output signal

\({b}_{i}\) :

Column of B corresponding to the system output signal

C & B :

Matrix in the state-space form of the overall system

\({k}_{f},{T}_{f}\) :

Proportional gain and the effective time constant of IBC.

\(\zeta ,\) \({w}_{n}\) :

Damping ratio and natural frequency of drive train

\({E}_{{\text{dg}}},{E}_{{\text{qg}}}\) :

WTG output voltage in d and q axis

\(V\) :

Grid voltage

\({R}_{L},\) \({X}_{L}\) :

Resistance and reactance of transmission line.

Φ,\(\gamma \) :

Phase angle and leading phase angle of transmission line current

\(E^{\prime}_{SCd}\) , \(E^{\prime}_{SCq}\) :

In phase and quadrature components of the injected voltage in SSSC

\({V}_{{\text{dc}}}\) :

DC voltage source

\({i}_{D},{i}_{Q}\) :

d and q axis transmission line current

\({E}_{D},{E}_{Q}\) :

d and q axis DFIG terminal voltages

\({R}_{{\text{sys}}},{X}_{{\text{sys}}}\) :

Resistance and inductive reactance connected between DFIG to the infinite bus system

\({V}_{{\text{cd}}}, {V}_{{\text{cq}}}\) :

Series capacitor voltage in the transmission line

\({K}_{m}\) :

Modulation index

\(k\) :

Transformation ratio of the coupling transformer

\(E^\prime_{SCA}\), \(E^\prime_{SCR}\) :

In phase and reactive component of compensated voltage in quadrature with the line current.

\(\gamma \),\({\beta }_{d}\) :

Phase angle and dead angle of SSSC

\({\alpha }_{i},{\xi }_{i}, { \beta }_{i}\) :

Real part, damping ratio and imaginary parts of eigenvalue \({\uplambda }_{i}\)

\({T}_{d}\) :

Time constant of SSSC

\({k}_{{\text{psssc}}}, {k}_{{\text{isssc}}}\) :

Proportional and Integral constants of SSSC

\({X}_{c}\) :

Compensation provided by SSSC

\(s\) :

Laplace operator

\(d,q\) :

Direct- and quadrature-axis components with respect to synchronized reference frame

\(0\) :

Initial values in steady-state condition

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Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Technology Calicut, NIT campus P O, 673601, Calicut, India

    M. Anju, K. V. Shihabudheen & S. J. Mija

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Contributions

All authors contributed to the conceptual idea for the article. AM contributed to the methodology, software, formal analysis and writing-original draft. SKV was involved in the supervision and writing-review and editing. MSJ assisted in the supervision and writing-review and editing. All authors have read and agreed to the final version of the manuscript.

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Appendix

Appendix

A1. Doubly fed induction generator (DFIG)-based wind farm

Stator resistance \({R}_{s}\) = 0.01 pu; Stator reactance \({X}_{s}\) = 0.10 pu; Rotor resistance \({R}_{r}\) = 0.01 pu. Rotor reactance \({X}_{r}\) = 0.08 pu; Magnetization reactance \({X}_{m}\) = 3 pu; Number of poles = 4; gear box ratio = 1:89; Blade length = 75.0 m; number of blade = 3.

A2. PI controller gain for RSC

Kp−1 = 0.1, KI−1 = 0.05, Kp−2 = 0.75, KI−2 = 0.055, Kp−3 = 0.01, KI−3 = 0.025, Kp−4 = KI−4 = 0.0155.

A3. PI controller gain for GSC

Kp−5 = 0.05, KI−5 = 0.0015, Kp−6 = 0.01, KI−6 = 0.05, Kp−7 = 0.5, KI−7 = 0.75.

A4. Transmission line parameters

Transmission line resistance,\( {R}_{L}\)=0.02pu, reactance, \({X}_{L}\)=0.5pu, capacitive reactance,\({X}_{c}\) at 50% compensation level = 64.8Ω, line length = 154mile.

A5. Relationship between wind speed \({(v}_{w})\), Rotor speed \({(w}_{r})\) and Electromagnetic torque \({(T}_{e})\)

\({v}_{w}\)(m/s)

\({w}_{r}\)(pu)

\({T}_{e}\)(pu)

7

0.76

0.26

8

0.87

0.33

9

0.98

0.42

10

1.09

0.52

11

1.20

0.63

12

1.20

0.79

A6. Optimization using PSO

Parameters (s)

PSO

Range

SSRDC

\({K}_{{\text{SSRDC}}}\)

120.13

0.00–200.00

IBC

\({K}_{f}\)

24.10

0.00–50.00

\({T}_{f}\)

1.35

0.00–2.00

SSSC

\({T}_{m}\)

2.4721

0.00–6.00

\({k}_{p}\)

0.9421

0.00–2.00

\({k}_{i}\)

0.035

0.00–1.06

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Anju, M., Shihabudheen, K.V. & Mija, S.J. Enhancing grid stability: a hybrid control strategy for DFIG-based wind turbines to mitigate sub-synchronous oscillations. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02387-8

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