Impact on Energy Yield of Varying Turbine Designs under Conditions of Misalignment to the Current Flow

Abstract

Tidal energy resource characterisation using acoustic velocimetry sensors mounted on the seabed informs developers of the location and performance of a tidal energy converter (TEC). This work studies the consequences of miscalculating the established flow direction, i.e., the direction of assumed maximum energy yield. Considering data only above the proposed TEC cut-in velocities showed a difference in the estimated flow direction of up to 4°. Using a power weighted rotor average (PWRA) method to obtain the established flow direction resulted in a difference of less than 1° compared with the hub-height estimate. This study then analysed the impact of turbine alignment on annual energy production (AEP) estimates for a non-yawing tidal turbine. Three variants of horizontal axis tidal turbines, which operate in different locations of the water column, were examined; one using measured data, and the other two via modelled through power curves. During perfect alignment to the established flow direction, natural variations in flow meant that the estimate of AEP differed by up to 1.1% from the theoretical maximum of a fully yawed turbine. In the case of misalignment from the established flow direction, the difference in AEP increased. For a 15° misalignment, the AEP differed by up to 13%. These results quantify important uncertainties in tidal energy site design and performance assessment.

Full text

Citation: Evans , L.; Ashton, I.; Sellar,
B.G. Impact on Energy Yield of
Varying Turbine Designs under
Conditions of Misalignment to the
Current Flow. Energies 2023,16, 3923.
https://doi.org/10.3390/en16093923
Academic Editors: Doug Arent,
Xiaolei Yang and Adam Warren
Received: 22 March 2023
Revised: 21 April 2023
Accepted: 27 April 2023
Published: 6 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Impact on Energy Yield of Varying Turbine Designs under
Conditions of Misalignment to the Current Flow
Luke Evans 1,2,* , Ian Ashton 3and Brian G. Sellar 4
1EPSRC and NERC Centre for Doctoral Training in Offshore Renewable Energy (IDCORE),
The University of Edinburgh, Edinburgh EH9 3DW, UK
2European Marine Energy Centre (EMEC), Research Engineer, Orkney, Old Academy Business Centre,
Back Road, Stromness KW16 3AW, UK
3College of Engineering Mathematics and Physical Sciences, University of Exeter, Penryn Campus,
Penryn TR10 9EZ, UK; i.g.c.ashton@exeter.ac.uk
4School of Engineering, The University of Edinburgh (UoE), Edinburgh EH9 3DW, UK; brian.sellar@ed.ac.uk
*Correspondence: luke.evans@emec.org.uk; Tel.: +44-793-5144-676
Abstract:
Tidal energy resource characterisation using acoustic velocimetry sensors mounted on the
seabed informs developers of the location and performance of a tidal energy converter (TEC). This
work studies the consequences of miscalculating the established flow direction, i.e., the direction of
assumed maximum energy yield. Considering data only above the proposed TEC cut-in velocities
showed a difference in the estimated flow direction of up to 4
◦
. Using a power weighted rotor
average (PWRA) method to obtain the established flow direction resulted in a difference of less
than 1
◦
compared with the hub-height estimate. This study then analysed the impact of turbine
alignment on annual energy production (AEP) estimates for a non-yawing tidal turbine. Three
variants of horizontal axis tidal turbines, which operate in different locations of the water column,
were examined; one using measured data, and the other two via modelled through power curves.
During perfect alignment to the established flow direction, natural variations in flow meant that the
estimate of AEP differed by up to 1.1% from the theoretical maximum of a fully yawed turbine. In
the case of misalignment from the established flow direction, the difference in AEP increased. For a
15
◦
misalignment, the AEP differed by up to 13%. These results quantify important uncertainties in
tidal energy site design and performance assessment.
Keywords:
marine renewable energy; tidal energy; tidal flow asymmetry; power curve; power
performance; uncertainty; IEC TS 62600-200; acoustic doppler profiler; turbine yaw misalignment
1. Introduction
Tidal-stream energy, the extraction of kinetic energy from tidal currents to generate
electricity, is becoming an increasingly attractive form of renewable energy due to the high
predictability of the tides [
1
–
3
]. This resource has the potential to provide energy security
and support a renewable grid network shift to decarbonised energy generation. Initial
feasibility studies and characterisation of high energy sites often focus on peak velocity
(
>
2.5 m
·
s
−1
) and a restricted range of water depths (25–50 m) [
1
,
4
,
5
]. However, peak
values do not accurately indicate the potential power production due to fine-scale temporal
and spatial variability in the flow. Therefore, gathering additional information from site
resource characterisations, while using Acoustic Doppler Current Profilers (ADCPs), is
vital for understanding the potential uncertainties. In addition to quantifying the available
resource, evaluating the tidal energy converters’ (TECs) performance in natural conditions
is challenging. Still, it remains an essential aspect of accelerating the tidal industry to the
commercialisation phase [6].
Most TECs frequently developed do not have the ability to actively respond to changes
in the current direction [
7
]. Thus, are of a non-yawing (no rotation in the nacelle) horizontal
Energies 2023,16, 3923. https://doi.org/10.3390/en16093923 https://www.mdpi.com/journal/energies

Energies 2023,16, 3923 2 of 17
axis design, [
8
–
13
], some designs yaw
≈
four times a day to face perpendicular to the
established flow direction, e.g., the 1 MW DEEP-Gen IV from Alstom [
14
,
15
]. However, the
tidal current magnitude and direction are typically asymmetric in highly energetic tidal
test sites [
3
,
4
,
16
,
17
], particularly in nearshore environments where the topography and
bathymetry vary significantly [
4
,
5
]. Despite that, resource assessments commonly assume
that the proposed TEC will always be aligned with the instantaneous tidal flow [4,5].
The International Electrotechnical Commission (IEC) Technical Specification (TS) on
Power Performance Assessment (PPA) [
18
] provides guidance for collecting potential
uncertainties associated with the measurement of current and power produced by TECs [
18
].
However, due to the limited number of grid-connected commercial-scale TECs deployed
(in the UK [
6
,
10
,
19
], France [
8
,
12
] and the US [
12
,
20
]), the standard IEC62600-200 has
been applied only to a limited number of turbines and, as a consequence, industry has
limited feedback on the use of the IEC62600-200. Typically, a PPA is undertaken as a key
step towards achieving type certification of the TEC [
6
], providing a basis to guarantee
the power performance of the device to interested parties, e.g., customers, investors and
insurers [21].
As part of the Reliable Data Acquisition Platform for Tidal (ReDAPT) project [
22
],
multiple ADCP deployments took place at the European Marine Energy Centre (EMEC)
full-scale tidal test site at Eday, the Fall of Warness (FoW), between 2011 and 2015. The aims
were to assess the flow characteristics and evaluate in situ measurements for the power
performance of the DEEP-Gen IV 1 MW tidal turbine. The location of the tidal test site is
presented in Figure 1a,b. Part of this work identified a twist in the flow along the water
column, where the current direction changed significantly through the water column by
as much as 10
◦
from the calculated mean [
14
]. At present, the flow direction measured by
the ADCP depth bin relative to the proposed TEC should be reported as per IEC62600-
200 [
18
]. Figure 1c presents the typical flow conditions at the tidal test site situated at the
FoW, taken from one of the ReDAPT measurement campaigns [
19
]. Flow velocity and
direction vary with depth—from bathymetry, seabed friction and interactions from the
wind and waves. If this variation could be captured along the rotor plane of a TEC, a more
accurate representation of the established flow could be estimated. This is performed for
the flow velocity, using the power-weighted rotor average (PWRA) method [
18
], as shown
in Figure 2.
Figure 1.
Location of the study site. (
a
) Orkney location relative to the UK [
23
]; (
b
) The Orkney
Islands with Eday and the falls of Warness full-scale tidal energy test site highlighted [
23
]; (
c
) Tidal
ellipse of data used from one instrument deployed at the FoW, flood (black marker) and ebb (grey
marker) flow directions are shown.
Studies have analysed the impact of flow misalignment on tidal turbines. For example,
Polagye and Thomson [
24
] used observations from an ADCP on a single point mooring to
assess individual locations within Admiralty Inlet (Puget Sound, Washington, WA, USA)
and estimated that the mean potential power generated by the non-yawing device may

Energies 2023,16, 3923 3 of 17
be, at most, 5% lower than for a passive yaw device at the same site. It was observed that
the penalty for using non-yawing devices increases as directional variation in the flow
increases [
24
], which agrees with work from Galloway and Frost et al. [
4
,
25
], where they
suggest that power reductions may only become apparent above a certain threshold of
misalignment (
>
7.5
◦
with an approximately 7% reduction of peak power at
±
10
◦
direc-
tional misalignment, and a 20% reduction at 22.5
◦
. Frost et al. [
4
] found that asymmetrical
regimes (difference in peak velocity between the flood and ebb tidal cycle) lead to unequal
power generation during the two tidal cycles. Since turbine power output is proportional
to the cube of the flow velocity, even a slight difference in the velocity magnitude between
tides can lead to a significant alteration in the power generated [
26
]. In addition, Piano et
al. [
5
] found that optimising turbine orientation to specific flow dynamics could reduce the
potential losses by up to
2% where
strong asymmetry occurs and as low as 0.25% for ideal
symmetrical conditions when considering a non-yawing TEC. However, tidal characteris-
tics are dissimilar across sites and have the potential for increased losses in annual energy
yield, exceeding 2% where the optimal orientation of non-yawing devices is ignored [5].
Figure 2.
The vertical variation of tidal current across the projected capture area—introducing the
importance for the power PWRA technique.
From the initial TEC concepts to the first pre-commercial tidal turbine prototypes, a
key requirement has been reliability and survivability [
27
]. The impact of turbulence on the
performance and loading acting on a tidal turbine has received little consideration to date.
Turbulence describes the chaotic motions within a fluid flow and can result in fluctuations
in force, which is detrimental to the fatigue life of the turbine [
27
,
28
]. The presence of
the turbine can increase the turbulence and vortices generated [
27
,
29
]. Although this is
recognised, and these effects can change the flow characteristics at the turbine location, this
is not the focus of this study due to instrument placement and resolution.
The flow direction matures over a tidal cycle. This effect on power performance
has not yet been quantified. Not knowing the impact on power will lead to an inaccurate
assessment of performance. This study aims to use in situ measurements obtained from two
ADCPs deployed at the FoW (Orkney, Scotland, UK) to quantify the impact off-axis currents
have on power production. In addition, the impact on performance and energy yield from
a rotor misalignment for three horizontal axis tidal turbines situated at different depths
is assessed. This work will inform developers on turbine installation design criteria by
highlighting how the temporal variation in the flow direction can result in a misalignment
between the current flow and turbine extraction plane. The methods used in this study
can be applied to in situ data gathered at different tidal test sites that exhibit complex
magnitude and directional asymmetries to maximise potential energy yields and help
interpret performance results more accurately. A method for estimating the established

Energies 2023,16, 3923 4 of 17
flow direction to inform tidal developers on turbine orientation is reported. The variation
in flow direction at different depths is necessary to predict the loading effects caused due
to being positioned off-axis to the established flow direction. We investigate the relative
impact of current flow maturity on the power performance of non-yawing TEC concepts.
We then investigate the misalignment of the turbine axis with the established flow to assess
the impact on the measured power curve, and AEP estimates. As numerous tidal turbines
exist and occupy different regions of the water column, three variants of a horizontal
axis tidal turbine were chosen for a case study to investigate the impact of flow direction
variation on machines with different operational characteristics. We suggest the optimum
period for utilising a yaw mechanism by interpreting the results.
This paper is structured as follows: Section 2introduces the theory behind the power-
weighted rotor average method. In addition, the characteristics of flow direction asymmetry
and maturity are presented; Section 3describes the FoW deployment site conditions, as
well as the instrumentation relevant to this work; while Section 4reports the results on the
estimates of established flow direction (Section 4.1) and the consequences of misalignment.
The analysis is then presented, which considers the impact on the measured power curve
(Section 4.2) and annual energy estimates with respect to off-axis currents approaching the
TEC (Section 4.2.3); Section 5presents the discussion around the hypothesis and results
generated. The main conclusions from this analysis are summarised in Section 6.
As this paper discusses the impact of flow direction estimates, some abbreviations will
be used throughout this paper. Where all the measured flow velocities are assumed to flow
through the TEC extraction plane for maximum energy capture was referred to as
Uinflow
;
the established flow direction estimate was
θ
and the methods used to obtain the estimate
were,
θHH
(hub-height),
θRA
(rotor average) and
θPWR A
(power-weighted rotor average);
the misalignment from the established flow direction is represented as α.
2. Theory
2.1. Estimate of Established Flow Direction—PWRA
Efforts to advise developers on how to record and report the flow direction at tidal
stream sites have been made by IEC/TS 62600-200—“Electricity producing tidal energy
converter—power performance assessment” [
18
]. This TS describes a method for ascertaining
the flow characteristics of a site, which underpins the prediction of the potential resource
and defines the local flow conditions and associated design considerations. Currently, the
TS requires the established flow direction to be reported for the profiler bin relative to the
hub-height (
θHH
) of the proposed TEC, along with instantaneous measurements for both
the flood and ebb (see Figure 1a) [4,18].
Tidal turbines with no yaw capabilities are deployed facing the established flow
direction with the most significant velocities. If the TEC is equipped with bi-directional
blades, it can capture energy from current flow travelling from two opposing directions.
However, highly energetic tidal sites typically have asymmetrical tides in both velocity
magnitude and direction [
4
]. Therefore, a robust estimate of the established flow direction
will inform the TEC orientation and increase power performance and quality while reducing
the total loads experienced on the rotor due to off-axis currents. The established flow
direction is an average of the measurements captured at the hub-height of the deployed
TEC. The reference velocity is calculated from the relative profiler bins that profile across
the rotor extraction plane as shown in Equation (1):
ˆ
Ui,j,n=1
AΣS
k=1U3
i,j,k,nAk1
3(1)
where
i
is the index number defining the velocity bin;
j
is the index number of the time
instant at which the measurement is performed;
k
is the index number of the current profiler
bin across the projected capture area (reflected in Figure 2as
Ak
);
S
is the total number of
current profiler bins across the projected capture area;
ˆ
Ui,j,n
is the instantaneous power

Energies 2023,16, 3923 5 of 17
weighted tidal current velocity across the projected capture area in m
·
s
−1
;
Ui,j,k,n
is the
magnitude of the instantaneous tidal current velocity, for time
j
, at current profiler bin
k
, in
velocity bin
i
, for data point
n
in m
·
s
−1
and
A
is the projected capture area of the proposed
TEC m2.
Equation (1) uses the velocity magnitude U, which assumes all energy is available to
the device, whereas expressed in Equation (2),
Uα
is the velocity component accounting
for periods of TEC rotor to flow misalignment, where
α
is directly related to the angle
of misalignment.
ˆ
Uαi,j,n=1
AΣS
k=1U3
α,i,j,k,nAk1
3(2)
2.2. Flow Direction Asymmetry between Flood and Ebb Tides
A tidal ellipse plot presents the velocity magnitudes (as a radius) and directions (as a
compass heading) in polar coordinates. The velocity data points are typically 5, 10 or 15 min
temporally averaged and spatially averaged (cube weighted) over the predicted swept area
of a turbine. These plots help determine the flow magnitude and direction variation at the
site of interest and identify the established flow direction to inform turbine developers.
If the flow direction for the ebb and flood tidal cycles are separated by
≈
180
◦
, the site is
described as symmetrical or rectilinear. Otherwise, the flow is described as asymmetrical.
The amount of asymmetry between the ebb and flood tide can be summarised by computing
the difference between the mean angle of both directions over a complete lunar cycle
(Equation (3)). Symmetrical sites are desirable as turbines can be mounted in a fixed
position, pitching the blades to capture the tides from both directions with little or no loss
of power. Sites with an offset between the ebb and flood tide may benefit from a turbine
that could yaw to capture both tides efficiently [4,30].
θmis = (θf l ood −θebb)−180 (3)
where θis the angle in degrees (◦).
2.3. Flow Direction Variation a Tidal Cycle
In addition to asymmetrical tides, the flow direction changes during the different
phases of the tide. As the tide evolves to the established flow direction, this will be referred
to as the ramping up (RU) of the tide, and as the tide begins to slow from peak flow (PF)
before changing tide, this phase will be referred to as waning down (WD), as seen in
Figure 3. For non-yawing TEC concepts, the ability to capture the largest amount of energy
will only take place once the TEC is positioned perpendicular to the flow. This variation in
direction results in a reduced velocity passing through the TEC rotor capture area. Hence,
this must be considered when evaluating and producing a measured power curve.
Figure 3depicts how flow varies with time during a flood cycle at the instrument
location (direction measurements are subject to variation based on instrument location) in
the FoW.
The measured flow evolves and a non-yawing TEC positioned towards the established
flow direction will be susceptible to off-axis currents throughout each tidal cycle.
Equation (4)
describes the inflow velocity (
Uinflow
) at the instrument location, and the velocity at the
TEC location (
Urotor
) when the turbine’s rotor heading is perpendicular to the free stream
flow at all times (
α=
0), thus capturing the maximum amount of energy available. In
misalignment circumstances, the inflow velocity becomes a component of the velocity,
and the parameter
α
quantifies the difference between
Uinflow
and
Urotor
. The impact
of misalignment can be described using a simple trigonometric cosine relationship [
4
], as
shown in Equation (5):
Urotor =Uα=0=Uinflow (4)

Energies 2023,16, 3923 6 of 17
Urotor,α=Uα6=0=Uinflow ·cosα(5)
Figure 3.
Flow direction variation over a flood tide at the FoW, where (
a
) the flow direction mean
(square markers) of 30 min periods throughout the flood cycle, the TEC yaw heading (solid black line)
and the min and max (crosses) variation in direction. (
b
) The tidal ellipse for the flood measurements
at a chosen hub-height (25 m), the black dashed line represents the TEC yaw heading.
Alternatively, the turbine’s swept area can be considered when misalignment is intro-
duced and it changes from a circle to an ellipse. The vertical radius of the ellipse will remain
the same, and the horizontal radius will decrease as the yaw angle increases from the estab-
lished flow direction. The resulting equation for a turbine’s projected area in aligned and
misaligned flow is described by Equations (6) and (7), respectively, as shown below:
Arotor =Aα=0=π·r2(6)
Arotor,α=Aα6=0=π·r2·cosα(7)
where
r
is the radius of the turbine and
α
is the misalignment in degrees between the
Uinflow and Urotor.
It is expected that either one of these two corrections, when applied to the theoretical
maximum power equation, may estimate the performance drop due to misalignment.
Tidal stream devices designed to react to tidal sites with asymmetrical tides may lack the
sufficient ability to extract energy efficiently from off-axis currents. The maximum power
can be calculated using Equation (8):
P=1
2·ρ·cp ·U3·A(8)
where Pis the power produced in MW,
ρ
is the density of water in kg
·
m
−3
,
Cp
is the power
coefficient,
U
is the instantaneous flow velocity in m
·
s
−1
and
A
is the cross-sectional area
of the TEC rotor in m2.
3. Methodology
3.1. Deployment Site Conditions
A measurement campaign was devised to assess the DEEP-Gen IV 1 MW tidal turbine
performance using two ADCPs over June and July 2013 at the FoW (Figure 1). The full-scale
tidal test site situated on the coast of Eday contains highly energetic tidal currents due to a
narrowing of the channel between Eday and Muckle Green Holm, a small outcrop south-

Energies 2023,16, 3923 7 of 17
west of the island. Figure 4presents the channel bathymetry and instrument locations. The
tidal current flows southeast and northwest throughout the flood and ebb tide, respectively.
The strength in the ebb tide at the FoW is larger and less spatially varied, reaching a PF
of 4 m
·
s
−1
with a flow direction spread of
≈
35
◦
from the RU to WD phase. The flood tide
reaches a PF of
≈
3.2 m
·
s
−1
with a much larger flow direction spread of
≈
75
◦
. The flood
tide is more turbulent due to the flow being disturbed by several features, including the site
bathymetry and nearby headlands [
31
]. For the following performance assessment, results
obtained in both tidal cycles are considered as the flow direction spread differs between
tidal cycles.
Figure 4.
(
a
) Channel bathymetry and ADCP locations relative to the DEEP-Gen IV at the FoW
tidal test site. (
b
) Tidal ellipse for three bin depths, where
z1
,
z2
and
z3
represent 15, 25 and
33 m
above the seabed. The generic established flow direction for both flood and ebb is presented. TEC
yaw heading rotations used throughout the analysis are illustrated, where both clockwise and
anticlockwise rotations are considered (
±α
). NOTE measurements shown indicate flow travelling
towards that direction.
The variation in flow direction at different heights above the seabed over each tidal
cycle is dissimilar. Therefore, three TEC concepts that occupy different regions of the water
column were chosen to assess the impact of power performance relative to the amount
of time spent off-axis to the established flow. Figure 4b depicts the measurements along
the water column at three depths. The flow direction is not symmetrical from the RU
phase to the PF phase and further during the WD phase (clockwise and anti-clockwise
from the established flow direction). Therefore, the analysis considers both positive (
+α)
and negative (
−α)
rotations of the TEC yaw to the established flow estimate (
θ
) seen in
Figures 3and 4b.
3.2. Instrumentation and Turbine Description
In situ measurements were made using Tenedyne RDI workhorse 600 kHz, with four-
beam ADCPs, fixed into gimbal support on a seabed frame. The locations of the ADCPs
were known to the nearest meter based on their Universal Transverse Mercator (UTM)
coordinates, see Table 1. Using a bathymetric map with each ADCP pressure data, their
depths relative to the TEC were estimated to the nearest meter (as the ADCPs were set up
with a resolution of 1 m).

Energies 2023,16, 3923 8 of 17
Table 1.
ADCP deployment specifications, showing the campaign ID, date deployed (dd-mm-yyyy)
and deployment duration. The position is UTM Zone 30 N.
ADCP Deployed Recovered Location East Location North Water Depth Resolution
ID (m) (m) (m) (m)
ADCP01-NW 18 February 2013 20 March 2013 511,054 6,555,328 44 1
ADCP02-SE 17 February 2013 20 March 2013 511,151 655,5241 45 1
Three TEC concepts were used to model the impact of misalignment between the flow
direction and TEC rotor on the measured power curve. These models are based on work
carried out in the RealTide advanced monitoring, simulation and control of tidal devices
project [
32
], where TEC
2
represents the DEEP-Gen IV which is used for this study (Table 2).
They have different operational characteristics and are deployed in distinct regions in the
water column; see Table 3for turbine dimensions and operational specifications.
Table 2. Generic tidal turbine concepts and features [32].
Simple Bottom Fixed Complex Bottom Fixed Floating Multi-Rotor
(TEC1) (TEC2) (TEC3)
Horizontal axis Horizontal axis Horizontal axis
Multi blade (>3) 3 Blades 2 Blades
Bottom fixed with pile Bottom fixed gravity base Floating— Moored in situ
No pitch control Pitch control No active yaw mechanism
Gearbox drive Direct drive Gearbox drive
Table 3. TEC operational characteristics and location in the water column.
TEC Concept Units TEC1TEC2TEC3
zfrom seabed (m) 15 25 33
Rotor diameter (m) 10 18 20
C-S Area (m2)78.5 254.4 628.3
Cut-in (m·s−1)0.75 1 1.2
Rated power (MW) 0.25 1 2
Rated velocity (m·s−1)1.8 2.6 3.1
Cut-out (m·s−1)3.5 4 4.5
3.3. Data Processing
All post-processing was applied to the data conformed to IEC/TS 62600-200 [
18
]. Each
instrument was processed with the same suite of methods and recommended measures
were based on internationally recognised QARTOD guidelines and the ADCP manufac-
turer’s best practices [
33
–
35
]. Measurements that lay outside the thresholds were flagged
and removed from the analysis. The IEC suggests using an averaging period between 2
and 10 min; the latter has been used for this analysis.
The measurement campaign used in this study featured periods with no generated
power or inconsistent generation from the DEEP-Gen IV, reducing the amount of compara-
ble data. For that reason, power was calculated using the published power curve provided
by Alstom (for the mid-depth TEC concept). Each velocity measurement was allocated an
active power value from the pre-defined power curve for the DEEP-Gen IV 1 MW TEC [
19
].
In addition, two separate power curves were produced to simulate power production for
the 0.25 MW and 2 MW TEC concepts. To illustrate the method, see Equation (9):
Pactive =Prated · U2−U2
ci
U2
r−U2
ci !(9)
where
Prated
is the predefined rated power,
U
is the in situ velocity measurement in m
·
s
−1
,
Uci
is the cut-in velocity for the proposed TEC and
Ur
is the rated flow velocity for peak

Energies 2023,16, 3923 9 of 17
power production. Velocity measurements that fall beneath the cut-in are rejected, and
above the rated are equal to the rated power defined.
The PWRA technique was used to calculate the two bottom-fixed TEC concepts
(insufficient data in the upper depth bins meant this technique was not usable) using
Equation (1). This was paired with the corresponding power produced. The following
steps were then performed using the bin methodology:
1.
Calculate the instantaneous PWRA velocity, using Equation (1), where
ˆ
Ui,j,n
, is the
instantaneous PWRA flow velocity,
Ak
is a profiler bin over the swept area of the
TEC and
Ui,j,k,n
is the velocity in the relative instrument depth bin; see Figure 2for
visual representation.
2.
Calculate the mean value of the velocity,
¯
Ui
and the respective data sources (TEC
power), ¯
Pactive,ias
¯
Ui="1
Ni
·
ni
∑
n=1
·ˆ
U3
i,n]#1
3
(10)
where
Ni
is the number of samples in the defined averaging period which produces
data point n.
¯
Pactive,i=1
Ni
·
ni
∑
n=1
·¯
Pactive,i,n(11)
3. Sort values into the corresponding flow velocity bin—increments of 0.1 m·s−1
The energy production was estimated from each instrument’s available time series
power data. This was derived via the trapezoidal method, which computes the approximate
power integral. The energy was then multiplied by the deployment campaign’s ratio to the
year’s length, as seen in the following Equation (12):
AEP =R·Σt2
t1·¯
Pdt (12)
where
AEP
is the expected annual energy production, in MWh, Ris the ratio of the number
of days a year over the duration of the deployment,
¯
P
is the mean calculated TEC power,
t1
is the index number defining the time start and
t2
is the index number of the end
time interval.
4. Results
4.1. Estimates of the Established Flow Direction
Table 4shows the effect of inclusion of data measured beneath the cut-in speed when
calculating the established flow direction. Differences of up to 4
◦
can be seen without
removing data under the proposed TEC cut-in speed. The estimate of the established flow
calculated using flow direction measurements aligned to the rotor plane (rotor average),
alongside the PWRA method, exhibited a less than 1.2
◦
difference, when compared with
the commonly used hub-height estimate (Table 4). Shown also in Table 4, the estimate of
the established flow direction varied across the three depths by up to 4
◦
. This highlights an
area where uncertainties may occur in using an ADCP for flow characterisation, causing
potential issues, for example, if they are used to instruct turbine heading.
Flow Variation along the Water Column
The 10 min averaged measurements were split by the acceleration and deceleration
of the tide, and into velocity bin increments of 1 m
·
s
−1
. Figure 5a,b shows a variation
with depth in the flow direction along the measured water column of
≈
8
◦
and 13
◦
for the
ebb and flood tide at peak flow (3–4 m
·
s
−1
), respectively. Shown also in Figure 5a,b, the
estimate of
θHH
(solid red line) and
θPWR A
(red cross), differed by
≈
0.9% at locations TEC
1
(presented in Figure 5) and TEC2.

Energies 2023,16, 3923 10 of 17
Table 4. Effect of pre-processing on the estimate of established flow direction.
TEC Concept Method EFD with All Data (◦)EFD with Speed <
Cut-in Removed (◦)Difference (◦)
θHH 130.7 133.8 3.1
TEC1,z1θRA 130.8 133.5 2.7
θPWR A 129.9 133.1 3.2
θHH 133.7 137.4 3.7
TEC2,z2θRA 133.2 136.8 3.6
θPWR A 132.5 136.5 4.0
θHH 134.7 138.6 3.9
TEC3,z3θRA 134.2 137.9 3.7
θPWR A 134.4 137.8 3.4
EFD: Established flow direction; HH: Hub-height estimate; RA: Rotor average estimate; PWRA: Power-weighted
rotor average estimate.
Figure 5.
Flow direction variation along the measured water column (z) during the acceleration and
deceleration phase of the tide for (
a
) the ebb tide measurements and (
b
) the flood tide measurements.
The established flow direction estimate using
θHH
(solid red line) and
θPWR A
(red cross) methods are
shown for TEC2. The position of all three TECs in the water column are shown in (b).
Figure 5b depicts the variation in flow direction in the lower region (
<
15 m) as
≈
11–13
◦
, compared to
≈
5–7
◦
, in the upper region (
>
35 m from the seabed) on the flood
tide. The ebb tide ranged from
≈
6
◦
down to 4
◦
between the lower and upper region,
as shown in Figure 5a. This highlighted that the two tidal cycles have different flow
direction characteristics and that the acceleration and deceleration phases of the tide differ
significantly between the flood and ebb tidal cycles.
4.2. Consequence of Misalignment on Performance Metrics
4.2.1. Axial Rotation Impact
The probability density distribution of flow direction, as shown in Figure 6, depicts
how the flow direction evolves over a tidal cycle. The density curves are right-skewed,
with the mean estimation greater than the median. The flow direction spends the majority
of the time clockwise from the established flow direction (towards the waning down phase)
of the tide for both tidal cycles. This highlighted that a TEC positioned off-axis from the
established flow by either a positive (clockwise) or negative (anti-clockwise) shift would
not perform identically.
4.2.2. Impact of Misalignment on the Power Performance
Figure 7a shows the generated power output for each 10 min measurement against the
flood tide velocity component approaching the DEEP-Gen IV. The theoretical maximum
power (red line) generated using the velocity magnitude
Uinflow
was compared with
the velocity component
Uθ±α
, where
α
is the streamwise misalignment between the TEC

Energies 2023,16, 3923 11 of 17
heading and established flow estimate (
θ
) of 5
◦
, 10
◦
and 15
◦
. As shown in Figure 7a, the
DEEP-Gen IV curves differed by up to
≈
1.5%, 4.9% and 10% at 2.5 m
·
s
−1
for a misalignment
of 5
◦
, 10
◦
and 15
◦
. Figure 7b–d depicts the power loss for each TEC case when misaligned
from the established flow, where the highest value of power lost per velocity bin was
measured from TEC
3
. At lower flow velocities, more visible differences exist between the
curves presented in Figure 7b–d. This is due to the variation between the 10 min samples of
flow direction and the averaged established flow direction
θHH
varying significantly more
during low flow speeds, thus causing a greater misalignment.
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Flow Direction [°, cartesian coordinates]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Flow Speed [m/s]
Flood [ -42.8° ]
( Bearing 132.8° )
Ebb [ +130.0° ]
( Bearing 320.0° )
Cut-in Speed [DeepGen IV]
Rated Speed [DeepGen IV]
IEC PC Lower Limit
IEC PC Upper Limit
"3 = +172.9°
EAST
NORTH
WEST
WEST
SOUTH
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Probability Density [ " 3 = 1.5 ° , "v = 0.015 m s-1]
Figure 6.
Probability density distribution for varying flow speeds and flow directions (in cartesian
coordinates) for flood and ebb tides. The data have been generated from hub-height measurements
sampled by an ADCP deployed
≈
40 m south-west of the DEEP-Gen IV TEC (in a region of flow
undisturbed by the presence of the turbine) [36,37]. The ADCP dataset is available at [38].
Figure 7.
Comparison of theoretical maximum power generated using
Uinflow
(red line) and the
realistic power generated using velocity component
Uθ−α
, where the TEC is misaligned to the
established flood direction. The DEEP-Gen IV power curve is presented (
a
) by the unfilled symbols,
where the circle, square and triangle represent a misalignment from the established flow of 5
◦
(
b
),
10
◦
(
c
) and 15
◦
(
d
), respectively. Filled symbols represent the percentage lost in power when flow
data used features misalignment for TEC1(filled grey) and TEC3(filled black).
The power lost from ebb measurements was lower than the flood measurements
(
Figure 7
). This is due to narrower flow direction spread (
≈
35
◦
) at this location and the
greater occurrence of the flow velocity exceeding (3.9 m
·
s
−1
), the TECs-rated velocities.
However, due to this narrow flow direction spread, the impact on the power curve was
more severe when the flow data used were a velocity component due to misalignment from
the established flow direction.

Energies 2023,16, 3923 12 of 17
4.2.3. Consequence to AEP
Figure 8is a graphical representation of the difference in AEP estimates when chang-
ing the TEC heading away from the established flow direction. It can be seen that the
introduction of misalignment reduces the total amount of energy captured and by different
amounts when misaligned clockwise or anti-clockwise to the established flow direction.
The greatest loss in AEP, when compared against the theoretical maximum, was found
when the TEC was positioned clockwise from the established flow direction on the ebb tide.
The results differed by up to 7.8%, 10.1% and 13.3% for TEC
1
, TEC
2
and TEC
3
, respectively.
A summary of the AEP losses found is provided in Table 5. The natural variation in flow
direction measured on the ebb tide is closer to the established flow direction, resulting
in a lower AEP loss of
≈
0.7%, 0.8% and 1.1% when TEC
1
, TEC
2
and TEC
3
are accurately
aligned with the established flow direction
θebb
. However, when the TEC is not aligned to
θebb
, the AEP losses are significantly greater when compared with a misalignment from
θf loo d, due to the narrow spread in the direction across the ebb cycle.
Figure 8.
AEP loss based on flow velocity used
Uα
, where
α
changed in increments of 1
◦
up to 15
◦
(
α1
,
α2
and
α3
represent 5
◦
, 10
◦
and 15
◦
, respectively). The flood (
right
) and ebb (
left
) tide AEP estimates
with a clockwise and anti-clockwise shift from the established flow.
Table 5.
AEP percentage loss from misalignment (
α
), where both flood and ebb tidal cycles were
analysed for a clockwise and anti-clockwise shift for the three TEC concepts. NOTE
θ
is equal to the
established flow direction.
TEC1TEC2TEC3
AEP Cases Flood Ebb Flood Ebb Flood Ebb
Uθ0.7 0.5 0.8 0.7 1.1 0.8
Uθ+α10.9 1.1 1.7 1.2 2.1 1.8
Uθ+α22.2 3.6 4.4 4.7 5.5 6.2
Uθ+α34.2 7.8 8.8 10.1 11.1 13.3
Uθ−α10.9 1.1 1.3 1.4 1.5 1.7
Uθ−α21.9 3.7 3.6 4.8 4.6 6.0
Uθ−α33.6 7.9 7.6 10.3 9.6 13.1
Figure 9shows a time-series of energy captured by TEC
2
for each tide across the
measurement campaign, where the lower energy yields are directly related to lower ve-
locities which occur during neap tidal cycles, experienced around periods 12–14 June and
24–26 June
. During these periods of lower tidal flow speeds, we see the greatest energy lost
due to the modelled misalignment. The amount of energy lost over each tidal cycle varies,

Energies 2023,16, 3923 13 of 17
but was as high as 3%, 7% and 12% when the TEC is misaligned to the established flow
direction by 5◦, 10◦and 15◦, respectively.
Figure 9.
Energy lost when TEC
2
is misaligned to the flow, where the grey bar is the energy captured
per tidal cycle. The blue, green, yellow and red bars represent the energy lost by the TEC facing the
established flow θ, misaligned by α1(5◦), α2(10◦) and α3(◦), respectively.
5. Discussion
This paper demonstrates the importance of accurately estimating the established flow
direction to inform tidal developers about TEC orientation and thereby maximise the energy
captured. First, it is shown that including data outside of the TECs’ operational limits
can skew the established flow direction estimate by up to 4
◦
(see Table 4). The greatest
variation in flow direction is found when the tide changes between flood and ebb. The
flow velocity and direction evolve over the tidal cycle; removing data beneath the cut-in
speed of the TEC will remove the large variations in flow direction and provide a more
accurate reference for TEC orientation. In addition, the flow direction can vary up to 13
◦
along the measured water column. The rotor average and PWRA methods are used in this
study to capture the variation in the direction along the rotor plane. The results differ by
less than 1.2% when comparing the two methods against the averaged hub-height estimate.
This work highlights that misalignment between the TEC extraction plane and the flow
direction will impact the energy captured. Furthermore, aligning the depth bin from the
ADCP to the proposed TEC hub-height when estimating the established flow direction is
key, and inaccuracies can impact the amount of energy captured when the TEC orientation
is incorrectly informed.
A key objective of this study was to assess the impact on power production when flow
data used features misalignment from the TEC extraction plane. The flow direction evolves
over a tidal cycle, resulting in the TEC being susceptible to off-axis currents, even when
the TEC is aligned to the averaged (over a tidal cycle) flow direction. This is evidenced
by the temporal variation in the flow direction, shown in Figures 3and 4and the vertical
variation displayed in Figure 5. The AEP estimate calculated from assuming the TEC tracks
the flow, compared with a fixed TEC heading towards the established flow angle, differed
by up to 1%. This is site-specific and will be based on the natural flow direction variation
at a tidal site. The variation in the flood tide direction was
≈
75
◦
, and whilst the ebb tide
direction varied by
≈
35
◦
(Figure 6), this resulted in the TEC being off-axis more frequently
during the flood tidal cycles; thus, the AEP losses were greater. Furthermore, if the TEC is
misaligned with the established flow angle once deployed, the AEP will be overestimated.
For a non-yawing TEC, the total AEP loss, as shown in Table 5, can be up to
≈
2%, 6%
and 13%, when the TEC is incorrectly aligned to the established flow by 5
◦
, 10
◦
and 15
◦
,

Energies 2023,16, 3923 14 of 17
respectively. This highlights an area of uncertainty when deploying a TEC at a tidal site, as
the accuracy of both the TEC heading and flow direction will reduce the uncertainty in the
measured power curve and energy yield estimates.
A case study using three horizontal-axis TECs rated at 0.25 MW, 1 MW and 2 MW and
occupying the lower, mid and upper regions of the water column, respectively, is presented.
The 1 MW machine used real world data as this was available.
Figures 5b and 8
show
the position of the three TECs and the AEP loss when misaligned to the established flow
direction, respectively. Of the three TECs assessed, the 2 MW variant exhibits the greatest
AEP losses under misalignment. This is a result of the operational characteristics of the
TEC, where the rated velocity is 3.1 m·s−1, and the flow velocity at the site on a flood tide
was
3.2 m·s−1
, whereas the smaller-scale TECs (TEC
1
and TEC
2
) experience more frequent
flows in excess of their rated velocity, which mitigates the impact of misalignment. Overall,
a tidal energy converter that has a rated velocity beneath the tidal site flow characteristics
by
≈
10% will operate at full capacity during peak flow conditions even during periods
of excessive misalignment up to 25
◦
, at the expense of capturing significantly less energy
during times below peak flow conditions. On the other hand, TECs with a rated velocity
over or close to the peak flow tidal conditions will suffer significantly if the flow velocity is
lower than the rated. This is evident in Figure 9, where the AEP losses are greater under
lower flow conditions, commonly referred to as neap cycles. An active yaw mechanism may
be most efficient during periods of lower velocity, where the TEC operating characteristics
are close to the flow characteristics at the tidal site, to maximise the energy captured and
minimise losses.
6. Conclusions
Using methods for data processing that only consider conditions across the turbine
during power production will give a more accurate estimate of the established flow direc-
tion to inform turbine installation and power performance assessments. The established
flow direction estimate used to inform developers about TEC orientation was found to vary
by up to 1.2
◦
when using rotor averaging methods and up to 4
◦
when restricting data used
to velocities when the turbine is operational.
The performance characteristics of three horizontal-axis tidal turbines manually posi-
tioned towards the oncoming flow have been measured relative to a yaw misalignment
from the established flow direction. The flow direction naturally evolves over a tidal cycle.
When the turbine was aligned to the established flow direction, this caused a difference
in energy estimates of up to 1.1% from the theoretical maximum production of a perfectly
yawing turbine. When the turbine was misaligned from the established flow direction, the
difference in AEP increased. For a 5
◦
, 10
◦
and 15
◦
misalignment, the AEP differed by 2%,
6% and 13% respectively.
The difference between the flow velocity on site and the TEC-rated velocity governs
the impact of misalignment on AEP. The observed differences will all have a greater impact
when a turbine is rated close to, or above, the maximum flow velocity. Turbines rated
beneath the maximum flow velocity at the site by at least 10% will operate at full rated
capacity during peak flow conditions even if the TEC is misaligned to the flow direction by
up to 25
◦
. Furthermore, the velocity is significantly slower during neap tidal cycles, which
is undesirable as it means the turbine is only at an extractable flow velocity for a smaller
proportion of the time (further reduced when misaligned to the established flow), reducing
the availability of the turbine to generate and capture the extractable resource.
The local bathymetry and channel boundaries differ significantly across different
tidal test sites. This work highlights the importance of understanding how the flow
direction evolves over a tidal cycle and how this characteristic impacts non-yawing TECs’
performance. Future work can compare and quantify the uncertainty from the variability
of the flow direction over a tidal cycle at different sites.

Energies 2023,16, 3923 15 of 17
Author Contributions:
L.E.: Conceptualisation, Methodology, Formal analysis, Investigation,
Writing—original draft, revision. I.A.: Supervision, Writing—review, editing & revision. B.G.S.:
Conceptualisation, Methodology, Supervision, Writing—review, editing & revision. All authors have
read and agreed to the published version of the manuscript.
Funding:
This work was funded as part of the EPSRC, United Kingdom and NERC, United Kingdom
Industrial Centre for Doctoral Training in Offshore Renewable Energy (IDCORE), Grant number
EP/S023933/1, and sponsored by EMEC.
Data Availability Statement: The datasets used in this research are publicly available at [38].
Acknowledgments:
The author would like to thank Mike Partridge (EMEC) and Laibing Jia (Strath-
clyde) for their support in reviewing the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
TEC Tidal Energy Converter
ADCP Acoustic Doppler Current Profiler
PPA Power Performance Assessment
AEP Annual Energy Production
EMEC European Marine Energy Centre
FoW Fall of Warness
ReDAPT Reliable Data Acquisition Platform for Tidal
DE Equivalent Diameter
QC Quality Control
PWRA Power Weighted Rotor Average
RU Ramp Up
WD Wane Down
PF Peak Flow
IEC International Electrotechnical Commission
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