Maximum power extraction from fractional order doubly fed induction generator based wind turbines using homotopy singular perturbation method

Abolvafaei, Mahnaz; Ganjefar, Soheil

doi:10.1016/j.ijepes.2020.105889

Cited by 24 publications

(9 citation statements)

References 57 publications

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“…Investigating the behaviour of systems has demonstrated that many real-world dynamics generally or most likely are fractional order in nature. Hence, the behaviour of most systems is better explained by fractional-order modelling [16,17]. In control engineering, fractional modelling has been offered and successfully applied in various fields, such as stability analysis [18] and controller design [9,19].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The fractional‐order mechanical model of the two‐mass WT can be described as follows [10, 15, 17]:

J_{r} D_{t}^{α} ω_{r} = T_{a} - T_{l s} - D_{r} ω_{r}

n_{g} J_{g} D_{t}^{α} ω_{g} = T_{l s} - n_{g} T_{e} - n_{g} D_{g} ω_{g}

T_{l s} = k_{l s} (θ_{r} - θ_{g} / n_{g}) + D_{l s} (ω_{r} - ω_{g} / n_{g})

where

D_{t}^{α}

denotes the fractional‐order derivative,

J_{r}

and

J_{g}

denote the rotor and generator inertia, respectively,

D_{r}

D_{g}

, and

D_{l s}

are the rotor external damping, generator external damping, and low‐speed shaft damping, respectively,

T_{l s}

represents the low‐speed shaft torque,

ω_{g}

is the generator speed,

T_{e}

denotes generator torque,

k_{l s}

is the low shaft speed stiffness,

θ_{r}

and

…”

Section: Dynamics Of the Fractional‐order Wt Modelmentioning

confidence: 99%

“…The power of

P_{w}

and

P_{a}

can be defined as [7]

P_{a} = C_{p} (λ, β) P_{w} = 0.5 ρ π R^{2} C_{p} (λ, β) v^{3} false(t false)

where ρ is the air density, R denotes the WT rotor radius,

v (t)

is the wind speed,β is a blade pitch angle, and λ is the tip speed ratio (TSR), which is defined as

λ = R ω_{r} / v

, where

ω_{r}

denotes the rotor speed. The power coefficient depends on the shape and the geometry of the blades and is a nonlinear function of the blade pitch β and λ described as in [15, 17]. The aerodynamic torque

T_{a}

is obtained as

T_{a} = P_{a} / ω_{r} = 0.5 ρ π R^{3} v^{2} false(t false) C_{p} (λ, β) / λ

…”

Section: Dynamics Of the Fractional‐order Wt Modelmentioning

confidence: 99%

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Adaptive second‐order terminal PID sliding mode control design for integer‐order approximation of wind turbine system for maximum power extraction

Abolvafaei

Ganjefar

2021

IET Control Theory & Appl

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The main purpose of this paper is to extract the maximum power from the variable speed wind turbine (VSWT), which is modelled using fractional calculus. The use of the fractional-order operator can harden the practical implementation and numerical simulation of the fractional-order systems. To apply the fractional calculus theory, we assume that the orders of all fractional derivatives of the system have a small deviation from the nearest integers. By defining this small deviation as a perturbation parameter, an integer-order approximation method is presented for approximating the fractional-order system into a perturbed integer-order system in the time domain. Then, a new adaptive second-order sliding mode control (SOSMC) method is proposed using the terminal proportional integral derivative (TPID) sliding surface to achieve maximum power extraction and reduce mechanical loads and chattering. A TPID sliding surface is employed to ensure better tracking, have a zero steady-state error, decrease the mechanical stresses, and eliminate the chattering phenomenon. The stability of the adaptive SOSMC based on the obtained integer-order approximation is analyzed using the Lyapunov stability criterion. The simulation results of the proposed method are presented and compared with some designed controllers for wind turbines (WTs) modelled with fractional and integer derivatives. The obtained results show the effectiveness of the proposed strategy.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Literature Reviewmentioning

confidence: 99%

“…The fractional‐order mechanical model of the two‐mass WT can be described as follows [10, 15, 17]:

J_{r} D_{t}^{α} ω_{r} = T_{a} - T_{l s} - D_{r} ω_{r}

n_{g} J_{g} D_{t}^{α} ω_{g} = T_{l s} - n_{g} T_{e} - n_{g} D_{g} ω_{g}

T_{l s} = k_{l s} (θ_{r} - θ_{g} / n_{g}) + D_{l s} (ω_{r} - ω_{g} / n_{g})

where

D_{t}^{α}

denotes the fractional‐order derivative,

J_{r}

and

J_{g}

denote the rotor and generator inertia, respectively,

D_{r}

D_{g}

, and

D_{l s}

are the rotor external damping, generator external damping, and low‐speed shaft damping, respectively,

T_{l s}

represents the low‐speed shaft torque,

ω_{g}

is the generator speed,

T_{e}

denotes generator torque,

k_{l s}

is the low shaft speed stiffness,

θ_{r}

and

…”

Section: Dynamics Of the Fractional‐order Wt Modelmentioning

confidence: 99%

“…The power of

P_{w}

and

P_{a}

can be defined as [7]

P_{a} = C_{p} (λ, β) P_{w} = 0.5 ρ π R^{2} C_{p} (λ, β) v^{3} false(t false)

where ρ is the air density, R denotes the WT rotor radius,

v (t)

is the wind speed,β is a blade pitch angle, and λ is the tip speed ratio (TSR), which is defined as

λ = R ω_{r} / v

, where

ω_{r}

T_{a}

is obtained as

T_{a} = P_{a} / ω_{r} = 0.5 ρ π R^{3} v^{2} false(t false) C_{p} (λ, β) / λ

…”

Section: Dynamics Of the Fractional‐order Wt Modelmentioning

confidence: 99%

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Adaptive second‐order terminal PID sliding mode control design for integer‐order approximation of wind turbine system for maximum power extraction

Abolvafaei

Ganjefar

2021

IET Control Theory & Appl

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“…Berrada and Boumhidi (2020) proposed a new SMC method to implement MPPT strategy and diminish the transient loads on shafts. Abolvafaei and Ganjefar (2020) considered a fractional order model for double-fed induction generator (DFIG)-based wind turbines, according to which a homotopy singular perturbation method was proposed to maximize the captured power from wind energy. In Wang et al (2021), for maximum power tracking in a DFIG-based WECS, a multivariable super-twisting control was designed and composed with an adaptive control approach to overcome model uncertainties and external disturbances without any requirement for prior knowledge about the upper bound of them.…”

Section: Introductionmentioning

confidence: 99%

Design of an adaptive controller to capture maximum power from a variable speed wind turbine system without any prior knowledge of system parameters

Neya

Saberi

Rezaie

2021

Transactions of the Institute of Measurement and Control

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Even though some wind turbine manufacturers are no longer active, and are not willing to disclose their intellectual property, their turbines are still in operation. Since the exact values of wind turbine parameters like the aerodynamic model, drive-train model and generator parameters are not always accessible, the design of a controller which does not require prior knowledge of the system parameters can be very useful and effective. As a result, this paper proposes a disturbance observer-based controller to harvest the maximum power from a wind turbine system with fully unknown parameters. To reduce control efforts, a disturbance observer is designed to estimate unknown nonlinear terms caused by unknown model parameters in the presence of unknown control coefficient that uses only the tracking error to estimate nonlinear disturbance. Compared with previously published works, in this paper, both aerodynamic model and drive-train model parameters are assumed to be fully unknown. Closed-loop stability of the proposed controller is analyzed by the Lyapunov stability theorem. To demonstrate the performance of the proposed controller, it is compared with some existing controllers. Comparative simulation results show its effectiveness. Furthermore, although the proposed controller does not require system parameters and includes fewer tuning parameters, it shows the same tracking performance as the other three controllers. The numerical comparative results are listed in a table, which shows that Mean Square Error (MSE) of the proposed controller is 75% less than minimum MSE of the other three controllers of previous works, while its control effort is 1.7% higher than the minimum control effort of the other three.

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“…Then, this method has been extended by many other researchers for solving different problems. The HPM was applied to find the approximate analytical solution of the Allen-Cahn equation in [28], to study the maximum power extraction from fractional order doubly fed induction generator based wind turbines in [29], dissipative nonplanar solitons in an electronegative complex plasma in [30] and others [31][32][33]. Convergence of the parameter continuation method in the homotopy method based on the theorem of V.A.…”

Section: Introductionmentioning

confidence: 99%

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

Noeiaghdam

Dreglea

et al. 2020

Symmetry

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This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.

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Maximum power extraction from fractional order doubly fed induction generator based wind turbines using homotopy singular perturbation method

Cited by 24 publications

References 57 publications

Adaptive second‐order terminal PID sliding mode control design for integer‐order approximation of wind turbine system for maximum power extraction

Adaptive second‐order terminal PID sliding mode control design for integer‐order approximation of wind turbine system for maximum power extraction

Design of an adaptive controller to capture maximum power from a variable speed wind turbine system without any prior knowledge of system parameters

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

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