Environmental Engineering Reference
In-Depth Information
where PVF( n ) present value factor for year n (1 I ) n ; I discount rate 0.07, and RC( n )
replacement cost in year n .
The levelized replacement cost is the sum of the present values multiplied by the capital recovery
factor (CRF):
20
£
LRC
CRF
*
PV
( )
n
(12.6)
n 1
where CRF 0.093.
EXAMPLE 12.7
Calculation of levelized replacement cost for 50 kW turbine. Work done in a spreadsheet.
LRC Calculation
Component
Year, n
RC( n )
I
PVF( n )
PV( n )
Bearings
10
6,500
0.07
0.508
3,304
Blades
10
5,000
0.07
0.508
2,542
Subtotal
5,846
LRC, $/year
544
Now the COE (120,000 * 0.08 544)/120,000 0.01 $0.095/kWh. This value can be com-
pared with the value in Example 12.5. The problem is the determination of major repairs, year, and
replacement cost.
12.3.3 V ALUE OF E NERGY
Another formula [3] for estimating the value of energy is
f
c
L
(
1
r L
r
)
A
o
q
(12.7)
§ ©
L
¸ § ©
L
¸
(
1
A
)
(
1
)
1
where f o value of energy saved per year, $; c initial installed cost, $; L years to payback; ]
fuel inflation rate; and r interest rate.
Because there is not a factor for operation and maintenance, the interest rate should be increased
by 1-2%. Equation 12.7 can be solved by iteration by using different values of L to calculate the
right-hand side and then comparing that to the left-hand side of the equation. As interest rates
increase, payback times increase; as fuel inflation factors increase and cost of electricity increases,
payback times decrease.
12.4 LIFE CYCLE COSTS
A life cycle cost (LCC) analysis gives the total cost of the system, including all expenses incurred
over the life of the system and salvage value, if any [1, 4, 5]. There are two reasons to do an LCC
analysis: (1) to compare different power options, and (2) to determine the most cost-effective system
designs. The competing options to small renewable energy systems are batteries or small diesel
 
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