- Email: [email protected]
Device interactions in reducing the cost of tidal stream energy
Energy Conversion and Management 97 (2015) 428–438
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Device interactions in reducing the cost of tidal stream energy A. Vazquez a,⇑, G. Iglesias b a b
University of Santiago de Compostela, EPS, Hydraulic Eng., Campus Univ. s/n, 27002 Lugo, Spain University of Plymouth, School of Marine Science and Engineering, Drake Circus, Plymouth PL4 8AA, UK
a r t i c l e
i n f o
Article history: Received 15 January 2015 Accepted 12 March 2015 Available online 8 April 2015 Keywords: Tidal stream energy Levelised cost of energy Tidal device interactions Energy production
a b s t r a c t The levelised cost of energy takes into account the lifetime generated energy and the costs associated with a project. The objective of this work is to investigate the effects of device interactions on the energy output and, therefore, on the levelised cost of energy of a tidal stream project, by means of numerical modelling. For this purpose, a case study is considered: Lynmouth (North Devon, UK), an area in the Bristol Channel in which the first tidal stream turbine was installed a testimony of its potential as a tidal energy site. A state-of-the-art hydrodynamics model is implemented on a high-resolution computational grid, which allows the demarcation of the individual devices. The modification to the energy output resulting from interaction between turbines within the tidal farm is thus resolved for each individual turbine. The results indicate that significant changes in the levelised cost of energy values, of up to £0.221 kW h1, occur due to the aforementioned modifications, which should not be disregarded if the cost of tidal stream energy is to be minimised. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Tidal stream energy is called to play a major role in meeting future energy needs due to its advantages relative to other renewable energies; inter alia, predictability, stability and high load factor [1]. The interest of the tidal stream resource has driven intense research during the last decades, which has mainly centred on resource assessments and technological advances [2]. Concerning the assessments of the tidal resource, they allowed the quantification of the potential energy production in a number of promising tidal stream areas worldwide, including sites around headlands, straits between islands or enclosed bodies of water, such as estuaries [3]. In previous works, different methodologies were applied, including numerical modelling and direct flow measurements [4]. Having quantified the available energy resource, the final decision concerning a future tidal stream installation at a potential site is subject to several practical constraints, such as the existence of tidal asymmetry, i.e. differences between flood and ebb phases of the tidal cycle. These differences can affect the performance of tidal stream converters and can serve as a criterion to decide if bi-directional turbines should be preferred, as discussed by Neill et al. [5] with reference to Orkney (Northern Scotland). The relationship between tidal flow and bathymetry
⇑ Corresponding author. Tel.: +34 982823295; fax: +34 982285926. E-mail address: [email protected] (A. Vazquez). http://dx.doi.org/10.1016/j.enconman.2015.03.044 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.
constitutes another aspect that cannot be disregarded: shear stress and topographic features can influence tidal hydrodynamics, and in some cases induce flow obstruction or recirculation [6]. Finally, the proximity to a grid connection point and the final consumer minimises the loses due to energy transmission. A recent work showed how the electricity needs of a port in Ria de Ribadeo (NW Spain) could be fulfilled through tidal stream energy production [7]. As regards the technological advances, they allowed the development of a range of tidal stream energy converters, including [8]: reciprocating and rotating principle converters, vertical- and horizontal-axis turbines, as well as floating and bottom-fixed devices. As a result, the tidal energy industry is growing rapidly, with commercial designs, such as the SeaGen turbine [9]. However, so far none of the existing designs has gained universal acceptance (as in the case of e.g. the three-bladed horizontal-axis wind turbine [10]). Rather, a number of analyses on different designs are being conducted with a view to determining which characteristics can maximise the power output of converters [11]. It is not only the performance of these converters that is of importance, but also their survivability under extreme conditions, since they are to be deployed in harsh environments [12]. The potential impacts of tidal stream energy are also being investigated, and indeed quantifying and minimising them is a requirement for tidal stream energy to be sustainable [13]. These studies are helping designers to establish a basis on which prototypes can be successfully deployed in real environments [14]. Although there is no doubt that it is technically feasible to
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
429
Nomenclature and units
Roman symbols A turbine aperture (m2) c salinity or temperature (transported substance) CD drag coefficient Cp power coefficient CT thrust coefficient C2D Chézy coefficient d local water depth (m) Dh horizontal eddy diffusivity (m2 s1) Fx x component of the flow retarding force per unit volume (N) Fy y component of the flow retarding force per unit volume (N) f Coriolis parameter g gravitational acceleration (m s2) Mx x component of the momentum generated by an external force (N m) My y component of the momentum generated by an external force (N m) n Manning coefficient Pt tidal stream available power (W) Q intensity of mass sources per unit area (m2 s1) r discount rate R source term per unit area t time (years)
extract energy from tidal currents, only a few tidal stream projects are now operating at a commercial scale [15]. Having observed also proactive public attitudes and positive externalities towards this renewable [16], the primary reason for the scarcity of commercial plants is that the cost of generation from the tidal stream resource, the so-called levelised cost of energy (LCOE), is typically higher than that from traditional sources (coal, natural gas, etc.) [17]. On these grounds, it is crucial to understand the parameters affecting this cost so as to provide a framework of potential areas of reduction [18]. Estimating the LCOE for a tidal stream farm requires information on the expected energy output from the farm and the costs involved in the construction, operation and maintenance of the tidal stream installation [19]. Although the information on the capital and operational cost-values of tidal stream devices is limited due to the technological stage of development, the sensitiveness of their values is well known [20]. In this regard, several areas can contribute to lower the capital and operational costs of tidal stream farms [21]. They include technological innovation, which can lead to improve the performance, efficiency and reliability of tidal stream energy converters; as well as economies of scale [22]. The innovation process should be aligned with policy strategies, including the public subsidisation of this energy [23]. The relationship between the variations of energy output and the LCOE is an aspect that has received less attention. Previous works analysed how the hydrodynamic interactions between tidal stream turbines placed at a real tidal site could modify the flow patterns, such as the transient and residual flows [24]. The alteration of the hydrodynamics has inevitably an effect on the energy available for conversion, and hence, the energy production [25]. In addition, the work of Ahmadian et al. [26] investigated the relationship between the aforementioned modifications with the shape of a tidal stream farm, whereas Neil et al. [27] and Robins et al. [28] focused on the
ti T U V Vc
time instant project lifetime vertically integrated eastward component of the flow velocity (m s1) vertically integrated northward component of the flow velocity (m s1) volume of control
Greek symbols f water level (m) g efficiency kd first order decay process q0 water reference density (kg m3) q0 anomaly density (kg m3) q seawater density (kg m3) sb shear stress at the bottom (N m2) ss shear stress at the surface (N m2) th kinematic horizontal eddy viscosity (m2 s1) Abbreviations AEP annual energy production CAPEX capital expenditures LCOE levelised cost of energy OPEX operational expenditures TST tidal stream turbine
potential effects on sedimentary processes. Notwithstanding, the numerical modelling of the performance of a tidal stream turbine (used in most of the previous studies) has not been applied to the LCOE calculation so far, and this is the main objective of the present work. Lynmouth, on the North Devon coast, constitutes an excellent tidal stream site (Fig. 1). The nearby grid connection point at Lynton and the research facilities of the South West Marine Energy Park [29] are testimony to the potential of this site for tidal stream energy exploitation. Indeed, Lynmouth has been recently included as a new tidal stream energy demonstration zone to be managed by the Wave Hub [30] and the South West Marine Energy Park [31]. This decision based on the experience acquired during 2003, when Lynmouth was the scenario of the world’s first tidal current installation to be deployed in a working environment [32] (the 300 kW tidal stream turbine ‘‘Seaflow’’ of Marine Current Turbines). Lynmouth stands out for tidal streams over 2.25 m s1 in conjunction with water depths in the range 15–25 m, which make it an ideal location for the deployment of the majority of first generation tidal energy converters. As a case study, a high resolution model of Lynmouth is implemented and successfully validated in order to simulate the operation of a tidal farm. The resolution of the model allows the demarcation of individual devices on the grid. The LCOE for each device is examined in two scenarios: without (baseline) and with the tidal stream farm. A comparison between the different estimates is presented, showing a maximum LCOE variation of £0.221 kW h1. As explained below, different values of LCOE are found for each single tidal stream device, ranging from £0.556 kW h1 to £0.663 kW h1 for the baseline case; and from £0.714 kW h1 to £0.828 kW h1 for the farm case. These ranges suggest that the effects on the LCOE are associated with the specific position of the tidal stream converter within the farm which indicates the need for the optimisation of the tidal stream farm.
430
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Mumbles
Celtic Sea boundary
Newport
Ilfracombe
Bristol Channel
Hinkley
Lynmouth North Devon
Coarser domain High-resolution domain
Fig. 1. Study area: Lynmouth (UK).
This article is structured as follows. Section 2 deals with the materials and methods. In Section 3, the results are analysed and discussed. Finally, conclusions are drawn in Section 4. 2. Materials and methods 2.1. The LCOE method The levelised cost of energy (LCOE) is the most extended approach for estimating the cost of lifetime generated energy [33]. This metric has been defined as the ratio of the total cost to the total energy output, expressed in terms of the present value equivalent [34]. Therefore, it constitutes a measure of the marginal cost of electricity over a period of time and it is appropriate for comparing single generation units. According to this definition, the LCOE is calculated as follows:
PT LCOE ¼
t¼0 ðCAPEX þ OPEXÞð1 PT t t¼0 AEPð1 þ rÞ
þ rÞt
ð1Þ
Here, r is the interest rate used for discounting costs each year t back to a reference time period (t = 0), during the lifetime of the
project under consideration (T). CAPEX and OPEX represent the capital and operational expenditures, respectively, and AEP is the annual energy production. It should be noted that the summation calculation starts from t = 0 to include the project cost at the beginning of the first year that is not discounted and there is no system energy output to be degraded. Other methods can include the initial cost or down payment outside the summation, with t starting from 1. As shown in Eq. (1), there are a number of major components determining the LCOE of tidal stream energy. All of them can vary significantly between individual projects (e.g. between solar power systems [35] and offshore wind energy installations [36]) and in some cases, also between countries. Their values are discussed below. a. Capital expenditures (CAPEX) This is the total capital required to build the tidal stream plant. It includes the pre-development costs, electrical systems infrastructure and construction costs. The CAPEX is sensitive to the stage of technological development, since learning and economies of scale are to reduce its value. In addition, different CAPEX values are expected for tidal stream turbines deployed in shallow and deep water (Table 1) [37].
Table 1 Summary of costs (low–high) referred to 2010a [37].
a
Pre-demonstration
Demonstration
Commercial
Tidal stream (shallow) CAPEX (£/MW) OPEX (£/MW/year)
11.2 m (7.5–12.4 m) 0.47 m (0.32–0.56 m)
4.3 m (3.5–5.1 m) 0.31 m (0.23–0.38 m)
3.2 m (2.7–13.9 m) 0.15 m (0.12–0.19 m)
Tidal stream (deep) CAPEX (£/MW) OPEX (£/MW/year)
8.6 m (7.3–9.9 m) 0.31 m (0.27–0.39 m)
3.5 m (3–4.1 m) 0.16 m (0.12–0.2 m)
3.3 m (2.8–4 m) 0.12 m (0.09–0.16 m)
m = Million (106).
431
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
The conservation of momentum is expressed as follows:
b. Operational expenditures (OPEX) Operation and maintenance costs are related to the power capacity of the plant and they are normally expressed in terms of installed power. Like the CAPEX, the OPEX are also dependent on the stage of technological development (Table 1). They include labour, equipment and overhead charges as well as the insurance expenses and the decommissioning costs [37].
The discount rate is the interest rate used for discounting costs each year during the lifetime of the project. It takes into account both the time value of the money and the risk of the investment, which are aspects that vary by circumstance, location and time period considered [35]. Nowadays, tidal stream energy projects involve high capital costs and, due to their novelty, are associated with greater technological risks (if compared to conventional power plants). In this respect, conservative discount rates are considered to range between 10% and 12% [38]. d. Lifetime of the installation (T) The lifetime of the installation refers to the time that the tidal stream farm is working and producing energy and therefore, it is a determinant factor when estimating the LCOE. Nowadays, tidal stream energy farms are expected to be operating during 20 years [39]. After this time, gradual degradation may occur as a consequence of the chemical and material processes associated with corrosion and weathering. Ongoing research will eventually improve project lifetimes as a result of knowledge gained about failure mechanisms. e. Annual Energy Production (AEP) The term AEP represents the amount of generated electricity over a year t, from a reference initial time ti = 0 and it is calculated as follows:
AEP ¼
t i ¼t
t i ¼0
AC p P ti dt
0
ð4Þ Finally, Eq. (5) represents the transport equation, which is solved for both salinity and temperature.
¼ Dh r2 c kd ðd þ fÞc þ R
2.2. Numerical model: governing equations The numerical model, Delft 3D-FLOW, is used in this work for assessing the annual energy production of a prospective tidal stream farm in Lynmouth. It is a finite difference code that solves the Navier–Stokes equations together with the transport equation. Previous assessments of the tidal stream resource used the vertically averaged equations in their baroclinic form [40]. Following them, the present study used these equations and thus, the model took into account the flow driven by horizontal density gradients [41]. On these grounds, the conservation of mass under the assumption of incompressible fluid reads:
ð3Þ
ð5Þ
In the previous equations, there are a number of parameters involved, which are explained as follows. First, U and V represent the vertically integrated velocity components in the east (x) and north (y) directions, respectively. Second, d is the local water depth relative to a reference plane; Q stands for the intensity of mass sources per unit area; f is the Coriolis parameter; th is the kinematic horizontal eddy viscosity; and qo is the reference density, while q0 is the anomaly density. The shear stress components are represented by ssx, ssy, sbx and sby. Finally, in Eq. (5) (the transport equation) c stands for salinity or temperature, Dh is the horizontal eddy diffusivity, kd represents the first order decay process, and R is the source term per unit area. For the model, the Arakawa-C grid is used. This is a staggered grid that allows the spatial discretization of the model used in this study. In this grid, the water levels f are defined at the centre of the grid cell, whereas flow velocity components (U and V) are defined at the mid-points of the grid cell faces to which they are perpendicular. In the momentum and transport equations, i.e. Eqs. (3)–(5), the discretization of the horizontal advection terms is carried out by the Cyclic method [42], as in Ramos et al. [43]. The operation of a tidal farm can be modelled by modifying the 2DH water momentum equations (Eq. (4)). This has been made in previous works (e.g. [43]) and it is summarised here for the sake of completeness. The aforementioned modification is based on the addition of the terms (Mx, My):
(
ð2Þ
where Pti represents the available power density per area in the instant ti, A is the turbine aperture and Cp is the power coefficient that accounts for limitations related to turbine efficiency. This parameter (AEP) is geographically dependent and, therefore, in this work, the power density in the instant ti is obtained through numerical modelling (Sections 2.2 and 2.3), which constitutes a novelty with respect to previous LCOE studies.
@f @½ðd þ fÞU @½ðd þ fÞV þ þ ¼Q @t @x @y
0
@ðf þ dÞc @½ðd þ fÞUc @½ðd þ fÞVc þ þ @t @x @y
c. Discount rate (r)
Z
8 9 R 0 < @U þ U @U þ V @U fV ¼ g @f g f @ q dz þ ssx sbx þ mh r2 U = @t @x @y q0 d @x q0 ðdþfÞ @x : @V þ U @V þ V @V fU ¼ g @f g R f @ q0 dz þ ssy sby þ mh r2 V ; @t @x @y q d @y q ðdþfÞ @y
Mx ¼ Fqx My ¼
) ð6Þ
Fy
q
The previous terms are used to simulate the contribution of momentum generated by each tidal stream turbine on the flow, in the east (x) and north (y) directions, respectively [44]. Thus, the parameters Fx and Fy are the components in the x and y directions of the flow retarding force per unit volume, respectively, as a result of the presence of a tidal stream turbine (TST) [45]. These components have the same value that the thrust force exerted by the flow on each tidal device, but they are opposite to it. This is in line with the Newton’s third law [25]. In this regard, the momentum contribution terms can be written as:
(
Mx ¼ 12
CT A jUjU Vc
My ¼ 12
CT A jUjV Vc
) ð7Þ
where CT is the thrust coefficient, A represents the turbine aperture or swept area and Vc is the volume of control. The magnitude of the flow velocity is represented by |U|, whereas U and V stand for the magnitudes of the velocity in the x and y direction, respectively. On the basis of the previous insights, the momentum equations of the model in the x and y directions are rewritten and finally expressed as follows: 9 8 R 0 < @U þ U @U þ V @U fV ¼ g @f g f @ q dz þ ssx sbx þ mh r2 U þ Mx = q0 d @x q0 ðdþfÞ @t @x @y @x ð8Þ : @V þ U @V þ V @V fU ¼ g @f g R f @ q0 dz þ ssy sby þ mh r2 V þ My ; @y q d @y q ðdþfÞ @t @x @y 0
0
432
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
2.3. Numerical model: implementation In the present study two computational grids were used (Fig. 1). The coarser grid, encompassing the Bristol Chanel with a resolution of 500 m 500 m, was used to provide boundary conditions for the fine nested grid that covers the area of interest (Lynmouth). The grid resolution of the coarser domain resulted in a computational grid of 419 (direction M) 324 (direction N) cells and was chosen so as to provide relatively high spatial resolution at a relatively low computational cost. The bathymetric data, from the General Bathymetric Chart of the Oceans (GEBCO), was interpolated onto this grid. Along the Celtic Sea boundary, a Dirichlet boundary condition was imposed with the sea level prescribed as a function of time using the nine major tidal harmonics shown in Table 2. These tidal harmonics were obtained for eight sections along the open boundary (Celtic Sea Boundary) from the global ocean tide model TPXO 7.2 [46]. This model has been shown to produce good results in previous works (e.g. [47,48]). Table 2 shows the amplitudes and phases for one of the eight sections. Salinity and temperature at the Celtic Sea boundary were imposed using data from the British Oceanographic Data Centre [49]. At the land margins the boundary conditions were free slip (i.e. zero shear stress) and null flow. The shear stress at the sea-bed was computed from:
sbx ¼
1 C 22D
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q0 gU ðU 2 þ V 2 Þ; sby ¼
1 C 22D
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q0 gV ðU 2 þ V 2 Þ
ð9Þ
where C2D is the 2D Chézy coefficient, which depends on the water depth and bottom roughness. In terms of the Manning coefficient, n, this relationship of dependency can be written as:
C 2D ¼
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6 ðd þ fÞ n
ð10Þ
The value of the Manning coefficient was determined as a function of the water depth following previous studies [50]. The high resolution domain, implemented to investigate the power potential and energy output of a tidal stream farm located in Lynmouth, extends from 3°520 W to 3°460 W and from the coastline to 51°170 N at a grid resolution of 20 m 20 m (which was gradually increased eastward and westward up to the outer boundary, where it reaches a cell size of 100 20 m). This resolution allowed the demarcation of individual devices on the grid. The bathymetry was digitized from the Admiralty Charts No. 1160 and No. 1165 from the UK Hydrographic Office and it was interpolated into this grid. The model was run for 51 days (from 1st March 2011 to 20th April 2011), being the computational domain of the high resolution grid nested within the coarser grid. The first 31 days constituted the spin-up period, in which the flow field was adjusted dynamically [51]. As a result, the starting conditions did not influence the results of the model during the period of interest (the validation period, extended from 1st to 20th April) [3]. The initial hydrodynamic conditions were null velocity and surface elevation throughout the grid (cold-start) [52]. Based on earlier sensitivity Table 2 Main tidal harmonics for the Celtic Sea boundary. Constituent
Amplitude (cm)
Phase (°)
M2 S2 N2 K2 K1 O1 P1 Q1 M4
235.24 84.17 44.79 24.45 6.77 6.70 2.23 1.95 3.69
156.87 201.21 138.48 195.80 127.34 351.17 121.81 305.66 290.99
and calibration analyses the model, a value of 30 m2 s1 was chosen for the horizontal eddy viscosity parameter. Upon validation, this model was used to compute the available power density (Pti in Section 2.1) for a spring–neap cycle, without the tidal stream farm (baseline case) and with the tidal stream turbines (farm case). In order to simulate the operation of the TSTs of the farm the momentum equations were modified as indicated in Section 2.2 for the cells of the computational domain where the TSTs were located. The value of the thrust coefficient (CT) introduced in the numerical model was 0.8 [43]. 2.4. Farm projection The characteristics of the prospective tidal farm of this study are shown in Fig. 2 and summarised in Table 3. As it can be seen, the farm is placed in a location ‘P’, with peak currents above 2.25 m s1 (Fig. 2c), a water depth of 20–25 m (Fig. 2b) and a near potential grid connection at Lynton (3.5 km from ‘P’), which would allow the energy produced to be delivered at reasonably low cost. Therefore, this tidal site satisfies the energetic requirements (i.e. fast flowing water) and technical constraints (such as sufficient water depth for installing large enough turbines). Besides, the previous conditions extend over a wide enough area to permit the installation of a large enough array of TST a requirement if the project is to be cost effective [53]. The selection of the TST diameter and capacity (Table 3) was based on publically available data from prototypes of horizontal axis TST, such as the SeaGen Turbine [9], which was tested off Lynmouth in 2003 [32]. A triangular configuration for the tidal farm was chosen following Ramos et al. [43], with the rotors laterally separated three-diameters and longitudinally separated five-diameters from each other within the array (Fig. 2b) and orientated in the direction of the main flow (Fig. 2c) [25]. Finally, it was assumed that the development of the tidal stream project starts in 2015 and lasts two years. Then, the tidal farm will operate during 20 years [54]. 3. Results and discussion 3.1. Model validation The nested model was validated against measured tide levels at four gauge stations obtained from the UK National Tide Gauge Network [49] and tidal stream data given at five tidal diamonds taken from the Admiralty Chart No. 1165, covering both the coarser and the high resolution domain. Fig. 3 shows comparisons of the tidal levels between 1st and 20th April 2011 (period of validation), at all the four stations placed within the model domain (Newport, Mumbles, Hinkley Point, and Ilfracombe, see Fig. 1). As it can be seen, the water levels computed by the model match well in terms of both magnitudes and phases. The correlation between the predicted and observed data is generally high at each station, with the correlation coefficients being greater than 0.97. The correlation coefficient and RMSE for the computed tidal currents within both the coarser (site F, G, H and K) and high resolution (site L) domain are presented in Table 4. Because similar comparisons can be observed at the four locations, only one comparison at location K is presented in Fig. 4 for illustration purposes. The results indicate that the model accurately predicts the current speed variations at these sites for both spring and neap tides, as confirmed by the high correlation coefficients (Table 4). 3.2. Impacts on the available resource and energy production The effects of the operation of the proposed tidal farm on the available resource were investigated by computing the differences
433
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
(a)
(b) B1 A1
P
C1 B2
A2
C2 B3
A3
C3 B4
(c) Point C3
Fig. 2. Tidal stream farm: (a) location, (b) site details and layout, and (c) tidal stream currents at point ‘C3’.
Table 3 Assumptions for the reference tidal stream farm. Number of turbines Installed capacity per turbine Power coefficient Diameter Years of development Years of operation
10 2 MW 0.35 20 m 2015–2017 20
in the velocities without (baseline) and with the tidal stream turbines (farm) at mid-ebb and mid-flood of a mean spring tide. The results obtained for the area of interest (the tidal stream farm site ‘P’, in Fig. 2a) are represented in Fig. 5. As it can be seen, the velocities are reduced both upstream and downstream of the turbines. These reductions are more important downstream of the turbines, reaching values close to 0.5 m s1 during both the flood and the ebb. Although the velocity experiences its maximum reduction behind each individual device, the flow does not fully recover as the distance from the turbine increases. As a result, a reduction in the flow incident on the turbines downstream is observed (compared to the undisturbed flow or baseline case). The magnitude of this reduction varies from 6.66% to 11.96% during the flood and from 7.71% to 14.00% during the ebb (Table 5). The alterations presented in Table 5 affect the power density distribution that is available for conversion at each single tidal stream turbine (TST), and thus the annual energy production (AEP) decreases. In order to quantify the impacts on the available energy, the time distribution of the power density on the incoming flow at the TST was computed for both the case of power extraction (farm) and the baseline case (without TSTs). Fig. 6 illustrates an example for turbine ‘B3’. As can be seen, the presence of the tidal stream farm involves significant variations in the tidal resource.
For the spring–neap cycle considered, the energy density available in the incoming flow of each TST is the area under the curve in Fig. 6. A numerical integration yields the values needed to compute the results presented in Fig. 7. Additionally, an area (A) of 314.16 m2 and a power coefficient (Cp) of 0.35 were considered (see Eq. (2)), in line with the characteristics of the prospective tidal stream farm (Table 3). Different values of energy production are observed for each TST (Fig. 7). Such differences, far from being exclusively produced by the device interactions, are already observed for the baseline case (estimation of the AEP on the basis of the available resource, without considering the device interactions). This reveals the spatial variability of the tidal stream resource and thus the important role that the specific location of the TSTs plays in the amount of energy delivered. In the investigated tidal farm, the AEP varies from a minimum of 1341.77 MW h year1 (turbine ‘A3’) to a maximum value of 1599.52 MW h year1 (turbine ‘C3’) in the baseline case; and from 1074.13 MW h year1 (turbine ‘A3’) to 1246.03 MW h year1 (turbine ‘B1’) in the farm case. Setting aside the differences between the baseline and the farm case, the variations in the AEP among the TSTs are of 15%, and then, they should not be disregarded when assessing tidal stream resource, if realistic results are to be obtained. Indeed, this site-dependence may be used to optimise the energy production of a tidal farm, by choosing the individual position if each TST, for example. This would contribute to reducing the associated cost. Having explained this, the results (Fig. 7) suggest that device interactions may also play a decisive role in the AEP values: a maximum reduction of up to 27.47% is observed for the AEP in the TST ‘C2’ (difference between baseline and farm case). It seems that the effects of device interactions are directly related to the baseline AEP (available resource), i.e. the higher the available
434
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Ilfracombe Water level (m)
8 6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
Hinkley Water level (m)
8 6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Newport
Water level (m)
10
Gauge Model
5
0
-5
-10 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Mumbles 8
Water level (m)
6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Fig. 3. Comparisons between the predicted (model values) and the observed (gauge values) tidal elevations.
resource, the stronger the device effects. Thus, TSTs placed at row ‘C’ experience the highest AEP variations of 26% lower with respect to the baseline case. They are followed by TSTs of the central row (‘B2’ and ‘B3’), which are associated with a reduction of 24% in the AEP. As regards row ‘A’, the AEP is 20% lower at the TSTs, due to device interactions. In row ‘B’ this tendency does not apply to TSTs ‘B1’ and ‘B4’. For example, turbine ‘A3’ experiences similar variation in the AEP (19.95%) than TSTs ‘B1’ and ‘B4’ (17.42% and 18.08%, respectively); however, the baseline resource differs in more than 150 MW h year1. These findings reveal that apart from the spatial distribution of the resource, the layout of the farm is responsible for the magnitude of the device interactions. In this particular case, ‘B1’ and ‘B4’ are TSTs affected directly by only one TST: ‘A1’ and ‘A3’ during the flood, respectively; and ‘C1’ and ‘C3’ during the ebb, respectively. Therefore, although being placed in more energetic sites, the effects on the AEP are lower. According to this explanation, ‘B2’ and ‘B3’ may be expected to experience the highest reductions, since they are
placed in the central positions and receive the influence of rows ‘A’ and ‘C’ during the flood and the ebb, respectively. However, the results suggest that the interactions of two rows are more important than those of one row, as the effects have an incremental character. Thus, in spite of having similar AEP values that row ‘C’ (of around 1500 MW h year1), the effects on the central TSTs are not as strong as it could be expected. This ‘‘incremental effect’’ can be seen in Fig. 5, where the incoming flow at row ‘C’ (‘A’) is significantly less energetic than the one at row ‘B’ for the flood (ebb). This finding gives rise to a discussion about the appropriateness of adding turbines in a row or rows in a tidal farm, as presented in Section 3.4. But before that, the economic implications of the effects mentioned above are investigated in the next section. 3.3. Impact on the LCOE In order to examine the cost implications of the hydrodynamic effects of the performance of the tidal farm, the cost per energy
435
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438 Table 4 Correlation coefficient (R) and RMSE values of predicted and measured currents. Location
RMSEa
R 0
0
Site F (51°33.3 N, 3° 56.9 W)
Spring tide Neap tide Direction
0.9054 0.8908 0.9956
0.1406 0.1568 4.5546
Site G (51°270 N, 3°55.60 W)
Spring tide Neap tide Direction
0.8770 0.8853 0.9948
0.2241 0.1543 9.9818
Site H (51°32.50 N, 3°53.50 W)
Spring tide Neap tide Direction
0.8960 0.9170 0.8966
0.1646 0.1239 13.4300
Site K (51°20.10 N, 3°50.30 W)
Spring tide Neap tide Direction
0.8581 0.9062 0.8911
0.2833 0.1475 15.2310
Site L (51°160 N, 3°47.40 W)
Spring tide Neap tide Direction
0.8689 0.8702 0.9946
0.3436 0.2163 9.4107
a RMSE values in m/s for the Spring tide and Neap tide velocities and in degrees for the direction.
Spring tide velocity (m s–1)
unit produced was calculated for the baseline case and the farm case, by applying the LCOE method described in Section 2.1. The results are presented in Fig. 8. For this study, the capital expenditures (CAPEX) were considered to be a onetime cost in the range of £4.3 m/MW, and the operational expenditures (OPEX) were included in Eq. (1) as an annual cost of £0.31 m/MW/year, both quantities are referred to shallow water devices at a demonstration stage of development
(Table 1) [37]. Other assumptions included a constant amount of energy output for each year (AEP) during the useful lifetime of the installation [54] and a discount rate (r) of 10%. The results agree well with the comments on the AEP variations (since this is a parameter of the LCOE). In this regard, a range of LCOE values was obtained for each TST, from £0.556 kW h1 to £0.663 kW h1 for the baseline case; and from £0.714 kW h1 to £0.828 kW h1 for the farm case. As commented above, these variations put forth the importance of using numerical modelling in estimating the LCOE (a novelty of this study with respect to previous works), since the project location and its peculiarities play a role in the available tidal stream resource for conversion a key parameter in the LCOE. Likewise, device interactions should be included in the LCOE estimations. In economic terms, the maximum and minimum AEP reductions (experienced at turbines ‘C2’ and ‘B1’, respectively) result in an increase of £0.221 kW h1 and £0.125 kW h1 in the LCOE (Fig. 8). The scope of these LCOE variations need to be contextualised, in order to better understand what do they mean and represent. To this aim, Fig. 9 is included. On the one hand, it shows that the absolute LCOE value of some technologies, both renewable (such as onshore wind energy) and non-renewable (i.e. CCGT), is lower than the minimum LCOE increase due to device interactions found in this study. On the other hand, the range of potential variation in the LCOE values of both on- and offshore wind energy (associated with the highest uncertainties due to the variable character of the resource), represents less than half of the range of LCOE variations due to tidal stream device interactions (see error bars). The previous comparisons help to understand that the device interactions can produce
3
Site K (51º 20.1' N, 3º 50.3' W) Observed Predicted
2.5 2 1.5 1 0.5 0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
4
5
6
4
5
6
Neap tide velocity (m s–1)
Time referred to HW at Swansea (h) 3 2.5 2
Site K (51º 20.1' N, 3º 50.3' W) Observed Predicted
1.5 1 0.5 0
-6
-5
-4
-3
-2
-1
0
1
2
3
Time referred to HW at Swansea (h) 180
Direction (degrees)
Site K (51º 20.1' N, 3º 50.3' W) 120
Observed Predicted
60
0 -60
- 120 - 180 -6
-5
-4
-3
-2
-1
0
1
2
3
Time referred to HW at Swansea (h) Fig. 4. Comparisons between observed and predicted current speed: (a) spring tide, (b) neap tide, and (c) current direction.
436
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Fig. 5. Velocity difference between the baseline and the farm case, during (a) the flood and (b) the ebb.
Table 5 Variation of the velocities on the incoming flow of each tidal stream turbine during the flood and the ebb. Turbine
A1 A2 A3 B1 B2 B3 B4 C1 C2 C3
Flood
than the 20%. Thus, tidal stream farms should be designed so as to attenuate the aforementioned effects, if the cost is to be minimised. In this vein, the results suggest that such attenuation could be made by adjusting the following array parameters.
Ebb
Max. V diff. (m/s)
% Reduction
Max. V diff. (m/s)
% Reduction
0.1806 0.1907 0.1751 0.1934 0.2399 0.2337 0.1675 0.2939 0.3050 0.2646
7.43 7.84 7.24 7.59 9.44 9.35 6.66 11.56 11.96 10.41
0.3002 0.3608 0.3752 0.2080 0.3013 0.3247 0.2900 0.2316 0.2552 0.2614
11.29 13.43 14.00 7.71 11.14 11.97 10.53 8.67 9.46 9.67
– Longitudinal spacing. As shown in Fig. 5, the velocity (and hence the available kinetic energy for conversion) is reduced downstream of each turbine. The size of the affected area is large enough to produce an alteration in the available resource and the AEP at the turbines placed in the vicinity (see Fig. 7). This is due to the fact that the chosen longitudinal spacing for this study (five-diameters) impeded the recovery of the tidal flow. In order to minimise the LCOE, then the turbine spacing should be increased. In order to investigate what may be a better longitudinal spacing, the TST ‘B1’ (Fig. 5) is taken for illustration. In this vein, if a site placed at a distance of ten-diameters (the double) downstream of ‘B1’ is considered – coordinates (x, y): (4.428 105, 5.6805 106) and (4.423 105, 5.6805 106) in the cases of flood and ebb tide, respectively – the velocity would be reduced in a magnitude of less than 0.1 m s1, whereas if the five-diameter spacing is maintained, the velocity reduces between 0.1 and 0.2 m s1. Since the output is proportional to the cube of the velocity, such appreciation is of major economic interest. Of course, the previous values are indicative and may need specific studies (with isolated TSTs) to better calculate the different effects. This is going to be carried out in future works.
significant variations in the cost of energy produced and then should be considered when optimising the cost of a tidal farm. 3.4. Potential for reducing the cost of a tidal stream farm As it had been expected – and after demonstrated by the results presented in the previous sections – the interactions among the TSTs have a bearing on the economics of a tidal stream farm. In particular, it has been found that these interactions play a decisive role in the cost of energy, which experiences increases of more
Power density (W m–2)
12000 Baseline
Farm (B3)
10000 8000 6000 4000 2000 0 14/03/2011 0:00
21/03/2011 0:00
28/03/2011 0:00
Time Fig. 6. Available energy density in the incoming flow of the turbine ‘B3’. Baseline vs. Farm.
437
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438 1800
0.25 Baseline
£0.221 kWh−1
Farm
1600 0.2
LCOE (£ kWh–1)
AEP (MWh year
–1)
1400 1200 1000 800 600
0.15
£0.125 kWh−1
0.1
0.05
400 0
200
1
3
4
5
CCGT
2
OCGT
3
Onshore
4
Offshore
5
Biomass
6
Large scale Solar
6
Technology
0 A1
A2
A3
B1
B2
B3
B4
C1
C2
C3
Turbine Fig. 7. The annual energy production (AEP) for each turbine without (baseline) and with the consideration of the device interactions (farm).
– Array shape. A triangular configuration has been usually adopted in previous studies (e.g. [25]), by means of placing the turbines downstream of the gaps between turbines in an upstream row with the extra rows of TSTs placed between the gaps of the previous row. Thanks to this configuration, the shadow effect produced by each turbine is partially reduced. However, in view of Fig. 8, the central TST of each row are those that suffer higher alterations. This suggest the possibility of moving the central TSTs to an outer position. – Array size. How many TSTs are to be placed in the farm and how many rows are to be installed, while maintaining the installed capacity, are also questions of interest. On the one hand, it has to be mentioned that realising all the potential of a tidal place is much more complex with less devices than installing more turbines of lower capacity. This is due to the fact that higher scenarios of power extraction reduce more significantly the tidal currents throughout the tidal site (as suggested by Ramos et al. [25]). On the other hand, adding rows of turbines to arrays decreases the individual output of all turbines within the array. With this is view, it is concluded that less rows are more beneficial in terms of device interactions. Besides, fewer rows may allow for having a higher longitudinal spacing, which has been suggested to be also beneficial. If the installed capacity is not to be maintained, then it should be better to add turbines. Although having a negative effect in the individual TSTs, a higher number of devices increases the total energy production of the array. – Individual positioning of each single TST. As for all the previous comments, it may be understood that the relative position (and also the capacity) of each TST might be individually chosen 1 0.9
LCOE (£ kWh–1)
2
1
0.8 0.7 0.6 0.5 0.4 A1
A2
A3
B1
B2
B3
B4
C1
C2
C3
Turbine Fig. 8. LCOE variations due to device effects (lowest values correspond to the ‘baseline case’ and greatest values refer to the ‘farm case’).
Fig. 9. LCOE estimates for a number of technologies (including combines and open cycle gas turbines, CCGT and OCGT, respectively) vs. LCOE variations [minimum (£0.125 kW h1) and maximum (£0.221 kW h1)] due to device interactions.
in order to optimise the cost of the tidal farm. This accords well with the comments of Section 3.2, where it is suggested that the resource available at each point plays also a role in the AEP, and hence in the LCOE. As a consequence, the computational effort may be significantly increased. In further works, all the previous insights are going to be considered and thus, this work is going to be extended in order to optimise the layout of the tidal stream farm. Finally, it should be mentioned that when optimising the array layout for minimum interactions and costs, other factors may be accounted for. The available space, water depth constrictions and potential conflicts with other economic activities (fisheries and navigation) are some of the aspects that should be considered. 4. Conclusions The cost of generation from the tidal stream resource, the socalled levelised cost of energy (LCOE), is typically higher than that from traditional sources (coal, natural gas, etc.) On these grounds, it is crucial to understand the parameters affecting this cost so as to provide a framework of potential areas of reduction. With this in view, this work investigates for the first time the role of the effects of tidal energy extraction in the energy output and, hence, in estimating the LCOE of a prospective tidal stream farm. For this purpose, a case study was considered: Lynmouth (UK). Here, a numerical model was implemented and validated against observations of tidal level and current velocities. Based on the results of the numerical modelling, an area with peak currents above 2.25 m s1, a water depth of 20–25 m and a nearby grid connection point was chosen as the best site for studying the effects of a prospective tidal stream farm. Thanks to the high resolution of the computational grid in the area of interest it was possible to resolve the different turbines of the farm individually. The integration of the numerical modelling results into the LCOE calculation – an aspect that had not been addressed so far – showed that the presence of the tidal stream turbines has a significant effect on the available resource, and hence on the LCOE values. The LCOE for each device was examined in two scenarios: without (baseline) and with the tidal stream farm. A comparison between the different estimates was presented, showing a LCOE variation of up to £0.221 kW h1. Different values of LCOE were found for the individual TSTs, ranging from £0.556 kW h1 to £0.663 kW h1 in the baseline case; and from £0.714 kW h1 to £0.828 kW h1 in the farm case. Such a wide range of values suggests that the effects on the LCOE depend on the specific position
438
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
of the TST within the farm hence the importance of optimising the layout of the farm. In summary, the LCOE is sensitive to the effects of the tidal stream devices within a tidal stream farm. The quantification of such effects is, therefore, of economic interest and should not be disregarded, if the LCOE of tidal energy is to be minimised. Understanding the true costs and energy production would contribute to improve the design of competitive tidal stream energy farms. The results presented in this study provide preliminary insights to optimise the layout of a tidal stream farm. Acknowledgements The authors wish to thank the British Oceanographic Data Centre for providing tide gauge records. During this work A. Vazquez has been supported by FPU grant 13/03822 of the Spanish Ministry of Education, Culture and Sport, and by a grant from the Barrie Foundation for undertaking a predoctoral fellowship at Plymouth University, UK. References [1] Vazquez A, Astariz S, Iglesias G. A strategic policy framework for promoting the marine energy sector. In: Proc. 3rd IAHR Europe congress, Porto, Portugal; 2014 [ISBN 978-989-96479-2-3]. [2] Iglesias G, Sánchez M, Carballo R, Fernández H. The TSE index – A new tool for selecting tidal stream sites in depth-limited regions. Renewable Energy 2012;48:350–7. [3] Carballo R, Iglesias G, Castro A. Numerical model evaluation of tidal stream energy resources in the Ría de Muros (NW Spain). Renewable Energy 2009;34:1517–24. [4] Fairley I, Evans P, Wooldridge C, Willis M, Masters I. Evaluation of tidal stream resource in a potential array area via direct measurements. Renewable Energy 2013;57:70–8. [5] Neill SP, Hashemi MR, Lewis MJ. The role of tidal asymmetry in characterizing the tidal energy resource of Orkney. Renewable Energy 2014;68:337–50. [6] Evans P, Armstrong S, Wilson C, Fairley I, Woolridge C, Masters I. Characterisation of a highly energetic tidal energy site with specific reference to hydrodynamics and bathymetry. In: Proc. 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark; 2013. [7] Ramos V, Carballo R, Álvarez M, Sánchez M, Iglesias G. A port towards energy self-sufficiency using tidal stream power. Energy 2014;71:432–44. [8] Rourke O, Boyle F, Reynolds F. A. Tidal energy update 2009. Appl Energy 2010;87:398–409. [9] http://www.marineturbines.com. [10] Li Y, Çalisßal SM. Numerical analysis of the characteristics of vertical axis tidal current turbines. Renewable Energy 2010;35:435–42. [11] Liu P, Bose N. Prototyping a series of bi-directional horizontal axis tidal turbines for optimum energy conversion. Appl Energy 2012;99:50–66. [12] Sanchez M, Carballo R, Ramos V, Iglesias G. Floating vs. bottom-fixed turbines for tidal stream energy: A comparative impact assessment. Energy 2014;72:691–701. [13] Sanchez M, Carballo R, Ramos V, Iglesias G. Energy production from tidal currents in an estuary: A comparative study of floating and bottom-fixed turbines. Energy 2014;77:802–11. [14] Willis M, Masters I, Thomas S, Gallie R, Loman J, Cook A, et al. Tidal turbine deployment in the Bristol Channel a case study. Energy 2010;163(EN3). [15] Fallon D, Hartnett M, Olbert A, Nash S. The effects of array configuration on the hydro-environmental impacts of tidal turbines. Renewable Energy 2014;64:10–25. [16] Vazquez A, Iglesias G. Public perceptions and externalities in tidal stream energy: A valuation for policy making. Ocean Coast Manage 2015;105:15–24. [17] Carbon Trust. Accelerating Marine Energy. The potential for cost reduction – insights from the Carbon Trust Marine Energy Accelerator. Carbon Trust 2011;CTC797. [18] Denny E. The economics of tidal energy. Energy Policy 2009;37:1914–24. [19] Li Y, Lence BJ, Calisal SM. An integrated model for estimating energy cost of a tidal current turbine farm. Energy Convers Manage 2011;52:1677–87. [20] Li Y, Florig HK. Modeling the operation and maintenance costs of a large scale tidal current turbine farm. OCEANS 2006:1–6. [21] Verbruggen A, Fischedick M, Moomaw W, Weir T, Nadaï A, Nilsson LJ, et al. Renewable energy costs, potentials, barriers: Conceptual issues. Energy Policy 2010;38:850–61. [22] Al-Nimr MA. Principles of sustainable energy. Energy 2011;36:3613–4.
[23] Owen AD. Environmental externalities, market distortions and the economics of renewable energy technologies. The Energy Journal 2004;25(3):127–56. [24] Sanchez M, Carballo R, Ramos V, Iglesias G. Tidal stream energy impact on the transient and residual flow in an estuary: A 3D analysis. Appl Energy 2014;116:167–77. [25] Ramos V, Carballo R, Álvarez M, Sánchez M, Iglesias G. Assessment of the impacts of tidal stream energy through high-resolution numerical modeling. Energy 2013;61:541–54. [26] Ahmadian R, Falconer RA. Assessment of array shape of tidal stream turbines on hydro-environmental impacts and power output. Renewable Energy 2012;44:318–27. [27] Neill SP, Jordan JR, Couch SJ. Impact of tidal energy converter (TEC) arrays on the dynamics of headland sand banks. Renewable Energy 2012;37:387–97. [28] Robins PE, Neill SP, Lewis MJ. Impact of tidal-stream arrays in relation to the natural variability of sedimentary processes. Renewable Energy 2014;72:311–21. [29] South West Marine Energy Park. (last accessed 14 October 2014). [40] Blunden LS, Bahaj AS. Initial evaluation of tidal stream energy resources at Portland Bill. UK. Renewable Energy 2006;31:121–32. [41] Iglesias G, Carballo R. Effects of high winds on the circulation of the using a mixed open boundary condition: the Ría de Muros. Spain. Environmental Modelling & Software 2010;25(4):455–66. [42] Stelling JLG. Approximation of convective processes by cyclic ADI, methods; 1992. [43] Ramos V, Carballo R, Sanchez M, Veigas M, Iglesias G. Tidal stream energy impacts on estuarine circulation. Energy Convers Manage 2014;80:137–49. [44] Defne Z, Haas KA, Fritz HM. Numerical modeling of tidal currents and the effects of power extraction on estuarine hydrodynamics along the Georgia coast. USA. Renewable Energy 2011;36:3461–71. [45] Ahmadian R, Falconer R, Bockelmann-Evans B. Far-field modelling of the hydro-environmental impact of tidal stream turbines. Renewable Energy 2012;38:107–16. [46] Dushaw BD, Egbert GD, Worcester PF, Cornuelle BD, Howe BM, Metzger K. A TOPEX/POSEIDON global tidal model (TPXO.2) and barotropic tidal currents determined from long-range acoustic transmissions. Prog Oceanogr 1997;40:337–67. [47] Ramos V, Iglesias G. Performance assessment of Tidal Stream Turbines: A parametric approach. Energy Convers Manage 2013;69:49–57. [48] Sánchez M, Iglesias G, Carballo Rodrigo, Fraguela JA. Power peaks against installed capacity in tidal stream energy. IET Renew Power Gener 2013;7:246–53. [49] BODC. British Oceanographic Data Centre.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Device interactions in reducing the cost of tidal stream energy A. Vazquez a,⇑, G. Iglesias b a b
University of Santiago de Compostela, EPS, Hydraulic Eng., Campus Univ. s/n, 27002 Lugo, Spain University of Plymouth, School of Marine Science and Engineering, Drake Circus, Plymouth PL4 8AA, UK
a r t i c l e
i n f o
Article history: Received 15 January 2015 Accepted 12 March 2015 Available online 8 April 2015 Keywords: Tidal stream energy Levelised cost of energy Tidal device interactions Energy production
a b s t r a c t The levelised cost of energy takes into account the lifetime generated energy and the costs associated with a project. The objective of this work is to investigate the effects of device interactions on the energy output and, therefore, on the levelised cost of energy of a tidal stream project, by means of numerical modelling. For this purpose, a case study is considered: Lynmouth (North Devon, UK), an area in the Bristol Channel in which the first tidal stream turbine was installed a testimony of its potential as a tidal energy site. A state-of-the-art hydrodynamics model is implemented on a high-resolution computational grid, which allows the demarcation of the individual devices. The modification to the energy output resulting from interaction between turbines within the tidal farm is thus resolved for each individual turbine. The results indicate that significant changes in the levelised cost of energy values, of up to £0.221 kW h1, occur due to the aforementioned modifications, which should not be disregarded if the cost of tidal stream energy is to be minimised. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Tidal stream energy is called to play a major role in meeting future energy needs due to its advantages relative to other renewable energies; inter alia, predictability, stability and high load factor [1]. The interest of the tidal stream resource has driven intense research during the last decades, which has mainly centred on resource assessments and technological advances [2]. Concerning the assessments of the tidal resource, they allowed the quantification of the potential energy production in a number of promising tidal stream areas worldwide, including sites around headlands, straits between islands or enclosed bodies of water, such as estuaries [3]. In previous works, different methodologies were applied, including numerical modelling and direct flow measurements [4]. Having quantified the available energy resource, the final decision concerning a future tidal stream installation at a potential site is subject to several practical constraints, such as the existence of tidal asymmetry, i.e. differences between flood and ebb phases of the tidal cycle. These differences can affect the performance of tidal stream converters and can serve as a criterion to decide if bi-directional turbines should be preferred, as discussed by Neill et al. [5] with reference to Orkney (Northern Scotland). The relationship between tidal flow and bathymetry
⇑ Corresponding author. Tel.: +34 982823295; fax: +34 982285926. E-mail address: [email protected] (A. Vazquez). http://dx.doi.org/10.1016/j.enconman.2015.03.044 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.
constitutes another aspect that cannot be disregarded: shear stress and topographic features can influence tidal hydrodynamics, and in some cases induce flow obstruction or recirculation [6]. Finally, the proximity to a grid connection point and the final consumer minimises the loses due to energy transmission. A recent work showed how the electricity needs of a port in Ria de Ribadeo (NW Spain) could be fulfilled through tidal stream energy production [7]. As regards the technological advances, they allowed the development of a range of tidal stream energy converters, including [8]: reciprocating and rotating principle converters, vertical- and horizontal-axis turbines, as well as floating and bottom-fixed devices. As a result, the tidal energy industry is growing rapidly, with commercial designs, such as the SeaGen turbine [9]. However, so far none of the existing designs has gained universal acceptance (as in the case of e.g. the three-bladed horizontal-axis wind turbine [10]). Rather, a number of analyses on different designs are being conducted with a view to determining which characteristics can maximise the power output of converters [11]. It is not only the performance of these converters that is of importance, but also their survivability under extreme conditions, since they are to be deployed in harsh environments [12]. The potential impacts of tidal stream energy are also being investigated, and indeed quantifying and minimising them is a requirement for tidal stream energy to be sustainable [13]. These studies are helping designers to establish a basis on which prototypes can be successfully deployed in real environments [14]. Although there is no doubt that it is technically feasible to
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
429
Nomenclature and units
Roman symbols A turbine aperture (m2) c salinity or temperature (transported substance) CD drag coefficient Cp power coefficient CT thrust coefficient C2D Chézy coefficient d local water depth (m) Dh horizontal eddy diffusivity (m2 s1) Fx x component of the flow retarding force per unit volume (N) Fy y component of the flow retarding force per unit volume (N) f Coriolis parameter g gravitational acceleration (m s2) Mx x component of the momentum generated by an external force (N m) My y component of the momentum generated by an external force (N m) n Manning coefficient Pt tidal stream available power (W) Q intensity of mass sources per unit area (m2 s1) r discount rate R source term per unit area t time (years)
extract energy from tidal currents, only a few tidal stream projects are now operating at a commercial scale [15]. Having observed also proactive public attitudes and positive externalities towards this renewable [16], the primary reason for the scarcity of commercial plants is that the cost of generation from the tidal stream resource, the so-called levelised cost of energy (LCOE), is typically higher than that from traditional sources (coal, natural gas, etc.) [17]. On these grounds, it is crucial to understand the parameters affecting this cost so as to provide a framework of potential areas of reduction [18]. Estimating the LCOE for a tidal stream farm requires information on the expected energy output from the farm and the costs involved in the construction, operation and maintenance of the tidal stream installation [19]. Although the information on the capital and operational cost-values of tidal stream devices is limited due to the technological stage of development, the sensitiveness of their values is well known [20]. In this regard, several areas can contribute to lower the capital and operational costs of tidal stream farms [21]. They include technological innovation, which can lead to improve the performance, efficiency and reliability of tidal stream energy converters; as well as economies of scale [22]. The innovation process should be aligned with policy strategies, including the public subsidisation of this energy [23]. The relationship between the variations of energy output and the LCOE is an aspect that has received less attention. Previous works analysed how the hydrodynamic interactions between tidal stream turbines placed at a real tidal site could modify the flow patterns, such as the transient and residual flows [24]. The alteration of the hydrodynamics has inevitably an effect on the energy available for conversion, and hence, the energy production [25]. In addition, the work of Ahmadian et al. [26] investigated the relationship between the aforementioned modifications with the shape of a tidal stream farm, whereas Neil et al. [27] and Robins et al. [28] focused on the
ti T U V Vc
time instant project lifetime vertically integrated eastward component of the flow velocity (m s1) vertically integrated northward component of the flow velocity (m s1) volume of control
Greek symbols f water level (m) g efficiency kd first order decay process q0 water reference density (kg m3) q0 anomaly density (kg m3) q seawater density (kg m3) sb shear stress at the bottom (N m2) ss shear stress at the surface (N m2) th kinematic horizontal eddy viscosity (m2 s1) Abbreviations AEP annual energy production CAPEX capital expenditures LCOE levelised cost of energy OPEX operational expenditures TST tidal stream turbine
potential effects on sedimentary processes. Notwithstanding, the numerical modelling of the performance of a tidal stream turbine (used in most of the previous studies) has not been applied to the LCOE calculation so far, and this is the main objective of the present work. Lynmouth, on the North Devon coast, constitutes an excellent tidal stream site (Fig. 1). The nearby grid connection point at Lynton and the research facilities of the South West Marine Energy Park [29] are testimony to the potential of this site for tidal stream energy exploitation. Indeed, Lynmouth has been recently included as a new tidal stream energy demonstration zone to be managed by the Wave Hub [30] and the South West Marine Energy Park [31]. This decision based on the experience acquired during 2003, when Lynmouth was the scenario of the world’s first tidal current installation to be deployed in a working environment [32] (the 300 kW tidal stream turbine ‘‘Seaflow’’ of Marine Current Turbines). Lynmouth stands out for tidal streams over 2.25 m s1 in conjunction with water depths in the range 15–25 m, which make it an ideal location for the deployment of the majority of first generation tidal energy converters. As a case study, a high resolution model of Lynmouth is implemented and successfully validated in order to simulate the operation of a tidal farm. The resolution of the model allows the demarcation of individual devices on the grid. The LCOE for each device is examined in two scenarios: without (baseline) and with the tidal stream farm. A comparison between the different estimates is presented, showing a maximum LCOE variation of £0.221 kW h1. As explained below, different values of LCOE are found for each single tidal stream device, ranging from £0.556 kW h1 to £0.663 kW h1 for the baseline case; and from £0.714 kW h1 to £0.828 kW h1 for the farm case. These ranges suggest that the effects on the LCOE are associated with the specific position of the tidal stream converter within the farm which indicates the need for the optimisation of the tidal stream farm.
430
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Mumbles
Celtic Sea boundary
Newport
Ilfracombe
Bristol Channel
Hinkley
Lynmouth North Devon
Coarser domain High-resolution domain
Fig. 1. Study area: Lynmouth (UK).
This article is structured as follows. Section 2 deals with the materials and methods. In Section 3, the results are analysed and discussed. Finally, conclusions are drawn in Section 4. 2. Materials and methods 2.1. The LCOE method The levelised cost of energy (LCOE) is the most extended approach for estimating the cost of lifetime generated energy [33]. This metric has been defined as the ratio of the total cost to the total energy output, expressed in terms of the present value equivalent [34]. Therefore, it constitutes a measure of the marginal cost of electricity over a period of time and it is appropriate for comparing single generation units. According to this definition, the LCOE is calculated as follows:
PT LCOE ¼
t¼0 ðCAPEX þ OPEXÞð1 PT t t¼0 AEPð1 þ rÞ
þ rÞt
ð1Þ
Here, r is the interest rate used for discounting costs each year t back to a reference time period (t = 0), during the lifetime of the
project under consideration (T). CAPEX and OPEX represent the capital and operational expenditures, respectively, and AEP is the annual energy production. It should be noted that the summation calculation starts from t = 0 to include the project cost at the beginning of the first year that is not discounted and there is no system energy output to be degraded. Other methods can include the initial cost or down payment outside the summation, with t starting from 1. As shown in Eq. (1), there are a number of major components determining the LCOE of tidal stream energy. All of them can vary significantly between individual projects (e.g. between solar power systems [35] and offshore wind energy installations [36]) and in some cases, also between countries. Their values are discussed below. a. Capital expenditures (CAPEX) This is the total capital required to build the tidal stream plant. It includes the pre-development costs, electrical systems infrastructure and construction costs. The CAPEX is sensitive to the stage of technological development, since learning and economies of scale are to reduce its value. In addition, different CAPEX values are expected for tidal stream turbines deployed in shallow and deep water (Table 1) [37].
Table 1 Summary of costs (low–high) referred to 2010a [37].
a
Pre-demonstration
Demonstration
Commercial
Tidal stream (shallow) CAPEX (£/MW) OPEX (£/MW/year)
11.2 m (7.5–12.4 m) 0.47 m (0.32–0.56 m)
4.3 m (3.5–5.1 m) 0.31 m (0.23–0.38 m)
3.2 m (2.7–13.9 m) 0.15 m (0.12–0.19 m)
Tidal stream (deep) CAPEX (£/MW) OPEX (£/MW/year)
8.6 m (7.3–9.9 m) 0.31 m (0.27–0.39 m)
3.5 m (3–4.1 m) 0.16 m (0.12–0.2 m)
3.3 m (2.8–4 m) 0.12 m (0.09–0.16 m)
m = Million (106).
431
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
The conservation of momentum is expressed as follows:
b. Operational expenditures (OPEX) Operation and maintenance costs are related to the power capacity of the plant and they are normally expressed in terms of installed power. Like the CAPEX, the OPEX are also dependent on the stage of technological development (Table 1). They include labour, equipment and overhead charges as well as the insurance expenses and the decommissioning costs [37].
The discount rate is the interest rate used for discounting costs each year during the lifetime of the project. It takes into account both the time value of the money and the risk of the investment, which are aspects that vary by circumstance, location and time period considered [35]. Nowadays, tidal stream energy projects involve high capital costs and, due to their novelty, are associated with greater technological risks (if compared to conventional power plants). In this respect, conservative discount rates are considered to range between 10% and 12% [38]. d. Lifetime of the installation (T) The lifetime of the installation refers to the time that the tidal stream farm is working and producing energy and therefore, it is a determinant factor when estimating the LCOE. Nowadays, tidal stream energy farms are expected to be operating during 20 years [39]. After this time, gradual degradation may occur as a consequence of the chemical and material processes associated with corrosion and weathering. Ongoing research will eventually improve project lifetimes as a result of knowledge gained about failure mechanisms. e. Annual Energy Production (AEP) The term AEP represents the amount of generated electricity over a year t, from a reference initial time ti = 0 and it is calculated as follows:
AEP ¼
t i ¼t
t i ¼0
AC p P ti dt
0
ð4Þ Finally, Eq. (5) represents the transport equation, which is solved for both salinity and temperature.
¼ Dh r2 c kd ðd þ fÞc þ R
2.2. Numerical model: governing equations The numerical model, Delft 3D-FLOW, is used in this work for assessing the annual energy production of a prospective tidal stream farm in Lynmouth. It is a finite difference code that solves the Navier–Stokes equations together with the transport equation. Previous assessments of the tidal stream resource used the vertically averaged equations in their baroclinic form [40]. Following them, the present study used these equations and thus, the model took into account the flow driven by horizontal density gradients [41]. On these grounds, the conservation of mass under the assumption of incompressible fluid reads:
ð3Þ
ð5Þ
In the previous equations, there are a number of parameters involved, which are explained as follows. First, U and V represent the vertically integrated velocity components in the east (x) and north (y) directions, respectively. Second, d is the local water depth relative to a reference plane; Q stands for the intensity of mass sources per unit area; f is the Coriolis parameter; th is the kinematic horizontal eddy viscosity; and qo is the reference density, while q0 is the anomaly density. The shear stress components are represented by ssx, ssy, sbx and sby. Finally, in Eq. (5) (the transport equation) c stands for salinity or temperature, Dh is the horizontal eddy diffusivity, kd represents the first order decay process, and R is the source term per unit area. For the model, the Arakawa-C grid is used. This is a staggered grid that allows the spatial discretization of the model used in this study. In this grid, the water levels f are defined at the centre of the grid cell, whereas flow velocity components (U and V) are defined at the mid-points of the grid cell faces to which they are perpendicular. In the momentum and transport equations, i.e. Eqs. (3)–(5), the discretization of the horizontal advection terms is carried out by the Cyclic method [42], as in Ramos et al. [43]. The operation of a tidal farm can be modelled by modifying the 2DH water momentum equations (Eq. (4)). This has been made in previous works (e.g. [43]) and it is summarised here for the sake of completeness. The aforementioned modification is based on the addition of the terms (Mx, My):
(
ð2Þ
where Pti represents the available power density per area in the instant ti, A is the turbine aperture and Cp is the power coefficient that accounts for limitations related to turbine efficiency. This parameter (AEP) is geographically dependent and, therefore, in this work, the power density in the instant ti is obtained through numerical modelling (Sections 2.2 and 2.3), which constitutes a novelty with respect to previous LCOE studies.
@f @½ðd þ fÞU @½ðd þ fÞV þ þ ¼Q @t @x @y
0
@ðf þ dÞc @½ðd þ fÞUc @½ðd þ fÞVc þ þ @t @x @y
c. Discount rate (r)
Z
8 9 R 0 < @U þ U @U þ V @U fV ¼ g @f g f @ q dz þ ssx sbx þ mh r2 U = @t @x @y q0 d @x q0 ðdþfÞ @x : @V þ U @V þ V @V fU ¼ g @f g R f @ q0 dz þ ssy sby þ mh r2 V ; @t @x @y q d @y q ðdþfÞ @y
Mx ¼ Fqx My ¼
) ð6Þ
Fy
q
The previous terms are used to simulate the contribution of momentum generated by each tidal stream turbine on the flow, in the east (x) and north (y) directions, respectively [44]. Thus, the parameters Fx and Fy are the components in the x and y directions of the flow retarding force per unit volume, respectively, as a result of the presence of a tidal stream turbine (TST) [45]. These components have the same value that the thrust force exerted by the flow on each tidal device, but they are opposite to it. This is in line with the Newton’s third law [25]. In this regard, the momentum contribution terms can be written as:
(
Mx ¼ 12
CT A jUjU Vc
My ¼ 12
CT A jUjV Vc
) ð7Þ
where CT is the thrust coefficient, A represents the turbine aperture or swept area and Vc is the volume of control. The magnitude of the flow velocity is represented by |U|, whereas U and V stand for the magnitudes of the velocity in the x and y direction, respectively. On the basis of the previous insights, the momentum equations of the model in the x and y directions are rewritten and finally expressed as follows: 9 8 R 0 < @U þ U @U þ V @U fV ¼ g @f g f @ q dz þ ssx sbx þ mh r2 U þ Mx = q0 d @x q0 ðdþfÞ @t @x @y @x ð8Þ : @V þ U @V þ V @V fU ¼ g @f g R f @ q0 dz þ ssy sby þ mh r2 V þ My ; @y q d @y q ðdþfÞ @t @x @y 0
0
432
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
2.3. Numerical model: implementation In the present study two computational grids were used (Fig. 1). The coarser grid, encompassing the Bristol Chanel with a resolution of 500 m 500 m, was used to provide boundary conditions for the fine nested grid that covers the area of interest (Lynmouth). The grid resolution of the coarser domain resulted in a computational grid of 419 (direction M) 324 (direction N) cells and was chosen so as to provide relatively high spatial resolution at a relatively low computational cost. The bathymetric data, from the General Bathymetric Chart of the Oceans (GEBCO), was interpolated onto this grid. Along the Celtic Sea boundary, a Dirichlet boundary condition was imposed with the sea level prescribed as a function of time using the nine major tidal harmonics shown in Table 2. These tidal harmonics were obtained for eight sections along the open boundary (Celtic Sea Boundary) from the global ocean tide model TPXO 7.2 [46]. This model has been shown to produce good results in previous works (e.g. [47,48]). Table 2 shows the amplitudes and phases for one of the eight sections. Salinity and temperature at the Celtic Sea boundary were imposed using data from the British Oceanographic Data Centre [49]. At the land margins the boundary conditions were free slip (i.e. zero shear stress) and null flow. The shear stress at the sea-bed was computed from:
sbx ¼
1 C 22D
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q0 gU ðU 2 þ V 2 Þ; sby ¼
1 C 22D
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q0 gV ðU 2 þ V 2 Þ
ð9Þ
where C2D is the 2D Chézy coefficient, which depends on the water depth and bottom roughness. In terms of the Manning coefficient, n, this relationship of dependency can be written as:
C 2D ¼
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6 ðd þ fÞ n
ð10Þ
The value of the Manning coefficient was determined as a function of the water depth following previous studies [50]. The high resolution domain, implemented to investigate the power potential and energy output of a tidal stream farm located in Lynmouth, extends from 3°520 W to 3°460 W and from the coastline to 51°170 N at a grid resolution of 20 m 20 m (which was gradually increased eastward and westward up to the outer boundary, where it reaches a cell size of 100 20 m). This resolution allowed the demarcation of individual devices on the grid. The bathymetry was digitized from the Admiralty Charts No. 1160 and No. 1165 from the UK Hydrographic Office and it was interpolated into this grid. The model was run for 51 days (from 1st March 2011 to 20th April 2011), being the computational domain of the high resolution grid nested within the coarser grid. The first 31 days constituted the spin-up period, in which the flow field was adjusted dynamically [51]. As a result, the starting conditions did not influence the results of the model during the period of interest (the validation period, extended from 1st to 20th April) [3]. The initial hydrodynamic conditions were null velocity and surface elevation throughout the grid (cold-start) [52]. Based on earlier sensitivity Table 2 Main tidal harmonics for the Celtic Sea boundary. Constituent
Amplitude (cm)
Phase (°)
M2 S2 N2 K2 K1 O1 P1 Q1 M4
235.24 84.17 44.79 24.45 6.77 6.70 2.23 1.95 3.69
156.87 201.21 138.48 195.80 127.34 351.17 121.81 305.66 290.99
and calibration analyses the model, a value of 30 m2 s1 was chosen for the horizontal eddy viscosity parameter. Upon validation, this model was used to compute the available power density (Pti in Section 2.1) for a spring–neap cycle, without the tidal stream farm (baseline case) and with the tidal stream turbines (farm case). In order to simulate the operation of the TSTs of the farm the momentum equations were modified as indicated in Section 2.2 for the cells of the computational domain where the TSTs were located. The value of the thrust coefficient (CT) introduced in the numerical model was 0.8 [43]. 2.4. Farm projection The characteristics of the prospective tidal farm of this study are shown in Fig. 2 and summarised in Table 3. As it can be seen, the farm is placed in a location ‘P’, with peak currents above 2.25 m s1 (Fig. 2c), a water depth of 20–25 m (Fig. 2b) and a near potential grid connection at Lynton (3.5 km from ‘P’), which would allow the energy produced to be delivered at reasonably low cost. Therefore, this tidal site satisfies the energetic requirements (i.e. fast flowing water) and technical constraints (such as sufficient water depth for installing large enough turbines). Besides, the previous conditions extend over a wide enough area to permit the installation of a large enough array of TST a requirement if the project is to be cost effective [53]. The selection of the TST diameter and capacity (Table 3) was based on publically available data from prototypes of horizontal axis TST, such as the SeaGen Turbine [9], which was tested off Lynmouth in 2003 [32]. A triangular configuration for the tidal farm was chosen following Ramos et al. [43], with the rotors laterally separated three-diameters and longitudinally separated five-diameters from each other within the array (Fig. 2b) and orientated in the direction of the main flow (Fig. 2c) [25]. Finally, it was assumed that the development of the tidal stream project starts in 2015 and lasts two years. Then, the tidal farm will operate during 20 years [54]. 3. Results and discussion 3.1. Model validation The nested model was validated against measured tide levels at four gauge stations obtained from the UK National Tide Gauge Network [49] and tidal stream data given at five tidal diamonds taken from the Admiralty Chart No. 1165, covering both the coarser and the high resolution domain. Fig. 3 shows comparisons of the tidal levels between 1st and 20th April 2011 (period of validation), at all the four stations placed within the model domain (Newport, Mumbles, Hinkley Point, and Ilfracombe, see Fig. 1). As it can be seen, the water levels computed by the model match well in terms of both magnitudes and phases. The correlation between the predicted and observed data is generally high at each station, with the correlation coefficients being greater than 0.97. The correlation coefficient and RMSE for the computed tidal currents within both the coarser (site F, G, H and K) and high resolution (site L) domain are presented in Table 4. Because similar comparisons can be observed at the four locations, only one comparison at location K is presented in Fig. 4 for illustration purposes. The results indicate that the model accurately predicts the current speed variations at these sites for both spring and neap tides, as confirmed by the high correlation coefficients (Table 4). 3.2. Impacts on the available resource and energy production The effects of the operation of the proposed tidal farm on the available resource were investigated by computing the differences
433
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
(a)
(b) B1 A1
P
C1 B2
A2
C2 B3
A3
C3 B4
(c) Point C3
Fig. 2. Tidal stream farm: (a) location, (b) site details and layout, and (c) tidal stream currents at point ‘C3’.
Table 3 Assumptions for the reference tidal stream farm. Number of turbines Installed capacity per turbine Power coefficient Diameter Years of development Years of operation
10 2 MW 0.35 20 m 2015–2017 20
in the velocities without (baseline) and with the tidal stream turbines (farm) at mid-ebb and mid-flood of a mean spring tide. The results obtained for the area of interest (the tidal stream farm site ‘P’, in Fig. 2a) are represented in Fig. 5. As it can be seen, the velocities are reduced both upstream and downstream of the turbines. These reductions are more important downstream of the turbines, reaching values close to 0.5 m s1 during both the flood and the ebb. Although the velocity experiences its maximum reduction behind each individual device, the flow does not fully recover as the distance from the turbine increases. As a result, a reduction in the flow incident on the turbines downstream is observed (compared to the undisturbed flow or baseline case). The magnitude of this reduction varies from 6.66% to 11.96% during the flood and from 7.71% to 14.00% during the ebb (Table 5). The alterations presented in Table 5 affect the power density distribution that is available for conversion at each single tidal stream turbine (TST), and thus the annual energy production (AEP) decreases. In order to quantify the impacts on the available energy, the time distribution of the power density on the incoming flow at the TST was computed for both the case of power extraction (farm) and the baseline case (without TSTs). Fig. 6 illustrates an example for turbine ‘B3’. As can be seen, the presence of the tidal stream farm involves significant variations in the tidal resource.
For the spring–neap cycle considered, the energy density available in the incoming flow of each TST is the area under the curve in Fig. 6. A numerical integration yields the values needed to compute the results presented in Fig. 7. Additionally, an area (A) of 314.16 m2 and a power coefficient (Cp) of 0.35 were considered (see Eq. (2)), in line with the characteristics of the prospective tidal stream farm (Table 3). Different values of energy production are observed for each TST (Fig. 7). Such differences, far from being exclusively produced by the device interactions, are already observed for the baseline case (estimation of the AEP on the basis of the available resource, without considering the device interactions). This reveals the spatial variability of the tidal stream resource and thus the important role that the specific location of the TSTs plays in the amount of energy delivered. In the investigated tidal farm, the AEP varies from a minimum of 1341.77 MW h year1 (turbine ‘A3’) to a maximum value of 1599.52 MW h year1 (turbine ‘C3’) in the baseline case; and from 1074.13 MW h year1 (turbine ‘A3’) to 1246.03 MW h year1 (turbine ‘B1’) in the farm case. Setting aside the differences between the baseline and the farm case, the variations in the AEP among the TSTs are of 15%, and then, they should not be disregarded when assessing tidal stream resource, if realistic results are to be obtained. Indeed, this site-dependence may be used to optimise the energy production of a tidal farm, by choosing the individual position if each TST, for example. This would contribute to reducing the associated cost. Having explained this, the results (Fig. 7) suggest that device interactions may also play a decisive role in the AEP values: a maximum reduction of up to 27.47% is observed for the AEP in the TST ‘C2’ (difference between baseline and farm case). It seems that the effects of device interactions are directly related to the baseline AEP (available resource), i.e. the higher the available
434
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Ilfracombe Water level (m)
8 6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
17/04/2011 0:00
21/04/2011 0:00
Hinkley Water level (m)
8 6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Newport
Water level (m)
10
Gauge Model
5
0
-5
-10 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Mumbles 8
Water level (m)
6
Gauge Model
4 2 0 -2 -4 -6
-8 01/04/2011 0:00
05/04/2011 0:00
09/04/2011 0:00
13/04/2011 0:00
Fig. 3. Comparisons between the predicted (model values) and the observed (gauge values) tidal elevations.
resource, the stronger the device effects. Thus, TSTs placed at row ‘C’ experience the highest AEP variations of 26% lower with respect to the baseline case. They are followed by TSTs of the central row (‘B2’ and ‘B3’), which are associated with a reduction of 24% in the AEP. As regards row ‘A’, the AEP is 20% lower at the TSTs, due to device interactions. In row ‘B’ this tendency does not apply to TSTs ‘B1’ and ‘B4’. For example, turbine ‘A3’ experiences similar variation in the AEP (19.95%) than TSTs ‘B1’ and ‘B4’ (17.42% and 18.08%, respectively); however, the baseline resource differs in more than 150 MW h year1. These findings reveal that apart from the spatial distribution of the resource, the layout of the farm is responsible for the magnitude of the device interactions. In this particular case, ‘B1’ and ‘B4’ are TSTs affected directly by only one TST: ‘A1’ and ‘A3’ during the flood, respectively; and ‘C1’ and ‘C3’ during the ebb, respectively. Therefore, although being placed in more energetic sites, the effects on the AEP are lower. According to this explanation, ‘B2’ and ‘B3’ may be expected to experience the highest reductions, since they are
placed in the central positions and receive the influence of rows ‘A’ and ‘C’ during the flood and the ebb, respectively. However, the results suggest that the interactions of two rows are more important than those of one row, as the effects have an incremental character. Thus, in spite of having similar AEP values that row ‘C’ (of around 1500 MW h year1), the effects on the central TSTs are not as strong as it could be expected. This ‘‘incremental effect’’ can be seen in Fig. 5, where the incoming flow at row ‘C’ (‘A’) is significantly less energetic than the one at row ‘B’ for the flood (ebb). This finding gives rise to a discussion about the appropriateness of adding turbines in a row or rows in a tidal farm, as presented in Section 3.4. But before that, the economic implications of the effects mentioned above are investigated in the next section. 3.3. Impact on the LCOE In order to examine the cost implications of the hydrodynamic effects of the performance of the tidal farm, the cost per energy
435
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438 Table 4 Correlation coefficient (R) and RMSE values of predicted and measured currents. Location
RMSEa
R 0
0
Site F (51°33.3 N, 3° 56.9 W)
Spring tide Neap tide Direction
0.9054 0.8908 0.9956
0.1406 0.1568 4.5546
Site G (51°270 N, 3°55.60 W)
Spring tide Neap tide Direction
0.8770 0.8853 0.9948
0.2241 0.1543 9.9818
Site H (51°32.50 N, 3°53.50 W)
Spring tide Neap tide Direction
0.8960 0.9170 0.8966
0.1646 0.1239 13.4300
Site K (51°20.10 N, 3°50.30 W)
Spring tide Neap tide Direction
0.8581 0.9062 0.8911
0.2833 0.1475 15.2310
Site L (51°160 N, 3°47.40 W)
Spring tide Neap tide Direction
0.8689 0.8702 0.9946
0.3436 0.2163 9.4107
a RMSE values in m/s for the Spring tide and Neap tide velocities and in degrees for the direction.
Spring tide velocity (m s–1)
unit produced was calculated for the baseline case and the farm case, by applying the LCOE method described in Section 2.1. The results are presented in Fig. 8. For this study, the capital expenditures (CAPEX) were considered to be a onetime cost in the range of £4.3 m/MW, and the operational expenditures (OPEX) were included in Eq. (1) as an annual cost of £0.31 m/MW/year, both quantities are referred to shallow water devices at a demonstration stage of development
(Table 1) [37]. Other assumptions included a constant amount of energy output for each year (AEP) during the useful lifetime of the installation [54] and a discount rate (r) of 10%. The results agree well with the comments on the AEP variations (since this is a parameter of the LCOE). In this regard, a range of LCOE values was obtained for each TST, from £0.556 kW h1 to £0.663 kW h1 for the baseline case; and from £0.714 kW h1 to £0.828 kW h1 for the farm case. As commented above, these variations put forth the importance of using numerical modelling in estimating the LCOE (a novelty of this study with respect to previous works), since the project location and its peculiarities play a role in the available tidal stream resource for conversion a key parameter in the LCOE. Likewise, device interactions should be included in the LCOE estimations. In economic terms, the maximum and minimum AEP reductions (experienced at turbines ‘C2’ and ‘B1’, respectively) result in an increase of £0.221 kW h1 and £0.125 kW h1 in the LCOE (Fig. 8). The scope of these LCOE variations need to be contextualised, in order to better understand what do they mean and represent. To this aim, Fig. 9 is included. On the one hand, it shows that the absolute LCOE value of some technologies, both renewable (such as onshore wind energy) and non-renewable (i.e. CCGT), is lower than the minimum LCOE increase due to device interactions found in this study. On the other hand, the range of potential variation in the LCOE values of both on- and offshore wind energy (associated with the highest uncertainties due to the variable character of the resource), represents less than half of the range of LCOE variations due to tidal stream device interactions (see error bars). The previous comparisons help to understand that the device interactions can produce
3
Site K (51º 20.1' N, 3º 50.3' W) Observed Predicted
2.5 2 1.5 1 0.5 0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
4
5
6
4
5
6
Neap tide velocity (m s–1)
Time referred to HW at Swansea (h) 3 2.5 2
Site K (51º 20.1' N, 3º 50.3' W) Observed Predicted
1.5 1 0.5 0
-6
-5
-4
-3
-2
-1
0
1
2
3
Time referred to HW at Swansea (h) 180
Direction (degrees)
Site K (51º 20.1' N, 3º 50.3' W) 120
Observed Predicted
60
0 -60
- 120 - 180 -6
-5
-4
-3
-2
-1
0
1
2
3
Time referred to HW at Swansea (h) Fig. 4. Comparisons between observed and predicted current speed: (a) spring tide, (b) neap tide, and (c) current direction.
436
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
Fig. 5. Velocity difference between the baseline and the farm case, during (a) the flood and (b) the ebb.
Table 5 Variation of the velocities on the incoming flow of each tidal stream turbine during the flood and the ebb. Turbine
A1 A2 A3 B1 B2 B3 B4 C1 C2 C3
Flood
than the 20%. Thus, tidal stream farms should be designed so as to attenuate the aforementioned effects, if the cost is to be minimised. In this vein, the results suggest that such attenuation could be made by adjusting the following array parameters.
Ebb
Max. V diff. (m/s)
% Reduction
Max. V diff. (m/s)
% Reduction
0.1806 0.1907 0.1751 0.1934 0.2399 0.2337 0.1675 0.2939 0.3050 0.2646
7.43 7.84 7.24 7.59 9.44 9.35 6.66 11.56 11.96 10.41
0.3002 0.3608 0.3752 0.2080 0.3013 0.3247 0.2900 0.2316 0.2552 0.2614
11.29 13.43 14.00 7.71 11.14 11.97 10.53 8.67 9.46 9.67
– Longitudinal spacing. As shown in Fig. 5, the velocity (and hence the available kinetic energy for conversion) is reduced downstream of each turbine. The size of the affected area is large enough to produce an alteration in the available resource and the AEP at the turbines placed in the vicinity (see Fig. 7). This is due to the fact that the chosen longitudinal spacing for this study (five-diameters) impeded the recovery of the tidal flow. In order to minimise the LCOE, then the turbine spacing should be increased. In order to investigate what may be a better longitudinal spacing, the TST ‘B1’ (Fig. 5) is taken for illustration. In this vein, if a site placed at a distance of ten-diameters (the double) downstream of ‘B1’ is considered – coordinates (x, y): (4.428 105, 5.6805 106) and (4.423 105, 5.6805 106) in the cases of flood and ebb tide, respectively – the velocity would be reduced in a magnitude of less than 0.1 m s1, whereas if the five-diameter spacing is maintained, the velocity reduces between 0.1 and 0.2 m s1. Since the output is proportional to the cube of the velocity, such appreciation is of major economic interest. Of course, the previous values are indicative and may need specific studies (with isolated TSTs) to better calculate the different effects. This is going to be carried out in future works.
significant variations in the cost of energy produced and then should be considered when optimising the cost of a tidal farm. 3.4. Potential for reducing the cost of a tidal stream farm As it had been expected – and after demonstrated by the results presented in the previous sections – the interactions among the TSTs have a bearing on the economics of a tidal stream farm. In particular, it has been found that these interactions play a decisive role in the cost of energy, which experiences increases of more
Power density (W m–2)
12000 Baseline
Farm (B3)
10000 8000 6000 4000 2000 0 14/03/2011 0:00
21/03/2011 0:00
28/03/2011 0:00
Time Fig. 6. Available energy density in the incoming flow of the turbine ‘B3’. Baseline vs. Farm.
437
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438 1800
0.25 Baseline
£0.221 kWh−1
Farm
1600 0.2
LCOE (£ kWh–1)
AEP (MWh year
–1)
1400 1200 1000 800 600
0.15
£0.125 kWh−1
0.1
0.05
400 0
200
1
3
4
5
CCGT
2
OCGT
3
Onshore
4
Offshore
5
Biomass
6
Large scale Solar
6
Technology
0 A1
A2
A3
B1
B2
B3
B4
C1
C2
C3
Turbine Fig. 7. The annual energy production (AEP) for each turbine without (baseline) and with the consideration of the device interactions (farm).
– Array shape. A triangular configuration has been usually adopted in previous studies (e.g. [25]), by means of placing the turbines downstream of the gaps between turbines in an upstream row with the extra rows of TSTs placed between the gaps of the previous row. Thanks to this configuration, the shadow effect produced by each turbine is partially reduced. However, in view of Fig. 8, the central TST of each row are those that suffer higher alterations. This suggest the possibility of moving the central TSTs to an outer position. – Array size. How many TSTs are to be placed in the farm and how many rows are to be installed, while maintaining the installed capacity, are also questions of interest. On the one hand, it has to be mentioned that realising all the potential of a tidal place is much more complex with less devices than installing more turbines of lower capacity. This is due to the fact that higher scenarios of power extraction reduce more significantly the tidal currents throughout the tidal site (as suggested by Ramos et al. [25]). On the other hand, adding rows of turbines to arrays decreases the individual output of all turbines within the array. With this is view, it is concluded that less rows are more beneficial in terms of device interactions. Besides, fewer rows may allow for having a higher longitudinal spacing, which has been suggested to be also beneficial. If the installed capacity is not to be maintained, then it should be better to add turbines. Although having a negative effect in the individual TSTs, a higher number of devices increases the total energy production of the array. – Individual positioning of each single TST. As for all the previous comments, it may be understood that the relative position (and also the capacity) of each TST might be individually chosen 1 0.9
LCOE (£ kWh–1)
2
1
0.8 0.7 0.6 0.5 0.4 A1
A2
A3
B1
B2
B3
B4
C1
C2
C3
Turbine Fig. 8. LCOE variations due to device effects (lowest values correspond to the ‘baseline case’ and greatest values refer to the ‘farm case’).
Fig. 9. LCOE estimates for a number of technologies (including combines and open cycle gas turbines, CCGT and OCGT, respectively) vs. LCOE variations [minimum (£0.125 kW h1) and maximum (£0.221 kW h1)] due to device interactions.
in order to optimise the cost of the tidal farm. This accords well with the comments of Section 3.2, where it is suggested that the resource available at each point plays also a role in the AEP, and hence in the LCOE. As a consequence, the computational effort may be significantly increased. In further works, all the previous insights are going to be considered and thus, this work is going to be extended in order to optimise the layout of the tidal stream farm. Finally, it should be mentioned that when optimising the array layout for minimum interactions and costs, other factors may be accounted for. The available space, water depth constrictions and potential conflicts with other economic activities (fisheries and navigation) are some of the aspects that should be considered. 4. Conclusions The cost of generation from the tidal stream resource, the socalled levelised cost of energy (LCOE), is typically higher than that from traditional sources (coal, natural gas, etc.) On these grounds, it is crucial to understand the parameters affecting this cost so as to provide a framework of potential areas of reduction. With this in view, this work investigates for the first time the role of the effects of tidal energy extraction in the energy output and, hence, in estimating the LCOE of a prospective tidal stream farm. For this purpose, a case study was considered: Lynmouth (UK). Here, a numerical model was implemented and validated against observations of tidal level and current velocities. Based on the results of the numerical modelling, an area with peak currents above 2.25 m s1, a water depth of 20–25 m and a nearby grid connection point was chosen as the best site for studying the effects of a prospective tidal stream farm. Thanks to the high resolution of the computational grid in the area of interest it was possible to resolve the different turbines of the farm individually. The integration of the numerical modelling results into the LCOE calculation – an aspect that had not been addressed so far – showed that the presence of the tidal stream turbines has a significant effect on the available resource, and hence on the LCOE values. The LCOE for each device was examined in two scenarios: without (baseline) and with the tidal stream farm. A comparison between the different estimates was presented, showing a LCOE variation of up to £0.221 kW h1. Different values of LCOE were found for the individual TSTs, ranging from £0.556 kW h1 to £0.663 kW h1 in the baseline case; and from £0.714 kW h1 to £0.828 kW h1 in the farm case. Such a wide range of values suggests that the effects on the LCOE depend on the specific position
438
A. Vazquez, G. Iglesias / Energy Conversion and Management 97 (2015) 428–438
of the TST within the farm hence the importance of optimising the layout of the farm. In summary, the LCOE is sensitive to the effects of the tidal stream devices within a tidal stream farm. The quantification of such effects is, therefore, of economic interest and should not be disregarded, if the LCOE of tidal energy is to be minimised. Understanding the true costs and energy production would contribute to improve the design of competitive tidal stream energy farms. The results presented in this study provide preliminary insights to optimise the layout of a tidal stream farm. Acknowledgements The authors wish to thank the British Oceanographic Data Centre for providing tide gauge records. During this work A. Vazquez has been supported by FPU grant 13/03822 of the Spanish Ministry of Education, Culture and Sport, and by a grant from the Barrie Foundation for undertaking a predoctoral fellowship at Plymouth University, UK. References [1] Vazquez A, Astariz S, Iglesias G. A strategic policy framework for promoting the marine energy sector. In: Proc. 3rd IAHR Europe congress, Porto, Portugal; 2014 [ISBN 978-989-96479-2-3]. [2] Iglesias G, Sánchez M, Carballo R, Fernández H. The TSE index – A new tool for selecting tidal stream sites in depth-limited regions. Renewable Energy 2012;48:350–7. [3] Carballo R, Iglesias G, Castro A. Numerical model evaluation of tidal stream energy resources in the Ría de Muros (NW Spain). Renewable Energy 2009;34:1517–24. [4] Fairley I, Evans P, Wooldridge C, Willis M, Masters I. Evaluation of tidal stream resource in a potential array area via direct measurements. Renewable Energy 2013;57:70–8. [5] Neill SP, Hashemi MR, Lewis MJ. The role of tidal asymmetry in characterizing the tidal energy resource of Orkney. Renewable Energy 2014;68:337–50. [6] Evans P, Armstrong S, Wilson C, Fairley I, Woolridge C, Masters I. Characterisation of a highly energetic tidal energy site with specific reference to hydrodynamics and bathymetry. In: Proc. 10th European Wave and Tidal Energy Conference (EWTEC), Aalborg, Denmark; 2013. [7] Ramos V, Carballo R, Álvarez M, Sánchez M, Iglesias G. A port towards energy self-sufficiency using tidal stream power. Energy 2014;71:432–44. [8] Rourke O, Boyle F, Reynolds F. A. Tidal energy update 2009. Appl Energy 2010;87:398–409. [9] http://www.marineturbines.com. [10] Li Y, Çalisßal SM. Numerical analysis of the characteristics of vertical axis tidal current turbines. Renewable Energy 2010;35:435–42. [11] Liu P, Bose N. Prototyping a series of bi-directional horizontal axis tidal turbines for optimum energy conversion. Appl Energy 2012;99:50–66. [12] Sanchez M, Carballo R, Ramos V, Iglesias G. Floating vs. bottom-fixed turbines for tidal stream energy: A comparative impact assessment. Energy 2014;72:691–701. [13] Sanchez M, Carballo R, Ramos V, Iglesias G. Energy production from tidal currents in an estuary: A comparative study of floating and bottom-fixed turbines. Energy 2014;77:802–11. [14] Willis M, Masters I, Thomas S, Gallie R, Loman J, Cook A, et al. Tidal turbine deployment in the Bristol Channel a case study. Energy 2010;163(EN3). [15] Fallon D, Hartnett M, Olbert A, Nash S. The effects of array configuration on the hydro-environmental impacts of tidal turbines. Renewable Energy 2014;64:10–25. [16] Vazquez A, Iglesias G. Public perceptions and externalities in tidal stream energy: A valuation for policy making. Ocean Coast Manage 2015;105:15–24. [17] Carbon Trust. Accelerating Marine Energy. The potential for cost reduction – insights from the Carbon Trust Marine Energy Accelerator. Carbon Trust 2011;CTC797. [18] Denny E. The economics of tidal energy. Energy Policy 2009;37:1914–24. [19] Li Y, Lence BJ, Calisal SM. An integrated model for estimating energy cost of a tidal current turbine farm. Energy Convers Manage 2011;52:1677–87. [20] Li Y, Florig HK. Modeling the operation and maintenance costs of a large scale tidal current turbine farm. OCEANS 2006:1–6. [21] Verbruggen A, Fischedick M, Moomaw W, Weir T, Nadaï A, Nilsson LJ, et al. Renewable energy costs, potentials, barriers: Conceptual issues. Energy Policy 2010;38:850–61. [22] Al-Nimr MA. Principles of sustainable energy. Energy 2011;36:3613–4.
[23] Owen AD. Environmental externalities, market distortions and the economics of renewable energy technologies. The Energy Journal 2004;25(3):127–56. [24] Sanchez M, Carballo R, Ramos V, Iglesias G. Tidal stream energy impact on the transient and residual flow in an estuary: A 3D analysis. Appl Energy 2014;116:167–77. [25] Ramos V, Carballo R, Álvarez M, Sánchez M, Iglesias G. Assessment of the impacts of tidal stream energy through high-resolution numerical modeling. Energy 2013;61:541–54. [26] Ahmadian R, Falconer RA. Assessment of array shape of tidal stream turbines on hydro-environmental impacts and power output. Renewable Energy 2012;44:318–27. [27] Neill SP, Jordan JR, Couch SJ. Impact of tidal energy converter (TEC) arrays on the dynamics of headland sand banks. Renewable Energy 2012;37:387–97. [28] Robins PE, Neill SP, Lewis MJ. Impact of tidal-stream arrays in relation to the natural variability of sedimentary processes. Renewable Energy 2014;72:311–21. [29] South West Marine Energy Park.