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Calculations

Levelized Cost of Energy

The equation for LCOE used is:

where CapEx is capital expenditure in $/W, capacity is the installed capacity of the wind or solar project, FCR is the fixed capital charge, OpEx is the operational expenditure of the project in $/W and Annual Energy Production is the amount of power generated by the project in a given year. A breakdown of how each of these components is calculated is given below.

Annual Energy Production

Solar

The calculation of solar panel power output follows the methodology of the Renewables Ninja software package, as described in (Pfenninger & Staffell, 2016).

The primary source of data for this calculation is a satellite reanalysis known as MEERA-2, provided by NASA. This dataset was chosen because it has global coverage and is from a robust source. An alternative dataset is SARAH-2 produced by the ESA, although this dataset only covers Europe and Africa.

For solar projects, the three key variables of interest are the incoming direct normal irradiance (GDN), the surface direct normal irradiance (TDN) and air temperature (T). These parameters can be downloaded from the MEERA-2 dataset with global coverage and at hourly resolution. The grid provided by MEERA-2 has a resolution of approximately 50km in the latitudinal and longitudinal directions, which is then linearly interpolated to the location of a given project.

For a given project location, a parameter known as the clearness index is calculated, which is the fraction of direct normal irradiance to surface normal irradiance. This parameter is then used to calculate what is known as the diffuse fraction, using the Boland-Ridley-Lauret (BRL) model.

This diffuse fraction is then used alongside geometry calculations and a solar panel efficiency model to calculate power output on an hourly basis, for whatever time span of satellite data is required These hourly power readings can then be summed over a year to generate an Annual Energy Production figure.

Wind

The calculation of wind power output follows the methodology of the Renewables Ninja software package, as described in (Pfenninger & Staffell, 2016).

For wind power calculations, the raw data is again the MEERA-2 database provided by NASA. For the wind calculation, the parameters downloaded are the wind speed in the two orthogonal directions at heights of 2m, 10m and 50m and the zero plane displacement height. Again, these parameters can be downloaded from the MEERA-2 dataset with global coverage and at hourly resolution. The grid provided by MEERA-2 has a resolution of approximately 50km in the latitudinal and longitudinal directions, which is then linearly interpolated to the location of a given project.

For each height (2m, 10m and 50m) the wind speed in the northward and eastward directions is resolved into a total wind speed vector. These values are then used to generate a logarithmic wind profile at that location, which allows interpolation of the wind speed at an arbitrary height. Knowledge of the wind turbine power curve and hub height then allows the wind turbine power output to be calculated. The final stage is to apply a country-wide bias correction factor, as outlined in Staffell & Pfenninger (2016).

Capital Expenditure

Solar

The capital expenditure is the upfront cost of developing a project and is typically calculated using a bottom-up model. The bottom-up model used in this analysis assumes a ground-mounted utility scale project in the capacity range 1MW – 100MW. It assumes that individual solar panels in the assembly have a nominal power output of 250W and are rack mounted with no axis tracking.

For convenience, the capital cost of a project is broken down into the following categories:

Tabs

Module cost

Module costs is a significant component in capital expenditure for solar projects and is a component with significant price volatility. In order to get up-to-date module costs, module prices are read from the website of the solar panel supplied ENFSolar. Three distinct panel types (monocrystalline, polycrystalline and PERC) are identified and the average cost across 100 panels is calculated. To avoid extreme cases, outliers are removed using a z-score outlier detection mechanism. It is assumed, for this initial case, that solar panel module costs are independent of location, since the overwhelming majority of panels are produced in China and transport costs are assumed a negligible component of overall cost.

Balance of system cost

(inverter, cabling etc)

The term ‘balance of system’ describes the electrical and mechanical equipment required for the solar project, excluding the solar modules. It includes for example, the inverters for conversion from DC to AC, the electrical wiring required to connect all equipment and the electrical substation. For this model, it is assumed that each inverter in the installation has a capacity in the range 50kW. The cost of the wiring is calculated from an assumed panel peak Watt rating of 250W and a cost of $15 wiring per panel, including stringers. Costs associated with ‘other electrical’ include combiner boxes, monitoring equipment, and grounding and disconnects. The mounting hardware consists of the racking required to support the solar panels and costs are calculated from example utility-scale racking prices on the market. Costs for wiring and other electrical are taken from the most recent NREL report on solar cost benchmarks.

Equipment Type Unit Cost / Unit Source
Inverter 500 kW 0.07 USD / Wp ENF Solar
Wiring 0.10 USD / Wp NREL Report
Other Electrical 0.07 USD / Wp NREL Report
Mounting Hardware 0.23 USD / Wp ENF Solar
Equipment Type Inverter
Unit 500 kW
Cost / Unit 0.07 USD / Wp
Source ENF Solar
   
Equipment Type Wiring
Cost / Unit 0.10 USD / Wp
Source NREL Report
   
Equipment Type Other Electrical
Cost / Unit 0.07 USD / Wp
Source NREL Report
   
Equipment Type Mounting Hardware
Cost / Unit 0.23 USD / Wp
Source ENF Solar

Labour cost

For the calculation of labour rates, major installation tasks are assigned a time per hour of skilled or unskilled labour, based on figures reported in the NREL costings report. The skilled labour category includes trades such as electricians, whilst the unskilled labour rate includes construction and groundworks staff. An approximate time is allocated to installation of each component (such as modules and inverters) and then a standard US labour rate of 40 $/hr for skilled staff and 25 $/hr for unskilled staff is assumed. An approximate cost per watt for labour can then be calculated. For projects in countries other than the US, the hourly labour rate is adjusted using OECD data, which is read using an API call.

Equipment Type Installation time (hrd/ unit) Source
Skilled Unskilled
Module 0.45 0 NREL Report
Inverter 40 8 NREL Report
Wiring 0.1 0 NREL Report
Other Electrical 0.2 0 NREL Report
Mounting Hardware 0 0.3 NREL Report
Equipment Type Module
Installation time (hrd/ unit)  
Skilled 0.45
Unskilled 0
Source NREL Report
   
Equipment Type Inverter
Installation time (hrd/ unit)  
Skilled 40
Unskilled 8
Source NREL Report
   
Equipment Type Wiring
Installation time (hrd/ unit)  
Skilled 0.1
Unskilled 0
Source NREL Report
   
Equipment Type Other Electrical
Installation time (hrd/ unit)  
Skilled 0.2
Unskilled 0
Source NREL Report
   
Equipment Type Mounting Hardware
Installation time (hrd/ unit)  
Skilled 0
Unskilled 0.3
Source NREL Report

Engineering cost

The engineering cost of a solar project is the work associated with the system design, the substation and the interconnection with the main electricity grid. These project costs are estimated from the NREL cost benchmarking report, although it is hoped that a more accurate grid interconnection cost could be calculated from open-data models of transmission networks.

Cost Type Value / Unit Source
System design 0.02 NREL
Site development / infrastructure 0.04 NREL
Substation 0.02 NREL
Interconnection 0.05 NREL
Cost Type System design
Value / Unit 0.02
Source NREL
   
Cost Type Site development / infrastructure
Value / Unit 0.04
Source NREL
   
Cost Type Substation
Value / Unit 0.02
Source NREL
   
Cost Type Interconnection
Value / Unit 0.05
Source NREL

Developer cost

The final component of capital cost is the developer cost, which includes costings for permitting, developer profit, financing cost and contingency. Typical values for a solar project are taken from the NREL costings report, and are not currently adjusted for location.

Cost Type Value / Unit Source
Permitting 0.07 NREL
Developer profit 0.03 NREL
Financing cost 0.05 NREL
Contingency 0.02 NREL
Cost Type Permitting
Value / Unit 0.07
Source NREL
   
Cost Type Developer profit
Value / Unit 0.03
Source NREL
   
Cost Type Financing cost
Value / Unit 0.05
Source NREL
   
Cost Type Contingency
Value / Unit 0.02
Source NREL

Adjusting cost for project capacity

In our analysis of costs, some account is made of economies of scale for certain project components. At this level of analysis, it is assumed that there are no economies of scale for module cost or balance of system costs. A correction factor is however applied to account for economies of scale in labour rates, developer cost and engineering cost.

These cost components are assumed to follow a logarithmic profile in the range 1MW – 100MW, the parameters of which are calculated through curve fitting to existing cost data. This cost data, to which a curve is fitted, is taken from the NREL cost report.

This breakdown in the data was chosen because it broadly follows the cost breakdown presented in the NREL report: U.S. Solar Photovoltaic System Cost Benchmark, a leading costings analysis for the solar industry. The following sections describe how each of these costs are calculated.

Capital Expenditure

Wind

The calculation of capital expenditure for wind projects follows a similar methodology as the calculation for solar projects. Overall project costs are broken down into four categories, a common approach in other bottom-up costing methodologies for wind, such as the NREL 2017 Cost of Wind Energy Review. These categories are:

Tabs

Turbine cost

The cost of various turbine components is difficult to estimate accurately, as there is wide variation between suppliers and most manufacturers do not publish costs. Where possible, costs for a specific turbine are scraped from open sources such as online turbine marketplaces. If such costings are not available directly, the NREL model for turbine cost is adopted. Cost breakdown for an example turbine is given below for the case where direct costs are not available from the supplier.

Equipment Type Cost / Unit ($/Wp) Source
Rotor Blades 0.292 NREL
Hub 0.05 NREL
Pitch Mechanism 0.05 NREL
Drivetrain Gearbox 0.144 NREL
Electronics 0.108 NREL
Generator 0.09 NREL
Mainframe 0.126 NREL
Other 0.420 NREL
Tower Tower 0.300 NREL
Rotor  
Equipment Type Blades
Cost / Unit ($/Wp) 0.292
Source NREL
   
Rotor  
Equipment Type Hub
Value / Unit 0.05
Source NREL
   
Rotor  
Equipment Type Pitch Mechanism
Value / Unit 0.05
Source NREL
   
Drivetrain  
Equipment Type Gearbox
Value / Unit 0.144
Source NREL
   
Drivetrain  
Equipment Type Electronics
Value / Unit 0.108
Source NREL
   
Drivetrain  
Equipment Type Generator
Value / Unit 0.09
Source NREL
   
Drivetrain  
Equipment Type Mainframe
Value / Unit 0.126
Source NREL
   
Drivetrain  
Equipment Type Other
Value / Unit 0.420
Source NREL
   
Tower  
Equipment Type Tower
Value / Unit 0.300
Source NREL

Labour cost

Labour cost is a small component of wind turbine capital expenditure and is fixed at 0.05 $/W for this model.

Engineering cost

The engineering cost element for a wind turbine project relates to ground works and installation costs. At present, a model is being developed for interconnection costs and substation costs. For the time being, these costs are taken from the estimates given in NREL 2017 Cost of Wind Energy Review.

Equipment Type Cost / Unit ($/Wp) Source
Installation Transportation 0.06 NREL
Access Road 0.04 NREL
Foundations 0.06 NREL
Erection 0.06 NREL
Electrical material 0.07 NREL
Electrical installation 0.03 NREL
Interconnection 0.02 NREL
Substation 0.02 NREL
Installation  
Equipment Type Transportation
Cost / Unit ($/Wp) 0.06
Source NREL
   
Installation  
Equipment Type Access Road
Cost / Unit ($/Wp) 0.04
Source NREL
   
Installation  
Equipment Type Foundations
Cost / Unit ($/Wp) 0.06
Source NREL
   
Installation  
Equipment Type Erection
Cost / Unit ($/Wp) 0.06
Source NREL
   
Installation  
Equipment Type Electrical material
Cost / Unit ($/Wp) 0.07
Source NREL
   
Installation  
Equipment Type Electrical installation
Cost / Unit ($/Wp) 0.03
Source NREL
   
Installation  
Equipment Type Interconnection
Cost / Unit ($/Wp) 0.02
Source NREL
   
Installation  
Equipment Type Substation
Cost / Unit ($/Wp) 0.02
Source NREL

Developer cost

The final component of capital cost is the developer cost, which includes costings for permitting, developer profit, financing cost and contingency. Typical values for a wind project are taken from the NREL costings report.

Cost Type Value / Unit Source
Permitting 0.07 NREL
Developer profit 0.03 NREL
Financing cost 0.05 NREL
Contingency 0.02 NREL
Cost Type Permitting
Value / Unit 0.07
Source NREL
   
Cost Type Developer profit
Value / Unit 0.03
Source NREL
   
Cost Type Financing cost
Value / Unit 0.05
Source NREL
   
Cost Type Contingency
Value / Unit 0.02
Source NREL

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