X-Rotor, an Innovative Offshore Wind Turbine to Reduce Cost of Energy ^†

Abstract

The cost of energy generated by large-scale vertical-axis wind turbines faces great challenges for it to be competitive with conventional horizontal-axis wind turbines for offshore deployment. To become competitive, significant reductions in capital cost and operational costs would be competitive. A novel vertical-axis wind turbine that aims to meet these requirements is proposed: the X-rotor wind turbine. An early-stage feasibility study of exemplary two- and three-bladed 5 MW turbines is reported. The cost savings arising from two aspects of the concept that have the greatest impact, namely the power take-off system and O&M, are quantified. Two other aspects that could have a major impact on the cost of energy are the vertical axis rotor and the jacket. The masses for both are evaluated as proxies for their costs. The former costs are determined to be substantial relative to those of conventional HAWTs. Whereas the latter masses are determined not to be prohibitively greater relative to conventional HAWTs.

1. Introduction

Vertical Axis Wind Turbines (VAWTs) have been unsuccessful as far as large-scale commercial generation of electricity is concerned. The only commercial manufacturer of consequence, Flowind Inc. (Wisbech, UK), supplied more than 100 MW (over 500 wind turbines) of the Darrieus “egg-beater” type VAWT to Californian wind farms in the 1980s. VAWT Ltd. in Wigan, UK built a number of H-rotor prototypes up to a rating of 500 kW. The VAWT 850, a 500 kW prototype, was run for a period on a test site at Carmarthen Bay, UK. High torque levels on the main transmission shaft caused a number of failures, and the designs were never commercialised. Compared to state-of-the-art Horizontal Axis Wind Turbine (HAWT) designs, there are two fundamental challenges for VAWT design:

(1)

The aerodynamic efficiency is intrinsically lower because the angle of a blade to the incident wind flow must vary over each rotational cycle and cannot be maintained at an optimum value. This typically means that the swept area of a VAWT must be 15% to 20% larger than that of a HAWT in order to produce the same power.

(2)

The optimum rotor speed is roughly half that of comparable HAWTs. Due to the intrinsic differences in aerodynamics, VAWTs typically have reduced rotor speed. Combined with the fact that the drive-train has approximately double the rated torque for any given power rating, VAWT drive-trains tend to be much heavier and more expensive.

With respect to these core challenges, the Flowind design avoided the second one by running at higher than optimum speed, but this so degraded the aerodynamic performance that these designs (at typical good land-based sites with mean wind speed ~8 m/s) produced about half the energy output of a HAWT of the same power rating. The VAWT Ltd. designs had much better power performance with increased swept area (bigger blades) to compensate for the first issue, but with a disadvantageous accompanying increase in weight and cost.

In a VAWT with a V-rotor, the drive-train components can be situated at ground level with associated maintenance and assembly benefits. In the VAWT 850 design with an H-rotor, this was achieved by using a torque transmission tube, but it proved too expensive and impractical, provoking a redesign with the drive-train relocated to the tower top. The V-VAWT requires the least rotor material of all VAWT configurations for the required swept area, and the low centre of thrust has advantages for offshore siting. Unfortunately, it suffered from extreme overturning moments on the main bearing. In a modification to the V-VAWT proposed by Sharpe, “sails” are added transversely to the blades (see Figure 1, left) to provide partial cancellation of the overturning moment [1]. The NOVA concept, Figure 1 (right), was similar but with only a single set of “sails” situated at the end of the blades [2]. The diameter of the rotor was estimated to be 270 m with a height of 130 m. However, the large rotor and resulting intrinsically low rotational speeds drove up the weight and cost of the drive-train.

To reduce the cost of large wind turbines, it has been proposed that the conventional power-train be dispensed with. Instead, power is generated directly using generators driven by secondary rotors [3,4,5] (also reported in [6]) and [7] mounted on the blades of the main or primary rotor for both HAWTs and VAWTs. For such an approach to be viable, the following requirements must be met:

(a)

The tip speeds of the secondary rotors must be kept comfortably below the speed of sound; that is, the product of the tip speed ratios of the primary and secondary rotors is subject to an upper limit.

(b)

The rotational speed of the secondary rotors must be sufficiently high that neither a gearbox nor a multi-pole generator is required; that is, a conventional generator suffices without a gearbox.

(c)

The induced wind speed acting on the secondary rotors should be sufficiently high that a low secondary rotor radius suffices to meet (2) and structural requirements.

(d)

The overall efficiency of power conversion of the combined primary and secondary rotors must be high.

(e)

Mounting the secondary rotors on primary rotor blades that are pitched to regulate the turbine should be avoided.

None of the proposed concepts in [3,4,5,7] meet all the above requirements. Furthermore, it is not established that the direct drive of conventional generators without a gearbox is possible. In [3], the primary rotor is a horizontal axis. In [4], both horizontal and vertical primary rotors are considered. In [3,4], the secondary rotors are horizontal axes. In both cases, as pointed out in [5], sufficient information about the operating conditions and the aerodynamic characteristics of the primary and secondary rotors is not provided to specify a realisable design or, indeed, judge whether one is possible. In [7], a Darrieus-type vertical axis primary rotor is combined with horizontal axis secondary rotors. Similar to [3,4], insufficient information is provided. In addition, the efficiency of the primary rotor would be very low. In [5], both the primary and secondary rotors are horizontal axes. It is claimed that a secondary rotor thrust coefficient of 0.4 with a power coefficient between 0.85 and 0.9 is possible. In fact, the power coefficient must be less than the thrust coefficient. Consequently, the feasibility of the proposed design is not established.

To address the fundamental challenges for VAWT design mentioned above, a novel wind turbine concept is proposed, combining a vertical axis primary rotor with horizontal axis secondary rotors, the “X-rotor offshore wind turbine” (see Figure 2). The X-rotor concept directly targets cost of energy reduction and addresses scalability of VAWTs through the following [8]:

(1)

Large reductions in the cost of drive-trains through an easily scalable approach to power take-off (PTO) that does not require a gearbox or multi-pole generator while achieving comparable efficiency levels in power conversion innovations.

(2)

Large reductions in Operation and Maintenance (O&M) costs through having no heavy components situated at great height above sea level and through general simplification of the machinery.

Having a low centre of mass with no heavy machinery at height may have advantages for floating offshore usage, particularly when reconfigured to have 3 blades rather than 2, as in Figure 2.

This paper aims to establish the feasibility of the X-rotor wind turbine concept, primarily through the presentation of baseline 5 MW designs. However, complete design studies and so absolute determination of the cost of energy are beyond its scope. Instead, the focus is on the potential benefits with regard to the reduction in capital costs arising from the replacement of a conventional power-train by the secondary rotor power take-off and the benefits with regard to the related reduction in operational costs relative to those costs of a conventional HAWT. In addition, potential showstoppers are considered, namely, the design of the rotor to establish its aerodynamic performance and since VAWT rotors have a greater swept area and solidity compared to HAWT rotors, an estimate of the former’s mass as a proxy for cost. For a similar reason, the design of the jacket for offshore installation is also considered.

The paper is structured as follows. In Section 2, the requirements for a turbine that meets requirements (a) to (e) are discussed. In Section 3, a baseline 5 MW turbine, the X-rotor, that meets the requirements defined in Section 2, is described. The aerodynamic and mechanical design of the primary rotor and jackets are discussed for both two-bladed and three-bladed primary rotors. In Section 4, the O&M costs associated with the 5 MW X-rotor are estimated, and in Section 5, the associated Costs of Energy (CoE) are discussed. In Section 6, alternative configurations for the X-rotor are presented, whereby the configuration of the X-rotor’s design space is discussed with reference to upscaling. Finally, conclusions and an outline of future work are presented in Section 7.

2. The X-Rotor Concept

2.1. Overview

The X-rotor concept is a radical rethink of the VAWT, constituting a V-VAWT that is heavily modified to address its disadvantages while retaining many of the advantages, i.e., minimal use of material and a low centre of mass with no heavy machinery at height. As depicted in Figure 2, the X-rotor concept has a primary vertical-axis rotor consisting of an upper and lower part with relatively conventional blades, angled both upwards and downwards from the ends of a relatively short, stiff cross-arm. The role of the upper part is to provide the major contribution to mechanical power extraction from the wind. The lower half of the primary rotor acts similarly to the transverse blade elements in the NOVA concept. Attached to the ends of the primary rotor’s lower blades are secondary horizontal-axis rotors; see Figure 2. The roles of the lower half of the X-rotor are, thus, to reduce the overturning moment and support the secondary rotors, but also increase mechanical power extraction. The secondary rotors’ primary role is to drive generators and, thereby, produce electrical power.

Unlike conventional vertical-axis wind turbines, the purpose of the vertical-axis rotor in the X-rotor concept is not to directly generate electrical power; that is, there is no conventional drive-train connected to and driven by the primary rotor. Rather, its purpose is to considerably increase the wind speed impacting the secondary horizontal axis rotors. The size of the secondary rotors is consequently much reduced, and their rotor speed is much increased, sufficiently to enable direct generation of electrical power without recourse to a gearbox or bespoke multi-pole generator. Indeed, only a rotor and generator are housed at the end of each lower blade. Irrespective of the technology used, whether direct or indirect drive, conventional power-trains driven by the primary rotor have a weight and cost that are directly related to torque rating [2]. Because the rotor speed of the primary rotor is very low and the rated torque is very high, a fundamental issue for large-scale VAWTs is in converting the rotor’s mechanical power to electrical power. Being able to dispense with the conventional drive-train and replace it with a direct-drive power train driven by secondary rotors has a very considerable cost benefit. An additional advantage of the secondary rotor power take-off system, i.e., the secondary rotor and power-train, is that, due to the relative wind speed on the rotors being induced by the near-constant rotation of the primary rotor, the combined power generated by the secondary generators is fairly constant over each revolution of the primary rotor, only varying with changes in the rotational speed of the primary rotor. Consequently, the power electronics do not necessarily need to cater to the generated power having a strong sinusoidal variation, as can be the case for VAWTs.

The efficiency of the secondary rotor power conversion, i.e., the ratio of the power delivered to the generators by the secondary rotors to the power extracted from the wind by the primary rotor, is proportional to the ratio of the aerodynamic power coefficient to the aerodynamic thrust coefficient of the secondary rotors. To keep this efficiency high, the secondary rotor must be designed to operate at a low tip speed ratio with low aerodynamic efficiency, necessitating slightly larger secondary rotors. In addition, the combined tip speed ratio, i.e., the product of the tip speed ratios for the primary and secondary rotors, is subject to an upper limit to avoid further reduction in efficiency arising from aerodynamic compressibility effects.

By varying the frequency of the electrical connection to a generator, the secondary rotors are controlled to maintain a constant tip speed ratio. (The power electronics to provide this frequency variation are housed at the hub of the X-rotor.) Since the inertia of the secondary rotors is low, their response time is sufficiently fast that the tip speed ratio can be kept constant at all times. Consequently, the efficiency of power conversion of the secondary rotor is increased by about 5% in below-rated operation and 10% in above-rated conditions. In below-rated operation, by keeping the tip speed ratio of the secondary rotor constant, the tip speed ratio of the primary rotor is also kept constant. The primary rotor is designed such that this constant tip speed ratio corresponds to maximum aerodynamic efficiency.

The blades in the upper part of the rotor have the capability to pitch about their longitudinal axis. The primary purpose is to provide overspeed protection and to control the speed of rotation of the primary rotor in above-rated conditions. Overall, the efficiency in power delivered to the generators from power extracted from the wind by the primary rotor is about 90%. With synchronous generators having an efficiency close to 99% when operating at rated power, the overall generation efficiency is close to 90%, i.e., not very different from that achieved by a conventional power-train. However, by varying the pitch cyclically in below-rated wind speed conditions, it would be possible to increase the power extracted by the primary rotor by possibly 5% to 10% [9]. Cyclic pitching can also be used to reduce loadings on the blade whilst achieving only a slightly lower increase in efficiency [10].

Power transfer between the rotating primary rotor and the stationary support structure would be achieved by either slip rings or a variable speed transformer [11]. Power electronics would act to adjust the frequency on the primary rotor to that on the support structure.

For the X-rotor, the PTO systems scale in a straightforward manner, in fact, linearly. Instead of increasing the rating of each PTO system as the rating of the turbine increases, their number is increased. This can be achieved by attaching more than one PTO system to each lower blade of the primary rotor and/or increasing the number of blades on the primary rotor, keeping the number of power take-off systems attached to each lower blade the same.

2.2. Secondary Rotors

Direct drive without resorting to a multipole generator is one of the key innovations of the X-rotor concept, but it is accompanied by some strict constraints on the design of the secondary rotors.

The design of the secondary rotors is subject to two significant constraints. Firstly, the rotational speed of the secondary rotor, and so the generator rotor speed, is subject to an upper constraint in order for the drive-train attached to the secondary rotor to be direct drive. Secondly, their tip speed is subject to a maximum to avoid aerodynamic compressibility; that is,

$${\Omega }_{s}r={\lambda }_s{\lambda }_{p}V<V_m$$

(1)

where ${\Omega }_s$ is the rotational speed of the secondary rotors, $r$ is the radius of the secondary rotors, ${\lambda }_s$ is the tip speed ratio of the secondary rotors, ${\lambda }_p$ is the tip speed ratio of the primary rotor, $V$ is the wind speed and $V_m$ is the maximum allowed tip speed roughly 60% to 70% the speed of sound. Hence, there is a maximum value imposed on $r$ and, thereby, on the area of the secondary rotors, corresponding to $V_m$ and the minimum value of ${\Omega }_s$. It follows that to maximise the rated power of the secondary rotors, their incident wind speed

$$V_I={\lambda }_{p}V$$

(2)

must be maximised. However, for the primary rotor to achieve high aerodynamic efficiency below and at rated wind speed, ${\lambda }_p$ is constrained to a narrow range of values, and, to achieve high lifetime energy capture, rated wind speed is, likewise, constrained to a narrow range of values. Consequently, there is a maximum imposed on the rated power of the secondary rotors.

When operating in steady state, the aerodynamic power of the primary rotor is balanced by the thrust of the secondary rotors multiplied by their speed relative to the ground, i.e., by

$$n{\displaystyle \frac{1}{2}}\rho A_s{V}_I^3{C}_{Ts}$$

(3)

where $n$ is the number of secondary rotors, $\rho$ is the density of air, $A_s$ is the area of each secondary rotor, $C_{Ts}$ is the aerodynamic thrust coefficient for the secondary rotors and their speed is equal to the incident wind speed, $V_I$. Hence, the ratio of the total power extracted from the wind by the secondary rotors

$$n{\displaystyle \frac{1}{2}}\rho A_s{V}_I^3{C}_{Ps}$$

(4)

to that of the primary rotor is $C_{Ps}/C_{Ts}$, where $C_{Ps}$ is the aerodynamic power coefficient for the secondary rotors. During below-rated operation, to avoid low efficiency in the transfer of power from the primary rotor to the secondary rotor, the value of this ratio must be considerably higher than 2/3, the value, according to standard actuator disc theory, for a conventional HAWT rotor at the maximum value of the power coefficient. Rather than designing a rotor, as in the conventional HAWT case, with a radius chosen to maximise power, it is designed with a fixed blade root bending moment [12], equal to that for the conventional rotor, but with a non-fixed rotor radius. The resulting rotor has lower aerodynamic efficiency, requiring an 11.6% increase in radius but achieves an increase in power of 7.6% and a 10% decrease in thrust. The ratio, $C_{Ps}/C_{Ts}$, for this rotor is 0.8 according to actuator disc theory. By adopting a similar approach, secondary rotors with a high power coefficient to thrust coefficient ratio can be obtained at low tip speed ratios. This low-efficiency, low-thrust design of the secondary rotors is one of the key innovations of the X-rotor concept.

The maximum power that each secondary rotor can generate is limited by inherent constraints arising from their drive-train being required to be direct drive. However, this does not limit the power rating of the X-rotor concept. A higher rating is achieved by simply increasing the number of secondary rotors. In this way, power take-off is easily scalable, with the costs increasing linearly with turbine rating.

2.3. Primary Rotor

The swept area of the rotor for a V-VAWT is greater than the swept area of the upper half of an H-VAWT for the same lengths of cross-arm and blade, with the consequence that the former generates greater power. In addition, a V-VAWT has a higher maximum tip speed ratio than that for an equivalent H-VAWT, thereby increasing the incident wind speed on the secondary rotors and so their rated power. For these reasons, together with the requirements to partially cancel the blade overturning moments and to have the secondary rotors close to the surface of the sea to facilitate easy access for O&M, the rotor in the shape of a modified X is preferred to a V or H.

2.4. Control

During below-rated operation, the controller of the X-rotor is required to maximise energy capture. By varying the frequency of the electrical connection to the generators and so their rotational speed, the secondary rotors are controlled to maintain a constant tip speed ratio. Consequently, their thrust will vary as the square of the secondary rotor rotational speed, as does the retarding torque the secondary rotors apply to the primary rotor. In a similar fashion to the control of the rotor of a variable-speed HAWT in below-rated operation, the tip speed ratio of the primary rotor is kept close to the value at which its power coefficient is a maximum.

During above-rated operation, the controller is required to maintain a constant rotational speed and torque/power of the primary rotor by varying both the rotational speed of the secondary rotors and the pitch angle of the upper blades of the primary rotor. The pitch angle is controlled to maintain a constant rotational speed of the primary rotor, thereby also keeping constant the wind speed incident on the secondary rotors. The rotational speed of the secondary rotors continues to be controlled to maintain a constant tip speed ratio, thereby keeping the retarding torque the secondary rotors apply to the primary rotor constant. Consequently, the torque of the primary rotor is kept constant as well as the rotational speed.

Since the inertia of the secondary rotors is low, their response time is sufficiently fast that the tip speed ratio can be kept constant at all times; that is, in addition to varying with the ambient wind speed acting on the turbine, the rotational speed of a secondary rotor would vary with the azimuthally dependent incident wind speed. The most significant component of the latter is due to the secondary rotor rotating into and out of the ambient wind; that is, the $1P$ component, $Vcos{\theta }_P$, where ${\theta }_P$ is the azimuthal angle of the primary rotor. The total wind speed incident on the secondary rotor is

$$V_I\approx \left({\overline{V}}_I+Vcos{\theta }_P\right)={\overline{V}}_I(1+{\lambda }_p^{-1}cos{\theta }_P)$$

(5)

where ${\overline{V}}_I$ is the average incident wind speed over one revolution. Since the average over one revolution of ${(1+{\lambda }_p^{-1}cos{\theta }_P)}^2$ is

$$\overline{{(1+{\lambda }_p^{-1}cos{\theta }_P)}^2}=(1+{\displaystyle \frac{1}{2}}{\lambda }_p^{-2})$$

(6)

and average of ${(1+{\lambda }_p^{-1}cos{\theta }_P)}^3$ is

$$\overline{{(1+{\lambda }_p^{-1}cos{\theta }_P)}^3}=(1+{\displaystyle \frac{3}{2}}{\lambda }_p^{-2})$$

(7)

the ratio of power conversion of the secondary rotor to that of the first is increased by a factor $(1+{\displaystyle \frac{3}{2}}{\lambda }_p^{-2})/(1+{\displaystyle \frac{1}{2}}{\lambda }_p^{-2})$; that is, the efficiency of power conversion is increased to

$$({\displaystyle \frac{C_{Ps}}{C_{Ts}}})(1+{\displaystyle \frac{3}{2}}{\lambda }_p^{-2})/(1+{\displaystyle \frac{1}{2}}{\lambda }_p^{-2})$$

(8)

This increase in efficiency is automatically realised by the control strategy of keeping the tip speed ratio of the secondary rotors constant. The associated increase in the primary rotor torque by a factor, $(1+{\displaystyle \frac{1}{2}}{\lambda }_p^{-2})$, is relatively modest.

Additional options for control include the following:

(1)

In above-rated conditions, switch control of the secondary rotors from maintaining a constant tip speed ratio to maintaining a constant rotational speed. Although the total power generated would no longer vary with wind speed, there would be little reduction in the primary rotor torque.

(2)

In below-rated conditions, vary the pitch cyclically to increase the efficiency of the primary rotor by possibly 5% [9]. It would be straightforward to estimate the azimuthal angle of the primary rotor from the cyclically varying power generated by each secondary rotor.

(3)

In above-rated conditions, vary the pitch cyclically to reduce loadings on the blade while achieving only a slightly lower efficiency [10].

2.5. Power Converter System

The power electronics, while delivering the combined power output from the secondary rotor generators at a frequency to match the wind power network, are required to enact the controller demands to vary the frequency of the power connection to the generators. The frequency of each secondary rotor is varied independently over a wide range. Because of their higher efficiency, synchronous generators would be preferable to induction ones, in which case the power electronics might be required to supply damping.

2.6. O&M

A key innovation of the X-rotor concept is the significant reduction in O&M costs achieved. The X-rotor concept does not have any machinery at a large height above sea level, such as the nacelle on a tall tower in a HAWT. The power electronics are housed in the hub at the centre of the primary rotor, thereby being readily accessible. The main bearing is similarly housed at a substantially lower height than in a comparable HAWT. One possibility is that the main bearing could be lowered, leaving the primary rotor independently supported, to improve access for repair and maintenance. The power take-off systems are housed at the ends of the lower blades of the primary rotor, and their components are very much lighter than those of the drive-train for a comparable HAWT. Consequently, access to the power take-off systems would be readily available without the need for specialist and expensive heavy-lift vessels. Indeed, since each power take-off system would only weigh a few tonnes, it would be possible to carry out onshore maintenance by detaching a power take-off system and replacing it with a fresh unit. This possibility for carrying out onshore maintenance, through the secondary rotors being detachable, would lead to improved Health and Safety for service technicians as well as improved wind turbine availability. Improved wind turbine availability would be driven by the fact that technicians would not need to remain at the turbine for long periods to complete maintenance offshore. Shorter visits would allow for shorter accessibility windows to be used. This in turn will increase availability.

A further consideration relevant to O&M costs for a large-scale X-rotor turbine with multiple secondary rotors is that, in the event of failure of one secondary rotor, it would potentially be possible to continue operating the turbine while awaiting repair. Of course, the implications for loads and control of the turbine would need to be fully assessed.

2.7. Integrated X-Rotor Design

The design space pertaining to the choice of configuration for the X-rotor is restricted by the direct-drive nature of the secondary rotor-based power take-off. In general, the limits on the secondary rotor speed (imposed by the drive-train) combine with a maximum tip speed limit to define the maximum radius of the secondary rotor. This requirement restricts the combined tip speed ratios of the primary and secondary rotors to below 15 for rated wind speeds of approximately 12.5 m/s. In order to achieve efficient power conversion, the primary rotor tip speed ratio should also be sufficiently high to reduce the required axial induction factor of the secondary rotors. This, in turn, defines a limited range of primary rotor configurations for efficient power takeoff and associated power capacity.

3. Baseline 5 MW Wind Turbine Designs for the X-Rotor

This section introduces a pair of exemplar X-Rotor designs with 2 and 3 blades; both machines share a power rating of 5 MW. There are few possibilities for alternative designs of the X-Rotor wind turbine, with the number of blades on the primary rotor a key variable. The rationale behind increasing the blade number is to distribute the imposed aerodynamic loads over a higher number of blades to reduce and smooth the loads on other rotor elements and other structural elements. However, it should be noted that increasing the number of blades increases the number of components (primary blades, secondary rotors) and the crossarm complexity. Consequently, the number of failure modes may be increased with an associated reduction of the system reliability. Additionally, each individual blade is subject to larger bending stresses as the blade number increases, a consequence of the second moment of area decreasing faster than the aerodynamic force as the chord length is reduced. In this context, both a two-bladed and three-bladed X-Rotor design have been considered at this early stage.

The geometry for each turbine design is provided in

Table 1. Primary rotor geometry for the 5 MW X-Rotor turbine.

	Rotor	Cone Angle [deg]	Chord (Root) [m]	Chord (Tip) [m]	Thickness (Root) [%]	Thickness (Tip) [%]
Two Bladed	Upper	30	10	5	25	8
	Lower	50	14	7	25	8
Three Bladed	Upper	30	6.67	3.33	25	8
	Lower	50	9.33	4.67	25	8

. The rotor blades use symmetric NACA aerfoil sections (NACA00XX) with a linear taper in chord and relative thickness between the blade root and the blade tip; see Table 1. The blades are untwisted. The blades are designed in such a way that the distances between the pivoting line of the blades and the leading edge are kept constant along the blades. The leading edges are thus positioned on a straight line, whereas the trailing edges form an inclined line along the blades. From Table 1, it is clear that the three-blade X-Rotor variant has a chord length scaled at 66% (2/3) of that of the two-blade in order to maintain rotor solidity across the designs.

This section introduces two exemplary 5 MW turbine designs, a two-bladed configuration and a three-bladed configuration. The operational regime of each turbine is discussed in Section 3.1 alongside the aerodynamic load calculations. Section 3.2 gives an overview of the structural design of the rotor, and Section 3.3 details the structural design of the sub-structure. Finally, Section 3.4 introduces the secondary rotor design and discusses the power capture from each turbine.

3.1. Turbine Operational Regime and Aerodynamic Loads

The turbine is designed to operate between mean wind speeds of 4 m/s and 25 m/s, with a rated wind speed of 12.5 m/s. In below-rated conditions, the primary rotor is operated at a constant tip speed ratio (variable rotational speed) to ensure maximum power tracking, and, in above-rated conditions, the upper blades of the primary rotor are pitched cyclically to maintain a constant primary rotor speed. The maximum pitch rate is limited to 3 deg/s. The pitching strategies at 3 operating points for the two-bladed and three-bladed designs are shown in Figure 3. The blades are pitched to stall in both the upwind and downwind sectors of the rotor sweep, leading to nose-in pitching for $0\le \theta <180$degrees and nose-out pitching for $180\le \theta <360$ degrees, where $\theta$ is the azimuth angle with $\theta$ being 0 degrees when the blade is fully upwind. Simulation of the operational loads is performed at wind speeds of 4.5, 6.5, 8.5, 10.5, 12.5, 14.5, 16.5, 18.5, 20.5, 22.5, and 25 m/s. The details of the primary rotor operating points for each load case are given in

Table 2. Operating points for the 5 MW X-Rotor turbine.

Load Case	Wind Speed [m/s]	Rpm		Pitch Amplitude [deg]
		2-Blade	3-Blade	2-Blade	3-Blade
1	4.5	2.88	2.7	0	0
2	6.5	4.16	3.9	0	0
3	8.5	5.44	5.1	0	0
4	10.5	6.72	6.3	0	0
5	12.5	8	7.5	0	0
6	14.5	8	7.5	3.5	3
7	16.5	8	7.5	3.5	2.7
8	18.5	8	7.5	3.15	2.4
9	20.5	8	7.5	2.75	2
10	22.5	8	7.5	2.3	1.7
11	25	8	7.5	1.8	1.1

.

The aerodynamic simulations of the primary rotor are undertaken using the free vortex wake solver in QBlade CE v2.0.6.4. The rotor is discretised into 18 panels for each blade (72 for the full rotor), and simulations were completed for 10 rotor revolutions, at which point the power coefficient was observed to have converged with a residual of $1\times {10}^{-3}$. These simulations ignored both the tower and the cross arm. As the secondary rotors are attached below the blade tips of the lower rotor, the influence of the secondary rotor wake on the primary rotor aerodynamics is also not considered in these simulations.

The power curve for two-bladed and three-bladed X rotors is shown in Figure 4, and the instantaneous streamwise thrust loading on the rotor for load cases 4, 5, and 6 is shown in Figure 5.

The rated aerodynamic power of the primary rotor is 6 MW for both the 2-bladed and 3-bladed configurations. Considering the efficiency of the power transfer to the secondary rotors and the drive-train components, a 5 MW power rating can be readily achieved (83.33% efficiency required). At rated wind speed, the power contribution from the upper and lower rotors is split with a 2:1 ratio for both the 3-bladed and the 2-bladed designs. However, the maximum contribution from the lower rotor occurs at 25 m/s for the 2-bladed rotor (5:1) and at 22.5 m/s (3:1) for the 3-bladed rotor. This occurs as the 3-bladed lower rotor stalls at a lower windspeed than the 2-bladed lower rotor, as it is operating at a lower rotor speed (and tip speed ratio). This effect also explains why the pitch amplitude is required to be larger for the 2-bladed design, as more power must be shed from the upper rotor.

The load balancing from a 3-bladed primary rotor is clearly demonstrated by Figure 5, with a significantly smaller amplitude visible for the 3-bladed primary rotor. The number of load cycles per revolution is also clear, with a 2P load visible for the 2-bladed rotor and a 3P load visible for the 3-bladed rotor. Both rotors have a similar mean thrust level at each operating point.

3.2. Structural Analysis of Primary Rotor Blades for Two-Blade Design

3.2.1. Primary Rotor Blade Design

The primary rotor blades consist of symmetric aerfoil profiles, which are strengthened by two spar caps that take most of the bending loads. The spar caps are connected by two parallel shear webs, and the blade shell is reinforced at the leading and trailing edges. In Figure 6, the layout of blade internals at an arbitrary cross-section is indicated. The mechanical properties of the blade components, including the spar caps, shear webs, edge reinforcements, and blade shell, are given in

Table 3. Mechanical properties of blade components.

	Shell	Spar Cap	Reinforcement	Shear Webs
Property	Triaxial	Uniaxial (CF)	Uniaxial (GF)	Biaxial
E11 [GPa]	21.790	115.00	41.630	13.920
E22 [GPa]	14.670	7.560	14.930	13.920
ν12 [-]	0.478	0.30	0.241	0.533
G12 [GPa]	9.413	3.96	5.047	11.500
Ρ [Kg/3]	1845.000	1578	1915.000	1845.000
σ11-Ten [MPa]	480.400	1317.60	876.100	223.200
σ11-Comp [MPa]	393.000	620.13	625.800	209.200
σ22-Ten [MPa]	90.400	21.88	74.030	223.200
σ22-Comp [MPa]	152.700	76.25	189.400	209.200
τ12 [MPa]	114.000	45.53	56.580	140.300

.

According to the wind turbine design guidelines [13,14], the wind turbine blade structure should be able to pass the following checks: ultimate strength, buckling, fatigue, and deflection. The deflection check refers to the clearance between the tip of the blade and the tower for horizontal-axis turbines. Due to the configuration of X-Rotor, this check is irrelevant as there are no feasible scenarios in which tower strikes could occur. The deflection values of the blade tips should still remain limited, since unfavourable aerodynamic damping might occur. Additionally, since the tensile and compressive strains under operational loads at the highest mean wind speed, namely 25 m/s, are lower than those under extreme loads (detailed in Section 3.2.3), the design guidelines render a detailed fatigue check unnecessary.

3.2.2. Ultimate Limit State Analysis

The rotor blades need to have sufficient strength under extreme loads. The extreme loads correspond to the extreme wind speed of 52 m/s with a 50-year recurrence period while the turbine is in the parked position, and simultaneous loss of grid connection may occur (DLC 6.2 of IEC 61400-1 [13]). Thus, there is the possibility of the turbine being caught in a locked position with the wind blowing parallel to the rotor plane. To simulate this situation, ANSYS CFX [15] is used to obtain the blade loads through CFD analysis [15]. In this analysis, the turbine’s body is modelled as a void inside a tunnel, which determines the airflow boundaries. For computational efficiency, considering the significantly large scales of the turbine, an interface is defined between the turbine and the tunnel. The interface incorporating the turbine has a much finer mesh in comparison to that of the tunnel in order to have a reasonable simulation runtime.

Figure 7 depicts the CFD model of X-Rotor embedded in the modelled boundary conditions, and Figure 8 shows the streamlines of the air flow passing through the turbine. The resulting blade moments are given in

Table 4. The extreme values for flap and edge bending moments.

Blade	Two-Bladed		Three-Bladed
	Flap [MNm]	Edge [MNm]	Flap [MNm]	Edge [MNm]
Upper	79.6	3.12	50	0.7
Lower	45.4	2.26	26.5	0.41

. In parked positions, where the extreme load occurs, the blade acts like a barrier against the wind, and consequently, the loads (mainly drag) are quite proportional to the chord length. Comparison of the extreme blade loads demonstrates that the extreme loads of the three-blade version are about 2/3 of those of the two-blade version, i.e., proportionate to the chord length ratios between the three- and two-blade versions.

The pre-dimensioning of the cross-sections of the blades is performed by imposing that the stress in the material is not to exceed the allowable value under the extreme loads. A partial safety factor of 1.35 is chosen for loads [13], and for the short-term verification, the partial safety factor for material is set to 1.2 [14].

The blade is divided into 17 segments. Thus, there are 18 sections analysed under loading. The blade sections start with NACA 0025 at the root and end with NACA 0008 at the tip. Pre-dimensioning of blade internals is performed for each section where the aerofoil profiles are changing. The bending and edge moments are computed for each section using ANSYS CFX [15]. Subsequently, for each section, a finite element (FE) model of the blade section with a constant cross section is developed in ANSYS Mechanical [15] using shell elements (see Figure 9). The model consists of a beam with a constant section modelled with shell elements. One end is clamped, and the other end is loaded with corresponding flap and edge moments. The load is applied via a rigid region with a master node. At the midsection of the model, the stress state corresponding to the real situation is reproduced. The beam is chosen to be sufficiently long that the influences of clamped support and concentrated loads fade away in the middle of the beam.

According to [13], a structure whose load-bearing laminate consists of unidirectional carbon-fibre reinforcement layers may, with regard to short-term and fatigue strength, qualify for a simplified strain verification, provided a high laminate quality can be verified. The simplified strain verification states that the strain along the fibre directions shall remain below the following design values: tensile strain ${\epsilon }_{Rd,t}\le 0.24\%$ and the compressive strain ${\epsilon }_{Rd,c}\le \left|-0.18\right|\%$.

Dimensions are adopted such that the above strain constraints are fulfilled together with the stress criteria. Therefore, there is no need for a detailed fatigue check under these circumstances, and the rigidity condition is fulfilled a priori.

For all sections, the position of the internals relative to the leading edge is

Leading edge reinforcement ends at 1% of the chord;

Spar caps start from 15% and end at 47% of the chord;

Shear webs are equally spaced inside the spar caps;

The trailing edge reinforcement begins at 99% of the chord.

The locations of the internals are determined such that the spar caps are positioned to achieve maximum bending resistance, whilst keeping the mass as low as possible.

Figure 10 represents the normal stress failure criterion and strain distribution for the lower blade root section (profile NACA 0025) for the two-bladed design. The failure criterion requires the ratio between existing and allowable stress to be set below one. However, here, for additional safety measures, the stress ratio in all upper and lower blade sections does not exceed 0.8. As expected, the most stressed component is the spar caps. Moreover, all sections are dimensioned so as to have strain values less than 0.18%.

As a consequence of the initial blade design, the masses obtained for each upper and lower blade and the rotor are given in

Table 5. Details of blades/rotor mass.

Variant	2-Blade Design [kg]	3-Blade Design [kg]
Upper blade	40,500	39,947
Lower blade	23,384	16,266
Upper rotor	81,000	104,841
Lower rotor	46,768	48,798
Total rotor	127,768	153,639

. The full-scale finite element models of the blades are developed based on the dimensions given in Appendix A. These are then used for the rest of the analysis. Based on the above information, a two-bladed X-Rotor would have a primary rotor mass of 127,768 kg, and the 3-blade X-Rotor would have a primary rotor mass of 153,639 kg. As mentioned earlier, the blade dimensions of the three-blade variant are downscaled with respect to those of the two-blade variant, whereas the aerfoil profiles are kept the same. This implies that the blade section modulus of the three-blade variants is reduced by a third order of magnitude. As such, the spar cap’s thickness has to be increased proportionately to preserve the section’s strength. Consequently, despite lower loads on each blade of the three-blade design in comparison to those of the two-blade variant, the three-blade design has a heavier rotor.

3.2.3. Buckling Verification

Finite element models are developed for the blades, using beam elements, with each of the 17 blade elements represented by an average of the initial and final sections. The extreme load is applied as pressure on each element. For the lower blade, a concentrated mass is put at the tip to simulate the nacelle of the secondary rotor. According to the design guidelines, a partial material safety factor of 1.85 is applied in order to determine the design values of the components’ stability strength [14].

For the initial check, the buckling eigenvalue analysis, accounting for the first five modes, is performed (see

Table 6. Buckling load factors of the two-bladed and three-bladed X-Rotor variants.

Mode Number	Buckling Load Factor
	Two-Bladed Design		Three-Blade Design
	Upper Blade	Lower Blade	Upper Blade	Lower Blade
1	2.7	9.9	3.6	7.3
2	4.6	15.9	6.7	12.2
3	6.4	23.6	10.0	17.7
4	8.6	31.8	13.4	23.5
5	10.9	41.1	16.9	30.0

). The resulting buckling load factors of the upper and lower blades are so high that the blades will not become unstable under the extreme loads, and as such, nonlinear buckling analysis is not considered to be necessary at this early design stage.

3.2.4. Modal Analysis and Dynamic Response Simulation

For the analysis of the blades’ natural frequencies, a concentrated mass of 10 tonnes is added at the lower blade tip to account for the presence of the secondary rotor. The secondary rotor’s moment of inertia is neglected due to its substantially smaller dimensions relative to those of the primary rotor. The first four upper and lower blades’ natural frequencies for the two-bladed and three-bladed designs are given in

Table 7. The eigenfrequencies of the upper blade (left) and a lower one (right) for the two-bladed design.

Mode Number	Natural Frequencies [Hz]
	Two-Bladed Design		Three-Bladed Design
	Upperr Blade	Lower Blade	Upper Blade	Lower Blade
1	0.60	0.52	0.47	0.35
2	0.69	0.77	0.66	0.60
3	1.59	2.61	1.12	2.02
4	1.82	2.70	1.83	2.31

. The blades of the three-bladed rotor have lower natural frequencies than those of the two-bladed rotor due to its higher mass.

It is important that the natural frequencies of the blade do not coincide with the operational harmonic frequencies. A Campbell diagram for rotor blades, Figure 11a, shows that there is a near coincidence between the first lower blade natural frequency and the 4P harmonic within the operational regime of the turbine for the two-blade design; the first natural frequency of the upper blade is also very close to the 4P frequency at the rated rotor speed of 0.838 rad/s (8 rpm). The blades would need to be stiffened to avoid exciting this frequency in future work. For the 3-bladed variant, harmonics up to 6P must be considered, and the blades have a lower natural frequency due to their more slender nature. For these reasons, there are more crossings between the structural frequencies and the operational frequencies. A resonance from the 3P harmonic at 0.733 rad/s (7 rpm) for the lower blade is apparent; this could be mitigated through stiffening of the lower blade. Further higher-order excitations of the upper and lower blade modes are also visible at lower rotational speeds. For these cases, control measures should be implemented to mitigate excessive damage from mode excitation. To avoid rotational speeds where resonance will occur, the machine should pass rapidly through that rotational speed, operating at 10% below or above. Implementing this solution is left to future work.

Simplified, uncoupled models of the blades are developed for modal analysis and dynamic response simulation with no coupling between the blades, connecting crossbeam, and the support structure. A coupled model of the rotor would be necessary for a more detailed analysis to assure avoidance of resonance across the rotor’s operational speed range. However, modal analysis of the isolated blade model seems to be adequate for this feasibility study.

The dynamic response of the blades is evaluated using FE blade models under aerodynamic loads applied as tangential and normal pressure components. Figure 12 depicts the displacement of the blade tip corresponding to the rotor operation at a rated wind speed of 12.5 m/s for the 2-bladed design. This figure shows that, after the initial transient response decays, the upper blade reaches a maximum displacement of around 8 m. For the lower blades, the corresponding displacement is less than one meter, about 0.9 m. It is expected that excessive aerodynamic damping would be quite unlikely at these displacements.

The tip displacement of the upper and lower blades of the three-blade design is presented in Figure 13, with the rotor operating at a rated wind speed of 12.5 m/s. The larger tip displacements presented here indicate that the blade tip displacement of the three-blade design might need to be reduced.

There are several options to optimise the blade pre-dimensioning and improve the performance of the three-bladed variant. The most direct would be to design the rotor with thicker aerfoil profiles. Currently, the blade’s cross-section begins with NACA0025 at the root and reduces linearly to NACA08 at the tip. However, increasing the relative thickness by 5% at each blade section would significantly reduce the bending stresses without compromising aerodynamic performance. Additionally, a more aggressive taper in the blade chord could provide more stiffness at the blade root. Further optimisation tasks are required to determine the most suitable solution but are out of the scope of this paper.

A frequency domain analysis was also performed to determine the dominant frequencies contained in the blades’ dynamic response for the two-blade variant. The response power spectrum plots for the upper and lower rotors’ displacements are shown in Figure 14. On both plots, the first four peaks correspond to the first 4 blade passing frequencies, 1P to 4P, at rated wind speed. Note that the first peak occurs at the frequency of 0.13 Hz, which corresponds to the rotor speed at 0.838 rad/s (0.133 Hz). On the upper blade, the 4P peak is higher than the 2P and 3P peaks due to its close proximity to the upper blade’s first vibrational mode, visible in the Campbell plot in Figure 11. For the lower blade, the excitation of the first structural blade mode can be seen as a wide peak that pushes up the 3P and 4P peaks.

3.3. Rotor Loads on Tower and Substructure

The cost of the offshore substructure and foundation is reportedly 14% of the total project capital cost; it would be even higher when the tower cost is taken into account [16,17]. Therefore, it is important to compare the performance of both X-Rotor variants as related to the loads they impose on the support structure. In this subsection, the impact of the X-Rotor’s aerodynamic loads on the design of the tower and substructure is investigated.

The X-Rotor is assumed to be installed at a water depth of around 50 m. According to the literature, jacket structures are preferred in terms of structural performance and cost efficiency for water depths greater than 30 m [18,19]. Considering tripod and jacket structures as the possible options for the proposed water depth, the jacket is the most suitable support structure for the assumed offshore conditions for 5 MW turbines. Jacket structures with four legs have some advantages over three-legged ones, for instance, larger angles between the legs and braces for manufacturing detailing and smoother transfer of the loads into the seabed [20]. Therefore, a four-leg jacket constitutes a suitable choice for hosting the X-Rotor. The schematic picture of the two-blade X-Rotor wind turbine, including its substructure, is represented in Figure 15. The aim of this subsection is to compare the impact of the two- and three-blade variants’ loads on the substructure global design, rather than the detailed design of the substructure.

As discussed in relation to Figure 5, the X-Rotor with a 3-blade design imposes operational thrust loads with significantly lower ranges within each loading reversal in comparison to those of the two-blade variant. However, the three-blade design applies three reversals in one complete rotor revolution, as opposed to two reversals for the two-blade variant. Fatigue damage is exponentially proportional to the stress range, whereas it is linearly proportional to the number of reversals. As such, the imposed fatigue damage on the substructure associated with the three-blade concept’s operation is expected to be less than that of its two-blade counterpart.

The X-Rotor’s substructure must be designed such that any structural resonance is avoided. The augmented Campbell plot of the two- and three-blade X-Rotor variants is presented in Figure 16. According to this figure, a stiff-stiff substructure must be selected due to the overlapping interval of operational harmonic peaks for the two- and three-blade variants. The design of the jacket is a two-stage procedure, that is, selection of the jacket’s global dimensions (upper and lower width) that substantially influence the jacket’s eigenfrequencies and then choosing the cross sections of the jacket components. For the initial design of the jacket, the dimensions of the Upwind jacket reference structure [20] are adapted to develop a finite element model of the X-Rotor’s substructure in ANSYS [15]. The Upwind reference structure is a four-leg jacket with four X-braces on each side. The Upwind jacket reference structure was originally designed to host a typical 5 MW horizontal-axis wind turbine. As such, modification of the initial jacket’s sections and dimensions to host the X-Rotor with a rated power a little higher than 5 MW is deemed necessary. The Upwind substructure has its first natural frequency at about 0.3 Hz, which may be suitable for the two-blade variant but is not obviously appropriate for the 3-blade X-Rotor design, according to Figure 16. The selection of the final substructures’ dimensions and their associated natural frequencies are subsequently discussed below.

The tower and jacket design are driven by the ultimate strength requirements based on the limit state analysis, specifically when the turbine is in a parked position and undergoes extreme wind loads. In this analysis, the resultant aerodynamic loads at the centre of the cross-beam, derived from blade forces, are applied to the tower top.

Table 8. Comparison of X-Rotor variants’ extreme loads on substructure.

X-Rotor Variant	Fx [N]	Fy [N]	Fz [N]	Mx [Nm]	My [Nm]	Mz [Nm]
2-blade	−54,871	−106,315	−3.79 × 106	−6.34 × 107	−1.07 × 107	861,663
3-blade	−32,899	27,572	−2.52 × 106	−3.54 × 107	−4 × 106	1.14 × 106

presents the extreme aerodynamic loads transferred to the substructure at tower top from the two- and three-blade variants, which correspond to rotor loads in parked position under extreme wind speed. The associated reference coordinate systems of the substructure loads are illustrated in Figure 17. According to Table 8, X-Rotor with a 3-blade design imposes considerably lower extreme loads on the substructure.

As previously explained, the aerodynamic loads are obtained using rigid structural rotor components. Rotor aeroelasticity, or rotor-substructure coupling, is neglected. Nevertheless, this is sufficient for comparison of the two- and three-blade concepts and assessing their potential impact on the support structure prior to a detailed rotor design. The wind direction is set to align with the diagonals of the jacket square cross sections, as higher stresses arise with this choice. Partial load and material safety factors of 35% and 20% are applied here, respectively. The allowable stresses are reduced by an additional 35% as a reserve for the hydrodynamic loads for ultimate state analysis. It is known that the wave load does not have a considerable contribution to the substructure’s fatigue damage compared to the damage caused by the turbine’s operational loads [21]. From this analysis, the cross sections of the Upwind jacket reference structure need to be increased to meet the failure criterion for both two- and three-blade variants.

For the fatigue analysis of the tower and jacket, a representative site in Stornoway is chosen. The Weibull distribution for the wind speed over the 20-year lifetime of the turbine is shown in Figure 18. The cycle number is calculated for the Weibull distribution and the operational strategy (noting that the two-blade and three-blade variants impart 2 and 3 load cycles per revolution, respectively).

The stress ranges are calculated by applying the resultant shear forces and overturning moments at cross-beam height (tower top) for each wind speed and converting these into stresses at the critical joint. The critical nominal stresses associated with the unit loads (shear and bending) are obtained using the developed finite element models. The variation of the stresses at different wind speeds is then applied by scaling the unit load stresses with respect to the time histories of the operational loads within one complete rotor revolution, essentially applying a linear approximation. Only the streamwise loading is considered in the fatigue analysis, as the cross-stream loads occur out of phase with the streamwise loads, indicating that there will not be a significant contribution to the amplitude of the stress cycles. Using the methodology from Eurocode 3 [22]. The total damage corresponding to 20 years of operation is obtained. The S-N curve is selected with a detail category of 90. A partial safety factor of 1.15 is used for the detail category, corresponding to safe life—low consequence; and a partial safety factor of 1.1 is used for the conversion of the loads to stress ranges.

The results from the fatigue analysis indicate that the initially designed jacket structure for the two-blade variant (designed for extreme wind loads) cannot provide the 20-year lifetime due to excessively large stresses in jacket legs. Consequently, the fatigue criterion is the driver for the substructure design of the 2-blade variant. There are two options available to increase the fatigue strength of the jacket: enlarging the jacket dimensions (upper and lower jacket widths) or selecting larger cross-sections for jacket components. Increasing the jacket’s geometrical dimensions can increase the installation cost, while increasing cross-sections raises the manufacturing cost. Here, a combination of these two options is adopted, i.e., enlarging the jacket widths by 2.5 times the original Upwind design and increasing the jacket legs’ cross-sectional areas by 20%. To avoid stability issues and large local mode shapes’ deflection of the brace elements, the cross-sections of the braces are also increased.

For the three-blade variant, the original dimensions are suitable for the three-blade X-Rotor since the operational loads are considerably more benign than those of the two-blade variant. Thus, the extreme loads drive the design of the substructure for the three-bladed X-Rotor variant.

Table 9. Normal stresses (MPa) at critical points of support structures under unit loads for fatigue damage analysis.

	Two-Blade		Three-Blade
	Unit Force [1 × 106 N]	Unit Moment [1 × 107 NM]	Unit Force [1 × 106 N]	Unit Moment [1 × 107 NM]
Jacket leg	14.5	1.8	55	6
Tower	22	4	65	12

presents the most critical normal stresses under the unit forces and moments for those support structures that pass the lifetime fatigue control based on the above-mentioned methodology. The stress range, cycle count, and damage accumulated at each load case are shown in

Table 10. Fatigue calculation for X-Rotor variants’ support structure.

Load Case	Cycle Count [Million]		Stress Range		Damage
	2-Blade	3-Blade	2-Blade	3-Blade	2-Blade	3-Blade
1	8.60	12.13	4.34	2.40	0	0
2	14.22	20.05	9.05	4.26	0	0
3	18.04	25.42	15.49	7.32	0	0
4	19.10	26.90	23.64	11.18	0	0
5	17.57	24.70	33.48	16.56	0.23	0
6	12.35	17.36	36.29	28.58	0.24	0
7	7.69	11.19	37.03	34.19	0.17	0.16
8	4.73	6.65	38.79	38.56	0.13	0.18
9	2.60	3.65	41.44	41.31	0.10	0.14
10	1.32	1.86	44.63	43.82	0.07	0.09
11	0.51	0.72	49.46	46.61	0.05	0.05
Total	106.99	150.64	-	-	0.999	0.62

. The dimensions of the jackets and towers, as well as the associated support structures’ first natural frequencies, are given in

Table 11. Properties of X-rotor variants’ support structure.

	Tower Base Outer Radius [m]	Jacket Upper Width [m]	Jacket Lower Width [m]	Jacket Mass [×103 kg]	First Natural Frequency [Hz]
2-blade	3.79	8.00	12.00	940	0.77
3-blade	2.60	20.00	30.00	655	0.45

.

Comparison of the stresses at critical locations of the support structures, shown in Table 9, demonstrates that the two-bladed design requires much lower levels of stress, equivalently higher strength for structural components, in order to provide the 20-year fatigue life. The fatigue-driven design of the jacket for the two-bladed variant means the lifetime damage approaches the critical value. However, for the three-bladed variant, the lifecycle damage is considerably below the critical value. Comparing Table 11 and Figure 16, the natural frequencies of X-Rotor support structures are located within the allowable frequencies.

Since the imposed loads for the two-bladed variant are larger than its three-bladed counterpart, the two-bladed turbine’s jacket is consequently expected to be heavier. The results show that the mass of the three-bladed turbine’s jacket is about 70% less than that of the two-bladed variant. Taking into account the higher power production of the X-rotor primary rotor, it is similar to the mass of the initial Upwind jacket reference structure (545 tonnes) [20]. However, it should be noted that further detailed structural optimization is required to identify the optimal jacket dimensions and cross sections [21,23]. Another interesting point to mention is the fact that the three-blade X-Rotor variant’s total rotor mass is 1.2 times that of its two-blade counterpart, but its support structure is remarkably lighter. Therefore, there is room for further studies to find the optimal X-Rotor designs, using the coupled X-Rotor–support structure models and incorporating ecological and environmental aspects in addition to the CoE issues.

3.4. Secondary Rotor Design

As previously discussed, the secondary rotors must be designed to be compliant with maximum tip speed limits yet must rotate at a sufficient speed to facilitate the use of small direct drive generators. Imposing a maximum tip speed of 184 m/s and a rated rotor speed of 39.1 rad/s limits the maximum secondary rotor radius to 4.7 m and the maximum swept area to 69 m². The average thrust required from each secondary rotor is 48 kN in the case of the 2-bladed design and 34 kN in the case of the 3-bladed design. This corresponds to a thrust coefficient of 0.28 and 0.2, respectively, and an axial induction factor of 0.09 and 0.07 (including tip losses). Treating the secondary rotors as an actuator disc, this would represent a possible conversion efficiency of 91% and 93%, respectively. However, more realistically treating the rotors as optimally designed 5-bladed rotors with a flat induction distribution, a design lift-to-drag ratio of 100, and a hub radius of 0.4 m, the maximum achievable conversion efficiency drops to 86% and 89%, respectively. This implies a rated power of 5.18 MW and 5.36 MW for 2- and 3-bladed designs before considering additional losses from the power-train.

4. O&M Cost Analysis

A key innovation of the X-rotor concept is the potential for significant reduction in O&M costs. The X-rotor concept does not have components at the top of a tall tower, as in existing HAWTs. The power electronics are housed in the hub at the centre of the primary rotor, thereby being readily accessible. The main bearing is similarly housed at a substantially lower height than in a comparable HAWT. The power take-off systems are housed at the ends of the lower blades of the primary rotor, and their components are very much lighter than those of the drive-train for a comparable HAWT. Consequently, access to the power take-off systems would be readily available without the need for specialist and expensive heavy-lift vessels. Indeed, since each power take-off system would only weigh a few tonnes, it would be possible to carry out onshore maintenance by detaching a power take-off system and replacing it with a reconditioned unit. This possibility for carrying out onshore maintenance, through the secondary rotors being detachable, would lead to improved Health and Safety for service technicians as well as improved wind turbine availability. Improved wind turbine availability would be driven by the fact that technicians would not need to remain at the turbine for long periods to complete maintenance offshore. Shorter visits would allow for shorter accessibility windows to be used. This, in turn, will increase availability. A further consideration relevant to O&M costs for a large-scale X-rotor turbine with multiple secondary rotors is that, in the event of failure of one secondary rotor, it would potentially be possible to continue operating the turbine while awaiting repair. Of course, the implications for loads and control of the turbine would need to be fully assessed. One of the biggest O&M cost savings relative to existing wind turbines is that the X-Rotor does not contain either of the two components that contribute most to offshore wind turbine downtime, namely the gearbox and/or a multi-pole generator. Additionally, the X-Rotor does not require a jack-up vessel for drive train failures, substantially reducing O&M vessel costs.

For X-Rotor maintenance costs to be compared to existing offshore wind turbines, the O&M costs for the X-Rotor must first be calculated. A comparison to O&M costs for existing wind turbine types can then be carried out. The following subsections outline the methodology and results obtained from comparing the X-Rotor O&M costs to the O&M costs for existing offshore wind turbines.

For X-Rotor maintenance costs to be compared to existing offshore wind turbines, the O&M costs for the X-Rotor must first be calculated. A comparison to O&M costs for existing wind turbine types can then be carried out. The methodology and results obtained from comparing the X-Rotor O&M costs to the O&M costs for existing offshore wind turbines are outlined below; for further details, see [8].

A hypothetical site is used for each wind turbine type in the comparison to ensure a like-for-like comparison. The site contains the same environmental (wind speed and sea state) conditions for each turbine type compared and is located 50 km from shore. The lifetime O&M costs for the X-Rotor were calculated using the same methodology and O&M cost model from [24,25]. The model is a time-based simulation of the lifetime operations of an offshore wind farm. A Monte Carlo Markov Chain is used to implement failure behaviour, and maintenance and repair operations are simulated based on available resources and site conditions. The model determines accessibility, downtime, availability, maintenance resource utilisation, and power production of the simulated wind farms. The model outputs for this work were the operations and maintenance costs for a hypothetical wind farm located 50 km offshore, consisting of 100 X-Rotor offshore wind turbines. The model inputs are adjusted to represent the X-Rotor as detailed in the following paragraphs.

The site environmental and sea state data required for the model included wind speeds, wave height, and wave period data. Data are taken from references [24,25,26,27]. Component failure rate, repair times, repair costs, and “number of technicians required for repair” inputs were obtained from an empirical analysis of existing operational wind turbines as detailed in [24,27,28]. Inputs were assumed to be the same for common wind turbine components between the X-Rotor and existing wind turbines, such as the tower, blades, pitch system, etc. An example of inputs that differed from existing wind turbines is the gearbox failure rate, repair times, and repair costs. Those inputs were removed, while the generator failure rate, repair times, and repair costs were doubled (as a conservative estimate to represent the two lower-rated generators). Additionally, the failure rate, repair times, and repair costs of the X-Rotor power take-off are added and assumed to be the same as a wind turbine transformer. The vessel costs are taken from [24].

The O&M cost model was populated with the inputs required to model the X-Rotor O&M costs as outlined above. The results were compared to O&M costs for 4 different existing wind turbine types at the same hypothetical wind farms. The four existing wind turbine types for comparison are detailed in Figure 19, and the results of the comparison are summarised by Figure 20 [8].

When compared to the average O&M cost of existing wind turbine types, the X-Rotor has ~43% lower O&M costs. It can be seen that the X-Rotor has ~55% lower O&M costs than the worst-performing existing wind turbine type (3 Stage DFIG) and ~25% lower O&M costs than the best-performing existing wind turbine type (DD PMG). Further details on these O&M findings are seen in [8]. The key drivers for the O&M cost savings are lower failure rates and lower downtime related to no gearbox or direct drive generator (two of the highest downtime-related components), redundancy in operation, and a greatly reduced requirement for Jack-Up vessels. Operational realisation of the above savings will require change management due to the need for adjusting maintenance practices such as onshore maintenance of secondary rotors and increased usage of mid-sized field service vessels over jack-up vessels.

X-Rotor O&M costs may be further reduced once future work is carried out on the modelling methodology to capture additional X-Rotor inputs. For the results shown in this paper, conservative assumptions were made for all uncertainties in model inputs, for example, around failure rates, repair times, repair costs, etc. Specific examples of the conservative approach include the use of higher repair times based on field data from early offshore wind turbines for which it is now known repair times have reduced. Additionally, failure rates for larger-rated components were used when failure rates could not be obtained for components of the required rated power. As it is generally agreed that larger components have larger failure rates, this can also be seen as a conservative approach. Conservative estimates were adopted to ensure X-Rotor O&M cost benefits were not over-estimated.

5. CoE Discussion

To complete an early-stage differential CoE comparison between the X-Rotor and existing offshore wind turbines, inputs from the CoE equation for existing turbines were compared with the same inputs for the X-Rotor. The CoE inputs for comparison were O&M costs and turbine component costs; all other costs were assumed to be the same, resulting in a differential CoE comparison rather than absolute CoE figures.

As reported in Section 4 the X-Rotor has lower O&M costs than each of the four existing wind turbine types used in this comparison. O&M costs accounted for approximately 30% of the overall cost of energy [24], and based on that 30%, the previously mentioned O&M cost savings equate to X-Rotor CoE savings of 17% when compared to the 3 stage DFIG configuration, 15% when compared to the 3 stage PMG configuration, 13% when compared to the 2 stage PMG configuration, and 7% when compared to the DD PMG configuration. Through O&M cost savings, the X-Rotor achieves a 13% CoE savings on average across all four existing wind turbine types. It should be noted that all O&M cost savings presented in this section are based on the assumption that failure rates, failure costs, the number of technicians required for repair, and downtimes of components that are used in both the X-Rotor concept and existing turbines are the same, resulting in differential CoE savings rather than absolute CoE savings.

The turbine component costs for the four existing turbines shown are taken from [29]. For the purpose of this comparison, it is assumed that outside of the gearbox and generator, all other turbine costs in the X-Rotor are the same as existing turbines. This assumption is based on the fact that outside of the gearbox and direct drive generator, the main difference between the X-Rotor and existing wind turbines is the X-Rotor’s novel X-shaped rotor. As shown in Section 3, the mass of the X-Rotors primary rotor has been determined to be in the same ballpark as that of existing direct-drive turbines. Based on this mass similarity, it has been assumed that costs will be similar. In reality, the assumption may be a conservative estimate because no twist is required in the X-rotor blades, simplifying the production process. Further cost savings could be seen by the X-Rotors removal of the requirement for a yaw system. However, in this analysis, the cost difference is driven by the removal of the requirement for a gearbox/multi-pole generator. All other turbine costs are assumed to be the same. Consequently, the capital cost savings from the X-Rotor compared to the cost of the four existing turbines range from 5% for the DFIG and 32% for the DD PMG, with an average of 17% across all four existing turbines, as seen in Figure 19. Ref. [28] indicates that costs make up 30% of the overall cost of energy. Using that 30%, the X-Rotor’s differential turbine cost results show an average CoE saving of ~5% compared to existing turbines. Do we just not talk about support structure mass increase? The cost comparison is not comprehensive, even for the turbine. The former is much more dependent on 2 or 3 blades. These cost estimates were really only conducted to get an idea if the x-rotor stood a reasonable chance of being cost-competitive. I think that has been done.

The existing turbine types with the lowest capital cost have the highest O&M cost and vice versa. For example, the 3 stage DFIG configuration has the highest O&M cost but the lowest turbine cost. Consequently, to calculate the total potential CoE savings from the X-Rotor compared to the average of the 4 other drive train configurations, the addition of the average cost of energy savings from O&M and the average cost of energy savings from turbine costs does not provide a true indication of the overall CoE savings. Instead, each of the four drive train types must have its O&M cost savings and capital cost savings added together individually before an average can be taken. When the O&M and turbine cost savings are added for each of the four turbine types, CoE saving from the X-Rotor compared to the other drive train types ranged from 22% to 26%, with an average of 24%. It should be noted that all CoE savings presented in this section are based on the assumption that, outside of the differences outlined earlier in Section 4 and Section 5, all costs remain equal between the turbine types compared, thereby providing a differential CoE comparison rather than an absolute CoE analysis.

6. X-Rotor’s Alternative Configurations (Beyond 5 MW)

As discussed in Section 2, a number of different configurations for the X-rotor concept are possible. In addition to the two 5 MW variants presented in detail in the previous sections, another two are described below to illustrate some of the design options and demonstrate the potential for upscaling. No design analysis comparable to that undertaken for the 5 MW configurations has been undertaken. In each case, the aerodynamic characteristics of the secondary rotors and generators remain the same as those in the 5 MW exemplary configuration; namely, the generator has 4 pole pairs and a nominal frequency of 25 Hz, corresponding to a rated rotor speed of 39.21 rad/s for the secondary rotors; the secondary rotor has a $C_{Pop}$ of 0.27 at a ${\lambda }_{op}$ of 3.12. In addition, the primary rotor has a $C_{Pmax}$ of 0.4 at a ${\lambda }_{max}$ of 4.7. All machines have a rated windspeed of 12.5 m/s.

7.5 MW (Figure 21): The primary rotor comprises three upper and three lower blades, with one secondary rotor attached to the tip of each lower blade. The power extracted from the wind by the primary rotor is $P_F=8.82 \mathrm{M}\mathrm{W}$ at a rated wind speed of 12.5 m/s. The secondary rotors deliver 7.5 MW of mechanical power to the generators at 12.5 m/s wind speed (85% of the power delivered by the primary rotor). The secondary rotors have a combined area of 177.2 m² and the primary rotor has a swept area of 18,432 m².

10 MW Configuration (Figure 22): The primary rotor comprises two upper and two lower blades with two secondary rotors attached to the tip of each lower blade. The power extracted from the wind by the primary rotor is $P_P=11.75 \mathrm{M}\mathrm{W}$ at rated wind speed of 12.5 m/s. The power extracted from the wind by the secondary rotors deliver 10 MW of mechanical power to the generators in 12.5 m/s wind speed, (85% of the power delivered by the primary rotor). The secondary rotors have a combined area of 242.3 m² and the primary rotor has a swept area of 24,500 m².

In each of the above configurations, the choice of rated power, rated windspeed, primary rotor tip speed ratio, and secondary rotor drive-train dictates the full turbine design. The maximum achievable conversion efficiency between the primary and secondary rotors is dictated by the secondary rotor drive-train, rated power, and primary rotor tip speed ratio. Combined with the rated windspeed, this defines the required primary rotor area.

The secondary rotor drive-train could be modified to increase their rotational speed facilitating a larger torque reduction and a cheaper drive-train. It should be noted, however, that the secondary rotor area is inversely proportional to the secondary rotor speed and that there is a positive correlation between the secondary rotor area and the conversion efficiency. Increasing the rotational speed of the secondary rotors by 10% in the 10 MW configuration drops the mechanical power of the secondary rotors to 8.9 MW, corresponding to a 10% drop in conversion efficiency. At present, the 7.5 MW configuration is likely the most suitable option for offshore siting with a jacket foundation since loads on the support structure are much reduced, as discussed in Section 3.

7. Conclusions

This paper provides an overview of the novel X-Rotor offshore wind turbine concept. Both two-bladed and three-bladed variants are investigated. It is established that combining a vertical-axis primary rotor with inclined upper and lower blades together with horizontal-axis secondary rotors, which directly drive conventional generators, is feasible. Everything else being equal, the cost savings, relative to those for a conventional HAWT, for the X-rotor are estimated to be the following:

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CAPEX savings from 5% for a 3-stage DFIG-based power-train to 35% for a DD PMG-based power-train.

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OPEX savings from 55% for a 3-stage DFIG-based power-train to 35% for a DD PMG-based power-train.

The combined cost of energy savings is estimated to be about 26%. Because of the inevitably increased swept area of the X-rotor’s primary rotor compared to that for an equivalent conventional HAWT, its cost is likely to be greater. To provide a measure of that increase, a detailed design has been undertaken to determine its mass and so obtain an indirect estimate of its cost. The mass of the rotor would be increased by about 50% relative to that for a conventional HAWT, but the impact on the CoE would easily be outweighed by the other cost savings. The implications for the cost of the jacket for deployment in deep water are also investigated in a similar manner to that of the primary rotor. The mass of the jacket for 50 m water depth deployment is determined to be substantially greater than an equivalent HAWT for the two-bladed variant but comparable for the three-bladed variant. From the foregoing, it is concluded that further development to take the concept forward towards TRL3 is justified.