Performance analysis of two generations of heaving point absorber WECs in farms of hexagon-shaped array layouts

Figures & data

Figure 1. Tools and programmes of DNV Sesam used in this study.

Table 1. LCoE costs of an isolated WaveEL 4.0 unit and the four farms with different array layouts. The definition of different layouts can be found in Section 2.4.2; Ringsberg et al. (2020a) provided a detailed presentation of all the financial parameters and costs.

Costs [EUR]	Isolated unit	Hex1-80	Hex1-120	Hex2	StarBuoy
Concept definition, C1	3,164,467	3,172,738	3,469,703	4,819,595	3,429,219
Design and development, C2	2327	2327	2327	2327	2327
Manufacturing, C3	867,908	4,097,553	4,104,187	4,147,660	6,693,678
Installation, C4	116,896	413,160	413,160	666,160	691,600
Exploitation, C5	1,975,377	4,920,796	5,637,277	6,185,174	11,424,737
Dismantling, C6	20,874	60,390	60,390	60,390	91,990
Sum of costs C1-C6, LCC	6,147,848	12,666,937	13,687,017	15,881,280	22,333,525

Figure 2. (a) The geometries of WaveEL 3.0 (left) and WaveEL 4.0 (right); (b) an isolated WaveEL 4.0 unit with moorings (Shao et al., 2023).

Table 2. Geometric parameters of the two WEC configurations.

Parameter	WaveEL 3.0	WaveEL 4.0
COG [m] (the origin is at the still water level)	−1.9	−10.6
Weight [kg]	140,000	217,000
Tube length [m]	10.7	37.1
Buoy diameter [m]	8	8.6
Tube outer diameter [m]	3.5	3.5

Figure 3. (a) Three array layouts for WEC farms. The numbered yellow circles show the WEC units, green circles show the floaters, and blue squares show the anchors. From left to right: Hex1 (with a distance of 80 or 120 m for Hex1-80 or Hex1-120, respectively), Hex2, and StarBuoy. Examples of incident wave directions are marked with blue arrows. (b) The evolution roadmap of the three studied array layouts.

Table 3. Key parameters of the conceptual array layouts.

Layout	Number of units	Distance of units [m]	R [m]	r [m]
Hex1-80; Hex1-120	6, sharing a centre anchor	80; 120	139; 208	80; 120
Hex2	6, not sharing a centre anchor	260	390	130
StarBuoy	10 (Yang et al. 2020a)	52	200	100

Table 4. Definition of three environmental conditions selected for detailed study by numerical simulations.

EC	Wave amplitude, A [m]	Wave period, T [s]	Wavelength [m]	Occurrence probability [%]
EC1	0.25	4.5	31.6	6.84
EC2	0.75	5.5	47.2	10.14
EC3	1.75	7.5	87.8	5.63

Figure 4. (a) Heave amplitude response per unit wave height with respect to wave period (Shao et al., 2023). (b) power generation of the isolated single WEC units under different environmental conditions (EC1 to 3).

Figure 5. Normalised power absorbed by each WEC unit in the Hex1-80 layout for (a) WaveEL 3.0, (b) WaveEL 4.0, and (c) WaveEL 4.0 but normalised with the reference value of WaveEL 3.0. The incoming wave angle is 180°, which is marked with red arrows. The polar coordinate system is used here, and the unit positions are indicated in Figure 3(a).

Figure 6. Normalised total power of the Hex1-80 layout with the incident wave direction of 180^o.

Figure 7. Normalised power output from each WEC unit in the Hex1-80 layout under EC2, using (a) WaveEL 3.0 and (b) WaveEL 4.0. The arrows indicate the incident wave directions.

Figure 8. Normalised total power of the Hex1-80 layout with different incident wave directions under the various environmental conditions: (a) EC1, (b) EC2, and (c) EC3.

Figure 9. Normalised power generated from each WEC unit in the Hex1-120 and Hex2 layouts under EC2 with the incident wave direction of 150° for (a) WaveEL 3.0 and (b) WaveEL 4.0, and 180° for (c) WaveEL 3.0 and (d) WaveEL 4.0. Note that the polar coordinate system is used here, and the unit positions correspond to Figure 3(a). The red arrows indicate the incident wave directions.

Figure 10. Normalised power generated from each WEC unit in the Hex1-120 and Hex2 layouts under EC3 with the incident wave direction of 150° for (a) WaveEL 3.0 and (b) WaveEL 4.0, and 180° for (c) WaveEL 3.0 and (d) WaveEL 4.0. Note that the polar coordinate system is used here, and the unit positions correspond to Figure 3(a). The red arrows indicate the incident wave directions.

Table 5. Power interaction factors I_p [-] for Hex1-80, Hex1-120, and Hex2.

WaveEL; EC	Incident wave direction [deg.]	Hex1-80	Hex1-120	Hex2
3.0; EC1	150	1.21	1.44	1.86
	160	1.20	1.19	1.80
	170	1.38	1.25	1.80
	180	1.43	1.05	1.80
3.0; EC2	150	1.09	1.30	1.40
	160	1.24	1.15	1.32
	170	1.25	1.07	1.34
	180	1.30	1.25	1.35
3.0; EC3	150	0.92	0.98	0.96
	160	0.97	0.98	0.98
	170	0.99	0.99	1.03
	180	1.00	1.00	1.03
4.0; EC1	150	1.26	1.76	1.10
	160	1.29	1.48	1.02
	170	1.45	1.44	1.02
	180	1.32	1.22	1.09
4.0; EC2	150	1.18	1.44	1.17
	160	1.41	1.31	1.14
	170	1.44	1.18	1.16
	180	1.49	1.39	1.22
4.0; EC3	150	0.92	1.44	0.94
	160	0.97	1.31	0.97
	170	0.99	1.18	0.99
	180	1.00	1.01	0.99

Table 6. Power interaction factors I_p [-] for StarBuoy with WaveEL 4.0 under EC2.

Wave encounter direction [deg.]	Ip [-]
150	1.41
165	1.45
180	1.63
195	1.59
210	1.67
225	1.66
240	1.70
255	1.68
270	1.81
285	1.68
300	1.51
315	1.57
330	1.39

Table 7. Mean values of the interaction factors I_p [-] in Table 5 and Table 6.

WaveEL; EC	Hex1-80	Hex1-120	Hex2	StarBuoy
3.0; EC1	1.31	1.23	1.82	N.A.
3.0; EC2	1.22	1.19	1.35	N.A.
3.0; EC3	0.97	0.99	1.00	N.A.
4.0; EC1	1.33	1.48	1.06	N.A.
4.0; EC2	1.38	1.33	1.17	1.60
4.0; EC3	0.97	1.24	0.97	N.A.

Table 8. LCoE [EUR/kWh] estimated with/without the power interaction factors I_p presented in Table 7.

	Hex1-80	Hex1-120	Hex2	StarBuoy
Assume Ip = 1	0.76	0.80	0.94	0.72
3.0; EC1	0.58	0.65	0.52	N.A.
3.0; EC2	0.62	0.67	0.70	N.A.
3.0; EC3	0.78	0.81	0.94	N.A.
Mean value: 3.0 EC1-EC3	0.66	0.71	0.72	N.A.
4.0; EC1	0.57	0.54	0.89	N.A.
4.0; EC2	0.55	0.60	0.80	0.45
4.0; EC3	0.78	0.65	0.97	N.A.
Mean value: 4.0 EC1-EC3	0.64	0.60	0.89	0.45

Figure 11. Normalised total power from the entire layouts, Hex1-120 and Hex2, using WaveEL 3.0 and 4.0 under the different environmental conditions, EC1–3.

Figure 12. Normalised total power from the entire StarBuoy layout for incident wave directions of 150° to 330°, using StarBuoy with WaveEL 4.0 under EC2.

Table 9. LCoE from other studies for comparison.

References	Description	LCoE (EUR/kWh)
Sandberg et al. (2016)	1 WECs, CorPower WEC	0.633
	2 WECs, CorPower WEC	0.282
	4 WECs, CorPower WEC	0.310
Sergent et al. (2020)	Oscillating float, r = 0.1	0.27–0.37
	Oscillating float, r = 0.075	0.23–0.32
Giassi et al. (2020)	10 WECs, interaction cutoff distance 40 m or 100 m	0.240 (40 m); 0.245 (100 m)
	20 WECs, interaction cutoff distance 40 m or 100 m	0.238 (40 m); 0.242 (100 m)
	50 WECs, interaction cutoff distance 40 m or 100 m	0.245 (40 m); 0.247 (100 m)
Oliveira-Pinto et al. (2019)	Bref-SHB, point absorber	0.389
	F-HBA, point absorber	0.188
	Bref-HB, point absorber	0.428
	F-2HB, point absorber	0.220

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Data availability statement

There is no data availability statement.