Wind turbine#

The unit is a wind turbine that converts wind motion into rotational mechanical energy. Wind turbines (WT) use wind energy to generate electricity.

This block can be used to simulate both individual wind turbines (to study mechanical characteristics) and entire wind power plants. This model is designed to evaluate the performance of WT using different control strategies and placement topologies.

The main input variables are the incoming wind speed v and the blade rotation angle β. It is also possible to additionally calculate the thrust force acting on the turbine and the shaft inertia (with the option of specifying the initial angular velocity).

The block calculates the power factors \(C_p\) and the traction force \(C_t\) (with the Calculate thrust force toggle switch on) on the shaft using the look-up table:

\(C_p = table(β_{ref}, λ_{ref}, C_{p_{ref}}, β, λ_{smooth}, interpolation = linear, extrapolation = nearest)\);
\(C_t = table(β_{ref}, λ_{ref}, C_{t_{ref}}, β, λ_{smooth}, interpolation = linear, extrapolation = nearest)\),

where:

\(β_{ref}\) - blade rotation angle vector (the length of this vector determines the number of rows in the table);

\(λ_{ref}\) is the speed coefficient vector (the length of this vector determines the number of columns in the table);

\(C_{p_{ref}}\) and \(C_{t_{ref}}\) are the tabular parameters of the power factor and the traction factor, respectively;

β - blade rotation angle;

\(λ_{smooth}\) - smoothed speed coefficient;

\(C_p(β,λ)\) is a two-dimensional table (matrix), where at the intersection of each row (a certain angle β) and each column (a certain ratio λ) there is a value of the power factor for this operating mode;

\(C_t(β,λ)\) - a similar table for the thrust coefficient.

Note

The dimensions of the tables are (length β) × (length λ).

During the calculation, the block performs a two-dimensional interpolation (linear) on your table to find the corresponding coefficients \(C_p\) and \(C_t\) with respect to the blade rotation angle β and the smoothed speed coefficient \(λ_{smooth}\). If the current point is outside the given vectors \(β_{ref}\) or \(λ_{ref}\), extrapolation to the nearest point is used (saturation).

The block uses the following expression as the basis for the instantaneous velocity ratio (1) :

(1)#\[λ=\frac{R \cdot \omega}{\nu}\]

where:

\(R\) - turbine radius parameter, [m];

\(\omega\) - angular velocity of the turbine shaft, [rad/s];

\(\nu\) - oncoming wind speed, [m/s].

When calculating the speed coefficient, a smoothed version of the above equation (2) is used:

(2)#\[λ_{smooth}=\frac{R \cdot \omega}{\sqrt{\nu^2+\nu^2_{thr}}}\]

where \(\nu_{thr}\) is the wind speed threshold.

The block uses the following equations as the basis for calculating the power and thrust of (3):

(3)#\[\begin{split}P=\frac{1}{2} \cdot C_p \cdot \rho \cdot A \cdot \nu^3\\ F_t=\frac{1}{2} \cdot C_t \cdot \rho \cdot A \cdot \nu^2\end{split}\]

where:

\(P\) - power, [W];

\(F_t\) - traction force, [N];

\(\rho\) - air density, [kg/m\(^3\)];

\(A\) is the area swept by the turbine blades, [m\(^2\)].

The block uses numerically smoothed equations for thrust, power, and torque (4):

(4)#\[\begin{split}P=\frac{\rho \cdot A \cdot C_p \cdot |\nu|^3}{2}\\T_{smooth}=\frac{P}{\sqrt{\omega^2+\omega^2_{thr}}}, если \omega > 0, при\hspace{2mm} \omega <-\omega_{thr} \implies T_{smooth}=0\\ P_{smooth}=T_{smooth} \cdot \omega\\F_{tsmooth}=\frac{1}{2}\cdot C_t \cdot \rho \cdot A \cdot \nu^2\end{split}\]

where \(\omega_{thr}\) is the threshold of the angular velocity of the rotor shaft.

Note

When \(\omega < \omega_{thr}\), the unit smoothly reduces power to zero.

The generated power is zero when the rotor speed is zero or less, and a non-zero value of \(C_p(λ=0)\) significantly affects the starting torque. The expression for the starting torque is (5) :

(5)#\[T_{start}=\frac{\rho \cdot A \cdot C_p \cdot |\nu|^3}{2 \cdot \omega_{thr}}\]

1. Properties#

Property	Default Value	Description	Units of measurement
Turbine radius	80.0	-	m
Pitch angle vector β	0.0;3.0;5.0;10.0;20.0;90.0	-	degrees
Tip speed ratio vector λ	0.0;2.0;4.0;6.0;8.0;10.0;12.0;14.0;15.0	-	-
Power coefficient table \(C_p(β,λ)\)	<0.001;0.0161;0.1446;0.3865;0.5009;0.4404;0.2545;2.0E-4;-0.1384><0.0016;0.0173;0.1079;0.2676;0.3779;0.4111;0.3838;0.3176;0.2753><0.0027;0.0197;0.1151;0.2606;0.3469;0.3558;0.3069;0.2222;0.1718><0.0054;0.0283;0.1315;0.2364;0.2589;0.2022;0.0929;-0.0455;-0.1204><0.0109;0.0536;0.132;0.1256;0.012;-0.1752;-0.4017;-0.6435;-0.7655> _<-0.01;-0.01;-0.01;-0.01;-0.01;-0.01;-0.01;-0.01;-0.01>	-	-
Rotational velocity threshold	0.01	-	rad/s
Wind speed threshold	0.01	-	m/s
Air density	1.225	-	kg/m\(^3\)
Calculate thrust force”	Off	-	-
Thrust coefficient table \(C_t(β,λ)\)	<0.0;0.2451;0.674;0.9616;1.0;0.9882;0.843;2.0E-4;-0.1341> <0.0016;0.2541;0.5942;0.8582;0.9561;0.9754;0.9599;0.9092;0.8669> <0.0027;0.2705;0.6113;0.8503;0.9339;0.9407;0.8993;0.8016;0.7239><0.0054;0.3215;0.6475;0.8205;0.8482;0.7727;0.5565;-0.045;-0.1171><0.2035;0.4335;0.6485;0.6348;0.2129;-0.1684;-0.3701;-0.5712;-0.6681> _<-0.05;-0.05;-0.05;-0.05;-0.05;-0.05;-0.05;-0.05;-0.05>	Available, when `Calculate thrust force` - `On`	-
Model inertia	Off	-	-
Rotor inertia	0.75	Available, when `Model inertia` - `On`	kg\(\cdot\)m\(^2\)
Initial rotor rotational velocity	0.0	Available, when `Model inertia` - `On`	rad/s

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Wind speed \(\nu\)	Input	-	m/s	Automation
Pitch angle β	Input	-	degrees	Automation
Thrust	Output	Available, when `Calculate thrust force` - `On`	N	Automation
Rotor shaft	Output	-	-	Rotational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports