POWER June 2011 - 63

PLANT ECONOMICS
years to come. Consequently, an overhaul
of the standard COE formula is needed to
determine the value added by improved operational
flexibility, such as better part-load
efficiency and faster starts.
Cyclical Operation
Typical daily operation of a " two-cycled "
CC plant is shown in Figure 1. The plant
is operated five days a week year-round or
perhaps only during the summer months.
In this example, every Friday, the plant is
shut down at 10 p.m. for the weekend and
is restarted the following Monday at 5 a.m.
Twice a year, the plant is shut down for
one week to carry out scheduled maintenance
tasks. Thus, the annual plant start
schedule comprises 250 starts (two cold,
48 warm, and 200 hot starts).
Ignoring the time spent during start-up
(the added generation is estimated later)
and the seasonal ambient variation, the
plant is expected or planned to operate
(H) 4,250 hours per year with a service
factor (SF) of 4,250 / 8,760 = 48.5%. At
a nominal 500 MW baseload power, the
total annual energy production (E) can be
calculated as 1,700,000 MWh for a capacity
factor (CF) found as 1,700,000 / (500
x 8,760) = 38.8%. Similarly, the load factor
(LF) is calculated as 1,700,000 / (500 x
4,250) = 80%, or nearly twice the CF.
Power generation during start-ups can
be estimated via simple integration (see the
shaded area in Figure 1 for a hot start) based
on applicable start-up curves provided by
the manufacturer. Using the load profile in
Figure 1 and typical start-up curves, an additional
29,400 MWh per year of start-up
electric generation is estimated.
Load ramps can be found in a similar
fashion to contribute another 5,200 MWh,
assuming a rate of 10% per minute. Adding
these two unsteady-state generation
quantities to the nominal generation of
1,700,000 MWh calculated above, you
find the effective total generation (Eeff
) is
1,734,600 MWh. Total or effective operating
hours (Heff
= 4,250 + 200 x 1 + 48 x 2
) are higher than the nominal
operating hours, H, by the total time
spent during plant starts (shutdowns are
ignored), or Heff
+ 2 x 3 = 4,552 hours. This corresponds to
an effective plant output (Peff
) of 1,734,600
/ 4,552 = 381 MW. Thus, the correction
due to the dynamic effects of start-up results
in an effective load factor (LFeff
) of
381 / 500 = 76.2%.
Note how accounting for the energy
generated during start-ups reduced the
load factor by about four percentage
points when the additional operating
hours at low loads are included. This fact
June 2011 | POWER
hints at a key advantage of fast-start plants
that spend less time at low loads: the LFeff
and heff
are higher, resulting in a favorable
(lower) COE.
Average cycling plant load factors of
75% to 80% and the adverse impact of the
time spent during plant starts (200 or even
more per year for such units) suggest that
an improvement could be made to the basic
COE equation to account for plant cycling
effects. In addition to accounting for the
The reliability of these turbines can be taken
into account by multiplying the total energy
generation with an assumed reliability factor
(R) of 99% (the complement of the forced
outage rate).
Continuing with the example above, R x
Eeff = 99% x 1,734,600 MWh = 1,717,250
MWh. The expected reduction in the unit
service hours due to a less-than-perfect
reliability is thus reflected in a reduction
of the unit's total energy generation and,
An overhaul of the standard COE formula
is needed to determine the value added by
improved operational flexibility.
load factor variation just discussed, many
other key plant operability considerations
could be included in the COE formula. The
following four key factors, when added to
the basic COE equation, will produce a
more accurate evaluation of real CC plant
operation:
■ Seasonal temperature variation
■ Nonrecoverable performance degradation
■ Reliability (forced outage rate)
■ System (dispatch) considerations
The first two factors can be readily accounted
for by calculating a corrected base
performance. Ambient correction factors
can be found from OEM-supplied curves
using an appropriate annual load-weighted
average temperature, which can be directly
calculated using a seasonal temperature
variation chart. (For most moderate climates,
the deviation from the ISO value is
less than ~5F.)
Average or mean-effective values of
output and efficiency degradation factors
can also be easily found from supplier-provided
curves. Both corrections
are multiplicative and less than unity in
magnitude (unless the plant is located in
an extremely cold site), so the net overall
impact is higher COE via lower effective
values of power output, energy production,
and load factor.
The availability of CC power plants based
on advanced combustion turbines is normally
quite high: usually above 90% and often
above 95%, especially for F-Class units operated
in large fleets, even in cycling service.
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consequently, the load factor. The reduction
in the latter will manifest itself in
lower effective plant efficiency and, as
will be shown below, in higher costs associated
with capacity and energy replacement.
Even a small reduction in reliability
(worth ~17,350 MWh for 1 percentage
point in this example) can easily negate a
perceived advantage in rated performance
or operational flexibility.
A New Formula
These system interactions suggest a modified
and expanded COE formula that tailors
the original formula, adds emission
costs, and adds system impact costs such
as capacity and energy replacement during
outages.
At this time, there is no industry-wide
accepted method to convert specific plant
emissions (that is, pounds of pollutants
such as NOx
, SOx, CO2, unburned hydrocarbon,
particulate matter, and so on per
generated MWh) into cost. Nevertheless,
emission costs (or penalties) can be added
to the COE via a term comprising two new
parameters: ci
terms of $/ton) and mp,i
(price/cost of pollutant i in
(plant generation of
pollutant i in tons/kWh). These terms can
also be used to represent a cost of emissions
during start-up. Although they are
not a concern at baseload, CO emissions
can be a problem when the unit is turned
down, especially during plant starts when
the unit spends a considerable amount of
time at low loads.
The last new term added, system impact,
accounts for the variation in effective
63
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POWER June 2011

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