Hydrokinetic Tidal Energy Resource
H = a0+ ∑N
i = 1
aicosðσit +δiÞ ð1Þ
where H is the tidal water level, a0 is the vertical offset, and ai,σi,δi are the amplitude, angular frequency, and phase angle of the ith tidal constituents, respectively. The constituent frequencies range over different timescales (hours, months, years); but once the constituent amplitudes and phases are determined for a particular location, the tides are easy to predict. The spatial variability in the water level generates pressure gradients which drive tidal currents, often magnified in locations with flow constrictions such as inlets. A similar procedure can be followed for computing the tidal current constituents using complex amplitudes representing the vector components of the velocity from long-term-recorded time series. This predictability of the tides makes it attractive relative to other renewables which suffer from intermittency with low predictability of capacity such as wind and solar (Naksrisuk and Audomvongseree 2013). However, there are limits to the pre-dictability of tidal power; atmospheric forcing may modify the currents, although large disturbances are typically rare and will only occasionally result in major modifications to the currents (Adcock et al. 2015). Of more concern is the obser-vations that harmonic analysis has limitations for predicting strong tidal currents (e.g., Polagye et al.2010and Stock-Williams et al.2013).
There are generally two different approaches for capturing tidal energy: either extracting the (1) potential or (2) kinetic energy. Capturing the potential energy is similar to classical hydropower where a barrier, also known as a tidal barrage, is constructed across an estuary. Alternatively, kinetic energy may be extracted from the tidal currents using hydrokinetic turbines, conceptually analogous to wind energy. Hydrokinetic turbines have some advantages over other forms of renewable energy as suggested by Yuce and Muratoglu (2015). Hydrokinetic turbines do not require water impoundment and therefore do not include the significant costs associated with the construction of dams. They are significantly smaller in scale than tidal barrages, requiring much smaller capital expenditures. They are typically deployed in arrays with many individual units much like wind farms, increasing system redundancy and resilience.
As with other forms of energy, resource assessments are necessary to determine the feasibility of hydrokinetic tidal energy for a particular region, to help with the project layout design and to ultimately provide the projected annual energy pro-duction (AEP). The methods for performing the resource assessments depend on both the desired scope (feasibility or design) as well as the project scale. To help clarify the types of resource assessments, the International Electrotechnical Com-mission (IEC) has defined a conceptual framework for assessing marine hydroki-netic resources (IEC 2013) which the United States Department of Energy has adopted (The National Research Council2013). The overall assessment process is considered in three stages: theoretical, technical, and practical. The theoretical resource consists of the hydrokinetic energy available for conversion without consideration of any turbine properties. In essence, this is the power within the
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undisturbed flowfield. The technical resource is the amount of power that can be generated considering the particular technology to be utilized. This resource assessment will incorporate turbine efficiencies and interactions with the flow field and will be a fraction of the theoretical resource. Finally, the practical resource includes the additional constraints of turbine operation such as regulatory, envi-ronmental, economic, and life cycle constraints.
Performing a hydrokinetic tidal energy resource assessment requires an accurate determination of the tidal water levels and currents. While high-quality tidal ele-vation predictions are readily available, accurate tidal current predictions based on recorded data are scarce. Furthermore, proposed project sites may have spatially varying hydrodynamics and constituents; costly hydrodynamic measurements in a single location may not be adequate to assess the full hydrokinetic resource. In addition, arrays of devices will induce further complexity to existing hydrody-namics and alter the tidal constituents and the available energy resource, thereby restricting the use of direct observations of tidal currents for use in resource assessments. Therefore, due to the deterministic nature of tidal flows, numerical modeling of hydrodynamics with and without hydrokinetic tidal energy extraction provides a description of a site’s resource resolved in both space and time.
The focus of this chapter is on performing numerical modeling resource assessments for in-stream tidal hydrokinetic turbine projects. Within this chapter, the following sections explain the different methodologies for using numerical models to determine the tidal energy resource at various stages and scales, begin-ning at the scale of an individual turbine, followed by feasibility assessments and ending with thefinal project assessment. The chapter concludes with examples of employing these methodologies as a case study.
Individual Turbine Assessments
To identify the resource available for an individual device, the theoretical power density in a free stream, Pt, is readily computed as a cube of the free stream velocity
Pt=1
2ρV3 ð2Þ
whereρ is the density of the fluid and V is the current speed. This equation can be modified to incorporate the efficiency of a turbine in producing electricity by adding the power coefficient Cp
Pd=1
2CpρV3 ð3Þ
where Pd is the technical power density. Sometimes, Cp is referred to as the per-formance coefficient and represents the mechanical shaft power rather than the Hydrokinetic Tidal Energy Resource Assessments Using Numerical… 101
actual electrical power output efficiency. An upper efficiency bound for turbines in an unconstrained flow can be derived using actuator disk theory. The upper limit is formally referred as the Lanchester–Betz–Joukowsky limit; however, it is most frequently called the Betz limit (Betz 1920; Lanchester1915; Juokowsky 1920).
The theoretical limit was derived by applying conservation of mass, momentum, and energy for the volume of the flow passing through the turbine. The maximum power coefficient was determined to be 16/27 or 59.3%. This analysis was per-formed for wind turbines; however, it is generally accepted to apply for tidal energy, provided the turbine swept area is small relative to the channel depth and width (Blunden and Bahaj2007).
The actual power output for a particular device must take into account several additional properties of the turbine. For horizontal axis turbines, the incoming current speed V needs to be the component of the velocity normal to the extraction plane whereas for the vertical axis turbines this is not an issue. In addition, neglecting turbulence is generally not significant if deploying near the free surface and away from any boundary layers and wake turbulence generated from upstream turbines or in-stream structures, e.g., bridge piers, as shown by Neary et al. (2013).
However, if turbulence intensities are at or exceed 20%, power is underestimated by over 10%. This is the case at the RITE site at hub height for currents just above cut-in speed at 1 m/s; turbulence intensities were about 23% (Gunawan et al.2014).
In this case, not accounting for turbulence in the power equation could result in significant underestimation of AEP.
In addition to representing the turbine efficiencies, the power coefficient Cpalso incorporates a minimum cut-in speed below which the turbine does not operate and a rated speed at which the turbine does not generate more power for higher current velocities. The power coefficient may be determined empirically using the method outlined by the IEC technical specification (TS) (IEC 2014). This specification provides a standardized methodology for measuring the incoming-free stream velocity along with the electrical power output of the turbine to be used for com-puting the power coefficient. Optimal efficiencies of tidal energy converters are generally lower than the Betz limit and are reported to be typically between 16 and 50% (Gorban et al.2001and Ben Elghali et al.2007). However, the Betz limit no longer applies and may be exceeded under conditions with constrained flow or when using turbines with ducted intakes (e.g., Lawn2003).
The actual power output for the turbine (P) is found by multiplying the power density by the swept area of the turbine, As
P =1
2CpρV3As. ð4Þ
The turbine AEP is essentially the time integral of the power production of turbine over a year. However, the predicted AEP is generally computed based on the annual probability distribution of the current velocities in conjunction with the power curve. The probability distributions are derived using data from either model
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simulations or long-term observations directly at the turbine location. The AEP is computed according to the following equation:
AEP = Nh ∑NB
i = 1
Pið Þ ⋅ fVi ið ÞVi ð5Þ
where AEP is the expected annual power production in kWh, Nhis the number of hours for the year, NBis the total number of velocity bins in the device power curve, Pið Þ is the power in kW generated by the ith velocity bin, UVi iis the mean current velocity in m/s of the ith bin, and fið Þ is the probability ith bin of the annualVi
velocity probability distribution.
The AEP is a good aggregate measure of annual power production at a given site; however, it does not provide an adequate description of the power production on shorter timescales, particularly the degree of intermittency needed for full-fledged project design. For example, tidal flows at energetic sites which are dominated by the semidiurnal M2constituent will fluctuate with a primary period slightly greater than 12 h, leading to low velocities and hence no power generation during slack water times, about every 6 h. This leads to a substantial quarter-diurnal variation in the theoretical power as well as the turbine efficiency and thus technical turbine power output (Adcock et al.2014).
Significant variability can also occur over the timescale of an individual tidal cycle. As an example, the tidal distortion, which is the inequality of the ebb to flood tide generated by different harmonic constituents or geometric features (Bruder et al. 2014), can lead to significant differences of the power produced by the turbines and again is dependent on the turbine characteristics (Bruder and Haas 2014). In particular, the tidal distortion is quantified by skewness, the degree of symmetry about the horizontal axis, taking into account the relative broadness and magnitudes of the peaks of flood and ebb currents and the asymmetry which is the degree of symmetry about the vertical axis, the relative duration of periods of increasing and decreasing velocity magnitudes. The degree of skewness and asymmetry is highly dependent on the relative phase between the M2 and M4 constituents. Bruder and Haas (2014) found that while the theoretical available power for a signal with or without distortion is similar, the technical power had up to 15% variations depending on the turbine properties. For highly skewed time series, because peak flood and ebb velocities will be very different, it is important to have a broad operating range for the turbine whereas this is less important for asymmetric time series.
For locations where the lunar and solar semi-diurnal constituents (M2and S2) are significant, the superposition of these two constituents leads to a beating of the tidal signal producing a roughly two-week cycle of large (spring) and small (neap) tides (Adcock et al.2015). This causes a significant variability in the power output of tidal turbines over the spring/neap cycle (Adcock and Draper2014).
Generally speaking, any location will have multiple tidal constituents with significant energy and thereby will have some sort of beating, distortion, or diurnal Hydrokinetic Tidal Energy Resource Assessments Using Numerical… 103
inequalities leading to tidal power variability. Clearly, a full and accurate charac-terization of the tidal energy resource, including resolution of the intermittency of the power, requires an accurate determination of all the relevant tidal constituents, the amplitudes, and phases. The IEC technical specification for tidal energy re-source assessments (IEC2015) recommends resolving at least the 20 largest con-stituents. Finally, to maximize the ultimate technical power produced by an individual turbine requires a good understanding of the relationship with the the-oretical power through the turbine power coefficient and how this depends on the tidal characteristics such as tidal distortion.