Energy and Power Engineering, 2013, 5, 26-30
doi:10.4236/epe.2013.54B005 Published Online July 2013 (http://www.scirp.org/journal/epe)
Research on Storage Capacity of Compressed Air Pumped
Hydro Energy Storage Equipment*
Jingtian Bi, Tong Jiang, Weili Chen, Xian Ma
State Key Laboratory of Alternate Electrical Power, System with Renewable Energy Sources,
North China Electric Power University, Beijing, China
Received January, 2013
ABSTRACT
Compressed air pumped hydro energy storage equipment combines compressed air energy storage technology and
pumped storage technology. The water is pumped to a vessel to compress air for energy storage, and the compressed air
expanses pushing water to drive the hydro turbine for power generation. The novel storage equipment saves natural gas
resources, reduces carbon emission, and improves the controllability and reliability. The principle of compressed air
pumped hydro energy storage is introduced and its mathematical model is built. The storage and generation process of
the novel equipment is analyzed using the model. The calculation formula of the storage power is deduced in theory in
different situations of isothermal and adiabatic compression. The optimal storage scheme is given when the capacity
and withstand pressure of the vessel is definitive, and the max available capacity and the equipment utilization effi-
ciency evaluation of the scheme is given.
Keywords: Power Storage; Compressed Air Energy Storage; Hydraulic Equipment; Optimal Operation; Isothermal
Process; Adiabatic Process; Equipment Utilization Efficiency
1. Introduction
In recent years, as the problems of resources shortage
and environment pollution become serious, the new en-
ergy generation increases rapidly, especially the wind
power[1]. However, compared with the traditional gen-
eration, the wind power generation is characteristic of
intermittence, volatility and randomness. The large scale
integration of wind power will aggravate the unbalance
of the supply and the demand of power grid, and the peak
regulation ability of power grid is a serious obstacle to
the development of the wind power[2]. Energy storage
technology will provide a very effective way to solve
these problems.
In various energy storage technologies, the practical
large scale storage only includes pumped storage and
compressed air energy storage. The pumped station re-
quires high geographical conditions, the long construc-
tion period, the large initial investment and damages to
the ecological environment. Compressed air energy stor-
age (CAES) technology is a very promising energy stor-
age system and attracts great attentions in the world, as it
does not require strict geographical conditions and is
economic[3].
Traditional CAES power station is divided into energy
storage subsystem and power generation subsystem[4].
The energy storage subsystem, comprised of compressor,
motor and gas chambers, converts the low-cost electrical
energy to the compressed air stored in gas chambers such
as caves and abandoned mines. During the peak load
period, the power generation subsystem, comprised of
the gas turbine, combustion chamber as well as the heater,
generates power energy by the gas turbine driven by the
compressed gas combustion[5].
Compare with other energy storage technologies, ad-
vantages of compressed air energy storage system in-
clude[6]:
(1) It is suitable for the construction of large power
plants (>100MW). Its storage capacity is just less than
the pumped storage power station. CAES has long
working time, and it can continue working for a few
hours or even a few days.
(2) The unit construction costs and operating costs of
large-scale CAES stations are lower than the pumped
storage power station. CAES has good economic effi-
ciency.
(3) CAES has a long lifespan, and it can store/release
energy tens of thousands of times. Its efficiency can
reach about 70%, which is close to the pumped storage
power station.
*Supported by the National High Technology Research and Develop-
ment of China 863 Program (2012AA050208).

J. T. BI ET AL. 27
However, every storage technology has shortcomings
[7,8]. The disadvantages of compressed air energy stor-
age system include:
(1) Traditional compressed air energy storage system
must work with gas turbine power station, which con-
sumes a lot of natural gas when generation. The tradi-
tional scheme consumes a large amount of non- renew-
able energy and releases a large amount of CO2, mis-
matching the development requirements of reducing
carbon emission and preventing of global warming[9,10].
(2) Compressed air energy storage systems require
conditions of high temperature and high pressure. It
needs high requirements and high maintenance costs. In
addition, the failure rate of the turbine is high and its
service life is short.
2. Compressed Air Pumped Hydro Energy
Storage
The compressed air storage technology combined hydro
equipment attracts great attentions of technicians. The
essence is that the energy is stored in the compressed air,
and is extracted by the hydro turbines driven by high
pressure. Therefore the equipment can be called com-
pressed air pumped hydro energy storage equipment.
Many delightful progresses in this area appear in recent
years.
An implementation of compressed air pumped hydro
energy storage is put forward in [11]. Its block diagram is
shown in Figure 1. The system includes an air compres-
sor, a reservoir, a tank of gas-water and a pump/turbine-
motor/generator. Before the first storage process, air is
compressed into the tank of gas-water by the compressor,
reaching a preset pressure in the tank. Since then the
compressor would not work anymore. During valley de-
mand periods, water in the reservoir is pumped to the
tank by the water pump. With the increase of the water
level, water squeezes gas in the tank, and the gas is com-
pressed. The result is the increase of the pressure. During
peak demand periods, the high-pressure water promotes
the hydraulic turbine to generate power.
A similar compressed air pumped hydro energy stor-
age system is proposed in [12]. Its block diagram is
shown in Figure 2. It is different from the previous en-
ergy storage system in a tank of high-pressure gas, which
stores only compressed air. The tank of high-pressure gas
is connected with gas compressor and gas turbine gen-
erator. Before storage, compressor compresses air to the
tank of high-pressure gas. The tank of high-pressure gas
supplies preset pressure for the tank of gas-water. During
the peak load, the high-pressure gas in the tank of gas-
water push the water, driving the hydraulic turbine to
generate power. During the valley load, the motor-pump
pumps the water in the reservoir to the tank of gas-water
using the surplus power of the grid. The gas pressure
increases in the tank of gas-water, and the pressured gas
is stored in the tank of high-pressure gas at last. During
the peak load, the gas turbine generator can be used to
generate power as a supplement. When the air pressure is
insufficient, the gas compressor will work again.
Compared with the traditional CAES system, the two
compressed air pumped hydro energy storage systems
don’t consume natural gas, and don’t need the air turbo-
expander, nor the gas turbine or auxiliary heating sys-
tems, solving the two problems of traditional CAES sys-
tems mentioned above. In addition, generating by the
hydro turbine improves the controllability of the system
and the reliability of the equipment operation, and sim-
plifies the energy storage system. The novel system com-
bines pumped storage and compressed air energy storage
technology by the tank of gas-water which is buried in
the rock layer deep underground. It can be used widely in
areas short of water and heating fuel.
3. The Principle Analysis of Compressed Air
Pumped Hydro Energy Storage
The mentioned two compressed air pumped hydro energy
storage systems above can be described by the following
model.
The vessel is shown in Figure 3. Its volume is V1, and
the initial pressure of inner air is an atmospheric pressure
(shown in Figure 4(a)). Before storage, compressed air
of certain pressure is preset by the gas compressor. P1 is
the preset pressure (shown in Figure 4(b)). During valley
load period, external water is pumped into the vessel
consuming the surplus power of the grid. With the in-
crease of the amount of water, the inner air is compressed
and the pressure increases. The power energy is con-
verted to the potential energy of the compressed air. The
Figure 1. The block diagram of an implementation pro-
posed in [11].
Figure 2. The block diagram of an implementation pro-
posed in [12].

J. T. BI ET AL.
28
Figure 3 . The model of compressed air pumped hydro en-
ergy storage.
Figure 4. The relationship between E and V2 in isothermal
process.
max pressure of the compressed air is P2, which is the
withstand pressure value of the vessel, and the volume of
the air is V2 at the moment (shown in Figure 4(c)).
When generation, the high pressure water is pushed out,
driving the hydro turbine to generate electrical power
energy. When all the water from the vessel is discharged,
all the energy which can be emitted is released.
Obviously, in order to store the most energy in the
storage system, the air in the vessel should be com-
pressed to the withstand pressure value of the vessel P2.
Besides, the amount of energy is related to the volume of
the compressed air V2. By setting the volume ratio of the
gas and water reasonably, the largest amount of energy
can be stored, maximizing the utilization of storage de-
vices. Because compression and expansion are isother-
mal or adiabatic process, the following formula of the
relationship between the volume of the compressed air
V2 and the energy E is deduced individually in two dif-
ferent situations. And then get the volume of air when the
energy maximizes.
3.1. Isothermal Process
In the process of power generation, the volume of the air
in the vessel is Vx, and the pressure is Px. In the isother-
mal process, the relationship between the volume and the
pressure is as following:
22 x
VPVP
The process of power generation is over after all the
water in the vessel is discharged. The converted energy
in this process is:
11
22
1
22 1
22 22
22
Eln|
VV
xxx x
x VV
V
PV V
PdVdVPV VPVln
V VV
 

(2)
For a given vessel, its capacity V1 and withstand pres-
sure value P2 are fixed values. Form the formula (2), the
amount of released energy is just determined by the vo-
lume of the compressed air when pressure maximizes.
The preset pressure is 1221 /PPVV

. Thus, the other
conclusion is that the amount of released energy is just
determined by the preset pressure.
Get the derivative to V2 from (2), and the equation is
as follows:
1
2
22
V dE Pln P
dVV 2

 (3)
When the derivative equals 0, the volume of com-
pressed air is 21 /VVe

. At the moment, the preset pres-
sure is 12 /ePP

, and the energy is 21 . The
relationship curve between E and V2 is shown in Figure
4.
EPV e/
It can be concluded, in the isothermal process, in order
to release the most energy from a vessel whose volume is
V1 and withstand pressure value is P2, the initial pressure
should be preset to 12 /PPe

. When the air is com-
pressed to the max pressure P2, the volume of the air is
21
/VVe

. The max energy which can be released in the
process of power generation is .
21
E/PV e
3.2. Adiabatic Process
In the adiabatic process, the relationship between the
volume and the pressure is as following:
22 x
P
x
PV V



 (4)
where

is the heat capacity ratio of the air. The heat
capacity ratio of the atmosphere is 1.4. And then, the
converted energy in this process can be computed:
11
22
1
1 22 22
2
E|
1
VV
xxx x
VV x
V
PV PV
PdVdVV V
V





 


11
22
12
(
1
PV VV

)





 (5)
Get the derivative to V2 from (5), and the equation is
as follows:
22
21
[γ() 1]
1
PV dE
dV V




 (6)
When the derivative equals 0, the volume of com-
x
(1) pressed air is 1
21
/VV



. At the moment, the preset

J. T. BI ET AL. 29
pressure is P/1
12
/P




, and the energy is E

/1
21
/PV




. hip curve between E and
igure 5.
It can be concluded
The relations
F
, in th
V2
order
is shown in
to
e adiabatic process, in
release the most energy from a vessel whose volume is
V1 and withstand pressure value is P2, the initial pressure
should be preset to /1
12
/PP




. When the air is com-
pressed to the max pressue volume of the air is re P2, th
1
21
/VV



. The max energy which can be released in
power generation is /1
21
E/PV

 the process of

 . In
the process of adiabatic compressture
increase of the gas can be computed using the following
equation:
ion, the
11
x
Tx V
 

V1 is 10m3, an
tempera
(7)
with-
e sys-
22
TV
ple Calculation 3.3. Exam
d the
g
te
Assume the volume of vessel
stand pressure value P2 is 10MPa. By (2)(3)(5)(6), the
max extracted energy E and preset pressure P1 can be
calculated in isothermal and adiabatic processes.
In compressed air pumped hydro energy stora
ms, the preset pressure of the vessel needs to consume
power energy to supply, which cannot be extracted by
the hydro turbine. The consumed power needed to preset
pressure is E0. In single storage-generation process, the
ratio of extracted energy to the total stored energy is:
0
100%
EE

ed into
erature of preset air
η
the preset gas is compress
e initial temp
E
Assume the vessel i
an
hin th
se
sh
(8)
n
e ves-
cesses are
isothermal way. By the formula (2), the consumed
energy E0 can be calculated, and then the ratio η can be
calculated.
Assume t
l is t0 = 0℃. The temperature rise in the adiabatic com-
pression can be calculated by the formula (7).
The results in isothermal and adiabatic pro
own in Table 1.
Figure 5. The in adiabatic
process. relationship between E and V2
Table 1. The results in isothermal and adiabatic processes.
Index Isothermal process Adiabatic process
P0(MPa)3.68 3.08
E(×106 J)36.8 30.77
E0(×106 J)1
0
10
32.68 105.57
η 21.7 22.57
t0( )℃0
t( )℃ 0 9.27
As can be seen fro the above data, in the adiabatic
r
s
ped hydro energy storage has good
m
pocess, the gas pressure will be affected by the tem-
perature of the gas, which will promote the increase of
the gas pressure when the air is compressed. Thus the
stored energy in the adiabatic process is less than that in
the isothermal process. The compressed air pumped hy-
dro energy storage systems mentioned above have no
adiabatic treatment, nor isothermal measures. So the
practical systems will work at a state between the adia-
batic and isothermal results. When the extracted energy
reaches maximum, the preset pressure will be a value
between 3.08 MPa and 3.68 Mpa, and the max power
energy released will be a value between 30.77 × 106 J and
36.8 × 106 J, and the ratio η will be a value between
21.7% and 22.57%. Based on these data, we can draw the
following conclusions. Compared with traditional CAES
systems, the compressed air pumped hydro energy stor-
age systems store less “effective” energy, that is, the en-
ergy which can be released when peak load period. Con-
sidering the construction costs in the engineering projects
accounted for a large proportion, for the same equipment,
the unit electricity cost in the compressed air pumped
hydro energy storage systems is higher than the tradi-
tional systems.
4. Conclusion
Compressed air pum
prospects for development. The generation unit is con-
structed by hydraulic equipment, breaking through the
shackles of traditional mechanical power generation by
turbines and avoiding the problems of excessive increase
of carbon emissions. The principle of compressed air
pumped hydro energy storage is analyzed. The calcula-
tion formula of the storage power is deduced in theory in
different situations of isothermal and adiabatic compres-
sion. The relationship curve between the storage power
and the initial state is obtained. The optimal storage
scheme is given when the capacity and withstand pres-
sure of the vessel is definitive, and the max available
capacity and the equipment utilization efficiency evalua-

J. T. BI ET AL.
30
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