Journal of Energy Storage 11 (2017) 178–190

Contents lists available at ScienceDirect

Journal of Energy Storage

journal homepage: www.elsevier.com/locate/est

Dynamic modeling and simulation of an Isobaric Adiabatic Compressed

Air Energy Storage (IA-CAES) system
Youssef Mazloum* , Haytham Sayah, Maroun Nemer
MINES ParisTech, PSL – Research University, CES – Center for Energy Efficiency of Systems (CES), Z.I. Les Glaizes – 5 rue Léon Blum, 91120 Palaiseau, France

A R T I C L E I N F O A B S T R A C T

Article history:
Received 14 January 2017 This paper discusses the dynamic modeling of an innovative Isobaric Adiabatic Compressed Air Energy
Received in revised form 4 March 2017 Storage (IA-CAES) system using “Dymola”. The system is a solution to reduce the effect of the
Accepted 5 March 2017 intermittence of the renewable energy sources and thus improve the penetration of these sources into
Available online 17 March 2017 the energy mix. It also enables restoring the balance between supply and demand for electricity and
supporting the electrical grid. The proposed system is characterized by the recovery of the compression
Keywords: heat and the storage of air under fixed pressure in order to improve its efficiency and its energy density.
Dymola The dynamic model takes into account the mechanical inertia of the turbo-machinery as well as the
Dynamic modeling
thermal inertia of the heat exchangers and the storage tanks. This allows the model to evaluate the
Isobaric Adiabatic Compressed Air Energy
response time of the storage system and its ability to meet the power demand. Then, it allows studying
Storage (IA-CAES) system
Primary reserve the flexibility of the storage system by evaluating the durations of the transient states and the proposals
Secondary reserve to reduce these durations. The system efficiency is 53.6%. The results show that the time required to reach
the steady state is about 120 s during storage periods and 382 s during production periods. In addition,
the power consumed or produced by the storage system matches with the set point with maximum delay
of 6 s and maximum relative error of 9%. The system is then able to reach the nominal power in few
minutes (secondary reserve). Finally, a standby mode with minimal energy consumption is studied in
order to reduce the durations of the transient states and then to be able to meet the primary reserve (by
reaching 33% of the nominal power in 10 s). It consists in operating the compressor at 54% and the turbine
at 72% of their nominal speeds.
© 2017 Elsevier Ltd. All rights reserved.

1. Introduction Among the large scale energy storage technologies [5], the
pumped hydro storage system and the compressed air energy
The contribution of the renewable energy sources in the energy storage (CAES) system are the only storage technologies with high
generation mix is increasing due to the rarefaction of the fossil fuel energy storage capacity and power capacity. However, these
sources and the global warming. However, these sources are systems have high capital costs, negative environmental impacts
intermittent and break the balance between the grid load demand and their propagation is limited by the availability of suitable
and the generation. In addition, the peak consumption periods geological sites [6]. This paper develops an Isobaric Adiabatic
cause hard constraints on the electrical grid to maintain the quality Compressed Air Energy Storage (IA-CAES) system. It has the
of the power supply (frequency and voltage) [1,2]. Hence, the advantages of being an ecological solution, by avoiding the use of
energy storage technologies are required to manage the balance hydrocarbon fuels, and does not require suitable sites.
and provide steady and predictable power. The energy is then Many studies have been reported in the literature regarding the
stored during the off-peak load hours and released back during the dynamic modeling of the CAES systems. M. Saadat et al. [7] studied
peak load hours to support the electrical grid [3,4]. the dynamic modeling and control of an innovative CAES system to
store the energy produced by wind turbines as compressed fluid in
a high pressure dual chamber liquid-compressed air storage vessel
(
200 bar). The system consists of a piston pump, a liquid piston
* Corresponding author at: MINES ParisTech, CES - Center for energy efficiency of air compressor/turbine and a hydro-pneumatic accumulator. The
systems (CES), 5 rue Léon Blum, 91120 Palaiseau, France. dynamic model was constructed by taking into account the
E-mail addresses: youssef.mazloum07@gmail.com (Y. Mazloum),
haytham.sayah@mines-paristech.fr (H. Sayah), maroun.nemer@mines-paristech.fr
mechanical inertia of the system and by neglecting its thermal
(M. Nemer). inertia. The storage plant was regulated by a non-linear controller

http://dx.doi.org/10.1016/j.est.2017.03.006
2352-152X/© 2017 Elsevier Ltd. All rights reserved.
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 179

to optimize the power produced by the wind turbines, ensure the

Nomenclature
electric demand and maintain a fixed storage pressure. S. K.
Khaitan and Raju [2] analyzed a conventional CAES system using
A Area, (m2)
the data of the Huntorf installation. This system involves various
CAES Compressed air energy storage
components such as the compressor, the underground cavern, the
C Torque
turbine, the combustion chamber and so on. A static model is
Cp Specific heat capacity, (J/kg K)
developed by assembling the models of the system components.
Dh Hydraulic diameter, (m)
Just the cavern was dynamically modeled. The latter was used to
E Energy, (J)
assess the air pressure and temperature variations over time in
F Friction coefficient
order to study the dynamics of the cavern. L. Nielsen and Leithner
f Frequency, (Hz)
[8] proposed an isobaric adiabatic CAES system combined with a
g Slip factor
heat recovery steam generator. Air is compressed and stored in an
H Piezometric head, (m)
underground cavern where the pressure is kept almost constant
h Mass enthalpy, (J/kg)
through a counter hydraulic pressure ensured by a brine shuttle
hcv Heat convection coefficient, (W/m2 K)
pond at the surface. A detailed dynamic model of the cavern was
HPC High pressure compressor
developed and simulated. It was used to evaluate the thermody-
HPT High pressure turbine
namic characteristics of the stored air by taking into account the
HR Humidity ratio
heat exchange with the water and the outside. E.O. Sampedro [9]
I Moment of inertia, (kg m2)
considered a hydro-pneumatic storage system using a rotody-
IA-CAES Isobaric adiabatic compressed air energy storage
namic machine (pump/turbine). A dynamic model was carried out
K Constant
to study the thermodynamic characteristics and the evolution of
KT Constant
the air diffusion into the water over time in the storage reservoirs.
LPC Low pressure compressor
Dynamic models were also constructed to study the dynamics of
LPT Low pressure turbine
the hydraulic circuit, the rotodynamic machine and the shafts.
m_ Mass flow rate, (kg/s)
This paper focuses on the dynamic modeling of an IA-CAES
M Mass, (kg)
system in order to study the flexibility of the storage system, the
MPC Medium pressure compressor
response time of its elements and its ability to meet the electrical
MPT Medium pressure turbine
demand presented by the primary and secondary reserves.
P Power, (W)
According to the grid manager, the primary reserve consists in
Per Perimeter, (m)
reaching 33% of the nominal power in 10 s and the secondary
Po Number of pole pairs
reserve consists in reaching the nominal power in few minutes.
p Pressure, (Pa)
Then, the dynamic model takes into account the mechanical inertia
pv Saturation pressure, (Pa)
of the turbo-machinery (centrifugal machines) as well as the
qV Volume flow rate, (m3/s)
thermal inertia of the heat exchangers and the storage tanks. A
R Resistance, (V)
control system is also integrated in the dynamic model to control
RP Pressure ratio
the energy produced/consumed by the storage system, to manage
S Cross sectional area, (m2)
the heat exchangers and to keep a fixed pressure in the air storage
t Time, (s)
reservoirs.
T Temperature,  C
The dynamic model is developed using Dymola [10], a software
u Internal energy, (J/kg)
designed to enable a practical modeling of complex systems. The
V Volume, (m3)
simulation language “Modelica” of the Dymola software is an
VN Tension, (V)
object oriented language. It is a modeling language, rather than a
v Velocity, (m/s)
conventional programming language. The thermodynamic prop-
x Abscissa, (m)
erties of the working fluids (dry air and water) are calculated by the
X Reactance, (V)
Dymola fluid libraries [11,12].
This paper is organized as follows. A brief overview of the IA-
Greek symbols
CAES architecture is presented in Section 2. After that, the dynamic
h Efficiency, (%) model of each component of the storage plant is carried out in
r Density, (kg/m3) Section 3. The simulation results are analyzed in Section 4. And
v Angular velocity, (rad/s) finally, the conclusions are drawn in Section 5.
V Angular velocity, (RPM)
l Thermal conductivity, (W/m K) 2. System overview
j Pressure loss coefficient
D Difference w water The IA-CAES system is shown in Fig. 1. This system consists of a
multi-stage centrifugal compressor with inter-cooling (3 stages), a
Subscripts
multi-stage centrifugal turbine with inter-heating (3 stages), 4
elec Electric
centrifugal pumps, 1 Pelton turbine, air/water tanks and hot water
G Gas
tanks.
i Space step
The system can be divided into two subsystems (see Fig. 1),
in Input
namely, the storage and the production subsystems. During off-
ise Isentropic
peak periods, air is pressurized into the air/water tanks maintained
out Output
under a pressure of 120 bar. The compression is performed in 3
W Wall
stages using the excess energy available on the electrical grid. A
heat exchanger is installed after each stage of compression to cool
down the exiting hot air by water. Then, the hot water is stored in
thermally insulated tanks under pressure. During peak periods, the
180 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

Fig. 1. Schematic diagram of the proposed IA-CAES system.

compressed air is expanded through 3 air turbines to release back since these components are expected to be maintained hot and the
the stored energy. The compressed air is heated before each stage fact that we don’t have enough data from the suppliers. Moreover,
of expansion through heat exchangers using the stored hot water. the thermal inertia of the hydraulic turbine and the pump is
The air storage pressure is maintained constant using a counter- neglected given that water is an incompressible fluid, and the
hydraulic pressure. This is done by adding/removing water to/from compression and expansion processes are then done with small
the air/water reservoirs during the storage and the production variation in water temperature.
phases. A Pelton turbine is installed at the water outlet of the The modeling validation is based on a model by model
storage tanks to recover the potential energy from the compressed validation of the system elements by using data from the literature
water during the storage phase and a pump is also installed for and experimental measurements from test benches constructed at
pumping water into the tanks during the production phase to keep our laboratory.
the storage tanks at constant pressure.
The hot water is stored under a pressure slightly higher than the 3.2. Air turbine
saturation vapor pressure of water to prevent its evaporation. The
vapor condenses because of the storage pressure increase while Starting and shutting down of the centrifugal machines affect
the hot water fills the tanks in storage mode. However, the hot the performance of the storage system, the characteristic time of
water evaporates while it is destocked and the pressure slowly these machines depends mainly on their kinetic inertia, thermal
decreases in production mode so as to maintain the thermal inertia and technical constraints (friction forces between the
storage pressure above the saturation pressure. moving elements of the machine). The dynamic model of the air
The storage of air under fixed pressure in steel tanks leads to turbine is composed of three stages of expansion. This model takes
overcome the problem of the site constraints, reduce the efficiency into account in each stage the mechanical inertia of the machine
losses due to pressure variation and use the total air inside the and the different efficiencies (isentropic, mechanical and electri-
tanks to produce electricity unlike caverns with constant volume cal) which allow assessing the changes in pressure and tempera-
[13]. Moreover, the adiabatic operation of the cycle avoids the ture at the air outlet and the corresponding losses. The transient
usage of an external thermal supply during the air expansion, phases of the turbine are modeled by taking into account the
unlike the non-adiabatic CAES plants. Finally, the adiabatic storage instructions of the supplier (General Electric). A description
under fixed pressure improves the performance and the energy scheme for the air turbine model is presented in Fig. 2 for one
density (up to 12 kWh/m3) of the storage plant. stage.

3. Dynamic modeling

3.1. Introduction

The dynamic model is divided into subsystems which present

the components of the storage plant. Each component encloses the
mass and the energy conservation laws. A control model is also
included to control and optimize the system operation.
The flow regime is assumed to be stationary because its
characteristic time is lower than that of the other components. The
thermal inertia of the compressor and the air turbine is neglected
Fig. 2. Description scheme for the air turbine model.
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 181

The relation between the rotational speed of the rotor and the
motor and resistance torques is expressed by the Newton's Second
law as follows [9]:
dv
I ¼ C motor þ C resistance ð1Þ
dt
The motor torque “Cmotor” is provided by the fluid flowing through
the machine and the resistance torque “Cresistance” is induced by the
generator load.
The expansion process is assumed to be polytropic and the
isentropic efficiency is assessed by an empirical polynomial Fig. 3. Description scheme for the compressor model.
equation specific for each stage of expansion, it takes into account
the variation of the flow rate and the angular velocity. The by the electric motor in this case and the resistance torque is
efficiency equations are calculated based on curves given by the caused by the circuit load. The angular velocity is given as a
supplier. The outlet enthalpy is given by (2) where “hise” is the parameter during the startup phase.
isentropic enthalpy assessed by assuming an isentropic transfor- However, the outlet enthalpy, the consumed power and the
mation. resistance torque are given by (8), (9) and (10) respectively.
hout ¼hin hise ðhin hise Þ ð2Þ hise  hin
hout ¼ hin þ ð8Þ
The motor torque is given by (3) and the electric power,
hise
produced by the generator, is calculated by (4) by taking into
account the friction loss (friction on the bearings) and the electrical
C motor v
loss. Pelec ¼ ð9Þ
helec
_ ðhin  hout Þ ¼ C motor v
Pmotor ¼ m ð3Þ



 Presistance ¼ C resistance v ¼  m_ ðhout  hin Þ þ F v1:6 ð10Þ
Pelec ¼ helec C resistance v ¼  Pmotor  F v2 helec ð4Þ
Assuming a known pressure ratio (computed through the air/
The pressure ratio and the mass flow rate of the turbine are water tanks model as a function of the stored air and water
linked by the Stodola equation (Eq. (5)) which determines the flow characteristics), the flow rate is computed by an empirical
behavior depending on the pressure ratio [14,15]. characteristic equation assessed through curves given by the
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi manufacturer. This equation is a relation between the compression
 
pin Pout 2 ratio and the flow rate, it takes into account the losses and the flow
_
m ¼ kT p ffiffiffiffiffiffi
ffi 1 ð5Þ
T in Pin leakage inside the machine. The characteristic equation varies also
with the rotational speed of the rotor and then is determined by
Where “kT” is a constant that can be obtained by the data extracted
the similitude laws. For a given angular velocity, it is described as
from the turbine’s responses [16].
[18]:
The turbine model includes a control system which serves to
adjust the flow rate (through PID) through a valve installed at the _ i ÞÞ1 ð1  expðkmÞÞ
Rp ¼ ð1  Rp;i Þð1  expðkm _ þ Rp;i ð11Þ
inlet so as to always have the rated speed which depends on the
electric generator properties and the grid frequency. This control Where “Rp,i” is the pressure ratio at zero flow, it is calculated using a
system is divided into two subsystems, a speed control system, and three-order polynomial function having the square of the
a power control system. The speed control system regulates the rotational speed as a variable. The variable “m _ i ” is the mass flow
flow during the starting phase to reach the rated speed. Once the rate for a unit pressure ratio, it is evaluated by the similitude laws
rated speed is reached, the power control system regulates the [19]. “k” is a constant which depends on the curvature of the
produced power as a function of the requested electrical load and curves. These variables are calculated by minimizing the difference
this is achieved by controlling the generator speed according to the between the empirical curves and the characteristic function.
set point speed (vsetpoint). A three-phase asynchronous generator is The consumed power of the compressor is controlled by the air
used in this case. The slip factor and the resistance torque are pressure ratio since the pressure ratio and the mass flow rate are
described by the following equations [17]: related by (11). The discharge pressure of the compressor is
imposed by the air/water tanks model and the inlet pressure is
vsetpoint  ð2pf =PoÞ controlled by a linear valve installed at the compressor air inlet.
g¼ ð6Þ
ð2pf =PoÞ Therefore, this valve regulates the compression ratio according to
the set point power.
The motor is a three-phase synchronous type, the relation
3PoR2 V 2N between the frequency and the angular velocity is defined by the
C reistance ¼     ð7Þ
2pf 2 following equation:
Po g R1 þ Rg2 þ ðX 1 þ X 2 Þ2
60f
V¼ ð12Þ
Po
3.3. Compressor
3.4. Pump
The dynamic model of the centrifugal compressor is similar to
that of the turbine (Fig. 3). The compressor is divided into 3 stages The pump model is similar to that of the compressor with a
and the compression process is assumed to be polytropic. The three-phase synchronous motor. The isentropic efficiency is given
angular velocity is given by (1) where the motor torque is provided by a polynomial equation, as function of the flow rate and the
182 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

angular velocity, based on empirical curves provided by the

supplier. Then, the resistance torque and the flow rate are given as
follows [20,21]:

Presistance ¼ C resistance v ¼  m
_ ðhout  hin Þ þ F v2 ð13Þ

 2
v v
Hout  Hin ¼ aq2V þ b q þc ð14Þ
vn V vn
Where “vn” is the nominal speed of the pump. The constants of
Eq. (14) are calculated based on the pump characteristic curves
provided by the supplier.
Furthermore, the Net positive suction head available (NPSHa)
should be higher than the Net positive suction head required
(NPSHr) in order to avoid the suction cavitation. This phenomenon
is considered in the numerical model. Fig. 5. Air mass flow rate.
Finally, the pump is controlled through a speed variator, it
regulates the pump frequency and hence the water flow rate so as
to maintain a fixed pressure in the air/water storage tanks.

3.5. Hydraulic turbine

The hydraulic turbine model is similar to the air turbine model.

However, the generator type is synchronous. In addition, the mass
flow rate is controlled by the intake valve [22] considered linear in
our application.
The control system of this component is similar to that of the air
turbine, it avoids the damage of the turbine and the water hammer
phenomenon. The set point power is evaluated as to preserve a
fixed pressure in the air/water tanks.

3.6. Validation of the centrifugal machines

A test bench was constructed in order to validate experimen- Fig. 6. Angular velocity of the turbo-compressor, comparison of theory and
tally the numerical model of the air turbine. A turbo-compressor, experiment.
which has the same technology of the centrifugal turbine, was then
used for this purpose. It has a mechanical inertia of 2.8  106 kg the turbine. Moreover, the theoretical and experimental curves are
m2 and a friction factor F of about 200  108 (supplier data). The also in agreement during the transient operation of shutdown. The
inlet pressure and mass flow rate are given in Fig. 4 and Fig. 5 angular velocity is a result of the physical phenomena taking place
respectively, the air inlet temperature is about 62  C and the in the turbine. Thus, the validation of this variable implicitly
pressure ratio is about 1.033. The resulted angular velocity is given validates all the physical phenomena included in the numerical
in Fig. 6. model (the air expansion, the torque, the isentropic efficiency,
The theoretical and experimental angular velocities of the . . . ).
turbine (see Fig. 6) have the same shape and are in agreement The models of the other centrifugal machines are based on the
during the steady and the transient states. The angular velocity same physical phenomena and approximations included in the air
increases at the startup for reaching the stationary value in 5 s. This turbine model. The empirical equations included in these models
value is validated by the numerical model for the given inertia of are, in addition, verified with the curves supplied by the
manufacturers. Hence, these models can be adopted.

3.7. Heat exchanger

The heat exchangers used in the storage system are counter

flow shell and tube heat exchangers. These components are
essential to recover the compression heat during the storage
periods and release it back to warm up the compressed air during
the production periods. The thermal inertia of the heat exchanger
increases the transient state durations. The waste heat and the
homogenization of the temperature, when the heat exchangers are
in standby mode, are also important. Hence, the dynamic modeling
of the heat exchangers by taking into account all these losses is
essential.
The model of the heat exchangers consists in modeling the heat
transfer between two fluids through a tube in a tube, and by taking
into account the geometric characteristics of the heat exchanger
(tubes number and length, tube and shell diameters, baffles and
Fig. 4. Air intake pressure.
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 183

number of tube-side passes) [23,24]. A one-dimensional approach The pressure loss coefficient is computed by the Haaland
is considered. Therefore, the flow is simplified to a counter current correlation as stated in [27]. The hydraulic diameter is given by:
flow of a tube in a tube and the thermal inertia of the shell is
4S
equally distributed between the outer tubes. The air circulates in Dh ¼ ð20Þ
Per
the inner tube and the water in the outer tube.
The heat exchanger is divided into several elementary volumes The transitional behaviors of the heat exchanger are validated
with length Dx as shown in Fig. 7 in order to define the partial by comparison with experimental measurements from a test
differential equations that govern the heat transfer. The local bench that was built for this purpose. A shell and tube heat
energy balances applied to the elementary volumes of gas, the exchanger with 31 tubes (length = 1.115 m, tube radius = 19.05 mm
inner tube, the liquid and the outer tube give the Eqs. (15), (16), and shell radius = 150 mm) is considered. The air inlet pressure is
(17) and (18) respectively [24,25]. equal to 2.1 bar, the air and water inlet temperatures are equal to
25  C and the air mass flow rate is of 55 g/s. The water input flow
@uG;i _


rate and temperature are given in Fig. 8 and Fig. 9 respectively and
MG;i ¼ mG hG;i1  hG;i þ hcv;i A T W in;i  T G;i
@t the resulted output air and water temperatures are given in Fig. 10
lG;i S


þ T G;i1  T G;i þ T G;iþ1  T G;i ð15Þ and Fig. 11 respectively. The temperature drop in Fig. 9 is due to the
Dx
cold water initially contained in the heat exchanger since water
circulates in a closed circuit. Once the steady state is established,
@T W;i
 the water mass flow rate is reduced as shown in Fig. 8.
MW CpW ¼ hcv T G;i  T W;i
in;i Ain During the transient phase, the theoretical and experimental air
@t

þ hcv out;i Aout T L;i  T W;i output temperatures (Fig. 10) have the same profile with a
lW S

 maximum gap of about 10% (5  C). This discrepancy is caused first,
þ T  T W;i þ T W;iþ1  T W;i ð16Þ
Dx W;i1 by the differences between the theoretical curves used to assess
the experimental input parameters and the real input parameters
(3.5% of gap on the water mass flow rate and 2.5  C of gap on the
@uL;i _

 water input temperature) and secondly, by the assumptions used
ML;i ¼ mL hL;iþ1  hL;i þ hcv in;i Ain TW  T L;i
@t in;i
in the model (one dimensional approach of heat transfer between

 two fluids through a tube in a tube). The two curves are in
þhcv out;i Aout  T L;i
TW out;i
lL S

 agreement at the steady state phase. Regarding the water output
þ T  T L;i þ T L;iþ1  T L;i ð17Þ temperature, the theoretical and experimental curves (Fig. 11) are
Dx L;i1
in agreement with a maximum relative deviation of 5% (3  C).
Consequently, the dynamic model of the heat exchanger is
@T W;i
 experimentally validated.
MW CpW ¼ hcv T L;i  T W out;i
in;i Ain
@t

þ hcv out;i Aout T a  T W;i 3.8. Hot water tanks
lW S


þ T  T W;i þ T W;iþ1  T W;i ð18Þ
Dx W;i1 The description scheme of the hot water tanks model is
Where “A” represents the longitudinal heat transfer area and “S” is illustrated in Fig. 12. The dynamic model is carried out assuming
the cross-sectional area. that air and water are in direct contact, hence the need to take into
The convection and axial conduction phenomena are consid- account the mass transfer in the modeling. A one-dimensional
ered in the above equations. The conduction phenomenon leads to model is adopted to examine the transient states due to its
calculate the temperature homogenization during the standby simplicity and its rapid calculation [28]. In addition, this model
periods. The convective heat transfer coefficients between the fluid takes into account the losses due to the water evaporation. Finally,
(air or water) and the tube are calculated, as function of the the cross sectional area depends on the volume of air and water in
geometric characteristics of the heat exchanger, by using the tanks since the flow is perpendicular to the cylinder axis.
correlations based on the Reynolds, the Prandtl and the Nusselt The meshes temperatures in Fig. 12 are calculated by the energy
numbers as stated in [26]. conservation law presented by (21) and (22) for the fluid (air or
The pressure losses are approximated by the Darcy-Weisbach water) and the wall respectively [2,24], they are similar to those of
equation as follows: the heat exchanger with an additional term in (21) corresponding
to the pressure variation (Vi@p/@t). The thermal conduction is taken
Dxrvjvj
Dp ¼ j ð19Þ
Dh 2

Fig. 7. Description scheme of the model of the shell and tube heat exchanger. Fig. 8. Water mass flow rate.
184 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

@T W;i

MW CpW ¼ hcv in;i AinT i  T W out;i
@t

þ hcv out;i Aout T a  T W;i
lW S


þ T  T W;i þ T W;iþ1  T W;i ð22Þ
Dx W;i1
The mass transfer occurs by evaporation and condensation of
water and then by varying the humidity ratio. The latter is
calculated by (23) according to the properties of the water mesh
(mesh N) in contact with air [29].
Mvapor pv
HR ¼ ¼ 0:62198 ð23Þ
Mdry air pN;water  pv

In order to calculate the heat transfer resulting from the mass

transfer at the air/water interface, the terms presented in (24)
Fig. 9. Water inlet temperature.
should be added to (21) to calculate the temperature of the hot
water mesh in contact with air. In Eq. (24), the latent heat term is
added in case of evaporation and the third term in case of
condensation.

@hN dMvap
MN ¼ Eq:ð21Þ  DhLatent ðT N Þ
@t dt
dMvap

 h T air;1 ; pair;1  hN ð24Þ
dt
The masses of the moist air and the hot water are calculated by
(25) and (26) respectively (mass conservation law). The inside
pressure of the water tanks is a result of saturation between the
water and the moist air. And the pressure losses are assumed to be
zero because the flow velocity inside the tanks is low (high cross
sectional area). The convective heat transfer coefficients in (21)
and (22) are calculated using correlations based on the Reynolds,
Rayleigh, Prandtl and Nusselt numbers as stated in [26].

dMair dMvap
Fig. 10. Theoretical and experimental air output temperatures.
¼ ð25Þ
dt dt

dMwater dMvap
_ in;water þ m
¼m _ out;water  ð26Þ
dt dt
The model is validated by comparison with experimental
measurements from the literature. S. Alizadeh [26] carried out an
experimental and numerical study of the thermal stratification of
warm water in a horizontal cylindrical tank of a solar thermal
system (Fig. 13). The tank is made of Plexiglas and insulated with
glass fiber (negligible heat loss), it has as dimensions a diameter of
0.5 m and a length of 1.5 m. The hot water is initially at 42  C. The
tank is then fed by a cold water flow rate of 6 l/min at 20  C. The
comparison between the simulation results of the theoretical
model of Dymola with those experimental and theoretical of S.
Alizade is shown in Fig. 14.
The maximum relative error between the theoretical results of
our model and the experimental ones does not exceed 9%. This
Fig. 11. Theoretical and experimental water output temperatures. difference occurs mainly at the tank bottom, it is due to the fact
that the mixture produced at the bottom of the tank by the input
stream is not taken into account by the numerical model [28]. The
into account in these equations in order to assess the homogeni- relative difference between the theoretical results of our model
zation of the temperature during the standby phases. and the numerical model of S. Alizadeh is 4% maximum. Hence, the
Note that the mesh size varies with the filling ratio of the hot model of the hot water tanks is validated.
water tanks. The model of the air/water tanks is similar to that of the hot
water tanks with two differences, the flow is parallel to the
@hi _
 cylinder axis (constant cross flow section) and the mass transfer at
Mi ¼ mðhi1  hi Þ þ hcv;i A T W in;i  T i
@t the air/water interface is neglected.
lS @p
þ i ½ðT i1  T i Þ þ ðT iþ1  T i Þ þ V i i ð21Þ Note that the maximum gap between the theoretical and
Dx @t
experimental results occurs on the air output temperature of the
heat exchanger. It is then the most likely to distort outcomes
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 185

because it affects mainly the power produced by the turbine.

Moreover, a parametric study was carried out and showed that the
system efficiency is most sensitive to the turbine power. According
to the simulation results, a gap of 10% on the air temperature
induces a maximum error of 8% on the produced power.
A global control model is designed for the dynamic model of the
storage system. It is modeled by first order PIDs and permit
adjusting the produced/consumed power, regulating the storage
pressure and the water mass flow rate in the heat exchangers. The
results of the dynamic simulations are presented in the next
section in order to verify the capacity of the system to react facing a
power demand and its ability to respond to the primary and
secondary reserves.

4. Results and discussion

4.1. Secondary reserve

The inertias that increase the response time of the storage

system are the thermal inertia of the heat exchangers and the
mechanical inertia of the centrifugal machines. A scenario is
Fig. 12. Discretisation of the hot water tanks.. simulated below to study the system behavior at the start-up and
shut down, and to prove its capacity to meet the secondary reserve.
The electrical efficiency of the centrifugal machines is consid-
ered fixe and equal to 98%, the optimal isentropic efficiency of the
compressor and the air turbine is assumed to be 87% and that of the
pump and the hydraulic turbine is supposed equal to 92 (suppliers
data). The mechanical inertia, the rated angular velocity and the
friction coefficient (mechanical losses) of these machines are
summarized in Table 1 based on data supplied by the manufac-
turers.
At the start-up phase, all the heat exchangers are cold and the
centrifugal machines are off. This scenario is simulated over a
period of 17 h, the storage phase duration is 12 h whereas the
Fig. 13. Scheme diagram of the hot water tank. production phase duration is 5 h. The consumed power (PCompressor
 PHydraulic_turbine) is 16.4 MW and the produced power (PTurbine 
PPump) is 18.5 MW. For this capacity, 35 air/water tanks of 308 m3 of
unit volume and 6 hot water tanks of 226 m3 of unit volume are
required. The transitional phases are discussed in the following,
the ascent and descent in power are taken equal to 15 MW/min
(secondary reserve).

4.1.1. Air/water tanks

The variation of the storage pressure is shown in Fig. 15. During
storage mode, the compressor delivers air in the reservoirs. In
order to compensate the pressure raise at the start-up phase, the
set point power of the hydraulic turbine is regulated to retouch the
storage pressure of 120 bar. Thus, the pressure increases to
123.2 bar before reaching again the stationary pressure. The offset
between the times of the flow rate rise of the compressor and the
Pelton turbine is 136 s. Indeed, the compressor control is more
sensitive and rapid than that of the hydraulic turbine because a
storage pressure range of [115 bar, 125 bar] is acceptable.
During production mode, the air expansion in the turbine
Fig. 14. Variation of the water temperature in the tank at t = 28 min, comparison
causes the pressure drop at the beginning of this phase. This fall is
between theory and experiment.
caught by a water flow provided by a centrifugal pump whose

Table 1
Parameters of the centrifugal machines.

LPC MPC HPC LPT MPT HPT Pump H_Turbine

Inertia (kg.m2) 200 200 200 60 60 120 50 50
Angular velocity (RPM) 6487 6507 11292 8000 8000 17000 3000 750
Generator inertia (kg.m2) 300 540 85 20
Generator velocity (RPM) 1500 1500 3000 750
Friction factor 3.20 3.28 1.53 0.17 0.17 0.02 0.27 8.1
186 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

other words according to the power generated by the hydraulic

turbine to recover the water potential energy.
Fig. 17 shows the mass flow rate and the power produced by the
turbine. The turbine flow rate is controlled to attain the rated
speed. Similarly to the compressor, the flow rate varies first
according to the mechanical inertia and the friction forces on the
turbine rotor to reach the required speed. Once the desired speed is
reached, a minimum flow rate of 8.5 kg/s is imposed in order to
overcome the friction forces and therefore maintain the turbine
rotational speed at the desired value. The turbine is then kept
under this state (standby mode) for 1 min in order to synchronize
and couple it to the power grid (supplier data). The total duration of
this step is 5 min. The flow rate increases then as function of the
requested power and its slope varies with the enhancement of the
turbine isentropic efficiency. Furthermore, the flow rate and the
power vary later after the synchronization of the turbine with the
grid depending on the storage pressure. Consequently, the
Fig. 15. Air storage pressure. characteristic time of the turbine is 353 s and the time needed
to reach the stationary power is 382 s.
control is realized by its frequency to keep a fixed storage pressure. As already seen, the minimum flow rate required to maintain
Hence, the pressure decreases to 116.7 bar before reaching again the turbine in standby mode is 8.5 kg/s. The origin of this value is
the stationary value. The offset between the times of the flow rate the low efficiency of the turbine (15% on average), the friction
rise of the both machines is 700 s. It is 5 times higher than that forces and the pressure loss at the admission.
during the storage phase. Indeed, the tanks are filled with air at 84% The angular speed of the compressor motor and the turbine
at the beginning of the production phase whereas they were filled generator are illustrated in Fig. 18 and Fig. 19 respectively. The
at 10% at the beginning of the storage phase. The pressure control angular velocity of the compressor increases at the start-up
becomes easier to handle with the rise of the air ratio in the storage according to the ramp imposed as a parameter (supplier data) and
reservoirs since the latter is a compressible fluid. decreases during the shutdown phase as function of the friction
forces.
4.1.2. Compressor/air turbine Regarding the turbine, its rotational speed increases first to
The mass flow rate and the power consumed by the compressor reach the operating speed imposed by the speed controller. When
are exhibited in Fig. 16. First, the consumed power, at the the turbine is first connected to the grid, the speed decreases
compressor start-up, increases according to the mechanical inertia slightly, because of the load imposed by the grid, before the
of the compressor's rotor and the friction forces. Next, the effect of stationary regime is restored after few seconds. At the shutdown
the mechanical inertia decreases with the increase of the rational phase, the speed is governed by the friction forces subjected to the
speed and thus the power consumption decreases. Once the rotor. A slight increase in the speed is recorded at the beginning of
pressure at the compressor exit becomes higher than the storage the shutdown phase due to the disconnection of the grid load. The
pressure (at time t = 47 s), the air flow rate rises above zero and the rotational speed remains within the permissible margin ([48 Hz,
consumed power will be then regulated according to the power 52 Hz]) during the operating mode.
demand. The slope of the flow rate curve increases during the
transient state due to the isentropic efficiency enhancement. The 4.1.3. Hydraulic turbine/pump
actual flow rate tends to the optimum flow rate of the compressor. The mass flow rate and the power produced by the hydraulic
The characteristic time of the compressor to achieve 67% of the set turbine are shown in Fig. 20. The start-up phase of the hydraulic
point power is 100 s, the set point power is reached in 120 s. The turbine is similar to that of the air turbine. The flow rate is
consumed power also varies depending on the storage pressure, in controlled to maintain the set point speed. At the beginning of the

Fig. 16. Mass flow rate and electrical power consumed by the compressor. Fig. 17. Mass flow rate and electric power generated by the turbine.
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 187

Fig. 18. Motor angular velocity of the compressor during the transient states.

Fig. 21. Mass flow rate and electrical power of the pump.

inertia and the friction forces and subsequently based on the set
point frequency.

4.1.4. Hot water tanks

The thermal storage pressure varies with the hot water
temperature as shown in Fig. 22. At the storage phase, the storage
temperature increases in transient state from 195  C to 222  C and
the water vapor condenses as the tanks are filled due to the
increase in the storage pressure. At the production phase, the
pressure decreases with the draining of hot water and the water
evaporates so as to maintain the pressure above the saturation
pressure. Therefore, the storage temperature decreases, it is due to
the latent heat loss during the water evaporation. The initial
Fig. 19. Generator angular velocity of the air turbine during the transient states.
pressure and temperature of the hot water tanks are taken equal to
those reached at the end of the simulation period.

4.1.5. Heat exchangers

The heat exchangers are controlled to rapidly reach the steady
state phase, overcome the thermal inertia and then optimize the
operation of these components. Thus, the water flow rate in the
cooling heat exchangers (Fig. 23, low pressure cooler) stays zero
about 6 min at the start-up phase in order to warm up the heat
exchanger, reach the set point temperature as quickly as possible
and prevent the storage of cold water in the hot water tanks. The
water flow rate increases then according to the air flow rate and
temperature as function of the desired water output temperature.
The characteristic time of this component is 193 s (medium
pressure cooler 156 s and high pressure cooler 169 s), the
stationary state is reached in 540 s.

Fig. 20. Mass flow rate and electrical power of the hydraulic turbine.

storage period, the storage pressure increases above 120 bar and
hence the flow expanded through the hydraulic turbine increases
20% above the stationary value to compensate the pressure raise
and stabilize it again at 120 bar. As soon as the storage pressure is
reached, the flow rate decreases and a value of 181 kg/s (stationary
flow rate) will be still required to keep a constant storage pressure.
The pump flow rate increases first by 30% above the stationary
value to compensate the pressure drop and retouch the storage
pressure (see Fig. 21). Once the desired pressure is reached, a
minimum flow rate of 416.5 kg/s remains required to maintain the
storage pressure. The pump is controlled by its frequency, the
power increases at the start-up as a function of the mechanical Fig. 22. Inlet temperature and storage pressure of the hot water tanks.
188 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

Fig. 25. Consumed power and set point power of the storage system.
Fig. 23. Water mass flow rate and output temperature of the low pressure cooling
heat exchanger.

Fig. 26. Produced power and set point power of the storage system.

Fig. 24. Air mass flow rate and output temperature of the low pressure heating heat
our application according to the grid manager. Regarding the
exchanger.
production phase, the power produced by the system follows the
set point with a maximum delay of 3 s during the two phases of
The water flow rate in the heating heat exchangers (Fig. 24, low start-up and shutdown and with a relative error of 3.5% maximum
pressure heater) increases at the beginning rapidly to warm up the (Fig. 26). Accordingly, the storage cycle is able to meet the power
heat exchanger within an optimum time and reach the set point air demand with a delay that varies between 3 s and 6 s. The storage
output temperature. Then, the flow rate varies as a function of the cycle is therefore capable to ensure the secondary reserve with a
air flow rate and temperature so as to ensure the desired slope of 15 MW/min, and the startup from zero to the steady state
temperature. is carried out in few minutes (2 min is storage mode, and 6 min and
Note that at the end of the production period, the flow of hot 22 s in production mode).
water injected into the heaters increases in the aim to compensate Nevertheless, the storage system is unable to meet the primary
the decrease of the thermal storage temperature (Fig. 22) and limit reserve unless it operates in standby mode as described in the
the decrease of the air temperature at the heaters exit. The following paragraph.
characteristic time of this component is 50 s (medium pressure
heater 41 s and high pressure heater 36 s) and the stationary state 4.2. Primary reserve
is reached in 500 s.
The assurance of the primary reserve is mainly affected by the
4.1.6. Consumed/produced power mechanical inertia of the rotating machinery. According to the
The dynamic modeling aims to assess the response time of the simulation results, the heat exchangers keep their temperatures
storage system and therefore the variations of the consumed/ from one period to another with just losses of dozen degree due to
produced power over time. Fig. 25 shows that the power consumed the temperature homogenization and the waste heat. Hence, the
by the storage plant matches with the set point with maximum thermal inertia of the heat exchangers helps the storage plant to
delay of 6 s during the two phases of start-up and shutdown. The meet the primary reserve.
increase in power at the beginning is due to the mechanical inertia The speed at which the centrifugal machine can be started is
of the compressor. The required power (16.4 MW) is reached with limited by the thermal constraints, the differential expansion and
1 s of delay and 9% of overshoot. This overshoot is acceptable for the mechanical constraints [30,31]. The mechanical constraints
 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190 189

related to the torsion torque will be studied in order to find a

standby mode from which the storage plant can meet the primary
reserve without damaging the centrifugal machines. The bending
constraint serves to determine the natural frequencies to avoid the
resonance phenomenon, it has already been taken into account in
the machine design and is not affected by the overload submitted
to the rotor [32]. The other constraints are not studied because the
system will be in standby mode and then the torsion torque is the
most critical. The fast start-up of the hydraulic turbine and the
pump is not required in our application because a storage pressure
variation of 5 bar is allowed. Consequently, the fast startup of the
compressor and the air turbine is just required.
The allowable torque of the compressor and the turbine is
supposed equal to 1.3 times the nominal torque. The simulation
results show that the rotors of the compressor and the turbine will
be damaged if these machines are started within 10 s (from a zero
speed). Furthermore, the operation of the storage system in
standby mode at its nominal regime induces high efficiency losses.
For all these reasons, a standby mode with low regime should be Fig. 28. Angular velocity and power produced by the turbine in transient state.

studied in order to be able to meet the primary reserve with low

efficiency losses. Based on this fact, a minimum speed, from which
the centrifugal machine should be started, is evaluated in the the turbine is already preheated and the synchronization could
following based on the allowable torsion torque. already be done using a gearbox.
The minimum regime from which the compressor is capable of The system efficiency, given by (27), is equal to 53.6%.
meeting the primary reserve is 54% of the rated speed. This value is ETurbines  EPump
calculated so as to avoid the critical torsion torque to reach the hnet ¼ ð27Þ
ECompressors  EHydraulicTurbine
admissible value at the switch moment to the nominal regime. And
then as shown in Fig. 27, the compressor has to over-consume The energy consumption of the compressor and the turbine in
energy during the transient state to overcome its mechanical standby modes are illustrated in Table 2. The efficiency loss due to
inertia and reach the nominal speed. Then, the power consumption the compressor standby mode decreases 3.1 times when switching
decreases and reaches 33% of the rated power. The duration of this to the low speed. Indeed, the difference in the air enthalpy is a
phase is 11 s. The power increases then to the nominal power in substantial cause of this latter value, it decreases with the
20 s. Therefore, the primary reserve is ensured and the rated power compressor rotational speed (the output pressure is of 10 bar
is reached in 30 s. during the low speed operation). Moreover, the friction forces
Regarding the turbine, it must be started from a rate of 72% of its decrease.
nominal speed so that it will be able to meet the primary reserve The efficiency loss due to the turbine decreases 27% by
without damaging the machine. According to Fig. 28, the angular switching to the low speed regime. The pressure at the turbine
velocity goes up to the operating speed and the produced power to inlet is equal to the storage pressure, the flow rate is adjusted by a
33% of the nominal power in 11 s. Then, the generated power valve at the turbine inlet and a large pressure loss will then occur in
reaches the rated power in 20 s. Hence, the primary reserve is also the valve due to the low requested flow rate during standby mode.
ensured. The inlet pressure is 17 bar in the nominal mode and 14.5 bar in the
Note that the start-up of the turbine is distributed on 3 stages: reduced mode. This explains the origin of the small reduction in
the preheating, the increasing in speed and the synchronization losses, mainly caused by the reduction of the friction forces.
with the grid. The duration of the preheating phase is 10 s and the Finally, the efficiency loss due to the turbine standby mode is
synchronization duration is 60 s (supplier data). In standby mode, much greater than that due to the compressor standby mode for
the following reasons:

1. The duration of the compressor standby mode is 5 h and that of

the turbine is 12 h;
2. The pressure loss in the valve at the turbine admission; and
3. The low conversion efficiency of the compressed air energy into
mechanical energy on the blades of the turbine.

Consequently, it is recommended to operate the turbine

generator as a motor in standby mode and the turbine as a
compressor in order to reduce the energy losses. This maintains the
compressed air reserves and the stored hot water and limits the
efficiency loss to 3.4% in the low speed mode.

5. Conclusions

The dynamic modeling of an innovative isobaric adiabatic

compressed air energy storage system is presented in this paper.
The developed model takes into account the mechanical and the
thermal inertia of the system components in order to examine its
Fig. 27. Angular velocity and power consumed by the compressor in transient state. ability to meet the primary and the secondary reserves. Scenarios
190 Y. Mazloum et al. / Journal of Energy Storage 11 (2017) 178–190

Table 2
Energy losses in standby modes.

Compressor Turbine

Power (MW) Efficiency loss (%) Mass flow rate (kg/s) Efficiency loss (%)
Rated speed 0.85 2.2 8.5 14
Low speed 0.294 0.7 6.9 11

of charge/discharge are proposed and simulated to test the [9] E.O. Sampedro, Etude d'un système hydropneumatique de stockage d'énergie
flexibility of the storage system. utilisant une pompe/turbine rotodynamique, Ecole Nationale Supérieure
d'Arts et Métiers (2013).
Firstly, a scenario is simulated to analyze the transient states of [10] Dassault systems, the Official Web Site of Dymola. http://www.3ds.com/
the storage system. The time required by the system to reach the products-services/catia/capabilities/modelica-systems-simulation-info/
steady state during the storage period is 120 s and that during the dymola.
[11] J.R. Cooper, R.B. Dooley, The International Association for the Properties of
discharge period is 382 s. The storage system is also able to follow Water and Steam, (2007) Lucerne, Switzerland.
the power demand (having a slope of 15 MW/min) with a [12] B.J. McBride, M.J. Zehe, S. Gordon, NASA glenn coefficients for calculating
maximum delay of 6 s which is acceptable in the context of the thermodynamic properties of individual species, NASA Report TP-2002-
211556, (2002) .
secondary reserve. The storage system is then capable of ensuring [13] J. Mas, J.M. Rezola, Tubular design for underwater compressed air energy
the secondary reserve. However, the system is unable to ensure the storage, J. Energy Storage 8 (2016) 27–34.
primary reserve unless the system is already in standby mode. [14] J.H. Kim, T.W. Song, T.S. Kim, S.T. Ro, Model development and simulation of
transient behavior of heavy duty gas turbines, J. Eng. Gas Turbines Power 12/
Finally, suggestions are examined in the perspective of
589 (July) (2001).
improving the flexibility of the storage system and reducing the [15] S.E. Turie, Gas Turbine Plant Modeling for Dynamic Simulation, KTH School of
efficiency losses. They lead to determine a standby compressor and Industrial Engineering and Management, STOCKHOLM, 2012 Master’s Thesis,
turbine modes with minimal energy consumption, the compressor 29/03/2012.
[16] A. Chaibakhsh, A. Ghaffari, Steam turbine model, Simul. Modell. Pract. Theory
must operate at 54% and the turbine at 72% of their nominal 16 (2008) 1145–1162.
speeds. They also show that the turbine should be operated as a [17] D. Bendaoud, Théorie Des Machines Asynchrones, Université de Sidi Bel Abbès,
compressor in the standby mode to reduce the efficiency loss from 2017.
[18] P. Schalbart, Modélisation Du Fonctionnement En régime Dynamique d'une
11% to 3.4%. Machine Frigorifique Bi-étagée à Turbo-compresseurs-Application à Sa
It will be interesting in future work to build a demonstrator of régulation, Institut national des sciences appliquées de Lyon, 2006, pp. 195
this energy storage system in order to validate the technical and (61–73), December.
[19] O.E. Balje, Turbomachines, Wiley, New York, 1981.
commercial viability of the storage system. Moreover, this [20] G. Janevska, Mathematical modeling of pump system, Electronic International
demonstrator should be able to validate by experimental measure- Interdisciplinary Conference, September, 2–6, 2013.
ments the theoretical dynamic model of the system. [21] J. Ghafouri, F. Khayatzadeh, A. Khayatzadeh, Dynamic modeling of variable
speed centrifugal pump utilizing MATLAB/SIMULINK, Int. J. Sci. Eng. Investig. 1
(5) (2012).
References [22] E.D. Jager, N. Janssens, B. Malfliet, F. Van De Meulebroeke, Hydro turbine model
for system dynamic studies, IEEE Trans. Power Syst. 9 (4) (1994).
[1] Y. Mazloum, H. Sayah, M. NEMER, Exergoeconomic analysis and optimization [23] D.J. Bunce, S.G. Kandlikar, Transient response of heat exchangers, Mangalore
of a novel isobaric adiabatic compressed air energy storage system, India, Heat and Mass Transfer, Proceedings of the Second ISHMT?ASME Heat
Proceedings of the 29th ECOS Conference, Portoroz-Slovenia, June 19–23, and Mass Transfer Conference, vol. 951995, pp. 28–31.
2015, pp. 12. [24] N. Boultif, C. Bougriou, N. El Wakim, Comportement des échangeurs de chaleur
[2] S.K. Khaitan, M. Raju, Dynamic simulation of air storage–based gas turbine à tubes coaxiaux face aux perturbations, Revue des Energies Renouvelables 12
plants, Int. J. Energy Res. 37 (2013) 558–569. (2009) 607–615.
[3] Y. Mazloum, H. Sayah, M. NEMER, Static and dynamic modeling comparison of [25] J. Yin, M.K. Jensen, Analytic model for transient heat exchanger response, Int. J.
an adiabatic compressed air energy storage system, J. Energy Resour. Technol. Heat Mass Transf. 46 (2003) 3255–3264.
ASME 138 (November) (2016) 8. [26] F. INCROPERA, D. Dewitt, Fundamentals of Heat and Mass Transfer, vol. 886,
[4] P. Zhao, J. Wang, Y. Dai, Thermodynamic analysis of an integrated energy School of mechanical engineering, Perdue University, 1996, pp. 420–515.
system based on compressed air energy storage (CAES) system and Kalina [27] I.E. IDELCHIK, 3rd edition, Handbook of Hydraulic Resistance, vol. 788(1993) ,
cycle, Energy Convers. Manag. (2015). pp. 75–87.
[5] F. Klumpp, Comparison of pumped hydro, hydrogen storage and compressed [28] S. ALIZADEH, An experimental and numerical study of thermal stratification in
air energy storage for integrating high shares of renewable energies— a horizontal cylindrical solar storage, Sol. Energy 66 (6) (1999) 409–421.
potential, cost-comparison and ranking, J. Energy Storage 8 (2016) 119–128. [29] J.B. Chaddock, Moist air properties from tabulated virial coefficients, in: A.
[6] C.C. Bullough, C. Gatzen, M. Jakiel, A. Koller Nowi, S. Zunft, Advanced adiabatic Wexler, W.A. Wildhack (Eds.), Humidity and Moisture Measurement and
compressed air energy storage for the integration of wind energy, Proceedings Control in Science and Industry, vol. 3, Reinhold Publishing, New York, 1965,
of the European Wind Energy Conference, EWEC 2004, London UK, 22–25 pp. 273.
November, 2004, pp. 8. [30] M. Topel, M. Genrup, J. Spelling, B. Laumert, Operational improvements for
[7] M. Saadat, F.A. Shirazi, P.Y. Li, Modeling and control of an open accumulator startup time reduction in solar steam turbines, J. Eng. Gas Turbines Power 137
Compressed Air Energy Storage (CAES) system for wind turbines, Appl. Energy (4) (2015).
137 (2015) 603–616. [31] M. Topel, M. Jocker, S. Paul, B. Laumert, Differential expansion sensitivity
[8] L. Nielsen, R. Leithner, Dynamic simulation of an innovative compressed air studies during steam turbine startup, J. Eng. Gas Turbines Power 138 (June (6))
energy storage plant – detailed modeling of the storage cavern, WSEAS Trans. (2016).
Power Syst. 4 (8) (2009) 11. [32] M. Naudin, Vibrations et contraintes alternées dans les turbomachines,
Environnement – Sécurité, Technique de l'ingénieur, 06/02/2014.