Some Renewable Energy Calculations
*Article Revised June 2010*
How many renewable energy facilities covering how much area are required
to meet the electrical energy demand of the United States? The following
will identify some critical issues along with a possible solution, while
demonstrating that renewable energy resource installations could be
available to meet the required demand, should sufficient will be exerted
to actually install.
One of the major dilemmas facing the widespread implementation of
renewable energy resources is resolution of how to distribute the newly
installed resources. The existing grid is predicated on the use of very
large centralized generation sources, e.g., dams, power plants; while
most renewable energy, e.g., photovoltaic, wind, is very conducive for
distributed generation.
The existing very large generators are large in the sense of the amount
of power they produce per unit area. Renewable sources require much more
land area for a comparable power production. A major benefit of this
conundrum could be the installation of a large number of small
generation sources at existing sites, e.g., houses, businesses, ranches,
farms with no requirements to install additional distribution capacity.
The downside is how to plan for the transfer of energy from where
generated to where needed when the renewable energy generators are not
firm, i.e., the amount generated is neither constant nor predictable.
This is exacerbated by the financial consideration that nonrenewable
generators are generally most efficient and cost effective when operated
at full capacity.
A model for solving the problem or more accurately, debugging the
solution, is to initiate the widespread use of renewable energy
generation in rural areas. Although eventually the largest market will
be in urban areas, virtually all problems could be resolved on a small
scale by implementation in rural areas first. Rural areas have a small
fraction of the total population; however, this fraction is highly
independent and well skilled in solving problems. Unfortunately, this is
also the segment of the population that has the least disposable income
to invest in anything, much less energy with a long term payback. Thus,
some sort of cash flow assistance will be required, noting tax credits
are of little benefit to those whose income is not sufficient to pay
much in taxes.
In order to understand the magnitude of the task, one must consider how
much electrical energy is going to be required to be converted from
nonrenewable to renewable sources. The United States consumes ~ 4.1
trillion-kWh per year (4.1x1012 kWh/year), note this does not include
fossil fuel energy consumption for transportation, heating, and other
uses. Since a significant fraction is required for industrial use, which
requires large concentrated sources, e.g., existing power plant dams
will still be operational for 100 or more years depending on location,
one could then reasonably expect the want to generate ~ 3 trillion-kWh
per year with renewable sources.
There are 5 primary sources of renewable energy generators in operation
today; four sources can be used for large commercial (e.g., utility
scale, light industry, or towns) generation and three sources that are
primarily for residential use. Depending on size of the installation,
two of the sources can be in either category.
* Geothermal, usually available in ~ 5 MW increments for commercial use.
Note, geothermal is generally considered a firm source, so would be
preferred for ease of compatibility with existing distribution systems.
* Wind, usually available in 2-6 MW sources for commercial use and 1-25
kW sources for residential use.
* Photovoltaic (PV), usually available in 100-200 kW for commercial use
and 1-10 kW for residential use.
* Solar Thermal Electric using conventional generators connected to
steam turbines, usually available in 100-500 MW for utility scale
production
* Hydro, usually 1-3 kW for residential use (dammed hydro (could there
be a pun here?) is generally not considered renewable and dams are
needed for larger hydro units).
The following is a rather arbitrary assignment of expected capacities
from the various generator types, small hydro is not included for
convenience and lack of data on how many streams are available
(basically an assumption, the total production will be small compared to
the other sources):
* Geothermal, 0.5 trillion-kWh/year
* Wind, 1 trillion-kWh/year
* Photovoltaic (PV), 0.5 trillion-kWh/year
* Solar Thermal, 1 trillion-kWh/year
For geothermal, assume each 5 MW module operates 24 hours per day for
300 days per year (allowing time for maintenance and any possible
variation in steam flow). Each module then provides 36 Mega-kWh/year.
Thus, approximately 13,900 modules would be required. Note, most
geothermal locations in the USA would support the use of either larger
modules or multiple modules; therefore, the total number of needed
geothermal locations is probably less than 1,000.
For wind, assume that 0.99 trillion-kWh/year are produced by commercial
size wind generators and the rest with residential. Assume that each 5
MW wind generator operates 12 hours per day for 300 days per year
(allowing time for maintenance and variations in wind velocity and
duration). Each wind generator then provides 18 Mega-kWh/year. Thus,
approximately commercial 55,000 wind generators are needed. If each wind
generator occupies ~ 1 square mile, then ~ 55,000 square miles are
needed, noting that almost all the land near a wind generator can be
used for ranching or farming purposes. This represents a small fraction
of the land under cultivation in the western USA, where much of the wind
resources are. Also, wind generators can be place off-shore.
For residential wind generators, assume that each 15 kW windmill
operates 6 hours per day for 250 days per year (allowing for conversion
efficiency, time for maintenance, and variations in wind velocity and
duration). Each wind generator then provides 22.5 kilo-kWh/year. Thus,
approximately residential 450,000 wind generators are required, which is
significantly lower than the total number of small businesses, farms,
ranches, and rural residences in the USA. With larger residential
windmills, especially for farms and ranches, not so many windmills would
be required. A 25 to 50 kW windmill is much more appropriate for farm or
ranch use, noting some farms that use well irrigation would need several
wind generators or larger, e.g., 150-200 kW wind generators.
For residential PV, assume a module conversion efficiency of 15% from
the nominal solar radiance of 1000 W/m2. Assume a DC to AC conversion
efficiency of 85% and operation for 6 hours per day for 300 days per
year (allowing for variations for systems installed at a wide variety of
locations). Thus each m2 of solar module area will produce 230 kWh/year.
In order to generate, 0.5 trillion-kWh/year, there needs to be
~2,175,000,000 m2 of PV modules. This is about 840 square miles of solar
PV modules, smaller than most Western state counties. Assuming that the
majority, say 1,500,000,000 m2, are directly used on single family
dwellings, with the availability of 75 m2 per dwelling (still allowing
room for solar hot water heating collectors on the south facing roof),
then ~20,000,000 homes are necessary. The remaining PV generation (~
0.16 trillion-kWh/year) would come from commercial PV facilities.
Assuming a capacity of 200 kW operating 8 hours per day (use of at least
ground mount single-axis trackers) for 320 days per year (allowing for
variations for systems installed at a wide variety of locations) each
location would generate 512,000 kWh/year. There would need to be at
least 312,500 such installations, with each installation having about
1,570 m2 of PV modules and assuming an area efficiency of 10% (for
trackers and mounting) so occupying ~ 4 acres.
For solar thermal generation, assume each 100 MW of power capacity
requires 1000 acres, including all support structures. Since solar
thermal requires significant water usage for cooling (up to 1000
acre-feet/year per 100 MW), not all locations are suitable. Assuming a
500 MW plant produces 8 hours per day for 300 days per year, each
location produces 1.2 billion-kWh/year. For the 1 trillion-kWh/year,
then ~850 plants, occupying 4.25 million acres or 6,640 square miles
(the size of larger Western state counties)
All of these estimations are just that, estimations; however, the
numbers clearly show that renewable energy resources can provide the
majority of the electrical energy needs of the USA. As renewable energy
resources are installed, no new fossil fuel power plants need be built.
Eventually, all fossil fuel plants can be allowed to retire, starting
with the least efficient first. The transition cannot be smooth, since
both nonrenewable and renewable energy sources are only available in
discrete units; however, by starting with implementation in rural areas
the methods and techniques can be fully developed, which will ease large
scale implementation in urban areas.
Reference
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