# Economic analysis of tidal stream turbine arrays: a review

Z. L. Goss  Department of Earth Science and Engineering, Imperial College
London, SW7 2AZ, UK  D. S. Coles  School of Engineering, Computing and
Mathematics, University of Plymouth, Plymouth PL4 8AA, UK  M. D. Piggott
Department of Earth Science and Engineering, Imperial College London, SW7 2AZ,
UK

###### Abstract

This tidal stream energy industry has to date been comprised of small
demonstrator projects made up of one to a four turbines. However, there are
currently plans to expand to commercially sized projects with tens of turbines
or more. As the industry moves to large-scale arrays for the first time, there
has been a push to develop tools to optimise the array design and help bring
down the costs. This review investigates different methods of modelling the
economic performance of tidal-stream arrays, for use within these optimisation
tools. The different cost reduction pathways are discussed from costs falling
as the global installed capacity increases, due to greater experience,
improved power curves through larger-diameter higher-rated turbines, to
economic efficiencies that can be found by moving to large-scale arrays. A
literature review is conducted to establish the most appropriate input values
for use in economic models. This includes finding a best case, worst case and
typical values for costs and other related parameters. The information
collated in this review can provide a useful steering for the many
optimisation tools that have been developed, especially when cost information
is commercially sensitive and a realistic parameter range is difficult to
obtain.

###### Contents

  1. 1 Introduction & Motivation
  2. 2 Review of economic metrics for evaluating array design
    1. 2.1 Power
    2. 2.2 Break even power
      1. 2.2.1 Break even power with economies of volume
    3. 2.3 Net Present Value
      1. 2.3.1 Break even analysis
      2. 2.3.2 Discrete versus continuous discounted cash flow analysis
    4. 2.4 Levelised Cost of Energy
    5. 2.5 Payback Period
    6. 2.6 Internal rate of return
    7. 2.7 CAPEX versus OPEX
    8. 2.8 Other metrics to consider
      1. 2.8.1 Environmental impact
      2. 2.8.2 Location based costs
  3. 3 Cost reduction pathways
    1. 3.1 Learning rates
    2. 3.2 Economies of scale
    3. 3.3 Economies of volume
      1. 3.3.1 Expenditure break down
    4. 3.4 Revenue
  4. 4 Estimate of inputs to economic models
    1. 4.1 Relationship between cost and size of array
      1. 4.1.1 Method 1: Knowing two data points
      2. 4.1.2 Method 2: Knowing the ratio of fixed to turbine-dependent costs
    2. 4.2 Cost data available in literature
      1. 4.2.1 Higgins and Foley: The evolution of offshore wind power in the United Kingdom
      2. 4.2.2 Culley et al.: Optimisation of Cable Costs
      3. 4.2.3 OREC: Tidal Stream and Wave Energy Cost reduction and Industrial Benefit
      4. 4.2.4 IEA Technology: International LCOE for ocean energy technology
      5. 4.2.5 Orbital Marine Power Limited: Technology Update
      6. 4.2.6 Black & Veatch: Cost of and financial support for wave, tidal stream and tidal range generation in the UK
      7. 4.2.7 Summary of $\text{CA}_{t}$, $\text{CA}_{f}$, $O_{t}$ and $O_{f}$ estimates
      8. 4.2.8 Discount rate
      9. 4.2.9 Lifetime of array
      10. 4.2.10 Summary of all cost model inputs
    3. 4.3 Revenue inputs
      1. 4.3.1 Strike price of energy
      2. 4.3.2 Downtime and degradation
  5. 5 Conclusions and summary
  6. 6 Acknowledgements

##  1 Introduction & Motivation

Demand for sustainable and reliable energy sources is increasing, and tidal
energy could prove an important part of the future energy generation mix, due
to its predictable nature. However, tidal energy is a nascent industry
compared to more established renewables such as wind and solar. These
industries have seen significant costs reductions due to subsidies helping
them learn from expensive early demonstrator arrays. These initial subsidies
allowed wind and solar to progress to large-scale energy farms with a much
lower price of energy. At the time of writing, the UK’s largest onshore wind
farm now consists of 215 turbines (Whitelee Windfarm) and the largest offshore
farm has 189 (the Walney Extension). The maturity of the industry and the
economies gained from large numbers of devices has led to the UK seeing a
record low price per MWh from offshore wind of £39.65 in their third Contracts
for Difference auction, in September 2019, for less established renewable
technologies [1].

In order to compete with more established technologies, tools must be
developed to predict and help reduce the cost of tidal energy. In order for
academically produced tools to be useful for industry, they need to be
combined with the economic models and metrics that tidal investors are
interested in. The inputs to these models are typically commercially sensitive
and are therefore rarely publicly available. While exact values may only be
used internally within industry, estimates of the inputs are useful for
testing the academically developed tools.

Previous design optimisation studies, such as [2, 3, 4, 5], have optimised not
only an array’s design, but also the number of turbines in an array. This can
be important in order to take advantage of the cost reductions that can be
achieved with larger scale arrays, while also balancing against the
diminishing returns as the average power generation per device falls with
additional turbines. This review formats the cost inputs so they can be used
in an economic model with a varying number of turbines and therefore can be
used in the functional for a model that optimises both the location and the
number of turbines.

This review attempts to summarise the economic models most commonly used by
the tidal energy industry and associated academia and to collate the publicly
available cost information to produce appropriately formatted estimates for
the inputs into these models. Section 2 outlines the most commonly used
economic metrics and their advantages and disadvantages. Section 3 describes
the different mechanisms expected to lead to the reduction in the price per
MWh of tidal stream energy. Section 4 combines publicly available cost
information, yielding data in a format useful for the input into the models
described in Section 2. Finally, Section 5 discusses the uses and the
limitations of the information collated in this review.

##  2 Review of economic metrics for evaluating array design

When designing a tidal turbine array the choice of functional to optimise can
have a significant impact on the resultant array design. The following
sections outline common metrics that are used for evaluating the performance
of a tidal array, which could be used as the functional.

###  2.1 Power

Many papers [3, 6, 7] optimise array design for power alone, such that the
functional is $J=P_{\text{avg}}$. This can be an effective method of
determining a suitable layout, especially if the size of the array is already
specified, such as in [3, 7] In such cases the costs are relatively fixed,
except for the costs that depend on the individual turbine locations, such as
the cabling [4] or distance and depth related installation costs, which are
discussed in greater detail in Section 2.8.2. However, in general maximising
for power is a reasonable proxy for maximising the economic performance.

Problems in using the power alone as a functional arise, in particular, when
the number of turbines is also allowed to vary and becomes a free parameter
within the array design optimisation. Earlier work [6, 8] has shown that, when
optimising for power alone, the optimal design will feature an impractically
high number of turbines, where the overall power generation is at its maximum,
but the capacity factor of the array, and therefore its profitability, is
relatively low. The optimisation algorithms will keep adding turbines, which
slow the flow velocity through the site, until a point is reached where the
blockage is so high that adding any more turbines will decrease the overall
power generation. However, the extracted power per additional turbine will
diminish long before the threshold where the overall power decreases. Given
the high cost of installing devices the optimal economic performance will be
achieved at a far lower number of turbines than the optimal power.

###  2.2 Break even power

As established in earlier work [9, 6, 10], adding additional turbines to an
array may increase the overall power, but there comes a point where there are
diminishing returns for each extra turbine installed, for example due to
global blockage effects as well as the array being forced to expand into lower
flow areas [11]. From a financial perspective it may be more advantageous to
have a smaller array where the average power per device ($\text{PPD}=\text{Avg
Power}/n_{t}$) is higher, because tidal turbines are relatively costly to
manufacture and install. In recent work [8, 10] a break even power,
$P_{\text{BE}}$, is included in the optimisation functional to account for
this problem and ensure that turbines are only added if they can generate
enough power to cover their installation costs. Varying this parameter changes
the trade-off priorities between the objectives of maximising power generation
and minimising costs.

The break even power is the average power over all turbines that needs to be
generated in order for the array to break even over its lifetime. A formula
for choosing a suitable break even power can be found by first using a
simplified model for the expected cash flow as the functional, such that

$\displaystyle J$ $\displaystyle=\text{Revenue}-\text{Cost}$ (1)
$\displaystyle=\sum_{i=0}^{L}(P_{\text{avg}}\times t_{i}\times
T_{e})-\sum_{i=0}^{L}\text{Ex}_{i},$

where $i$ is the year the costs are being evaluated over, $L$ is the lifetime
of the array in years, $P_{\text{avg}}$ is the average power generated by the
whole array in MW, $t_{i}$ is the number of hours of generation in year $i$,
$T_{e}$ is the electricity tariff, i.e. the price per MWh the electricity
generated is sold at, and $\text{Ex}_{i}$ is the sum of all array expenditure
incurred in year $i$. If we assume $P_{\text{avg}}$ is independent of the year
we can use this to find a critical average power per device that must be
generated by the whole array to break even:

$P_{\text{BE}}\times n_{t}\sum_{i=0}^{L}(t_{i}\times T_{e}-\text{Ex}_{i})=0,$
(2) $\iff
P_{\text{BE}}=\frac{\sum_{i=0}^{L}\text{Ex}_{i}}{n_{t}\times\sum_{i=0}^{L}(t_{i}\times
T_{e})}.$ (3)

If we assume that total expenditure is just a multiple of the number of
installed turbines, $\text{Ex}_{i}=n_{t}\times\text{Ex}_{t,i}$, then a
constant value for $P_{\text{BE}}$ can be found which is independent of array
design:

$P_{\text{BE}}=\frac{\sum_{i=0}^{L}\text{Ex}_{t,i}}{\sum_{i=0}^{L}(t_{i}\times
T_{e})}.$ (4)

In practice, $P_{\text{BE}}$ would probably decrease for larger scale arrays,
due to economies of volume [12]. More sophisticated models to account for this
are discussed below. Since the functional defined in (1) is invariant with
respect to scaling, it can be seen that optimising with respect to expected
cash flow is equivalent to optimising a functional of the form

$J=P_{\text{avg}}-\frac{\sum_{i=0}^{L}\text{Ex}_{t,i}}{\sum_{i=0}^{L}(t_{i}\times
T_{e})},$ (5)

which combined with the aforementioned simplifying assumptions can be reduced
to

$J=P_{\text{avg}}-P_{\text{BE}}\times n_{t}.$ (6)

Therefore for the array to generate a profit the average total power generated
by the array must be more than the break even power times the total number of
devices. If an appropriate break even power is chosen to reflect all of the
costs in (1), this choice of functional effectively maximises the profit. It
penalises the addition of turbines which do not generate sufficient power to
offset their costs, or which due to hydrodynamic changes lead to reductions in
the yield of other turbines.

An advantage of using the functional described in (6) is that it incorporates
financial considerations to the optimisation through the use of just one
simple variable, $P_{\text{BE}}$. However, this simplification means that the
optimisation process has no flexibility to changes in strike price, annual
yield variability, maintenance costs and hours downtime throughout the many
years an array is operating for. It also excludes the effect of economies of
volume, where larger-scale arrays would require a lower $P_{\text{BE}}$ to
break even[12]. Both these limitations mean that, in reality, break even power
would be a function of time and the size of the array, rather than a constant
as assumed here. This might be an acceptable simplification if the optimal
design was robust to changes in $P_{\text{BE}}$ that arise from these factors;
however, previous studies [10] have shown the optimal design to be very
sensitive to even small changes in $P_{\text{BE}}$.

Other papers have used similar or equivalent metrics to the break even power,
with varying terminology. Iyer et al. [13] assessed the viability of tidal
sites around the UK and used the capacity factor as a simplified indicator of
the economic performance of a site, on a per MW basis. They found an average
capacity factor of 29.9% (but ranging between 23.3 and 43.6%) across all the
sites they investigated in the UK. They noted that this metric has limited
usefulness in models where turbine specifications chosen (such as diameter and
rated power) are generic rather than tailored to the site being evaluated,
therefore under-utilising the resource.

Funke et al. [2] first coined the term break even power, but also called it a
cost coefficient. Their definition was very similar to the one given in (4),
except instead of evaluating about the break even point, they assumed a profit
margin, $m$, was required such that

$m=\frac{\text{Revenue}-\text{Cost}}{\text{Revenue}}$ (7)

and they made the assumption $m=73\%$. They assumed that the 73% profit margin
could be achieved by a 20m diameter turbine if the peak speed was
$3.5\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$, and used this to estimate
a break even power of 452 kW. They only tested the optimisation for this one
break even power value, but noted that the break even power chosen was
expected to have a large impact on the optimal number of turbines.

Funke et al. [2] also noted that the break even power model does not take a
discount rate into account. Therefore no financial distinction is made between
capital expenditure, i.e. upfront investments such as turbine and installation
costs, versus operational expenditure, i.e. maintenance costs incurred years
into the future.

A further limitation of using break even power as the functional is that it
makes too many simplifying assumptions and has no way to account for economies
of scale. Below we discuss an adaptation to the functional to account for
this. Overall, break even power represents a good early measure while
insufficient financial information is available since all you need to know is
an aspirational capacity factor. For example, if the developer’s financial
model finds that an array of 2MW turbines needs to achieve a 40% capacity
factor to be profitable, then the break even power needs to be set to
$2000\times 0.4=800$kW. However, once a more complete model of the costs is
available a more detailed metric should be used that accounts for all the
effects ignored by the above assumptions.

####  2.2.1 Break even power with economies of volume

When the costs are assumed to increase linearly with the number of turbines,
the break even power is independent of the number of turbines and therefore
can be used as a constant value, as given in (4). In practice that
relationship will not reflect the true expenditure and the break even power
will likely decrease as $n_{t}$ increases due to economies of volume. There
are a number of ways this impact can be modelled, the simplest of which is to
linearly decrease the break even power with the number of turbines, such that
$P_{\text{BE}:\text{EV}}=P_{\text{BE}}-EV\times n_{t}$, where $EV$ is a
coefficient for economies of volume, and $EV\ll P_{\text{BE}}$. This change
can be made to the functional (6) so that

$J=P_{\text{avg}}-(P_{\text{BE}}-EV\times n_{t})\times
n_{t}=P_{\text{avg}}-P_{\text{BE}}\times n_{t}+EV\times n_{t}^{2}.$ (8)

Using a functional of this format is equivalent to the expenditure instead
decreasing quadratically with the number of turbines, such that:

$P_{\text{BE:EV}}=\frac{\sum_{i=0}^{L}\text{Ex}_{t,i}\times n_{t}-EV\times
n_{t}^{2}}{n_{t}\times\sum_{i=0}^{L}T_{e}\times
t_{i}}=\underbrace{\frac{\sum_{i=0}^{L}\text{Ex}_{t,i}}{\sum_{i=0}^{L}T_{e}\times
t_{i}}}_{P_{\text{BE}}}-\underbrace{\frac{\sum_{i=0}^{L}\text{EV}}{\sum_{i=0}^{L}T_{e}\times
t_{i}}}_{EV}\times n_{t}.$ (9)

Figure 1 shows how if the annual expenditure increases linearly with the
number of turbines the break even power is fixed, however, if the expenditure
declines quadratically with the number of turbines the break even power
declines linearly with the number of turbines. Both rely on assumed
relationships between the costs and number of turbines but are useful for
initial investigations into how bringing costs and economies of volume into
the functional effect the optimal array design.

Figure 1: A demonstration of how the relationship between expenditure per year
and number of turbines in an array corresponds to a fixed or linearly
decreasing break even power.

The impact of varying both the $P_{\text{BE}}$ and $EV$ parameters are
explored in [10]. It was found that as $P_{\text{BE}}$ falls, for example due
to costs falling in the tidal industry with experience gained, the optimal
array design features more turbines and generates more power overall, but the
average power per device drops. It was shown that optimal array properties
were more sensitive to changes in the region $300kW\leq P_{\text{BE}}\leq
500kW$. This was even more notable when including economies of volume too;
changing the value of $EV$ had little to no impact on the optimal design for
very high or very low values of $P_{\text{BE}}$. For $300kW\leq
P_{\text{BE}}\leq 500kW$ however, it was seen that as $EV$ increased the total
power generated and number of turbines increased, and the power generated per
device decreased.

###  2.3 Net Present Value

Equation (1) describes the sum of all cash flow across an arrays lifetime,
however in practice this value is rarely used by investors. Long term
investments, such as tidal arrays, rely on discounted cash flow (DCF) analysis
to quantify the idea that money today is worth more than money tomorrow to
investors. Current funds have the ability to earn interest and become worth
more in the future, so investors need to find a way to adjust future cash flow
to enable the comparison between costs and revenue in different time periods,
in terms of their present day value. The Net Present Value (NPV) is a measure
used to find the profit of a project is found by summing all incoming and
outgoing cash flows per year, i.e. the revenues minus the costs from each year
$i\in[0,L]$, adjusted according to the time value of money by a discount rate,
$r$, such that

NPV
$\displaystyle=\sum^{L}_{i=0}\frac{\text{Revenue}_{i}-\text{Cost}_{i}}{(1+r)^{i}}$
(10) $\displaystyle=\sum^{L}_{i=0}\frac{P_{\text{avg}}\times t_{i}\times
T_{e}-\text{Ex}_{i}}{(1+r)^{i}}.$

Using the NPV as the functional for tidal array optimisation has many
advantages. Unlike the previous metrics it takes into account the depreciating
time value of money, which is important to investors. It allows for far
greater flexibility in the financial modelling than the previous metrics. For
example, instead of basing analysis on a time averaged power generation,
$P_{\text{avg}}$, it is trivial replace this with a time-varying generation.
This can be used to model the impact that the power variation due to the 18.6
lunar nodal cycle [14, 15] has on the economic performance of the array. It
could also be used to include the effects of the anticipated degradation of
the turbine performance, for example due to biofouling and algae build up
[16], and increase in required downtime, due to a higher number of faults with
age, as commonly observed in the wind industry [17, 18]. However using an
average power generation is very useful while there is still a lot of
uncertainty about the planned installation year and fault rates decades into
the future.

A disadvantage of using NPV as the functional for tidal array optimisation, is
that it is hard to compare between projects of different sizes. A smaller
tidal array may have a far higher profit margin but a much lower NPV than a
large tidal array. It is hard to interpret directly from the NPV how
successful a project is.

####  2.3.1 Break even analysis

There are a number of different economic metrics which can be derived when
applying break even analysis to the Net Present Value formula. Equation (10)
can be set to zero in order to obtain a value for the so-called break even
point of an energy project. Then the resulting equation can be solved for each
of the input variables, to determine the parameter value that would need to be
achieved for the project to break exactly even over its lifetime. Each of
these parameters at break even can be seen as the minimum requirement, and any
improvement on these will result in a positive NPV and the project will
generate a profit.

The most common metrics are derived by solving for the strike price, to obtain
the levelised cost of energy (LCOE), solving for the lifetime, to obtain the
payback period (PP), and solving for the discount rate, to obtain the internal
rate of return (IRR).

####  2.3.2 Discrete versus continuous discounted cash flow analysis

All present value based calculations require summing all the cash flow over a
lifetime and discounting them according to the time at which they occurred.
The net present value calculation given in (10) is setup so that the discount
rate is applied on a yearly basis. It is possible to instead apply the
discounting on different time intervals, e.g. semiannually, quarterly or
monthly, or to use a natural log based formula to apply discounted cash flow
analysis continuously.

Using the discrete compounding method, the present value, $PV$, of a future
cash flow, $FV$, is

$\displaystyle\text{PV}=\frac{\text{FV}}{(1+\frac{r}{p})^{pi}},$ (11)

where $p$ is the number of compounding period per year (for example, $p=1$ for
annual compounding or $p=4$ for quarterly compounding), $i$ is the number of
periods into the future that the future cash flow occurs, and $r$ is the
annual discount rate.

By comparison the continuous compounding method has no period over which the
compounding is applied and can instead be found from

$\displaystyle\text{PV}=\text{PV}\times e^{-ri},$ (12)

where in this case $i$ is a continuous value for the number of years into the
future that the cash flow occurs.

A review into the use of discrete and continuous discount rates by Lewis et
al. [19] found, in a literature review of finance and engineering economics
journals, that the split between discrete and continuous discounting of future
cash flows was fairly even. More mathematical papers tended to use continuous
discounting, whereas more applied papers used discrete discounting. In
practice many tidal array developers are not likely to have precise knowledge
of when exactly costs will be incurred, especially not at the stage of
designing an array. Therefore discrete modelling on an annual, or quarterly,
basis is sufficient for this application.

###  2.4 Levelised Cost of Energy

The levelised cost of energy (LCOE) is a proxy for the average price of
energy, $T_{e}$ [$\pounds$/MWh], that an array must receive to break even over
its lifetime. It takes into account discounting and is calculated by finding
the Net Present Value of the unit-cost of electricity over the lifetime of the
array, by setting expression (10) to zero and rearranging to find the price of
energy;

$\displaystyle\text{LCOE}=\frac{\text{discounted cost}}{\text{discounted
energy}}=\frac{\sum_{i=0}^{L}\frac{\text{Ex}_{i}}{(1+r)^{i}}}{\sum_{i=0}^{L}\frac{P_{\text{avg}}\times
t_{i}}{(1+r)^{i}}}.$ (13)

LCOE will be focused on as the main metric for economic optimisation here
since many studies and organisation use it as the most established form of
estimating the lifetime costs of an energy generation project [20, 21, 22]. It
is an effective benchmarking technique for the comparison of multiple energy
generation technologies, and in this case multiple array designs. LCOE, IRR
and PP are all effectively simplifications of NPV, where an input variable can
be removed by instead only investigating the parameters required to break
even. Often it is sensible to isolate the variable which has the most
uncertainty in it. The price of energy $T_{e}$ can vary greatly depending on
subsidies available to early stage renewable energies, so LCOE predictions
often encapsulate less uncertainty than IRR and PP, because an assumption of
$T_{e}$ is not required.

The LCOE is the most commonly used approach for estimating the cost of energy
over the lifetime of a project, for both tidal energy and other renewables
[20, 21, 22, 12]. Since it is not as sensitive to array size as NPV or other
metrics, it enables simple comparison across a range of different projects.

###  2.5 Payback Period

Another metric that can be derived from break even analysis of the Net Present
Value formula is the Payback Period (PP), which is the lifetime array must
operate for in order to break even. If the planned lifetime of the array is
longer than this the array can be considered to be generating profit, if the
lifetime of the array is shorted than this it will be making a loss.

The Payback Period can be found by calculating the NPV of every year from 0,
until the NPV becomes positive. The critical year, $i_{c}r$, is the last year
before the NPV becomes positive, i.e. the year before the project breaks even.
A payback period can be calculated by estimating how far through the year the
project breaks even;

$\displaystyle\text{Payback
Period}=i_{cr}+\frac{\text{NPV}_{cr}}{\text{NPV}_{cr}-\text{NPV}_{cr+1}}.$
(14)

###  2.6 Internal rate of return

Finally, (10) can be rearranged to find the discount rate at which the project
breaks even, call the Internal Rate of Return (IRR). If the IRR is higher than
the projected discount rate, then investors can anticipate a profit over the
course of the array’s lifetime. IRR is harder to calculate because, when
trying to find the discount rate at which a project breaks even,
$r=\text{IRR}$, the formula can be expanded,

$\displaystyle 0$ $\displaystyle=(E_{0}\times
T_{e}-\text{Ex}_{0})(1+\text{IRR})^{L}+(E_{1}\times
T_{e}-\text{Ex}_{1})(1+\text{IRR})^{L-1}+(E_{L}\times T_{e}-\text{Ex}_{L}),$
(15)

but never to a form which can be solved analytically. However, a nonlinear
solver such as the Secant method can be applied to find the IRR numerically.
Each new iteration, at iteration number $n+1$, is found from the previous two
estimates, such that

$\displaystyle\text{IRR}_{n+1}=\text{IRR}_{n}-\text{NPV}_{n}\times\left(\frac{\text{IRR}_{n}-\text{IRR}_{n-1}}{\text{NPV}_{n}-\text{NPV}_{n-1}}\right).$
(16)

Solving this is more computationally expensive than finding the NPV, LCOE or
PP. While the difference may be negligible if only performing the computation
a small number of times for finalised array design, it may become a
significant hindrance when used as the functional for a large number of
optimisation and adjoint evaluations.

###  2.7 CAPEX versus OPEX

The expenditures in each year, $\text{Ex}_{i}$, can be split up according to
whether they occur before or after the array goes into production. Businesses
typically describe all costs involved acquiring assets and setting up the
business as Capital Expenditure (or CAPEX). Vasquez et al. [23] estimated that
the capital costs for a tidal stream array break down as 41% device costs, 26%
foundations costs, 15% installation costs, 13% cable costs and 5% grid
connection costs. By comparison, the MeyGen1A project found that the main
contributors to the CAPEX were turbines (39%), onshore balance of plant (BoP,
the supporting components and auxiliary systems, 19%), offshore works (13%)
and substructures (11%) [24].

In the cash flow model described in (1), the CAPEX would typically be

$\displaystyle\text{CAPEX}=\sum_{i}\text{Ex}_{i},\;\forall
i\;\;\text{s.t.}\;\;t_{i}=0,$ (17)

where $t_{i}$ is the number of hours of generation in year $i$ i.e. the costs
incurred before the array is operational. In more complicated arrays the CAPEX
may include the expenses associated with upgrading physical assets, for
example in arrays which expand from small demonstrator arrays to larger scale
farms, the installation costs are still considered to be CAPEX, even if they
are incurred after the first turbines start generating. For simplicity, in
this work it will be assumed that all the capital expenditures occur in year
$i=0$ and that the array will start production in year $i=1$. This is an easy
assumption to remove when applied to real tidal arrays, by developers who have
full cash flow models of their anticipated costs. CAPEX will be represented in
the following models as $\text{CA}\equiv\text{Ex}_{0}$.

The expenses of normal business operations are called the operational
expenditure (or OPEX). OPEX is measured on an annual basis, here starting from
year $i=1$ up to $i=L$, the operational lifetime of the array, and will be
represented in the following models as $\text{O}_{i}$. Typically OPEX includes
costs such as rent, payroll, insurance and maintenance. For a tidal farm this
may include standard inspections, maintenance, repairs and costs of vessels
and staff to perform these tasks. The MeyGen 1A project reported a £1.4m OPEX
per year in its four turbine array, with its main components being lease and
insurance (32%), unplanned maintenance (21%), planned maintenance (15%) and
spare parts (14%) [24].

The final costs to be considered in a tidal energy deployment are the
decommissioning costs. These are the costs or removing the turbines, anchoring
and cabling from the water and safely ending the operation. There are a number
of different ways in which these costs may be covered - from upfront cash
security to accrual or insurance[25]. Since these costs could either be
incurred through an agreement as part of the CAPEX, or will be delayed to
after the final year of operation $i=L+1$ it is not clear how to include these
costs in an academic model at this time. If incurred in year $i=L+1$ the costs
are likely to have very little impact on metrics based on net present value
analysis because the cost will be heavily deprecated due to discounting. Due
to minimal present value impact and the large amount of uncertainty about how
this will be finances for large-scale tidal stream arrays and limited
information to base estimates on how much it will cost, this is not included
in our economic assessments at this point in time.

An investigation into decommissioning costs by Marine Scotland [25] found that
many developers acknowledged that decommissioning had not been an explicit
consideration on the design of devices, however a focus on reducing the cost
of installation lead to designs which were inherently easier to remove.
Technological advances which reduced the decommissioning cost as a by product
included devices designed to be towed to (or from) location and devices that
could be removed in modules for maintenance. Full decommissioning plans are
not enforces by regulators at the marine licensing stage because the design
may not be fixed. [25] found that the main cost driver is the cost of the
vessels required to remove the infrastructure. Many tidal developers have
designed devices to allow installation and removal with low cost multi-cat
vessels, for example see Figure 2. In demonstrator arrays material costs are
low as many parts can be repurposed or stored. As arrays become larger the
cost of dismantling and recycling the devices and foundations is likely to
increase.

(a)

(b)

Figure 2: (a) The Leask Marine Ltd. MV C-Odyssey, an example of a multi-cat
vessel used for installation and removal of turbines. (b) The Leask Marine
Ltd. team after the successful removal of a Nautricity turbine’s base with a
multi-cat vessel.

[25] estimated that floating tidal has a decomissioning cost of approximately
£100,000 per device, with gravity-base foundations costing £200,000 per device
and monopile foundations costing £500,000 per device. However, it is noted
that these estimated could change substantially as design concepts and vessel
rates change. Predicting these costs a couple of decades into the future
leaves a lot of uncertainty for developers.

###  2.8 Other metrics to consider

####  2.8.1 Environmental impact

The metrics described in the sections above all focus on the financial
performance of a tidal array, however there are many other factors to
consider. One of the most important, for ensuring that developments get
consent to deploy, is minimising the negative environmental and ecological
impact of the array.

There have been numerous studies on environmental impact assessment in tidal
and other ocean energies [26, 27, 28]. The most significant effects to account
for are damage to habitat and health of marine species, and sediment
transport. While the problem of assessing the environmental impact of a tidal
stream array is well researched, there are limited studies on how to optimise
array design whilst accounting for both the economics and the environmental
impact. A notable and novel example of using power and environmental impact
for multi-objective optimisation is du Feu et al. [5, 29].

[5] uses the extent to which an array alters the flow in the region as a proxy
for the environmental concerns and demonstrates a method of finding a Pareto
front where there is a trade-off between the conflicting objectives of
maximising array yield while minimising the change in the hydrodynamics. This
approach is useful for minimising the negative impacts on marine ecosystems
because alteration of the tidal flow can affect the dispersion of propagules,
material used by marine organisms to propagate between areas and a key part of
many marine life-cycles, [30] and there are habitats which are sensitive to
flow speed, direction and level of turbidity, for example scallop nurseries
[31]. [5] combined environmental impact assessment at the array design stage
by maximising a functional of the form $J=w_{p}\times P(m)-w_{i}\times I(m)$,
where $P(m)$ is the power generated by the set of turbine locations, $m$, and
$I(m)$ is the impact of those turbines, measured as the array’s effect on the
ambient flow velocities. The relative importance of each term is modelled by
$w_{p}$ and $w_{i}$, the power and impact weights, respectively. However, only
a limited set of weighting were tested ($w_{p}=1$ and $w_{i}=0$, $w_{p}=0$ and
$w_{i}=1$, $w_{p}=1$ and $w_{i}=1$) and realistic values for the weightings
were not discussed. A further limitation of this approach is that the number
of turbines was fixed, so varying the number of turbines would allow for
greater exploration of the trade-off between power, and therefore profit, and
environmental impact.

[29] extended upon the approach of [5], however it optimised the functional
$J=w_{p}\times\text{Profit}(d)-w_{h}\times H(d)$, where $H(d)$ is a measure of
habitat impact, $w_{h}$ is the relative importance of the habitat impact, and
the turbines are instead modelled by a continuous density function, $d$, which
allows for the number of turbines and their locations to be optimised
simultaneously. $\text{Profit}(d)$ takes the same format as the break even
power optimisation described in Section 2.2. The habitat impact, $H(d)$, was
found through maximum entropy modelling, which was used to generate habitat
suitability maps for species that respond to changes in bed-shear stress. The
maximum entropy was calculated using MaxEnt, an open-source habitat
suitability model [32], and was used to evaluate the impact of a tidal array
on the distribution of a specific species at each timestep of the hydrodynamic
model. This study investigated the impact of different tidal arrays on two
species, the acorn barnacle (Balanus crenatus) and the brown crab (Cancer
pagurus), because the former prefers higher flows speeds and tends to react
negatively to reductions in bed shear stress and the latter prefers lower flow
speeds and reacts positively to reductions in bed shear stress. The relative
importance of habitat suitability compared to profit is modelled by the choice
of weights of each corresponding term in the functional. The results were
demonstrated on four example sites, including the Pentland Firth, location of
the world’s highest capacity tidal stream array, at the time of writing. While
this paper demonstrated a useful method for incorporating the concerns of
habitat suitability into the functional, each example site was only
demonstrated for one species at a time, either the corn barnacle or the brown
crab, and more work needs to be carried out to automate the combination of
economics and environmental impact optimisation.

[33] compared the energy extraction of small-scale (five turbine) array
designs that considered environmental constraints compared to those that do
not. They found that taking into account environmental constraints decreased
the overall power generation of the optimised array design slightly. However,
they developed a flexible framework that allowed power maximisation while
remaining within the bounds of easily defined constraints to changes in the
flow and seabed stress.

The present work does not include environmental impact in the economic
analysis and optimisation methods discussed. As demonstrated by the studies
discussed above, minimising the environmental impact often leads to a trade-
off where the array yield, and therefore profitability, are reduced. It is
acknowledged that further work should combine the economic optimisation
methods with the environmental optimisation techniques outlined in works such
as [5, 29, 33], but this would require overcoming the limitations of each
study (for example by studying the impact of a broader range of species) and
selecting weightings for the trade-off between optimal economics and
environmental impacts.

####  2.8.2 Location based costs

In Section 2.2, expenditure is assumed to be a function of the number of
turbines, but in practice is it likely to depend on their location too. Two of
the most significant factors in tidal energy costs that vary with location are
the depth and the distance to shore [23], and both have been demonstrated to
be two of the main cost drivers in offshore wind [34]. As both increase the
installation and maintenance of the turbines become harder to carry out, and
the costs increase. They also affect the environmental loads to which the
turbines are exposed, the cable costs and electricity losses.

There have been some studies which optimise the design tidal arrays based on
the location dependent costs. On a macro-level Vazquez et al. [23] assesses
the spatial distribution of capital costs, coupled with a Navier-Stokes flow
solver, to balance the capital investment against the energy productions and
find a map of the LCaOE (levelised capital cost of energy). This is used as a
decision parameter to identify the best sites to install tidal stream arrays.
This can be done as a precursor to the array optimisation methods where the
number of turbines and their individual locations are optimised.

Studies in which the micro siting of tidal stream arrays is optimised with
respect to location-varying costs include [35] and [4]. [35] and [4] focus on
optimisation of a given number of turbines, where the functional is based on
an approximation to profit. [35] includes a model for cable costs per metre
and support structure costs that depend on the nature of the seabed, the depth
and the peak moment resistance required. [4] optimises the income as a
function of power minus the cost as a function of cable length. Both use
genetic algorithms to minimise the cable length.

While important, the costs that depend on the individual turbine locations
make up a smaller variation in the overall costs than those due to changes in
the number of turbines. Vasquez et al. [23] estimated that the cabling costs
make up 13% of the CAPEX for a typical tidal stream array, whereas it
accounted for 9% of the CAPEX and none of the OPEX breakdown reported by
MeyGen Phase 1A [24]. Culley et al. demonstrated an optimisation of a tidal
array in Orkney, where they optimised for power alone, maximisation of
financial return including cable costs, as well as the maximisation of
financial return where the cost of the cable per unit length is doubled; in
each case the returned cable lengths of the optimal arrays were found to be
9.70km, 9.23km, and 8.71km respectively [4]. So even when optimising for an
exaggerated cable cost, including the cabling in the functional in this case
only reduced the cabling cost by around 10% and therefore the overall cost in
the order of 1%.

Optimisation while accounting for location varying costs can be very
computationally expensive, and usually comes at the sacrifice of other
modelling capabilities. For example, [35] uses a genetic algorithm to optimise
the locations while taking into account variations in cable and support
structure costs with location, but only within the framework of a relatively
simple 2D wake deficit based model, and only for uniform flow in one
direction. Optimisation of the cable routes can produce savings that are
significant, but are a lower priority compared to optimising the balance
between power and number of turbines. It is therefore suggested in the
following work that location varying costs need not be included as another
variable in very computationally expensive micro-siting optimisation. Instead
location based costs can be taken into account either at the macrositing
stage, as demonstrated by [23], through exclusion zones, where a maximum depth
or steepness requirement is enforced [36], or post micro-siting, for example
where a genetic algorithm or travelling salesman type problem [4] is used to
minimise the cable length for a given set of turbine locations.

Furthermore, currently there is not enough publicly available information to
build a model that can predict the costs as a function of different distances
to shore, depths and number of turbines, so this paper just focuses on varying
the latter. Furthermore the sites selected for first-generation tidal turbine
arrays are usually a relatively short distance to shore and require depths of
25–50m [13, 37]. It is anticipated that later generations of tidal stream will
be designed for operation in deeper water, where modelling of location-varying
costs will become more crucial [13].

##  3 Cost reduction pathways

Estimates from the Offshore Renewable Energy Catapult (OREC) in 2018
anticipated that tidal stream energy costs in the UK could come down by 70%
from a representative LCOE of £300/MWh to £90/MWh as the installed operational
capacity rises from 10MW to 1GW [12]. Part of this reduction in costs is due
to saving time and cost through “learning rates”, part is due to “economies of
scale”, such as moving to larger rotor and higher rated devices, and part is
due to the move to larger scale arrays which benefit from “economies of
volume”. It is important to be aware of the distinction between the different
types of cost reduction, because they present opportunities at different
stages of array development to cut to cost of energy. Learning rates can only
be exploited by delaying the deployment of an array to avoid the first mover
disadvantage, and the latter two can be exploited by choosing the optimal
turbine specification and the optimal number of turbines respectively. The
following work using the same terminology of each type of cost reduction as
the OREC report on tidal stream and wave energy cost reduction [12] and a
study by Coles et al. on mechanisms for reducing the cost of tidal stream
energy, applied to the context of the expansion of the MeyGen tidal array from
currently operational Phase 1A to the plans for Phase 1C [38].

###  3.1 Learning rates

Learning rates encompass all cost reductions where the costs of an industry
fall with time due to increased knowledge. This will not be included in the
following models as we assume we are optimising arrays for developers which
have a fixed level of experience. However, it is worth considering that our
bounds for costs will likely become overestimates with time, and that sources
for typical values to use in the following models will be more reflective of
the current state of the industry if more recent. The extent to which learning
rates will impact costs can be estimated by observing what has happened in
other industries, such as wind power, where costs are decreasing as the
cumulative installed capacity increases. They are typically represented by a
percentage reduction in costs with each doubling in cumulative capacity. An
Arup produced ‘Review of Renewable Electricity Generation Cost and Technical
Assumptions’ estimates that the doubling of installed tidal capacity will
result in a 13% CAPEX cost reduction and a 19% OPEX fall [39], whereas OREc
assumed 13% for CAPEX but a more conservative learning rate of and 11% for
OPEX [12]. The impact of learning rates are most significant in the near term
for fledgling industries like tidal, because when the cumulative installed
capacity is so low it is easier for it to double. Learning rates can be
accelerated by collaboration, but hindered by protection of intellectual
property preventing these opportunities. Cost reduction through learning can
be grouped into two main categories; learning-by-doing and learning by
innovation.

Learning-by-doing cost reduction relates to project developers repeating
processes with each array that they install, thus learning how to optimise
procedures and minimise costs. Examples of cost reductions through learning
include better planning of operations and maintenance using operational and
weather data, supply chain optimisation and automation, and familiarity with
installation sites [12]. Standardisation of foundation and component design
will become possible as the number of devices deployed increases, so costs for
the industry will fall.

Repeat installations of tidal arrays can also lead to improved proof of
concept, resulting in increased confidence from investors and a reduction in
the cost of capital as projects are seen as less risky. The cost of capital is
the required return for a project to be worthwhile, for internally financed
projects it is the cost of equity (mostly comprising of dividends), and for
externally finance projects it is the cost of debt (the effective interest
rate paid on debts). The weighted average cost of capital (WACC) is used to
combine the cost of equity and debt into one figure and it is often used as
the discount rate for present value analysis of future cash flows, such as the
NPV and LCOE models in Equations 10 and 13 respectively. Currently tidal
projects are financed through a combination of grant support and private
finance, and tidal has a far higher cost of capital than the more established
offshore wind industry. Increased confidence from financial institutions will
see a rise in financing from commercial debt too. OREC estimated the cost of
capital for 10MW cumulative capacity is 10% and that it will fall to 8.4% by
100MW, 8.0% by 200MW and 7.1% by 1GW [12]. They believe that these reductions
can be achieved through increasing the proportion of debt finance (which has a
lower interest rate of around 4.5%) and reducing the rate of equity premiums
(from around 10% to 8%). The more familiar and stable the technology is
perceived to be, the greater the cost of capital reductions that can be
obtained. OREC noted that each 1% reduction in WACC (and therefore discount
rate) resulted in a 6% reduction in LCOE in their studies. MeyGen released
their lessons learnt report from the 1A construction phase [40] which found
that the turbines were exceeding their contractual key performance indicators
such as average power coefficient (8% increase), capacity factor (20%
increase) and lifetime energy yield estimate (18% increase). These substantial
improvements demonstrate a reduced risk to investors and could lead to a
reduction in the cost of capital for future tidal arrays.

Learning by innovation covers cost reductions due to technological
improvements such as improved performance and reliability of individual
components. Some of these innovations may arise from the experience gained in
the more mature offshore oil, gas and wind industries, and will therefore
reduce the level of perceived risk to investors. Innovation may reduce the
operational costs or improve the structure or the availability of the
turbines. For example, a consortium led by ITPEnergised, has designed a
customised barge for installing turbines which may allow the industry to move
away from hiring expensive dynamic positioning vessels. These barges are
anticipated to be much cheaper for installation of larger scale arrays [41].
Leask Marine Ltd have successfully used multi-cat vessels to install and
remove multiple tidal turbines and their subsea bases, demonstrating the
potential for multi-cat vessels to replace the need for multi-million-pound
large dynamic positioning drilling ships and jack-ups. Improved electrical
connectors are also expected to reduce the cost of tidal in the short term.
Wet mate connectors are a technological development that allow the cable
connections to the turbines to be made sub-sea rather than on the vessel, thus
simplifying the installation on operations. They allow turbines to be
installed onto their foundations in less than 60 minutes, and reduce the
installation cost by 65% compared to a turbine with a dry mate connector where
the export cable must be brought onto the vessel to connect it to the turbine
[38]. Again the following models will not include learning by innovation,
because this work is aimed at developing a method to assist developers in
optimising array design given the technology options currently available to
them.

###  3.2 Economies of scale

The following work uses the same distinction between the economies of scale
and volume as [12, 38]. Economies of scale is used to exclusively refer to the
cost reductions gained from moving to larger rotor, higher wattage turbines
(i.e. increased scale of the turbines themselves) and not to the effects of
increasing the number of turbines.

Coles et al. [38] demonstrated the significant impact that economies of
turbine scale could have, by investigating the predicted yield of the 1.5MW
rated AR1500 device compared to the 2MW rated AR2000. The AR1500 is currently
operational as part of the MeyGen Phase 1A, the AR2000 is the next generation
device by SIMEC Atlantis Energy, which is expected to be deployed in future
phases of the MeyGen project. Both devices are capable of accommodating a
range of physical options, but Coles et al. assessed an 18m diameter AR1500
with a hub height of 14m to a 20m diameter AR2000 with a hub height of 15m.
Coles et al. [38] estimated that economies of turbine scale could lead to a
reduction in LCOE of 17%, 20% or 23% due to the 29% uplift in anticipated
yield when progressing from the AR1500 to the AR2000, depending on whether the
CAPEX increases by 10%, 5% or 0% between the two devices. It is difficult to
predict how much CAPEX will increase between the turbine designs, because the
costs are commercially sensitive. They are likely to increase due to higher
loading from larger blades, increased generator size and hub height, but the
AR1500 was designed to meet conservatively high loads, and through the proof
of concept in MeyGen 1A, the AR2000 may not require as conservative a design.
However, for each of the CAPEX scenarios investigated, it was shown that small
achievable changes to the turbine specification can result in significant
near-term reductions to the LCOE of tidal energy.

Foundation costs also make up a significant proportion of the lifetime costs
of an array, so some developers plan to use several rotors on the same
supports to spread the foundation costs over a higher rated power, and achieve
economies of scale [42].

###  3.3 Economies of volume

Economies of volume are found when costs can be spread across more turbines in
an array; when the installed capacity in MW for a potential tidal site is
increased, the effective cost per MW decreases. For example, the cost of
mobilising (preparing the vessel) and demobilising (unloading and returning of
the vessel) for offshore operations, installations and maintenance falls per
turbine as the number of turbines increases. For small arrays these activities
take up a significant proportion of the total vessel time. [38] demonstrated
that in MeyGen 1C the anticipated number of mobilisation and demobilisation
days per turbine falls from 1.13 to 0.83 if the number of turbines increases
from the current 4 to a planned 36.

There are fixed costs in tidal array development, such as the site evaluation
and substation costs, which lead to a reduced cost per MW when they are split
across a greater number of turbines. Potential cost reductions due to
economies of volume can also include bulk order discounts, reduced production
costs per unit and savings due to serial production and standardisation of
common components. For example, dedicated manufacturing facilities for large-
scale turbine orders will be more cost-effective, but this is not possible for
smaller arrays. Also, inter-array cable costs may increase approximately
linearly with the number of turbines but the costs of a substation and the
much more expensive export cables to shore will be roughly fixed, so the more
turbines generating power, the lower the total cable cost per MW.

To date tidal stream has only been demonstrated in arrays with small numbers
of turbines; the world’s first arrays being three turbines by Nova Innovation
off the coast of Shetland and four turbines installed by Meygen in the Inner
Sound of the Pentland Firth. Even without cost reductions due to experience or
improved technology, substantial cost reductions could be seen in the
immediate term, just by moving from these demonstrator sized arrays to
commercially sized ones.

It is worth noting that while costs are expected to fall with time and volume,
there are more significant cost reductions to be made while tidal energy is a
relatively new industry. The cost reductions as the tidal industry advances
from small demonstrator arrays to the first large-scale commercial arrays will
be significant but as the industry develops the potential to reduce costs will
diminish. Some aspects of tidal arrays are already well-established, building
on what can be learnt from other offshore energies. For example, electrical
connection to the grid (which makes up around 5% of the lifetime costs of
tidal arrays) has less potential for dramatic cost reduction due to
developments already being carried out by the offshore wind industry, so the
learning reductions have to some extent plateaued [42]. However, there is
still potential for significant economies of volume to be achieved on these
costs through subsea hubs which will allow the electrical connection of
multiple devices resulting in cheaper configurations.

####  3.3.1 Expenditure break down

The capital costs are split into fixed costs and turbine-dependent costs, to
help include economies of volume into the model. There are some costs that
need to be overcome no matter how many turbines are installed and some that
increase linearly with number of turbines. For example, the inter-array
cabling may be considered a turbine-dependent cost because the length of
cables will be proportional to the number of turbines. However, the export
cable will be a fixed cost, since there will always need to be a cable that
transports power generated from the substation to shore, regardless of number
of turbines. The CAPEX can therefore be written as

$\displaystyle\text{Ex}_{i=0}=\text{CAPEX}=\text{CA}_{f}+\text{CA}_{t}\times
n_{t}.$ (18)

Similarly the operational expenditure are the costs incurred every year after
installation and are assumed to linearly increase with number of turbines.
Furthermore, this study assumes that the OPEX is the same year on year, for
simplicity, however developers could use this model with costs that vary very
easily. For example, some components of the array may need maintenance every
year whereas others may need maintenance every few years, causing a routine
increase in costs. By splitting the OPEX into fixed and turbine dependent
costs it can be written as

$\displaystyle\text{Ex}_{i>0}=\text{OPEX}=\text{O}_{f}+\text{O}_{t}\times
n_{t}.$ (19)

###  3.4 Revenue

In order to build a complete financial model, income must be accurately
predicted, as well as expenditure. For a tidal farm, income depends primarily
on two factors – the net energy output and the tariff at which this energy is
sold to the grid (which may well be higher than the market price due to
subsidies and other government schemes).

Since early stage tidal energy deployments often receive a fixed price per
MWh, through subsidy schemes described below, most hydrodynamic models used
for optimisation of tidal array design produce an average power estimate for
the array, $P_{\text{avg}}$, rather than a time varying prediction of the
instantaneous power over the whole lifetime. Therefore, the energy generated
in each year is assumed to be constant, such that $E_{i}=E\;\forall
i=1,\ldots,L$. In practice, even when evaluating metrics such as NPV and LCOE
on an annual level, lunar nodal cycles cause variations in the yearly average
yield over an 18.6 year cycle [14, 15]. Since the earlier years of generation
count more towards these metrics, due to discounted cash flow, this could lead
to an effective difference in the performance of the array depending on which
stage of the tidal cycle it begins generating in.

Assuming a constant power, $P_{\text{avg}}$, year on year, the annual energy
generation, $E_{i}$, can be found by multiplying the number of hours of
generation each year, $t_{i}$, with the average power, to find the gross
energy output in MWh;

$\displaystyle E_{i}=t_{i}\times P_{\text{avg}}.$ (20)

$t_{i}$ can be approximated as the number of hours in a year minus the
anticipated number of hours of downtime for maintenance. The MeyGen Phase 1A
reported an average availability of 95% in 2020 (having entered its
operational phase in 2018), with a higher availability of 98% in the summer
compared to 90% in the winter [24]. Increased experience in planning and
predicting operations and maintenance could see these downtime windows
decrease and availability increase in future tidal projects. When used in
industry the availability could be modelled to depreciate throughout an
array’s lifetime, to account for decreases in efficiency as devices age, e.g.
due to component wear or bio-fouling. This effect has been well documented in
the wind industry [18, 17]. However, for simplicity it can be kept constant
for initial investigations. This is a reasonable assumption because there is
limited information on the rate of degradation of tidal stream arrays, with
few years of operational experience to date, and due to the high discount rate
currently used in tidal the latter years of the array’s generation (where
degradation would be highest) contribute significantly less to the NPV and
LCOE. Finally, the net energy output can be found from the gross energy output
by a factor, $C_{E}$, to account for electrical efficiency losses. The net
energy output can be multiplied by the electricity tariff, $T_{e}$
[$\pounds$/MWh], to find the expected revenue of a tidal array in a year. The
market price may fluctuate over days and years, however government schemes can
often make this value more predictable and stable, the details of these
schemes are discussed below in Section 4.3. In initial economic models it can
be assumed that arrays receive a constant price per unit energy, however
future models could estimate $P_{\text{avg}}$ over smaller time scales and use
this in conjunction with a fluctuating energy price to determine the impact on
revenue, cf. related optimisation work in the context of tidal lagoons [43].

According to the simplifications of the economic model made in equations (18),
(19) and (20), the model for LCOE from (13) can be rewritten as

$\displaystyle\text{LCOE}=\frac{\text{CA}_{f}+\text{CA}_{t}\times
n_{t}+\sum_{i=1}^{L}\frac{O_{f}+O_{t}\times
n_{t}}{(1+r)^{i}}}{\sum_{i=1}^{L}\frac{C_{E}\times E_{i}}{(1+r)^{i}}}.$ (21)

##  4 Estimate of inputs to economic models

The following section compiles a series of tidal energy cost estimates and
reformats them appropriately for use in a LCOE model such as (21). The main
inputs needed are CAPEX split up into fixed, $\text{CA}_{f}$, and turbine-
dependent, $\text{CA}_{t}$, components, OPEX split up into fixed, $O_{f}$, and
turbine-dependent, $O_{t}$, components, lifetime, $L$, and the discount rate,
$r$. Data from different sources is discussed below along with the methods
used to convert this into the format we need where total CAPEX and OPEX can be
broken down into the forms shown in (18) and (19) respectively. Some
information from the offshore wind industry is used to guide our estimates and
the relationship between them.

###  4.1 Relationship between cost and size of array

Firstly, information on how CAPEX and OPEX in the wind industry varies in
relation to number of turbines is used to justify the relationship assumed in
(18) and (19). Wind is the more established industry and can therefore be used
to help predict the cost reductions that can be realised through economies of
volume for tidal. CAPEX and OPEX values are commercially sensitive and hard to
establish, and while there have been a number of studies which have
communicated with many different developers of varying sizes [12], they often
anonymise this data by converting to a metric that is independent of array
size, such as cost per MW installed capacity.

(a)

(b)

Figure 3: Variation in the total CAPEX of an array and the CAPEX per MW
installed capacity as functions of the number of turbines, according to (18)

Much of the available information found in this literature review on the costs
of tidal turbine arrays is given as a CAPEX/MW, for an array of a certain
rated capacity. Figure 3 shows how the total CAPEX increases with number of
turbines if the linear relationship given in (18) is assumed. This can be used
to show the relationship between CAPEX/MW and number of turbines, by dividing
equation (18) by the total capacity of the array ($n_{t}$ turbines, each with
a rated capacity of $MW_{t}$) to get

$\displaystyle\text{CAPEX/MW}=\frac{\text{CA}_{f}+\text{CA}_{t}\times
n_{t}}{n_{t}\times MW_{t}}.$ (22)

Since there are two unknowns in each of (18) and (19), two simultaneous
equations must be used to solve each in order to find $\text{CA}_{t}$,
$\text{CA}_{f}$, $\text{O}_{t}$ and $\text{O}_{f}$. In order to convert from
the CAPEX/MW to $\text{CA}_{f}$ and $\text{CA}_{t}$ values, (estimates for)
the CAPEX/MW for arrays of two different sizes is needed, allowing the
conversion to total CAPEX, which would give two points on the line in Figure
3a) and allow the gradient (i.e. $\text{CA}_{t}$) and the intercept (i.e.
$\text{CA}_{f}$) to be calculated. Alternatively, if the total CAPEX is only
known at one array size then the ratio of the fixed component of CAPEX over
the turbine-dependent component of CAPEX, $\text{CA}_{f}/\text{CA}_{t}$, must
be known or estimated. The ratio can be used to split the total cost into each
of its components, such that
$\text{CAPEX}=(\frac{\text{CA}_{f}}{\text{CA}_{t}}+n_{t})\text{CA}_{t}$. The
same is needed for operational costs to find $O_{f}$ and $O_{t}$, however
limited OPEX data is available, since very few tidal arrays have been in
operation and only for a relatively short period, so sometimes OPEX must be
estimated as a percentage of CAPEX.

####  4.1.1 Method 1: Knowing two data points

If the total CAPEX is known for two values of $n_{t}$, e.g. $n_{t_{1}}$,
$n_{t_{2}}$, $\text{CAPEX}(n_{t_{1}})$ and $\text{CAPEX}(n_{t_{2}})$, then we
can solve the following simultaneous equations:

$\displaystyle\text{CAPEX}(n_{t_{1}})=\text{CA}_{f}+\text{CA}_{t}\times
n_{t_{1}},$ (23)
$\displaystyle\text{CAPEX}(n_{t_{2}})=\text{CA}_{f}+\text{CA}_{t}\times
n_{t_{2}}.$ (24)

When subtracting these two equations to solve for $\text{CA}_{t}$, we find

$\displaystyle\text{CAPEX}(n_{t_{2}})-\text{CAPEX}(n_{t_{1}})=\text{CA}_{t}\times(n_{t_{2}}-n_{t_{1}})$
(25)
$\displaystyle\Rightarrow\text{CA}_{t}=\frac{\text{CAPEX}(n_{t_{2}})-\text{CAPEX}(n_{t_{1}})}{n_{t_{2}}-n_{t_{1}}}$
(26)

$\text{CA}_{f}$ can then be found from (23) and the $\text{CA}_{t}$ value just
found.

The turbine-dependent and fixed components of the OPEX can be found similarly
by evaluating (19) at two values of $n_{t}$ and similarly rearranging.

####  4.1.2 Method 2: Knowing the ratio of fixed to turbine-dependent costs

Alternatively, if the ratio of the fixed costs to the turbine-dependent costs
is known, such that

$\displaystyle\text{CA}_{ft}\coloneq\frac{\text{CA}_{f}}{\text{CA}_{t}},$ (27)

then the total CAPEX only needs to be known for one value of $n_{t}$, e.g.
$n_{t_{1}}$ and $\text{CAPEX}(n_{t_{1}})$. The turbine-dependent CAPEX,
$\text{CA}_{t}$, can be found by solving

$\displaystyle\text{CAPEX}(n_{t_{1}})=\text{CA}_{ft}\times\text{CA}_{t}+\text{CA}_{t}\times
n_{t_{1}}$ (28)
$\displaystyle\Rightarrow\text{CA}_{t}=\frac{\text{CAPEX}(n_{t_{1}})}{\text{CA}_{ft}+n_{t_{1}}}$
(29)

and $\text{CA}_{f}$ is simply found from

$\displaystyle\text{CA}_{f}=\text{CA}_{ft}\times\text{CA}_{t}.$ (30)

The same relationship can be applied for OPEX.

###  4.2 Cost data available in literature

Using the two methods described above, a literature review of publicly
available cost information for tidal stream arrays has been performed. While
there are many studies on the economics of tidal energy, not all of them are
useful for building an economic model that is flexible to array size. For
example, if given the cost of energy as an LCOE, there is rarely enough
information to back calculate the raw CAPEX and OPEX values in order to
predict how much impact changing the number of turbines would have on the
array economics. This would make it very difficult to model the cost
reductions that can be found through economies of volume. Instead most studies
collated in this work refer to raw CAPEX and OPEX values or CAPEX/MW and
OPEX/MW estimates.

####  4.2.1 Higgins and Foley: The evolution of offshore wind power in the
United Kingdom

Firstly the assumptions made in (18) and (19), and demonstrated in Figure 3,
can be validated by comparing them to actual trends found in the wind
industry. Higgins and Foley [44] performed a review of offshore wind power in
the United Kingdom, where they aggregated cost data from multiple wind farms
and presented anonymised cost information in the form of a normalised
CAPEX/MW. Higgins and Foley [44] investigated how the costs of offshore wind
farms increases with cost per device and distance from shore, and decreases
with number of turbines. Figure 4(a) shows the relationship they found between
number of turbines and normalised CAPEX/MW, and how this varies depending on
the price of individual turbines. The costs are normalised by the CAPEX/MW of
an array consisting of ten turbines each costing £2m, so for example these
figures show that if there are ten turbines but they each cost £4m, the
CAPEX/MW of the overall array is 36% higher.

Figure 4(b) shows that when multiplying this by the number of turbines to find
normalised total CAPEX values, a linear relationship is obtained, further
justifying the relationship defined in (18). The exact values of
$\text{CA}_{f}$ and $\text{CA}_{t}$ cannot be found, since the information was
normalised due to commercial sensitives. However, it can be shown that for
arrays made of turbines which cost $\pounds$4 million, $\pounds$3 million and
$\pounds$2 million, the fixed component of CAPEX would be 2.6, 3.1 and 3.9
times the turbine-dependent component of CAPEX respectively. The cheaper the
devices become the more important economies of volume are (since the fixed
costs make up a bigger portion of the overall costs). These $\text{CA}_{ft}$
values can be used in method 2 for calculating the cost components.

(a)

(b)

Figure 4: (a) How the normalised capital costs per MW installed capacity
varies with the number of turbines from [44]. (b) How this corresponds to a
linear relationship between total CAPEX and number of turbines, for wind
turbine arrays where each turbine costs £2, 3 or 4 million.

Higgins and Foley also presented how the CAPEX/MW would change with number of
turbines for different distances to shore – 5km, 15km, 25km, 35km, 45km, 75km
and 150km. The southern part of the Pentland Firth, which passes between
Stroma Island and the Scottish mainland is only approximately 3km wide. By
comparison the narrowest distance between Alderney and Cap de la Hague is 15km
wide. Therefore we only consider the $text{CA}_{ft}$ ratios from the CAPEX
curves defined from data from turbines 5 to 15km from shore, which have a
$\text{CA}_{ft}$ value of 2.3 and 2.7 respectively. As the distance to shore
increases the $\text{CA}_{ft}$ ratio increases, since economies of volume
become more important to overcome the fixed costs of long cable routing and
shipping distances. At 150km to shore $\text{CA}_{ft}=8.4$, however, this
distance is very unlikely for a tidal energy site in the foreseeable future,
since the required high energy flows are generally accelerated near islands
and other coastal features. Therefore upper and lower bounds of
$2.3<\text{CA}_{ft}<3.9$ were used in method 2, for calculating
$\text{CA}_{f}$ and $\text{CA}_{t}$ separately when given one fixed CAPEX or
CAPEX/MW value. There is limited information on OPEX varying with the size of
the array so it is assumed that the ratio remains the same. i.e.
$\text{O}_{ft}\coloneq\text{CA}_{ft}$.

####  4.2.2 Culley et al.: Optimisation of Cable Costs

One easy-to-visualise example of how capital costs can be split into a fixed
and turbine-dependent component is cable based costs. Culley et al. [4]
investigated the optimisation of cable routing and array layout and used
estimates for the total cabling costs of between £254.51 per meter with a
fixed £5.16 million vessel mobilisation fee and £862.48 per meter with a fixed
£6.22 million vessel mobilisation fee. These estimates were based on the costs
given for wind energy from Green et al. [45] in 2007, adjusted for inflation
to 2016 levels and with an assumed 51% rise in costs applied, in line with the
51% rise in wind energy costs between 2006 and 2010, as outlined by
Heptonstall et al. [46]. Depending on the weighting of the cable cost in the
functional they found optimised configurations of their model of eight
turbines with total cable lengths of 9.70km, 9.23km, and 8.71km. This leads to
a total cost per metre of $254.51\times 8.71\times 1000=\textsterling 2.22$
million to $862.48\times 9.7\times 1000=\textsterling 8.37$ million, or a cost
of $\textsterling 0.28$ to $\textsterling 1.04$ million per turbine. Therefore
for the cable costs alone there is a fixed cost an order of magnitude higher
than the per turbine cost. These cost estimates are not included in the
calculation of $CA_{f}$ and $CA_{t}$ values, because they only cover cable
costs, which account for approximately 10% of the total CAPEX. However, they
do help demonstrate why the method of splitting CAPEX into $CA_{f}$ and
$CA_{t}$ is appropriate.

####  4.2.3 OREC: Tidal Stream and Wave Energy Cost reduction and Industrial
Benefit

A recent cost analysis was performed by the Offshore Renewable Energy Catapult
(OREC) based on aggregated data from tidal developers working in the kW to MW
scale [12]. They also forecast the costs and job creation of a potential
deployment scenario for the UK, where 1GW of tidal stream is deployed by 2030
at a rate of 100MW per year from 2020. The predicted UK 2030 spend in this
scenario was £307 million; with £227 million spent on CAPEX for a 100MW array
and £80 million on cumulative OPEX for the existing 10 100MW arrays. The study
investigated arrays with turbines in the 1–2MW range, so a turbine rating of
1.5MW is assumed in the following calculations. The CAPEX/MW of an 100MW array
in the OREC report is £2.27 million, which combined with the ratio
$2.3<\text{CA}_{ft}$ from [44] and using method 2 results in a fixed CAPEX of
$\textsterling 7.6\text{m}\leq\text{CA}_{f}\leq\textsterling 12.8\text{m}$ and
a turbine-dependent CAPEX of $\textsterling
3.26\text{m}\leq\text{CA}_{t}\leq\textsterling 3.34\text{m}$. The OPEX/MW of a
100MW array is £0.08 million/year, which can be similarly split into
$\textsterling 0.27\text{m}\leq O_{f}\leq\textsterling 0.45\text{m}$ and
$\textsterling 0.113\text{m}\leq O_{t}\leq\textsterling 0.116\text{m}$.

####  4.2.4 IEA Technology: International LCOE for ocean energy technology

An IEA Technology report estimated costs for different ocean technologies at
different stages of their development [47]. Looking at the first commercial
scale projects with a capacity of 3–90MW and assuming that the maximum project
capacity corresponds to the minimum CAPEX/MW, and vice-versa, their minimum
and maximum scenarios correspond to a small array with two 1.5MW turbines and
a larger array of 60 turbines with a total CAPEX of $16.8m and $297m,
respectively. These two points can be converted to GBP (assuming a rate of $1
= £0.79) and used in method 1 to find a fixed CAPEX of
$\text{CA}_{f}=\textsterling 5.6m$ and a turbine-dependent CAPEX of
$\text{CA}_{t}=\textsterling 3.8m$.

Similarly, IEA Technology found a small (3MW) commercial array has an
OPEX/year of $1.2m and the large array (90MW) is $8.1m/year. From this, method
1 can be use to calculate the fixed OPEX per year as $O_{f}=$ £0.76m/year and
the turbine-dependent OPEX per year as $O_{t}=$ £0.094m/year.

####  4.2.5 Orbital Marine Power Limited: Technology Update

Orbital Marine Power Limited (formerly known as Scotrenewables Tidal Power)
issued a cost analysis for a 10MW array, with their cost assumptions and
methodology approved by the Carbon trust. It predicted a base CAPEX/MW of
£2.60m with a pessimistic prediction of £2.80m and an optimistic one of £2.50m
[48]. Furthermore they had a base OPEX/MW/year prediction of £0.1982m with a
pessimistic value of £0.235m and an optimistic value £0.16m. Since this range
of CAPEX and OPEX predictions were only for 10MW arrays, they can be combined
via method 2 with the $2.3<\text{CA}_{ft}<3.9$ ratio from Higgins and Foley
[44], which defines the shape of the cost reductions with economies of volume.
This results in six estimates of each of $\text{CA}_{f}$, $\text{CA}_{t}$,
$O_{f}$ and $O_{t}$, which are summarised in Table 1. Taking the extremes for
each value, the fixed CAPEX may lie in the range $\textsterling
6.3\text{m}<\text{CA}_{f}<\textsterling 10.4\text{m}$, turbine-dependent CAPEX
may be $\textsterling 2.4m<\text{CA}_{t}<\textsterling 3.1m$, fixed OPEX per
year may be $\textsterling 0.41\text{m}<O_{f}<\textsterling 0.87\text{m}$, and
turbine-dependent OPEX per year may be $\textsterling
0.15\text{m}<O_{t}<\textsterling 0.26\text{m}$.

Table 1: The CAPEX and OPEX components found by combining the optimistic (Opt), typical (Typ) and pessimistic (pes) estimates of Orbital Marine Power Ltd [48], with the upper and lower $\text{CA}_{ft}$ limits found in [44]. | $\text{CA}_{ft}=2.3$ | $\text{CA}_{ft}=3.9$
---|---|---
| Opt | Typ | Pes | Opt | Type | Pes
$\text{CA}_{f}$ (£m) | 6.4 | 6.7 | 7.2 | 9.2 | 9.6 | 10.3
$\text{CA}_{t}$ (£m) | 2.4 | 2.5 | 2.6 | 2.8 | 2.9 | 3.1
$O_{f}$(£m/year) | 0.41 | 0.49 | 0.60 | 0.59 | 0.71 | 0.87
$O_{t}$(£m/year) | 0.15 | 0.18 | 0.22 | 0.18 | 0.21 | 0.26

####  4.2.6 Black & Veatch: Cost of and financial support for wave, tidal
stream and tidal range generation in the UK

An executive summary by Ernst & Young and Black & Veatch [49] investigated the
relative costs of wave and tidal energy in the UK, at different stages of
deployment. They provided cost estimates for tidal arrays in both deep ($\leq
40m$) and shallow ($>40m$) water for a 10MW tidal stream array at different
stages of developer experience; for a developer’s first 10MW demonstration
project and for a 10MW commercial project where the developer has already
deployed over 50MW in the past. Since these economic models are to be used to
optimise large-scale tidal arrays, commercial figures are used, and because
the likely locations of the UK’s first commercial tidal arrays, e.g. in the
Alderney Race and Pentland Firth, are approximately 30–40m in depth, the
shallow water values are used in this work.

Black & Veatch estimated that the typical CAPEX/MW for a 10MW tidal stream
array is £3.2m/MW, with a lower and upper bound of £2.7m/MW and £3.9m/MW,
respectively. By comparison they estimated that a developer’s first 10MW
demonstrator array would have a CAPEX/MW of £4.3m/MW, showing the significant
impact that learning-by-doing can have on the cost of tidal stream in the
short term. A commercial array in deep water rather than shallow saw only a
small increase in CAPEX/MW to £3.3m/MW, which was attributed to a different
deployment method, structure foundations or mooring possibly being needed in
greater depths, but otherwise the shallow and deep technologies may be largely
the same, and can therefore benefit from learning from each other.

Similarly, Black & Veatch estimated that the typical OPEX/MW for a 10MW tidal
stream array is £150k/MW, with a lower and upper bound of £120k/MW and
£190k/MW, respectively. Demonstrator arrays are substantially more expensive
with an OPEX/MW of £310k/MW. Deeper projects were predicted to have a lower
OPEX/MW of £120k/MW. Black & Veatch noted that all costs were expected to
decline due to the anticipated future global deployments and corresponding
impact on learning in the industry.

These typical and lower/upper bounds can be converted into their separate
fixed and turbine-dependent components using method 2 and the
$2.3<\text{CA}_{ft}<3.9$ ratio from Higgins and Foley [44]. The three values
given for each of CAPEX/MW and OPEX/MW by Black & Veatch, along with the upper
and lower values for $\text{CA}_{ft}$ result in six estimates for each
parameter, which are summarised in Table 2. The maximum and minimum values in
this table provide the parameter ranges that can be estimated using the Black
& Veatch cost information for commercial arrays. The fixed CAPEX may lie in
the range $\textsterling 6.9\text{m}<\text{CA}_{f}<\textsterling
14.5\text{m}$, turbine-dependent CAPEX may be $\textsterling
2.5\text{m}<\text{CA}_{t}<\textsterling 4.4\text{m}$, fixed OPEX per year may
be $\textsterling 0.31\text{m}<O_{f}<\textsterling 0.70\text{m}$, and turbine-
dependent OPEX per year may be $\textsterling 0.11\text{m}<O_{t}<\textsterling
0.21\text{m}$.

Table 2: The CAPEX and OPEX components found by combining the optimistic (Opt), typical (Typ) and pessimistic (Pes) estimates of Black & Veatch [49], with the upper and lower $\text{CA}_{ft}$ limits found in [44]. | $\text{CA}_{ft}=2.3$ | $\text{CA}_{ft}=3.9$
---|---|---
| Opt | Typ | Pes | Opt | Type | Pes
$\text{CA}_{f}$ (£m) | 6.9 | 8.2 | 10.0 | 10.0 | 11.8 | 14.5
$\text{CA}_{t}$ (£m) | 3.0 | 3.6 | 4.4 | 2.5 | 3.0 | 3.7
$O_{f}$(£m/year) | 0.31 | 0.38 | 0.49 | 0.44 | 0.55 | 0.70
$O_{t}$(£m/year) | 0.13 | 0.17 | 0.21 | 0.11 | 0.14 | 0.18

####  4.2.7 Summary of $\text{CA}_{t}$, $\text{CA}_{f}$, $O_{t}$ and $O_{f}$
estimates

This literature review sought to collate CAPEX/MW and OPEX/MW estimates from a
range of sources and convert them to a format more suitable for modelling the
impact of economies of volume, to enable the comparison of arrays of different
sizes. Table 4 summarises the upper and lower bounds and the average of the
different estimates for $\text{CA}_{t}$, $\text{CA}_{f}$, $O_{t}$ and $O_{f}$
found in each of the sources reviewed above.

Table 3: A summary of the typical (Typ), optimistic (Opt) and pessimistic (Pes) estimates of $\text{CA}_{t}$, $\text{CA}_{f}$, $O_{t}$ and $O_{f}$ from IEA Technology [47], Orbital Marine Power Limited [48], Black & Veatch [49] and OREC 2018 report [12]. Source: | OREC | IEA | Orbital Marine Power Ltd | Black & Veatch
---|---|---|---|---
Type: | Opt | Pes | Typ | Opt | Pes | Opt | Pes
$\text{CA}_{f}$ (£m) | 7.6 | 12.8 | 5.6 | 6.3 | 10.4 | 6.9 | 14.5
$\text{CA}_{t}$ (£m) | 3.26 | 3.34 | 3.8 | 2.4 | 3.1 | 2.5 | 4.4
$O_{f}$(£m/year) | 0.27 | 0.45 | 0.76 | 0.41 | 0.87 | 0.31 | 0.70
$O_{t}$(£m/year) | 0.113 | 0.116 | 0.094 | 0.15 | 0.26 | 0.11 | 0.21

####  4.2.8 Discount rate

The discount rate, $r$, is a key parameter when evaluating the economic
success of a project over its lifetime as it determines the present value of
future cash flows. It is the interest rate used in discounted cash flow
analysis. It reflects that future cash flow has less value than current cash
flow to investors due to opportunity costs and risks. In general higher rates
are applied to less developed technologies, to account for the greater risks
and uncertainty associated with the novel design and speculative cost
estimation. Determining an appropriate discount rate is important for any
economic metrics such as net present value, LCOE and payback periods.

Ouyang and Lin [22] investigated the LCOE of different renewable energy
technologies in China and the appropriate subsidies and policies to support
them. They found the discount rates required for different forms of renewables
varied through 5, 8 and 10%, with the higher rates being needed for novel
renewable energy sources, such as tidal, which are seen as more risky compared
to more established forms of renewables, such as onshore wind or solar PV. In
general it can be shown that a transition to lower discount rates will help
renewable energy become more cost competitive with fossil fuels. Khatib [50]
performed a review of generation costs in OECD countries and found that as the
discount rates fall from 10% to 5% more capital intensive forms of energy,
such as nuclear, wind and tidal, become more cost competitive compared to coal
and gas. Both papers used a common discount rate across the whole energy
market due to limited data to distinguish the relative risks for different
technologies. Common discount rates have been criticised for not reflecting
these risks appropriately, and more recent studies have suggested specific
values for the tidal other ocean energy industries, which are on the higher
end of the spectrum due to their novelty and perceived risk.

A report on the cost of ocean energy, by SI Ocean for the European Commission
[42], used a discount rate of 12% for both wave and tidal, but also
investigated how changes in the rate chosen could have a significant impact on
the LCOE. Reducing $r$ from 12% to 6% results in a decrease in their predicted
LCOE of demonstrator arrays, from 32.0c/kWh (£288/MWh) to 23.1c/kWh
(£208/MWh).

The OREC 2018 report estimated a discount rate at 10MW cumulative tidal
capacity of 10%, but their models predicted this would fall to 8.4% by 100MW,
8.0% by 200MW and 7.1% by 1GW global installed capacity, reflecting the
potential that learning has to reduce the cost of capital. They also
demonstrated that each percentage point reduction in discount rate leads to a
significant LCOE reduction (of approximately 6%), for example the discount
rate changing from 7.1% to 6.1% would reduce their 1GW cummulative capacity
LCOE estimate from £91 per MWh to £80 per MWh[12]. This is consistent with SI
Oceans’s results, which fell by 6.4% on average per percentage point reduction
in discount rate. Falls in $r$ could be achieved as the industry matures and
investing in tidal energy is seen as less of a risk.

The Carbon Trust predicted that the first commercial marine energy schemes
would have a discount rate of around 15%, which could fall to 8% as the
technology matures [51]. Vazquez and Iglesias [23, 21] used a discount rate of
10% in their Levelised CAPEX of Energy tool. In another paper they argued that
tidal stream energy projects have greater technological risks, due to their
novelty compared to conventional types of energy generation, and high capital
costs which results in a conservative discount rate being needed of between
10% and 12% [20].

Allan et al. [52] used a high and low discount rate of 15% and 6%
respectively, with 10% used as the central value when finding the LCOE of wave
and tidal, which is often used as a common rate across multiple different
technologies [53, 54]. Allan et al. [52] noted that higher discount rates
adversely affect technologies with longer lifetimes and high CAPEX as a
proportion of the LCOE. Both of these factors apply to tidal, so it is
anticipated to be highly sensitive to variation in the discount rate.

Culley et al. [4] also used a 10% discount rate for their study into cost
modelling and micro-siting of tidal stream, and found that this amounted to a
35% reduction in income when compounded over an assumed 20 year array
lifetime. Coles et al. [38] used a discount rate of 12% when investigating
mechanisms for reducing the LCOE of tidal. Dalton et al. [55] suggested a
discount rate of 8% to 15% is typical in UK ocean energy, however they noted
that more in-depth economic studies could use multiple rates within one
project to reflect the different risks of individual cash flows. Klaus et al.
[56] assumed a financial discount rate of 10% but also tested the impact of
varying it over the range 5–15%. They emphasised the importance of thorough
investigation into the choice of discount rate, by demonstrating the the
results of LCOE comparisons between technologies can be inverted as the
discount rate is varied through its conventional range.

This present study therefore recommends using a discount rate of 5 to 15% with
a typical value of 10%. However, due to the high sensitivity of LCOE to the
discount rate, sensitivity analysis of the final LCOE prediction to the choice
of $r$ should be performed.

####  4.2.9 Lifetime of array

The lifetime of the array is the number of years that the tidal project is
planned to operate for. It is normally determined by contracts and insurance
based on the assumed time an array can perform well before there is too much
degradation due to environmental conditions. Vazquez and Iglesias [23, 20, 21]
used an expected lifetime of installation of 20 years in their Levelised CAPEX
of Energy tool. Likewise Dalton et al. [55] and the report by SI Ocean[42]
assumed a lifetime of 20 years. The Department of Business, Energy and
Industry Strategy (BEIS) assumed an operating period of 22 years for tidal
stream in their 2016 generation costs report[54].

The world’s largest currently operating, the MeyGen 6MW array in the Pentland
Firth, announced in 2018 it had entered into its 25 year operations phase [57,
24]. Similarly Johnstone et al. [58] assumed a lifetime of 25 years in their
techno-economic analysis of tidal energy, and as did Coles et al. [38]. As the
technology becomes more tested and proven lifetimes are likely to increase
even further. Therefore a typical value of 25 years with an upper and lower
bound of 30 and 20 years respectively was used in this study.

Tidal energy is currently perceived as a relatively risky investment, and
therefore has a high discount rate, this makes the NPV and LCOE less sensitive
to the choice of array lifetime, because both revenue and costs many years
into the future are heavily discounted. At a discount rate of 10% cashflows
20, 25 and 30 years into the future have a present value reduced by 85%, 91%
and 94% respectively, so adding additional years to the project lifetime does
not contribute much to the overall LCOE. If the discount rate falls to 5% then
the present value reductions fall to 62% 70% and 77% respectively.

####  4.2.10 Summary of all cost model inputs

The maximum, minimum and mean values of the cost parameters and other economic
inputs (discount rate and lifetime of an array) across all the sources
discussed above are summarised in Table 4, as the Pessimistic, Optimistic and
Typical values. It should be noted that the cost information summarised in
this review is based on the limited publicly available information at the time
of writing and that there is a significant difference between the optimistic
and pessimistic values due to the high degree of uncertainty in this
relatively new industry. These estimates are suitable for academic modelling
and optimisation of tidal stream arrays, but in practice tidal developers
should use their internal cost information for more accurate economic array
design.

Table 4: Estimates for the parameters used in the economic models, and the amount they vary. Symbol | Description | Value range | Units
---|---|---|---
|  | Optimistic | Typical | Pessimistic |
$\text{CA}_{f}$ | Fixed CAPEX | 5.6 | 9.2 | 14.4 | £m
$\text{CA}_{t}$ | Turbine dependent CAPEX | 2.4 | 3.3 | 4.4 | £m per turbine
$O_{f}$ | Fixed OPEX | 0.27 | 0.32 | 0.87 | £m per year
$O_{t}$ | Turbine dependent OPEX | 0.094 | 0.15 | 0.26 | £m per year per turbine
$r$ | Discount rate | 0.05 | 0.10 | 0.15 | N/A
$L$ | Lifetime of an array | 30 | 25 | 20 | years

###  4.3 Revenue inputs

In all of the financial models above, the income must be estimated, to be able
to analyse the cost-benefit balance of different array designs. Assuming that
the main source of income for an array operator is the from selling the energy
generated, then the revenue, in year $i$, can be approximated from

$\displaystyle\text{Revenue}_{i}=P_{\text{avg}}\times t_{i}\times T_{e}.$ (31)

Where $P_{\text{avg}}$ is the average power generated, predicted using a
hydrodynamic model of the array, and either used as an average over the whole
lifetime of the array, or calculated over smaller time scales, for example to
take into account variation due to the lunar cycle. $t_{i}$ is the number of
hours of generation each year, which can be multiplied by the average power,
to find the gross energy output in MWh. Below is a discussion on factors that
affect the ratio of operational hours to hours downtime. $T_{e}$
[$\pounds$/MWh] is the electricity tariff, i.e. the price per MWh the
electricity generated is sold at. This price is greatly dependent on the
subsidies and other schemes available to developers, and the schemes available
in the UK are discussed in greater detail below.

####  4.3.1 Strike price of energy

Traditionally, large scale electricity generators sell their energy to
suppliers at a time varying market price. In the UK, the wholesale electricity
market price (or ‘reference price’) hovers between £40–£50/MWh. This market
price changes throughout the day and the year in response to the balance of
supply and demand.

Renewable energy sources often need subsidies and schemes for additional
income support for a number of reasons. Firstly, many forms of renewables,
especially the tidal industry, have a relatively high LCOE due to their
relative infancy. Governments often seek to subsidise the expensive new forms
of energy by paying higher than the market rate. This helps decarbonise the
electricity grid and support in the early stages may help new technologies
become cost competitive by the time they are deployed on a larger scale.
Secondly, renewable energy technologies are often non-dispatchable, in that
the production cannot be scaled up and down on demand easily. This means they
cannot react to falls and rises in the market prices, which can lead to
worsening problems as renewables account for increasingly high portions of the
energy generation mix. The wind energy industry has already seen that during
times where the wind is high at one farm often correlates with high winds at
other farms in the surrounding regions, and therefore the price falls and
operators get a low return per unit during their periods of highest
production. In the US this has led to a rise in the frequency of negative
prices in areas with high levels of wind and solar and which have transmission
constraints [59]. To address this problem governments can offer schemes that
guarantee a fixed electricity tariff. These tariffs are not necessarily higher
that the market price, but the guarantee reduces the uncertainty the investors
and can result in lower discount rates and protect the income of operators
during times where supply is high. This is less likely to be a problem for
tidal energy because it accounts for a far lower proportion of total energy
generation than wind energy and it is possible to take advantage of phase
differences across the country to smooth out the daily power production[60].
Improvements to the grid, such as increased storage, may reduce the need for
these kind of subsidies in the future.

Power Purchase Agreements (PPAs) are contracts between the generators and the
suppliers that outline how much generators will be paid for the power exported
over the duration of the contract. PPAs enable generators to earn payments for
the energy they export to the grid. These agreements can be long or short
term, so could be negotiated to last the full lifetime of a tidal array. PPAs
ca be negotiated to be market-varying price or fixed price, the latter being
preferable for a predictable income for tidal projects. Similarly to ROCs,
PPAs help remove exposure to price volatility and make cost planning more
predictable. The advantages of PPAs from a supplier’s perspective include
fixed prices to reduce exposure to makret fluctuations and guarantees of
renewable origin, to help meet the business’s sustainability goals. MeyGen
Phase 1A in Pentland Firth signed a 10-year PPA with SmartestEnergy, to
guarantee revenue on the power generated up to 2025. DeltaStream in Wales
signed a PPA with EDF for their first tidal turbine in 2014.

The Renewables Obligation (RO) scheme incentivised large-scale ($\geq 5$MW
capacity) renewable electricity in the UK by requiring UK electricity
suppliers to source a specified proportion of the electricity they provide to
customers from eligible renewable sources. The scheme closed to new generators
in March 2017, but electricity sources already accredited under ROs will
receive their 20 year lifetime support until the final close of the scheme in
2037. Under this scheme, Renewable Obligation Certificates (ROCs) are issued
to accredited renewable energy generators for the eligible electricity they
generate. Generators can sell their ROCs to suppliers through the e-ROC
auction, receiving a premium ontop of the wholesale electricity price.
Suppliers present the ROCs bought from generators to Ofgem, and if they do not
have enough ROCs to cover their obligation they must make a payment into the
buy-out fund at a fixed price per MWh. Ofgem then redistributes the buy out
funds proportionately to the suppliers who presented sufficient ROCs. When
first introduced in 2002, one ROC is issued to the generators per MWh
generated, to emphasise competition between technologies. However this
favoured more established technologies, so in 2006 it was reformed to have
different banding levels for different types of technology. Tidal stream
projects accredited before the scheme closed in 2017 were issued 5 ROCs (the
highest banding level), subject to a 30MW cap at each generating station.
Power generated above the 30MW cap receives 2 ROCs. PPAs with a particular
energy supplier can also guarantee the purchase of the ROCs issued to that
generator over a specified period. The MeyGen Phase 1A was awarded Ofgem
accreditation as a 5 ROC project in 2017, meaning that their revenue was
comprised of power generation sales (as agreed by a PPA) and a buy-out price
of £44.77/MWh from each of the ROCs (which has since risen to £50.80/MWh in
2021/22), which would bring the total $T_{e}$ is circa £250 to £300/MWh,
depending on the price agreed in the PPA.

As the ROC scheme was phased out in 2017 it was replaced with the Contracts
For Difference (CfD) scheme, for guaranteeing low-carbon electricity
generators a long-term energy price. A fixed “strike price” for each unit of
energy produced is guaranteed, leading to a promise of steady returns for
investors. During the contract period, typically 15 years, a low-carbon energy
project is paid the difference between the market price and the strike price
(or they pay back the difference, if the market price rises above the strike
price). In the UK’s most recent round (the third allocation in 2019), CfDs
were allocated as low as £39.65/MWh, mostly for offshore wind. In its current
state of deployment, the tidal industry cannot compete with these low prices.
Alternative subsidy schemes, which allow developers of new forms of green
energy greater funding until their costs can fall due to learning and
economies of volume, are being investigated.

A recent Marine Energy Council report [61] proposed a number of different
subsidy schemes to provide a route to market for the tidal energy industry and
other innovative clean energy technology types, such as wave and Advance
Combustion Technologies. An Innovation Power Purchase Agreement (IPPA) could
support small-scale (up to 5MW) novel projects by starting at a guaranteed
price, far above the market rate, at prices starting at £290/MWh and falling
by 15% for every 30MW of deployment (where each individual technology type can
only make use of 5MW out of every 30MW price band) down to £150/MWh by 120MW
of net deployment. The idea would help enable each novel technology to
demonstrate their performance and cost reduction potential, without having to
compete against far more established technologies.

Marine Energy Council also proposed an Innovation Contract for Difference
(iCfD) to allow for a new pot within the government’s existing CfD framework
for new technologies [61]. This would act as a bridging mechanism to allow
projects of larger than 5MW but less than 100MW and exploit economies of
volume until they can compete in open CfD rounds or other PPAs which could
enable a higher revenue than the UK market price. It could be limited to
projects of up to 100MW and could see the costs fall by 7% per 100MW from
£150/MWh to £90/MWh, based on the predictions of the OREC 2018 report [12].
Marine Energy council anticipated that these proposed schemes would support
tidal energy to reach target costs of less than £100MWh after 1GW of
deployment

These wide ranges of prices represent the highs and lows of what may be
achievable through subsidy for tidal energy in different stages of global
deployment. This study proposes a typical strike price of £150/MWh, chosen to
represent the gap bridged between small scale demonstrator arrays and larger
ones which can use iCfDs, with a lower bound of £40/MWh and an upper bound of
£290/MWh to represent the market prices or open CfDs and the propose iPPA
starting prices respectively. However it should be noted that there is a great
deal of uncertainty in these prices and they will depend greatly on the state
of the marine energy industry and government decisions at the time. Using LCOE
for evaluating the economics of tidal arrays removes the need for assuming the
strike price of energy in the calculations, so it can be a suitable metric
until more information about the subsidy levels available are known.

####  4.3.2 Downtime and degradation

Availability is a measure of the time that an array is available for
operation. Availability can be calculated from the number of hours downtime
over a given period, such that

$\displaystyle\text{Availability}=1-\frac{\text{hours downtime}}{\text{total
hours}},$ (32)

therefore the number of hours of generation in year $i$, as used in the LCOE
expression (13), can be predicted as $t_{i}=365\times 24$ multiplied by the
anticipated availability in year $i$. In the wind industry it has been found
that turbines often have lower availabilities during high-wind periods, where
the production and loads are higher so faults are more likely to occur. To
account for this effect, availability is sometimes calculated in two ways – as
a time-based availability given in (32) or as a production-based availability,
found as the percentage of actual energy produced over energy expected. The
former is easier to calculate but the latter is a better representation of the
energy lost. Downtime in high winds often results in the percentage energy
lost being higher than the percentage of hours lost, with one study finding
that a 3% non-availability in time resulted in an 11% reduction in energy
generated in the Irish wind farm investigated [62], whereas DNV-GL found that
the two metric differed by up to 2%[63]. The production-based availability can
be improved by scheduling maintenance, where possible, during periods of low
resource.

Hours of downtime, or non-availability, can have several causes; turbine
availability can include scheduled or unscheduled maintenance or faults in the
turbines causing periods of non-operation, grid availability can include
periods of time where the grid is unable to accept electricity due to lack of
capacity or grid failure, or balance of plant (BoP) availability, where
electricity generated at the turbines is lost due to failure of supporting
components and auxiliary systems [63].

Turbine suppliers will often guarantee a minimum turbine availability rate
when they sell their turbines to operators and if turbine failures cause the
availability to drop below that value the suppliers will pay compensation to
the operators. This contractual availability is negotiated during the turbine
supply agreement (TSA). In wind energy a typical value of 97% is used as the
industry standard [62]. There is limited operational data to form conclusions
about the typical time-based versus production-based availability in tidal,
but the MeyGen Phase 1A guaranteed a contractual availability of 95%, and
anticipated that the turbines would exceed their target performance in
practice[64, 24].

When more data becomes available from operational tidal stream arrays, it may
become possible to model the downtime as a function of time. There are likely
to be cyclic patterns to the number of hours downtime needed a year for
scheduled maintenance, as some operations may need to occur on a five year
cycle for example. There is also evidence from the wind industry that failure
rates vary greatly depending on the year in the operating lifetime [18].
Faulstich et al. [17] demonstrated that wind farms often follow a “bathtub
curve” where there is a high failure rate in the early life due to teething
problems or ‘infant mortality’, a period where the failure rate is
approximately constant and low, with just intrinsic random failures occurring
and a wear-out period near the end of an array’s lifetime, where damage
accumulates and the failure rate increases. This degradation could be due to
increased component wear or bio-fouling impacts.

##  5 Conclusions and summary

There are a great number of metrics that can be used to evaluate the
performance of tidal energy arrays. These include power alone (which results
with array designs with too many turbines if the number is not pre-specified),
purely economic metrics such as break-even power analysis, NPV, LCOE, IRR and
PP. Some studies have expanded upon performance metrics further to include the
trade-off between economic performance and environmental impacts of the
arrays, however this requires decisions on the relative weightings each
criteria. This study proposes that many of these economic metrics can be
estimated for large scale arrays by assuming a linear relationship between
CAPEX and OPEX and the number of turbines, an therefore splits each of these
expenditures into their fixed and turbine-dependent components, $CA_{f}$,
$CA_{t}$, $O_{f}$ and $O_{t}$ respectively. The data collection study
identifies a realistic range for each of the parameters needed in a simple
economic model of a tidal stream array, summarised in Table 4. Additionally,
the range of past, present and proposed subsidy schemes in the UK were
examined, to identify possible upper and lower bounds on strike prices,
however it is noted that the actual value will be highly dependent on the
state of the industry and levels if government support at the time. It should
be noted that there is a great deal of uncertainty in each of the economic
input estimates and they should be used for the purpose of providing a
reasonable range for academic studies and may not reflect the real economic
performance of a potential tidal site. These estimates are useful in the
absence of real financial data from developers, which is often highly
commercially sensitive, and can be used for proof of concept when
demonstrating new techniques for optimising tidal array designs. In practice,
array design studies should be repeated with a developers internally-validated
financial models.

##  6 Acknowledgements

ZLG acknowledges the support of Engineering and Physical Sciences Research
Council (EPSRC) Centre for Doctoral Training in the Mathematics of Planet
Earth [grant number EP/L016613/1].

DSC acknowledges the financial support of the Tidal Stream Industry Energiser
project (TIGER), co-financed by the European Regional Development Fund through
the Interreg France (Channel) England Programme.

MDP would like to acknowledge the support of the UK’s Engineering and Physical
Sciences Research Council (EPSRC) [grant numbers EP/M011054/1, EP/L000407/1
and EP/R029423/1].

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