NEF4205 - Sustainable Energy Systems
Tutorial 5
NEF4205 - Sustainable Energy Systems
Question 1 - A naturnl-gas fueled, 250-kW, solid-oxide fuel cell with a heat rate of 7260 Btu/kWh costs
$1.5 million. In its cogeneration mode, 300,000 Btu/hr of exhaust heat is recovered, displacing the need
for heat that would have been provided from a 75% efficient gas-fired boiler. Natural gas costs $5 per
million Btu and electricity purchased from the utility costs $0.10/kWh. The system operates with a
capacity factor of 80%.
(
a. What is the value of the fuel saved by the waste heat ($/yr) (Ans: 14,016 per year)?
b. What is the savings associated with not having to purchase utility electricity ($/yr) (Ans:
$175,200 per year)?
c. What is the annual cost of natural gas for the CHP system (Ans: $63,598 per year)?
d. With annual O&M costs equal to 2% of the capital cost, what is the net annual savings of the
CHP system (Ans: $95,618 per year)?
e. What is the sin1ple payback (ratio of initial investment to annual savings) (Ans: 15.6 years)?
Question 2: An ideal PEM cell needs 30.35 g H2 to produce one kWh of electrical output. Suppose an
electric car can travel 10 miles per kWh. How much hydrogen would be needed to give the car a range of
300 miles if the source of elecnicity is an on-board fuel cell with an efficiency that is 50% of the ideal
(Ans: 1.821 kg)?
Question 3
You are designing a solar electricity system and don't have access to the grid, you are going to have to
deal with batteries. Your goal is to design an off-grid battery bank is to get a system that is big enough to
supply all your needs for a few cloudy days. Your room has two 60 watt light bulb and a 300 watt desktop
computer. Light bulbs run for 8 hours a day. Computer rnns for 5 hours a day. System losses account for
50 % of the consumption. You want the battery bank to last five days without recharging and not to fall
below 50 % d<;!pth of discharge. Calculate the storage capacity you require in kWh and Amp Hours
(AH). You are thinking of getting a 24 V system! What would be the rating of the system in kW (Ans:
36.9 kWh, 307.5 W)?
(
Question 4
A local utility company is planning to build an energy storage facility using lithium-ion batteries to store
excess energy generated by a solar fa1m. The solar faim generates an average of 500 kW of excess energy
daily, which needs to be stored and discharged during peak demand hours. The efficiency of the energy
storage system is 90 %, meaning that 90 % of the energy stored can be retrieved. The utility company
wants to ensure they have enough capacity to meet the peak demand for 5 hours.
a) Calculate the total energy that needs to be stored daily to meet the peak demand. (Ans: 2,777.8 kWh)
b) If the utility company wants to ensure they have a 20% reserve capacity, how many kWh of energy
storage capacity should they install? (Ans: 3,472 kWh)
(c) If the cost of one kWh of energy storage capacity is $200, what will be the total cost of the energy
storage system? (Ans: $694,444)
Page 1 of 1
Aroisal
5
Oveshion- 4
Ca)
Fuel
scavek lo
Boiler Pel
Saving >
260
—~
©:*S
fel
_
Saving>
~
Betler
()
Electricity
(c)-
Annval
vane.
heet
00, $5
*
be
Ss
Sau tags
Ko o.lo= gf 175, 220/,
Cost
ase
Cos rs
Casta
Gus
.
vi ite
4
= 250 kw x 0.8 x Soho
Gos
yo. 8x SPO hon
8760 hows KO-F
Brey
Bi
as K Pree
qak
74
q 63, 548 [yr
SAY Graal Sasigs
=
A-naval
‘
SovinyS
tuanen!
(e)
*
d Hal ie
Sasings
=
+
2oo —
& (5,
$45,617
4
-
$63,597 ( -—(Husarl
snd
4 68,
[yc
Paryback
Payback
=
HLS KE
4
475,618
-
a
Too
Cots -( 902%
4 ism)
telectsavings — Fuel
savims
Ses
xd
£194
years
A
2
Svestton
will neg
de-ruing, the f$se\ cell
Werk
| 4 ke Ha/eush
2% 0.02035
50%
miles at lo miles per lewsh
Bee ce range ef 260
Tote!
kwh
Zeomiles_
—————_
Jo flew
—
Suestion 3
E te qoved
=
Erequired
Total
oa
E
* Capaciby
attec
._
Ugo
ao
Ww
Systen
- 2690
KVP
20 leh
2
*
20 Lie
Tord
ty7 w2¥ eo?
\ n’
\ 32ao
a
e
si
x Z
( & housX
=
—
Gow) + ( 5 hous (Zoow)
-
= YB
(Soow
Leotses >
wh XS
fu
24ybO
+480 +
doy> _
S
oO
2.400 lew
*hIokuh
2460
@2.. FeSbb
2
aco
GB
26,700
wok
Cushion |
_—
Ener
(a
See
buarlable
K S hove _ Seo kwXS
Geo KW
Stomst
©
Etftctenss
oO
Enery
(r)
eas
Ao
Ta
~
Resetve
%
| Erensy
Steray
Resene
)
Ce
C
:
‘
Energy
to
(|
_
2,799.8 “wh
cupactty
=
Capactty
=
Cost =
Ord
0-2)
AA
3B, GF.
Shere
Total Gar= GeeCapacity
Tetal
2, +78
=
Store
200 per Wah
“Thal Cabs
4
—
lewh
STE
Cost
pel
3472.22 bh * 4 260 [Igor
4 64 my Get
key