1. Introduction
Tidal stream energy resource in coastal areas is estimated to exceed 8,000 TWh/yr (Perez-Ortiz et al., 2017), with a significant part of this resource concentrated in interconnected channels between nearby islands. Some examples are the Goto Islands in Japan, which features areas of high energy density located in four parallel channels between five main islands (Sun et al., 2014), and the Orkney Islands in Scotland, where potential tidal energy sites lie in several interconnected channels between the many islands that form the archipelago (Neill et al., 2017).
Because of the proximity of the different tidal energy sites described in the previous paragraph, it can be expected that changes in the hydrodynamics caused by the conversion of the kinetic energy of currents (Ramos et al., 2019) in one tidal farm will affect the flow conditions in nearby farms and thereby impact their performance and operation. Draper et al. (2014) numerically analyzed the interactions of tidal farms in adjacent channels in the Orkney Islands, Scotland, and concluded that the extraction of tidal current energy in parallel channels has a positive impact on the generated power, compared to the performance of every individual array when operating alone. However, arrays located upstream and downstream in the same channel diminish each other’s energy outputs. Waldman et al. (2019) analyzed the policy implications of these interactions between farms and argued that, if the maximization of the energy yield produced by several farms in one or a group of channels is pursued, then the interactions between upstream and downstream farms, side-by-side farms, and farms in parallel channels must be considered.
In addition to this impact on the generated power, changes in the hydrodynamics can also affect the design and planning of installation, maintenance, and decommissioning work in other farms within the same channel or in interconnected channels. During the first phase of the tidal energy demonstration project in the Naru Strait, Goto Islands, the main restriction for scheduling offshore work was the tidal current velocity at the site. The dynamic positioning (DP) vessel used for turbine installation and decommissioning had a current velocity operational limit of 1 m/s (ToYo Construction, 2024), and periodic work involving divers for the visual monitoring of the conditions around the turbine had a maximum current velocity threshold of 0.35 m/s. Thus, the duration of each work window – and hence, the overall cost of installation – is influenced by the times at which these velocities are reached. Thus, changes in hydrodynamics caused by the operation of tidal farms near the farm under construction may affect the time available for subsea operations, and hence the design and planning of installation, maintenance, and decommissioning work.
In addition to the Naru Strait, resource assessment studies for the Goto Islands have presented the Tanoura and Takigawara Straits (parallel to the Naru Strait) as promising sites for the commercial exploitation of tidal stream energy. The Tanoura and Naru Straits have already been designated by the Japanese government as areas for tidal energy development (Coles et al., 2018). Each of these channels is divided into two parts, differing in the body that owns the fishery rights. For example, fishing rights on the western side of the Naru Strait are owned by the Hisaka Fishery Union, while fishing rights in the eastern half of this channel are owned by the Naru Fishery Union. Therefore, it is thought that the exploitation of tidal energy in different channels and fishing areas may occur at different stages of tidal energy development in the Goto Islands. In particular, the different jurisdictions on either side of each strait may lead to the creation of two separate tidal farms in each strait, perhaps owned by different companies and operated separately.
This study aims to quantify the impacts on the flow, and hence on the lengths of offshore work windows, of four hypothetical tidal energy farms in the Goto Islands. Two farms are located side-by-side in the Naru Strait, and the other two are in the Tanoura and Takigawara Straits.
2. Case Study
2.1 Area of Study
The Goto Islands (Fig. 1) form an archipelago located in south-west Japan, part of Nagasaki Prefecture. The main flow direction in the three main channels follows a south-east – north-west direction (from the Pacific Ocean to the East China Sea) during flood tides, and vice versa during ebb tides.
The three channels examined in this study differ in their dimensions and available tidal energy resource. The Tanoura Strait is 7 km long and 2 km wide, and the depth in its central part ranges between 40 and 50 m. According to numerical models available in the literature (Garcia-Novo et al., 2018), the strongest currents are expected near the southern entrance of the channel, with maximum velocities of approximately 2.9 m/s. The Naru Strait is 7 km long and has a width of 2 km for most of the channel, with the exception of a narrowing to 1 km caused by a headland protruding from its eastern bank. The highest current velocities are found in this narrowing, where current velocities slightly higher than 3.0 m/s were measured in the autumn of 2016 (Garcia-Novo et al., 2024). The maximum depth in the Naru Strait is 55 m. The Takigawara Strait is the shortest (4 km), narrowest (780 m at its shortest cross-section), and deepest (up to 75 m) of the three channels. The highest current velocity estimated from numerical simulations is approximately 4 m/s.
2.2 Scenarios
For simplicity, only one turbine type was considered for this study. This turbine is a generic horizontal-axis 1 MW machine of 20 m diameter, as presented by Baston et al. (2015). The thrust coefficient is considered to be constant for current velocities less than or equal to the turbine rated speed (2.5 m/s). For higher velocities, the thrust coefficient is scaled such that the power output is constant.
In this work, interactions among four hypothetical tidal farms were analyzed. The first was on the western side of the Naru Strait, located in the Hisaka Fishery Union fishing rights zone (hereafter Farm A). The second was located on the eastern side of the channel, corresponding to the Naru Fishery Union fishing rights zone (Farm B). The other two farms were located in the Tanoura Strait (Farm C) and Takigawara Strait (Farm D). In order to allocate a number of turbines to each channel in approximate proportion to the available power, the maximum extractable power of each channel was estimated using the method described by Garrett and Cummins (2005).
where Qmax is the volume flux in a given cross-section of the channel, a is the amplitude of the tidal wave, ρ is the density of the seawater, and γ is a parameter that varies within a small range, depending on the balance between friction and inertia in the channel. In this study, γ was set as 0.22 for the three channels, as this is an intermediate value that is guaranteed to be within 10% of the correct value (Garrett and Cummins, 2005).
Calculations based on numerical model results for a scenario without energy extraction provided maximum extractable powers of 96 MW for the Naru Strait, 116 MW for the Takigawara Strait, and 82 MW for the Tanoura Strait. Considering a conversion efficiency of 50% (Waldman et al., 2017), which is consistent with the results from experimental studies on similar converters (Bahaj et al., 2007; Olvera-Trejo et al., 2024), these values lead to a maximum power generation of 48, 58, and 41 MW, respectively. These results are consistent with those presented by (Waldman et al., 2017), who found a maximum of 36 MW using simulations forced only with the M2 tidal constituent, which accounts for approximately 65% of the energy in the Naru Strait. This ratio of 48:58:41 was used to determine the number of turbines assigned to each channel. Note that the total capacity of the installed generation is not expected to directly correspond to the power generated, because not every turbine is expected to operate at its rated capacity. The purpose of this exercise was to ensure that proportionate levels of generation were placed in each channel.
Regular grids with staggered distributions were generated for the spatial distribution of the turbines within each farm. Based on tidal stream energy farming studies available in the literature (Ouro and Nishino 2021; Noble et al., 2020), the distance between two consecutive turbines perpendicular to the flow was three rotor diameters. In the flow direction, the distance between two consecutive rows of turbines was five diameters. Because of the staggered distribution used for the farms in this study, the distance between two consecutive turbines in the direction of the main flow was 10 rotor diameters (Yang et al., 2022). The power generated for each point of these grids for a spring–neap tidal cycle was calculated based on results for current velocity from a model that simulated the flow conditions without energy extraction. The 24 nodes with the highest energy yield in the Hisaka Fishery Union fishing rights zone were selected as the locations for the 24 1 MW turbines of Farm A. The locations of 24 turbines in Farm B, 41 turbines in Farm C, and 58 turbines in Farm D were determined analogously. Fig. 2 shows a map of the turbine positions for the four farms.
3. Methods
The analysis of the impact of tidal current energy exploitation on the capacity factor and offshore work planning of nearby farms presented in this work is based on results from ocean regional models simulating the different scenarios differing in the operating farms presented in Section 2.2.
3.1 Numerical Model
The finite-volume community ocean model (FVCOM) was used for these simulations. FVCOM is an unstructured finite-volume three-dimensional numerical ocean model (Chen et al., 2003) that solves the three-dimensional primitive equations for momentum (Eqs. (2)–(4)), continuity (Eq. (5)), temperature (Eq. (6)), salinity (Eq. (7)), and density (Eq. (8)):
These equations are closed with the Mellor and Yamada level 2.5 turbulence closure scheme for vertical eddy mixing (Mellor and Yamada, 1982) and with the Smagorinsky parameterization for horizontal eddy viscosity (Smagorinsky, 1963). The numerical domain of the model covers an area of more than 50,000 km2 around the Goto Islands, with every open boundary node at least 100 km from the area of interest to minimize the impact of open boundary numerical instabilities on the results. The model was forced at each open boundary node with 10-minute tide elevation results from the Matsumoto model (Matsumoto et al., 2000), which is a 0.5° resolution Japan Ocean Model that estimates tidal elevations based on 16 constituents’ amplitudes and phases calculated from data measured by 219 tidal gauges and TOPEX/Poseidon. The bathymetry for each mesh node was calculated by spatial interpolation of 1 m resolution data for the three channels under study and the Wakamatsu Strait (the easternmost channel of the Goto Islands), digitization of NewPec maps for Goto Island approaches, and 500 m resolution data from the Japan Oceanographic Data Center.
The mesh resolution of the FVCOM model is approximately 250 m in the Tanoura and Takigawara Straits. The mesh resolution was reduced to 125 m in the Naru Strait to better simulate the interaction between the two side-by-side farms. The element size increases from these three channels to approximately 4.3 km in the cells adjacent to the open boundary. For vertical discretization, 10 uniform sigma layers were set. The water temperature and salinity were kept constant in time and space, and the meteorological conditions (wind, air temperature, etc.) were not considered in order to reduce the required computational time. The simulated period for each scenario was 15 days, starting on November 14, 2016, which allowed a direct comparison with an available Acoustic Doppler Current Profiler (ADCP) record.
A spin-up period of 4 days was added to ensure that the model reached a state of equilibrium before the validation period. The timestep was set as 0.25 s, and model results were output every 10 min.
3.2 Tidal Turbine Implementation
The effect of the tidal turbines on the flow velocity in the FVCOM code was implemented using an additional momentum sink term in Eqs. (2) and (3), as per Murray and Gallego (2017). This momentum sink term is applied to all vertical layers containing a part of the turbine, the relative weight of each depending on the rotor area covered by this layer.
3.3 Data Measurement
The numerical model was validated with data measured using an ADCP in the narrowing of the Naru Strait where the highest current velocities are expected (32° 49′ 6.6″ N, 128° 54′ 37.8″ E) from October 25 to December 18, 2016. The average depth during the measurement period was 40.02 m. The ADCP was set to measure current velocity data with a sampling frequency of 0.5 Hz at 45 vertical layers, each with a 1 m width, thus covering the entire water column. A blanking space of 0.5 m was set between the ADCP and deepest measured layer. After noise filtering (correlation < 50 and SNR < 3 dB data were discarded), the data were separated into 5-minute groups. The maximum 5-minute averaged current velocity at this point during the measuring period, at the height of the hub of the turbine presented in Section 2.2, was 3.02 m/s for the flood tide and 2.91 m/s for the ebb tide. Water flows in a southeast to northwest direction during the flood tide and vice versa during the ebb tide, with an asymmetry of approximately 24°. A more detailed analysis of the ADCP data is available in Garcia-Novo et al. (2024).
4. Results
4.1 Model Validation
5-minute averaged values for u, v, and velocity magnitude obtained from the analysis of ADCP data were compared with results from the model simulating the conditions in the Goto Islands in October 2016 (i.e. with no turbines installed) for the cell containing the ADCP installation point. Fig. 3 presents the model validation for the layer corresponding to the rotor hub height (15 m from the sea bottom). It shows a slight underestimation of tidal current velocity, particularly during ebb tides. Numerically, the correlation coefficient and the root mean square error (RMSE) between the measured data and model results at this depth are 0.9574 and 0.21 m/s, respectively.
Regarding the flow direction (Fig. 4), the model had a mean deviation of 2.92° for flood tides and 6.50° for ebb tides. An analogous evaluation was performed for the model results at 5 and 25 m from the sea bottom to confirm the accuracy of the model for the vertical area covered by the rotor, and the results were similar to those obtained for the rotor hub layer. Table 1 presents the RMSE and correlation coefficients for the magnitude, as well as the u and v components, of the velocity at the three representative vertical layers. The high correlation coefficients and relatively low errors found for current velocity and direction suggest that the model is an acceptable tool for simulating tidal currents in the study area.
4.2 Side-by-side Farms in the Same Channel
To analyze the impact of the two parallel farms in the Naru Strait on each other, the three scenarios presented in Table 2 were simulated: 1) a scenario with no energy extraction; 2) a scenario with Farm B operating; and 3) a scenario with both Farms A and B operating. The impact of Farm B on Farm A was evaluated by comparing the results of the models simulating scenarios 1 and 2. The impact of Farm A on Farm B was approximated by comparing the results from the models that simulated scenarios 2 and 3.
Fig. 5 shows the differences in current velocity between Scenarios 1 and 2 for the highest current velocities during the spring flood and ebb tides. Due to the flood–ebb asymmetry shown in the tidal rose in Fig. 4, the turbines of the Hisaka area farm closest to the boundary between the two sides of the channel fell into the wakes generated by the turbines in the Naru farm. The increase in current velocity at both sides of Naru farm owing to its blockage effect was negligible, compared to the velocity deficit in the wakes. Consequently, both farms cause a decrease in the power generated by the other. The velocity deficit in the wakes of the turbines in Farm B led to a decrease of 5.37% in the estimated capacity factor of Farm A. Similarly, the reduction in the capacity factor of Farm B caused by energy extraction in Farm A was 2.22%.
The maps presented in Fig. 5 show that the turbines most affected by neighboring farms are those closest to the boundary between the fishing rights areas. Separately analyzing the impact of Farm A on every individual turbine in Farm B, maximum deficits in the capacity factor were found in the turbines in the central part of the channel (up to 18.1%). In contrast, an increase in energy yield of up to 0.64% was obtained for turbines closer to the eastern shore.
These changes in the flow in the Naru Strait have an impact on the available time for offshore work on side-by-side farms. To evaluate this impact, only a 3 d period from day 8 to day 11 (Fig. 6) was used, since offshore work is mainly scheduled during neap tides. Energy extraction at Farm B increased DP vessel operation time by 9.1% for Farm A’s turbines near the fishing rights boundary. This effect on the available working time was reduced in the following turbine rows, with differences of only 35 s (0.2%) in the turbines closer to the western shore. Similarly, the operation of Farm A caused a considerable increase in the length of the DP vessel working windows for the turbines of Farm B located in the central part of the channel (up to 8.1%). In the turbines closer to the Naru Island coastline, a slight reduction in the available time was found (up to 0.12%).
In contrast, since the current velocity threshold for diver work (0.35 m/s) is much lower than the cut-in speed of the turbine considered for this work, the impacts of Farm A and Farm B on the lengths of the diving windows of the other are marginal. In both cases, an extension of the work window was estimated, but this effect was limited to 0.14% (3 s) or less.
4.3 Farms in Parallel Channels
To analyze the interactions between farms installed in parallel channels, the three cases presented in Table 3 were simulated: 4) a scenario with Farm A and Farm B (both Naru Strait) operating; 5) a scenario with Farm C (Tanoura Strait) and Farm D (Takigawara Strait) operating; and 6) a scenario with energy extraction in all three channels. Fig. 7 shows maps of the change in current velocity caused by Farms A, B, C, and D all operating together at the time of the highest current velocity in the Naru Strait.
These maps confirm that the increase in current velocity in the parallel channels is at least one order of magnitude lower than the velocity deficit related to the turbine wake. This was confirmed by the null impact on farms in parallel channels in terms of capacity factor and operation window duration. The operation of Farms C and D would increase the capacity factor of the 48 MW farm in the Naru Strait by only 0.086%. Likewise, the differences in the available time for DP vessel works during ebb tides between the two scenarios with and without energy extraction in the Tanoura and Takigawara Straits are less than 2.3 s in all cases. Taking the ADCP installation point as a reference, the maximum difference in current velocity caused by Farms C and D in the area of energy extraction in the Naru Strait is 0.0016 m/s. Similarly, energy extraction in Farms A and B in the Naru Strait would lead to increases of only 0.054% and 0.038% in the capacity factors of Farms C and D, respectively, and changes in the lengths of the offshore working windows would be negligible.
These maps show that the areas of velocity deficit downstream of the turbines extend closer to the southern channel entrances during ebb tides than to the northern entrances during flood tides. In the cases of farms in the Naru and Tanoura Straits, this can be explained by the position of the farms, located in the southern half of the channel. In the case of the Naru / Takigawara Strait system, this is due to the triangular shape of the island between the two channels (Naru Island). The northern entrances of the two channels are separated by one side of the triangle (approximately 6 km), and the southern entrances of the channels are separated by the southern vertex of the triangle. Thus, the interactions between farms in these parallel channels are expected to be more significant during ebb tides than during flood tides. For this reason, further analysis of the impacts of the simulated farms on the flows in parallel channels was performed based on the model results for ebb tides.
Fig. 8 shows the changes in surface elevation caused by the 48 MW farm in the Naru Strait (resulting from the combination of Farms A and B) as well as the farms in the Tanoura and Takigawara Straits at peak ebb. For a better visualization of the impacts of tidal farms in parallel channels, the colormap limits are set to ±1 mm. The extraction of energy in the Naru Strait causes a small increase in head across both the Tanoura and Takigawara Straits. This result is consistent with the slight increase in the capacity factors of Farms C and D. Similarly, energy extraction in the Tanoura and Takigawara Straits causes a small drop in surface elevation at the southern entrance of the Naru Strait and a small increase at its northern entrance. This slight increase in the potential difference along the strait explains the small increase in the capacity factors of Farms A and B.
5. Discussion and Conclusion
Several studies have highlighted the potential for both near- and far-field interactions between tidal farms within a region (Draper et al, 2014; Waldman et al, 2019). In this work, we have performed an initial investigation of the magnitudes of these effects for realistically sized arrays in the Goto Islands, and the changes that they might cause in the duration of velocity-constrained work windows.
Interactions between tidal farms in separate but parallel channels were observed, with blockages in one channel increasing the capacity factor of an array in the other channel, but these effects were small. These results are consistent with the findings of Waldman et al., (2017), who noted that the channels interact weakly due to the geometry of the islands.
Interactions between two tidal farms built in opposite cross-stream halves of a single strait were somewhat greater; however, the increase in power that each farm might be expected to provide to the other from blockage effects was negligible compared to the velocity deficits experienced by one farm when close to, or impacted by the wake of, the other. These results highlight the importance of designing adjacent tidal arrays to avoid the wakes of each others and, more generally, of designing each array taking account of the effects of its neighbours, rather than (as in this study) simply selecting the areas of highest undisturbed velocity magnitude. Such a design approach may pose challenges to developers and for regulatory/consenting processes, as noted by Waldman et al. (2019).
It is interesting to note that the construction of two or more separate tidal arrays on opposite sides of the same strait is likely to occur in Japan, despite the difficulties in optimisation that it brings, because of the system of fishery unions that have authority over marine developments in their waters. As these unions, at least in Goto, are defined around landmasses, the boundaries between their areas of authority tend to lie along the centerlines of tidal straits.
The lengths of the windows during which the currents are sufficiently slow to work on site are important factors in the installation costs, and perhaps also the maintenance costs, of tidal stream arrays. Here, we have shown that changes in the flow caused by tidal farms can cause small but significant changes in the lengths of these windows for DP operations, with the greatest observed in this study being a 9% increase. This may make it possible to extend operational windows slightly by scheduling work downstream of operating turbines - although further attention to turbulence, turbidity, etc., would be required to determine whether conditions would be safe.
There were no changes in the duration of the work windows for diving, because the maximum flow velocities for diving are below the cut-in speed of current-generation tidal turbines.
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