the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Jan 2025
Control Strategies for Multirotor Wind Turbines
Abstract. This work considers steady-state aspects of multirotor windturbine control. In contrast to most literature on the topic, the underlying multirotor model includes the aerodynamic interactions between the rotors. The model predicts that these interactions are central for effective control of multirotor windturbines under some conditions. A numerical optimization problem is formulated to find the optimal control solutions, and two adaptations of the MPPT algorithm for the multirotor case are suggested. By employing furling for multirotor windturbines, it is also shown that one can drastically reduce the bending moment of the structure. Other physical effects such as operation with wind shear and simple failure handling are also presented using a 23-rotor fixed-pitch multirotor windturbine with a total rated power of 5 MW. The results are meant as an enabling work, showcasing the possibilities and challenges involved in multirotor stability analysis and control problems.
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Status: closed
- RC1: 'Comment on wes-2024-185', Anonymous Referee #1, 21 Jan 2025
-
RC2: 'Comment on wes-2024-185', Anonymous Referee #2, 24 Jan 2025
I think this paper reveals and very smartly addresses the fundamentally important aerodynamic effects of rotor interaction in a multi rotor system. This arises when adjacent rotors responding to local wind conditions operating at different loads (thrust coefficients) modify the flow field and create oblique average local flow angles. It also arises fundamentally as with a single rotor because the flow diverges across the system as a whole. If we consider a single actuator disc/rotor, the streamlines diverge increasingly from the center of the disc when the disc is loaded. The inflows are consequently yawed across the surface of the disc . If you imagine the same disc size then filled with multiple smaller discs/rotors, then, even if they are all loaded identically and in uniform far upstream flow, there will be angled inflow to all the rotors except in the center - with ever more complex interactions if the multi rotors are not uniformly loaded. It may help the reader if some discussion equivalent to what is just mentioned is included in the introduction. I think this would be better than the isolated statement (lines 29,30) asserting that the interactions are likely to be important in view of that being the case with multirotor helicopters which can be far different from wind turbines in their operational envelop.
The complexity and computational demands of modelling loads and control of interacting rotors implies that there is much need for effective simplified methods and this paper exploits previous modelling work of the authors with promise of highly simplified methods being effective for control, at least from a steady state perspective.
In Section 3, Modelling, it is understandable to use the NREL 5 MW as an extremely well documented design in the public domain and, as a simplification, to eliminate the overall effect of torque reaction on the structure by counter-rotation of adjacent turbines. At a later stage, the NREL 5 MW would be inadequate for comparisons of multi rotor systems with the largest single rotor systems. It is also unlikely that rotors would be designed for rotation in both directions. Blade production for example would then divide with one half of the population being of opposite hand to the other and with added manufacturing costs implicit.
It is asserted (line 65) that the net rated power of 5MW is equally divided among all the turbines. How is this done ? For example is it on the basis of equal total active swept area? If so, much prior analysis, modelling, wind tunnel test and very limited field testing indicates there is a blockage effect (applicable also to tidal turbine arrays) such that the power of the multi rotors will exceed the power of the equivalent (active area) single rotor. According to prior analyses, theoretical and numerical (CFD, vortex methods etc.) limited wind tunnel testing and minimal field experiments (Vestas) on wind turbines this is due to a blockage effect (recognized also as applying to tidal turbine arrays) which is predicted to be significant ( power gains ~ 10% and thus possibly in a range more significant than the differences between independent MPPT power control of the turbines and optimized power control of the array) for a multi rotor system with many closely spaced rotors. I assume this is not accounted in your modelling as I cannot see how training data could be produced except say by extensive CFD analyses of the test case array? I think this needs some discussion or at least an acknowledgement whether the blockage affect is accounted.
Vertical variation in the angle of the net flow incident on each rotor is both inherent in the array being finite vertically and that variation is augmented in the case of differential rotor loading caused by wind shear which is later discussed. Regarding the statement (lines 94-95) and Figure 4 in section 3, is this vertical variation accounted? It would be useful to have text fully clarifying this.
In Section 3.2, I would advise against the re-definition of tsr with the usual lambda symbol. Purely for clarity it is better to preserve the established definition and talk about local tsr with some prime/subscript or other modifier on the lambda symbol or some other symbol.
In Section 4.3, line 175, the peak restoring moment is described as equivalent to a 3m upwind movement of the center of thrust. It is hard to interpret the significance of this. Maybe mention the height and width of the array or maybe the restoring moment could be compared to the maximum moment that can be generated with all the turbines on one side at rated thrust and all on the other switched off? The discussion in Section 4.3 about azimuthal stability is nevertheless very interesting and it is encouraging that yaw moments on the misaligned system are restoring.
In Section 6.1, line 290 to end, I think that "performs identically ........turbine is more or less aligned" is too modest! Single large turbines would usually be controlled to keep alignment within ranges like ±10 or ±15 deg and maybe shut down as in a fault case if the error exceed 30 deg. Thus based on Fig 28, the SMPPT controller performs identically over the whole range of practical interest and this could be said. A reason for avoiding operating at large yaw error, in addition to incurring an obvious drop in power, is that cyclic loads in yaw and stall dynamic effects cause additional blade and system fatigue which may be unacceptable. That thought suggests that it would be interesting to see (as figures or tables) the distributions of resultant wind and skew angle χ over the multi rotor array in the aligned case. It would also be interesting to see what difference results when the aligned case is optimally controlled v MPPT on each turbine. An inference regarding the skewed flows may be that the rotors of a multi rotor system need to be designed for fatigue loading additional to what would apply if the same rotors were operated in isolation.
Regarding any minor corrections I think Reviewer 1 has fully covered this.
In conclusion I think this paper taken alongside prior work of the authors is developing a very promising approach for multi rotor control
Citation: https://doi.org/10.5194/wes-2024-185-RC2 - AC1: 'Comment on wes-2024-185', Finn Matras, 17 Feb 2025
Status: closed
- RC1: 'Comment on wes-2024-185', Anonymous Referee #1, 21 Jan 2025
-
RC2: 'Comment on wes-2024-185', Anonymous Referee #2, 24 Jan 2025
I think this paper reveals and very smartly addresses the fundamentally important aerodynamic effects of rotor interaction in a multi rotor system. This arises when adjacent rotors responding to local wind conditions operating at different loads (thrust coefficients) modify the flow field and create oblique average local flow angles. It also arises fundamentally as with a single rotor because the flow diverges across the system as a whole. If we consider a single actuator disc/rotor, the streamlines diverge increasingly from the center of the disc when the disc is loaded. The inflows are consequently yawed across the surface of the disc . If you imagine the same disc size then filled with multiple smaller discs/rotors, then, even if they are all loaded identically and in uniform far upstream flow, there will be angled inflow to all the rotors except in the center - with ever more complex interactions if the multi rotors are not uniformly loaded. It may help the reader if some discussion equivalent to what is just mentioned is included in the introduction. I think this would be better than the isolated statement (lines 29,30) asserting that the interactions are likely to be important in view of that being the case with multirotor helicopters which can be far different from wind turbines in their operational envelop.
The complexity and computational demands of modelling loads and control of interacting rotors implies that there is much need for effective simplified methods and this paper exploits previous modelling work of the authors with promise of highly simplified methods being effective for control, at least from a steady state perspective.
In Section 3, Modelling, it is understandable to use the NREL 5 MW as an extremely well documented design in the public domain and, as a simplification, to eliminate the overall effect of torque reaction on the structure by counter-rotation of adjacent turbines. At a later stage, the NREL 5 MW would be inadequate for comparisons of multi rotor systems with the largest single rotor systems. It is also unlikely that rotors would be designed for rotation in both directions. Blade production for example would then divide with one half of the population being of opposite hand to the other and with added manufacturing costs implicit.
It is asserted (line 65) that the net rated power of 5MW is equally divided among all the turbines. How is this done ? For example is it on the basis of equal total active swept area? If so, much prior analysis, modelling, wind tunnel test and very limited field testing indicates there is a blockage effect (applicable also to tidal turbine arrays) such that the power of the multi rotors will exceed the power of the equivalent (active area) single rotor. According to prior analyses, theoretical and numerical (CFD, vortex methods etc.) limited wind tunnel testing and minimal field experiments (Vestas) on wind turbines this is due to a blockage effect (recognized also as applying to tidal turbine arrays) which is predicted to be significant ( power gains ~ 10% and thus possibly in a range more significant than the differences between independent MPPT power control of the turbines and optimized power control of the array) for a multi rotor system with many closely spaced rotors. I assume this is not accounted in your modelling as I cannot see how training data could be produced except say by extensive CFD analyses of the test case array? I think this needs some discussion or at least an acknowledgement whether the blockage affect is accounted.
Vertical variation in the angle of the net flow incident on each rotor is both inherent in the array being finite vertically and that variation is augmented in the case of differential rotor loading caused by wind shear which is later discussed. Regarding the statement (lines 94-95) and Figure 4 in section 3, is this vertical variation accounted? It would be useful to have text fully clarifying this.
In Section 3.2, I would advise against the re-definition of tsr with the usual lambda symbol. Purely for clarity it is better to preserve the established definition and talk about local tsr with some prime/subscript or other modifier on the lambda symbol or some other symbol.
In Section 4.3, line 175, the peak restoring moment is described as equivalent to a 3m upwind movement of the center of thrust. It is hard to interpret the significance of this. Maybe mention the height and width of the array or maybe the restoring moment could be compared to the maximum moment that can be generated with all the turbines on one side at rated thrust and all on the other switched off? The discussion in Section 4.3 about azimuthal stability is nevertheless very interesting and it is encouraging that yaw moments on the misaligned system are restoring.
In Section 6.1, line 290 to end, I think that "performs identically ........turbine is more or less aligned" is too modest! Single large turbines would usually be controlled to keep alignment within ranges like ±10 or ±15 deg and maybe shut down as in a fault case if the error exceed 30 deg. Thus based on Fig 28, the SMPPT controller performs identically over the whole range of practical interest and this could be said. A reason for avoiding operating at large yaw error, in addition to incurring an obvious drop in power, is that cyclic loads in yaw and stall dynamic effects cause additional blade and system fatigue which may be unacceptable. That thought suggests that it would be interesting to see (as figures or tables) the distributions of resultant wind and skew angle χ over the multi rotor array in the aligned case. It would also be interesting to see what difference results when the aligned case is optimally controlled v MPPT on each turbine. An inference regarding the skewed flows may be that the rotors of a multi rotor system need to be designed for fatigue loading additional to what would apply if the same rotors were operated in isolation.
Regarding any minor corrections I think Reviewer 1 has fully covered this.
In conclusion I think this paper taken alongside prior work of the authors is developing a very promising approach for multi rotor control
Citation: https://doi.org/10.5194/wes-2024-185-RC2 - AC1: 'Comment on wes-2024-185', Finn Matras, 17 Feb 2025
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