Efficiency improvement of a variable speed wind turbine: Effect of controller design and generator speed range

Abstract

In this paper, a theory and practice-based research is conducted using real data, in order to increase the efficiency of a Vestas 660 kW wind turbine. The data obtained from Binalood’s wind farm, shows the degraded performance of these turbines. This is mainly because of the weak performance of the classical controller in tracking to reach the maximum power in the partial load region. Another factor with a negative effect on efficiency of the turbines, is the low range of generator speed variation. In this research, two solutions are proposed to solve these problems. First, a nonlinear state feedback controller with wind speed calculator is designed which improves the turbine performance. Second, it is shown by simulation results that the turbine efficiency is improved by increasing the range of generator speed variation. Also, the model is validated using actual data and FAST model.

Keywords

Wind turbine modeling controller design efficiency improvement FAST

1. Introduction

In recent years, using wind turbines to generate electricity are increasingly growing due to the significant progress in the industry. Because of the environmental, social and economic benefits, the use of wind energy is increased even against other renewable energies. According to generator operating conditions, wind turbines are divided into fixed and variable speed turbines. Variable speed wind turbines have advantages such as increased extracted energy from the wind, and reduced load on the drivetrain. Because of these advantages, these kinds of wind turbines are widely used nowadays (Colombo et al., 2019; Gustavo and Enrique, 2011; Yuan et al., 2020).

In variable speed wind turbines, it is possible to achieve the maximum amount of power coefficient at the optimum blade tip speed ratio, in the partial load area (Chatratana, 2010; Ebrahimi and Orlando, 2018). According to equation (1), blade tip speed ratio is a function of wind speed and rotor angular velocity.

λ = \frac{ω_{r} R}{V_{wind}}

(1)

In the partial load area, generator speed should change proportional to the wind speed variations, in order to keep the blade tip speed ratio in its optimal value, while the pitch angle remains constant in its optimal value ( $β = 0$ ).

In this region, where the wind speed is less than the rated value, extracting the maximum energy from wind is the goal of wind turbine control. Different studies have been conducted to achieve this goal in this region. Muljadi et al. (1998) evaluated a variable-speed, stall-regulated strategy which eliminates the need for ancillary aerodynamic control systems. The potential benefit is a lower cost of energy resulting from lower capital cost, improved reliability and reduced maintenance expense. In the strategy to be investigated, the turbine is controlled to operate near maximum efficiency (energy capture) in low and moderate wind speeds. Leith and Leithead (1988) considered a conventional PI controller for a typical 300 KW two laded full span Horizontal Axis Wind Turbine (HAWT). This controller is compared with a linear controller designed using classical loop shaping. Kalaivani and Magesh (2014) showed that the variable speed wind turbine with Maximum Power Point Tracking (MPPT) controller as a fixed speed wind turbine is not suitable for most of the applications. Including an MPPT algorithm in a wind energy system is necessary due to the instantaneous and unpredictable change of the wind speed. The MPPT is implemented in wind turbines to maintain the output power constant at variable speeds and a PI controller is used to calculate the error value as the difference between a measured process variable and a desired set point. The controller attempts to minimize the error.

Nowadays due to the significant progress that is made in the industry, new controllers are designed which improves the turbine performance. Carlin et al. (2001) described an MPPT method to achieve maximum power of wind, in the variable speed wind turbines. In addition, they used fuzzy controller in the partial load area, to achieve the maximum power. Ganjefar and Ghasemi (2014) proposed a new control strategy for an optimal extraction of output power from stand-alone windmill systems. The system consists of a variable-speed wind turbine directly coupled to a PMSG (permanent magnet synchronous generator), a diode bridge rectifier, a DC-to-DC boost converter, and a battery bank. This control method, with its higher speed, directly creates a control signal for handling DC-to-DC converters. Adding an ESN (Echo State Network) to this method can result in extracting maximum power from the wind turbine without measuring the wind speed. Heidari et al. (2013) presented a comparison of different methods to extract maximum energy from wind turbines and explained the benefits and weaknesses of each of them. Esbensen et al. (2008) proposed a method to realize the robust controller takes parametric uncertainties into account, in order to handle nonlinearities in the aerodynamic model. Since large parameter variations are present in the model, the operating range of the wind turbine is divided into smaller regions. Fazlollahi et al. (2019a) ANFIS modeling and validation of Vestas 660 kW wind turbine based on actual data obtained from Eoun-Ebn-Ali wind farm in Tabriz, Iran, and FAST is performed. Salomao et al. (2012) presented a comparison between three types of control algorithms for a 1.5 MW horizontal axis fixed speed wind turbine. They proposed a fuzzy logic proportional integral control (Fuzzy PI), a fuzzy logic control (FLC) and a classical proportional integral (PI) control. Boukhezzar and Siguerdidjane (2011) presented a nonlinear approach, using a two-mass model and a wind speed estimator, for variable-speed wind turbine (WT) control. The use of a two-mass model is motivated by the need to deal with flexible modes induced by the low-speed shaft stiffness. The main objective of the proposed controllers is the wind power capture optimization while limiting transient loads on the drivetrain components. Laks et al. (2009) reviewed the objectives and techniques used in the control of horizontal axis wind turbines at the individual turbine level, where controls are applied to the turbine blade pitch and generator. After reviewing basic turbine control objectives, they provided an overview of the common basic linear control approaches and then described advanced control architectures and why they may provide significant advantages. Fazlollahi et al. (2019b), in order to improve the control performance and alleviate fluctuations in the full-load region, considering the nonlinear and complex behavior of the system, a neuro-fuzzy controller is designed to control the pitch angle. In this controller, neural network is used to adjust the membership functions of the fuzzy controller. Živković et al. (2012) utilized an advanced fuzzy controller for controlling wind turbine. In this paper, a model is also analyzed and combined with a stochastic wind model for simulation purposes.

This proposed method has four main advantages:

Here, a theory and practice-based research is conducted using real data, in order to increase the efficiency of a Vestas 660 kW wind turbine used in Binalood wind power plant, Mashhad, Iran.

In order to increase the efficiency of the mentioned wind turbine, two practical solutions are proposed; (1) a nonlinear dynamic state feedback controller with a newly proposed wind speed calculator and (2) improving the turbine efficiency by increasing the range of generator speed variation. Therefore, using a generator with high range of speed changes is suggested instead of optislip generator. Simulations show the effect of each solution separately and simultaneously.

By using this new approach of wind speed calculator in the proposed nonlinear controller, in order to extract the maximum energy from wind, feedback of the generator speed and aerodynamic torque are employed to control the generator torque. Due to the rapid response of the designed controller, it is possible to track the maximum power coefficient in the partial load area as the wind speed varies. Therefore, maximum energy is extracted from wind in different wind speeds and efficiency is increased.

In this paper, the mechanical stress on the wind turbine structure is investigated as well and it is shown that the designed controller does not increase the stress on the turbine structure compared to the proposed real wind turbine controller.

The structure of this paper is as follows. In section 2, wind turbine performance is discussed. In section 3, a model of the wind turbine is presented. Model validation with actual data is done in section 4. Controller design is discussed in section 5. Simulation results are presented in section 6, and Finally the last section concludes the conclusion.

2. Wind turbine performance

When the wind blows through the turbine blades with sufficient speed, blades move and cause the low-speed shaft rotation. This shaft is connected to the gearbox to increase rotational speed. When high-speed shaft reaches the rated speed of the generator, it drives the generator and electrical energy produces (Ansari, 2019; Civelek, 2020; Jiang et al., 2015; Pao and Johnson, 2009; Pintea et al., 2011) To explain the performance of wind turbines, $C_{P} (λ, β)$ curve has depicted as follows.

2.1. $C_{P} (λ, β)$ Performance curve

A common method to show the performance of wind turbines is the dimensionless curve of power coefficient-blade tip speed ratio. In variable speed wind turbines, the maximum value of power coefficient is equal to 0.48, approximately, which is obtained at the blade tip speed ratio of 8.1. The mentioned value is lower than the determined value by the Betz limit (Bianchi et al., 2006a). One of the reasons for the difference between the optimal value of power coefficient and the Betz limit is the losses that occurs in the blades. However, it should be noted that, even if these losses would not happen, it is not possible to reach the amount of Betz limit, since the design of wind turbine blades is not quite accurate and flawless (Burton et al., 2001; Jelavic et al., 2007)

In Figure 1, the $C_{P} (λ, β)$ diagram is shown for a three-blade wind turbines.

Figure 1.

3D diagram of $C_{P} (λ, β)$ .

3. Wind turbine modeling

In this part, wind turbine blades have been assumed to be perpendicular to the wind direction and the wind shear has been ignored. The wind turbine divided into aerodynamic, mechanical, pitch angle, and electrical subsystems which models as follows.

3.1. Aerodynamic subsystem

Equation (2) shows the aerodynamic power absorbed by the wind turbine rotor. Equation (3) represents Aerodynamic torque.

P_{a} = \frac{1}{2} ρ π R^{2} C_{P} (λ, β) V_{wind}^{3}

(2)

T_{a} = \frac{ρ π R^{3}}{2} C_{Q} (\frac{ω_{r} R}{V_{wind}}, β) V_{wind}^{2}

(3)

3.2. Mechanical subsystem

In order to modeling the mechanical subsystem, the low-speed shaft dynamics can be obtained by the following equation (Esbensen et al., 2008; Fazlollahi et al., 2019a, 2019b).

J_{r} \frac{d^{2}}{d t^{2}} θ_{r} = T_{a} - T_{1} - B_{r} \frac{d}{dt} θ_{r}

(4)

Dynamics of the high-speed shaft is calculated as follows.

J_{gen} \frac{d^{2}}{d t^{2}} θ_{gen} = T_{h} - T_{gen} - B_{gen} \frac{d}{dt} θ_{gen}

(5)

Then, the gearbox is modeled as a gear ratio in equation (6).

T_{h} = η_{dt} \frac{T_{1}}{N_{gear}}

(6)

Torsion of the drivetrain is modeled using a torsion spring and the friction coefficient as follows:

T_{1} = K_{s} δ θ + B \frac{d}{dt} δ θ

(7)

δ θ = θ_{r} - \frac{θ_{gen}}{N_{gear}}

(8)

\frac{d}{dt} (δ θ) = δ ω = ω_{r} - \frac{ω_{gen}}{N_{gear}}

(9)

By substituting equation (7) in equation (4)equation (10) is obtained. Similarly, by substituting equation (7) in equations (6) and (5), equation (11) is obtained. Then dynamics of the drivetrain is expressed by following equations.

J_{r} \frac{d}{dt} ω_{r} = [T_{a} - (k_{s} δ θ + B δ ω)]

(10)

J_{gen} \frac{d}{dt} ω_{gen} = [\frac{η_{dt}}{N_{gear}} (k_{s} δ θ + B δ ω) - T_{gen}]

(11)

Note that the viscous friction of low speed shaft and high-speed shaft are neglected due to the insignificance amount.

Wind turbine is modeled as a two mass model in Figure 2.

Figure 2.

Two mass model of the wind turbine.

3.3. Pitch angle subsystem

This subsystem can prevent excessive load on the wind turbine structure at higher wind speeds and keeps the generator speed and power at a nominal value (Rasel and Hasnat, 2011; Sandhya and Chandan, 2011; Tiwari et al., 2014)

Dynamic behavior of the pitch actuator is described by equation (12).

\overset{\cdot}{β} = - \frac{1}{τ} β + \frac{1}{τ} β_{opt}

(12)

3.4. Electrical subsystem

The feature of this generator (Optislip) allows having a variable slip which reduces fluctuations in output power and torque by selecting optimum slip value. Optislip is a simple, reliable, and economical method for reducing the loads. These generators have a variable external rotor resistance, which is controllable by slipping. Also, their stator is directly connected to a power network (Bianchi et al., 2006b; Esbensen and Sloth, 2009; Guo et al., 2013; Gustavo and Enrique, 2011; Moradi, 2019; Muller et al., 2002; Yin et al., 2015)

Generator losses can be considered using equation (13).

P_{e} = η_{gen} ω_{gen} T_{gen}

(13)

Finally, the dynamics of the generator subsystem is obtained by equation (14).

{\overset{\cdot}{T}}_{gen} = \frac{1}{τ_{gen}} (T_{g, ref} - T_{gen})

(14)

4. Model validation with actual data and FAST

In this section, in order to validate the proposed model, real data (wind speed, pitch angle, generator speed, generator torque, and output power) obtained from Eoun-Ebn-Ali wind power plant, Tabriz, Iran, is used. For this purpose, inputs to the real wind turbine (wind speed, pitch angle and generator torque) considered as inputs to the model in MATLAB software. Then obtained output power of simulation is compared with real wind turbine output power. Also, in order to validate the proposed model with FAST, inputs to the real wind turbine (wind speed, pitch angle and generator torque) considered as inputs to the FAST as an open loop model and then output power of FAST model is compared with actual data and data obtained from Simulink model. The wind speed profile is shown in Figure 3 (obtained from from Eoun-Ebn-Ali wind farm) is used to simulate the wind turbine behavior. As shown in the Figure 4, the value of the output power in the real wind turbine and simulation results and FAST, match with proper accuracy. The RMSE¹ between the actual data & Simulink output, and FAST & Simulink output are compared.

Figure 3.

Wind speed curve used in simulation.

Figure 4.

Comparison of wind turbine output power in Simulink, FAST and real curves.

RMSE of actual & Simulink data = 33.5418 kW

RMSE of FAST & Simulink data = 23.3247 kW

5. Controller design

As mentioned already, in the partial load area extracting the maximum power from the wind in different wind speeds is the goal of the control system. To achieve this goal, the rotor angular velocity has to be changed proportionally to the wind speed variation. Thus, the value of the blade tip speed ratio remains at its optimal value. In this case, the pitch angle is kept constant at its optimal value (β = 0). In this angle, the power coefficient reached into its maximum value with the optimum blade tip speed ratio. To fulfill this goal, this paper sought to design a nonlinear dynamic state feedback controller with wind speed calculator. In this controller as shown in Figure 5, feedback of the generator speed and aerodynamic torque are employed to control the generator torque. Due to the dynamics of the gearbox and rotor shaft, feedback of the generator speed is taken instead of the rotor speed. This increases the accuracy of the controller, due to the more accurate information which comes from different subsystems operating conditions of the wind turbine. In order to get more detailed information from the initial conditions of the wind, when it blows to the blades, feedback of the aerodynamic torque is also taken. So this controller has significant advantages over the other state feedback controller, due to using generator speed, rotor speed and aerodynamic torque simultaneously. As a result, a performance of the control system is improved, due to the more information obtained from the very important sections of the wind turbine. Finally, simulation results show that due to the favorable performance of the designed controller and wind speed calculator, extracted energy from the wind is increased. It should be noted that calculating wind speed by equation (19) and designing proposed controller have especially done in this paper.

Figure 5.

Nonlinear dynamic state feedback controller with wind speed calculator scheme.

In order to design the proposed controller, by selecting a second order dynamic, tracking error of rotor angular velocity has calculated by following equations.

\overset{\cdot\cdot}{ε} + a_{1} \overset{\cdot}{ε} + a_{0} ε = 0

(15)

ε = ω_{opt} - ω_{r}

(16)

by using equations (10) and (11) equation (17) is obtained.

J_{r} {\overset{\cdot}{ω}}_{r} = T_{a} - N_{gear} J_{gen} {\overset{\cdot}{ω}}_{gen} + N_{gear} T_{gen}

(17)

Then, by using equations (15) to (17), equation (18) is obtained.

{\overset{\cdot}{T}}_{gen} = \frac{{\overset{\cdot}{T}}_{a}}{N_{gear}} - J_{gen} {\overset{\cdot\cdot}{ω}}_{g} - \frac{J_{r}}{N_{gear}} ({\overset{\cdot\cdot}{ω}}_{opt} + b \overset{\cdot}{e} + ce)

(18)

In order to calculate ${\overset{\cdot\cdot}{ω}}_{opt}$ , wind speed is calculated by equation (19).

T_{a} = \frac{ρ π R^{3}}{2 λ_{opt}} C_{P \max} (\frac{ω_{r} R}{V_{wind}}, β) V_{wind}^{2}

(19)

By solving equation (19), wind speed is obtained to calculate optimum rotor angular velocity, as follows:

ω_{opt} = \frac{V_{wind} λ_{opt}}{R}

(20)

As shown in equation (18), the rate of generator torque is a function of the aerodynamic torque, generator angular speed rate and the second derivative of rotor angular optimal velocity. The designed controller is a nonlinear dynamic state feedback controller. The reason for using this controller instead of a static state feedback controller is that the static state controller is not resistant to disturbances in wind speed variations, therefore the efficiency of wind turbine decreases. The dynamic state feedback controller has an acceptable resistance to disturbances in different wind speeds, which enhances the efficiency. For a desirable performance of the controller, the power coefficient in different wind speeds is kept in the range of its optimal value. Therefore, according to the simulation results, the efficiency of wind turbines increases significantly. This is the main advantage of this controller compared to the static state feedback controller and the classical PI controller.

Figure 5 shows the scheme of the designed nonlinear dynamic state feedback controller with wind speed calculator.

In the following classical controller, used in a proposed real wind turbine, is described.

This controller has been used in 660 kW Vestas wind turbine in the partial load area in Binalood, Mashhad, Iran, wind power plant. According to the equation (21) for designing the controller, a coefficient k is used. This coefficient is obtained from equation (22). According to equation (22), k is a function of fixed parameters, which causes this coefficient to be constant in different wind speeds. In the wind turbines to extract the maximum energy from wind in the partial load area, proportional to the wind speed variation, this coefficient must be changed. Due to use of the maximum power coefficient in the equation (22), the maximum coefficient k is obtained. With this maximum and constant coefficient, until the wind speed remains at its nominal value, the controller has a desirable performance. But due to the wind speed high fluctuations, to extract the maximum energy from wind, this coefficient has to be changed proportionally to the available wind power. Therefore, this problem has been resolved by designing a proposed nonlinear dynamic state feedback controller.

T_{g} = k ω^{2}

(21)

k = \frac{1}{2} ρ A \frac{η_{th} R^{3}}{N_{gear}^{3} λ_{opt}^{3}} C_{P, \max}

(22)

6. Simulation results

In this section, simulations have been done for a Vestas 660 kW variable speed wind turbine with a horizontal axis, in a MATLAB/ Simulink environment.

The dimensions used in the model are exactly the same as the real wind turbine in Binalood wind power plant. This wind turbine consists of three main components including the rotor, tower, and nacelle. The rotor consists of three blades and accessories that is called a hub. The tower is a cylindrical column and the nacelle sits at the top of the tower. A nacelle is a case that includes the drivetrain within it. The drivetrain includes a low-speed shaft, gearbox, high-speed shaft and generator. Simulation results indicate the efficiency improvement due to each solution separately and simultaneously.

In the following, information of the real and simulated wind turbine is shown in “Table 1.”

Table 1.

Real wind turbine and simulation data.

	Value	Units (SI)
Item
Rotor diameter	47	(m)
Gear ratio	52.65
Rated Power	660	(kw)
Cut in wind speed	4	(ms⁻¹)
Rated speed	15	(ms⁻¹)
Cut out wind speed	25	(ms⁻¹)
Air density	1.205	(kgm⁻³)
Rotor inertia	354,000	(kgm²)
Generator inertia	37.5	(kgm²)
Shaft stiffness coefficient	293,563	(Nm.rad⁻¹)
Shaft damping coefficient	10,363	(Nm.s.rad⁻¹)
Tower height	40	(m)
Optimal pitch angle	0	(deg)
Optimal tip speed ratio	8.1

6.1. Results for designed controller with wind speed calculator

In this section, designed nonlinear dynamic state feedback controller has implemented on the wind turbine model and simulated with MATLAB software. Simulation results have compared with actual data (obtained from Binalood wind power plant) and a classical controller to validate designed controller.

In Figure 6, The wind speed obtained from Binalood wind power plant is depicted. In order to simulate the designed controller, this wind speed curve is used.

Figure 6.

Wind speed curve.

In Figures 7 and 8, due to the desired performance of the designed controller, according to the wind speed change, the generator speed is changing fast. Therefore, the power coefficient in different wind speeds remains in the range of its optimal value. Finally, this favorable performance of the controller, with respect to the Figures 9 and 10, causes to increase the extracted energy by 6.91% compared to the classical controller and by 13.49% compared to the actual data.

Figure 7.

Simulated and actual rotor angular speed curves.

Figure 8.

Simulated and actual generator angular speed curves.

Figure 9.

Simulated and actual power coefficient curves.

Figure 10.

Simulated and actual output power curves.

6.2. Results for designed controller without wind speed calculator

In this section, simulation has been done without calculating wind speed with designed nonlinear dynamic state feedback controller in MATLAB software. In this section, wind speed is calculated as the same to the other dynamic state feedback controller. According to the Figure 11 the amount of extracted energy from the wind, in this case, is increased by 1.68% compared to the classical controller and is increased by 8.26% compared to actual data obtained from Binalood wind power plant. But in comparison with a designed controller with calculating wind speed, efficiency decreased by 5.23%.

Figure 11.

Simulated and actual output power curves without wind speed calculator.

6.3. Results for increased range of generator speed

Blade tip speed ratio is a function of the rotor angular velocity and wind speed. To extract the maximum energy from wind, the amount of blade tip speed ratio at various wind speeds should be at its optimal value. To achieve this goal, generator speed must change quickly proportional to the wind speed variation at any time with minimum delay, in order to the blade tip speed ratio remains at its optimum value. But because of the low range of generator speed changes in Vestas 660 kW wind turbine used in Binalood wind power plant, in this paper the range of generator speed changes is increased. Finally, simulation results have been shown in different diagrams.

According to the Figures 12 and 13, it can be seen that the range of the generator speed variation in a real wind turbine is low while in the simulated curve, this range increases significantly. Therefore, according to the Figures 14 and 15, this causes the power coefficient to track its optimal value. Therefore, by using this method extracted energy from the wind is increased by 11.49% compared to the classical controller and is increased by 18.07% compared to the actual data obtained from Binalood wind power plant.

Figure 12.

Simulated and actual rotor angular speed curves.

Figure 13.

Simulated and actual generator angular speed curves.

Figure 14.

Simulated and actual power coefficient curves.

Figure 15.

Simulated and actual output power curves.

6.4. Results for using both solutions simultaneously

In this section, both proposed solutions are used at the same time in simulations. Due to the Figure 16, by using both solutions simultaneously, the extracted energy from the wind is increased by 19.57% compared to the classical controller and is increased by 26.15% compared to the actual data.

Figure 16.

Simulated and actual output power curves.

6.5. Effect of stress on wind turbine structure

In this section, the effect of the designed controller on the wind turbine structural loads is investigated. The stress on the turbine’s structure can be presented by the following equations.

\int {\overset{\cdot}{θ}}_{Δ}^{2} (t) dt

(23)

{\overset{\cdot}{θ}}_{Δ} (t) = ω_{r} (t) - \frac{1}{N_{g}} ω_{g} (t)

(24)

In fact, the proposed controller should not increase the stress compared to the classical controller while increasing the extracted energy. Using the classical controller, used in the proposed real wind turbine, the amount of stress on the turbine’s structure is calculated as follows:

\int {\overset{\cdot}{θ}}_{Δ}^{2} (t) dt = 1.14311 * 10^{- 5} Ra d^{2} / S

Using the designed controller, the amount of stress on the turbine’s structure is obtained as follows:

\int {\overset{\cdot}{θ}}_{Δ}^{2} (t) dt = 1.02556 * 10^{- 5} Ra d^{2} / S

As it can be seen, the stress don’t increase compared to the classical controller. The effect of the stress on the turbine’s structure is shown in Figure 17. This curve and the amount of stress are obtained by simulating the proposed wind turbine in MATLAB software.

Figure 17.

Effect of stress on drivetrain.

7. Conclusion

Results of this research indicate that the wind turbine used in Binalood wind power plant with classical controller and optislip generator, has a poor performance and low efficiency. Due to the importance of extracting the maximum energy from wind, because of the economic and environmental benefits, it is necessary to increase the efficiency of these turbines.

In this paper, it is shown that in the partial load area, the efficiency of 660 kW Vestas wind turbines was increased by designing a nonlinear dynamic state feedback controller with wind speed calculator, and by increasing the range of generator speed variation. According to the simulation results, the efficiency was increased by 6.91% due to the favorable performance of the designed controller with wind speed calculator and by 1.68% without wind speed calculator, and by 11.49% due to the increase of generator speed range. Also, simultaneous application of both proposed solutions increased the efficiency by 19.57%. Moreover, the mechanical stress on the wind turbine structure was investigated and it was shown that the designed controller does not increase the stress on the turbine’s structure.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Vahid Fazlollahi

Mostafa Taghizadeh

Farzad A Shirazi

Notes

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Efficiency improvement of a variable speed wind turbine: Effect of controller design and generator speed range

Abstract

Keywords

1. Introduction

2. Wind turbine performance

2.1. C P ( λ , β ) Performance curve

3. Wind turbine modeling

3.1. Aerodynamic subsystem

3.2. Mechanical subsystem

3.3. Pitch angle subsystem

3.4. Electrical subsystem

4. Model validation with actual data and FAST

5. Controller design

6. Simulation results

6.1. Results for designed controller with wind speed calculator

6.2. Results for designed controller without wind speed calculator

6.3. Results for increased range of generator speed

6.4. Results for using both solutions simultaneously

6.5. Effect of stress on wind turbine structure

7. Conclusion

Footnotes

Appendix

Declaration of conflicting interests

Funding

ORCID iDs

Notes

References

2.1. $C_{P} (λ, β)$ Performance curve