POWER June 2013 - 63

PLANT ECONOMICS
The More Rigorous Approach
Even after separating plant output and heat
consumption effects to arrive at the intrinsic
value of heat rate/efficiency improvements,
there are still some deficiencies in
the evaluation. The traditional LCOE forTable
1. Parameters used in expanded
COE formula. Data is partially
taken from Table 1, " A More Useful Way of
Calculating the Cost of Electricity, " June 2011.
Source: Bechtel
Parameter
Capacity factor
Load factor
Effective hours/year
Effective energy generation
Mean-effective output
Mean-effective efficiency
Specific price
Fixed O&M
Variable O&M
Capacity replacement cost
CO2 emissions
Reliability
Maintenance factor
Lifetime average output degradation
Lifetime average efficiency degradation
Value
51.60%
76.30%
6,302
2,270,000 MWh
360 MW
53.70%
$895/kW
$15/kW
3.5 mils/kWh
$50/kW-yr
$15/ton
99%
2.5
4%
2%
mula does not account for many factors
that affect field performance, operability,
maintenance, and cost of generation over
the economic life of the CC power plant,
as was discussed in the June 2011 POWER
article. Other factors of interest include annual
site ambient and load variation, startstop
cycles, unrecoverable degradation,
maintenance factors, reliability, emissions,
and replacement costs (capacity and energy).
A revised and expanded formula to
account for all these factors was proposed
in that article.
Although the new formula introduced
in the earlier article is reasonably compact
and easy to implement in a spreadsheet for
rigorous evaluation of a cycling CC power
plant, it does not lend itself to algebraic
manipulation to arrive at simple formulas
similar to Equations 2 and 3. Thus, in order
to evaluate VHR or VEFF (while accounting
for the effect of efficiency on
plant emissions, maintenance factors, and
reliability in a realistic operating scenario,
including ambient and load variations) one
should simply calculate LCOE for base
and improved plants and find the allowable
capital cost increase to set the difference
between the two equal to zero. The key to
the evaluation is to use the same kilowatthours
of generation for base and improved
LCOE calculations. The higher power
output will be reflected in the capacity re3.
Realization factors from Equation 4 and from the solution of equalCOE
construction using the expanded COE formula. E is the efficiency improvement
factor, which is defined as percentage change in h per percent change in P. Plant
reliability, maintenance, and degradation factors are kept constant. Source: Bechtel
Expanded COE
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Simple COE
placement term and the load factor, which
determines the mean-effective plant efficiency,
and appears in the fuel and emissions
costs.
The earlier sample calculation (F-Class
CC plant, 500 MW, 58% thermal efficiency,
$6 fuel, and 6,000 operating hours
per year) is updated for a typical cycling
duty (with a capacity factor of ~50% and
load factor of ~75%) at a site with annual
average temperature of 65F; the assumptions
are summarized in Table 1. Values
of RF have been calculated for varying
efficiency improvement factors, using the
calculation procedure described in the
previous paragraph. The results are shown
in Figure 3.
Two items of interest emerge from Figure
3. First, accounting for the real plant capacity
factor (~50% instead of 6,000/8,760
= 68.5%) and load factor (~75% instead of
base load) results in lower RF at high E and
higher RF at low E. In other words, significant
efficiency improvement at base load
does not translate well into real operation at
lower effective load factors. Second, modest
efficiency improvement at base load is
still modest at such low load factors, but it
is not wiped out either. Revisiting the earlier
CT compressor upgrade example, RF at
E = 0.43% is 0.38 (instead of 0.53), so that
the intrinsic value of each basis point net
CC efficiency (or each Btu/kWh of CC net
heat rate) for this CT compressor upgrade
is 0.38 · 148K = $56K.
A Simple Rule of Thumb
Obviously, results will change if a certain
improvement is expected to have a favorable
(or, more likely, unfavorable) effect
on overall plant reliability, maintainability,
or performance degradation. Furthermore,
only CO2
emissions are considered here,
Equation 4
and only at an assumed cost (see Table 1).
Penalties associated with other emissions
(such as NOx
emissions during startup) and
0.53
0.38
their inclusion should also affect the final
result. All these factors can be evaluated
rigorously by the full application of the
expanded COE model and underlying assumptions
on a case-by-case basis.
For most up-front conceptual studies
Upgraded GT compressor
+0.7% CC output, +0.3% CC eff.
E=0.43%
0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4%
Efficiency improvement factor
June 2013 | POWER
www.powermag.com
and back-of-the-envelope-type preliminary
evaluations, discounting the heat rate value
obtained from the original formula by the
factors read from Figure 3 should be sufficient.
In fact, for most practical purposes,
just using a realization factor of 0.5 across
the board is a good first-cut approximation
to start the discussion on a given CC performance-cost
trade-off topic. ■
-S.C. Gülen (scgulen@bechtel.com) is a
principal engineer for Bechtel.
63
Realization factor
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POWER June 2013

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