In this study different multi-rotor wind turbine systems (MRSs) are designed in such a way that the space frame, forming the connection between rotor nacelle assemblies (RNAs) and the tower, is modeled as an ideal truss work. To dimension the tube diameters and wall thicknesses, a simplified load case is used with an adjusted safety factor for loads. This simplified approach allows for fast computations of a large variety of different support structure designs. By variation of rotor number, space frame topology, space frame depth and positioning of yaw bearings, it is possible to gain an understanding of the optimal MRS design. As such, the simplified approach is a preliminary step helping to choose a good design parameter combination for a more detailed and comprehensive analysis.

In times when the sizes of wind turbines and their components are ever growing, the industry is facing new challenges in manufacture and transportation, as well as in terms of loads and strength. A multi-rotor wind turbine system (MRS) could overcome the obstacles of this growth trend.

Studies from the INNWIND project showed the potential of a 20

Assuming an MRS with an overall capacity of 20

The Technical University of Denmark (DTU) 10

In this study different designs for the MRS are designed based on ultimate loads and buckling. The designs are built in such a way that the space frame is modeled as an ideal truss work. To dimension the tube diameters and wall thicknesses, a simplified load case of maximum thrust force at the steady rated wind speed on all rotors and the gravitational forces resulting from the RNA weights is used with an adjusted safety factor for loads. The axial forces of the truss members are calculated via finite element analysis (FEA). Diameter and thicknesses are first dimensioned against material strength and second, if necessary, against stability (Euler buckling). The following aspects in design are not considered for reasons of simplicity: fatigue analysis of space frame and tower, local shell or plate buckling, dynamic behavior (modal analysis), and design load cases according to

The weights of tower, space frame and RNAs are multiplied with cost-per-mass factors. The space frame topology is varied with respect to the depth of the structure and the yaw bearing positions. The optimum of each design is determined based on the minimal cost of the capital expenditure (CAPEX) for RNAs, space frame and tower. An assumed Rayleigh wind speed distribution is used for the annual energy yield for each design and results in very simplified levelized cost of energy (SCoE). SCoE means that the operational expenditure (OPEX), the decommissioning expenditure (DECOMMEX) and interest rate as well as balance of plant (BoP) are not considered.

This simplified approach allows for fast computations of a large variety of different support structure designs. By the variation of rotor number, space frame topology, space frame depth and the positioning of yaw bearings, it is possible to gain an understanding of the optimal MRS design. As such, the simplified approach is a preliminary step helping to choose a good design parameter combination for a more detailed and comprehensive analysis.

An overall capacity in the 20

Scaling is carried out under the assumption of similarity rules for wind turbines and a constant tip speed ratio

The wind industry almost exclusively applies upscaling, due to the growth trend of turbines for a higher energy yield. For the MRS, downscaling is of importance. Downscaling with an exponent of around 2 seems not to be suitable. Then the gain from new materials, technology and experience would be discarded and would result in a heavier and not modern blade.

An upscaling exponent of

SD-MRS design no. 2. Tri-rotor with bearing positions and design parameters.

The simplified support structure design is described with the example of an SD-MRS with three rotors, as seen in Fig.

In the INNWIND project

All chosen layouts are based on equilateral triangles, so the vertical distance between rotor rows results in

The tower and space frame are connected through yaw bearings, in this study always with a fixed–loose bearing combination. The MRS should be able to follow the wind via a global yaw system, meaning that the whole space frame should be able to align itself perpendicularly to the actual wind direction, rather than each rotor aligning itself. How the yaw bearings would be connected to the tower in detail is of no importance for this preliminary concept design study. The gravitational forces caused by the space frame and RNAs are transferred through the fixed bearing to the tower. Thrust forces vertical to the rotor planes are transferred through both fixed and loose bearings.

The vertical positions of the fixed and loose bearings, characterized with

Tower and space frame connection via yaw bearings.

To dimension both the tower and the space frame, a simplified design load case is defined: maximum thrust force (at the steady rated wind speed) on all rotors simultaneously. Because of wind shear, turbulent wind, gusts and the pitching behavior, this is an artificial and somehow unlikely case, but for this study it represents a worst-case scenario regarding the ultimate loads.

The MRSs are designed in such a way that the space frame is modeled as an ideal truss work. To determine the member forces of the space frame, a finite element analysis (FEA) carried out via ANSYS APDL is used. The space frame members are modeled with bar elements. Bar elements have one local degree of freedom (DoF) per element node, the axial displacement, resulting in three global DoFs per node. The corresponding reaction force to the local axial displacement is the local axial force. The FEA requires initial diameters and wall thicknesses of the space frame members to determine and use the stiffness matrix. Since the space frame is modeled as an ideal truss work, the FEA solution of interest, the axial member force, is independent of the initial cross-section parameters.

The use of bar elements implies that there are no other DoFs and reaction forces in the nodes, apart from the axial ones. In reality the connections between the space frame elements and the rotors would be welded or bolted. Therefore, shear forces as well as bending and torsional moments would occur in the nodes. This could be modeled in the FEA via beam elements with six DOFs and reaction forces per node. With the use of beam elements, the FEA solution would depend on the initial cross section and the dimensioning process would be an iterative one for each space frame member. The differences between bar and beam element solutions were investigated and deemed neglectable for this preliminary study.

The thrust forces

Also acting on the support structure are the gravitational forces of the RNAs with an applied partial safety factor of

The yaw bearings are modeled as boundary conditions with their respective DoFs on the respective space frame nodes. The fixed bearing disables all three spatial translations; the lower loose bearing has one DoF in the tower height direction. In Fig.

The dead load of the space frame and the drag forces of both the space frame and the tower are neglected. This is due to the fact that both the tower and the space frame are going to be dimensioned and an iterative process is to be avoided.

The space frame members are first dimensioned against ultimate strength with an applied safety factor for material of

A ratio for the wall thickness to diameter is defined as

In the case of a positive member axial force, the member is in a tension state and stability is of no concern. A negative axial force means a compression state. If the difference

The tower diameters and wall thicknesses are determined by the tower bending reaction moment. The bearing reaction forces from the FEA solution are checked against the analytical solution. There, the space frame is assumed as a rigid beam supported through a fixed and a loose bearing, loaded with the thrust forces of the rotors. The reaction forces of the bearings are the external forces on the tower. These reaction forces induce a tower bending reaction moment

After dimensioning the space frame and tower, the volume of each part can be calculated and therefore the masses with the density

Cost fractions after

Scaled rotor values for the SD-MRSs and initial DTU rotor values.

Overview and numbering of the SD-MRS designs.

2D view of the response surface. Design no. 1, normalized cost (CAPEX).

Each SD-MRS design is simulated for each design parameter combination of

The energy yield of the MRS is determined based on an assumed Rayleigh wind speed distribution with a mean wind speed

With the cost and the annual energy production (AEP) of the designs, the SCoE can be calculated:

To compare and normalize the SCoE values, a power-equivalent SR is designed with the same assumptions as the SD-MRS (blade tip clearance, loads, etc.).

To keep the design space somehow limited and to reflect currently available turbines on the market, the rotors for the SD-MRS are set to a single capacity of 2, 4 or 8

Possible rotor numbers are set to three (tri-rotor), five (penta-rotor), seven (hepta-rotor) or nine (ennea-rotor) rotors. An even-numbered SD-MRS would result in a cantilever design with or without steel ropes to reduce loads. These cantilever designs and therefore even-numbered SD-MRSs are not considered in this study. The odd-numbered SD-MRS layouts are all designed with equilateral triangles, which results in the highest packing density of the rotor area.

Three possible rotors and four possible numbers of rotors would result in 12 possible overall capacity combinations, ranging from

This results in an overall number of 18 designs for the SD-MRS, as seen in Fig.

The design parameters shown earlier,

Almost all designs have three design parameters, since they have two

The edges in the response surface are due to changes in the load distribution and the compression–tension behavior of the members, resulting in steep changes in the masses and therefore the cost.

In Fig.

The three levels of SCoE values correlate with the rotors used in the designs. The designs with the lowest SCoE are the ones with the 2

The lower costs are due to the small fraction of tower and space frame mass relative to the overall mass. Design drivers for the SD-MRS are the RNA masses; they benefit from smaller rotors based on cubic scaling.

Normalized SCoE of the optimized SD-MRS designs.

As a first venture into MD-MRS designs, the INNWIND design with 45 rotors is used in a slightly modified version. The number of rows and rotors per row are unchanged, and the layout can be seen in Fig.

MD-MRS design for 45 rotors based on

The overall capacity for the MD-MRS is set to the same values as the SD-MRS to obtain a direct comparison. This results in the values shown in Table

Scaled rotor data for the 45-rotor MD-MRS.

The design parameters to be varied are again the depth of the structure and the fixed bearing position and therefore the tower height. Instead of a quasi-continuous variation of the fixed bearing position over the height, three discrete positions are investigated: position 1 in the second row at the bottom, position 2 in the middle of the space frame and position 3 at the top. All three variants have the loose bearing in the first space frame row.

Normalized cost (CAPEX) of the 14

Figure

SD-MRS, MD-MRS and SR results for normalized SCoE.

In Fig.

The aim of this study was to develop a simplified method for preliminary calculations of masses and therefore costs of multi-rotor wind turbine systems. The simplifications in the dimensioning process were used to avoid iterations for convergence and to allow for a fast way to investigate a variety of designs and design parameters.

Several SD-MRS designs were designed, simulated and optimized regarding the cost. The optimal design configurations were determined manually based on the simplified and fast dimensioning approach used.

The space frame of an MRS is sensible to the design parameters, since the load distribution can change with the design. Members can change from a tension to a compression state or the other way around. Stability seems to have a big influence since many space frame members needed to be redimensioned when in the compression state.

The SD-MRS designs with small single rotors showed the highest potential to reduce cost. One particular MD-MRS design with 45 rotors was also investigated and showed an optimal depth-to-width ratio for the space frame of 10 %–13 %. A fixed bearing position and therefore a tower height in the middle of the space frame was most promising. Overall the MD-MRS showed more potential than the SD-MRS to reduce cost.

Next steps include more MD-MRS designs with variable numbers of rotors. With increasing complexity in future works due to a growing number of designs and design parameters, a framing of the dimensioning process as part of a formal optimization approach needs to be considered.

After that, one or two promising designs will be analyzed in detail, regarding design load cases according to

All necessary research data have been included in the paper. For further information please contact the authors.

SvS performed all simulations and wrote the pre- and postprocessing code as well as this paper. PD and MT helped formulate the ideas and gave technical advice in the regular discussions. PD helped with the cost-to-mass factors. All authors reviewed this paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

The content of this paper was developed within the project X-Rotor/X-Multirotor, part of X-Energy, which is in cooperation with Siemens Gamesa Renewable Energy (SGRE), who we would like to thank here.

This research has been supported by the German Federal Ministry of Education and Research – BMBF (grant no. 13FH1I04IA).

This paper was edited by Athanasios Kolios and reviewed by two anonymous referees.