Yaw control strategies for 20 MW multi-rotor systems

In this paper, the control of an active yaw system for a 20 MW multi-rotor wind turbine system (MRS) is considered. The MRS under investigation consists of five 4 MW turbines in two rows, which are connected to the tower via a space frame. A central yaw bearing at the height of the lower rotors is provided for active yaw. The paper aims to show that active aerodynamic yaw is possible by changing the thrust of certain rotors and should be considered for further research in the field of yawing of an MRS. Two different simulation environments are used in the paper. The MRS is modeled and simulated in Matlab/Simulink. Simulink’s own control modules are used as controllers. In the other simulation approach, the same MRS is modeled and simulated in Bladed and controlled with an external controller based on C++. The use of Bladed and Matlab/Simulink enables the plausibility and verification of the results. Matlab/Simulink is faster based of its simpler models but Bladed is more sophisticated. This paper also briefly presents the state of the art for yaw systems and yaw control of conventional single rotor wind turbines and initial research literature on yaw control of MRS.


Introduction
The yaw system of a wind turbine consumes 1.3 -5 % of the turbines estimated capital expenditures, according to a percentage-wise cost distribution of different studies [1] [2].Taking the growth trend of wind turbines in consideration, it shows that the cost trend exponent of the yaw system is the second most affected by the upscaling of wind turbines, with the blades on first place [3].A multi-rotor wind turbine system (MRS) could not only bypass the cost trend for the blades by using smaller rotors with the same overall capacity of the whole system but also provides the possibilities for yaw strategies to eliminate yaw actuators and therefore decreases the overall costs of wind turbines.Those yaw strategies were first mentioned in [4] where they were categorized in two sections.In the passive yaw system the yaw bearing could be located upwind of the wind turbine for yaw stability.This distance acts as a lever arm, and the aerodynamic drag and rotor thrust of the structure and rotors generates the yaw moment.For the active yaw, the yaw moment is created by actively controlling the thrust of the rotors to generate a thrust difference between the right and left side of the MRS.In this paper the focus is on the active yaw strategy by pitching the blades to generate a yaw moment.In [5] the feasibility of this approach was proven.There, the thrust of the rotors was controlled in a way, that the MRS holds its position when a turbulent wind field is applied.The performance and energy capture for this approach was improved afterwards in [6].The thrust of a rotor can be changed by either lowering the tip speed ratio or by pitching the blades.

State of the art
Current single rotor turbines with an upwind rotor use active yaw systems.These consists of yaw bearings with external teeth and several yaw motors that mesh with the yaw bearings.Since the teeth are not free of play, the nacelle could move back and forth in changing wind conditions.To prevent this, the nacelle is fixed by brakes when there is no yaw activity [7].Currently, yaw controls are used in which the wind direction is averaged over two to three minutes and the yaw is only changed if the defined tolerance range is significantly exceeded.This serves to protect the tooth flanks of the gears between the yaw drive and the yaw bearing.For the yaw movement, the yaw brakes are released and fixed again after reaching the end value [7].

Yaw control of a conventional single rotor wind turbine
In the field of yaw control of a conventional wind turbine, many scientific papers have already been published that investigate the implementation of different control strategies.The aim is to significantly reduce the yaw error and the operating cycles of the yaw motors.A classification of the different strategies of yaw control of wind turbines was presented in [8].According to [8], the control of yaw systems can be divided into three categories according to their purpose: • Increase energy yield of the individual wind turbine • Reduce loads of the individual wind turbine • Increase energy yield of a wind farm and reduce loads The controller to increase the energy yield of a single wind turbine is further distinguished according to [8] by which source the controller has for the wind direction information.According to [8], a distinction is made between "normal wind direction sensors", where the wind turbine has conventional wind vane to determine the wind direction.Controllers can use e.g.conventional controllers like the proportional-integral-derivative (PID) or fuzzy control for this purpose [8].The other possibility of wind direction information is the "wind direction estimation", where by advanced measurements by e.g.LiDAR (light detection and ranging) or by time-series models a prediction of the wind direction at a certain time is made.The last possibility is the control without wind direction information.For this purpose e.g.controllers with climbing methods or Max Power Point Tracking (MPPT) integration can be used using the generator power as input signal.In [9], a survey presents many of the control types studied so far and listed in the survey by [8].One of these, the hill climbing control algorithm is based on the hill climbing control mechanism and aligns the turbine based on the highest power into the wind.
The investigation of the hill climbing control algorithm for yaw control was studied in the work of [10].The method was found to have good control time and control performance, but the controller starts to oscillate when reaching the optimal yaw alignment, as the algorithm continues to search for the optimal yaw position.It must also be mentioned that the algorithm generates large overshoots and undershoots with large deviations [10].
Another type of controller is the PID Neural Network (PIDNN) controller.This uses a cooperative particle swarm optimization algorithm that converges very quickly, but this intelligent algorithm is difficult to implement on equipment and controllers.The fuzzy-PID controller uses a fuzzy controller in combination with a PID controller.As in the overview by [8], the fuzzy PID controller requires the wind direction information.The fuzzy-PID controller has been studied and evaluated in more detail in the work of [9].
In [9], the objective is to reduce the yaw error of a multi-megawatt turbine and reduce the frequency of starting the yaw motors to minimize the wear of the drives.For this objective, the problem was divided into three steps.First, the determination of the wind field should be done by a LiDAR installed on the nacelle to reduce measurement errors.Second, includes the classification of the wind into a total of four classes.For each class, the probability of occurrence of the yaw error was determined.For each class, dead times and maximum alignment error are defined respectively to ensure optimal alignment for each wind class.Third a variable universal fuzzy controller in combination with a conventional PID controller was used as the optimal controller for yawing.This uses the dead time and maximum yaw error parameters set according to the wind class.The fuzzy controller has a good control speed and minimizes overshooting of the output signal, while the downstream PID controller reduces the control error.The results show good yaw control with optimised operating cycles for the yaw system [9].
Another way is described in the work of [11], in which a control system of a yaw system was developed and simulated, which is based on the biological endocrine immune system.This control concept consists of a total of 5 units: wind direction detection unit, the wind deviation present unit, the wind deviation processing unit, the control unit, and the optimization unit.The present unit contains the current information of the wind and nacelle orientation.The present unit is comparable to the antigen recognition of the immune system, and can recognize the deviation of the wind to the nacelle orientation very quickly.In the present unit, a function determines the deviation which is processed in the wind deviation processing unit where it be amplified or attenuated depending on the yaw error.The parameters for this are influenced by the control unit.The wind deviation processing unit processes the deviation to the control signal for the yaw of the wind turbine.The control unit regulates and adjusts the present unit and the processing unit via parameters.
The optimization unit regulates the whole yaw controller to reduce the yaw error as fast as possible.A fitness function is used for optimization.The fitness function uses the control deviation, the yaw signal to the turbine, the overshoot and the control time.The goal of the fitness function is to ensure the stability and speed of the controller.The results obtained in the work show a very good control behavior also in comparison to PID and fuzzy-PID controllers [11].

Yaw control of an MRS
In the field of yaw control of an MRS, there have been only a few scientific studies so far.The work of [12] should be mentioned, in which an MRS consisting of two rotors was investigated with respect to the yaw control.A robust integral backstepping controller (IBC) was used as the controller to pitch the rotor blades to change the drag of the rotors.This creates the necessary torque to turn the two turbines.Additionally, to optimize performance, the turbines are held at the optimal power coefficient c P .This is done by adjusting the speed by changing the generator torque.According to [12] the control was divided into two steps, "Speed Control" to control the c P of the turbines and "Yaw angle Control" to control the yaw of the two turbines.The controller was simulated in Matlab/Simulink and compared against a classical proportional-integral (PI) controller.The PI controller has, according to [12] significantly higher power losses than the IBC.One other example is [13], which was developed within the InnWIND.euproject, in which the control of an MRS on a floating foundation using variable rotor thrust was investigated.Initially, a PID controller was used for control, which was then replaced by two control loops with a P controller.The controller strategy provides for a central controller that supplies inputs to the individual turbine controllers and also receives feedback from the individual turbines.As a result, a reduction in the generated power was determined in addition to a wind speeddependent control quality [13].As a conclusion, the control of the yaw system of an MRS was equated with the central yaw controller of a wind farm [13].
The work of [14] should also be mentioned regarding the yawing of MRS, as they offer the possibility to reduce the wake effect for downstream turbines by individually yawing the rotors to each other.

MRS simulation model
In this paper, the yaw system of a 20 MW MRS is investigated.The MRS consists of five turbines with a capacity of 4 MW each.The MRS and the 20 MW single rotor turbines are scaled and based on the 10 MW DTU reference turbine [15].The design is based on concept studies done in [16] and [17] and is shown in Figure 1. Figure 2 shows the numbering of the rotors and the position of the yaw bearing.In [16] and [17] different concepts for the yaw bearing of an MRS are shown, whereby the twin-bearing approach with fixed and floating bearing was considered.The modelling of such a twin-bearing in Bladed is not possible at the moment, which is why a central yaw bearing is assumed for both simulations.Further technical characteristics are summarized in Table 1.

MRS simulation yaw system
The basis for the yaw movement is the generation of a yaw moment that is greater than the frictional torque of the yaw bearing.The yaw system of an MRS can therefore be generally described by the equation of motion: Here ψ is the angular acceleration of the yaw system and results from the quotient of the difference between the drive torque M A and the friction torque M F and the mass moment of inertia of the MRS J A .The drive torque M A is generated in the yaw-by-pitch method by changing the thrust forces of the rotors.For this purpose, the pitch angles of the two outer rotors The frictional torque M F is determined via the Thyssenkrupp Rothe Erde formula [18]: In Equation 3, µ is the coefficient of friction, M k is the tilting moment, F r and F a are the shear forces in radial and axial directions acting on the bearing.D L describes the diameter of the bearing.The forces F r and F a contain the thrust forces in radial direction, and the mass of the MRS in axial direction.The drag forces acting on the space frame are not considered.The tilting moment M k results in each case as the product of the thrust force F T and the lever arm z pos in the z-direction as the difference from hub height to yaw bearing and as the product of the x-distance of the rotors to the center of the yaw bearing x pos and the mass of the rotor-nacelle assembly m RN A times the acceleration due to gravity g.

Simulation setup
The investigation of the yaw system of the MRS is performed in two different environments.To ensure comparability between the two simulation environments, the following global conditions are assumed.The first point concerns the wind.Wind with a constant wind speed is assumed in both simulation environments.The wind is defined at a height of 151.99 m, which is equivalent to the hub height of a 20 MW single rotor offshore wind turbine with the same distance between sea level and blade tip.The MRS consists of five rotors with a diameter of 112.7 m and the  spacing between the rotor tips is 3% of the rotor diameter.The calculation of the wind speed for the two rows of rotors is performed using the wind profile power law and an exponent α = 0.1.
In the simulation with Bladed, the vertical wind shear over the rotor circle area is also taken into account, this is not implemented in Matlab/Simulink, here a constant wind over the entire rotor circle area is assumed.All wind direction changes are done according to the GL guideline "Extreme coherent gust with direction change (ECD)".The wind direction change occurs in a sinusoidal increase within 10 s.For the simulation itself, a simulation time of 200 s is used with a simulation step size of 0.005 s.The wind direction change takes place after at least 20 s to ensure the initialization of all parameters in Bladed.For the definition of the angles and the coordinate system the convention from Bladed is used as shown in Figure 4.The thrust forces F T,i for the active yaw system are determined differently within the two simulation environments.In Bladed, the thrust forces are determined via the integrated aerodynamic simulation adapted for the multi-rotor.In Matlab/Simulink, a Blade Element Momentum theory (BEM) implemented in Matlab is used for this purpose.
The central element of this paper is the controller for the yaw system of the MRS.In both simulation environments a PID controller is used for the control of the yaw system.In Bladed this controller is programmed in C ++ and integrated via a dynamic link library (.dll).In Matlab/Simulink the controller is implemented from Simulink's own blocks.In Bladed as well as in Matlab/Simulink the pitch angles of the rotors 3 and 5 are controlled for the yaw-by-pitch to regulate the yaw error.In both simulation environments, a delta is added to the current pitch angle.

Simulation Bladed
Yaw-by-pitch is used to implement yaw tracking in Bladed.For implementation of new controllers Bladed features the possibility to replace its own controllers for pitch and torque demand with external controllers.In each time step the external controller is read in as a .dll,which was written and compiled in C ++ .
To design a suitable controller, the behavior of the controlled system must be analysed first.For the yaw controller, the command tracking is to be optimised during the design.Decisive for this control concept is the influence of the actuator on the feedback variable.The controlled system consists of equations of BEM and multibody simulation.For the yaw control, a step change in the pitch angle was used to analyse the response of the controlled system.The control system was identified as a first-order linear transfer function combined with a time delay, known as an IT 1 transfer function.For IT 1 controlled systems, the PI controller was generally found to be optimal.
The first design of the controller is based on the symmetric optimum.For this, the openloop response is considered in the frequency response by plotting the magnitude and phase over frequency.The classical PI behavior is achieved with a phase margin of 45°.The design was carried out in Matlab.To avoid overshoot the control parameters were tuned by trial and error.Figure 5 shows the control strategy for yaw-by-pitch in Bladed.As a control error, the yaw error ∆θ, which is composed of the measured yaw angle θ measured and the target value of the yaw error θ SP , is fed into the PI controller.For this calculation the mean value of the measured yaw angles at each rotor is considered.As an actuator, the controller outputs a pitch angle change β P I .To prevent the yaw control from constantly tracking the MRS, a tolerance range is defined where the yaw controller is not considered.The actual pitch angle β i is defined by a lookup table .Here, the pitch angle is stored as a function of the wind speed U ∞ .If the yaw error is positive and outside of the tolerance range, the pitch angle of the actuator is summed with that of the lookup table for rotor 3. Equivalently, rotor 5 is controlled in case of negative yaw error.Thus, only one controller is needed for yaw tracking.The generator torque Q i is calculated and specified by the optimal mode gain K and the generator speed ω i .

Simulation Matlab/Simulink
In the Matlab simulation, the yaw-by-pitch strategy is modeled.For this purpose, a simulation model of the yaw system of the MRS is created in Matlab/Simulink.The model is designed as a closed loop.The wind direction and wind speed can be changed as disturbance variables.
The basis for the simulation model is the determination of the drive torque required for the yaw system according to Equation 1.
The thrust forces of the rotors are determined using the BEM, created as a Matlab function and integrated into the model.In addition to the thrust forces, it also provides the power of the individual rotors.The wind speed u required for this is fed into the Simulink model via the Simulink Signal Builder for a height of 151.99 m.This wind speed is converted to the hub heights of the two rotor rows via the power law.In the next step, the oblique wind flow of the individual rotors and from this the wind acting orthogonally to the rotor plane is determined.For this, the wind speed u i at hub height, the wind direction γ and the current yaw angle ψ of the MRS are used.
In addition to the oblique flow, the wind speed change due to the yaw motion of the MRS is considered.For this purpose, the angular velocity ψ of the MRS as well as the position of the rotors with respect to the center of the yaw bearing is used.The corrected wind speed u cor is passed to the BEM function for each rotor to determine the power and thrust forces.The pitch angles and the angular velocity of the rotors are interpolated from lookup tables for the current wind speed u cor and used in the BEM to determine the thrust forces and rotor power.
The frictional torque of the yaw system to be overcome is determined according to Equations 1 to 4. The control of the yaw system in Matlab/Simulink is done via two PID controllers.For the rotors 3 and 5 to be controlled a separate PID controller with the same control parameters is used.The control difference is determined from the yaw error from the simulation model and the control target.An upstream Matlab function decides, based on the control difference, which PID controller is given the control difference to control.Each PID controller uses the pitch angle as the manipulated variable by adding a delta to the active pitch angle.The maximum rate of change of the pitch angle is limited to 8 °/s via the Simulink rate limiter, which is based on the pitch control of the 10 MW DTU reference turbine design [15].In the preceding Matlab function (see Figure 6) a flag is set if a yaw control is to take place.The flag causes the Simulink model to no longer use the values from the lookup table for rotors 3 and 5. Instead, the pitch value of rotor 4 is used and the control delta of the controllers is added to it.Rotor 4 is used instead of the lookup table because changes in u cor occur due to the movement of the MRS during yaw.These changes would lead to a change in the pitch angles when lookup tables are used, which can counteract and neutralise the control delta.Rotor 4 is located close to the center of the yaw bearing and is therefore hardly affected by the movement of the MRS.
The adjustment of the PID controllers is done by parameter studies.The controlled system is nonlinear, therefore many design methods are not easily applicable.The performance of the MRS is determined by the individual rotor powers determined by the BEM.The individual rotor powers are summed with a loss factor and represented as energy yield over the simulation time.

Results
As described in Section 5.1 and 5.2, the control parameters for the controllers were determined by parameter studies.For this purpose, simulations were performed with different proportional values K P , while the integral and differential components are disregarded.Once the value for K P is found, the integral component K I is determined using the previously determined K P through several simulations.The final step is the determination of the differential component K D with the previously determined values for K P and K I .Criteria for control parameters are fast control without overshoot as well as maximising energy yield.Selections of the simulations   3.
To investigate the effects of yaw-by-speed control on energy yield, different wind speeds and wind direction changes were studied.It was also investigated how the size of the tolerance range and the change of the friction coefficient affects the control performance and the energy yield.For the sake of clarity, the wind direction is shown with a negative sign.The Figures 9  and 10 show the results for the control yaw-by-pitch at 5 m/s and 15°wind direction change and 11 m/s wind speed and 15°wind direction change from Bladed and Matlab/Simulink at a tolerance range of ±2°.Once the yaw error is outside the tolerance range, the pitch angles for rotor 5 are increased by the controller.At the same time a reduction in the power of the rotors is noticed.The MRS follows the change in wind direction and the pitch of rotor 5 is reduced again by the controller when the yaw error is within the tolerance range.It can also be seen how, when the MRS overshoots in Bladed (seen in Figure 10), the rotor 3 is driven by the controller to turn the MRS back into the tolerance range.Figure 9 and 10 show that the rotors do not reach the power of 4 MW at 11 m/s, in Bladed they are below and in Matlab/Simulink above.It was noticeable, that if the pitch is regulated back by the controller, the power of individual rotors exceed the rated power.

Summary and further steps
The MRS yaw control in Bladed and Matlab/Simulink show good first results.The yaw-by-pitch strategy works for both simulation environments at different wind speeds and different wind direction changes.In Matlab/Simulink this is achieved with different sets of control parameters for different wind speeds, in Bladed this is done with one set.In the parameter study in which the tolerance range was varied, a change in energy yield was observed.The variation of the bearing friction coefficient did not result in a significant change in the energy yield.Noticeable was, that in Bladed and Matlab/Simulink, the rated power could not be achieved due to missing fine tuning of the simulation models.The use of lookup tables in Matlab/Simulink causes the change in pitch angle due to the change in wind (induced by the movement of the MRS) to override the change in pitch angle by the controller.This is solved by using the rotor 4 as a reference.One further step is the replacement of the lookup tables for pitch and rotor speed with independent controllers in Bladed and Matlab/Simulink.Additional points are the implementation of the yaw concept of yaw-by-speed control for a more efficient yaw system in the partial load range and the optimisation of the simulation models in Bladed and Matlab/Simulinks as well as further optimisation of the control parameters.In addition a yaw brake should be considered.In Bladed, active yaw with yaw-by-pitch and yaw-by-speed control under turbulent wind conditions will also be investigated.Furthermore, a wind tracking concept must be investigated, which tracks the MRS at no or below cut-in wind speeds in combination with large yaw misalignments.For this purpose, it should be investigated whether the yaw-bypitch strategy can be implemented in idling mode or if the rotors can act in motor mode.

Figure 1 .
Figure 1.Illustration of the 20 MW MRS model in Bladed with five rotors Figure 2. Numbering of rotors

Figure 3 .
Figure 3. Illustration of the operating principle of the yaw-by-pitch

Figure 4 .
Figure 4. Illustration of the angle convention used for the yaw system of the MRS.

Figure 6 .
Figure 6.Schematic diagram of the control loop for the yaw-by-pitch of the MRS in Matlab/Simulink

5 Figure 7 .Figure 8 .
Figure 7. Plot of the parameter study for the control parameter K P at 11 m/s and 15°w ind direction change in Bladed

Figure 10 .
Figure 10.Representation of the values for yaw, power and pitch of the 3 rotors in upper row at 16 m/s, 15°wind direction change and a tolerance of ±2°for Matlab and Bladed

Table 2 .
Position of the rotors in relation to the center of the yaw bearing in m

Table 3 .
Control parameters for Bladed and Matlab/Simulink

Table 4 .
Energy yields in kWh over 200 s simulation time at different wind speeds and wind direction changes at different tolerance ranges.