Page 403 - A Comprehensive Guide to Solar Energy Systems

412 A COmpREHENSIvE GUIDE TO SOLAR ENERGy SySTEmS

While it may seem straightforward to decide what the boundaries of a specific calcula­
tion should be, in terms of the protocol for all EROI analysis, it is quite difficult. At some
point the question becomes less scientific and more an issue of philosophy. The literature
on EROI analysis has yet to reconcile the issue of differing perspectives on boundaries of
analysis. According to Hall [8], for now, the general method in dealing with this uncertainty
in methods is through sensitivity analysis—report the results for systems using different
assumptions about the data or philosophy and leave the final choice with the reader.

21.2.2 Energy Payback Times
As it is a renewable resource, EROI for pv is not calculated using the same method as for
finite resources. In general, the energy cost for renewables is a very large capital cost per
unit output, especially given backup systems such as batteries. As a result the input for
the EROI equation is mostly upfront, while returns are realized throughout the lifetime of
the system. Historically, there are very few attempts at studies that perform “bottom­up”
analysis. Alternatively, we can calculate EROI by dividing the lifetime (T life(yr) ) of a system
by its “Energy pay Back Time,” (EpBT (yr) ).

EROI=Tlife(yr)/EpBT(yr) EROI = T life(yr) /EPBT (yr) (21.2)
EpBT is the time it takes for the system to generate the amount of energy equivalent to the
primary energy or kWh equivalent that was used to produce the system itself. pv EpBT
can vary depending on the technology, location of production and installation, material
requirements, and operating efficiency. Factors that can lower the EpBT include lower ore
grades of rare metals used in production caused by depletion or competing industries
(Chapter 25), lower than projected lifetimes and efficiencies, problems with energy stor­
age, and intermittence. The following is an example of a common EpBT calculation [20]:

=
EpBT=(Emat+Emanu+Etrans+Eins EPBT ( E mat + E manu + E trans + E inst + E eol )/( E agen − E aoper ) (21.3)
t+Eeol)/(Eagen−Eaoper)
where E mat is the primary energy demand to produce materials for the system; E manu is the
primary energy demand to manufacture the system; E trans is the primary energy demand
to transport materials used during the lifecycle; E inst is the primary energy demand to in­
stall the system; E eol is the primary energy demand for end­of­life management; E agen is
the annual electricity generation in primary energy terms; and E aoper is the annual energy
demand for operation and maintenance in primary energy terms. The annual electricity
generation (E agen ) is defined as primary energy based on the efficiency of electricity trans­
formation on the demand side.
Eq. (21.3) employs a method and boundaries derived from the LCA of a given system.
Raugei et al. [21,22] and Hall [8] summarized the differences and similarities between this
method and others, discussed in the following section, stressing the importance of bound­
aries and physical definitions. variables that affect the energy cost of pv systems include
cell material, encapsulation matter, cell production process, capital equipment, frames,