Environmental Engineering Reference
In-Depth Information
storage cavern capacity (E
GEN
/V
S
). The electrical output of the turbine (E
GEN
)
is given by
t
∫
E
=
η η
m w
dt
(5.9)
GEN
M G
T
CV TOT
,
0
where the integral is the mechanical work generated by the expansion of air
and fuel in the turbine, w
CV,TOT
= total mechanical work per unit mass gener-
ated in this process,
m
.
T
= air mass flow rate, t = time required to deplete a
full storage reservoir at full output power, η
M
= mechanical efficiency of the
turbine (which reflects turbine bearing losses), and η
G
= electric generator
efficiency.
Since all CAES systems to date are based on two expansion stages, the
work output can be expressed as the sum of the output from the two stages.
The first term reflects the work output from the hp turbine that expands the
air from the hp turbine inlet pressure (p
1
) to the lp turbine inlet pressure
(p
2
). Likewise, the second term reflects the expansion work derived from the
expansion from p
2
to barometric pressure (p
b
).
p
p
∫
2
−
∫
b
w
=
w
+
w
= −
vdp
vdp
(5.10)
CV TOT
,
CV
1
CV
2
p
p
1
2
Consider first the work output from the first expansion stage. Assuming adi-
abatic compression and that the working fluid is an ideal gas with a constant
specific heat (so that P ⋅ v
k
= c, a constant, where k
1
≡ C
p1
/C
v1
), the work per
unit mass is
p
p
dp
p
∫
1
∫
1
w
=
vdp
=
c
1
/
k
(5.11)
1
CV
1
1
/
k
1
p
p
2
2
p
1
/
k
1
1
k
c
p
k
[
]
=
1
p
=
1
p v
−
p
2 2
(5.12)
1 1
k
1
k
1
−
−
1
1
p
2
c
c
c
p v
p v
p
=
v
p v
−
2 2
1
(5.13)
1 1
c
c
−
p
v
v
1 1
