1. Marine Hydrokinetics--LCOE & Sensitivity Analysis
Alex Yu-Lin Pan & Zach Sutton-Giglia and Louis Klapper
Levelized cost of energy (LCOE), expressed in units of $/kWh, measures the value of the total energy produced by a system over its lifespan. Marine hydrokinetics LCOE models and sensitivity analysis are
developed at a reference site. We applied two different financial models to evaluate LCOE, and then applied physical parameters, cut-in and rated speeds, to determine how the annual energy production (AEP)
influenced LCOE. For resource sites lacking precise data, statistical models called Rayleigh and Weibull distributions produce velocity probability curves, based on the average velocity of the site. These curves were
generated as part of this project, and they reveal what kinds of current velocity distributions could give the lowest LCOE.
ABSTRACT
Problem Statement LCOE Calculation
The company deployed their tidal current turbines at a resource site. The speed of the
currents and the properties of the turbines can directly affect the LCOE. Therefore, we
produced various AEPs based on different current speed and turbine parameters to
potentially optimize the design for economically competitive LCOE.
𝑃𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 =
1
2
𝜌𝐴𝑣3
𝑃𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑒𝑑 =
1
2
𝜌𝐴𝑣3
𝐶 𝑝 𝐶𝑔
𝜌: 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟
𝐶 𝑝: 𝑟𝑜𝑡𝑜𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐶𝑔: 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝑣: 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
The rated speed is the speed at which a turbine generates its maximum, or rated, power.
The cut-in speed is the velocity at which a turbine starts generating power. Rated speed
and cut-in speed both reduce the energy collected by a turbine.
We calculated LCOE by following two models:
(1) Sandia Model 𝐿𝐶𝑂𝐸 =
𝐶𝑎𝑝𝐸𝑥∗𝐹𝐶𝑅+𝑂𝑝𝐸𝑥
𝐴𝐸𝑃
= $0.104/kWh
(2) NPV Model 𝐿𝐶𝑂𝐸 =
𝑁𝑃𝑉
𝐴𝐸𝑃×𝑙𝑖𝑓𝑒𝑡𝑖𝑚𝑒
= $0.074/kWh
Key Results
Figure 1 above demonstrates the necessary reduction in cost for the
LCOE to remain constant, when cut-in speeds and rated speeds are
considered.
Figure 2 above shows the percentage change of LCOE when the cost is held
constant.
Figure 3 above plots the velocity distribution for the reference
site (black) and statistical distributions generated by Rayleigh
and Weibull functions.
Figure 4 shows the LCOEs corresponding to the velocity distributions from Figure 3.
The Weibull distribution 1 apparently has the highest LCOE due to the low current speed
dominating the probabilities.
Conclusions and Implications
1. LCOE is a useful metric to assess the economic viability of a marine hydrokinetic system at a given location, The Sandia model of LCOE seeks to standardize this type of economic analysis across the industry.
2. For both percentage change of LCOE and costs, either increasing the cut-in speed or decreasing rated speed will lower the AEP. The data we obtained from Figures 1 and 2 show that a very significant cost reduction (15.41% for rated speed = 1.5 and cut-in =
0.7) would have to occur to maintain the a constant LCOE. They also reveal the importance of matching the cut-in and rated speed of the turbines to the resource, in order to achieve economic viability.
3. At sites where a precise current velocity distribution is uncertain, a Rayleigh or Weibull distribution provides velocity curves. Such analyses gives an initial assessment of a resource. Since the AEP is related to the cube of velocity (v3), the ability of capturing
higher velocities are more than offset by increasing the cut-in speed in a strategy to reduce capital and maintenance costs..
Acknowledgements:
Kathie Leighton, Jeff Glick, John Ashbourne
FCR =
1 + 𝑑 𝑛
1 + 𝑑 𝑛 − 1
×
1 − 𝑇 × 𝑃𝑉𝑑𝑒𝑝
1 − 𝑇
d = discount rate %
n = operational life year
PVdep = present value of depreciation %
T = effective tax rate (%)
Inadequate
Match of Actual
Data with
Modeled Curves