GB2580735A - Cable-driven cross-stream active mooring for tidal stream power systems - Google Patents

Abstract

A method and system for mooring multiple tidal stream power generating turbines is provided. The system features mooring multiple turbines on a common tether TA with anchoring only at two ends ANhead, ANtail of the common tether TA. Th e whole array of turbines is submerged, floating with only two major lifting buoys LBhead, LBtail partially submerged above the water surface. Each individual single turbine TU comprises a pair of mooring handles (MH, Figure 2(a)) and is moored onto the common tether TA by a turbine mooring system that comprises a torque balancing stage (BS, Figure 2(a)) and an arrangement of mooring line systems (ML01, ML02, etc., Figure 2(a)) which prevents the single turbine TU from rolling and also allows bi-directional operation by a vertical flipping motion. The system further includes an end clamp system CLPhead, CLPtail together with designs of lifting buoy (see Figure 6) for maintaining the turbines within a desired depth range in varying operating flow speeds.

Description

Cable-driven Cross-stream Active Mooring for Tidal Stream Power Systems This present invention relates to system and method of mooring multiple flow kinetic power generators in a tidal stream and also relates to system and method of mooring a single power generating turbine for hi-directional operation in a periodically revering tidal flow.

This application claims the benefit of priority of the United States provisional patent application no. 62728820 filed Sep. 9, 2018 titled "Cable-driven Cross-stream Active Mooring for Tidal Stream Power Systems".

I. INTRODUCTION

Tidal stream power is stable, predictable and can be found in many locations. In addition, compared to other approaches for harnessing ocean tidal power, tidal stream power systems may have the least impacts on environments [1]. Currently, there are many on-going efforts in developing practical tidal stream power systems. Typical examples include systems from the Atlantic Resources (e.g. the SeaGen featuring horizontal axis turbine fixed to seafloor) [2], the Open Hydro (tube turbine placed on seafloor) [3], the Scotrenewables (e.g. SR2000 floating system) [4], the Blue Energy Services (the B1ueTEC floating single turbine) [5] and the Blackrock Tidal / Schottel (semi-submerged system) [6]. There are also examples from the GIST (floating single turbine) [7] and the II-11 Engineering (submerged floating twin turbines) [8].

Pilot plants of some of the above systems have been constructed and some of them have already been connected to local grid to start generating power. However, the supporting/mooring methods used by the above systems still have issues that may hinder their installations in large scale due to cost-effectiveness.

First, systems fixed to or placed on seafloor requires larger hub elevation in waters of larger depth in order to access faster flow closer to sea surface, which may not he cost-effective.

Second, individual installation or mooring of each turbine unit on scafloor is associated with high construction cost and environmental impacts.

Further, floating systems are disadvantageous to other usages of water surface, although they have cost advantage over fixed systems in waters of significant depth.

Still further, individually moored floating or submerged floating systems must he placed with enough spacing among adjacent systems to avoid interference in variant flows. This spacing becomes larger in areas of deeper waters, because longer mooring lines must be used, which could reduce efficiency of area usage, given that the area of fast streams in a tidal flow zone is limited.

Another issue involves natural variations of flow patterns. It has been shown that turbines in a multi-row formation should he arranged in staggered positions to minimize wake effects [9-10J. Due to winds and other effects such as non-tidal currents, directions of tidal flows may sway frequently. Examples can be seen in Penghu Channel west of Taiwan [11-13]. Systems fixed to or placed on seafloor cannot accommodate such variations and the overall efficiency of the formation could suffer. Even more serious, in some locations, core passages of flood flow and of ebb flow deviate significantly, posing problems to bidirectional operations. Such cases can be found, for examples, in the Pentland Firth, Scotland [14, 22], Coto Islands of Kyushu, Japan [15], and Zhoushan of Zhejiang, China [16].

Still another issue concerns balancing of turbine torque and ease of bi-directional operation. When applying a floating or submerged floating system to support a turbine, torque created by the turbine's rotor needs to be balanced. A typical approach is using a twin-turbine unit, connecting two counter-rotating turbines into a rigid unit and let the two torques cancel each other [4, 8, 17]. However, because flows are turbulent and rarely uniform, not only torques but also thrusts can become uneven and result in yawing and rolling instability [17]. Therefore, additional stabilizing means, such as rotor speeds controlling, hydrodynamic control surfaces and hydraulic pose balancing, may he necessary. Furthermore, effects of torques on the internal structure of the unit cannot he reduced. The structure must have enough material in order to resist the associated internal stress, which also increases complexity and costs.

Another approach capable of supporting a single turbine applies a vertical structure with a buoy (or a floating body) at top and a ballast (or the turbine itself) at bottom for torque balancing. Examples can he found in the designs by the Bluewater [5] and by the Okinawa institute of Science and Technology [7]. However, when turning with flow this configuration must turn about a vertical axis. Therefore, it may need an auxiliary mechanism to make sure that mooring lines and power takeoff cables are not over twisted in repeated hi-directional operations.

The Cross-stream Active Mooring (CSAM) is a concept recently proposed by the inventor of the present invention for mooring generator turbines in arrays in an ocean current over deep seafloor. Large formations of turbines can he deployed from concentrated small anchoring footprints, potentially saving significant undersea construction costs and making minimal impact to the seafloor. improved gravity anchors arc used to anchor tethers of the arrays on shallow locations, such as on tops of undersea ridges and a submerged hydro sail system close to the generator turbines acts as "active anchors" to deploy the arrays of turbines transversely across current streams and hold the systems in position over deep sea. Further, the hydro sail system can adjust the position of the system arrays to track current meanders and place turbines always within fast streams in the current velocity core. [18-20] The CSAM concept, with proper adjustments, can also be applied to scenarios in tidal streams.

This present invention is a new mooring design for tidal stream power based on the CSAM concept with the features of mooring by linear an-ays, submerged floating systems and capability of array lateral displacement for the purpose of construction cost savings, environmental considerations and increasing power capturing efficacy.

II. BASIC CONCEPT Figure 1 (a) and (b) illustrate the basic configurations of the proposed 'Tidal CSAM" system (or Cable-driven CSAM system) in different layouts. The features of the design concept and their design goals are described as follows: A. Mooring turbines on a common tether Multiple turbine units (TU) are moored onto a common tether (called array tether TA), instead of on seafltxw, in series to form a linear an-ay of generators. Each turbine units is moored to a connection point (called mooring base MB) on the array tether. The two ends of the array tether are connected to two main mooring tethers respectively. The two main mooring tethers (called head tether TMtext and tail tether TM:di) are then anchored to seafloor at two main anchors (called head anchor ANhead and tail anchor ANtall) respectively. (For convenience, the direction toward the flooding tide is called head and the opposite direction tail.) The connection between the two ends of the array tether and the two main tethers may be through the use of a pair of lifting buoys (LBtead and LBtaii) and end clumps (head clump CLFilear or tail clump CLP,:,), functions of which will be explained later. Power transmission cables CE from the turbine units travel along the array tether and the main mooring tether at one end (e.g. TMhead) and then go off the system.

This design requires only very limited marine construction works, reducing installation costs and minimizing environmental impacts. Further, because turbines are moored to the array tether with relatively short mooring lines, turbines in the same array can he placed closely without the risk of mechanic al interference.

il. Submerged floating turbines Most part of the tidal CSAM system is kept in submerged floating under sea surface. Each turbine unit is built with extra buoyancy so that it floats upwards. But all turbine units in the array, their mooring lines and connection structures on the array tether and the array tether as a whole are kept at near neutral buoyancy. At both ends (head and tail), the end section of the array tether (TAtt or TAtt) connects first to an end clump (head clump CLPhe",, or tail clump CLP,an) and then, through a hanging section of tether (TAbli or TAhr), to a lifting buoy (LBhead or LBhead). The two end clumps provide extra weight over the near-neutral buoyancy turbine array and pulls the whole array downwards. The lifting buoys, moored by main mooring tethers (TMiead and TATO toward the head direction and the tail direction, are semi-submerged and provide extra buoyancy to counter the downward pulls from the end clumps. As a result, the whole system is kept floating by the two lifting buoys but the array of turbines is kept in submerged floating.

By proper design, to be discussed later, the array tether can be maintained within a prescribed depth range regardless of depth of scafloor. In this way, most sea surface areas can still be utilized.

C. Single turbine mooring, torque balancing, bi-directional operations Although the design features described above can be applied to various forms of marine turbine unit, a unit of a single horizontal axis turbine could be the most cost effective choice. Among various types of fluid kinetic power convertor, horizontal axis turbines have been shown to be the most efficient by the wind power industries [21]. A single turbine of simple construction with minimal external structure will have the lowest unit cost.

A new turbine mooring system is devised to moor a single turbine on the horizontal array tether and at the same time balance turbine torque, while also being capable of bi-directional operations by turning with tidal flows by flipping along a vertical path (i.e. about a horizontal axis).

Figure 2(a) shows the new single turbine mooring system with the turbine in operational pose in a flow with direction indicated by the arrow 200, in perspective view, with a x-y-z coordinate frame 100 showing the 3D perspective relation. The turbine unit TU comprises a long nacelle TU02, a downstream rotor TUO1 and a pair of mooring handles MH at the left and right sides of the nacelle. In operational pose, the nacelle is oriented horizontally with the rotor axis also oriented horizontally (that is, parallel to the x-y plane). The turbine unit is tethered to a balancing stage BS by two mooring lines (ML01, ML02). The balancing stage comprises a horizontal beam BS01 and a downward extending structure BS02 attached with a ballast BS03. Mooring line ML02 connects the turbine at the left tip of the left mooring handle to the left end 202 of the horizontal beam BS01; line ML01 connects the turbine at the right tip 201 of the right mooring handle to the right end of the horizontal beam BS01. A spacing is maintained between the two mooring lines by the mooring handles and the balancing stage. The balancing stage is in turn moored to a mooring base MB that is fixed to the array tether by another two mooring lines (ML03, ML04), which connect to the horizontal beam BS01 of the balancing stage at its two ends (201, 202) respectively. The two mooring lines ML03 and ML04 and the beam BS01 basically forms a triangle.

The turbine is built with extra buoyancy so that it not only floats above the depth of the array tether but also raises the balancing stage above the array tether. In a flow, the extra buoyancy and thrust on the rotor create tensions on the mooring lines (ML01-ML04) and the mooring lines (ML01, ML02) form an angle (EL) with respect to the horizon. The torque (Mr) exerted by the rotor to the nacelle makes the nacelle to roll. Because of the mooring handles MH and the connections of the mooring lines ML01 and ML02, the balancing stage also rolls. The balancing stage comprises a horizontal beam BSOI and a downward extending structure BSO2 attached with a ballast weight (Wb) BSO3. As the balancing stage rolls, the balancing stage creates a countering torque to the rotor torque. As a result, the tension (TT))) on the left mooring line ML02 is larger than that on the right mooring line (T",,R) (ML01) and this tension difference acts on the mooring handles to counter the turbine torque and prevent the turbine from over-rolling. Because the balancing stage is only attached to the mooring lines (ML01-ML04) at the two ends of the horizontal beam BS01, the downward extending structure BS02 and ballast BS03 will always point downward even if the inclination angle Om) of the mooring lines varies in flow of varying speed. And because the two mooring lines ML03 and ML04 and the beam BS01 basically forms a triangle, when the flow changes direction, the turbine unit and the balancing stage will follow and turn to the new downstream direction. As a result, the mechanism of Fig. 2(a) is able to provide balancing torque to counter rotor torque in flows of varying speed and direction.

Figure 2(h) depicts the turbine in its horizontal operational pose in side view, marked with force vectors. To keep the turbine nacelle at horizontal pose during operation, the positions of the buoyancy center (b) and mass center of the turbine (c) with respect to the fairleads (a) need to be arranged as depicted in the figure so that the moment of buoyancy force cancels the moment of weight, while thrust on the downstream rotor keeps the nacelle in near-horizontal pose along the flow.

The moment of buoyancy force with respect to the fairleads is further made slightly larger than the moment of weight and the fairleads on the torque handles are placed in the same line as the buoyancy center and the mass center but to their upstream direction, so that in low or no flow conditions the extra moment will rotate the turbine up to a vertical pose. When the tidal stream reverses direction the turbine leans toward the reversed direction, passing across the array tether, and takes a horizontal operational pose again. Figure 3 illustrates the scenarios. When there is no flow, the turbine floats upward with its rotor axis pointing toward zenith (z-) direction. The turbine, the balancing stage and the mooring base are basically aligned on a vertical line. When the tide flows in flood direction, the system poses in a fashion similar to Fig. 2(a). When the tide reverses direction, the turbine leans toward the reversed direction, passing across the array tether, and takes a horizontal operational pose.

This arrangement can simplify configuration of the turbine. A rotor with fixed pitch blades or a passive pitch adjustment mechanism can be used. The turbine turns with tidal flows by flipping along a vertical path, with no need of slip joint nor risk of over-twisting either the mooring lines or power cable.

D. Array depth keeping The submerged floating turbines should be kept within a preferred depth range in most operating conditions. However, the vertical distance between the turbine and the array tether changes when the flow speed changes and when the turbine flips with tidal flows along the vertical path. Different flow speeds also result in varying total pulling force at the fairleads of the lifting buoys at the two ends of the array (LBFhcad or LBFtan), which could change their depths. The end clumps (CLPlicad, CLPuli) and the hanging sections of the array tether (TAN" TAI") are designed to compensate for these variations.

Figure 4 depicts side views of the array of turbine units as moored by the present invention in different scenarios to show the operation of the end clump depth keeping system.

Fig. 4(a) shows the scenario when there is no flow. The turbine TU floats upward, with its extra buoyancy, with its rotor axis pointing toward zenith (z-) direction and raises up the balancing stage BS. The weights of the balancing stage BS, the mooring base MB and part of the an-ay tether TA counter the buoyancy of the turbine so that the whole combination is of neutral buoyancy. The two end clumps (CLPheaa, CLPtaa) thus pull the whole array down, while the two lifting buoys (LBhcaa and LBteaa) suspend everything in between them in submerged floating.

The main tethers (TWIteat and TM,,,,,) have their own weights in water but the weights can be cancelled by attaching additional buoys along the main tether, as depicted by small buoy Br, in Fig. 1(a).

As depicted in Fig. 1(a) and (b), the positions of the two lifting buoys (LBhead and LBhead) are determined by locations of main anchors (A1\11,,,,,, and ANini), lengths of main mooring tethers (TMheaa and TMaii), lengths of the array tether (TA) and the two hanging sections (TAhh and TAhi), and lengths of lateral control lines (TC",,a,,,, TChend,re, TC,drz, TC,,a,R). Preferably, when there is no flow, the distance between the two lifting buoys are made to he larger than the length of the an-ay tether TA, so that the hanging sections TAhh and TAhi form an inclination angle Of measured relative to horizon, as shown in Fig. 4(a). This way, the weights of the two end clumps (CLPhead, CLPtaii) can produce horizontal force components that straighten the array tether.

When the flow starts and its speed increases, the vertical distance dTM between the turbines (measured from the mooring handle) and their mooring bases on the array tether decreases, because the thrusts over the turbine rotors increase and push the moored turbines lower. But increased thrusts on the whole turbine array also increase the pull on the end clump (head clump in the case of Fig. 4(b) and 4(c)). Thus, the inclination angle Of decreases and the whole array is raised up, compensating the loss of distance dm, between the turbines (measured from the mooring handle) and their mooring bases. This is depicted in Fig. 4(b) and 4(c).

Increased thrusts over the turbines due to faster flows could also pulls down the lifting buoy upstream and hence increase the depth of the fairlead (LBFhcad in the case of Fig. 4(b) and 4(c)) of the array. This increase of depth should also be considered. In summary, by matching the designs of the mooring system of the turbine unit, the end clump systems and the lifting buoys, the turbines can be kept within a preferred depth range (dn1) in most conditions.

E. Cross-stream deployment of turbine array By placing and mooring the two lifting buoys at the two ends of the array across the track of tidal streams, the turbine array can be deployed across the tidal stream so that downstream turbines are not blocked by upstream turbines. This is depicted in Fig. 1(a) and 1(h). The whole turbine array including the mooring tethers is anchored at two ends. When the tide floods, the whole array pulls on the head anchor; when the tide ebbs, the tail anchor takes loads.

F. 2D formation of multiple turbine arrays When a second array of turbines is added, proper spacing from behind the first array can be taken and turbines can be placed in staggered positions with respect to the first array to minimize wake effect. Thus, multiple linear arrays of turbines can be deployed to form a 2D formation.

G. Active positioning of turbines Since the whole turbine array is kept floating by the two lifting buoys and is anchored through mooring tethers only at two anchoring points, position and angle of deployment of the turbine an-ay can be adjusted by adjusting positions of the two lifting buoys. This can be done by applying a set of winched lateral control lines (TChead,r, TGth/T., TG]it,R) installed on the lifting buoys with the far ends of the lines anchored to seafloor at two sides of the system, as shown in Fig. 1(a) and 1(b). Pulling or relaxing the lateral control lines moves the lifting buoys laterally toward the left or the right of the tidal stream. Fig. 1(a) and Fig. 1(b) depict two different distribution orientations of the turbine array.

Alternatively, the lateral control lines can be fixed to the lifting buoys and winches can be placed, instead of on the lifting buoys, at the two far ends of the control lines.

Being able to adjust the angle of deployment of the array tether means the ability to adjust spacing and relative positions of turbine units. This enables turbines formation adjustment (1D array or 2D formation) in response to flow pattern variations to achieve best formation efficiency.

Further, large displacements of turbine arrays can accommodate deviations of tidal stream core passages. For example, in the case of Inner Sound of Pentland Firth, Scotland [14], Tanoura Strait in Goto Islands of Kyushu, Japan [15], or Zhoushan of Zhejiang, China [16], core passages of flood flow and of ebb flow deviate by a distance of 1-2 km By using the proposed cable-driven CSAM system with main mooring tethers (TMhead and TMtao) of a few thousand meters long and matching lateral control lines, one set of turbines can be positioned in the two deviated flood and ebb tidal streams alternately to maximize energy capture.

III. DESIGN EXAMPLE AND FEASIBILITY ANALYSIS An example turbine design was made to illustrate the design details and the feasibility of the proposed mooring concept. Rotor radius R of the example turbine was set to 10 m; operational flow speed Vo range 1-3 m/s. A water depth of 50-100 m is assumed for illustration purpose. Basic thrust D, torque Mr and power P, data can be estimated by the following relations: Power available for capture is Pro' which relates to torque and rotational speed = Mr (3)-The above equations lead to expression of torque as -R3 VIZ

-

2 (4).

And the thrust is D5 -(5).

Assuming a thrust coefficient CD, = 0.89 (the ideal Betz situation, as the worst scenario), rotor tip speed ratio X = 5 and a power coefficient Cr, = 0.5, the estimated basic data are shown in Tab. I.

TABLE II

BASIC POWER. THRUST AND TORQUE ESTIMATIONS OF THE EXAMPLE TURBINE Flow speed Power Thrust Torque Vo (m/s) P, (kW) D, (ton) Mr (ton-m) 1.0 81 16.4 16.4 2.0 644 58.4 65.6 3.0 2,174 132.0 148.0 A. Single turbine mooring and torque balancing From Fig. 2(b), force balance gives the tensions and the angle of the of mooring lines in relation to the turbine thrust, turbine buoyancy B, and turbine air weight W,", D, =i. T",".;) = erm, T.",, ) cos 'am (6).

Et = Cl;""z. = I;".n) sins.,, (7).

The locations of the buoyancy center and the mass center can he determined from )3,Cab) (ac) (8)-The torque from the rotor creates a difference in the tensions of the two mooring lines, which counter balances the torque, i.e., tz = trt",:". -Trni.,08 2 (9)-Regarding the design of the mooring base, Figure 5 shows a force analysis on the mooring base. The basically "T" shaped frame places a ballast (W") at a distance s",,, to the center of rotation o. When the base rotates by a small angle Ob, a change of potential energy of the ballast creates a recovery torque, as = ,3&",W, sin.61, (10).

This recovery torque Mb, should be made larger than M. By setting and adjusting total buoyancy B,, turbine air weight W," locations of buoyancy center and mass center ab and ac, mooring handle span d and mooring base ballasts span sz,"" an example mooring design was obtained. See Tab. II and Tab. III. A few limiting factors were considered in this example design. First, there is a practical range of turbine mass, considering masses of generators, gearbox and rotors of systems of similar power capacity. Second, the nacelle diameter should have a limit for not affecting the flow entering the rotor too much. The results in Tab. III give a nacelle dimension at about 2.5 in diameter by 25 m long. Third, the mooring angle under fast flow should be large enough so that the vertical force components are large enough to counter turbine torque. And finally, the roll angle should not be too large.

TABLE III

EXAMPLE TURBINE MOORING DESIGN PARAMETERS

Turbine buoyancy B, (ton) 115.0 Turbine mass W,,, (ton) 38.0 ab (m) 0.31 ac (m) 5.0 Mooting handles span ss, (m) 6.0 Ballast rotation radius Sim, (m) 12.0

TABLE IIIII

ESTIMATED MOORING TENSIONS, MOORING ANGLE AND ROIL ANGLE OF TILE EXAMPLE TURBINE MOORING DESIGN PER TAB. II Flow Tensions Mooring Roll speed L R angle angle Vo (m/s) La. (ton) 7' rn R an Ob (ton) (degree) (degree) 1.0 39.6 36.9 79.2 2.1 2.0 43.7 32.8 52.6 8.4 3.0 50.6 26.0 30.2 19.0 B. Turbine array depth keeping By matching the designs of the mooring system of the turbine unit, the end clumps systems at both ends of the array tether and the lifting buoys, the turbines can be kept within a preferred depth range in most conditions. Referring to Fig. 4(c), the depth of the turbine units is 77,' di.EP C1LM EITM (11).

dais the vertical distance between the turbines and their mooring bases on the array tether and can be determined from the mooring angle t9," and length of turbine mooring lines. dais the vertical distance between the lifting buoy fairlead (LBEhecid) and the array tether and can be determined from length 14th and angle 6} of the hanging section by d, m = Fin Bn (12).

The angle Oh can be determined by = Tn. tang, wherein Bica is weight of the end clump and 7"" is the total tension exerted by the array of turbines, referring to Fig. 4(d). In other words, for a given array of turbines, adjusting W" and Lig, can change dIM.

And finally, the depth of the lifting buoy fairlead dLBF depends on the structure of the main mooring tether (TMh"") and the net buoyancy of the lifting buoy BERE. Also take note that when the whole turbine array is kept near-neutral buoyancy, vertical downward pull W., from the end clump and horizontal pull T" from the array tether transmit to the lifting buoy fairlead directly and affect dna, as well. But the effect of W" can he removed by include it into the design of the lifting buoy BLBF. The shape of the main mooring tether and d/hBF can be simulated by a 2D finite element model.

Combining the above relations, an example end clump system and main tether design were made. Table TV lists major design parameters.

Fig. 6(a) shows estimated depths of turbines in the operating flow speed range when the above depth keeping method is applied, in comparison with the situation when no correction mechanism is used, and with other parameters. Fig. 6(b) shows the corresponding lifting buoy design, the buoyancy to depth relation, to achieve the depth keeping with the mechanism. The turbine can he maintained within a few meters around the target depth 30 m within the operating flow speed range. Fig. 6(c) depicts an example buoy shape design that can provide the buoyancy to depth relation of Fig. 6(h). The buoy has a shape profile that provides different horizontal cross-sectional area at the waterline when the depth changes.

TABLE IVV

EXAMPLE MOORING SYSTEM DESIGN

Turbines mooring turbine mooring line length A7, (m) 20 Array tether 8 number of example turbines in array hanging section length Li,h (m) 36 end clump net weight W., (ton) 100 inter-turbine distance (m) 100 array tether length (m) 900 no-flow tether tension (ton) 20 Main mooring tether 800 main mooring tether length (m) number of main tether buoys 10 Target hub (nacelle) depth (m) 30 (13), C. Turbine array deployment and bidirectional operations Figure 7 illustrates a top view of a generalized 2D layout of the array tether when deployed across stream, with force diagrams at nodes. The array tether has N sections with N+1 nodes. Node N+1 is the head node and node 0 is the tail node. N turbine units are attached respectively to nodes 1 to N. All forces shown arc on horizontal plane (x-y plane). Each turbine unit is subjected to a drag (thrust) force A. In this approximate analysis, drags over the tether and parts other than the turbines arc neglected because of their small frontal areas compared to the turbine rotor sweep areas. As a result, at peak flow, a force of NA in the -y-direction is needed at the head node to hold the turbine array. To deploy the turbine array across the tidal stream, a lateral control force a is applied to node 0 in x-direction. Balance of tension Tam in each tether section with external forces on each node (n= 0, 1, ... N) in x-and y-directions can then be written as rt,. "cos Oc," = s. (15) and T. "sin 6"," = nD, (16).

which lead to the deployment angle Ek" of each tether section as tan Oa, -rap, (17).

For n = N, ND. trn = (18).

Combining eqns. (17) and (18) gives tan Bc,, = (19).

Thus, total thrust (drag) in the turbine array and the lateral control force FA, determines the deployment angle (9",N of the leading section of the array tether by cqn. (18). And cqn. (19) determines deployment angles of other sections relative to a,,N.

From the above relations, it is interesting to note that, during operation in flood tide or in ebb tide, if the ratio of D, to Fk. is kept unchanged then the 2D layout of the turbine array will not change. This can be achieved by designing the main mooring tethers and arranging the tow lines at both sides of the system such that they are in tension and their lengths (spans) do not vary significantly within operating flow speed range. This way, by geometric similarity, A and a. will change in proportion and keep Ba,N roughly constant.

Figure 8 shows examples of 2D layout of a turbine array of the design of Tab. IV under different conditions as estimated by the above relations. When there is no flow, the array is pulled straight (curve A) by the two end clumps and moored at two ends (Al, and A,). When flood flow starts (toward y+ direction), the head end (Ax) is allowed to move until the main mooring tether's pull balances turbine thrusts but the tail end (At) does not move, thereby the array is pushed downstream to take a curve shape. For example, curve Br corresponds to Bo,y = 80° or = 5.67. When flood flow slows down and stop, the two end clumps pull the turbine array back to straight form (curve A). Then, when the reversed flow starts, the situation reverses and the turbine array is pushed to the opposite direction (curve Be).

From no-flow condition to operating conditions, the upstream end of the array is pulled downstream, e.g. from Al, to 13(in flood flow, by thrusts of the turbines so that the 2D curve of the array can form. Therefore, the main mooring tethers need a configuration that can provide this displacement. As shown in Fig. I, buoys Btm at equal distance along the main mooring tether suspend it in submerged floating so that catenary forms between adjacent buoys. The changes of the horizontal pull (from the turbine array) and the vertical force (buoyancy from the lifting buoy or LB,,,,,)) exerted at the fairlead (LB hie., or LBFL"11) change the total span of the main mooring tether, providing the needed displacement.

Figure 10 shows shapes of the example mooring tether of the design of Tab. IV when the turbine array is under different flow speeds, as computed by a basic finite element model. The total span of the mooring tether increases significantly from no-flow condition to operating conditions, providing the required displacement, but does not vary significantly within operating flow speed range, allowing the 2D layout of the turbine array to he kept unchanged.

D. Formations and Adjustments Pulling or relaxing the lateral control lines moves the lifting buoys laterally toward the left or the right of the tidal stream. For example, in Fig. 8, shortening lateral control lines to the left of the turbine allay increases Fs, and widens the spread of the layout, moving the turbine array from curve Br to Cf, which corresponds to 8,,,N= 74.9° (or SDIFk= 3.69).

Referring to Tab. I, within the 1-3 m/s operating flow speed range, total thrust 8D, varies from 131 ton to 1056 ton. For layout Br, the corresponding lateral force Fs: varies from 23.1 to 186 ton. For layout Cr, F1 varies from 35.6 to 286 ton.

Adjustment of array layout should be performed during no or low flow period so that the winches only need to deal with low flow drag over the system.

E. Tethers and Power takeoff Galvanized marine wire ropes are cost effective to he used to construct the tethers and the lateral control lines of the proposed system.

Power transmission cables from turbine units are first routed down to the mooring bases (Fig. 2(a)) and then placed along the array tether (CE, Fig. 1) and the main mooring tether to a position close to the main anchor (AI\11,,,,d). From there, the cable is connected to shore.

IV. CONCLUSIONS AND VARIATIONS IN APPLICATIONS

A new design for mooring tidal stream turbines is proposed and its feasibility is studied by analysis. The design features mooring multiple turbines on a common tether with anchoring only at two ends. The whole array of turbines is in submerged floating with only two major lifting buoys partially over water surface. Each turbine unit is moored to the common array tether by a system of dual mooring lines with mooring handles on the turbine and a mooring base on the array tether. The mooring system is able to moor a single turbine, prevent it from rolling and also allow bi-directional operation by a vertical flipping motion. An end clump system was also designed to work with individual turbine mooring and the lifting buoys to maintain the turbines within a depth range in varying operational flow speeds.

Analysis in mechanics provided example designs and corresponding parameters.

This design requires only very limited marine construction works, reducing installation costs and minimizing environmental impacts. It enables usage of most sea surface areas in a site by maintaining the turbines within a prescribed depth range regardless of depth of seafloor. It can place turbines closely while avoiding the risk of mechanical interference, because of the use of the common array tether. The single turbine mooring method can simplify configuration of the turbine. In addition, the design allows the application of lateral control lines to adjust array formation in response to flow pattern variations to achieve best formation efficiency. Further, large lateral displacements of turbine arrays can accommodate deviations of core passages of tidal flows.

In the above descriptions, all turbine units are moored in submerged floating. Whenever appropriate, this cable-driven CSAM system can also he used to moor floating marine turbines, such as the SR2000 floating system and the B1ucTEC system, as mentioned in the introduction section. The system will look similar to Fig. 1 except that the turbines float on the surface of water.

This cable-driven CSAM system can also he applied to mooring of floating wind turbine systems. The system will look similar to Fig. I except that, instead of turbine units (TU) and their mooring lines, multiple floating platforms, with wind turbines on them, are attached and moored to the array tether (TA). An array, either 1D or 2D, of wind turbines also has the issue of blockage or wake when wind direction changes. The Cable-driven CSAM system allows position adjustments of the array to overcome the issue. Further, the system will cost less than mooring individual floating wind turbines to seafloor.

Description of Figures

Fig. 1 (a) and (h): Basic concept of the Tidal CSAM system at two different distribution orientations. See texts for symbols.

Fig. 2 (a) The single turbine mooring system with a turbine in its operational pose; (b) force analysis of the turbine in side view.

Fig. 3 Bi-directional operations of the single turbine mooring system Fig. 4 (a), (h) and (c): The end clump depth keeping system, three different scenarios in side views; (d) force analysis.

Fig. 5 Mooring base design force analysis.

Fig. 6 (a) Estimated turbine depths in different flow speeds when the depth maintaining mechanism is applied, in comparison with the situation when no con-ection mechanism is used. d]]/B is depth of the mooring bases on the array tether. dim and drip; see Fig. 4(a) and texts. (b) Buoyancy to depth relation of the corresponding lifting buoy design.

Fig. 7 Generalized 2D layout of a turbine array when deployed across stream, with force analysis. Fig. 8 Examples of 2D layout of a turbine array of the design of Tab. IV under different conditions. Fig. 9 Shapes of the example mooring tether of the design of Tab. IV when the 8-turbine array is under different flow speeds, as computed by a basic finite element model. Horizontal pulls were based on Tab. I. Vertical forces and fairlead depths con-espond to data shown in Fig. 6.

REFERENCES

[1] S. J. Sangiuliano, "Turning of the tides: Assessing the international implementation of tidal current turbines," Renewable and Sustainable Energy Reviews. vol. 80, pp. 971-989, 2017.

[2] E. Rolling, "MeyGen Tidal Energy Project EIA Scoping Document", accessed May 2018 from http://www.gov.scot/resource/0043/00434044.pdf [3] Open Hydro Group., information from company website, see http://www.openhydro.com/ (Accessed May 2018) [4] Scotrenewables Tidal Power Ltd., information from company website, accessed May 2018 from http://www.scotrenewables.com/technology-development/the-concept [5] Bluewater Energy Services, "BlueTEC Texel Prototype," accessed May 2018 from http://www.bluewatercom/new-energy/texel-project/ [6] Black Rock Tidal Power, information from company website. accessed May 2018 from http://www.blackrocktidalpower.com/home/ [7] K. Shirasawa, K. Tokunaga, H. Iwashita and T. Shintake, "Experimental verification of a floating ocean cun-ent turbine with a single rotor for use in Kuroshio currents", Renewable Energy, vol. 91, pp. 189-195, 2016.

[8] Anonymous, "Power Generation Using the Kuroshio Current: Development of floating ocean current turbine system", IHI Engineering Review, Vol. 46, No. 2, 2014. Accessed July 2016 online: https://www.ihi.coj p/vailezwebin_site/storage/originallapplication/149ee9de3149aba2e1215fd5f 9cd46ec.pdf [9] L.-E. Myers and A.-S. Bahaj, "An experimental investigation simulating flow effects in first generation marine current energy converter an-ays", Renewable Energy, vol. 37, pp. 28-36, 2012 [10J P. Stansby and T. Stallard, "Fast optimization of tidal stream turbine positions for power generation in small arrays with low blockage based on superposition of self-similar far-wake velocity deficit profiles," Renewable Energy, vol. 92, pp. 366-375, 2016 [11] Y.-1-1. Wang, L.-Y.Chiao, K.M.M. Lwiza and D.-P. Wang, "Analysis of flow at the gate of Taiwan Strait", Journal of Geophysical Research, vol. 109, CO2025, 2004 [121 Y.-C. Chang, "Flow Observation in the Taiwan Strait and Adjacent Seas" (in Chinese with English summarizing paper manuscript), Ph.D. Thesis, National Sun Yat-Sen University, January 2008 [13] S.-F. Lin, C -K Hu and C.-W Yen, "The Estimation of ocean current power around Peng-hu," (in Chinese with English abstract) Proceedings of the 33rd Ocean Engineering Conference in Taiwan, National Kaohsiung Marine University, Dec. 2011, pp. 871 [14] L. Goddijn-Murphy, D.K. Woolf and M.C. Easton, "Current patterns in the Inner Sound (Pentland Firth) from underway ADCP data," Journal of atmospheric and oceanic technology, vol. 30, pp. 96-111, 2013 [1.5J P. Garcia Novo, "Study on ocean turbulence intensity around the Goto island by field observation and numerical simulation," Kyushu University, Jul. 2016. From https://catalogliblyushu-u.ac jp/opac_detail_mdfilang=08.camode=MD823&bibid=1785433 [16] H.-W. Qin, Z. Cai, H.-W. Zhou, H.-M. Hu, "Three-dimensional numerical simulation of Zhoushan area," (in Chinese with English abstract) Journal of Mechanical & Electrical Engineering, vol. 31, no. 4, Apr. 2014, pp. 541-544 [17] L.-Y. Chang, F. Chen and K.-T. Tseng, "Dynamics of a marine turbine for deep ocean currents", Journal of Marine Science and Engineering, 4, 59, 2016 [18] C.-C. Tsao, Feng, C. Hsieh and K.-H. Fan, "Marine Current Power with Cross-stream Active Mooring: Part 1", Renewable Energy, vol. 109, pp. 144-154, 2017.

[19] C.-C. Tsao, L. Han, W.-T. Jian, C.-C. Lee, J.-S. Lee, A.-H. Feng, C. Hsieh, "Marine Current Power with Cross-stream Active Mooring: Part II", Renewable Energy, vol. 127, pp. 1036-1051, 2018.

[20] C.-C. Tsao and A.-H. Feng, "Motion Model and Speed Control of the Cross-stream Active Mooring System for Tracking Short-term Meandering to Maximize Current Power Generation", Journal of Mechanics, published online Dec. 4th, 2017.

[21] J. Twele, C. Hellmann and M. Schubert, "Wind turbines -design and components", Chap. 3 of Wind power plants: Fundamentals, Design, Construction and Operation, ed. by Gasch, R. and Twele, J. Berlin, Springer-Verlag, 2011 [22] Fairley, et al., "The cumulative impact of tidal stream turbine arrays on sediment transport in the Pentland Firth", Renewable Energy, vol. 80, pp. 769, 2015

Claims (8)

1. Claims 1. A system for mooring multiple power generating units and distributing the units over a large area of a body water comprising: a common array tether onto which the multiple power generating units arc moored at intervals in series to form a linear array; two clumps, each attached to the common array tether at a position near each end of the common array tether respectively; two lifting buoys, each connected to each end of the common array tether respectively; and two main mooring tethers, each having one end connected to each of the lifting buoys respectively and the other end anchored to bottom of the water; wherein the two clumps pull the common array tether downward in submersion, the lifting buoys keep the whole common array tether and the clumps off bottom of the water, and the two main mooring tethers pull the two lifting buoys to make distance between the two lifting buoys larger than length of the common array tether in between the two clumps such that the two clumps pull and straighten the common array tether in between horizontally.
2. 2. The system of claim 1, wherein each of the multiple power generating units comprises a single horizontal axis turbine, the single horizontal axis turbine being moored to the common array tether by a turbine mooring system capable of mooring the single horizontal axis turbine in submerged floating state while balancing turbine rotor torque and allowing bi-directional operations in a tidal stream, the turbine mooring system comprising a pair of mooring handles attached to left and right sides of nacelle of the turbine respectively in front of and along axis of rotor of the turbine; a balancing stage comprising a horizontal beam and a downward extending structure with a ballast; a first pair of mooring lines connecting two ends of the horizontal beam to outer ends of the mooring handles respectively; a mooring base attached to the common array tether; and a second pair of mooring lines connecting two ends of the horizontal beam to one single position on the mooring base; wherein buoyancy center of the turbine lies between the mooring handles and the rotor, mass center of the turbine lies between the buoyancy center and the rotor, buoyancy of the turbine can pull up the balancing base and moment of buoyancy force of the turbine with respect to fairleads on the mooring handles can rotate the nacelle of the turbine to an upright pose under low or no flow situations.
3. 3. The system of claim 1, further comprising a number of lateral control lines connecting to and mooring the lifting buoys from two lateral sides of the main mooring tethers; a set of winches for pulling and relaxing the lateral control lines selectively to adjust positions of the lifting buoys thereby changing position and angle of deployment of the common array tether.
4. 4. A system for mooring a single-turbine fluid kinetic power generator in submerged floating condition while balancing turbine rotor torque and allowing bi-directional operations in a tidal stream, the system comprising: a pair of mooring handles attached to left and right sides of nacelle of the turbine respectively in front of and along axis of rotor of the turbine; a balancing stage comprising a horizontal beam and a downward extending structure with a ballast; a first pair of mooring lines connecting two ends of the horizontal beam to outer ends of the mooring handles respectively; a mooring base; and a second pair of mooring lines connecting two ends of the horizontal beam to one single position on the mooring base; SO, wherein buoyancy center of the turbine lies between the mooring handles and the rotor, mass center of the turbine lies between the buoyancy center and the rotor, buoyancy of the turbine can pull up the balancing base and moment ot buoyancy force of the turbine with respect to fairleads on the mooring handles can raise the nacelle of the turbine to an upright pose under low or flow situations.T
5. 5. A method for mooring multiple power generating units and distributing the units over a large area of a body water including: providing a common an-ay tether and mooring the multiple power generating units at intervals in series onto the common array tether to form a linear array; providing two clumps and attaching the two clumps to the common array tether with each to a positon near each end of the tether respectively so that the two clumps pull the common array tether downward in submersion; providing two lifting buoys and connecting each to each end of the common array tether respectively so that the lifting buoys keep the whole common array tether and the clumps off the bottom of the water; providing two main mooring tethers to moor the two lifting buoys to two anchors on bottom of the water respectively; and making distance between the two lifting buoys greater than length of the common array tether in between the two clumps such that the two clumps pull and straighten the common array tether in between horizontally.
6. 6. The method of claim 5, wherein each of the multiple power generating units comprises a single horizontal axis turbine, the method further including a turbine mooring method to moor the single horizontal axis turbine to the common array tether in submerged floating state while balancing turbine rotor torque and allowing bi-directional operations, the turbine mooring method including: providing a pair of mooring handles attached to left and right sides of nacelle of the turbine respectively in front of and along axis of rotor of the turbine; providing a balancing stage comprising a horizontal beam and a downward extending structure with a ballast; connecting outer ends of the mooring handles to two ends of the horizontal beam of the balancing stage by a first pair of mooring lines respectively, this connection enabling the balancing stage to counter the turbine rotor torque and prevent continuous rolling of the turbine under various flow speeds; providing a mooring base attached to the common array tether; connecting two ends of the horizontal beam to one single position on the mooring base by a second pair of mooring lines; making buoyancy center of the turbine lie between the mooring handles and the rotor; making mass center of the turbine lie between the buoyancy center and the rotor; making buoyancy of the turbine he able pull up the balancing base; and SO, making moment of buoyancy force of the turbine with respect to fairleads on the mooring handles be able to raise the nacelle of the turbine to upright pose when there is low or no flow condition.
7. 7. The method of claim 6, further including a method of changing position and angle of deployment of the common array tether by adjusting positions of the lifting buoys by applying a number of lateral control lines connecting to and mooring the lifting buoys from two lateral sides of the main mooring tethers and by pulling and relaxing the lateral control lines selectively.
8. 8. The method of claim 6, further including a depth keeping method for maintaining the turbines within a preferred range of submerged floating depth under various flow speeds, the depth keeping method including matching changes of vertical distance between the turbines and the conullon array tether, of vertical distance between the common array tether and fairleads on the lifting buoys and of depth of the fairleads on the lifting buoys; and controlling relation between the depth of the fairlead of the lifting buoy and the buoyancy of the lifting buoy by design of the lifting buoys.