Simplified & Generalised LCOE

Simplified Levelised Cost of Energy (LCOE)

The simplified LCOE by NREL uses fixed initial values related to the FOWT (CAPEX, OPEX, interest rate on debt, lifetime of the FOWT, capacity factor and number of hours the FOWT operates in a year). It is given by the following formula:

Formula

$$\text{sLCOE} \;=\; \frac{\text{CAPEX}\cdot \text{FCR} + \text{OPEX}}{8760 \cdot \text{Capacity Factor}}$$

Where FCR is the Fixed Charge Rate and is given by:

Fixed Charge Rate (FCR)

$$\text{FCR} \;=\; \frac{\text{CRF} + (1-\text{TR})\cdot \text{PVD}}{\,1-\text{TR}\,}$$

Where PVD is the depreciation rate, TR is the tax rate and CRF is the capital recovery factor which is given by:

Capital Recovery Factor (CRF)

$$\text{CRF} \;=\; \frac{i(1+i)^{t}}{(1+i)^{t}-1}$$

where i is the interest rate, and t is the operational lifetime of the FOWT.

Note that the simplified LCOE uses the initial values provided by the user, not the simulated values, and is provided for the sake of comparison with the general LCOE.

Generalised LCOE

The generalised LCOE model provides a range of possible LCOEs for the duration of the FOWT operational lifetime using simulated macroeconomic variables such as:

Inflation rate
Interest rate on debt
Equity share
OPEX
Weibull Scale and shape factors of the capacity factor

And fixed values for the following variables:

Annual CAPEX
Capacity of the FOWT
Lifetime of the FOWT
Corporate tax rate
Feed in Tariff

The generalised LCOE formula is given by:

Discounted LCOE

$$\text{LCOE} \;=\; \frac{\displaystyle\sum_{t=1}^{n} \frac{\text{CAPEX}_{t} + \text{OPEX}_{t}}{(1+\text{WACC}_{t})^{t}}} {\displaystyle\sum_{t=1}^{n} \frac{\text{Capacity factor}_{t}\cdot \text{Hrs}}{(1+\text{WACC}_{t})^{t}}} $$

Where WACC is the weighted average cost of capital and is given by:

WACC

$$\text{WACC}_{t} \;=\; \frac{ 1 \;+\; (1-\text{DF})\big((1+\text{ROE}_{t})(1+t)-1\big) \;+\; \text{DF}\big((1+r_{t})(1+\pi_{t})-1\big)(1-\text{TR}) } {1+\pi_{t}} \;-\; 1 $$ $$\text{r}_{t} \;=\; \frac{ 1 \;+\; i_{t} } {1+\pi_{t}} \;-\; 1 $$

Where DF is the debt factor, t is the inflation rate, rt is the real interest rate, TR is tax rate and ROE is return on equity and is given by:

Return on Equity (ROE)

$$\text{ROE} \;=\; \frac{\text{Net income}}{\text{shareholder equity}} \cdot (1-\text{Tax rate})$$

Net income

$$\text{Net income} \;=\; (\text{feed in tariff}\cdot \text{ Capacity factor}\cdot \text{Hr}) \;-\; \left(\text{CAPEX} \;+\; \sum_{t=1}^{\text{Life of FOWT}} \text{OPEX}_{t}\,(1+\text{WACC}_{t})^{t}\right)$$

Shareholder equity

$$\text{Shareholder equity} \;=\; \text{CAPEX} \cdot \text{Equity fraction}$$