Solar Notes and Computations
Norman Rogers
16 July 2024
This document is a companion to the short article Useless Utility Scale Solar.
The illustrative numbers used in the short article are intended to be mainstream for the cost of gas and the cost of solar farms. Numbers are often changed to round numbers to make the flow better without affecting the main conclusions.
Why estimate 12% rate of return for free market solar company and 8% for an environment with PPA’s?
The 12% Rate of return on investment for a free market solar company is a benchmark corresponding to a rate of return characteristic of typical successful companies. Once PPA’s are added much of the risk vanishes so 8%, four percentage points above 20-year treasury bonds, is a generous return.
Why we compare the marginal cost of gas against the full (LCOE) cost of solar
LCOE or levelized cost of energy is a measure often used in discussing electric power generation. If a free market electric utility is considering substituting some solar power for some natural gas generation the solar must be available for less than the saving from backing off gas generation and using less fuel. An error that is usually made is to compare LCOE for both types of generation. Instead we must compare LCOE for solar versus marginal cost of generation for gas.
The cost of fuel for natural gas we take as $20 per megawatt hour. That depends on the price of gas that we take as $3 per MMBtu (million Btu) and the efficiency of conversion to electricity that we take as 55%. One MMBtu equals 293 kilowatt hours at 100% conversion efficiency. These are values that fit in with actual experience.
The price of natural gas is volatile and underwent swings associated with the Ukraine war.
Natural Gas Pricing
The Energy Information Administration (eia) has figures on this:
U.S. Natural Gas Consumption by End Use (eia.gov)
The price by state for electric power generation can be found here:
Natural Gas Electric Power Price (eia.gov)
My estimated future price of $3 per MMBtu is for Nevada and assumes that prices will settle down once the Ukraine war is settled. Gas is much cheaper in Texas. Fundamentally the U.S. has plentiful supply transportable by pipeline.
In march 2024 the Nevada price was $2.36 per MMBtu (1000 cu ft).
Norman Rogers
16 July 2024
This document is a companion to the short article Useless Utility Scale Solar.
The illustrative numbers used in the short article are intended to be mainstream for the cost of gas and the cost of solar farms. Numbers are often changed to round numbers to make the flow better without affecting the main conclusions.
Why estimate 12% rate of return for free market solar company and 8% for an environment with PPA’s?
The 12% Rate of return on investment for a free market solar company is a benchmark corresponding to a rate of return characteristic of typical successful companies. Once PPA’s are added much of the risk vanishes so 8%, four percentage points above 20-year treasury bonds, is a generous return.
Why we compare the marginal cost of gas against the full (LCOE) cost of solar
LCOE or levelized cost of energy is a measure often used in discussing electric power generation. If a free market electric utility is considering substituting some solar power for some natural gas generation the solar must be available for less than the saving from backing off gas generation and using less fuel. An error that is usually made is to compare LCOE for both types of generation. Instead we must compare LCOE for solar versus marginal cost of generation for gas.
The cost of fuel for natural gas we take as $20 per megawatt hour. That depends on the price of gas that we take as $3 per MMBtu (million Btu) and the efficiency of conversion to electricity that we take as 55%. One MMBtu equals 293 kilowatt hours at 100% conversion efficiency. These are values that fit in with actual experience.
The price of natural gas is volatile and underwent swings associated with the Ukraine war.
Natural Gas Pricing
The Energy Information Administration (eia) has figures on this:
U.S. Natural Gas Consumption by End Use (eia.gov)
The price by state for electric power generation can be found here:
Natural Gas Electric Power Price (eia.gov)
My estimated future price of $3 per MMBtu is for Nevada and assumes that prices will settle down once the Ukraine war is settled. Gas is much cheaper in Texas. Fundamentally the U.S. has plentiful supply transportable by pipeline.
In march 2024 the Nevada price was $2.36 per MMBtu (1000 cu ft).
How the cost of solar (LCOE) is computed
I use the National Renewable Energy Laboratory Annual Technology Baseline Excel workbook (ATB), utility solar section, to estimate most input numbers. Our model solar farm costs $1.3 billion, but $1 billion is for the solar array and the other $300 million is for a battery assist that moves peak power from midday to early evening. New solar plants generally have such a battery assist in areas where solar is an important part of the mix.
The nameplate for a $1 billion solar array is taken as 750 megawatts or about $1330 per kilowatt construction cost (CapEx). I take the lifetime as 20 years and the interest rate as 12% corresponding the assumed rate of return of the free market solar company. Later I take it as 8% for the solar company with a PPA. At the end of life the residual value is assumed zero or equal to the decommissioning cost. The Excel PMT function allows computing the cost of the solar to yield the desired rate of return. The cost of the battery assist is roughly approximated adjusting figures previously computed, using figures from the Natonal Renewable Energy Laboratory for the GEMINI solar project near Las Vegas. The operating expense is roughly estimated using the ATB values with allowance for the battery assist. The overall conclusions are not sensitive to the exact LCOE.
How the cost of solar (LCOE) is computed
I use the National Renewable Energy Laboratory Annual Technology Baseline Excel workbook (ATB), utility solar section, to estimate most input numbers. Our model solar farm costs $1.3 billion, but $1 billion is for the solar array and the other $300 million is for a battery assist that moves peak power from midday to early evening. New solar plants generally have such a battery assist in areas where solar is an important part of the mix.
The nameplate for a $1 billion solar array is taken as 750 megawatts or about $1330 per kilowatt construction cost (CapEx). I take the lifetime as 20 years and the interest rate as 12% corresponding the assumed rate of return of the free market solar company. Later I take it as 8% for the solar company with a PPA. At the end of life the residual value is assumed zero or equal to the decommissioning cost. The Excel PMT function allows computing the cost of the solar to yield the desired rate of return. The cost of the battery assist is roughly approximated adjusting figures previously computed, using figures from the Natonal Renewable Energy Laboratory for the GEMINI solar project near Las Vegas. The operating expense is roughly estimated using the ATB values with allowance for the battery assist. The overall conclusions are not sensitive to the exact LCOE.