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Title: Thermodynamic Analysis on an Integrated Liquefied Air Energy Storage and Electricity Generation System
Author: Yingbai Xie and Xiaodong Xue

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energies
Article

Thermodynamic Analysis on an Integrated Liquefied
Air Energy Storage and Electricity Generation System
Yingbai Xie and Xiaodong Xue *
Department of Power Engineering, North China Electric Power University, Baoding 071003, China;
xieyb@ncepu.edu.cn
* Correspondence: 2162214059@ncepu.edu.cn
Received: 22 August 2018; Accepted: 20 September 2018; Published: 23 September 2018




Abstract: For an integrated liquefied air energy storage and electricity generation system,
mathematical models of the liquefied air energy storage and electricity generation process are
established using a thermodynamic theory. The effects of the outlet pressure of the compressor
unit, the outlet pressure of the cryogenic pump, the heat exchanger effectiveness, the initial air
temperature and pressure before throttling on the performances of the integrated liquefied air energy
storage, and the electricity generation system are investigated, using the cycle efficiency and liquid
air yield ratio as the evaluation indexes. The results show that if the compressor outlet pressure
is raised, both the compression work and the expansion work increase, but because the expansion
work increases more slowly, the cycle efficiency of the system gradually decreases. Increasing the
cryogenic pump outlet pressure and heat exchanger effectiveness can significantly increase the cycle
efficiency of the system; the higher the air pressure and the lower the air temperature before throttling,
the greater the liquid air yield after expansion, and the higher the cycle efficiency. The theoretical
analysis models and research results can provide a reference for the development of an integrated
system of liquefied air energy storage and electricity production, as well as for the development of
medium-capacity energy storage technology.
Keywords: liquefied air energy storage; cycle efficiency; liquid air yield ratio; electricity generation

1. Introduction
Solar, wind, and other renewable energies are widely used to generate electricity in the world [1–5].
For these energy forms, because of their characteristics of instability and intermittence [6,7], efficient
energy storage technologies are required in order for a sustained and stable output [8–12].
Energy storage technologies, such as bulk power management, compressed air energy storage
(CAES), and pumped hydroelectricity storage (PHS) [13–16], are presently relatively mature and
reliable. However, these two technical schemes [17] are limited by geographical or hydrogeological
conditions. PHS technology needs abundant water resources for support, while CAES requires
high-performance natural underground reservoirs. According to the Electric Power Research Institute
(EPRI), the total cost for CAES is around 1000 $/kW. It may be double this for PHS. As a result, there is
a demand to develop a general, cost-effective energy storage technology, regardless of local conditions.
Liquid air energy storage (LAES) is an innovative and leading universal industrial energy storage
technology [18–21]. The idea of LAES began in 1977 at the University of Newcastle, and was tested by
Mitsubishi Industries Ltd. (Tokyo, Japan) in 1998 [1]. Researchers at the University of Leeds together
with the Highview Power Storage Company developed the first 350 kW/2.5 MWh pilot demonstration
plant at the University of Birmingham in 2010. The data gathered from this pilot plant showed that the
efficiency of the total cycle is in the range of 50–60%.

Energies 2018, 11, 2540; doi:10.3390/en11102540

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Energies 2018, 11, 2540

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Since 2014, Viridor has selected Highview to design MW level pre-commercial, multi-MW,
and conceptual Giga-Plant LAES. However the round-trip efficiency is still approximately 60%.
Some literature has contributed to this topic.
The process can be divided into two parts, namely air liquefied and electric generation. As the
air liquefied process needs a lower temperature, while the electric generation process needs a higher
temperature, internal heat exchangers, such as regenerators, are needed to connect these two processes
in order to improve the cycle efficiency.
An integrated system was put forward so as to investigate the operational parameters of the
major devices effecting the cycle efficiency. Chino and Araki [22] also proposed an air liquefaction
plant integrated with a conventional combined cycle power plant. Li et al. studied a LAES system
integrated with a nuclear power plant [23]. The overall system efficiency is improved, owing to the
reheating arrangement.
In this paper, more detailed effects will be discussed regarding the outlet pressure of the
compressor and cryogenic pump, the efficiency of the heat exchanger, the air temperature and pressure
before the throttle on the cycle efficiency, and the liquid air yield.
2. System Description
Figure 1 shows the layout of an integrated liquefied air energy storage and electricity
generation system, referring to the literature [8]. The system adopts a two-stage compression and
two-stage expansion.
Compressor #1
5S

1L

Expander #2
7E

6S

12S

Hot S torage
Tank

2L

6E

11S
Heat
Exc hanger #2

Cooler #1
Compressor #2 3L

5E Expander #1

4L

4E

7S
Cooler #2

Heat
Exc hanger #1

Cold S torage
Tank #1
9S

10S

5L

8S

3E
10L

Cold
Stor age
Tank #2

Cold
Box
9L

3S

1S

6L

2S

Gasification Heat
Exc hanger
4S
2E

J-T Valve

Cryogenic
Pump

7L
Separator
8L

Liquid
Air Ta nk

1E

Figure 1.
1. Schematic
Schematicdiagram
diagramofof
integrated
liquid
air energy
storage
and electricity
generation
anan
integrated
liquid
air energy
storage
and electricity
generation
system.
system.

The left side is the air liquefying process. It contains two air compressors, a J–T valve (It is
a
throttle
valve),Models
a separator,
a liquid air tank, and some heat exchangers. When there is surplus
3. Mathematical
for Processes
electricity from the renewable energy sources or from the grid, the outer air is compressed by the two
air compressors,
its temperature and pressure are raised. Then, the gaseous air is cooled down
3.1.
Air Liquefyingand
Process
and throttled in the J–T valve. The liquefied air is then collected in the separator and stored in the
The outlet pressure and inlet pressure of the air compressors are as follows:
liquid air tank.
pac,out = pac,in ac
(1)
where pac,out is the outlet pressure of the air compressor, Pa; pac,in is the inlet pressure of the air
compressor, Pa; and πac is the compression ratio.
The relationship between the inlet and outlet temperature of the air compressor is as follows:

Energies 2018, 11, 2540

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When there is an insufficient supply of electricity available to meet the consumers’ demands,
the cryogenic pump is activated. The liquid air in the liquid air tank increases its temperature through
the heat exchangers, and recovers to a gaseous state. When it reaches the set-points for the temperature
and pressure, the air enters the two-stage expander in order to generate electricity. This is the electricity
generation process.
There are some regenerators between the two processes. To decrease the system fluctuation,
the large capacity storage method is used.
The above integrated system is modeled with the following assumptions:






Ignoring other components, it is assumed that the air is a mixture of 21% oxygen and 79%
nitrogen. The thermodynamic properties of nitrogen and oxygen are evaluated in REFPROP
(Reference Fluid Thermodynamic and Transport Properties Database), according to the authors
of [24,25], respectively.
According to thermodynamics, it is assumed that the compression and expansion processes are
polytropic processes.
The pressure losses along the cycle have been ignored, in order to have a solution that compares
different cycles under the same conditions. In the analysis, the system is assumed to be in a steady
state condition, and the thermal losses in the heat exchangers are ignored [26].

3. Mathematical Models for Processes
3.1. Air Liquefying Process
The outlet pressure and inlet pressure of the air compressors are as follows:
p ac,out = p ac,in π ac

(1)

where pac,out is the outlet pressure of the air compressor, Pa; pac,in is the inlet pressure of the air
compressor, Pa; and π ac is the compression ratio.
The relationship between the inlet and outlet temperature of the air compressor is as follows:
Tac,out = Tac,in π ac

n c −1
nc

(2)

where Tac,out is the outlet temperature of the air compressor, K; Tac,in is the inlet temperature of the air
compressor, K; and nc is the polytropic index of the compression process.
The efficiency of the compressor η ac can be expressed as follows:
ηac =

κ−1
nc
×
κ
nc − 1

(3)

where κ is the adiabatic index.
The specific work, wac , done to the compress air is as follows:
2

wac =

∑ cair (Tac,out,i − Tac,in,i ) = (h2L − h1L ) + (h4L − h3L )

(4)

i =1

where cair is the specific heat capacity of air, J/(kg·K).
After the two air compressors, two internal heat exchangers are used. The high-temperature
and high-pressure air is cooled down to heat the low temperature cold fluid within the internal heat
exchanger. Ignoring the heat dissipated to the surroundings, the outlet air temperature of the cold
side, Thex,cold,out , is as follows:
Thex,cold,out = (1 − ε) Tac,out + εThex,cold,in

(5)

Energies 2018, 11, 2540

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where ε is the efficiency of the heat exchanger, and Thex,cold,in is the inlet air temperature of the internal
heat exchanger on the cold side, K.
The lower the temperature of the air entering the second compressor, the smaller the power
consumption needed for compressing the air. Therefore, the cold side air from these two heat
exchangers is introduced from cold storage tank #1. When leaving the heat exchanger, the cold
side air discharges the absorbed heat into the hot storage tank. The heat stored in the hot storage tank
per unit mass is as follows:
qhst = h6S − h5S
(6)
The hot side air continues cooling down in the cold box. The parameters of point 6L (in Figure 1)
must be controlled to be below certain values. In the cold box, the energy balance equation must
include the mass flow rate of the three working fluid streams.
Then, the air passes the J–T valve and is throttled into the two-phase region. The gaseous air is
recovered to be reused. The liquefied air flows out from the bottom of the separator and is stored in
the liquid air tank. The ratio of liquid air yield is as follows:
Y=

m8L
m1L

(7)

where m8L is the mass flow rate of the liquid air that enters the liquid air tank, kg/s, and m1L is the
mass flow rate of the gaseous air being suctioned at air compressor #1, kg/s.
3.2. Electricity Generation Process
During the peak electricity demand period or in the case of a power failure, the electricity
generation process is activated. The liquid air in the liquid air tank is extracted by the cryogenic pump,
and the power consumption is as follows:
wcp = R air,gas T1E ln

p2E
p1E

(8)

where T1E is the liquid air temperature at the outlet of the liquid air tank, K; p1E is the pressure of liquid
air at the outlet of the liquid air tank, Pa; and p2E is the pressure of air at the outlet of the cryogenic
pump, Pa.
The air then absorbs heat from cold storage tank #2, turning into a gaseous state in the gasification
heat exchanger. The air temperature at the outlet of the heat exchanger is as follows:
T3E = (1 − ε) T2E + εT4S

(9)

In heater #1, the air heats to T4E , and enters expander #1 to produce work. The expansion process
is also a polytropic process, where the temperature at the outlet of each expander is as follows:
− (nen−e 1)

Tae,out = Tae,in πe

(10)

where ne is the polytropic index of the expansion process, and π e is the expansion ratio.
The polytropic efficiency and the polytropic index of the expander is as follows:
ηe =

( n e − 1)
κ
×
ne
κ−1

(11)

The work produced for the unit mass working fluid expansion in the expanders is as follows:
we = (h5E − h4E ) + (h7E − h6E )

(12)

Energies 2018, 11, 2540

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3.3. Cyclic Performance
A complete cycle of the liquefied air energy storage system includes two stages, the liquefied
energy storage and the energy released to power generation. The main parameter used to measure the
system performance is the system cycle efficiency, also called the round-trip efficiency, which can be
expressed as follows:
we − wcp
ηRT = Y
(13)
wac
4. Performance Analysis of an Integrated System of Liquefied Air Energy Storage and
Power Generation
MATLAB software is used to program the established models. Referring to the literature [27],
the basic operating parameters of the liquefied air energy storage and power generation system are
shown in Table 1.
Table 1. Basic operating parameters of the system.
Parameters

Value

Units

Ambient temperature (T0 )
Ambient pressure (p0 )
Outlet pressure of cryogenic pump (p2E )
Liquid air storage pressure (p1E )
Minimum temperature of cold storage tank #2
Maximum temperature of cold storage tank #2
Pinch point temperature of cold box (cold side)
Pinch point temperature of cold box (hot side)
Gross compression ratio of compressors
Isentropic efficiency of compressors
Isentropic efficiency of expanders
Heat exchanger effectiveness
Isentropic efficiency of cryogenic pump

293
100
7000
100
93
300
5
10
80
0.92
0.9
0.92
0.9

K
kPa
kPa
kPa
K
K
K
K
-

REFPROP (Reference Fluid Thermodynamic and Transport Properties Database) is an
internationally recognized physical property calculation software developed by the National Institute
of Standards and Technology (NIST). The properties of the working fluid at each point labeled in the
system are generated by the NIST REFPROP database. For the air liquefied process and the electric
generation process, the values of these points are shown in Tables 2 and 3, respectively.
Table 2. Parameters of the points in the air liquefied process.
Point

p/kPa

T/K

h/kJ·kg−1

ρ/kg·m−3

1L
2L
3L
4L
5L
6L
7L
8L

100.00
894.43
894.43
8000.00
8000.00
8000.00
100.00
100.00

293.00
578.60
315.85
623.72
319.46
98.00
79.11
79.11

293.27
584.91
314.67
632.65
305.60
−84.42
−84.42
−125.95

1.16
7.35
16.21
85.10
191.42
769.30
29.13
812.26

Energies 2018, 11, 2540

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Table 3. Parameters of the points in the electric generation process.
p/kPa

Point

4E
5E
6E
7E

7000.00
1E
836.66
2E
836.66
3E
100.00
4E

4.1. Outlet Pressure of

T/K

534.49
100.00
79.11
309.54
7000.00
79.11
7000.00 536.06
290.00
7000.00 310.44
534.49

5E
6E
Compressor
7E

836.66
836.66
(p4L100.00
)

h/kJ·kg−1

ρ/kg·m−3

308.36
540.48
310.83

812.26
813.12
81.53
18.14
8.89
2.28
1.21

537.19
−125.95
308.36
−121.22
274.45 540.48
537.19 310.83

309.54
536.06
310.44

18.14
8.89
2.28
1.21

The work consumption of the compressor is associated with the number of compression stages
4.1.compression
Outlet Pressuremode
of Compressor
(p4L )
and the
at the identical
rated isentropic efficiency of compressor, and the same
heat exchanger
effectiveness.
Theoretically,
the isothermal
compression
process
has a minimum
work
The work
consumption
of the compressor
is associated
with the number
of compression
stages
consumption,
while the mode
adiabatic
process
hasefficiency
a maximum
work consumption.
and the compression
at thecompression
identical rated
isentropic
of compressor,
and the sameThe
heat exchanger
effectiveness.
Theoretically,
the isothermal
compression
process has
a minimum
isothermal
compression
process can
be approached
if the number
of compression
stages
is increased
workand
consumption,
theare
adiabatic
compression
process has a maximum work consumption.
infinitely,
if internalwhile
coolers
put between
the stages.
The
isothermal
compression
process
can
be
approached
the number
compression
stagesa more
is
In fact, the number of compression stages are limited, asifincreasing
theofnumber
will cause
increasedsystem
infinitely,
and if internal
coolers
put in
between
theirreversible
stages.
complicated
configuration
and
will are
result
greater
losses, such as mechanical
In fact, the number of compression stages are limited, as increasing the number will cause a more
friction and flow resistance. According to the thermodynamic theory, for the multi-stage compression
complicated system configuration and will result in greater irreversible losses, such as mechanical
process, the compression work consumption will be at a minimum if the compressors of the different
friction and flow resistance. According to the thermodynamic theory, for the multi-stage compression
stagesprocess,
adopt identical
pressure ratios.
the compression work consumption will be at a minimum if the compressors of the different
For
the
aforementioned,
two-stage
stages adopt identical pressure
ratios. compression and intermediate cooling is adopted. Figure 2
shows theFor
relationship
betweentwo-stage
the outlet
pressure and
of the
compressor
unitis(p
4L) to the
work
the aforementioned,
compression
intermediate
cooling
adopted.
Figure
2 of
compression,
work
of expansion,
andthe
cycle
efficiency.
shows the
relationship
between
outlet
pressure of the compressor unit (p4L ) to the work of
compression, work of expansion, and cycle efficiency.
0.56

800
Work of compression
Work of expansion
Cycle efficiency

Cycle efficiency

0.52

750
700

0.50

650

0.48

600

0.46

550

0.44

500

0.42

450

0.40

2

4

6

8

10

12

14

16

18

20

Work /kJ/kg

0.54

400
22

Compressor outlet pressure p4 /MPa

Figure 2. Influence of the compressor outlet pressure (p4L ) on the work of compression, work of

Figureexpansion,
2. Influence
of the
compressor outlet pressure (p4L) on the work of compression, work of
and cycle
efficiency.
expansion, and cycle efficiency.
In Figure 2, with the increasing compressor outlet pressure (p4L ), the compression work and the
expansion
but,
the expansion
work
increases
slowly.
However,
the cycle
In Figure 2,work
withboth
the increase,
increasing
compressor
outlet
pressure
(pmore
4L), the
compression
work
and the
efficiency
of the
system
gradually
decreases.
expansion
work
both
increase,
but, the
expansion work increases more slowly. However, the cycle
increment
the compression
work because of the increase in the compression pressure ratio.
efficiency The
of the
systemofgradually
decreases.
Equations
(2) andof(4)the
indicate
that the greater
compression
ratio,
the compressor
The
increment
compression
workthe
because
of thepressure
increase
in the
thehigher
compression
pressure
outlet temperature. This means that the specific compression work increases. The elevation of the
ratio. Equations (2) and (4) indicate that the greater the compression pressure ratio, the higher the
compressor outlet temperature results in a higher temperature of the heat storage medium, which also
compressor outlet temperature. This means that the specific compression work increases. The
increases the heating temperature of the air in the electric power generation process.
elevation According
of the compressor
outlet
results
in a higher
the heat
storage
to Equation
(12),temperature
a higher inlet
air temperature
of temperature
the expander of
means
a higher
medium,
which
increases
thethe
heating
temperature
ofcompletely,
the air in therefore
the electric
power generation
specific
workalso
output.
However,
air cannot
be liquefied
the liquefaction
rate

process.
According to Equation (12), a higher inlet air temperature of the expander means a higher
specific work output. However, the air cannot be liquefied completely, therefore the liquefaction rate
cannot reach 100%. It can be seen from the conservation of energy, that the heat collected during the
compression process is not fully used in the release phase, so the increase of the expansion work is

Energies 2018, 11, 2540

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cannot reach 100%. It can be seen from the conservation of energy, that the heat collected during the
compression process is not fully used in the release phase, so the increase of the expansion work is
slowerPressure
than that
compression
4.2. Outlet
of of
thethe
Cryogenic
Pumpwork, resulting in a decrease in the cycle efficiency. Therefore,
the outlet pressure of the compressor unit (p4L ) should not be too high.

The cryogenic pump is a special pump that leads liquid air from the liquid air tank to the
4.2. Outlet
Pressure
of the Cryogenic
Pump The outlet pressure of the cryogenic pump is treated as
gasification
heat
exchanger
for gasification.
the inlet pressure
of the pump
expander,
the flowing
pressure
lossfrom
of the
in theairheat
exchangers
The cryogenic
is a ignoring
special pump
that leads
liquid air
theair
liquid
tank
to the
and the
pipelines.
inlet for
air gasification.
pressure and
the temperature
ofcryogenic
the expander
the as
primary
gasification
heatThe
exchanger
The outlet
pressure of the
pump isare
treated
the
parameters
that
determine
the
expansion
work
with
the
condition
of
the
constant
air
flow.
Therefore,
inlet pressure of the expander, ignoring the flowing pressure loss of the air in the heat exchangers and
the pipelines.
The and
inlettemperature
air pressure and
of the expander
are theasprimary
parameters
the inlet
air pressure
of the
the temperature
expander should
be increased
much as
possible, in
that
determine
the
expansion
work
with
the
condition
of
the
constant
air
flow.
Therefore,
the inlet
order to increase the output expansion work.
air pressure to
andbasic
temperature
of the expander
should be
as much as
possible, inprocess,
order to the
According
thermodynamic
principles,
forincreased
the multi-stage
expansion
increase
the
output
expansion
work.
expansion work reaches its maximum at the identical expansion ratio for each stage. Therefore, twoAccording to basic thermodynamic principles, for the multi-stage expansion process,
stage expansion and inter-stage reheating expansion modes are adopted in this paper. The inter-stage
the expansion work reaches its maximum at the identical expansion ratio for each stage. Therefore,
reheater is used to elevate the inlet air temperature of the next stage expander and the efficiency of
two-stage expansion and inter-stage reheating expansion modes are adopted in this paper.
the expander
unit. reheater is used to elevate the inlet air temperature of the next stage expander and the
The inter-stage
Figure
3 shows
the expansion
efficiency
of the expander
unit. work and cycle efficiency to the outlet pressure of the cryogenic
pump. Figure 3 shows the expansion work and cycle efficiency to the outlet pressure of the
cryogenic pump.
0.50
500
Cycle efficiency
Work of expansion

0.46

480

Cycle efficiency

460
0.44
440
0.42
420
0.40
400
0.38
380
0.36

Work of expansion /kJ/kg

0.48

360
0.34
340
0.32

2

4

6

8

10

Cryogenic pump outlet pressure /MPa

Figure 3. Influence of the outlet pressure of the cryogenic pump on the expansion work and the

Figure
3. Influence
cycle
efficiency.of the outlet pressure of the cryogenic pump on the expansion work and the cycle
efficiency.
As shown in Figure 3, the cycle efficiency and the expansion work increase in a similar way to the
increase
of in
theFigure
outlet pressure
of the
cryogenicand
pump.
example,work
whenincrease
the outlet
of way
the to
As shown
3, the cycle
efficiency
the For
expansion
inpressure
a similar
cryogenic
boostspressure
from 2 MPa
to 5cryogenic
MPa, the cycle
efficiency
increaseswhen
from 36%
to 44%,pressure
and the of
the increase
of pump
the outlet
of the
pump.
For example,
the outlet
expansion
work
increases
from
345
kJ/kg
to
425
kJ/kg.
the cryogenic pump boosts from 2 MPa to 5 MPa, the cycle efficiency increases from 36% to 44%, and
According
the basicfrom
principles
of thermodynamics,
the expansion
work to
increases
345 kJ/kg
to 425 kJ/kg. the higher the pressure and temperature
before the air enters the expander, the more work is output during the expansion process. Increasing
According to the basic principles of thermodynamics, the higher the pressure and temperature
the outlet pressure of the cryogenic pump is equivalent to increasing the pressure at the inlet of
before the air enters the expander, the more work is output during the expansion process. Increasing
the expander. Theoretically, augmenting the outlet pressure of the cryogenic pump is beneficial for
the outlet
pressure
of the
cryogenic
pump
is equivalent
increasing
the pressure
pressureofatthe
thecryogenic
inlet of the
improving
the cycle
efficiency
of the
system.
However, intoreality,
the outlet
expander.
augmenting
the
the equipment.
cryogenic pump is beneficial for
pump Theoretically,
is limited, considering
the harm
of outlet
the highpressure
pressure of
on the

improving the cycle efficiency of the system. However, in reality, the outlet pressure of the cryogenic
Heat Exchanger
Effectiveness
pump4.3.
is limited,
considering
the harm of the high pressure on the equipment.
Heat storage and cold storage tanks, as well as other heat exchangers are used to guarantee

4.3. Heat
Effectiveness
the Exchanger
independent
operation of the liquid air storage and electric power generation processes.
Heat storage and cold storage tanks, as well as other heat exchangers are used to guarantee the
independent operation of the liquid air storage and electric power generation processes. These heat
exchangers have the capacity to provide cooling or heating at any time during single or two-phase
processes.
The heat exchanger effectiveness is the maximum actual heat transfer. Figure 4 shows the heat

Energies 2018, 11, 2540

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These heat exchangers have the capacity to provide cooling or heating at any time during single
or two-phase processes.
The heat exchanger effectiveness is the maximum actual heat transfer. Figure 4 shows the
heat exchanger effectiveness compared to the compression work, expansion work, and the cycle
efficiency,
that
heater
#1, heater
cooler #1,
and
#2 haveofan
Withsupposing
the constant
outlet
pressure
of the #2,
compressor
unit
andcooler
inlet pressure
theidentical
expanderheat
unit,
With
the
constant
outlet
pressure
of
the
compressor
unit
and
inlet
pressure
of
the
expander unit,
exchanger
effectiveness.
increasing
the heat exchanger effectiveness will greatly decrease the compression work consumed,
increasingWith
the heatconstant
exchanger
effectiveness
will
greatly decrease the compression work consumed,
outlet
pressure
the
compressor
increase the
the expansion
work,
and theofcycle
efficiency. unit and inlet pressure of the expander unit,
increase
the expansion
andeffectiveness
the cycle efficiency.
increasing
the heat work,
exchanger
will greatly decrease the compression work consumed,
increase the expansion work, and the cycle efficiency.
0.52

0.52

0.50

0.50

0.48

0.48
0.46

650

650
600

0.46
0.44
0.42

Work of compression
Work of expansion
efficiency
Work Cycle
of compression

600

Work of expansion
Cycle efficiency

550

550

500

0.44

500
450

0.40

0.42
0.40

0.38
0.36

0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96

0.38
0.36

Work /kJ/kg
Work /kJ/kg

0.54

Cycle efficiency

Cycle efficiency

0.54

450
400

Efficiency of heat exchanger

0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96

400

Figure 4. Influence of heat exchanger Efficiency
effectiveness
on the compression work, expansion work, and
of heat exchanger
the cycle efficiency.
Figure 4. Influence of heat exchanger effectiveness on the compression work, expansion work, and the
Figure
4. Influence
cycle
efficiency. of heat exchanger effectiveness on the compression work, expansion work, and

Inefficiency.
Figure 4, when the heat exchanger effectiveness increases from 0.8 to 0.96, the compression
the cycle
work
decreases
from 630
to 585 kJ/kg,
the expansion
work increases
425the
kJ/kg
to 500 kJ/kg,
In Figure 4, when
the kJ/kg
heat exchanger
effectiveness
increases
from 0.8from
to 0.96,
compression
and
the
cycle
efficiency
increases
from
about
39%
to
around
52%.
work
decreases
fromthe
630 heat
kJ/kgexchanger
to 585 kJ/kg,
the expansionincreases
work increases
4250.96,
kJ/kg
to compression
500 kJ/kg,
In
Figure
4, when
effectiveness
fromfrom
0.8 to
the
According
to the
above from
analysis
data,
as
the heat
exchanger effectiveness increases, the
and
the
cycle
efficiency
increases
about
39%
to
around
52%.
work decreases from 630 kJ/kg to 585 kJ/kg, the expansion work increases from 425 kJ/kg to 500 kJ/kg,
compression
decreases
the expansion
work
so the cycle
efficiency ofincreases,
the system
Accordingwork
to the
aboveand
analysis
as
theincreases,
heat exchanger
effectiveness
and the cycle
efficiency
increases
from
aboutdata,
39% to
around
52%.
increases.
This result
also conforms
basic principles
of thermodynamics.
a larger
the
compression
work decreases
and to
thethe
expansion
work increases,
so the cycle Therefore,
efficiency of
the
According
to theeffectiveness
above analysis
data,
asheat
thetransfer
heat exchanger
effectiveness
increases,
the
heat
exchanger
means
better
effects.
Where
possible,
a
higher
system increases. This result also conforms to the basic principles of thermodynamics. Therefore,heat
a
compression
work
decreases should
and thebeexpansion
work increases, so the cycle efficiency of the system
exchanger
effectiveness
applied.
larger
heat exchanger
effectiveness
means
better heat transfer effects. Where possible, a higher heat

increases.
This effectiveness
result also conforms
to the basic principles of thermodynamics. Therefore, a larger
exchanger
should be applied.
4.4. Temperature
and Pressure
before better
Air Throttling
heat exchanger
effectiveness
means
heat transfer effects. Where possible, a higher heat
4.4.
Temperature
and
Pressure
before
Air
Throttling
exchanger effectiveness
be curve
applied.
Figure 5 is theshould
inversion
of air. The regions of cooling and heating are clearly shown on
theFigure
temperature
pressure coordinates.
If a regions
maximum
inversion
exists
with
an initial
5 is the inversion
curve of air. The
of cooling
and pressure
heating are
clearly
shown
on theair

4.4. Temperature
and
Pressure
before
AirIf Throttling
pressure greater
than
this
pressure,
will raise inversion
the temperature
ofexists
the air.
temperature
pressure
coordinates.
a itmaximum
pressure
with an initial air pressure
greater than this pressure, it will raise the temperature of the air.
Figure
5 is the inversion curve of air. The regions of cooling and heating are clearly shown on
the temperature pressure coordinates.
If a maximum inversion pressure exists with an initial air
1000
pressure greater than this pressure,900
it will raise the temperature of the air.
800
700
T/K

1000

900

T/K

800

600
500
400
300

700

200

600

100

500

0

400

0

5

10

15

20

25

30

35

p/MPa

300
200

Figure 5. Air inversion curve.
Figure 5. Air inversion curve.

100
0
Only if the initial pressure
and
temperature
the
zone, will the air lower its
0
5
10
15
20fall into
25
30 cooling
35
temperature by throttling. The envelope of the
cooling
zone
is
the
inversion
curve. In Figure 5, the
p/MPa
pressure of the air before throttling should be smaller than the maximum inversion pressure, which
is 34.16 MPa for air.
Figure 5. Air inversion curve.

Energies 2018, 11, 2540

9 of 12

The envelope temperature, which is larger than the corresponding temperature of the maximum
if theisinitial
pressure
temperature
into the
zone,ofwill
air lower
its is
inversion Only
pressure,
the upper
partand
of the
inversionfall
curve.
Thecooling
lower part
thethe
inversion
curve
temperature
by
throttling.
The
envelope
of
the
cooling
zone
is
the
inversion
curve.
In
Figure
5,
the boundary of the heating and cooling regions for temperatures below the corresponding
The
envelope
temperature,
which
is
larger
than
the
corresponding
temperature
of
the
maximum
the pressure
ofmaximum
the air before
throttling
should be
smaller
than theof
maximum
inversion
pressure,
temperature
of the
inversion
pressure.
The
temperature
the air before
throttling
must
inversion
is the
part of the inversion curve. The lower part of the inversion curve is
whichpressure,
is 34.16 MPa
forupper
air.
be in the envelope of the upper as well as the in the lower inversion curve.
the boundary
of the temperature,
heating and
cooling
regions
temperatures
below the
corresponding
The envelope
which
is larger
than thefor
corresponding
temperature
of the
maximum
The end state of the air expansion always falls into the two-phase liquid–vapor region, which
inversionofpressure,
is the upper
part of the
inversion
curve.
The lower part
of the
curve is the
temperature
the maximum
inversion
pressure.
The
temperature
of the
air inversion
before throttling
must
means that only a fraction of the gas expanded in this region is liquefied. The liquid air yield ratio
boundary
of
the
heating
and
cooling
regions
for
temperatures
below
the
corresponding
temperature
of
be in the envelope of the upper as well as the in the lower inversion curve.
and the
system cycle
efficiency with
to thethe
temperature
and pressure
of the
theenvelope
air before
the maximum
Therespect
temperature
air
throttling
must be in
The
end stateinversion
of the airpressure.
expansion
always fallsofinto
thebefore
two-phase
liquid–vapor
region, which
throttling,
shown
6 lower
and 7,inversion
assuming that the air is throttled down to atmospheric
the are
upper
wellinasFigures
the
meansofthat
only aasfraction
of in
thethegas
expanded incurve.
this region is liquefied. The liquid air yield ratio
pressure. The
pressure
are 10falls
MPainto
andthe
140two-phase
K, respectively.
The initial
end state
of theand
air temperature
expansion always
liquid–vapor region,
and the system cycle efficiency with respect to the temperature and pressure of the air before
which means that only a fraction of the gas expanded in this region is liquefied. The liquid air
throttling, are shown in Figures 6 and 7, assuming that the air is throttled down to atmospheric
yield ratio and the system cycle efficiency with respect to the temperature and pressure of the air
pressure.
The initial pressure and temperature are 10 MPa and 140 K, respectively.
before throttling, are shown in Figures 6 and 7, assuming that the air is throttled down to atmospheric
0.6

1.0

pressure. The initial pressure and temperature are 10 MPa
and
Liquid air
yield140 K, respectively.
Cycle efficiency

1.0
0.6

0.5
0.6
0.4

Liquid air yield
Cycle efficiency

0.8
0.4

0.5
0.3

0.6
0.2

0.4
0.2

0.4
0.0

0.3
0.1

0.2 70

80

Cycle efficiency
Cycle efficiency

Liquid air yield
Liquid air yield

0.8

90 100 110 120 130 140 150 160 0.2
Air temperature before the throttle /K

0.0

0.1

70 before
80 90air
100
110 120 130
140 150air
160
Figure 6. Influence of temperature
throttling
on liquid
yield ratio and cycle efficiency.
Air temperature before the throttle /K

In Figure
6, 6.
when
the pressure
is under
theon
airliquid
temperature
before
air throttling
Figure
Influence
of temperature
before 10
air MPa,
throttling
air yield ratio
and cycle
efficiency. is 75 K,
Figure 6. Influence of temperature before air throttling on liquid air yield ratio and cycle efficiency.
the liquid air yield ratio is close to 100%, and the cycle efficiency is close to 60%. If the air temperature
In Figure 6, when the pressure is under 10 MPa, the air temperature before air throttling is
is increased from 75 K to 155 K, the liquid air yield ratio and the system cycle efficiency decrease
In
when
pressure
under
10 MPa,
temperature
throttling
75 K,
75Figure
K, the 6,
liquid
airthe
yield
ratio isisclose
to 100%,
andthe
theair
cycle
efficiency before
is closeair
to 60%.
If theisair
monotonically.
temperature
increased
from
K to 155
thecycle
liquid
air yield is
ratio
andtothe
system
cycle
efficiency
the liquid
air yieldis ratio
is close
to75
100%,
andK,
the
efficiency
close
60%.
If the
air temperature
Therefore,
the lower the temperature before air throttling, the higher the liquid air yield ratio
decrease
monotonically.
is increased from 75 K to 155 K, the liquid air yield ratio and the system cycle efficiency decrease
and the cycle
efficiency
afterthe
expansion.
In field
the
temperature
the
throttling
Therefore,
the lower
temperature
beforeconditions,
air throttling,
theair
higher
the liquidbefore
air yield
ratio
and
monotonically.
should
be
as
low
as
possible.
the cycle efficiency after expansion. In field conditions, the air temperature before the throttling should
Therefore, the lower the temperature before air throttling, the higher the liquid air yield ratio
be as low as possible.
and the cycle efficiency after expansion. In field conditions, the air temperature before the throttling
should be as low as possible. 0.40
0.25
0.20

0.30
0.40
0.25
0.35
0.20
0.30
0.15
0.25
0.10
0.20
0.05
0.15
0.00
0.10
0.05

Liquid air yield
Cycle efficiency

Liquid air yield
Cycle efficiency

0.25
0.15
0.20
0.10
0.15
0.05
0.10
0.00

4

6

8

10

12

Cycle efficiency
Cycle efficiency

Liquid air yield
Liquid air yield

0.35

0.05

Air pressure before the throttle /MPa

0.00

0.00

Figure 7. Influence of pressure before air throttling on liquid air yield ratio and cycle efficiency.

4
8 on liquid
10
Figure 7. Influence of pressure before
air6throttling
air12yield ratio and cycle efficiency.
Air pressure before the throttle /MPa

From Figure 7, we can see that both the liquid air yield ratio and the system cycle efficiency are
Influence of pressure before air throttling on liquid air yield ratio and cycle efficiency.
0 in theFigure
5 MPa7.and
140 K initial state. When raising the pressure from 5 MPa to 6 MPa while keeping
the temperature stable, the liquid air yield ratio and system cycle efficiency increase rapidly.
From Figure 7, we can see that both the liquid air yield ratio and the system cycle efficiency are
Then, the liquid air yield ratio and system cycle efficiency increase gradually from 6 MPa to 12
0 in the 5 MPa and 140 K initial state. When raising the pressure from 5 MPa to 6 MPa while keeping
MPa. As shown in Figure 5, the maximum inversion pressure of the air is 34.16 MPa, so the pressure

Energies 2018, 11, 2540

10 of 12

From Figure 7, we can see that both the liquid air yield ratio and the system cycle efficiency are 0
in the 5 MPa and 140 K initial state. When raising the pressure from 5 MPa to 6 MPa while keeping the
temperature stable, the liquid air yield ratio and system cycle efficiency increase rapidly.
Then, the liquid air yield ratio and system cycle efficiency increase gradually from 6 MPa to
12 MPa. As shown in Figure 5, the maximum inversion pressure of the air is 34.16 MPa, so the pressure
before throttling must be less than the maximum inversion pressure, in order to ensure a cold effect
after throttling.
From Figures 6 and 7, for air at a temperature of 140 K, it is necessary to increase its pressure to at
least 6 MPa in order for it to liquefy.
According to the above analysis, the pressure before air throttling has a significant influence on
the liquid air yield ratio and the system cycle efficiency. Higher pressures and lower temperatures
before air throttling are beneficial for increasing the liquid air yield ratio and the system cycle efficiency.
5. Conclusions
For an integrated system of liquefied air energy storage and electricity production, a mathematical
model of the energy storage stage, energy release stage, and cycle parameter calculation has been
established, based on thermodynamic principles. Using the cycle efficiency and the liquid air yield
ratio as evaluation indexes, the influence of the outlet pressure of the compressor unit (p4L ), the outlet
pressure of the cryogenic pump, the heat exchanger effectiveness, the air temperature and pressure
before throttling on the performance of integrated system of liquefied air energy storage, and electricity
generation are discussed. The following conclusions have been obtained:







When raising the outlet pressure of the compressor unit (p4L ), both the compression work and the
expansion work are increased. However, the air is not completely liquefied. The heat collected
during the compression process is not fully used in the energy release phase, so the increase of
the expansion work is slower than that of the compression work, resulting in a decrease in the
cycle efficiency.
After the air is taken out of the liquid air tank, the pressure is increased by the cryogenic pump.
The increased air pressure of the cryogenic pump is equivalent to an increase in the air pressure
at the inlet of the expander, which increases the expansion work. In this process, the consumption
work of the cryogenic pump is much less than the increase in the expansion work, so the system
cycle efficiency increases. A larger heat exchanger effectiveness means a better heat transfer
effect. Therefore, increasing the outlet pressure of the cryogenic pump and the heat exchanger
effectiveness can significantly increase the cycle efficiency of the system.
According to the air inversion curve, the maximum inversion pressure of air is 34.16 MPa, so the
pressure before throttling must be less than the maximum inversion pressure, in order to ensure
the cold effect after throttling. Under the premise of not exceeding the maximum air inversion
pressure, the higher the air pressure and the lower the air temperature before throttling, the greater
the liquid air yield ratio after throttling, and the higher the system cycle efficiency.

Author Contributions: Y.X. proposed the research direction, the adaptive method, and the system model.
X.X. completed the establishment of the mathematical model of the system, programming with MATLAB,
mapping with Origin, and data analysis. X.X. wrote the paper.
Funding: This research received no external funding.
Acknowledgments: This paper was supported by the Natural Science Foundation of Hebei Province (E2014502085).
Conflicts of Interest: The authors declare no conflicts of interest.

Energies 2018, 11, 2540

11 of 12

References
1.

2.
3.
4.
5.
6.
7.

8.
9.
10.
11.
12.

13.
14.

15.
16.
17.
18.
19.
20.
21.
22.
23.

Sciacovelli, A.; Vecchi, A.; Ding, Y. Liquid air energy storage (LAES) with packed bed cold thermal
storage–From component to system level performance through dynamic modelling. Appl. Energy 2017,
190, 84–98. [CrossRef]
Liu, J.; Xia, H.D.; Chen, H.S.; Tan, C.Q.; Xu, Y.J. A novel energy storage technology based on liquid air and
ITS application in wind power. J. Eng. Thermophys. 2010, 31, 1993–1996.
Otsuki, T. Costs and benefits of large-scale deployment of wind turbines and solar PV in Mongolia for
international power exports. Renew. Energy 2017, 108, 321–335. [CrossRef]
Shi, K.; Xu, P.; Wan, Z.; Zhao, D. Grid-connected dual stator-winding induction generator wind power
system for wide wind speed ranges. J. Power Electron. 2016, 16, 1455–1468. [CrossRef]
Fan, X.C.; Wang, W.Q.; Shi, R.J.; Li, F.T. Analysis and countermeasures of wind power curtailment in China.
Renew. Sustain. Energy Rev. 2015, 52, 1429–1436. [CrossRef]
Ferreira, H.L.; Garde, R.; Fulli, G.; Kling, W.; Lopes, J.P. Characterisation of electrical energy storage
technologies. Energy 2013, 53, 288–298. [CrossRef]
Pazheri, F.R.; Othman, M.F.; Al-Ammar, E.A.; Safoora, O.K. Clean and efficient power dispatch at hybrid
power plant with energy storage. In Proceedings of the IEEE Power & Energy Society General Meeting,
Denver, CO, USA, 26–30 July 2015; pp. 1–5.
Guizzi, G.L.; Manno, M.; Tolomei, L.M.; Vitali, R.M. Thermodynamic analysis of a liquid air energy storage
system. Energy 2015, 93, 1639–1647. [CrossRef]
Weiji, H.; Changfu, Z.; Chen, Z.; Zhang, L. Estimation of cell SOC evolution and system performance in
module-based battery charge equalization systems. IEEE Trans. Smart Grid 2018. [CrossRef]
Zou, C.; Zhang, L.; Hu, X.; Wang, Z.; Wik, T.; Peche, M. A review of fractional-order techniques applied to
lithium-ion batteries, lead-acid batteries, and supercapacitors. J. Power Sour. 2018, 390, 286–296. [CrossRef]
Bianch, G.; Cipollone, R. Theoretical modeling and experimental investigations for the improvement of the
mechanical efficiency in sliding vane rotary compressors. Appl. Energy 2015, 142, 95–107. [CrossRef]
Marchionni, M.; Bianchi, G.; Tassou, S.A. Techno-economic assessment of Joule-Brayton cycle architectures
for heat to power conversion from high-grade heat sources using CO2 , in the supercritical state. Energy 2018,
148, 1140–1152. [CrossRef]
Evans, A.; Strezov, V.; Evans, T.J. Assessment of utility energy storage options for increased renewable energy
penetration. Renew. Sustain. Energy Rev. 2012, 16, 4141–4147. [CrossRef]
Rodrigues, E.M.G.; Godina, R.; Santos, S.F.; Bizuayehu, A.W.; Contreras, J.; Catalão, J.P.S. Energy storage
systems supporting increased penetration of renewables in islanded systems. Energy 2014, 75, 265–280.
[CrossRef]
Budt, M.; Wolf, D.; Span, R.; Yan, J. Compressed air energy storage—An option for medium to large scale
electrical-energy storage. Energy Procedia 2016, 88, 698–702. [CrossRef]
Klumpp, F. Potential for large scale energy storage technologies—Comparison and ranking including an
outlook to 2030. Energy Procedia 2015, 73, 124–135. [CrossRef]
Xu, Y.; Chen, H.; Liu, J.; Tan, C. Performance analysis on an integrated system of compressed air energy
storage and electricity production with wind-solar complementary method. Proc. CSEE 2012, 32, 88–95.
Brett, G.; Barnett, M. The application of liquid air energy storage for large scale long duration solutions to
grid balancing. In Proceedings of the EDP Sciences, Budapest, Hungary, 27 October 2014.
Antonelli, M.; Desideri, U.; Giglioli, R.; Paganucci, F.; Pasini, G. Liquid air energy storage: A potential low
emissions and efficient storage system. Energy Procedia 2016, 88, 693–697. [CrossRef]
Xue, X.D.; Wang, S.X.; Zhang, X.L.; Cui, C.; Chen, L.B.; Zhou, Y.; Wang, J.J. Thermodynamic analysis of a
novel liquid air energy storage system. Phys. Procedia 2015, 67, 733–738. [CrossRef]
Morgan, R.; Nelmes, S.; Gibson, E.; Brett, G. Liquid air energy storage: Analysis and first results from a pilot
scale demonstration plant. Appl. Energy 2015, 137, 845–853. [CrossRef]
Chino, K.; Araki, H. Evaluation of energy storage method using liquid air. Heat Tran. Asian Res. 2015,
29, 347–357. [CrossRef]
Li, Y.; Cao, H.; Wang, S.; Jin, Y.; Li, D.; Wang, X.; Ding, Y. Load shifting of nuclear power plants using
cryogenic energy storage technology. Appl. Energy 2014, 113, 1710–1716. [CrossRef]

Energies 2018, 11, 2540

24.

25.
26.

27.

12 of 12

Span, R.; Lemmon, E.W.; Jacobsen, R.T.; Wagner, W.; Yokozeki, A. A reference equation of state for the
thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and Pressures to 2200 MPa.
J. Phys. Chem. Ref. Data 2000, 29, 1361–1433. [CrossRef]
Schmidt, R.; Wagner, W. A new form of the equation of state for pure substances and its application to
oxygen. Fluid Ph. Equilibria 1985, 19, 175–200. [CrossRef]
Borri, E.; Tafone, A.; Romagnoli, A.; Comodi, G. A preliminary study on the optimal configuration
and operating range of a “microgrid scale” air liquefaction plant for Liquid Air Energy Storage.
Energy Convers. Manag. 2017, 143, 275–285. [CrossRef]
She, X.; Peng, X.; Nie, B.; Leng, G.; Zhnag, X.; Weng, L.; Tong, L.; Zheng, L.; Wang, L.; Ding, Y. Enhancement
of round trip efficiency of liquid air energy storage through. Appl. Energy 2017, 206, 1632–1642. [CrossRef]
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).


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