2.1 MS bladed model and NREL 5-MW wind turbine

The MS (Mustafa Sahin) Bladed Model, developed by the author, is a recently well-known equation-based simulation tool in the literature [Reference Sahin and Yavrucuk11, Reference Sahin and Yavrucuk43–Reference Sahin and Farsadi45, Reference Sahin, Yavrucuk, Diez and Icaza77]. It is created using MATLAB and Simulink programmes [46] and used for Horizontal Axis Wind Turbine (HAWT) simulations. The mainstay of the model is the Blade Element Momentum theory [Reference Hansen47, Reference Manwell, McGowan and Rogers48]. The model disregards the aerodynamic interactions between blade sections, treating each section’s aerodynamics independently. Additionally, it incorporates key aerodynamic corrections: turbulent wake state [Reference Hansen47, Reference Branlard49, Reference Wanderley and Levi76] skewed wake rotation [Reference Pitt and Peters50–Reference Moriarty and Hansen52], as well as hub and tip losses [Reference Moriarty and Hansen52]. Moreover, it has special coordinate systems [Reference Sahin44, Reference Ning53] for simulations of turbines with different structural angles such as rotor tilt angle, pre-cone angle. Some of these coordinate systems such as blade-aligned ( ${O_b}{x_b}{y_b}{z_b}$ ), aerodynamic-aligned ( ${O_{ae}}{x_{ae}}{y_{ae}}{z_{ae}}$ ), azimuth-aligned ( ${O_z}{x_z}{y_z}{z_z}$ ), yaw-aligned ( ${O_y}{x_y}{y_y}{z_y}$ ), wind-aligned ( ${O_w}{x_w}{y_w}{z_w}$ ) and hub-aligned ( ${O_h}{x_h}{y_h}{z_h}$ ) coordinate systems are seen in Figs 3 and 4. The MS Bladed Model assumes that turbines comprise one single mass (Fig. 2) with non-flexible structures including shaft(s) and blades, featuring a drivetrain encompassing a rotor, a gearbox, a variable torque generator, along with a frictionless drivetrain system comprising a LSS (low-speed shaft) and a HSS (high-speed shaft). Therefore, the model represents a turbine as follows:

(1) \begin{align} {J_t}\dot \Omega = {\tau _{aero}} - {\tau _{gen}}, \end{align}

(2) \begin{align} {J_t} = {J_r} + N_{gear}^2{J_{gen}}, \end{align}

where ${J_t}$ represents the total turbine inertia, $\Omega $ denotes the rotor speed, $\dot \Omega $ is the derivative of the rotor speed. ${\tau _{aero}}$ corresponds to the rotor aerodynamic torque, while ${J_r}$ stands for the rotor inertia and ${J_{gen}}$ for the generator inertia. ${N_{gear}}$ denotes the gearbox ratio, ${\tau _{gen}}$ means the generator torque in the rotor (LSS) shaft.

Figure 3.

Aerodynamic forces, angles and induced velocities on a blade section expressed in aerodynamic-aligned and blade-aligned coordinate systems (adapted from Refs [Reference Ning53, Reference Sahin, Yavrucuk, Diez and Icaza77]).

Figure 4.

Some coordinate systems and angles used in the MS Bladed Model: (a) blade-aligned, azimuth-aligned, yaw-aligned and wind-aligned coordinate systems with yaw and pre-cone angles and (b) hub-aligned and yaw-aligned coordinate systems with nacelle tilt angle (adapted from Refs [Reference Ning53, Reference Sahin, Yavrucuk, Diez and Icaza77]).

In the model, the blade pitch angle, $\beta $ , is calculated using Equation (3), whereas the angle-of-attack, $\alpha $ , of a blade section is estimated by Equation (4):

(3) \begin{align} \beta = {\beta _{{p_{i,j}}}} - {\beta _{{T_{i,j}}}}, \end{align}

(4) \begin{align} {\alpha _{i,j}} = {\varphi _{i,j}} - {\beta _{{p_{i,j}}}}, \end{align}

where ${\beta _T}$ represents the twist angle, ${\beta _p}\;$ is the summation of this angle, $\;{\beta _T}$ , and the blade pitch angle, $\;\beta $ , whereas $\varphi $ denotes the inflow angle, $i$ stands for the blade number: blade 1, blade 2, etc. and $j$ indicates the blade sections: 5^th section, 6^th section, etc. Figure 3 shows these angles on a blade aerofoil section with some velocities and forces in some coordinate systems: aerodynamic-aligned and blade-aligned coordinate systems.

In the MS Bladed Model, basically the axial, $a$ , and tangential, $a'$ , $\;$ induction factors (Fig. 3) are estimated through an iteration process at every blade section. Depending on the turbine operations, whether the turbine rotor operates with a turbulent wake state or a skewed wake rotation, the axial induction factor is corrected for each blade section. The effect of hub loss and tip loss is also included into the calculation of induction factors [Reference Hansen47, Reference Branlard49, Reference Pitt and Peters50–Reference Moriarty and Hansen52, Reference Wanderley and Levi76, Reference Sahin, Yavrucuk, Diez and Icaza77]. Using the estimated induction factors, the axially, ${V_{{b_{{x_{i,j}}}}}}\left( {1 - {\rm{\;}}{a_{i,j}}{\rm{\;}}} \right)$ and tangentially, ${V_{{b_{{y_{i,j}}}}}}\left( {1 + {\rm{\;}}a_{i,j}^{'}} \right)$ , induced velocities are calculated at each blade section, considering the transformed velocity components, ${V_{{b_{{x_{i,j}}}}}}$ , and, ${V_{{b_{{y_{i,j}}}}}}$ , of the freestream wind velocity, $U$ (Fig. 4(a)). From these induced velocities, the effective wind speed, ${V_{eff}}$ , (Fig. 3) experienced by each blade section of all blades is calculated as

(5) \begin{align} {V_{ef{f_{i,j}}}} = \sqrt {{{\left( {{V_{{b_{{x_{i,j}}}}}}\left( {1 - {\rm{\;}}{a_{i,j}}{\rm{\;}}} \right)} \right)}^2} + {{\left( {{V_{{b_{{y_{i,j}}}}}}\left( {1 + a_{i,j}^{'}} \right)} \right)}^2}} . \end{align}

Later, using the effective wind speed, the sectional aerodynamic lift, $d{F_{{L_{a{e_x}}}}}$ , and drag, $d{F_{{D_{a{e_y}}}}}$ , forces are obtained by:

(6) \begin{align} d{F_{{L_{a{e_{{x_{i,j}}}}}}}} = \frac{1}{2}\rho {C_{{l_{i,j}}}}V_{ef{f_{i,j}}}^2{c_{i,j}}d{r_{i,j}}, \end{align}

(7) \begin{align} d{F_{{D_{a{e_{{y_{i,j}}}}}}}} = \frac{1}{2}\rho {C_{{d_{i,j}}}}V_{ef{f_{i,j}}}^2{c_{i,j}}d{r_{i,j}}, \end{align}

where $\rho $ is the air density, $Cl$ and $Cd$ are the aerodynamic lift and drag coefficients, whereas $c$ is the sectional chord length, $dr$ corresponds to the sectional radius. From the aerodynamic lift and drag forces, flapwise, $d{F_{{F_{{b_{{x_{i,j}}}}}}}}$ and edgewise, $d{F_{{E_{{b_{{y_{i,j}}}}}}}}$ forces in the blade-aligned coordinate system (Fig. 3) are obtained, respectively, as follows:

(8) \begin{align} d{F_{{F_{{b_{{x_{i,j}}}}}}}} = \left( {d{F_{{L_{a{e_{{x_{i,j}}}}}}}}cos{\varphi _{i,j}} + d{F_{{D_{a{e_{{x_{i,j}}}}}}}}sin{\varphi _{i,j}}} \right), \end{align}

(9) \begin{align} d{F_{{E_{{b_{{y_{i,j}}}}}}}} = d{F_{{L_{a{e_{{x_{i,j}}}}}}}}sin{\varphi _{i,j}} - d{F_{{D_{a{e_{{x_{i,j}}}}}}}}cos{\varphi _{i,j}}. \end{align}

All these edgewise and flapwise forces (Fig. 3) are later transformed to the hub-aligned coordinate system (Fig. 4) and then summed to calculate the turbine aerodynamics torque, ${\tau _{aero}}$ , and thrust force, $T$ , using

(10) \begin{align} {\tau _{aero}} = \mathop \sum \limits_i^{{B_n}} \mathop \sum \limits_j^S d{F_{{E_{{b_{{y_{i,j}}}}}}}}{r_{i,j}}cos{\phi _{i,j}}, \end{align}

(11) \begin{align} T = \mathop \sum \limits_i^{{B_n}} \mathop \sum \limits_j^S d{F_{{F_{{b_{{x_{i,j}}}}}}}}cos{\phi _{i,j}}, \end{align}

where ${B_n}$ represent the total blade number, $S$ is the total blade section numbers, $r$ denotes the local radius, and $\phi $ is the pre-cone angle [Reference Sahin and Yavrucuk11, Reference Sahin and Yavrucuk43, Reference Sahin44, Reference Sahin and Farsadi54]. Taking into account the rotor speed, $\Omega \;$ information, turbine power, $\;P$ is calculated as

(12) \begin{align} P = \Omega {\tau _{aero}}. \end{align}

Also, turbine power coefficient, $\;{C_p}$ , power available in wind, ${P_{wind}}$ , and turbine tip speed ratio (TSR), $\;\lambda $ , are obtained by

(13) \begin{align} {C_p} = \frac{P}{{{P_{wind}}}}, \end{align}

(14) \begin{align} {P_{wind}} = \frac{1}{2}\rho {(Ucos\theta cos\varPsi )^3}\pi {\left( {Rcos\varPhi } \right)^2}, \end{align}

(15) \begin{align} \lambda = \frac{{\varOmega R\cos \phi }}{{{U^*}cos\theta }}, \end{align}

respectively, where $\;$ U means the freestream/relative wind speed, while $\;\theta \;$ and $\varPsi $ are respectively the turbine nacelle tilt angle and yaw angle, $\;R$ symbolises the rotor radius [Reference Sahin44], ${U^*}$ is the hub-height wind speed.

Figure 4 shows some of the coordinate systems and angles used in the MS Bladed Model. Figure 4(a) illustrates the blade-aligned, azimuth-aligned, yaw-aligned, and wind-aligned coordinate systems, along with the pre-cone angle, $\varPhi $ , and yaw angle, $\varPsi $ , from a top view. Figure 4(b) shows the hub-aligned and yaw-aligned coordinate systems, along with the tilt angle, $\theta $ , from a side view.

For validation purposes, Fig. 5 shows the measured power output results of the NREL Phase II experimental turbine [Reference Schepers, Brand and Bruining72], the MS Bladed Model power output results and the numerical results of Ceyhan [Reference Ceyhan73]. It is clearly seen that the MS Bladed Model predicts turbine power output very close to the experimental test results. The difference between the prediction of the MS Bladed Model and that of Ceyhan at high wind speeds is caused using slightly different experimental aerofoil data [Reference Sahin44]. Note that detailed information on the MS Bladed Model, including its underlying theory and validation studies, can be found in Ref. [Reference Sahin, Yavrucuk, Diez and Icaza77].

Figure 5.

Power prediction of the MS Bladed Model for the NREL Phase II experimental turbine [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45, Reference Sahin, Yavrucuk, Diez and Icaza77].

In the final configuration, the NREL 5-MW reference turbine specifications are incorporated into the MS Bladed Model, and baseline controllers are designed accordingly. This turbine is a commonly cited reference turbine in the literature. With its three blades, it serves as a representation of the standard turbines deployed in contemporary wind farms. Figure 6 shows the NREL 5 MW blade geometry and aerofoils along with their chord and twist distributions throughout the blade span. The blade aerofoils used towards the blade tip are DU4017, DU35A17, DU30A17, DU25A17, DU21A17 and NACA64A17, respectively. As with other turbines, the blade root sections are circular in shape. Operating with variable-speed in Region 2 and variable pitch-to-feather strategy in Region 3, the NREL 5 MW turbine has a rated rotor speed of 12.1 rpm and has cut-in, rated, and cut-out wind speeds of 3 m/s, 11.4 m/s, and 25 m/s, respectively [Reference Jonkman, Butterfield, Musial and Scott42]. It includes a rotor with a radius of 63 meters and an inertia of 38,759,228 kg-m² and a variable torque generator with an inertia of 534.116 kg-m². Between these two components, a gearbox with a 97:1 ratio is used to run the turbine generator. Further details regarding this turbine can be found in Ref. [Reference Jonkman, Butterfield, Musial and Scott42].

Figure 6.

NREL 5 MW turbine blade and its properties: (a) turbine blade and aerofoils (adapted from Ref. [Reference Joustra, Flipsen and Balkenende74]), (b) chord distribution [Reference Jonkman, Butterfield, Musial and Scott42] and (c) twist distribution [Reference Jonkman, Butterfield, Musial and Scott42].

Figure 7.

Wind turbine operating regions.

2.2 Turbine operating regions and baseline controllers

In this subsection, the operating regions and control purposes of turbines are first discussed. Subsequently, the design of baseline generator torque and collective pitch controllers is presented for the NREL 5 MW turbine [Reference Jonkman, Butterfield, Musial and Scott42]. Variable speed variable pitch turbines, such as the NREL 5 MW turbine, have three major operating regions: Regions 1, 2 and 3, as shown in Fig. 7. Region 1, given in orange, corresponds to wind speeds below the cut-in wind speed, ${U_{cut - in}}$ , where the turbine does not generate any electricity due to very low wind speeds. Between the cut-in and cut-out, ${U_{cut - out}}$ wind speeds lie Regions 2 and 3, which are shown in yellow and green, respectively. Region 2 spans from the cut-in to the rated wind speed, ${U_{rated}}$ and focuses on maximising energy capture since wind speeds in this region are not sufficient to achieve rated power. Region 3 extends from the rated to cut-out wind speed and involves limiting the turbine’s output to its rated power to avoid excessive mechanical and electrical loads. In Region 2, the maximum possible power, i.e. partial power, is obtained from the turbine through the generator torque controller, while in Region 3, the rated power is acquired from the turbine by the collective blade pitch controller. These two controllers are the baseline or standard turbine controllers on turbines. Regions 2 and 3 are also known as the below-rated and above-rated regions, respectively. Based on the controller design, transitional regions may exist between Regions 1 and 2, and between Regions 2 and 3, referred to as Region 1.5 and Region 2.5, respectively. There is also an optional turbine operating region called Region 4, indicated in red in Fig. 7. This region includes wind speeds above the cut-out wind speed. Although turbines are typically shut down in this region due to severe loading conditions, modern utility-scale turbines can remain operational beyond the cut-out wind speed by using control techniques, such as ramp or stepwise shaping algorithms [Reference Oudah, Mohd and Hameed55–Reference Fischer and Shan61].

In this study, the baseline generator torque controller and collective blade pitch controllers utilise the rotor speed measurement for feedback, instead of the generator speed. In below-rated region, a typical generator torque controller is employed for maximising turbine power capture, while in above-rated region, a collective blade pitch controller is employed to satisfy the rated power. The torque controller changes the turbine rotor/generator speed by altering the generator control torque, i.e. electromagnetic torque, to ensure that the turbine works at its optimum TSR, ${\lambda _*}$ , and consequently at its maximum power coefficient, ${C_{pmax}}$ . This enables the turbine rotor to harness the utmost kinetic energy or the maximum achievable power from the available wind. Here, the following standard generator torque controller algorithm is used in Region 2 to compute the required generator control torque, ${\tau _c}$ , as the controller output [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45, Reference Stol and Fingersh56–Reference Merabet, Thongam and Gu58]

(16) \begin{align} {\tau _c} = {K_c}{\Omega ^2}, \end{align}

where ${K_c}$ represents the torque controller gain, and $\Omega $ is the controller input and is the turbine rotor speed measurement in units of rad/s, as adopted in the MS Bladed Model. The controller gain, ${K_c}$ , is calculated as:

(17) \begin{align} {K_c} = \frac{1}{2}\rho \pi {\left( {R\;\textit{cos}\;\varPhi } \right)^5}\frac{{{C_{pmax}}\left( {{\lambda _*},{\beta _*}} \right)}}{{\lambda _*^3}}, \end{align}

where $\rho $ is the air density, $R$ stands for the rotor radius, $\varPhi $ means the rotor pre-cone angle and ${\beta _*}{\rm{\;}}$ denotes the turbine optimum blade pitch angle. Determining the optimum values for TSR and blade pitch angles, as well as the turbine ${C_{pmax}}$ involves generating the turbine ${C_p}$ surface. This surface is generated with the turbine model by rotating the turbine rotor at distinct rotor speeds and blade pitch angles at a constant wind speed. Here, following Ref. [Reference Jonkman, Butterfield, Musial and Scott42], the 5-MW turbine ${C_p}$ surface is obtained against 8 m/s wind speed. By investigating this surface, the 5-MW turbine optimal TSR is estimated to be 7.5, the optimum blade pitch angle is determined to be −0.875 degrees, and the ${C_{pmax}}$ is identified to be 0.4996. Figure 8 shows the ${C_p}$ surface contours obtained for the 5-MW turbine along with the turbine ${C_{pmax}}$ which corresponds to the turbine optimum TSR and blade pitch angle. Considering Refs [Reference Jonkman, Butterfield, Musial and Scott42, Reference Wright and Fingersh62], Region 1.5 and Region 2.5 torque controllers are also integrated into the torque control system. Here, the actuator dynamics are ignored, a 15000 Nm/s torque limiter is applied and the controller torque output is limited to 47,402.91 Nm. [Reference Sahin and Yavrucuk11, Reference Sahin44, Reference Sahin and Farsadi45]. Importantly, it should be highlighted that the torque controller output, ${\tau _c}$ in Equation (16) corresponds to the generator torque in the LSS shaft. Dividing this torque by the gearbox ratio, ${\rm{\;}}{N_{gear}}$ yields the generator torque in the HSS shaft.

Figure 8.

${\rm{\;}}{C_p}$ surface contours of the NREL 5-MW turbine.

In Region 3, utilising the pitch-to-feather strategy, a proportional-integral (PI) collective blade pitch controller with a gain-scheduling property is designed to collectively control blade pitch angles and regulate the rotor speed to its rated speed. Proportional gain, ${K_p}$ , and integral gain, ${K_i}$ , of the blade pitch controller are calculated as follows:

(18) \begin{align} {K_p} = \frac{{ - 2{w_n}\xi - A}}{B}, \end{align}

(19) \begin{align} {K_i} = \frac{{ - w_n^2}}{B}, \end{align}

where ${w_n}$ denotes the desired natural frequency, $\;\xi $ stands for the desired damping ratio, while A represents the turbine system gain, and B signifies the control input gain [Reference Sahin and Yavrucuk11, Reference Sahin44, Reference Sahin and Farsadi45, Reference Sahin and Yavrucuk63, Reference Sahin, Yavrucuk, Diez and Icaza64]. Here, ${w_n}\;{\rm{and}}\;\xi $ are selected as 0.6 and 0.8, respectively, whereas A and B are calculated by:

(20) \begin{align} A = \frac{1}{{{J_t}}}\frac{{\partial {\tau _{aero}}}}{{\partial \varOmega }},\\ \notag \end{align}

(21) \begin{align} B = \frac{1}{{{J_t}}}\frac{{\partial {\tau _{aero}}}}{{\partial \beta }}, \end{align}

where $\frac{{\partial {\tau _{aero}}}}{{\partial \varOmega }}$ and $\frac{{\partial {\tau _{aero}}}}{{\partial \beta }}$ represent the variations in turbine rotor aerodynamic torque in relation to changes in rotor speed and blade pitch angles, respectively, while ${J_t}$ , as defined previously, is the total turbine inertia. The turbine system gain, A, and the control input gain, B, are obtained as −0.0554 and −0.2658, respectively [Reference Sahin44], through model linearisation at an equilibrium operating point of ( ${U_e},{\varOmega _e}$ , ${\beta _e}$ ) = (11.5 m/s, 12.1 rpm, 2.2792^o), near the entrance of Region 2 to Region 3 [Reference Wright and Fingersh62].

Figure 9 illustrates the NREL 5 MW turbine rotor aerodynamic torque-blade pitch angle curves at distinct wind speeds; the red dashed curve indicates the rated torque. The crossing points of the red dashed line and the torque curves are the equilibrium operating points of the 5-MW turbine in Region 3. At these crossing points, the slopes of rotor aerodynamic torque increase as the wind speed or blade pitch angle increases. For this reason, the control input gain, B, considerably changes with varying pitch angles in Region 3, which reduces the performance of the pitch controller designed at an equilibrium point when operated throughout Region 3.

Figure 9.

NREL 5-MW turbine rotor aerodynamic torque-blade pitch angle curves at distinct wind speeds.

Therefore, to obtain better performance from the pitch controller throughout Region 3, i.e. from rated to cut-out wind speed, the following gain correction factor, $GK(\beta)$ [Reference Jonkman, Butterfield, Musial and Scott42, Reference Wright and Fingersh62], is employed to schedule the proportional gain, ${K_p}$ , and integral gain, ${K_i}$ , of the blade pitch controller:

(22) \begin{align} GK(\beta) = \frac{1}{{\left( {1 + \frac{\beta }{{{\beta _K}}}} \right)}}, \end{align}

where $\beta $ is the required turbine blade pitch angle for achieving the rated torque at any wind speed within Region 3, while the turbine is working at its rated rotor speed. Conversely, ${\beta _K}$ is another blade pitch angle at another operating point in Region 3, where the turbine control input gain, $\;B$ obtained at an operating point near the entrance of Region 2 into Region 3 has increased in its value by two times [Reference Wright and Fingersh62]. The NREL 5-MW turbine is estimated to have a ${\beta _K}$ value of 5.9676 degrees utilising the MS Bladed Model [Reference Sahin44, Reference Sahin, Yavrucuk, Diez and Icaza64]. Accordingly, the blade pitch control algorithm is expressed by Equation (23)

(23) \begin{align} \beta \left( t \right) = K_p^{GS}\varDelta \varOmega \left( t \right) + K_i^{GS}\smallint \varDelta \varOmega \left( t \right)dt, \end{align}

where $K_p^{GS}$ and $K_i^{GS}$ are the gain-scheduled proportional, and integral gains are calculated by multiplying $\;{K_p}$ and ${K_i}$ respectively by $GK(\beta)$ . Here, $\varDelta \varOmega $ represents the rotor speed difference, i.e. rotor speed error between the reference value, ${\varOmega _{ref}}$ and its actual measurement, $\;\Omega $ , while $\beta $ is the pitch controller output.

Considering Refs [Reference Jonkman, Butterfield, Musial and Scott42, Reference Wright65], a first-order model is used to include the pitch actuator dynamics within the blade pitch control system, with a time constant of 0.2 s. The pitch controller output then turns out to be, ${\beta _{ref}}$ , whereas $\beta $ turns out to be the pitch actuator output or the blade pitch input for the turbine/simulation model. Generator torque output does not change in the above-rated region and is equal to its rated value. Furthermore, a rate limiter of 8 deg/s is used at the pitch controller output. The pitch angles are also saturated to limits of −0.875, and +90 degrees [Reference Sahin and Yavrucuk11, Reference Sahin44, Reference Sahin and Farsadi45, Reference Sahin, Yavrucuk, Diez and Icaza64]. The block diagram of these controllers (Equations (16) and (23)) are connected to the MS Bladed Model, which employs the NREL 5-MW turbine, is depicted in Fig. 10. Notably, the rotor speed measurement, Ω is fed back to the controllers, relying on this information, the controllers are dynamically switched between each other from Region 2 to Region 3 and vice versa.

Figure 10.

Block diagram of the baseline turbine controllers integrated with the MS Bladed Model.

2.3 Simulation and verification of baseline controllers

In this subsection, the baseline turbine controllers are simulated and tested using the MS Bladed Model against 1 m/s step rising wind speeds of 8 to 9 m/s at the below-rated region, and 12 to 13 m/s at the above-rated region. To indicate that the controllers work satisfactorily, the obtained responses are also evaluated and verified with the formerly published responses generated using the NREL OpenFAST Model for the same NREL 5-MW turbine in Ref. [Reference Abbas, Wright and Pao66]. For comparison purposes, generator speed responses are acquired in units of rpm (revolutions per minute) instead of rad/s, which is adopted in the MS Bladed Model.

The simulation results of the generator torque and blade pitch controllers are shown on the left and right in Fig. 11, respectively. Simulations are generated for 55 s. Step rising wind speeds of 1 m/s are provided for the 5-MW turbine at 30 s of the simulations during operations at steady-state. Considering the torque control, the obtained transient and steady-state responses for the generator torque and speed obtained through the MS Bladed Model are similar to those obtained by the NREL OpenFAST Model. Furthermore, the aim to operate the turbine at its optimum TSR value is successfully achieved (Fig. 11(d)) at steady-state, and the turbine works at its maximum ${C_p}$ value (Fig. 11(e)). Note that in the previous subsection, the optimum values for the turbine TSR and blade pitch angle are obtained as 7.5 and 0.4996, respectively, just like the values in simulations at steady-state (Fig. 11(d) and (e)). Investigating the pitch controller simulations reveals that the steady-state values for the blade pitch angle and generator speed nearly resemble the responses of the FAST and OpenFAST models, respectively, attained by Jonkman et al. [Reference Jonkman, Butterfield, Musial and Scott42] and Abbas et al. [Reference Abbas, Wright and Pao66]. Some differences observed in transient responses may be caused by whether the rotor or generator speed is used as feedback to the pitch controller. Most importantly, in this study, the design purpose for the blade pitch controller is to obtain a slight overshoot and a rapid decay time in the rotor/generator speed response [Reference Wright and Fingersh62]. Adjusting the controller gains allows the generation of comparable responses to the OpenFAST model responses. As depicted in Fig. 11(h), reducing the proportional gain generates a very comparable rotor speed response to that of the OpenFAST model [Reference Sahin and Yavrucuk11]. Furthermore, as obtained in Ref. [Reference Abbas, Wright and Pao66], different rotor/generator speed responses can be obtained (Fig. 11(h)) for the same turbine. The simulations in Fig. 11 indicate that the baseline controller works successfully as targeted. This is because, at steady-state, the turbine operates at its optimum TSR and thereby at its ${C_{pmax}}$ in Region 2 through the torque control. The generator speed is regulated to its rated speed (Fig. 11(h)) in Region 3 by the blade pitch controller, which adjusts the pitch angles (Fig. 11(g)) collectively. Turbine efficiency is reduced (Fig. 11(j)) in Region 3 to obtain rated power (Fig. 11(i)).

Figure 11.

Performance comparison of generator torque controller (left) and blade pitch controller (right): (a) wind speed input [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (b) HSS torques [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (c) generator speed [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (d) turbine TSR [Reference Sahin and Yavrucuk11]; (e) turbine $\boldsymbol{C}_{\boldsymbol{p}}$ [Reference Sahin and Yavrucuk11]; (f) wind speed input [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (g) blade pitch angle [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (h) generator speed [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45]; (i) rotor power; and (j) turbine $\boldsymbol{C}_{\boldsymbol{p}}$ [Reference Sahin and Yavrucuk11].

According to the simulations, the generator torque controller operation might be defined as follows: first of all, the blade pitch angle is saturated to the optimum value at the below-rated region. Thus, during turbine operation at an equilibrium operating point in Region 2 if a step rising wind speed (Fig. 11(a)) is applied to the 5-MW turbine, the turbine rotor aerodynamic torque (Fig. 11(b)) increases, and the rotor/generator speed (Fig. 11(c)) starts increasing. Based on the rotor/generator speed, the controller increases the generator control torque, i.e. the generator electromagnetic torque (Fig. 11(b)). The increase in generator torque continues up until a new steady-state operation at another equilibrium operating point, where the aerodynamic torque becomes equal to the generator torque (Fig. 11(b)) and the rotor/generator speed reaches its steady-state (Fig. 11(c)).

When the rotor/generator speed reaches steady-state, rotor/generator acceleration becomes zero (Fig. 11(c)) and the turbine works at its optimum TSR (Fig. 11(d)), thereby achieving its maximum ${C_p}$ (Fig. 11(e)). At the maximum ${C_p}$ , the turbine rotor extracts the highest possible power from the available wind [Reference Sahin and Yavrucuk11, Reference Sahin44, Reference Sahin and Farsadi45, Reference Sahin, Yavrucuk, Diez and Icaza64]. In Region 2, the opposite scenario is also valid when a step decreasing wind speed is given to the turbine. Theoretical insights on how the torque controller works can be found in Refs [Reference Johnson, Pao, Balas and Fingersh57, Reference Pao and Johnson67].

The blade pitch controller operation, on the other hand, may also be defined as follows. During a steady-state turbine operation at an operating point in Region 3, when a step rising wind input is given to the turbine (Fig. 11(f)), the rotor aerodynamic torque increases, as the generator torque is equal to rated torque in this region, there occurs an imbalance between the two counter-acting torques, (Fig. 2), i.e. rotor aerodynamic and generator torques. Then, the turbine rotor/generator speed starts accelerating (Fig. 11(h)). Consequently, the rotor/generator speed measurement starts deviating from the rated rotor speed reference, which is the fixed input for the pitch controller (Fig. 10). This results in a rotor speed error, based on which the pitch controller adjusts proportional and integral gains considering the gain correction factor and collectively increases the pitch angles of all turbine blades (Fig. 11(g)). This action modifies the turbine rotor aerodynamic torque to adjust the rotor speed to its rated reference speed of 12.1 rpm, which corresponds to a generator speed of 1173.7 rpm (Fig. 11(h)). Note that the turbine ${C_p}$ is lower than its ${C_{pmax}}$ value (Fig. 11(j)) since the goal in Region 3 is to adjust turbine power output to the rated power (Fig. 11(i)) through reducing turbine efficiency or power capture, unlike the purpose in Region 2.

2.4 Ice accumulation modeling on 5-MW turbine blades and its effects on turbine efficiency

In the previous sections, baseline turbine controllers are defined and their simulations are realised for validation. In this section, ice accumulation modeling for the NREL 5-MW turbine blades and blade ice accumulation effects on turbine efficiency are discussed. Ice accumulation on turbine structures is commonly seen in winter months and at high altitudes in cold regions. Turbine blade surfaces are susceptible to ice formation, which occurs instantly or after a delay when super-cooled water droplets strike the turbine blades [Reference Jin and Virk23, Reference Pouryoussefi, Mirzaei, Nazemi, Fouladi and Doostmahmoudi68]. Ice accumulates on turbine blade surfaces, predominantly at their leading edges [Reference Hu, Zhu, Chen, Shen and Du13, Reference Jin and Virk23, Reference Lamraoui, Fortin, Benoit, Perron and Masson25], and manifests in glaze, rime, or mixed ice types [Reference Han, Palacios and Schmitz12, Reference Hu, Zhu, Chen, Shen and Du13, Reference Yirtici, Sevine, Ozgen and Tuncer26]. Using experimental as well as computational methods, in Ref. [Reference Brandrud and Krøgenes2], a comprehensive study was conducted on the NREL S826 turbine blade aerofoil to investigate these ice formations. Different ice shapes are generated by the LEWICE code and are produced artificially. Wind tunnel experiments were conducted with the S826 aerofoil with the artificial ice geometries fixed to its leading edge. Test results indicated that aerofoil aerodynamics is varied across all types of ice: there is a decline in lift and a rise in drag, as declared before.

For instance, Fig. 12 depicts ice accumulation predictions on the S826 blade aerofoil under the condition of glaze ice as well as its corresponding impacts on the experimental lift, Cl and drag, Cd coefficients. As seen in Fig. 12(a) and (b), ice primarily accumulates on the S826 aerofoil leading edge, leading to a reduction in the aerofoil’s lift coefficient and a rise in the drag coefficient. Therefore, a reduction is seen in the lift curve slope in the linear part, while a simple upward shift occurs in the drag curve due to ice accumulation in Fig. 12(b), in which $C{l_c}$ and $C{d_c}$ represent the aerofoil data for the clean blades, $C{l_i}$ and $C{d_i}$ stand for the data for the iced blades. To obtain such an ice accumulation on the S826 aerofoil, the requirements are available in Refs [Reference Brandrud and Krøgenes2, Reference Sahin and Farsadi45, Reference Sahin and Farsadi54].

Figure 12.

Ice accumulation on the NREL S826 aerofoil and impacts on its aerodynamics, (a) glaze icing and (b) experimental Cl and Cd data with clean and iced blades [Reference Brandrud and Krøgenes2, Reference Sahin and Yavrucuk10, Reference Sahin and Farsadi45, Reference Sahin and Farsadi54].

Here, the NREL 5-MW turbine blades’ leading edges, i.e. all blade sections, are presumed to be exposed to such an ice accumulation, i.e. glaze icing in Fig. 12, which linearly increases toward the blade tip [Reference Shu, Liang, Hu, Jiang, Ren and Qiu3], and remains stationary, and is firmly adhered to the blades’ surfaces. Ice accumulation is modeled considering icing characteristics and its consequences on blade mass and aerodynamics. Namely, ice does not evenly accumulate along the blades and increases towards the blade tips [Reference Shu, Liang, Hu, Jiang, Ren and Qiu3, Reference Hu, Zhu, Chen, Shen and Du13, Reference Homola, Virk, Nicklasson and Sundsbø41, Reference Alsabagh69]. It causes increasing alterations in blade aerodynamic performance, manifesting as reduced lift coefficient and increased drag coefficient for blade aerofoils along with augmented blade mass, i.e. the rotor inertia. To integrate these variations in rotor blades, the authentic aerodynamic data of each turbine blade aerofoil are modified by reducing the lift coefficient and increasing the drag coefficient, with more pronounced variations closer to the blade tips, accompanied by an increase in rotor inertia due to accumulated ice mass on the blades. Note that in Fig. 13, the authentic data ( $C{l_c}$ , $C{d_c}$ ) for the turbine aerofoils consist of corrected experimental data for rotational stall delay and extrapolated aerodynamic data [Reference Jonkman, Butterfield, Musial and Scott42]. For icing modeling ( $C{l_i}$ , $C{d_i}$ ), the authentic data at each section are modified based on their radial distances from the blade root. The farther an aerofoil is from the root, the greater the modifications applied to its authentic data [Reference Sahin and Farsadi45, Reference Sahin and Farsadi54].

Figure 13.

Blade ice accumulation on the NREL 5-MW turbine (Left) and its impacts on blade/aerofoil aerodynamic coefficients (Right) (a) DU40A17@4^th section [Reference Sahin and Yavrucuk11, Reference Sahin and Farsadi45, Reference Sahin and Farsadi54], (b) DU21A17@10^th section and (c) NACA64A17@16^th section [Reference Sahin and Farsadi45, Reference Sahin and Farsadi54].

The consequences are slighter and greater adjustments respectively in authentic aerodynamic data of aerofoils positioned nearer the blade root and tip (Fig. 13(a), (b), and (c)) and a slight increase in rotor inertia. A very slight accumulation of ice is assumed on the blades, ignoring their circular root connection sections. Consequently, the adjusted aerodynamic data are ensured to maintain a relatively close resemblance to the authentic data, encompassing those pertaining to the final blade tip section. Accounting for a linear ice accumulation [Reference Shu, Liang, Hu, Jiang, Ren and Qiu3] increasing from the root toward the tip of the blade, adjustments to Cl data show a decrease ranging from 1.76 to 9.27%, while Cd data exhibit an increase ranging from 7.84 to 48% at a 12-degree angle-of-attack [Reference Sahin and Farsadi45, Reference Sahin and Farsadi54]. Consequently, except for the circular root sections, all the 5-MW turbine aerofoils’ aerodynamic data [Reference Jonkman, Butterfield, Musial and Scott42] are modified and incorporated into the MS Bladed Model. The rotor inertia is augmented by 3% to investigate the performance effectiveness of the baseline controllers on the iced-bladed NREL 5-MW turbine. For instance, Ref. [Reference Sahin and Farsadi45], another study performed by the author of this paper as the corresponding author uses the same ice accumulation scenario to thoughtfully investigate icing impacts on the performance and behaviour of the NREL 5-MW turbine under uniform and turbulent wind speeds. Thus, the same ice accumulation condition is also adopted here to assess how baseline turbine controllers perform in response to blade ice accumulation.

Figure 13 shows the NREL 5-MW turbine with ice-accumulated blades (left), adapted from Ref. [Reference Liu, Xiao and Incecik70] alongside the aerodynamic data of some example aerofoils (right) with clean (authentic, $C{l_c},C{d_c}$ ) and iced (modified, $\;C{l_i},C{d_i})$ conditions. The example aerofoils are DU40A17, DU21A17 and NACA64A17 and are radially positioned as 11.75, 36.35 and 58.9 meters on the blades at the 4, 10 and 16th blade sections, respectively [Reference Jonkman, Butterfield, Musial and Scott42]. These sections are denoted by a, b and c letters in Fig. 13, respectively. Notably, due to the considered slight ice accumulation increasing toward the blade tip, the DU40A17 aerofoil located near the root shows negligible changes in aerodynamic Cl and Cd data, whereas NACA64A17 aerofoil, located close to the blade tip, exhibits more substantial variations in its aerodynamic data. Across all aerofoils of the turbine, lift coefficient is decreased, drag coefficient is augmented until an angle-of-attack of typically 50 degrees, where lift and drag curves intersect as in the authentic data. Note that icing changes the shape of aerofoils and different aerofoils have different aerodynamic data mainly between −25 and 90-degrees angle-of-attacks. Thus, for each aerofoil, the changes in their data are made in this interval [Reference Sahin and Farsadi45, Reference Sahin and Farsadi54].

In Subsection 2.2, the NREL 5-MW turbine optimum blade pitch angle, optimum TSR and maximum ${C_p}$ values are obtained as −0.875^o, 7.5, and 0.4996, respectively, and are used for the generator torque controller design [Reference Sahin and Yavrucuk11, Reference Sahin44, Reference Sahin and Farsadi45, Reference Sahin, Yavrucuk, Diez and Icaza64]. Namely, the maximum ${C_p}$ and optimum TSR are used to calculate the torque controller gain, ${K_c}$ in Equation (17). The optimum blade pitch angle, on the other hand, is used as a lower saturation limit for the blade pitch controller output. Due to the considered slight blade ice accumulation (Fig. 13), the turbine ${C_p}$ surface is expected to be varied since the shape of the blades and their aerodynamics have changed. Thus, the NREL 5-MW turbine is re-operated with iced blades at different pitch angles and various rotor speeds at the same uniform wind speed of 8 m/s, and the turbine ${C_p}$ surface is re-obtained.

Figure 14 depicts the ${C_p}$ surface contours of the turbine with the considered iced blades. As seen in Fig. 14, even a slight accumulation of ice on the blades causes a dramatic change in the NREL 5-MW turbine ${C_p}$ surface. When the ${C_p}$ surface contours with iced blades are investigated, it is seen that the efficiency/aerodynamic performance of the NREL 5 turbine rotor reduces at high TSR values and is lost beyond the TSR value of approximately 13. The reduction in turbine efficiency or ${C_p}$ gets larger at higher TSR values than at lower TSR values. More importantly, the optimum TSR, optimum blade pitch angle, including the turbine ${C_{pmax}}$ , have changed. All these findings can be obtained by comparing the 5 MW turbine ${C_p}$ surfaces in Figs 8 and 14 for clean and iced blades. Due to slight blade ice accumulation, turbine optimum TSR value drops to 7.375, the optimum blade pitch angle increases to −0.3750, while the ${C_{pmax}}$ reduces to 0.4333, which corresponds to a decrease of 13.72% in turbine efficiency compared to the ${C_{pmax}}$ of 0.4996 for the clean blades. Table 1 shows the variations in these variables.

Figure 14.

${C_p}$ surface contours of the NREL 5-MW turbine with ice accumulated blades.

Table 1.

Optimum operating points for the NREL 5-MW turbine